Mathematics High School

Based on what you've read, answer the following questions. Think about what you've learned about whole numbers. Then study the following sequence. What is the next letter in the sequence? O, T, T, F, F, S, S, ? In your own words, define each of the following terms. a. Whole number b. Digit c. Place value d. Rounded number e. Equals Insert commas in the following numbers. a. 13886 b. 365 c. 719463 d. 40047209 e. 2145739180 f. 1783457 Write the word names for each of the numerals in the following paragraph. One popular fast-food chain ordered (a) 2,400,000 slices of cheese last year. In December, the chain reached its goal of serving a total of (b) 40,000,000,000 cheeseburgers since opening. This was enough cheeseburgers to make a stack (c) 473,500 miles high. Also, the number of shakes served last year could have filled (d) 1,200 swimming pools. Write numerals for each of the italicized number word names found in these examples. Earth’s moon is (a) two million, one hundred fifty-five thousand, one hundred twenty miles across. The closest distance between Earth and the moon is (b) two hundred twenty-five million, sixty thousand miles. The farthest distance between them is (c) two hundred fifty-one million, seven hundred twenty thousand miles. Name the position held by the digit 5 in each numeral. a. 952 b. 5,432 c. 115 d. 50,768 e. 113,598 f. 5,027,649 In the number 7,890,432, name the digit located in each of these positions. a. Hundreds b. Millions c. Ten thousands d. Tens e. Hundred thousands f. Thousands Which of the numbers in each pair is farther to the left on the number line? a. 305 and 17 b. 187 and 900 c. 16 and 46 d. 157,019 and 149,984 Replace the ? in each of these statements with the symbol >, <, or =. a. 39 ? 38 b. 16 ? 16 c. 11 ? 315 d. 5 ? 4 In 2013, the population of China was estimated to be 1,360,760,100. Round off the number of people a. to the nearest thousand. b. to the nearest million. c. to the nearest hundred million. d. to the nearest hundred thousand.

Answers

Answer 1
1)
the letters in the sequence are in the order of first letter of numbers.
the sequence thats in the numerical order - one, two , three...
each number is taken and the first letter of the word is taken for the sequence,
one - first letter of one is O
O(one), T(two), T (three), F (four), F(five), S(six), S(seven),(eight)
first letter of eight is E, so next letter in the sequence is E

2)
a- whole number 
whole numbers are integers that don't have any decimal places and are not fractions either.
b- digit
digit is a single number that can hold a position in a numerical value. for example 7 in 7000 is holding the thousands digit. And in number 7000 we can call it a 4 digit number as there are 4 digits in it.
c - place value
this is when a number holds a certain value depending on its position/ place in the numerical value. for example in 200, number 2 is in the hundreds place therefore its having a value of 2 counts of hundred , therefore has a place value of 200. place value means that each place has a value 10 times of that of the value to its right. so 2 is in the hundreds place, right of that is tens place, hundreds place value is 10 times of tens value = 10*10 = 100 therefore when number 2 is in the hundreds places its 2*100 = 200
d - rounded number 
rounded number is when a number is made to a simpler form. rounding off can be done to any place of the number. Its to bring it to a simpler number by dropping off the unnecessary digits to make it easier to work with
e - equals
equals is when a number is equal in value to another number. By equalling it means that the value on the right side of the equals sign is equal to the value on the left side of the equals sign

3)
we are asked to insert commas in the following numbers. Commas are inserted for convenience to add breaks to the number so that its easy to read out the number and to see if the number is a thousand, million or billion by looking at the number of commas.
Commas are inserted in numbers with 4 or more digits, after every three digits from right to left.
a. 13,886
b. 365
c. 719,463
d.40,047,209
e. 2,145,739,180
f.  1,783,457

4)
when writing word names, the numbers are read out for every three digits for the right to left. first 3 digits are written as it is, next 3 digits are written as thousand, next 3 digits as million and 3 digits after that as billion
we are asked to write the word names for the following numerals;
(a) two million four hundred thousand 
(b) forty billion
(c)four hundred seventy three thousand five hundred
(d)one thousand two hundred

5) when writing numerals from thousands same rules apply. first three digits as it is, next three digits are thousands and 3 digits to the left of that are millions
(a)2,155,120
(b)225,060,000
(c)251,720,000

6)
depending on where number 5 is in the number, it will hold different values. 
for example in 5234, 5 holds the thousands place, 2 holds the hundreds place, 3 in tens place and 4 in ones place.         
a. tens 
b. thousands
c. ones
d. ten thousands
e. hundred thousands
f. millions

7)
this shows the value of each position
                           7,          8            9       0    ,          4         3       2
hundred   ten  ones      hundred   ten   ones      hundred   ten   ones                  
 --------million-------       ----------thousand---        ---------ones-----------
7,890,432, name the digit located in each of these positions.
a. Hundreds - 4
b. Millions - 7
c. Ten thousands - 9
d. Tens - 3
e. Hundred thousands - 8
f. Thousands - 0

8)
in the number line the lesser number to the left of the number line and the greater number is to the right of the number line
Which of the numbers in each pair is farther to the left on the number line?
a.17  -17 is smaller than 305 therefore its farther to the left than 305
b. 187 
c. 16 
d. 149 984

Q9)symbol > is when the number on the left is greater than the number on the right
symbol < is when the number on the right is greater than the number on the left 
= is when both the numbers on either side of the symbol are equal to each other
a.39 > 38
b. 16 = 16
c. 11 < 315
d. 5 > 4

10)
In rounding off, the digit which you're rounding off, the digit to the right of that digit should be considered. If the digit to the right is 5 or greater than 5, then the digit which you're rounding off increases by a value of 1. If the digit to the right is less than 5 then the digit which you're to round off stays as it is. All the digits too the right of the digit being rounded off becomes zeroes.
 1,360,760,100. Round off 
a. thousands place digit is 0,digit to the right is 1, since 1<5 then, 0 stays as it is and all the digits to the right of 0 are dropped off and becomes zeroes - 1,360,760,000
b. millions digit is 0, digit to the right is 7, then its greater than 5, 0 then increases by 1 and becomes 1, all the digits to the right of 1 become dropped off and turns into zeroes. 
- 1,361,000,000
c. hundred million is 3 right of that is 6, 6>5 therefore 3 increases by 1 
- 1,400,000,000
d. hundred thousand is 7 and digit to the right is 6, then 7 increases by 1
- 1,360,800,000
Answer 2

Answer:

a. A whole number is a counting number that represents a quantity of whole things.

b. A digit is any one of the numerals in the group 0 through 9.

c. Place value is the value that a digit has within a number. Place value is determined by the digit’s position in the number.

d. A rounded number is a close approximate for an exact whole number.

e. “Equals” means “exactly the same.”

a. 13,886

b. No commas are needed.

c. 719,463

d. 40,047,209

e. 2,145,739,180

f. 1,783,457

a. Two million, four hundred thousand

b. Forty billion

c. Four hundred seventy-three thousand, five hundred

d. One thousand, two hundred

a. 2,155,120

b. 225,060,000

c. 251,720,000

a. Tens

b. Thousands

c. Ones

d. Ten thousands

e. Hundreds

f. Millions

a. 4

b. 7

c. 9

d. 3

e. 8

f. 0

a.17

b. 184

c. 16

d. 149,984

a. >

b. =

c. <

d. >

a. 1,360,760,000

b. 1,361,000,000

c. 1,400,000,000

d. 1,360,800,000

Step-by-step explanation:

Related Questions

What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0

Answers

y=-1.5x or y=-(3/2)x

Answer:

The slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].

Step-by-step explanation:

If a line is defined as

[tex]Ax+By+C=0[/tex]        ... (1)

Then the slope of the line is

[tex]m=\frac{-A}{B}[/tex]

The given equation is

[tex]3x+2y-6=0[/tex]       .... (2)

From (1) and (2), we get

[tex]A=3, B=2, C=-6[/tex]

The slope of the line is

[tex]m=\frac{-3}{2}[/tex]

The slope of parallel line is same. So, the slope of required line is -3/2.

The slope intercept form of a line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The slope of required line is -3/2 and y-intercept is at (0,0).

[tex]y=\frac{-3}{2}x+0[/tex]

[tex]y=\frac{-3}{2}x[/tex]

Therefore the slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].

How to tell whether a slope is positive negative zero or undefined?

Answers

when the gradient of the slope is negative or positive, the slope is negative or positive respectively.
or if u wanna tell by looking at the straight line graph, then if it makes an acute angle with the x-axis it's positive, if it makes an obtuse angle with x-axis its negative.
the slope is zero when the graph is horizontal
then slope is undefined when eh graph is vertical.
hope this helps

Can anyone answer this for me?

Answers

For 24, the answer is 24.
For 19 to 21:

All you need to do is count the spaces between each line of the numerator and then the same with the denominator.

19. You can see that there are 4 spaces between Point A and Point B. There are 6 spaces between point A and Point C. So if you will get ratio you will get:

[tex] \frac{4}{6} [/tex] Then you simplify the expression.
[tex] \frac{2}{3} [/tex]

20. There are 2 spaces from points B to C. There are 3 spaces from points C to D. So the ration then will be:
[tex] \frac{2}{3} [/tex] 

This is already in its simplest form. You may be wondering why we did not count from 0. This is because the reference point for the two lines are given. For the first it is B and for the second is C.

21. Moving on to number 21. The distance from point B to D is 5 spaces, and the distance from point A to E is 12 spaces. So you can say that the ratio would be:

[tex] \frac{5}{12} [/tex] Again, this is already in its simplest form. 

22. To get the geometric mean between two numbers you first need to multiply them and then get the square root:

STEP 1: Multiply 7 and 28
                            7 x 28 = 196
STEP 2: Get the square root of the product
              √196 = 14

14 is the geometric mean.

23. Simplifying ratios is relatively easy. When you simplify the ratio between two values that are of different units, you first need to make both units the same. 
In your case, we need to either convert 10ft to inches or convert 30 inches to feet. So we will not come up with a decimal, let us just convert 10 ft into inches. 

[tex] 10 ft [/tex] x [tex] \frac{12in}{1ft} [/tex] = 120 inches

So our new ratio is:
[tex] \frac{120in}{30in} [/tex]
Now we simplify it to its simplest form:
[tex] \frac{4in}{1in} [/tex]

24. The two figures are what we call similar figures. This means that the lengths of each side are proportional to their corresponding sides. 

AB is proportional to line FG. 
AB = 4 and FG =8
This means that the sides of ABCDE is half the lengths of the sides of FGHJK. Thus we can say that the perimeter of ABCDE is half the perimeter of FGHJK
To get the perimeter of a polygon, all you have to do is add all the sides. 
Let's get the perimeter of FGHJK
8 + 8 + 10 + 12 + 10 = 48
Half of 48 =24 
So the perimeter of ABCDE is 24

If you want to double check your answer you can get the sides of polygon of ABCDE by getting half of each corresponding side. 
AB = 4
BC = 4
CD = 5
DE = 6
EA = 5

If you get the sum of all sides, you can get the perimeter:
4 +4 +5 + 6 + 5 = 24

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6 –2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6 14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6 n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3

Answers

The correct combining of like term is

f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

What is polynomial equation?

A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.

Given:

8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ +  [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³

Now, Combining the like terms

(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³   - 4m³n³ +  [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

=7m[tex]n^{5}[/tex]  + 14m²[tex]n^{4}[/tex]  - 5m³n³ - 6 [tex]m^{6}[/tex] +  [tex]n^{6}[/tex]

now, arranging according to their powers

[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

Learn more about polynomials here:

https://brainly.com/question/26411438

#SPJ6

Find the probability that when a couple has four four ​children, at least one of them is a girl girl. ​(assume that boys and girls are equally​ likely.)

Answers

Knowing that each gender has a 50/50 chance there are four in five chance that at least one is a girl. The sequences are BBBB,GGGG,BBGG,BBBG, and GGGB.

MATH HELP PLEASE LOOK AT THE PICTURES BELOW!!!
5 QUESTIONS

Answers

the answer is A, gonna let you know Desmos is your best friend. I use it all the time.
1)

The equation is in form y=mx+b

m is the slope and b is the y-intercept

Slope: -6 and y-intercept: 2

2)

The equation is in form y=mx+b

m is the slope and b is the y-intercept

Slope: 1 and y intercept: -3

3) 

C = 14d + 3

4) 

8x + 6y = 12
6y = -8x + 12
y = -4/3 + 2

5)

First change the equation to y=mx+b form.

4x + 6y = 12
6y = -4x + 12
y = -2/3x + 2

Slope: -2/3

Hope that helps :)

On Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. On Tuesday, apples were on sale for 20% off so she bought another 5 lbs. What was the price of apples on Tuesday? NEED ANSWER ASAP!

Answers

p=(3*4+5*4*(100-20)/100)/8

p=(12+16)/8

p=$3.50/lb

hopefully this is correct

It is given that on Tuesday, apples were on sale for 20% off. Now, we know that on Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. This means that if we have a 20% off on Tuesday then this must be with respect to the price on Monday which is $4. Thus the price of Tuesday can be calculated as:

[tex] 4-\frac{20}{100}\times 4=4-0.8=3.2 [/tex]

Thus, the per pound price of apples on Tuesday was $3.2

according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction

Answers

Let us check out the diagram. The probability that a person buys a paperback is 0.65. The next leafs of the diagram (to the right of choosing paperback) show two events: the event that the buyer who has bought a paperback buys fiction and the probability he buys non-fiction. So 65% of the buyers buy paperback and 0.45 (=45%) of them buy fiction. Hence the probability that they buy both fiction and paperback is 0.65*0.45=0.2925. This is always a helpful thought procedure with such exercises; we can solve the same way for hardcover non-fiction etc.

see the attached figure to better understand the problem

we know that

[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.

Hence

The probability that they buy both fiction and paperback is equal to

[tex]0.65*0.45=0.2925[/tex]

the answer is

[tex]0.2925[/tex]



One number is one less than five times another. if their sum is decreased by three, the result is eight. find the numbers.

Answers


One number is one less than five times another ....
Let one number be x
The other number is 5x - 1

Their sum ... 
x + 5x - 1 = 6x - 1

Their sum is decreased by 3
6x - 1 - 3 = 6x - 4

The result is eight
6x - 4 = 8
6x = 8 + 4
6x = 12
x = 2

x = 2
5x - 1 = 5(2) - 1 = 9
One number is 2 and the other is 9.

help plsss need this for tomorrow

Answers

Hello there! I can help you! So there is one blue counter added to two green counters. To solve this problem, we can write and solve an equation. Set it up like this:

12 + 1x = 8 + 2x

We do this, because there are already some of each color in the bag. 1x makes one counter each and 2x is two counters for every blue counter in the bag. Let's solve it. Subtract 1x from each side. 1x - 1x cancels out. 2x - 1x is 1x or just simply x. That simplifies to 12 = 8 + x. Subtract 8 from each side to get the variable by itself. 8 - 8 cancels out. 12 - 8 is 4. That leaves 4 = x. Nothing else needs to be done. Let's plug the value in and see if it works. 1 * 4 is 4. 12 + 4 is 16. 2 * 4 is 8. 8 + 8 is 16. 16 = 16. There. x = 4. 4 blue counters and 8 green counters were added to the bag.

Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer.

I understand the answer is x + y = 0
I want to understand how that is determined. Using point slope form and all that.,

Answers

ax+by=c
a=1 
b=1
slope= -a/b=-1
y=mx+b
y=-x+b
b=0
x+y=0

Find the perimeter of the rectangle.

If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?

Round each side length to the nearest tenth, if necessary.

Answers

All you have to do is find the length of the sides using the distance formula and then add the lengths together to find the perimeter

Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
Smaller figures volume is 216in.^3
Larger figures volume is 343in.^3

Answers

Final answer:

The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.

Explanation:

The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.

Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.


To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.

If a circle has an diameter of 14, what would the area be?
Use 3.14 for π

Answers

A = π r^2
A = 3.14 x 7^2
A = 3.14 x 49
A = 153.86

answer
153.86

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.


Answers

we know that
[Volume of a cone]=pi*r²*h/3
and
[Volume of a half-sphere]=(4/6)*pi*r³
then
h=14 in
r=9 in
[Volume of a cone]=pi*r²*h/3-------------> pi*9²*14/3------------> 1186.92 in³
[Volume of a half-sphere]=(4/6)*pi*r³--------->(4/6)*pi*9³------> 1526.04 in³

the volume of the prop=1186.92+1526.04--------> 2712.96 -----------> 2713 in³

the answer is 2713 in³

I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?

Please help me out :)

Answers

Lets cut it diagonally into 2 triangles.
The diagonal length will be 7 x 2 = 14yd

Area of one triangle = 1/2 x 14 x 7 = 49 yd²

Area of the polygon = 2 x triangles
Area of the polygon = 2 x 49
Area of the polygon = 98 yd²

Answer: The regular polygon is 98 yd²

What is the equation, in slope-intercept form, of the line that is perpendicular to the line Y-4=-2/3(X-6) and passes through the point (-2,-2)

Answers

That line is in point-slope form:

[tex]\sf y-y_1=m(x-x_1)[/tex]

Where 'm' is the slope and (x1, y1) is a point on the line.

Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.

[tex]\sf -\dfrac{2}{3}[/tex]

Reciprocal:

[tex]\sf -\dfrac{3}{2}[/tex]

Multiply by -1:

[tex]\sf\dfrac{3}{2}[/tex]

We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.

[tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\sf y-(-2)=\dfrac{3}{2}(x-(-2))[/tex]

Negatives cancel out:

[tex]\sf y+2=\dfrac{3}{2}(x+2)[/tex]

Distribute 3/2 into the parenthesis:

[tex]\sf y+2=\dfrac{3}{2}x+\dfrac{6}{2}[/tex]

Simplify the fraction:

[tex]\sf y+2=\dfrac{3}{2}x+3[/tex]

Subtract 2 to both sides:

[tex]\boxed{\sf y=\dfrac{3}{2}x+1}[/tex]

Answer:

d

Step-by-step explanation:

Factor completely. a2+3a−28 Enter your answer in the box.

Answers

By a2, I assume you mean a squared. If so, then the answer is (x+7)*(x-4).

Solution :

To factor completely

[tex] a^{2} + 3a-28 [/tex]

To factor it completely , first take the product of first and third term, and then break the second term in two parts in such a way that its sum equals the second term and the product equals the product of first and third term.

Product of first and third term is [tex] (a^{2})(-28) = -28 a^{2} [/tex]

Second term is 3a, Re-write 3a as sum of 7a and -4a.

Lets check it Product of 7a and -4a is [tex] -28 a^{2} [/tex] wich is eaqual to product of first and third term and sum of 7a and -4a is 3a which is the second term.

Now factorise, we get

[tex] a^{2}+3a-28\\\\ = a^{2} +7a-4a-28\\\\=a(a+7)-4(a+7)\\\\=(a+7)(a-4) [/tex]

Hence, [tex] (a+7)(a-4) [/tex] is the factor of [tex] a^{2}+3a-28 [/tex].

Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?

(from top to bottom, first pictures top option is A for example)

A.
B.
C.
D.

Answers

To prove similarity, the triangles must have three angles or any three components must be equal. According to the statement, option A seems to be proof the triangles are similar to each other.

There are two images given in the question.

Let us segregate the images into image 1 and image 2.

Take image 1.

In image 1, three different triangles are given,

One angle is equal in all the triangles, which is represented as a single arc.Another angle is represented as a double arc is equal.If two angles are equal in triangles then the third angle is automatic get equal.

According to the above bullet points, image 1 qualifies all the requirements for the similarity of the triangles.

To know more about similarity, please refer to the link:

https://brainly.com/question/20502277

The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .

Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)

Answers

Answer:

In first blank : y = - 2,

In second blank : ( 0, 1 )

Step-by-step explanation:

Given function is,

[tex]f(x)=3^{x+1}-2[/tex]

The horizontal asymptote of the function f(x),

[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]

[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]

[tex]y=3^{\infty+1}-2[/tex]

[tex]y=3^\infty - 2[/tex]

[tex]y=0-2[/tex]

⇒ y = -2

First option is correct.

Also, the function has no vertical asymptote,

2. For finding the y-intercept, x = 0,

[tex]f(0)=3^{0+1}-2=3-2=1[/tex]

Hence, the y-intercept = (0,1)

Third option is correct.

Final answer:

The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).

Explanation:

The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.

Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.

To find the y-intercept, we set x equal to 0 and solve for f(0):

f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.

Therefore, the y-intercept of the function is the point (0, – 1).

Select ALL the correct answers.
The square of the sum of a number and 6 plus twice the number is equal to 189.

Which equations could be used to represent this relationship?

(3x + 6)2 = 189
(x + 6)2 + 2x = 189
(x + 6)2 = 189 + 2x
x2 + 10x + 36 = 189
x2 + 14x + 36 = 189
x2 + 2x + 6 = 189

Answers

Answer:

[tex](x+6)^{2}+2x=189[/tex]  

and

[tex]x^{2}+14x+36=189[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represent the situation is

[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]

therefore

The equations that could be used are

[tex](x+6)^{2}+2x=189[/tex]  and [tex]x^{2}+14x+36=189[/tex]

Answer:

(x+6)^{2}+2x=189  

and

x^{2}+14x+36=189

Step-by-step explanation:

K - 263.48 = 381.09 solve this equation

Answers

k-263.48=381.09
we add 263.48 on both sides
k=644.57
K=644.57. This is easily found with the addition property of equality, aka adding 263.48 to both sides.

Please help me on that question for my Algebra. I don't understand it.

Also, how would you rate my pfp?

Answers

13 quarters = 13 *0.25 = 3.25

3.60 - 3.25 = 0.35

0.35 = 0.25 +0.10

he has 1 dime and 14 quarters

Answer is B
14 quarters x .25 = 3.50
1 dime is .10
3.50 + .10 = 3.60
B. 1 Is your answer.
Your pfp looks amazing btw.

Can someone please help? In the circle at right, AZB is a(n): (A) minor arc, (B) central angle, (C) major arc, (D) arcezoid, or (E). None of these? Thanks

Answers

In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.

As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.

Therefore, Option A, minor arc is the correct answer.

Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers

Answers

x^2−7x+10=0

Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
Answer:   x=2 or x=5
[tex] x^{2} - 7x +10 = 0 [/tex]

The middle term should be factored in such a way that the sum of two numbers is -7x and their product is 10x2. These two factors are -5x and -2x. So re-writing the equation, we get:

[tex] x^{2} - 5x - 2x +10 = 0[/tex]

Taking common, we get:

[tex]x( x - 5) -2 (x-5)=0 \\ \\ (x-5)(x-2)=0[/tex]

This means:
x - 5 = 0
⇒ x = 5

or

x - 2 = 0
⇒ x = 2

Therefore, the solution to the given equation are x = 2 and x = 5

what is the sum of the arithmetic series 18 t=1 (3t-4)

a. 234
b. 441
c. 25.5
d. 49

Answers

The given arithmetic series is

[tex] \sum_{t=1}^{18} (3t-4) [/tex]

When t =1, we will get the first term,a, which is

[tex] 3(1)-4 =3-4=-1 [/tex]

When t =18, we will get the last term,l , which is

[tex] 3(18)-4 = 50 [/tex]

Now we use the formula of sum of n terms which is

[tex] S = \frac{t}{2} (a+l) [/tex]

Substituting the values of t,a and l, we will get

[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]

Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]

Let t=1 in the given series, we get

first term = [tex] a_{1} [/tex] = 3-4 = -1.

Let t=2 in the given series, we get

second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]

Let t=3 in the given series, we get

third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]

Now, let t=18 in the given series, we get

last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]

We get the series as

-1, 2, 5,..... 50

Sum = [tex] \frac{n}{2}(a+l) [/tex]

= [tex] \frac{18}{2}(-1+50) [/tex]

= [tex] = 9 \times 49 [/tex]

= 441

Therefore, the sum of the given arithmetic series is 441.

1.One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 describes the boundary within which motion can be sensed.

What is the greatest distance, in feet, a person could be from the lamp and be detected?


5 ft

10 ft

50 ft

125 ft

Answers

Answer:

5ft

Step-by-step explanation:

The required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.

What is a circle?

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Given equation

(x+15)²+(y−12)²=25

The above equation is the equation of the circle, so the longest distance that person could be from the lamp and be detected is the radius of the circle,

Which is given as,
r² = 25
r = √25
r = 5

Thus, the required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.

Learn more about circle here:

brainly.com/question/11833983

#SPJ6

helppppppppppppppppppppp

Answers

Answer:
1/4

Explanation:
Assume that:
log base 625 of 5 = y
We will rewrite this in exponent form as follows:
log base (b) of x = y is equivalent to b^y = x
For the given, the exponent will be:
625^y = 5

Now, we know that 5^4 = 625
Therefore, to convert 625 to 5, we will take 4th root.

This means that:
625^y = 5
y = 1/4

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

Line r passes through points (2, 11) and (10, 4). Line s is perpendicular to r. What is the slope of line s?

Answers

Answer: 8/7

------------------------------------------------------

Work Shown:

Use the slope formula to find the slope of line r
m = (y2-y1)/(x2-x1)
m = (4-11)/(10-2)
m = -7/8

The slope of line r is -7/8

Now we take the negative reciprocal. In other words, we flip the fraction and flip the sign from negative to positive.

Flip the fraction: -7/8 ---> -8/7
Flip the sign: -8/7 ----> +8/7

The slope of line s is 8/7

Note how multiplying the slope of line r (-7/8) and the slope of line s (8/7) yields -1. Multiplying any two perpendicular slopes leads to a product of -1. This is excluding vertical lines as the slope is undefined. 

Cassandra lives in Oklahoma and makes $60,000 a year. If the median annual income in Oklahoma is $64,105 and the median annual income in the United States as a whole is $50,233, is Cassandra likely to qualify for Chapter 7 bankruptcy?

Answers


Yes, Cassandra is likely to qualify, since her yearly income is below the median annual income of Oklahoma.

Answer:

Cassandra is likely to qualify for Chapter 7 bankruptcy.

Step-by-step explanation:

Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.

A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.

So, she will qualify for chapter 7 bankruptcy.

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