Find the vertex of y = x2 + 14x − 40 by completing the square.

Correct Answer:
First Option

Let the first integer be n.
Since the integers are consecutive, the integer next to n will be n+1
and so the third integer will be n+2

Therefore, the three integers are:
n , n +1, n+2

Their sum is 75. So we can write the equation as:

n + (n+1) + (n+2) = 75

This equation can be used to find n. After finding n, we can find the next two integers by finding (n+1) and (n+2)

----------------------------------------------
Calculate Jean's rate
----------------------------------------------
Jean takes 8 hours to fill the pool.
So in 1 hour, she can fill 1/8 of the pool

----------------------------------------------
Calculate Mark's rate
----------------------------------------------
Mark takes 12 hours to fill the pool.
So in 1 hour, he can fill 1/12 of the pool.

----------------------------------------------
Calculate their rate if they work together
----------------------------------------------
Jean = 1/8
Mark = 1/12
1/8 + 1/12 = 3/24 + 2/24 = 5/24 
They will fill 5/24 of the pool in 1 hour

----------------------------------------------
Find number of hours needed to fill up the pool
----------------------------------------------
I hour = 5/24 of the pool
1 ÷ 5/24 hour = 5/24 ÷ 5/24 of the pool
24/5 hour =  Whole pool

Whole pool = 24/5 hours 
Whole pool = 4 4/5 hours  or 4.8 hours

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Ans: The supervisor is not correct, it will take only 4.8 hours if both of them work together.
----------------------------------------------

The number of hours to complete the work together is 4.8 hours.

No, the supervisor is not correct.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Jean:

Time taken to fill the pool =8 hours

In one hour, 1/8 of the work is done.

Mark:

Time taken to fill the pool = 12 hours.

In one hour, 1/12 of the work is done.

Now,

Together the time is taken to complete the work.

1/8 + 1/12 = (3 + 2)/24

1/8 + 1/12 = 5/24

This can be written as,

1/8 + 1/12 = 1/(24/5)

This means,

The time taken to complete the work together.

= 24/5

= 4.8 hours.

Thus,

The time taken to complete the work together is 4.8 hours.

Learn more about equations here:

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Final answer:

To find the range of a rational function with a slant asymptote, you first find the asymptote by long division. Then by examining the behavior of the function near the vertical asymptotes by plugging in values, you determine the limits of the range. Generally, the range is all real numbers except where interrupted by the asymptotes.

Explanation:

To find the range of a rational function with a slant asymptote, you need to first find the slant asymptote by dividing the numerator by the denominator using long division. When you perform the division, if the degree of the numerator is one more than the degree of the denominator, then the quotient (excluding the remainder) will be the equation for the slant asymptote.

Next, you need to explore the behavior of the function on the left and right of the vertical asymptotes, this is done by substituting values just to the left and right of each vertical asymptote into the function and observing the outputs.

If the function approaches negative infinity, the lower limit of the range will be negative infinity. If the function approaches positive infinity, the upper limit of the range will be positive infinity.

So, the range of the function is typically all real numbers except for the values that are 'cut out' by the asymptotes.

Learn more about Rational Functions here:

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Final answer:

To determine the range of a rational function with a slant asymptote, graph the function, analyze for vertical and horizontal asymptotes, discontinuities, and observe its long-term behavior relative to the slant asymptote. The range typically includes all real numbers except for values excluded due to vertical asymptotes or holes.

Explanation:

To find the range of a rational function with a slant asymptote, follow these steps:

Graph the rational function to observe its behavior and identify the slant asymptote.Analyze the graph to see where the function's output values (y-values) lie as the input (x-values) become very large or very small.Identify any horizontal or vertical asymptotes, as these will also affect the range.Look for any discontinuities such as holes or vertical asymptotes that might create gaps in the range.Combine all this information to determine the set of all possible y-values the function can attain, remembering that the function will approach but not touch the slant asymptote.

Considering the slant asymptote, the function will continue to increase or decrease without bound in at least one direction, unless there is another horizontal asymptote. Therefore, the range can often be all real numbers, except possibly excluding specific values or intervals due to vertical asymptotes or holes.

1. You have that Ken has 8 pennies and Ron has 3 pennies. Therefore, to calculate that ron has, you only has to substract the pennies of Ken and the pennies of Ron, as below:
 
 = 8 pennies-3 pennies
 
 2. Then, the result is:
 
 =5 pennies
 
 How many fewer pennies does ron have than ken? 
 
 The answer is the following:  Ron has 5 pennies fewer than Ken.

Fraction represents the quotient of two integers

Sharing 7 apples equally with 3 people means that:

[tex]\frac 73 = 2\frac 13[/tex]

In the above equation;

The whole number 2 means that, each person gets 2 apples

The numerator 1 means that, 1 apple is left after each person gets 2 apples

The denominator 3 represents the number of people that shared the apple

Read more about fraction division at:

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10(cos(4pi/3) + i sin(4pi/3)) To multiply complex numbers in trigonometric form, you simply multiply the radii and add the thetas. We have: z1=5(cos(pi/2)+i sin(pi/2)) z2=2(cos(5pi/6)+i sin(5pi/6)) The radii for the above 2 numbers are 5 and 2. So the result will have a radius of 5*2 = 10. The thetas are pi/2 and 5pi/6, so the new theta will be pi/2 + 5pi/6 = 3pi/6 + 5pi/6 = 8pi/6 = 4pi/3. So the answer is: 10(cos(4pi/3) + i sin(4pi/3))

what angles are you looking at?,
well one one angle is cos⁻¹∅=8/10 = cos⁻₁=0.8= 36.9
and the other angle is sin⁻¹∅=53.1

Answer: When the focus is on just one group of objects were are using categorical probabilities.

The easy why to think of this is the word category. In this case, we are looking at individual categories of probabilities. The rest of the choices involved dealing with multiple events and samples.

25% is the Answer  

$249-186.5 = 62.25
25% of 249 = 62.25
249- 62.25 = $186.25

Answer:

75% is the percent of which jack payed

Step-by-step explanation:

You can find this out by googling it, or even just using the elimination too. Right away 25% sounded way too low and if you look it up it says that its $68

instead of $186.75. And it can't be any higher than 100% because 186.75 is lower than 249, so that means that 75% is the only reasonable answer

Sure!

1) 5.1*10^-4
2) 5.5*10^-2 LEAST TO
3) 2.2*10^-2 GREATEST
4) 4.4*10^-2
5) 6*10^2
6) 3.5*10^4

If the exponent is negative go left, if it is positive, go right.

Example:

<------ (-4) (4) ------>

If you need anymore help, just ask... <3

Hope this helps! Good luck on Scientific Notation! :-)

The numbers ordered from least to greatest are: 5.1 × 10⁻⁴ ,2.2 × 10⁻²,5.5 × 10⁻²,4.4 × 10², 6 × 10², 3.5 × 10⁴. This ordering is based on comparing the exponents of 10 first and then the coefficients where the exponents are equal.

To order the numbers 5.5 × 10⁻², 6 × 10², 4.4 × 10², 3.5 × 10⁴, 2.2 × 10⁻², and 5.1 × 10⁻⁴ from least to greatest, you must understand scientific notation. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It's commonly used for very large or very small numbers.

5.1 × 10⁻⁴ : The smallest exponent of 10 and a small coefficient.

2.2 × 10⁻² : Next smallest exponent with a small coefficient.

5.5 × 10⁻² : Slightly larger coefficient but same exponent as the previous.

4.4 × 10² : Positive exponent and the smaller coefficient of the positive exponents group.

6 × 10² : Larger coefficient than the previous, but same exponent.

3.5 × 10⁴ : The largest exponent and a large coefficient, makes it the largest number.

The points would make a parallelogram

The answer for the blank is 0.003

This is the slope value, which is the number in front of the x in the least squares regression line. Each time x increases by 1, y increases by 0.003

This is the predicted y value of course. 

48 - 3 = 45.
45 divided by 6 = 7.5
That means that the width is 7.5 and the length is 18. Hope it helps! :)

Split it up into segments--

Red: 1/2(4×1) + 1/2 + 1 + 1/2 + 1/2 + 1×4 = 2+2+4.5 = 8.5 sq. units

Purple: 1/2(2×1) + 1/2 +1 + 1×4 + 1/2(2×4) + 1/2(1×4) = 1+1+4+4+2 = 12 sq. units

The Bible, a book that is considered the perfect word of a perfect god tells us what the value of Pi is. Let's see verse 1 Kings 7:23
 He also melted a sea of ​​ten cubits from one side to the other, perfectly round; Its height was five cubits, and a cord of thirty cubits encircled it.

 These are a list of specifications for the great temple of King Solomon, built about 950 BCE, and his interest here is that it gives a value of π = 3. If we divide 30 cubits between 10 cubits (which are the measures mentioned in written radical) gives us exactly 3.

 We know that the length of the circumference is calculated l = 2 · π · r; Since 2 · r is the diameter, it can also be said that

 circumference = diameter × π

 If we go back to what the Bible says, the diameter is 5 meters and the circumference of 15:

 circumference = diameter × π -> 15 = 5 × π

 with which the value of π is 3.

 This calculation of Pi is a bad approximation to the real value. The figure of 3 in the Bible compared with the real one which is 3.1416 ... indicates an error of about 6%.

for this problem recall the formula for polar to rectangular conversion is
[tex]x = r \cos(theta) [/tex]
[tex]y = \sin(theta) [/tex]
and the polar coordinates are in the form
note: the dot is a substitute for the comma
[tex](r.theta)[/tex]
so to find our coordinates we just need to plug our values of theta in
[tex]x = \cos( \frac{2\pi}{3} ) [/tex]
[tex]y = \sin( \frac{2\pi}{3} ) [/tex]
simplify and we get this as our final answer

[tex]( \frac{ - 1}{2} . \frac{ \sqrt{3} }{2} )[/tex]

Answers: You will have to plot the following values (3.3, -4.7, -0.7, 1.8, 0.8)

A residual is the difference between the predicted value and the actual value. You are given an equation that will make the predictions for you.

Input in the first number of your pairs to find the predicted output. Then, subtract that from the actual value.

Here is the work for the first point: 

6.5(1) + 63.8 = 70.3

70.3 - 67 = 3.3

The residual at x = 1 is 3.3.

Answer:

Correct answers below. :)

Step-by-step explanation:

Hope this helps! Have a good day!

Answer: (B) $8.00 per hour



Hope this helps.

Answer:

Option B is correct.

Step-by-step explanation:

Number of hours A courier worked = 39

Money a courier earned  = $ 429

⇒ Hourly Wage of the courier = [tex]\frac{429}{39}[/tex]

                                                  = $ 11 per hour

Let x be the rate shown on his pay stub.

According tot he Question,

x + 3 = 11

x = 11 - 3

x = 8

Therefor, Option B is correct.

1st find out how much the tip was:
88.50 - 75.00 = 13.50

Now find the percentage 13.5 is of 75
13.5/75 x 100 = 18% (C)

[tex]\ln e^5=5=5\ln e[/tex]

in rectangles, opposite sides are equal.
lets name the length as x
as stated in the question, width is 7 less than the length 
therefore length is --> x-7
perimeter = 2*(length) + 2(width)
substituting length and width 
perimeter = 2x +2(x-7)
as the perimeter given is 50 inches
70 = 2x + 2x - 14
4x = 84
x = 21 inches 
length of tablet - 21 inches 
width of tablet - 14 inches 

Answer:

Length = 16 inches and width = 9 inches

Step-by-step explanation:

The perimeter of a rectangle table = 50 inches

Rectangle table has equal sides of length and equal sides of width.

Let the length of the table be x.

It is given in the question that the table is 7 inches less wide than it is long.

So width of the table = x - 7

Perimeter = 2(length) + 2(width)

Perimeter = 2(x) + 2(x-7) = 50

                = 2x + (2)(x) + (2)(-7) = 50

                = 2x + 2x + (-14) = 50

                = 4x -14 = 50

                =  4x = 64

                 x = 16

Length = 16 inch Width = 16 - 7 = 9 inches

perimeter = 2(16) + 2(9) = 50 inches

To find the number, you need to do the opposite of the given process. 

30.3 + 4.04 = 34.34
34.34 + 0.58 = 34.92
34.92 - 0.43 = 34.49

Your answer is 34.49. 

Hope this helps!

Answer:

34.49.

Step-by-step explanation:

I believe the answer would be Whole Numbers

M= (y2-y1)/(x2-x1). the formula stated is how to find the slope of a line with two known points. plug in your numerical values and solve.

Answer:

[tex]m=\frac{-1-2}{7+3}[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]A(-3,2)\ B(7,-1)[/tex]

Substitute the values

[tex]m=\frac{-1-2}{7+3}[/tex]

[tex]m=\frac{-3}{10}=-0.3[/tex]

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:

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:

the answer is c the degree of the trinomial

The answer is {B}. You obtain the c value is the quadratic when you multiply m and n. This is also known at the y intercept. y intercepts are a constant.

The product of 9 multiplied by 1/5 is 1.8, which is less than 9 because multiplying by a fraction between 0 and 1 reduces the original number.

To find the answer, you simply multiply 9 by 1/5. When you multiply a whole number by a fraction less than 1, the product is always less than the original whole number because you are taking a part of it. So, 9 × 1/5 equals 9/5 or 1.8, which is definitely less than 9.

In mathematics, when you multiply a number by a fraction between 0 and 1, the result will be smaller than the original number. This is similar to taking a part of something. On the other hand, when you multiply a number by a fraction greater than 1 or by a whole number greater than 1, the result is greater than the original number because you are effectively adding the number to itself multiple times.

Only the second sequence has a common difference of -4.

1 sequence

_____
Common differences are 4, -4, 4, (no common difference).

For this case, we observe that the four options represent the steps to build a line similar to the PQ line segment.
 We have then that the first step is:
 Opening of the compass from P to Q to measure the length of the PQ line.
 Answer:
 An image that represents the first step in constructing the copy of a line segment is:
 option 1

Answer: $99

Step-by-step explanation:

Yvette's estimated cost for buying 9.3 yards of velvet fabric at $11.49 per yard is approximately $106.86. This is calculated by multiplying the price per yard with the number of yards. An initial rough estimate of $103.50 was also considered before doing a precise calculation.

To calculate the estimated cost of the velvet fabric Yvette buys, you need to multiply the price per yard by the number of yards:

Price per yard = $11.49

Number of yards = 9.3

Estimated cost = $11.49 × 9.3

Let's break it down step-by-step:

First, estimate the two numbers. $11.49 is close to $11.50, and 9.3 is close to 9. Then, multiply: 11.50 × 9 = $103.50.Now calculate more precisely: 11.49 × 9.3 = 106.857 but rounded to two decimal points, it's $106.86.

So, Yvette's estimated cost of the fabric is approximately $106.86.