Step-by-step answer:
If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear
Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.
To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or
slope, m = 3/6 = 1/2
Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation
y-y0 = m(x-x0)...........................(1)
since x0=1, y0=4, and m=1/2, we get the equation
y-4 = (1/2)*(x-1) .........................(2)
Simplify (2) to get the slope-intercept form of the linear relation:
y = (1/2)x + 7/2 ........................(3)
Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):
y(1) = 4
y(2)=7
y(3)=10
y(4)=13
all of which correspond exactly to original data, so the equation of the linear relation is correct.
?!-2?=34 pls help!! I need help :(
Answer:
(D) 6 & 7
Step-by-step explanation:
You are plugging in numbers into the question marks to make the equation true. In this case, plug in the numbers, 6 & 7 or (D)
Plug in 6 in the first ? mark and 7 in the second:
?1 - 2? = 34 = (61) - (27) = 34
61 - 27 = 34
34 = 34 (True) ∴ 6 & 7 is your answer.
~
Apply the distributive property to factor out the greatest common factor.
15+21= ?
Answer:
15 + 21 = 3(5 + 7)Step-by-step explanation:
[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\15=3\cdot5\\21=3\cdot7\\\\15+17=3\cdot5+3\cdot7=3\cdot(5+7)[/tex]
Find the area of the shaded region
Answer: Second Option
[tex]P (-1.17 <z <1.17) = 0.7580[/tex]
Step-by-step explanation:
The shaded area corresponds to the interval
[tex]-1.17 <z <1.17.[/tex]
By definition, for a standard normal distribution the area under the curve in the interval (b <z <h) is equal to:
[tex]P (b <z <h)[/tex]
So in this case we look for:
[tex]P (-1.17 <z <1.17)[/tex]
This is:
[tex]P (-1.17 <z <1.17) = P (z <1.17) - P (z <-1.17)[/tex]
Looking at the standard normal table we have to:
[tex]P (z <1.17) = 0.8790\\P (z <-1.17) = 0.1210[/tex]
So:
[tex]P (-1.17 <z <1.17) = 0.8790- 0.1210\\\\P (-1.17 <z <1.17) = 0.7580[/tex]
After the expression (x^16)3/4is simplified as much as possible, x is raised to what exponent? a0
Answer:
12
Step-by-step explanation:
Given expression is:
[tex](x^16)^\frac{3}{4}[/tex]
By the rues of exponents, when there is exponent on exponent then the exponents are multiplied.
So,
[tex]= x^{16*\frac{3}{4}}\\ = x^{4*3}\\=x^{12}[/tex]
The exponent of x will be 12 after the simplification ..
I NEED HELP NOW
The graph shown is a scatter plot:
Which point on the scatter plot is an outlier?
Point A
Point B
Point C
Point D
Answer: The outlier in this scatter plot is Point D.
Step-by-step explanation:
The reason its Point D because its the only one that is the farest away from the rest of the points on the plot.
The reason why "Point D" would be the correct answer because the point is no where near the "trend" of the scatter plot.
When you look at the scatter plot, you would notice that there following a "trend" when the graph increases.
However, you would notice that point D is not really near there, therefore making it an outlier.
An outlier is pretty much something that is left out, and in this case, point D would be the outlier since it's left out of the typical growth of the scatter plot.
I hope this helps!Best regards,MasterInvestorWhich property was used to write the equation in step 2?
Step 1: 5(x-7) = 55
Step 2: 5x-35 = 55
Step 3: 5x = 90
Step 4: X= 18
A) distributive property
B) addition property of equality
C) subtraction property of equality
D )division property of equality
Answer:
A
Step-by-step explanation:
Given
5(x - 7) = 55, then using the distributive property, that is
a(b - c) = ab - ac, then
5x - 35 = 55
The property that was used to write the equation in step 2 is option A) distributive property
Given that,
5(x - 7) = 55So here we have to use the distributive property i.e.
a(b - c) = ab - ac,So,
5x - 35 = 55
Therefore we can conclude that The property that was used to write the equation in step 2 is option A) distributive property
Learn more: brainly.com/question/6201432
solve the following equations:2x-5y-4 x+6y=15
Answer:
x= 3
y= 2
Step-by-step explanation:
The given equations are :
2x-5y = -4 equation 1
x +6y = 15 equation 2
We will multiply the equation:2 by 2
2(x+6y=15)
2x+12y=30 equation 3
Lets call this equation:3
Now we will use the elimination method:
Subtract equation 3 from equation 1:
2x-5y = -4
2x+12y=30
_________
-17y = -34
y= -34/-17
y = 2
Now put the value of y in any equation:
We will use equation 1
2x-5y = -4
2x-5(2)= -4
2x-10= -4
Move the constant to the R.H.S
2x= -4+10
2x=6
Divide both the terms by 2
x= 3
Therefore the solution set is (x,y){(3,2)}....
What is the common ratio for the geometric sequence
2. 4.8. 16, ...
Answer:
r = 2Step-by-step explanation:
[tex]a_n-\text{geometric sequence}\\\\a_1,\ a_2,\ a_3,\ ...,\ a_n-\text{terms of a geometric sequence}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\hdots=\dfrac{a_n}{a_{n-1}}-\text{common ratio}\\\\\text{We have:}\ a_1=2,\ a_2=4,\ a_3=8,\ a_4=16,\ ...\\\\\text{The common ratio:}\\\\r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=2[/tex]
Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 3x + 4) − (2x2 + 5x − 1), are subtracted?
A. 3x2 − 2x + 5; will be a polynomial
B. 3x2 − 2x + 5; may or may not be a polynomial
C. 3x2 + 8x + 3; will be a polynomial
D. 3x2 + 8x + 3; may or may not be a polynomial
Answer:
3x² - 2x + 5 ; will be a polynomial ⇒ answer A
Step-by-step explanation:
* Lets explain what is the polynomial
- A polynomial is an expression containing two or more algebraic terms.
- Polynomial is often the sum of some terms containing different powers
of variables.
- If you add or subtract polynomials, you get another polynomial.
- If you multiply polynomials, you get another polynomial.
* Lets solve the problem
∵ 5x² + 3x + 4 is polynomial
∵ 2x² + 5x - 1 is polynomial
- When we subtract them the answer will be polynomial
∵ (5x² + 3x + 4) - (2x² + 5x - 1)
- Open the second bracket by multiplying the negative sign by
each term in the bracket
∵ -(2x²) = -2x²
∵ -(5x) = -5x
∵ -(-1) = 1
∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 5x² + 3x + 4 - 2x² - 5x + 1
- Add the like terms
∴ (5x² - 2x²) = 3x²
∴ (3x - 5x) = -2x
∵ (4 + 1) = 5
∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5
∴ 3x² - 2x + 5 is a polynomial
∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5 ; will be a polynomial
* The answer is A
Answer:
A. 3[tex]x^{2}[/tex] − 2x + 5; will be a polynomial
Step-by-step explanation:
Give The Dood Above Brainliest
Simplify -4 1/4 - (9 1/2)
Answer:
-55/4
Step-by-step explanation:
-4 1/4 - (9 1/2)
Both the terms are given in whole fraction:
Change the terms into improper fraction
4*-4+1 = -17/4
2*9 + 1=19/2
Now,
-17/4 - 19/2
Now take the L.C.M of the denominator.
L.C.M of 4 and 2 is 4
Solve for numerator:
L.C.M (4) divided by denominator of first term will give quotient 1. Then 1 multiply by the numerator -17 will give us 1* -17 = -17
Then 4 divided by denominator of 2nd term will give us 2 as a quotient. Then quotient multiplied by numerator of 2nd term will give us 19*2 = 38
Therefore,
-17 - 38/4
= -55/4
The answer is -55/4....
The expression -4 1/4 - (9 1/2), is simplified to be expressed as -53/4
What is -4 1/4 - (9 1/2) after you simplify?To simplify the expression -4 1/4 - (9 1/2), we need to convert the mixed numbers to improper fractions and perform the subtraction.
First, let's convert the mixed numbers to improper fractions:
-4 1/4 = -4 + 1/4 = -4 * 4/4 + 1/4 = -16/4 + 1/4 = -15/4
9 1/2 = 9 + 1/2 = 9 * 2/2 + 1/2 = 18/2 + 1/2 = 19/2
Now we can substitute these values back into the original expression:
-15/4 - 19/2
To subtract fractions, we need a common denominator. The least common multiple (LCM) of 4 and 2 is 4, so we can rewrite the fractions with a common denominator of 4:
-15/4 - 19/2 = -15/4 - 38/4
Now we can subtract the fractions:
-15/4 - 38/4 = (-15 - 38)/4 = -53/4
Therefore, the expression -4 1/4 - (9 1/2) simplifies to -53/4.
Read more about how to simplify here: https://brainly.com/question/6979644
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I’m confused on how to do this
Answer:
(6,6) only goes with Line 2
(3,4) goes with neither
(7,2) goes with both
Step-by-step explanation:
Ok to decide if a point is on a line you plug it in. If you get the same thing on both sides, then that point is on that line. If you don't get the same thing on both sides, then that point is not on that line.
Test (6,6) for -5x+6y=-23.
(x,y)=(6,6) gives us
-5x+6y=-23
-5(6)+6(6)=-23
-30+36=-23
6=-23
So (6,6) is not on -5x+6y=-23.
Test (6,6) for y=-4x+30
(x,y)=(6,6) give us
y=-4x+30
6=-4(6)+30
6=-24+30
6=6
So (6,6) is on y=-4x+30.
Test (3,4) for -5x+6y=-23.
(x,y)=(3,4) gives us
-5x+6y=-23
-5(3)+6(4)=-23
-15+24=-23
9=-23
So (3,4) is not on -5x+6y=-23.
Test (3,4) for y=-4x+30.
(x,y)=(3,4) gives us
y=-4x+30
4=-4(3)+30
4=-12+30
4=18
So (3,4) is not on y=-4x+30.
Test (7,2) for -5x+6y=-23.
(x,y)=(7,2) gives us
-5x+6y=-23
-5(7)+6(2)=-23
-35+12=-23
-23=-23
So (7,2) is on -5x+6u=-23.
Test (7,2) for y=-4x+30.
(x,y)=(7,2) gives us
y=-4x+30
2=-4(7)+30
2=-28+30
2=2
So (7,2) is on y=-4x+30
(x,y) Line 1 Line 2 Both Neither
(6,6) *
(3,4) *
(7,2) *
(6,6) only goes with Line 2
(3,4) goes with neither
(7,2) goes with both
Please helpppppppppp me
Answer:
Please read explanation below.
Step-by-step explanation:
Let's go over what some of the symbols of inequalities represent:
[tex]>[/tex]: greater than
[tex]<[/tex]: less than
[tex]\ge[/tex]: greater than or equal to
[tex]\le[/tex]: less than or equal to
The symbol in the equation that is given to you is [tex]\ge[/tex]. It seems as though each of the answer choices have everything written as the same thing except for the description of the inequalities. Check the one that applies.
What is the sum and classification of [tex]\frac{2}{5} + \sqrt{88}[/tex]
A- 9.78083151..., irrational
B - 9.78083151..., rational
C-13.38083151..., irrational
D- 13.38083151..., rational
Answer:
The answer is def. A.
Answer: OPTION A.
Step-by-step explanation:
By definition:
A number is Rational when it can be written as a simple fraction.
A number is Irrational when it cannot be written as a simple fraction.
Notice that:
[tex]\frac{2}{5}[/tex] is a Rational number.
[tex]\sqrt{88}=2\sqrt{2}[/tex] It is an irrational number.
Therefore, the sum of these numbers is an Irrational number:
[tex]\frac{2}{5} + \sqrt{88}=\frac{2}{5} + 2\sqrt{22}=9.78083151...[/tex]
Use the diagram to answer the questions. What is the area of the circle in terms of pi? π units² What is the measure of the central angle of the shaded sector? ° What is the area of the shaded sector rounded to the nearest whole number? units²
The radius of the circle is 11, so the area is
[tex]A=\pi r^2 = 121\pi[/tex]
The central angles of the shaded and non-shaded regions sum up to 360 degrees, so the central angle of the shaded region is
[tex]360-217=143[/tex]
The area of the shaded region is in proportion with the area of the whole circle: if the whole area is given by a sector of 360°, the area of a 143° sector will be given by
[tex]A_{360}\div A_{143} = 360\div 143[/tex]
Since we know that the whole area is [tex]121\pi[/tex], we can solve for the area of the 143° sector:
[tex]121\pi\div A_{143} = 360\div 143 \iff A_{143}=\dfrac{121\pi\cdot 143}{360} \approx 151[/tex]
Answer:
121
143
151
Step-by-step explanation:
If g(x) = 2(x − 4), find the value of x if g(x) = 20. (2 points) 32 12 14 10
For this case we have a function of the form[tex]y = g (x)[/tex]
Where:
[tex]g (x) = 2 (x-4)[/tex]
We must find the value of "x" when the function has a value of 20, that is, [tex]g (x) = 20[/tex]:
[tex]2 (x-4) = 20[/tex]
We apply distributive property:
[tex]2x-8 = 20[/tex]
We add 8 to both sides of the equation:
[tex]2x = 20 + 8\\2x = 28[/tex]
We divide between 2 on both sides of the equation:
[tex]x = \frac {28} {2}\\x = 14[/tex]
Answer:
Option C
Answer:
option c 14
Step-by-step explanation:
did the test
What is the equation of a line that contains the points (2,-2) and (0, -2)?
y=0
x= -2
y=-2
x=0
Answer:
y = - 2
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
The points (2, - 2) and (0, - 2) have the same y- coordinate and therefore lie on a horizontal line with equation
y = - 2
Which of the following is the simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x?
x to the 1 over fifth power
x to the 4 over fifth power
x to the four over twentieth power
x
Answer:
[tex]\large\boxed{x^\frac{4}{5}}[/tex]
Step-by-step explanation:
[tex]\sqrt[n]{a}=a^\frac{1}{n}\Rightarrow\sqrt[5]{x}=x^\frac{1}{5}\\\\\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}=x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\cdot x^\frac{1}{5}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}=x^\frac{4}{5}[/tex]
Answer:
[tex]x^{\frac{4}{5}}[/tex]
Step-by-step explanation:
fifth root of x can be written in exponential for as:
[tex]x^\frac{1}{5}[/tex]
[tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex]
WE apply exponential property to multiply it
a^m times a^n= a^{m+n}
[tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex] times [tex]x^\frac{1}{5}[/tex]
[tex]x^{\frac{1}{5} +\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]
The denominator of the fractions are same so we add the numerators
[tex]x^{\frac{4}{5}}[/tex]
Simplify the given equation.
5x + 2(x - 3) = -2(x - 1)
078-6--2X-2
7x - 6 = -2x + 2
7x - 3 = -2x - 1
Answer:
x = 8/9
Step-by-step explanation:
5x + 2(x - 3) = -2(x - 1)
Distribute on both sides.
5x + 2x - 6 = -2x + 2
Combine like terms on the left side.
7x - 6 = -2x + 2
Add 2x to both sides.
9x - 6 = 2
Add 6 to both sides.
9x = 8
Divide both sides by 9.
x = 8/9
How much is a ton in pounds
[tex]\huge{\boxed{\text{2000 pounds}}}[/tex]
One ton is equal to [tex]\boxed{\text{2000 pounds}}[/tex].
For example, two tons is equal to [tex]4000[/tex] pounds, because [tex]2000*2=4000[/tex].
Answer is provided in the image attached.
an office worker earns R6400 per month. his monthly expenses are 1/5 for rent , 2/7 for car payment, 1/6 for insurance, 1/3 for other monthly living expenses and the rest he deposits into a savings account. how much does he save per month?
Answer:
The officer saves $91.45 per month
~Step-by-step explanation~
Ok this is how I do fractions and its not very good, but it works.
First I divided 6400 by 5, 6, and 7, (I didn't do 3 because you can just multiply the answer to 6 by 2.) the reason I divided these is to see how much 1 part of their fraction is worth. So in total I got 1066.66 (irrational number) for insurance which means I got 2133.32 for his monthly living ( had to multiply by 2). For his car payment I got 1828.57 (I divided and then multiplied by 2) and for his rent I got 1280. I added these all together to get the total he spends each month which was 6308.55, and I subtracted that from 6400 to figure out that he puts $91.45 in his savings account
Answer:
The answer is R91.43.
Step-by-step explanation:
Monthly salary of the worker = R6400
The monthly expenses are 1/5 for rent that is [tex]\frac{1}{5}\times6400= 1280[/tex]
The car payment is 2/7 that is [tex]\frac{2}{7}\times6400= 1828.57[/tex]
The insurance is 1/6 that is [tex]\frac{1}{6}\times6400= 1066.67[/tex]
Few other monthly living expenses are 1/3 that is [tex]\frac{1}{3}\times6400= 2133.33[/tex]
We will total these values:
[tex]1280+1828.57+1066.67+2133.33=6308.57[/tex]
So, the amount that is saved per month = [tex]6400-6308.57=91.43[/tex]
The answer is R91.43.
bob spent 3/8 of his birthday money at a baseball game and 5/12 ona new bat and glove.what fraction of his birthday money did bob spend?
Answer:
19/24
Step-by-step explanation:
Since you are looking for the fraction he spend, you have to add 3/8 and 5/12 with one another. To do this you have to change those fractions to have the same denominators. so you multiply 3/8 by 3/3 to get 9/24 and you multiply 5/12 by 2/2 to get 10/24. You then add 9/24 with 10/24 to get 19/24. Since you cannot simplify this further, 19/24 is your answer.
Bob spent [tex]\frac{19}{24}[/tex] of his birthday money
What is fraction?"It is a number is expressed as a quotient, in which the numerator is divided by the denominator.""It is used to represent the part of the whole thing. "For given question,
Bob spent 3/8 of his birthday money at a baseball game and 5/12 on a new bat and glove.
We need to find the fraction of his birthday money he spent.
so we add given two fractions.
[tex]\frac{3}{8}+ \frac{5}{12}\\\\ =\frac{3\times 3}{8\times 3}+ \frac{5\times 2}{12\times 2}\\\\=\frac{9}{24}+ \frac{10}{24}\\\\=\frac{9+10}{24}\\\\ =\frac{19}{24}[/tex]
Therefore, Bob spent [tex]\frac{19}{24}[/tex] of his birthday money.
Learn more about the fraction here:
https://brainly.com/question/12151403
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Is f(x)=3x^2+x an odd function
Answer:
No
Step-by-step explanation:
Given a function f(x)
For the function to be odd then f(- x) = - f(x)
f(- x) = 3(- x)² + (- x) = 3x² - x
- f(x) = - (3x² + x) = - 3x² - x
Since f(- x) ≠ - f(x) then f(x) is not an odd function
what is the 42 term where a1=-12 and a27=66
Answer:
111
Step-by-step explanation:
a1 = -12
a27 = 66
Now using the formula an = a1+(n-1)d we will find the value of d
here n = 27
a1 = -12
a27 = 66
Now substitute the values in the formula:
a27 = -12+(27-1)d
66= -12+(26)d
66 = -12+26 * d
66+12 = 26d
78 = 26d
now divide both the sides by 26
78/26= 26d/26
3 = d
Now put all the values in the formula to find the 42 term
an = a1+(n-1)d
a42 = -12 +(42-1)*3
a42 = -12+41 *3
a42 = -12+123
a42 = 111
Therefore 42 term is 111....
Answer:
Assuming it is arithmetic, the 42nd term is 111.
Assuming it is geometric, the conclusion says it isn't geometric.
Step-by-step explanation:
Let's assume arithmetic first.
Arithmetic sequences are linear. They go up or down by the same number over and over. This is called the common difference.
We are giving two points on our line (1,-12) and (27,66).
Let's find the point-slope form of this line.
To do this I will need the slope. The slope is the change of y over the change of x.
So I'm going to line up the points and subtract vertically, then put 2nd difference over 1st difference.
(1 , -12)
-(27,66)
------------
-26 -78
The slope is -78/-26=78/26=3. The slope is also the common difference.
I'm going to use point [tex](x_1,y_1)=(1,-12)[/tex] and [tex]m=3[/tex] in the point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-12)=3(x-1)[/tex]
Distribute:
[tex]y+12=3x-3[/tex]
Subtract 12 on both sides:
[tex]y=3x-3-12[/tex]
[tex]y=3x-15[/tex]
So we want to know what y is when x=42.
[tex]y=3(42)-15[/tex]
[tex]y=126-15[/tex]
[tex]y=111[/tex]
So [tex]a_{42}=111[/tex] since the explicit form for this arithmetic sequence is
[tex]a_n=3n-15[/tex]
-----------------------------------------------------------------------------------------
Let's assume not the sequence is geometric. That means you can keep multiplying by the same number over and over to generate the terms given a term to start with. That is called the common ratio.
The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex].
We are given [tex]a_1=-12[/tex]
so this means we have
[tex]a_n=-12 \cdot r^{n-1}[/tex].
We just need to find r, the common ratio.
If we divide 27th term by 1st term we get:
[tex]\frac{a_{27}}{a_1}=\frac{-12r^{27-1}}{-12r^{1-1}}=\frac{-12r^{26}}{-12}=r^{26}[/tex]
We are also given this ration should be equal to 66/-12.
So we have
[tex]r^{26}=\frac{66}{-12}[/tex].
[tex]r^{26}=-5.5[/tex]
So the given sequence is not geometric because we have an even powered r equaling a negative number.
Last year, there were 148 pies baked for the bake sale. This year, there were c pies baked. Using c, write an expression for the total number of pies baked in the 2 years
[tex]\huge{\boxed{c+148}}[/tex]
We need to find the number of pies baked in years 1 and 2.
There were 148 pies baked in year 1. [tex]148[/tex]
There were [tex]c[/tex] pies baked in year 2. [tex]148+c[/tex]
Rearrange the terms so the variable is first. [tex]c+148[/tex]
Answer:
since we know that there were 148 pies sold the first year, and c number of pies sold this year. You would add these two to find the total amount of both years.
148+c
Write the slope-intercept form of the equation that passes through the point (3,-2) and is parallel to the line y = -x - 5
Answer:
The equation of the line is y = -x + 1
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope-intercept form of the equation is y = mx + c, where m is
the slope of the line and c is the y-intercept
- To make this equation you need slope (m) and a point on the line to
find the value of c
- The parallel lines have same slopes
* Lets solve the problem
- The line is parallel to the line y = -x - 5
∵ y = mx + c
∵ The slope of the line y = -x - 5 is the coefficient of x
∴ m = -1
∵ Parallel lines have same slopes
∴ The slope of the line is -1
∴ the equation of the line is y = -x + c
- To find c substitute x and y in the equation by the coordinates of
any point lies on the line
∵ The line passes through point (3 , -2)
∵ y = -x + c
∴ -2 = -(3) + c
∴ -2 = -3 + c ⇒ add 3 for both sides
∴ c = 1
∴ The equation of the line is y = -x + 1
Which type of graph is typically not used for quantitative data?
Answer:
it’s a circle graph
seven friends go to the store and each wants a drink if each drink costs $2 how much was the total bill
Answer:
7 friends multiply $2
Its product is: $14
Step-by-step explanation:
Sani is factoring the polynomial 2x^2+5x+3. If one factor is (x+1), what is the other factor?
A. 2x-3
B. 2x+3
C. 3X-2
D. 3x+2
Answer:
B.
Step-by-step explanation:
So [tex]2x^2+5x+3[/tex] will have two factors if one factor in the form [tex](ax+b)[/tex] is given.
The other factor will also be in the form of [tex](cx+d)[/tex].
So we have
[tex](x+1)(cx+d)[/tex]:
Let's use foil.
First: x(cx)=cx^2
Outer: x(d)=dx
Inner: 1(cx)=cx
Last: 1(d)=d
---------------------Adding like terms:
cx^2+(d+c)x+d
We are comparing this to:
2x^2+ 5x+3
So we see that c=2 and d=3 where the other factor is cx+d=2x+3.
Also this works since c+d=5 (we know this because 2+3=5).
Answer:
B
Step-by-step explanation:
he height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
Answer:
[tex]\large\boxed{V=\pi r^3}[/tex]
Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
Let r - radius of the cone.
We have H = 3r.
The base of the cone: [tex]B=\pi r^2[/tex].
Substitute:
[tex]V=\dfrac{1}{3}\pi(r^2)(3r)[/tex] cancel 3
[tex]V=\pi r^3[/tex]
Answer:
For plato users is option A
Step-by-step explanation:
A. V =[tex]\pi[/tex]r3
Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from his starting point? Express your answer as a decimal to the nearest hundredth.
Answer:
1.25 mi
Step-by-step explanation:
Think of this in terms of a graph in the x-y axis
Bill starts out at point (0,0)
He walks 1/2 mile south (i.e 0.5 miles in the -y direction) and ends up at (0,-0.5)
Next he walks 3/4 mile (0.75 miles) in the +x direction and ends up at (0.75, -0.5)
Then he continues to walk 1/2 mile (0.5 miles) in south in the -y direction and ends up at (0.75, -1).
His final distance from the starting point (0,0) from his end point (0.75,-1) is simply the distance between the 2 coordinates (see picture for formula).
hence,
D = √ (0.75 -0)² + (-1 - 0)²
D = √ (0.75)² + (-1)²
D = 1.25
Answer:
1.25 M
Step-by-step explanation: