Solve for x. 9(x - 2) = 18
x = 0
x = 16/9
x = 20/9
x = 4

Final answer:

Kari had $13. We found this by dividing Penny's amount, $117, by 9, since Penny's amount is 9 times greater than Kari's.

Explanation:

The question is asking us to determine how much money Kari had if Penny had $117, which is 9 times as much as what Kari had. To do this, we need to perform a division, because if Penny's amount is 9 times Kari's, we can find Kari's amount by dividing Penny's $117 by 9.

 To solve for K, divide both sides of the equation by 9: K = $117 / 9.

Therefore, Kari had $13.

To get an A, David must score at least 85 on the last test.

David has taken three tests so far, with scores of 89, 92, and 95. To find out what score he needs on the last test to achieve a total of at least 360 points, we first calculate the total points he has accumulated from the first three tests:

[tex]\[ 89 + 92 + 95 = 276 \][/tex]

Now, we subtract this total from the minimum total points required for an A:

Therefore, David needs to score at least 84 points on the last test to reach a total of 360 points. However, since test scores are whole numbers, we round up to the nearest whole number that David can actually achieve on the test. Thus, David needs to score at least 85 on the last test to ensure he gets an A.

Factor out 4x from the given trinomial. Therefore, option C is the correct answer.

The factors are the polynomials which are multiplied to produce the original polynomial.

The given trinomial is 4x³-20x²+24x.

Here, 4x(x²-5x+6)

= 4x(x²-3x-2x+6)

= 4x[(x(x-3)-2(x-3)]

= 4x(x-3)(x-2)

Therefore, option C is the correct answer.

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Answer:

59 ft

Step-by-step explanation:

Given;

Then Darren's plane must have flown (2 × 20ft) = 40 ft

Amanda's plane would have flown (40ft + 19ft) = 59 ft

Amanda's plane flew 59 ft far.

The distance of the paper plane thrown by Amanda is given by the equation A = 59 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance of the paper plane thrown by Amanda be A

Now , the equation will be

The distance of the paper plane thrown by Rachel R = 20 feet

The distance of the paper plane thrown by Darren D = 2 x distance of the paper plane thrown by Rachel R

Substituting the values in the equation , we get

The distance of the paper plane thrown by Darren D = 40 feet

And , Amanda plane flew 19 ft farther than Darren plane Darren plane

Substituting the values in the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + distance of the paper plane thrown by Darren D

On simplifying the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + 40

The distance of the paper plane thrown by Amanda A = 59 feet

Hence , the distance is 59 feet

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Answer:

True

Step-by-step explanation:

If you look at the different countries ranked based off of the size of their ecological footprint, you will see that Japan is ranked around 5 and china around 10.

This means The average ecological foot print of a person living in Japan is larger than a person living in China.

Answer:

Option B and E

Step-by-step explanation:

A line is given as 3x - 4y = 7

We have to find the equation of a line parralel to the given line which passes through point (-4, -2).

Let the equation is y = mx + c

Line parallel to 3x - 4y = 7 will have same slope

3x - 4y = 7

-4y = 7 - 3x

4y = 3x - 7

y = [tex]\frac{1}{4}[/tex] (3x - 7 ) ≈ [tex]\frac{3}{4}[/tex]x - [tex]\frac{7}{4}[/tex]

So slope of the line will be m = [tex]\frac{3}{4}[/tex]

Since the given line passes through (-4, -2)

So we put the values in y = mx + c to get the value of c.

-2 = [tex]\frac{3}{4}[/tex] (-4 ) + c

-2 = -30 +c

c = 3 - 2 = 1

Therefore, equation will be

y = [tex]\frac{3}{4}[/tex]x + 1 ----------(1)

We further solve equation (1)

4y = 3x + 4

3x - 4y = -4 ---Option B

By solving the equation (1) in other way

y + 2 = [tex]\frac{3}{4}[/tex]x + 1 + 2

[tex]\frac{3}{4}[/tex]x + 3

y + 2 = [tex]\frac{3}{4}[/tex] (x+4)  --Option E

Option B and E are the answers.

The larger frustum has a surface area of 1516.875cm². This is calculated by first finding the ratio of the heights, then cubing this ratio and finally multiplying the result by the surface area of the smaller frustum.

In Mathematics, similar frustums follow a rule in which the ratio of their dimensions is the cube root of their surface area ratio. Since the height of the larger frustum is 30cm, and the height of the smaller one is 20cm, their ratio is 30:20 or 1.5:1.

To find the ratio of the surface areas, you'll want to cube this ratio (1.5 ^ 3 = 3.375).

So, the surface area of the larger frustum is the surface area of the smaller frustum (which is 450cm² ) multiplied by this ratio. In mathematical terms, 3.375 * 450 = 1516.875cm².

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y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We need to find the equation of line that includes the point (6, 3) has a slope of 2.

y minus y one equal to m time of x minus x one.

(y-y₁)=m(x-x₁)

x₁=6,y₁=3 and m is 2

y-3=2(x-3)

Apply distributive property on right hand side.

y-3=2x-6

Shift -3 to the RHS side

y=2x-6+3

y=2x-3

Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

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Answer:

Option A - Non-linear              

Step-by-step explanation:

Given : Graph the function by the table.

x           y

1          12.3

2         19.6

3         26.6

4         34.2

5         41.5

To find : Is the function linear or nonlinear?

Solution :

The function is linear when there slopes are equal.

So, we find the slope of the points.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]

[tex]m=\frac{19.6-12.3}{2-1}[/tex]

[tex]m=\frac{7.3}{1}[/tex]

[tex]m=7.3[/tex]

Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]

[tex]m=\frac{26.6-19.6}{3-2}[/tex]

[tex]m=\frac{7}{1}[/tex]

[tex]m=7[/tex]

We have seen that slope between points are not equal.

Therefore, The given points are non-linear.

So, Option A is correct.

After applying the translation (x - 1, y - 3), the vertices of the triangle originally at (-4, 5), (0, 0), and (4, 5) will move to new locations (-5, 2), (-1, -3), and (3, 2).

The question is about translation in mathematics, specifically in geometry. A translation is a function that moves every point a constant distance in a specific direction. If we have a point at coordinates (x, y), a translation of the form (x - a, y - b) will shift that point a units to the left and b units down:

So, the vertices of the triangle after the translation (x - 1, y - 3) will be (-5, 2), (-1, -3), and (3, 2).

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Answer:

Step-by-step explanation:

the right answer is a (-6,8) where x=-6 and y=8

We're going to use Cramer's rule to resolve this question.

First of all, we're going to give a number to the equations:

(1) -8x-8y=-16

(2) 6x-9y=-108

where constant 1=c1=-16 and the constant 2=c2=-108

now we need to find the next determinants:

D: system determinant,Dx and Dy.

now we're going to find "D."

for that, we're going to take the coefficients of  x and y in (1) and (2)

              x    y

D= [tex]\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right][/tex]     

this is how we need to put the matrix, using the numbers next to x and y in the (1) and (2) equation.

to solve this matrix, we need to multiplicate in X, and subtract the results; so for D we have:

(-8*-9)-(6*-8)

72-(-48)=

72+48=120

now we're doing the same process to find Dx and Dy, but in each case, we're going to replace x or y with the constants (the constants are the numbers right to the "=")

to find Dx we're going to use the values of c1 and c2 instead of x

            C1&2      y

Dx= [tex]\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right][/tex]

Now we do the same as with D

(-16*-9)-(-108*-8)=

144-(864)

144-864=-720

and now for Dy=

            x      C1&2

Dy=  [tex]\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right][/tex]

= (-8*-108)-(6*-16)=

864-(-96)=

864+96=960

now the last step is to find x and y .

x= [tex]\frac{Dx}{D}[/tex]   Y= [tex]\frac{Dy}{D}[/tex]

x= -720/120=-6

y=960/120=8

x=-6  y= 8

answer = (-6,8)

The equation of the line is y + 2 = −3 (x − 1). The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The points from which the line passes are ( 0,1) and (1,-2). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2 - 1 ) / ( 1 )

Slope = -3

The equation of the line will be written as,

y - y₁ = m ( x - x₁ )

y +2 = -3 ( x - 1 )

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The equation which is not necessarily true is that G'H' = 8 units.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraint.

Given that a polygon of GHIJ translates 8 units to the left to form polygon G 'H 'I 'J ' in the option it is necessary because GH is a side and G'H' will still be a side so they will be the same.

In option b G'G will be  8 units because the entire figure has shifted towards the left.

And the correct answer will be that G'H' = 8 units which are not true.

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True because their different

The equation of the line with a slope of 5 and a y-intercept of 7 is y = 5x + 7.

The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. Given that the slope (m) is 5 and the y-intercept (b) is 7, the equation of the line can be written as y = 5x + 7. This equation tells us that for every increase of 1 on the x-axis, the value of y rises by 5 units, and the line crosses the y-axis at the point (0, 7).

To convert 680% to a fraction, write it as 680/100 and simplify to 34/5. This improper fraction can also be written as the mixed number 6 [tex]\frac{4}{5}[/tex].

To convert 680% to a fraction or mixed number, follow these steps:

First, write the percent as a fraction with a denominator of 100. So, 680% becomes 680/100.

Next, simplify the fraction by finding the greatest common divisor (GCD) of 680 and 100. The GCD of 680 and 100 is 20.

Divide both the numerator and the denominator by their GCD:
680 ÷ 20 = 34
100 ÷ 20 = 5
So, 680/100 simplifies to 34/5.

Finally, convert the improper fraction to a mixed number. To do this, divide the numerator by the denominator:
34 ÷ 5 = 6 (with a remainder of 4).
This gives us the mixed number 6 [tex]\frac{4}{5}[/tex].

Therefore, 680% as a fraction is 34/5 and as a mixed number is 6 [tex]\frac{4}{5}[/tex].