Find f(6)+5g(-1) given f(x)=-5x+1 and g(x)=-2x2

Answer:

A

Step-by-step explanation:

The equation of the line perpendicular to the given line and passing through the point (-3, 5) is option C. y = 4x + 17.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given the equation of a line in point slope form as,

y - 2 = -1/4 (x + 3)

We have to calculate the equation of a line perpendicular to the given line.

Slope of a line perpendicular to another line is the reciprocal of the given line with opposite sign.

Slope of the given line = -1/4

Slope of the perpendicular line = - (1 ÷ -1/4) = 4

Given a point (-3, 5).

Equation of the required line in point slope form is,

y - 5 = 4 (x - -3)

y - 5 = 4 (x + 3)

y - 5 = 4x + 12

y = 4x + 12 + 5

y = 4x + 17

Hence the equation of the required line perpendicular to the given line is y = 4x + 17.

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Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° ( n - 2) ← n is the number of sides of the polygon

Answer:

B

Step-by-step explanation:

−10

3 /5 (5x + 10) = −24

3x + 6 = −24

3x = −30

x = −10

Answer:

y = [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + y = - 6 into this form

subtract 2x from both sides

y = - 2x - 6 ← in slope-intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (6, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of perpendicular line

Answer:

it took tamara an 1:49 in total

the difference was 41 minutes

Step-by-step explanation:

Answer:

41 minutes

Step-by-step explanation:

75 minutes minus 34 minutes equal 41 minutes

Chang spent $16 on fruit out of a total of $80 at the grocery store. In terms of percentages, this equals 20% of his total grocery bill spent on fruit.

The subject is about finding out what percentage of the total Chang spent on fruit at the grocery store. In order to solve this problem, we first need to know the total amount spent and how much was spent on one part, in this case, fruit.

Chang spent $16 on fruit and a total of $80 at the store. So, to find out the percentage spent on fruit, we divide the amount spent on fruit by the total amount spent, and then multiply by 100 to change the decimal to a percentage.

Here is the math: (16 ÷ 80) x 100 = 20%

So, Chang spent 20% of his total grocery bill on fruit.

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April sold 40 adult tickets and 35 child tickets.

To find the number of adult and child tickets sold, we can set up a system of equations based on the given information:

Let x be the number of adult tickets sold and y be the number of child tickets sold.

We can establish two equations:

To solve this system, we can use the method of substitution or elimination. Let's use the elimination method:

By multiplying equation 1 by 5, we get:

5x + 5y = 375 (equation 3)

Subtracting equation 3 from equation 2:

(8x + 5y) - (5x + 5y) = 495 - 375

Simplifying:

3x = 120

Dividing both sides by 3:

x = 40

Substituting the value of x into equation 1:

40 + y = 75

Solving for y:

y = 75 - 40

y = 35

Therefore, April sold 40 adult tickets and 35 child tickets.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (-3, 7) and (2, 9). Substitute:

[tex]d=\sqrt{(2-(-3))^2+(9-7)^2}=\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}[/tex]

Answer:

sqrt(29)

Step-by-step explanation:

To find the distance between two points, we use the formula

d =sqrt((x2-x1)^2 + (y2-y1)^2 )

= sqrt( (2--3)^2 + (9-7)^2)

 = sqrt( 2+3)^2 + (2)^2)

= sqrt( 5^2 + 4)

= sqrt( 25+4)

= sqrt(29)

The distance is the sqrt(29)

The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Lee needs 3/4 cup of white sugar for each batch of cookies, and she is making 2 batches, so she needs:

= 3/4 cup/batch x 2 batches

= 6/4 = 3/2 cups of white sugar

Lee needs 1 2/4 cups of brown sugar for each batch of cookies, and she is making 2 batches, so she needs:

= 1(2/4) cups/batch x 2 batches

= 3 cups of brown sugar

Therefore,

The total amount of brown and white sugar that Lee needs is:

= 3/2 cups of white sugar + 3 cups of brown sugar

= 4 1/2 cups of sugar

Thus,

The total amount of brown and white sugar that Lee needs is 4 1/2 cups of sugar

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Answer:

10 servings

Step-by-step explanation:

not very hard at all, all you have to do is do 4/(3/8) to get you 10.66, but since you need full servings, you leave out the decimal (logic) to get the answer

You can make 10 full servings of the recipe with 4 cups of raisins and have some leftover.

To determine how many full servings you can make with 4 cups of raisins when a recipe calls for 3/8 cup of raisins per serving, you can set up a division problem.

Divide the total amount of raisins, which is 4 cups, by the amount of raisins per serving, which is 3/8 cup.

You can convert 3/8 to a decimal by dividing the numerator (3) by the denominator (8).

This gives you 0.375.

Then, divide 4 by 0.375 to find the number of full servings.

The result is 10.67, which means you can make 10 full servings and have a little bit of raisins leftover.

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You have 4 cups of raisins. A recipe calls for 3/8 cup of raisins per serving. How many full servings can you make?

Answer:

S∞ = 7       Option C

Step-by-step explanation:

Given that:

∑21[tex](\frac{1}{4} )^{i}[/tex]     i = 1 to ∞

We need to find the sum.

Firstly we will find the sequence

a₁ = [tex]21(\frac{1}{4} )^{1}  = (\frac{21}{4} )[/tex]

a₂ = [tex]21(\frac{1}{4} )^{2}  = (\frac{21}{16} )[/tex]

a₃ = [tex]21(\frac{1}{4} )^{3}  = (\frac{21}{64} )[/tex]

a₄ = [tex]21(\frac{1}{4} )^{4}  = (\frac{21}{256} )[/tex]

this sequence is geometric

So, we use sum of infinite terms

a = [tex]\frac{21}{4}[/tex]

r = [tex]\frac{\frac{21}{16} }{\frac{21}{4} }  = \frac{1}{4}[/tex]

The sum of infinite terms of a GP series

S∞ = [tex]\frac{a}{1-r}[/tex]

where a is first term

r is common ratio and 0<r<1

S∞ = [tex]\frac{\frac{21}{4} }{1 - \frac{1}{4} }  = \frac{\frac{21}{4} }{\frac{3}{4} }[/tex]

S∞ = 7

Method 1:

[tex]F(1)=4\\\\F(n)=F(n-1)+7\\\\n\in\{2,\ 3,\ 4,\ 5,\ ...\}\\\\F(2)=F(1)+7\to F(2)=4+7=11\\\\F(3)=F(2)+7\to F(3)=11+7=18\\\\F(4)=F(3)+7\to F(4)=18+7=25\\\\F(5)=F(4)+7\to F(5)=25+7=32\\\\F(6)=F(5)+7\to F(6)=32+7=39\\\\F(7)=F(6)+7\to F(7)=39+7=46\\\\F(8)=F(7)+7\to F(8)=46+7=53[/tex]

Method 2:

The general formula of an arithmetic sequence:

[tex]a_n=a_1+(n-1)d[/tex]

We have:

[tex]a_1=F(1)=4,\ d=7[/tex]

Substitute:

[tex]a_n=4+(n-1)(7)=4+7n-7=7n-3[/tex]

Put n = 8 to the formula:

[tex]a_8=7(8)-3=56-3=53[/tex]

Answer:

5

Step-by-step explanation:

x + y + x + y + z = 5

Answer:

Step-by-step explanation: The correct answer is 18 boys.

First of all, we know that there is a ratio of 4 girls to three boys or 4:3.

Next we know that there are 24 girls so what we have to do is figure out which number 4 was multiplied by to get 24.

4 times 6 is 24 so since we know that four was multiplied by 6, we can now multiply 3 by 6 to keep the same ratio of girls to boys.

The question is about finding the number of boys in a class when the ratio of girls to boys is given and the number of girls is known. Set up a proportion and solve the equation to find that there are 18 boys in the 6th grade class.

This is a Mathematics problem on ratios. In this problem, the ratio of girls to boys is given as 4:3. This means for every 4 girls, there are 3 boys. If there are 24 girls, we can find the number of boys by setting up a proportion. Like this:

4 (girls) / 3 (boys) = 24 (girls) / x (boys)

Solve for x by cross multiplying: (4 * x) = (3 * 24) which simplifies to: 4x = 72. Solve for x by dividing both sides of the equation by 4 resulting in: x = 18. Hence, there are 18 boys in the 6th grade classes.

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Answer: 9^-8

Step-by-step explanation:

To get single positive exponent,

9^-5 / 9^3

Since the exponent is same

So we can solve the coefficient like this

9^-5-3

So

9^-8

The problem 9⁻⁵ /9³ simplifies to -8 by subtracting the exponent in the denominator (3) from the exponent in the numerator (-5). To achieve a single positive exponent, take the reciprocal of the base, then the final answer becomes 1/9⁸.

The question pertains to the laws of exponents in mathematics. To be specific, you are asked to simplify the expression 9⁻⁵ /9³ into a single positive exponent. In this case, you should remember that division of the same base translates to subtraction of exponents, according to the exponent laws. Therefore, you simply subtract the exponent of the denominator (3) from the exponent of the numerator (-5).

Following the rule, -5 - 3 results in -8. So the expression simplifies to 9^-8. But, since we need a single positive exponent, we take the reciprocal of 9. Remember that changing the sign of an exponent is equivalent to taking the reciprocal of the base. Hence, the final answer = 9⁻⁸ becomes 1/9⁸.

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Answer: No

Step-by-step explanation:

A right angle is exactly 90°

To determine if 50, 48, 14 form a right angle, we need to check if the sum of the squares of the two smaller numbers is equal to the square of the largest number. The sum of 48^2 and 14^2 is equal to 50^2, so 50, 48, 14 form a right angle.

To determine if 50, 48, 14 form a right angle, we need to check if the sum of the squares of the two smaller numbers is equal to the square of the largest number.

The largest number is 50. So, we need to check if 48^2 + 14^2 = 50^2.

48^2 equals 2304 and 14^2 equals 196. The sum of these two numbers is 2500, which is equal to 50^2. Therefore, 50, 48, 14 form a right angle.

Final answer:

A line is parallel to y=3/4x-3 if it has the same slope of 3/4.

Explanation:

A line is parallel to y = \frac{3}{4}x - 3 if it has the same slope as the given line.

The slope of y = \frac{3}{4}x - 3 is \frac{3}{4}. So, any line with a slope of \frac{3}{4} is parallel to it.

For example, a line with the equation y = \frac{3}{4}x + 2 is parallel to y = \frac{3}{4}x - 3 because they both have the same slope, \frac{3}{4}.

Answer:

4

Step-by-step explanation:

2025 - 2014 = 11

11 * 12 = 132

132% of $24,000 = $31680

I think this is right but I don't sure... sorry

Answer:

[tex]x=25[/tex]

Step-by-step explanation:

The given linear equation is

[tex]30=\frac{6}{5}x[/tex]

We multiply both sides by the reciprocal of [tex]\frac{6}{5}[/tex] which is [tex]\frac{5}{6}[/tex].

This will give us,

[tex]30\times \frac{5}{6} =\frac{5}{6}\times \frac{6}{5}x[/tex]

We cancel out common factors to get;

[tex]5\times \frac{5}{1} =x[/tex]

This implies that;

[tex]x=25[/tex]

To write the equation in slope-intercept form, rearrange the equation to isolate the y variable. Then, divide both sides by the coefficient of y to solve for y. The equation is y = 4/11, with a slope of 0 and y-intercept of 4/11.

To write the equation in slope-intercept form, we need to isolate the y variable on one side of the equation.

Start by rearranging the equation to get the y variable alone:

-12 + 11y = -8

Next, add 12 to both sides to move the constant term to the other side:

11y = 4

Then, divide both sides by 11 to solve for y:

y = 4/11

The equation in slope-intercept form is y = 4/11. The slope is 0 and the y-intercept is 4/11.

Final answer:

The equation -12 + 11y = -8 in slope-intercept form is y = 4/11. There's no x term in the equation, indicating that the slope is 0, and the y-intercept is 4/11.

Explanation:

To write the equation -12 + 11y = -8 in slope-intercept form, we start by isolating the y-variable on one side of the equation. Here's how you can do it:

Add 12 to both sides of the equation to get 11y = 4.

Divide both sides of the equation by 11 to solve for y, resulting in y = 4/11.

The equation in slope-intercept form is y = 4/11. In this form, y = a + bx, the slope (b) is the coefficient of x, and the y-intercept (a) is the constant term. Since our equation has no x term, the slope is 0 and the y-intercept is 4/11.

Therefore, the slope of the line is 0, and the y-intercept is the point (0, 4/11).

Answer:

Correct choice is C

Step-by-step explanation:

Consider segment AB with endpoints A(-2,1) and B(4,3).

1. Rotation counterclockwise of 90° has a rule

(x,y)→(-y,x),

then

2. x-axis reflection has a rule

(x,y)→(x,-y),

then

3. Rotation counterclockwise of 270° has a rule

(x,y)→(y,-x),

then

4. y-axis reflection has a rule

(x,y)→(-x,y),

then

Answer:

C) Rotation counter-clockwise of 90 degree → x-axis reflection → rotation counter-clockwise of 270 degree → y-axis reflection

Step-by-step explanation:

We are given the line segment AB with end points (-2,1) and (4,3).

It is provided that after applying rigid transformations the line segment AB maps onto itself.

So, according to the options,

1. Rotation counter-clockwise by 90 degree changes (x, y) into (-y, x)

i.e. (-2,1) → (-1,-2) and (4,3) → (-3,4)

2. X-axis reflection changes (x, y) into (x, -y)

i.e. (-1,-2) → (-1,2) and (-3,4) → (-3,-4)

3. Rotation counter-clockwise by 270 degree changes (x,y) into (y, -x)

i.e. (-1,2) → (2,1) and (-3,-4) → (-4,3)

4. Y-axis reflection changes (x,y) into (-x,y)

i.e. (2,1) → (-2,1) and (-4,3) → (4,3)

Hence, we see that after applying transformations to AB we are again obtaining the line AB as seen below in the figure.

So, option C is correct.  

Answer:

option B : [tex]f(x)= log_7(x-39)[/tex]

Step-by-step explanation:

(a) [tex]f(x) = 7^{x-39}[/tex]

For exponential function , there is no vertical asymptotes

General form of exponential function is

[tex]f(x) = n^{ax-b}+k[/tex]

[tex]f(x) = 7^{x-39}[/tex]

In the given f(x) the value of k =0

So horizontal asymptote is y=0

(b) lets check with option

[tex]f(x)= log_7(x-39)[/tex]

To find vertical asymptote we set the argument of log =0  and solve for x

Argument of log is x-39

x-39=0 so x=39

Hence vertical asymptote at x=39

Answer:

The correct answer is b. f(x) = log7(x-39)

All circles are similar because they can be transformed into each other through a series of transformations without changing their core properties. These transformations include translation (shifting the position) and scaling (resizing).

All circles are similar because they maintain the same shape and can be scaled up or down without changing their properties. A sequence of transformations such as scaling (resizing) can carry one circle onto another. Here is how:

By performing these transformations, Circle A transforms into Circle B. This holds true for any two circles, thus all circles are always similar.

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Answer:

(1, - 1 )

Step-by-step explanation:

using the midpoint formula

midpoint = [ [tex]\frac{1}{2}[/tex](- 2 + 4), [tex]\frac{1}{2}[/tex](5 - 7) = (1, - 1 )

Answer:

possible answrs addition, expanded form

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

6.7

Step-by-step explanation:

Answer:

6.4 is the correct answer.

Step-by-step explanation:

You can factor out the 4 and you would get....

[tex]4(2b-1)[/tex]