The graph of function g is a vertical stretch of the graph of function f ​​by a factor of 3. Which equation describes function g?
A. g(x)=3f(x)
​​B. g(x)=f(3x)
​​C. g(x)=f(x3)
D.​​ g(x)=13f(x)

What transformation takes the graph of f(x)=3x+8 to the graph of g(x)=3x+6 ?
A. translation 2 units up
B. translation 2 units left
C. translation 2 units down
D. translation 2 units right

The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.

To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.

We will first isolate x² by subtracting 24 from both sides of the equation:

x² = -24

Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:

x = ±√(-24)

This simplifies to:

x = ±√(24) × ±i

Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:

x = ±2√(6)i

[tex]\frac{(new) - (original)}{original} = \frac{\frac{3}{8}- \frac{5}{4} }{\frac{5}{4} }[/tex]

[tex]\frac{3}{8} - \frac{5}{4} (\frac{2}{2}) = \frac{3}{8} - \frac{10}{8} = \frac{-7}{8}[/tex]

 [tex]\frac{-7}{8}[/tex] ÷ [tex]\frac{5}{4}[/tex]

=  [tex]\frac{-7}{8}[/tex] * [tex]\frac{4}{5}[/tex]

= [tex]\frac{-7(4)}{8(5)}[/tex]

= [tex]\frac{-7}{2(5)}[/tex]

=  [tex]\frac{-7}{10}[/tex]

= -0.70

multiply by 100 to get the percent: - 70% (the negative represents decrease)

Answer: 70% decrease

Answer:

No

Step-by-step explanation:

11-10 = 1

He spent 1 hour more this week

Which is:

1/10 × 100 = 10% more

Marcus spent 10% more time doing homework this week. His calculation is wrong.

Time used last week by marcus = 10 hours

Time used this week by marcus = 11 hours

Difference in hours  = 11  - 10  = 1 hour

This means that Marcus used 1 more hour this week than last week

% increase = 1/10 * 100

% increase  = 10%

This shows that he spent 10% more time doing homework this week.

Learn more here: https://brainly.com/question/20710281

x > 4 is your answer

Answer: [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

First pick (blue)     and        Second pick (red)

             [tex]\frac{6}{10}[/tex]                  x                    [tex]\frac{4}{9}[/tex]

= [tex]\frac{6(4)}{10(9)}[/tex]

= [tex]\frac{2(2)}{5(3)}[/tex]

= [tex]\frac{4}{15}[/tex]

Answer:

The answer is 4/15 hopefully this helps!

ajbsdajhlschlsdvsasfgrgjnkjbjnm?

Answer:

Step-by-step explanation:

(2005, 12,000)        (2005, 12,000)

   x1          y1                x2           y2

m= (12,250-1200) /  (2010-2005) = 250/5 = 50/1 = or 50

Answer:

y = -8/7x - 3

Step-by-step explanation:

A line represents a linear relationship between x and y with constant slope and defined for all values of x and y.

Any line equation in slope intercept form would be of the form

y =mx+c where

m = slope of line

and c = y intercept

In our quesion we are given that slope of line = -8/7

and intercept = negative 3 = -3

Hence equation is

y =-8x/7-3

3 * 4 + 3 = 12 + 3 = 15

Answer: He had 15 apples.

Answer:

24 dozen chocolate chip

14 dozen peanut butter

Step-by-step explanation:

x = number of dozen chocolate chip cookies

y = number of dozen peanut butter cookies

Total number of cups of flour is:

2x + 3y ≤ 90

Total number of eggs is:

x + 4y ≤ 80

Total profit is:

P = x + 1.5y

Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.

But let's try solving this algebraically.  x and y are positive integers, and we want them to be as large as possible.

Let's start by assuming the solution is on the line 2x + 3y = 90.

x + 4y ≤ 80

2x + 8y ≤ 160

90 − 3y + 8y ≤ 160

5y ≤ 70

y ≤ 14

If y = 14, x = 24, and P = 45.

Now let's assume the solution is on the line x + 4y = 80.

2x + 3y ≤ 90

2 (80 − 4y) + 3y ≤ 90

160 − 8y + 3y ≤ 90

70 ≤ 5y

14 ≤ y

Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.

The formula of a slope:

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

We have

[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]

Substitute

[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]

Answer:

Stacy made a blanket using some fabric, she had 3 yards left over and decided to use the leftover pieces to make pot holders. She cut each piece into 8 inches long. Stacy had enough fabric to create 4.5 pieces.

Step-by-step explanation:

we find that 13 full pieces of fabric, each 8 inches long, can be cut from three yards of fabric.

The question asks how many pieces of fabric, each measuring 8 inches in length, can be cut from a total length of three yards of fabric. To begin with, we need to convert yards to inches, because the unit of measurement for the fabric pieces is in inches, not yards. We know that 1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches, hence 3 feet x 12 inches/foot = 36 inches). Therefore, three yards of fabric is 3 x 36 inches, which equals 108 inches.

Now, if each piece is to be 8 inches long, we divide the total number of inches by the length of one piece to find out how many pieces can be made:
108 inches / 8 inches/piece = 13.5 pieces.

However, since we cannot have half a piece of fabric, we can only make 13 full pieces, with a small remaining piece that would be less than 8 inches long.

f(x) = x2 ÷ 3 + x

f(6)

Replace X with 6 then follow order of operations.

6^2 / 3 + 6

6^2 = 36:

36 / 3 + 6

36 /3 = 12:

Add:

12 + 6 = 18

The answer is 18

All except generals

Union supported African Americans as soldiers

They worked as slaves so obviously cooks

Answer:

Step-by-step explanation:

The emancipation proclamation allowed the  African American men to serve in the Union army.

They worked as cooks. Enslaved blacks were sometimes used for camp labor also.

But they did not served as generals in the army.

Hence, the answer is :

[tex]-18-5y\geq52\qquad|\text{add 18 to both sides}\\\\-5y\geq70\qquad|\text{change the signs}\\\\5y\leq-70\qquad|\text{divide both sides by 5}\\\\y\leq-14\\\\Answer:\ \boxed{d.\ y\leq-14}[/tex]

The slope:

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

Look at the picture.

6 units down → -6

2 units right → 2

[tex]m=\dfrac{-6}{2}=-3[/tex]

answer:  [tex] \frac{3}{-1} x[/tex]

explanation:

slope-intercept formula ==> [tex]y = mx + b[/tex]

[tex]m[/tex] is slope , and [tex]b[/tex] is y-intercept

to find the slope you need to start at the y intercept and go 3 units up and 1 unit left. and if you repeat it again, until you reach the top of the graph and that would make partial of the line.

so, the slope is [tex]\frac{rise}{run}[/tex], so if you plug it in it would look like this

[tex]y = \frac{3}{-1} x + b[/tex]

A D D I T I O N A L  I N F O

then you find the y-intercept which would be where the line intersects at the y axis, which is -10. plug the number into the equation

[tex]y = \frac{3}{-1} x - 10[/tex]

and that would make our final answer.

hope this helps! correct me if there is anything wrong ❤ from peachimin

2 - 3(2x + 1) < 6x(2 - 4)

2 - 6x - 3 < 12x - 24x

-1 - 6x < -12x

-1 < -6x

Dividing by -6 both sides gives you;

1/6 < x or;

Final answer is x > 1/6

Answer:

A) x ≥ 1 6

: )

the time returning=x h,

the time going=(x-1) h,

s=t*v

s=(x-1)*50,

s=x*40,

(x-1)*50=x*40

x=5h,

s=t*v=5*50=250 miles

An integer is close to zero if it is "small".

By small, we mean that it is small in absolute value. In fact, for any given distance [tex] d [/tex], there are two integers that are [tex] d [/tex] units away from zero: [tex]d [/tex] and [tex] -d [/tex].

So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.

So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.

Explanation of how to find the remainder using long division with a polynomial expression.

Long Division Example:

We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.

Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.

Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.

Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.

Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.

Rays are always named with two points rays

To prime factorization would be A: 2 X 3 X 5 X 7

Because if your do 2 X 3 it would be 6

Then you do 5 X 7 it would be 35

And 6 X 35 would be 210

AND THAT IS FACTORING THE PROBLEM

[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]

Answer:

The value [fog](3) is 29.

Step-by-step explanation:

The given functions are

[tex]f(x)=2x+7[/tex]

[tex]g(x)=x^2+2[/tex]

We have to find [fog](3).

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(3)=f(g(3))[/tex]

[tex](f\circ g)(3)=f(3^2+2)[/tex]              [tex][\because g(x)=x^2+2][/tex]

[tex](f\circ g)(3)=f(11)[/tex]

[tex](f\circ g)(3)=2(11)+7[/tex]              [tex][\because f(x)=2x+7][/tex]

[tex](f\circ g)(3)=22+7[/tex]

[tex](f\circ g)(3)=29[/tex]

Therefore the value [fog](3) is 29.