Analyze the effects on the graph of f(x) = 10x that result from the parameter changes in the function, h(x) = 5(10)x–2 + 6. Explain how each transformation appears in the equation and its effect on the original function, f(x) = 10x. Be sure to use mathematical language in your explanation.

Answer:

26.563, 1.977

Step-by-step explanation:

I will be honest I'm not 100% sure but i believe that the total distance all together is 26.563. I simply added all the distances.

Jada ran 1.977 miles further than Noah.

I'm so sorry if im wrong hope this helps though <3

Step-by-step explanation:

ab = (x - 3)(x + 3)

multiply

ab = x² + 3x - 3x - 9

Simplify

ab = x² - 9

---------------------------

2ab = 2(x² - 9)

Distribute

2ab = 2x² - 18

Answer:

B. 7

Step-by-step explanation:

Answer:

The bounded area is 5 + 5/6 square units. (or 35/6 square units)

Step-by-step explanation:

Suppose we want to find the area bounded by two functions f(x) and g(x) in a given interval (x1, x2)

Such that f(x) > g(x) in the given interval.

This area then can be calculated as the integral between x1 and x2 for f(x) - g(x).

We want to find the area bounded by:

f(x) = y = x^2 + 1

g(x) = y = x

x = -1

x = 2

To find this area, we need to f(x) - g(x) between x = -1 and x = 2

This is:

[tex]\int\limits^2_{-1} {(f(x) - g(x))} \, dx[/tex]

[tex]\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx[/tex]

We know that:

[tex]\int\limits^{}_{} {x} \, dx = \frac{x^2}{2}[/tex]

[tex]\int\limits^{}_{} {1} \, dx = x[/tex]

[tex]\int\limits^{}_{} {x^2} \, dx = \frac{x^3}{3}[/tex]

Then our integral is:

[tex]\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx = (\frac{2^3}{2} + 2 - \frac{2^2}{2}) - (\frac{(-1)^3}{3} + (-1) - \frac{(-1)^2}{2} )[/tex]

The right side is equal to:

[tex](4 + 2 - 2) - ( -1/3 - 1 - 1/2) = 4 + 1/3 + 1 + 1/2 = 5 + 2/6 + 3/6 = 5 + 5/6[/tex]

The bounded area is 5 + 5/6 square units.

Answer: A. 1/4

Step-by-step explanation:

1/2 x 1/2= 1/4

since tails is the first one that landed, the probability for the other two to be heads is 1/4

Hope this helps!

Leaving a rating is appreciated!

Answer:

distributive

Step-by-step explanation:

you are distributing 5(d+1) into 5d +5

Answer:

Step-by-step explanation:

length of Legs of the right angle triangle = 22 (unit) and 26 (unit)

To find the length of hypotenuse of the right angle triangle, we have to use Pythagoras property

Lets keep hypotenuse as "h" and one leg as  "a" and another as "b"

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]h^{2}[/tex]

[tex]22^{2}[/tex] + [tex]26^{2}[/tex] = [tex]h^{2}[/tex]

484 + 676 = [tex]h^{2}[/tex]

[tex]h^{2}[/tex] = 1,160

h = [tex]\sqrt{1,160}[/tex]

h = 34.05 (unit)

Answer:

For the third time D because 60+30*2 is 120 and 30 of 120 is 25%

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

110-180=70

30+70=100

100-180=80

Answer:

I think the answer is 80

Step-by-step explanation:

Answer:

I think it is the second one

Step-by-step explanation:

Answer:

= 22 units

Step-by-step explanation:

Well, QS and RT are equal, so...

5x-3=3x+7

-3x -3x

2x-3=7

+3 +3

2x=10

÷2 ÷2

x=5

...and to find a side length...

3x+7=15+7=22

= 22 units

Answer:

352.

Step-by-step explanation:

The product will have 45 digits, the fisrt and last digit will be 4 and the middle 43 will be 8.

So the sum = 2*4 + 43*8

= 352.

Answer:

Tina is 18

Step-by-step explanation:

60 divided by 3 is 20 and 20-2 is 18

Answer:

20 cups of applesauce

Step-by-step explanation:

8 ounces = 0.5 pounds

Pounds of apples : cups of applesauce

0.5 pounds : 1 cup = 10 pounds : x cups

0.5/1 = 10/x

0.5*x = 1*10

0.5x = 10

x = 10/0.5

x = 20 cups of applesauce

10 pounds of apples will make 20 cups of applesauce

I'll help.

A student needs 15 minutes to solve an algebra problem. How many minutes does the student need to solve 5 problems?

it's easy, you only need to divide 15 by 5.

Like this :

15÷5= 3

• because 5×3 = 15 , so you just need to flip it over

so, the student need 3 minutes to solve 5 problems

Answer:

z = 113

y = 31

Step-by-step explanation:

j || n and line a is their transversal. (given)

Therefore,

z° = 180° - 67° (exterior angles on the same side of transversal)

z°= 113°

z = 113

(5y - 88)° = 67° (exterior alternate angles)

5y - 88 = 67

5y = 67 + 88

5y = 155

y = 155/5

y = 31

Answer:

4x = y

Step-by-step explanation:

A. The graph doesn't make sense to me. 2 would be 8 not 6 according to the problem.

The Graph would be:

1:4

2:8

3:12

4:16

5:20

6:24

B. I would make this equation: 4x = y

X is representing how many steps Audrey takes.

So then substitute:

4 · 50 = 200

Meg would travel 200 feet.

Answer:

The two hypotenuses.

Step-by-step explanation:

HL or Hypotenuse-Leg Theorem: two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.

Since we already know the bottom leg of each triangle is congruent, we only need to know the two hypotenuses.

Answer:

AB=ED

Step-by-step explanation:

the answer is F

or x=3

Hope this helped!

Answer:

X=2 and y=5

Step-by-step explanation:

2 represent x-value and 5 represent y- value

Answer:

x = 51.5

Step-by-step explanation:

Answer:

157

Step-by-step explanation:

I actually forgot the rules as to why it is, but you can clearly see that they are identical to each other!

Answer:

[tex] \displaystyle GH = 2 \sqrt{30} [/tex]

[tex] \displaystyle FH = 2 \sqrt{10} [/tex]

[tex] \displaystyle m \angle G = {30}^{ \circ} [/tex]

Step-by-step explanation:

we are given a right angle triangle

it's a 30-60-90 triangle of which FH is the shortest side

remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus

our equation is

[tex] \displaystyle 2FH=4\sqrt{10}[/tex]

divide both sides by 2

[tex] \displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}[/tex]

[tex] \displaystyle FH =2 \sqrt{10}[/tex]

in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle

as we want to figure out GH we'll use sin function

remember that,

[tex] \displaystyle \sin( \theta) = \frac{opp}{hypo} [/tex]

let our opp, hypo and [tex]\theta[/tex] be GH, 4√10 and 60° respectively

thus substitute:

[tex] \displaystyle \sin( {60}^{ \circ} ) = \frac{GH}{4 \sqrt{10} } [/tex]

recall unit circle:

[tex] \displaystyle \frac{ \sqrt{3} }{2} = \frac{GH}{4 \sqrt{10} } [/tex]

cross multiplication:

[tex] \displaystyle 2 GH = 4 \sqrt{10} \times \sqrt{3} [/tex]

simplify multiplication:

[tex] \displaystyle 2 GH = 4 \sqrt{30} [/tex]

divide both sides by 2:

[tex] \displaystyle GH = 2 \sqrt{30} [/tex]

Recall that, the sum of the interior angles of a triangle is 180°

therefore,

[tex] \displaystyle m \angle G + {60}^{ \circ} + {90}^{ \circ} = {180}^{ \circ} [/tex]

simplify addition:

[tex] \displaystyle m \angle G + {150}^{ \circ} = {180}^{ \circ} [/tex]

cancel 150° from both sides

[tex] \displaystyle m \angle G = {30}^{ \circ} [/tex]

Answer:

8×ED=3×15

ED=45/8

the radius is the half of the diameter

so its 45/16

Answer:

[tex] \frac{ae}{be} = \frac{ce}{de} = \frac{bc - be}{ad - ae} \\ \\ = > \frac{8}{3} = \frac{15 - 3}{ad - 8} \\ \\ < = > \frac{8}{3} = \frac{12}{ad - 8} \\ \\ = > ad - 8 = \frac{12 \times 3}{8} = 4.5 \\ \\ < = > ad = 4.5 + 8 = 12.5 \\ \\ = > r = 12.5 \div 2 = 6.25[/tex]

Answer:

multiply altogether a) will be 3696

b) will be 180