Hannah completed 40 problems in 32 minutes.
I have to put it in a unit rate pls help

Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = [tex]3^{x + 2}[/tex]

The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = [tex]3^{0 + 2}[/tex] = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = [tex]5^{1 - x}[/tex]

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = [tex]2^{x + 3}[/tex] - 1

The asymptote is [tex]2^{x + 3}[/tex]  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  [tex]2^{0 + 3}[/tex] - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0

[tex]2^{x + 3}[/tex] = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]

The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]

The y-intercept is (0, 6)

Answer:

56 + 77 + 88 + 99 = 320km²

Step-by-step explanation:

A triangular prism has 5 sides. We can start with the top and bottom, which have a base of 7 km and a height of 8km, making each of their areas equal to 7 * 8/2 = 28. Adding those up, we get 28+28 = 56 km² as the surface area of the top and bottom portions.

Next, we have the face that has 7 as the base and 11 as the height. The area of that is 7 * 11 = 77km²

After that, we have the face with 8 as the base and 11 as the height, making the area of that 8 * 11 = 88km²

Finally, we have the face with 9 as the base and 11 as the height, making that area 9 * 11 = 99km²

Adding these all up, the total surface area is

56 + 77 + 88 + 99 = 320km²

______________________________

[tex]\sf\bold{The\:above\:graph\:says:}[/tex]

$\space$

$\sf\bold{here:}$

$\space$

$\sf\bold{Find\:acceleration\:by\:v-t\:graph:}$

$\mapsto$ $\sf\small{TanØ =}$ $\sf\dfrac{slope\:of\:y}{slope\:of\:x}$= $\sf\dfrac{20}{8}$ $\sf{m/s^2}$

$\space$

$\space$

$\sf\bold{Now,calculate\:the\:distance:}$

$\space$

$\sf\bold{Given\:parameters:}$

$\space$

$\sf\bold{Substituting \: the\:values:}$

$\mapsto$ $\sf\small{s=0+}$ $\sf\dfrac{1}{2}$ $\times$ $\sf\dfrac{5}{8}$ $\sf\small{8^2}$

$\space$

$\longmapsto$ $\sf\underline\bold\purple{S=80m}$

$\space$

❍Therefore , the acceleration is $\sf\bold{2.5m/s^2}$ and the distance traveled by car is $\sf\bold{80m.}$

_______________________________

80 m is distance ! Please mark as brainliest

Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:

[tex]6=a(6-4)^2+5[/tex] and

[tex]6=a(2)^2+5[/tex] and

6 = 4a + 5 and

1 = 4a so

[tex]a=\frac{1}{4}[/tex] and the equation is

[tex]y=\frac{1}{4}(x-4)^2+5[/tex]

C 72°

Answer:

we have

f(c)=9/5C+32

now

22°C to °F

°C=22°

we have

f(c)=9/5C+32

f(c)=9/5*22+32=71.6≈72

answer is

22°C=72°F

Answer:  [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}[/tex]

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F[/tex]

Answer:

4x-7=-5x²

or, 5x²+4x-7=0

so the standard form of the equation is,

5x²+4x-7=0

or, f(x) = 5x²+4x-7

Answered by GAUTHMATH

Answer:

what is the question

Step-by-step explanation:

Answer:

C. 2.

Step-by-step explanation:

The graph descends from the left  so the coefficient of the leading term is negative. It is also a cubic equation with zeros of -20, about 6.5 and about 13. so we can write the equation as below.  The last 2 values can only be guessed because the x axis only shows values which are multiples of 5.

f(x) = a(x + 20)(x - 6.5)(x - 13)   where a is  a negative constant.

(This is only an approximation).

By the Remainder theorem, when the expression is divided by (x + 10):

f(-10) = -20 so we have

-20 = a (-10 + 20)(-10-6.5)(-10 - 13)

(10)(-16.5)(-23)a = -20

a = -20 / (10)(-16.5)(-23)

a = -0.0053

When  the equation is divided by (x - 10) then f(10)  is the remainder so substituting we have as the remainder:

-0.0053(10+20)(10-6.5)(10 -13)

-0.0053 * 30 * 3.5 * -3

= 1.7 approximately.

Looks like the answer is 2.

Answer:

-8x² - 106x + 175 = 0

Step-by-step explanation:

Given:

(2x - 7)²- 6(2x - 7)(x-3) = 0

Find:

Solution of the following explanation

Computation:

(2x - 7)²- 6(2x - 7)(x-3) = 0

[(2x)² + (7)² - (2)(2x)(7)] - (12x - 42)(x-3) = 0

[4x² + 49 - 28x] - [12x² - 36x - 42x + 126] = 0

[4x² + 49 - 28x] - [12x² - 78x + 126] = 0

-8x² - 106x + 175 = 0

Answer:

C

Step-by-step explanation:

We are given the function:

[tex]f(x) = 2x^2 -3x+4[/tex]

And we want to evaluate it for x = 3a.

Substitute:

[tex]f(3a) = 2(3a)^2-3(3a)+4[/tex]

Square:

[tex]f(3a) = 2(9a^2)-3(3a)+4[/tex]

Simplify:

[tex]f(3a) = 18a^2-9a+4[/tex]

Hence, our answer is C.

Answer:

option (D) is the answer

Answer:

[tex]-4x^{2} + 6x + 4[/tex]

Answer choice D

Step-by-step explanation:

x = number of hours

want to find probability (P) x >= 13

x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.

P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

To convert that to percentage, multiply 100, to get 84.13%

Please mark me brainliest

Answer:

5

Step-by-step explanation:

We know that we can use the Pythagorean theorem

a^2 + b^2 =c^2

where a and b are the legs and c is the hypotenuse

one of the legs is 12 and the hypotenuse (diagonal) is 15

a^2 + 12^2 = 15^2

a^2 +144 = 169

a^2 +144-144 =169-144

a^2 = 25

Taking the square root of each side

sqrt(a^2) = sqrt(25)

a = 5

Answer:

l = 9 cm

Step-by-step explanation:

Using Pythagoras' identity in one of the right triangles with legs width w, length l and hypotenuse h , then

l² + w² = h²

l² + 12² = 15²

l² + 144 = 225 ( subtract 144 from both sides )

l² = 81 ( take the square root of both sides )

l = [tex]\sqrt{81}[/tex] = 9

9514 1404 393

Answer:

  when the number of persons is less than 10

Step-by-step explanation:

The red line indicates the charges for Mount Joy Pool. It is below the blue line for "number of people" less than 10. That means Mount Joy Pool charges less than Woodbridge Pool for fewer than 10 people.

Assuming Arthur is interested in paying as little rent as necessary, he should select Mount Joy Pool when he is renting for less than 10 people.

__

Additional comment

The rent for 10 people is the same at either location, so there is nothing to favor Mount Joy Pool for 10 people. For more than 10 people, Woodbridge Pool charges less rent.

Answer:

x = 4

139.2

Step-by-step explanation:

Given the Cost function :

C(x) = 1.7x² - 13.6x + 166.4

To achieve minimum cost ;

dc/dx = 0

dc/dx = 2(1.7)x - 13.6

3.4x - 13.6 = 0

3.4x = 13.6

x = 13.6 / 3.4

x = 4

To achieve minimum cost, speed = 4 ;

Minimum cost will be :

C(x) = 1.7x² - 13.6x + 166.4

Put x = 4

C(4) = 1.7(4)² - 13.6(4) + 166.4

C(4) = 27.2 - 54.4 + 166.4 = 139.2

Minimum cost = 139.2

Answer: Its 5 units to the right and 2 units up.

Answer:

D

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 94 and d = a₂ - a₁ = - 112 -  (- 94) = - 112 + 94 = - 18 , then

S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × - 94) + (9 × - 18) ]

     = 5(- 188 - 162)

     = 5 × - 350

     = - 1750

Answer:

f(x)=2(x-3)-2

Step-by-step explanation:

when you hear if it translate to the right, it mean subtract " - "

so translate 3 unit right, it mean minus 3.

and same if translate left, it mean add, "+"

But if it mean shift down, it mean minus -

and if it mean shift up, it mean add +

so shift down 2 unit, mean -2

stretch factor of 2, mean multiply by 2

I hope this help! Im gonna explain further more if you have any question☺

The transformation of a function involves changing the features of the original function to another.

The new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]

The function is given as:

[tex]f(x) = (x + 2)^2 - 5[/tex]

When translated right, the rule is:

[tex](x,y) \to (x - h, y)[/tex]

In this case;

[tex]h= 3[/tex] --- i.e. 3 units right

So, the function becomes

[tex]f'(x) = (x + 2 - 3)^2 - 5[/tex]

[tex]f'(x) = (x - 1)^2 - 5[/tex]

When shifted down, the rule is:

[tex](x,y) \to (x, y - b)[/tex]

In this case;

[tex]b =2[/tex]  --- i.e. 2 units down

So, the function becomes

[tex]f'(x) = (x- 1)^2 - 5-2[/tex]

[tex]f'(x) = (x- 1)^2 - 7[/tex]

When vertically stretched, the rule is:

[tex](x,y) \to (x, ay)[/tex]

In this case;

[tex]a =2[/tex]  --- i.e. factor of 2

So, the function becomes

[tex]f"(x) = 2*[(x- 1)^2 - 7][/tex]

[tex]f"(x) = 2(x- 1)^2 - 14[/tex]

Hence, the new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]

Read more about function transformations at:

brainly.com/question/24326503

Step-by-step explanation:

the missing side is the adjacent side of the angle 66..which also has an opposite side of 19, therefore you use tan

tan66=19/x

tan66x/tan66=19/tan66

x=8.5

I hope this helps

Measure of base of the triangle, value of x is 8.46 unit.

Trigonometric ratios can be calculated by taking the ratio of any two sides of a right triangle. Given the scale of the other two sides, we can evaluate the third side using the Pythagorean theorem. We can compare the length of any two sides and the angle of the base using trigonometric ratio. The angle θ is an acute angle (θ < 90°) and  is usually measured counterclockwise with respect to the positive x-axis. The basic formula for trigonometric ratios is:

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

Given,

In right triangle,

Base of the triangle is x

Measure of angle = 66°

Perpendicular = 19 unit

tanθ = Perpendicular/base

tan66° = 19/x

2.246 = 19/x

x = 19/2.246

x = 8.46 unit

Hence, 8.46 unit is measure of base of the triangle, that is value of x.

Learn more about trigonometric ratio here:

https://brainly.com/question/25122825

#SPJ7

Answer:

100 ft

Step-by-step explanation:

We need to find the diagonal ( or hypotenuse)

We can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

80^2 + 60^2 = c^2

6400+3600 = c^2

10000 = c^2

Taking the square root of each side

sqrt(10000) = sqrt(c^2)

100 = c

Answer:

the school band

Step-by-step explanation:

the band, the band has a percentage of 53.85...,which is (14/26)x100, and the choir has 35.71% which is (5/14)x100

Answer:

n = 220, 4, -4, -220

Step-by-step explanation:

factors of 17: 17, 1, -1, -17

13 is prime number: 13 x  1 = 13

(ax+b)(cx+d) = axcx+axd+bcx+bd

(x + 17)(13x - 1) = 13x^2 + 220x - 17, n = 220

(x - 17)(13x + 1) = 13x^2 - 220x - 17, n = -220

(x + 1)(13x - 17) = 13x^2 - 4x - 17, n = -4

(x - 1)(13x + 17) = 13x^2 + 4x - 17, n = 4

Answer: x=35

Step-by-step explanation:

To find the value of x, we can use the Pythegorean Theorem because this is a right triangle.

Pythagorean Theorem: a²+b²=c²

[tex]12^2+x^2=(x+2)^2[/tex]             [exponent and distribute]

[tex]144+x^2=x^2+4x+4[/tex]       [subtract both sides by 144]

[tex]x^2=x^2+4x-140[/tex]             [subtract both sides by x²+4x]

[tex]-4x=-140[/tex]                       [divide both sides by -4]

[tex]x=35[/tex]

Now, we know that x=35.

9514 1404 393

Answer:

  53°

Step-by-step explanation:

The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.

  m∠Y = 53°

Answer: 53

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

<U + <T = 180

or, 6x-6+9x+21=180

or, 15x=165

or, x=11

so, <T = 9×11+21 = 120

Answer:

A = x + 15

B = 1 + 2

Step-by-step explanation:

x 2 + 17x + 30

x2 + 15 x + 2x + 30

1 ( x + 15 ) + 2 ( x + 15 )

 ( x + 15 ) ( 1 + 2 )

Hope this  answer helps you :)

Have a great day

Mark brainliest

Answer:

when you have items outside a parentheses that needs to be multiplied by the items inside

a(b+c) = ab + ac

Step-by-step explanation: