Find angle X in the angle diagram.

Step-by-step explanation:

2³×2^n+2=32

2^3+n+2=2⁵

n+5=5

n=0

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{ANSWER:}[/tex]

[tex]\tt n = 0[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]

[tex]_____________________________________[/tex]

[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]

[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]

[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]

Answer:

14.5%

Step-by-step explanation:

Use the number 100 as an example to find the single discount.

Take a 10% discount off of this:

100(0.9)

= 90

Take a 5% discount:

90(0.95)

= 85.5

So, after the successive discounts, $14.5 was discounted.

This means that the single discount is 14.5%.

So, the answer is 14.5%

Answer:

x=2

Step-by-step explanation:

the sides are proportional due the angles being equal

since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference

so 4÷2=x

x=2

the answer is b. insurance

9514 1404 393

Answer:

  u = -3 3/7

Step-by-step explanation:

The new value of v is 4/-7 = -4/7 of the old value. Because u varies directly, its new value will also be -4/7 of the old value.

  u = -4/7(6) = -24/7

  u = -3 3/7

Answer:

Buses - 43 people

Vans - 12 people

Answer and Step-by-step explanation:

Solve for x.

First, we divide both sides of the equation by 2.

2(8 - 2x) = 7 - x

Distribute the 2.

16 - 4x = 7 - x

Add 4x to and subtract 7 from both sides of the equation.

9 = 3x

Divide by 3 to both sides of the equation.

x = 3 <-- This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

x = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(8 - 2x) = 2(7 - x)

Step 2: Solve for x

Answer:

153.86.

Step-by-step explanation:

Use the formula pi times radius squared.

Answer:

Step-by-step explanation:

Split it into two:

Y<3x

Y<5

X = 1

Y = 3

(1,3)

X = 2

Y = 6

(2, 6)

Plot the line up to y = 4.999999999999999999999 and not higher.

Answer:

Plot the line up to y = 4.999999999999999999999 and not higher

Answer:

1)  2/20 x 200 = 1/10 x 200 = 20

2) 3/20 x 200 = 30

3) 4/20 x 200 = 1/5 x 200 = 40

4) 5/20 x 200 = 1/4 x 200 = 50

5) 18/20 = 9/10 x 200 = 180

Answer:

A (-1,-10) ; A (-1,14)

Step-by-step explanation:

[tex]\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169[/tex]

y^2 -4y - 140 = 0

Δ/4 = 4 + 140 = 144

y1 = 2 + 12 = 14

y2 = 2 -12= -10

Answer:

17.

Step-by-step explanation:

The differences form an arithmetic sequence 3, 5, 7, 9,,11.

The missing number  is 10 + 7 = 17.

This is a quadratic sequence.

The nth term = n^2 + 1.

Thus the 4th term = 4^2 + 1 = 17.

Answer:

we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm

The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

The function is given as:

[tex]f(x) = -2x + 8[/tex]

The above function is a linear function.

A linear function is represented as:

[tex]y =mx + c[/tex]

Where:

m represents the slope, and c represents the y-intercept.

So, by comparison;

[tex]m =-2[/tex]

[tex]c = 8[/tex]

This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

See attachment for the graph of the function

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:

(2,1)

Step-by-step explanation:

-3x + 7 = -2x + 5

x = 2

y = -6 + 7

y = 1

Answer:

(2,1)

Step-by-step explanation:

Remark

One thing you need to remind yourself of: The y value in both equations must be the same.

That means that the two right hand values are

-3x + 7 = - 2x + 5         Subtract 5 from both sides.

      -5              -5

-3x + 2 = - 2x               Add 3x to both sides

+3x          +3x

       2 = x

Now use one of the equations to solve for y

y = -2x + 5

y = -2(2) + 5

y = - 4 + 5

y = 1

We should check this by graphing it. Notice the two graphs do cross at (2,1) just as predicted.

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

Answer:

87 gallons

Step-by-step explanation:

5 gallons: 3 weeks = x gallons: 52 weeks

5/3 = x/52

3x = 260

x= 86.6, about 87 gallons

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the right trianglea are not given. The general explanation is as follows.

Using Pythagoras Theorem, we have:

a² = b² + c²

Where:

a => hypotenuse

Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.

The hypotension becomes

a² = 3² + 4²

a² = 9 + 16.

a² = 25

Take square roots.

a = 5

If any of the other side lengths is missing; you make that side the subject and then solve.

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

Answer:

38

Step-by-step explanation:

So, we know the formula is:

D=rt or D=r*t

We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.

Here are the two sets we can look at:

t=2, d=76

t=3, d=114

Lets plug these in and solve:

76=r*2

Divide both sides by 2 to get r alone:

38=r

Now lets check if this is true by pluggin in 38 for r in the second set, and seeing if it works:

D=r*t

114=38*3

=

114=114

So 38 is our answer.

Hope this helps!

Answer:

a.) 15 feet

b.) 3.25 seconds

c.) 17.1125 feet

d.) 12.5 seconds

Step-by-step explanation:

a

This is just asking for the y intercept

to get this just do h(0)= 15

b

This is asking for the x value of the vertex

solve that through -b/2a

-1.3/(2*-.2)= 3.25

c

This is asking for the y value of the vertex

to solve this plug in the x value from b

-.2*3.25²+1.3*3.25+15= 17.1125

d

This is asking for an x intercept

using the quadratic formula...

[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]

*note the (+-) before the radical is ± *

logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5

Answer:

80%

Step-by-step explanation:

Because Shirly spelled 12 out 15 correctly, she got a 12/15, which is equal to 4/5 or 80%

Answer:

E) π/9

Step-by-step explanation:

The angles are complementary meaning they add up to 90°.

Convert radians to degrees:

7π/18 · 180/π = 70°

Now we know that we need the radian equivalent of 20°.

Convert degrees to radians:

70 · π/180 = π/9

Therefore, the measure of the missing degree is π/9.

Answer:

I'd use A = πr^2

The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

The Probability is 1/2 or .5, .5 rounded to the nearest tenth would be irregular because .5 is already in the tenth place but according to the law of rounding since ut is five it would be rounded up giving the whole number 1

9514 1404 393

Answer:

  C.  -2.00 m/sec

Step-by-step explanation:

The average velocity on the interval [a, b] is found by ...

  m = (s(b) -s(a))/(b -a)

One end of the interval remains constant here, so we can define 'd' so that the interval is [4, 4+d]. Then the average velocity is ...

  m = (s(4 +d) -s(4))/((4 +d) -4)

  m = (s(4+d) -s(4))/d

The attached table shows the average velocity values on the intervals required by the problem statement. Respectively, they are ...

  -1.5 m/s, -1.7 m/s, -1.9 m/s, -1.99 m/s, 2.01 m/s, 2.1 m/s, 2.3 m/s, 2.5 m/s

We expect the instantaneous velocity at d=0 to be the average of the values at d=-0.01 and d=+0.01. We estimate the instantaneous velocity at t=4 seconds to be -2.00 m/s.

Answer:

(a) The time to complete 1 cycle and return is 16/3

(b) The minimum height is 30 inches and the maximum is 54 inches

Step-by-step explanation:

Given

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

Solving (a): Time to complete 1 cycle and return

This implies that we calculate the period.  This is calculated using:

[tex]T = \frac{2\pi}{w}[/tex]

Where:

[tex]w =\frac{3\pi}{8}[/tex]

So, we have:

[tex]T = \frac{2\pi}{\frac{3\pi}{8}}[/tex]

[tex]T = \frac{2}{\frac{3}{8}}[/tex]

[tex]T = \frac{2*8}{3}[/tex]

[tex]T = \frac{16}{3}[/tex]

Solving (b): The maximum and the minimum height

To do this, we have:

[tex]-1 \le \sin(\theta) \le 1[/tex]

Which means:

[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]

So, the minimum is:

[tex]\sin(\frac{3\pi}{8}) =- 1[/tex]

And the maximum is:

[tex]\sin(\frac{3\pi}{8}) =1[/tex]

Recall that the height is:

[tex]f(t) = 12\sin(\frac{3\pi}{8}t) + 42[/tex]

So, the maximum and the minimum of  are:

[tex]h_{min} =12 * -1 + 42[/tex]

[tex]h_{min} =30[/tex]

and

[tex]h_{max} =12*1+42[/tex]

[tex]h_{max} =54[/tex]