Is 152 a multiple of 8?

Answer:

34 cm

Step-by-step explanation:

The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.

Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm

Then, T₃/T₁ = ar²/a = r²

r² = T₃/T₁

r² = 64 cm/121 cm

r = √64/121

r = 8/11

So, the height of our fifth bounce T₅ = ar⁵⁻¹

= ar⁴

= 121 cm × (8/11)⁴

= 121 × 4096/14641

= 4096/121 cm

= 33.9 cm

≅ 34 cm to the nearest cm

Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

[tex]a_n = a_1r^{n-1}[/tex]

[tex]64 = 121r^{2}[/tex]

[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]

[tex]r = \frac{8}{11}[/tex]

Hence:

[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]

The height of the fifth bounce is of [tex]a_5[/tex], hence:

[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]

The height of the fifth bounce is of 33.85 cm.

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Answer:

52 sq mm

Step-by-step explanation:

you can break it into a long rectangle in the middle with dimensions of 2(6+8) or 2(14) = 28 sq mm

the triangle on the bottom has a base of (8-4) x height of 3, which gives 6 sq mm (you have to divide by 2)

the upper left rectangle is 6 x 3 = 18 sq mm

add: 28 + 6 + 18 = 52

Answer:

(2+1×-3)(x) = 3×(-3)(x) =-9x

Answer:

(g · ƒ)(x) = –3x2 – 3

Step-by-step explanation:I took the test

Answer:

I think the answer is letter C

Answer:

Step-by-step explanation:

sin A = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]

cos A = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

tan F = [tex]\frac{DE}{FE}[/tex] = [tex]\frac{24}{18}[/tex] = [tex]\frac{4}{3}[/tex]

tan D = [tex]\frac{FE}{DE}[/tex] = [tex]\frac{18}{24}[/tex] = [tex]\frac{3}{4}[/tex]

sin D = [tex]\frac{FE}{FD}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

Rewrite so x is on the left side of the inequality.

8 + 4.99x < 20

Move all terms not containing x to the right side of the inequality.

4.99x < 12

Divide each term by 4.99 and simplify.

x < 2.405

The result can be shown in multiple forms.

Inequality Form:

x < 2.405

Interval Notation:

( −∞ , 2.405 )

Step-by-step explanation:

Answer:

Both:

1

2

Inequality Only:

-4

3/4

2.3

Neither:

2.5

Answer:

51°

Step-by-step explanation:

so lets all know that the sum of a trapezoid is 360°

so lets find x

360-83-115-111=51

so your answer is 51°

Hope this helped :)

Answer:

D

Step-by-step explanation:

Dilating BC to B'C' by a factor of 1/2 makes each side of the triangle halved. Originally BC is 16, so when it's halved, it becomes 8

We know when triangle are similar and are changed only by a scale factor, the angle will not change. Angle A' = 28 degrees

Answer:

a) BOC = 80⁰

b) COD = 60⁰

Step-by-step explanation:

..................

Answer:

BOC is 80 and COD is 60

Step-by-step explanation:

If DOF is 120 you subtract 40 from it because of of AOB then COD is the remaining of 180

Answer:

im sorry i dont know

Step-by-step explanation:

Answer:

x=−3

Step-by-step explanation:

2(6x+1)−4(x−5)=−2

Step 1: Simplify both sides of the equation.

2(6x+1)−4(x−5)=−2

(2)(6x)+(2)(1)+(−4)(x)+(−4)(−5)=−2(Distribute)

12x+2+−4x+20=−2

(12x+−4x)+(2+20)=−2(Combine Like Terms)

8x+22=−2

8x+22=−2

Step 2: Subtract 22 from both sides.

8x+22−22=−2−22

8x=−24

Step 3: Divide both sides by 8.

8x/8=−24/8

Answer:

$7.44

Step-by-step explanation:

4.96/8= .62 per ounce

.62 x 12 = $7.44

Answer:

She must sell 1026.66666667 kites

Step-by-step explanation:

15,400/15

The number of kites that Ellen needs to sell to complete her annual goal is 1027.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Ellen can make a $15 profit on each kite she sells. Also, Ellen's annual income goal is to have $15,400. Therefore, the number of kites that Ellen needs to sell is,

Number of kites that Ellen will sell = Annual income goal/Profit on each kite

Number of kites that Ellen will sell = $15,400 / $15

                                                     = 1026.6667

Since Ellen can not sell half kites, therefore, she needs to sell 1027 kites to complete her annual income goal.

Hence, the number of kites that Ellen needs to sell to complete her annual goal is 1027.

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Answer:

Step-by-step explanation:

1. Not a function

2. Function

3. Function

4. Not a function

5. Not a function

6. Function

7. Function

8. Not a Function

9. Function

10. Not a Function

Answer:

1. Not a function

2. A function

3. A function

4. Not a function

5. Not a function

6. A function

7. A function

8. Not a function

9. A function

10. Not a function

Step-by-step explanation:

The only rule for a relationship to be a function is...

Only ONE output for ONE input

1. There is more than one output for one input

2. Each input has only one output

3. Each input has only one output

4. There is more than one output for one input

5. There is more than one output for one input

6. Each input has only one output

7. Each input has only one output

8. There is more than one output for one input

9. Each input has only one output

10. There is more than one output for one input

Hope this helps :)

Let me know if there are any mistakes!!

Answer:

9-x

Step-by-step explanation:

ez dub

Answer:

9-x

Step-by-step explanation:

the difference of (tells you to subtract) 9 and x (9-x)

hope this helps have a blessed

Answer:

Step-by-step explanation:

No, it is an exponential growth function because 1.03>1. An exponential decay function would have a rate less than 1.

Answer:

The answer is C. 82 degrees!

Step-by-step explanation:

Hope this helped! Have a fantastic rest of ur day/ night! :)))

Step-by-step explanation:

A function is a rule that relates how one quantity depends on other quantities

Answer:

C. 2x + 12

Step-by-step explanation:

2(10) + 2(x-4)

= 20 + 2x - 8

= 2x + 20 - 8

= 2x + 12

Answer:

4000π cm^2

Step-by-step explanation:

first we change the 1.6m to cm:

1.6m = 160cm

Now we can use the formula:

V = πr^2h

where π is just π, r is the radius (not the diameter) and h is the height

V = π * 5^2 * 160 = 4000π cm

Answer:

Step-by-step explanation:

[tex]\text{They give you the equation for the volume.}\\ \\ V=\pi r^2h\\ \\ \text{You simply need to plug in the values given to you for r and h.}\\ \\ r=10/2=5cm,\ h=1.6m(100cm/m)=160cm\\ \\

V=\pi 5^2(160)\\ \\ V=160(25)\pi\\ \\ V=4000\pi cm^3\\ \\ V\approx 12566.37 cm^3[/tex]

Answer:

157 - 70x

 —————————

     5    

Step-by-step explanation:

Answer:

31.4 - 14x

Step-by-step explanation:

4(5.8 - 9x) = 23.2 - 36x

23.2 - 36x + 8.2 + 22x

23.2 + 8.2 - 36x + 22x

only add/subtract LIKE terms

31.4 - 14x

Answer:

Step-by-step equation:

15% of 60 is nine.

Percentage is equivalent to the portion of a quantity present in the whole. The portion of each person’s tip amount shared by Sara and 3 of her friends is $2.65.

A percentage is a value that indicates 100th part of any quantity.

To convert percentage into a fraction it is divided by 100.

Given that,

The amount of tip is 15% of the total amount A.

The total amount of 4 lunches = $60.

As per the question, the total amount can be written as,

15% of A = A - 60

=> 15 / 100 × A = A - 60  

=> A - (3 / 20) × A = 60

=> A - (3 / 20) × A = 60

=> (17 / 20) × A = 60

=> A = (60 × 20) / 17

=> A = 70.58

Now, the total amount of tip is,

15% of 70.58

(15 / 100) × 70.58 = 10.58

The tip shared by each friend = 10.58 ÷ 4

                                                 = 2.65

Hence, the portion of each person’s tip amount is $2.65.

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Answer: 250 im not sure if its correct though

Step-by-step explanation: 8% = 8/100  

8 /100  × x = 20

Multiplying both sides by 100 and dividing both sides by 8,

we have x = 20 ×  100 /8

x = 250

If you are using a calculator, simply enter 20×100÷8, which will give you the answer.

this question answer is 4.25

Answer:

8, 15, 17

Step-by-step explanation:

The 2nd option. You know this by using this math formula: a^2 + b^2 = c^2. That is the formula to find a right triangle. So if you square 8 and 15 you get 64 and 225, and if you add them together you get 289, which is 17^2. Hope this helps! :)

Answer:

See below

Step-by-step explanation:

A series is the terms added together and a sequence is the list of terms.  When you add the terms of a sequence, then you have formed a series.

The congruency rules is as follows;

4)a) The triangles are congruent by SSS Congruency Postulate

b) Triangle PQR is congruent to Triangle PQS

5a) The triangles are not congruent

b) Triangle VWZ is not congruent to Triangle YXZ

6a) The triangles are congruent by SAS Congruency Postulate

b) ΔACB is congruent to ΔDBC by SAS Congruency Postulate

7) The triangles are not congruent

b) ΔKLJ is not congruent to ΔMNL

There are different congruency postulates or theorems as it pertains to congruent triangles and they are;

AAS theorem which denotes Angle-Angle-Side Theorem

HL theorem which denotes Hypotenuse-Leg Theorem

SSS Postulate which denotes Side-Side-Side Postulate

ASA postulate which denotes Angle-Side-Angle Postulate

SAS Postulate which denotes Side-Angle-Side Postulate

5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. However, the third side is also congruent by reflexive property of congruency and as such we now have three sides congruent by SSS Congruency Postulate.

5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. Now, the angle where the transverse lines intersect is not given but we can see that they are opposite angles by definition of opposite angles. Thus, the triangles are congruent by SSA Congruency Theorem because it has a non-included angle but SSA Congruency is not valid and so this is not congruent.

6) We can see that one side is given to be congruent. However, by reflexive property of congruence, we see that BC is congruent to itself and also the included right angle being congruent to each other. Thus, this is congruent by SAS Congruency postulate.

7) The triangles are not congruent because we are not given any third congruent side nor the angles and we can't use the given data to prove congruency.

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Answer:

Step-by-step explanation:

3x+y−7=0 and x+2y+9=0

write in the form y=mx+c

i.e.y=−3x+7,y=  

2

−x

​  

−  

2

9

​  

∴m  

1

​  

=−3 and m  

2

​  

∓−  

2

1

​  

tan(A−B)=  

∣

∣

∣

∣

∣

​  

1+tanAtanB

tanA−tanB

​  

∣

∣

∣

∣

∣

​  

∣

∣

∣

∣

∣

​  

1+(−3)(−y  

2

​  

)

−3−(−y  

2

​  

)

​  

∣

∣

∣

∣

∣

​  

=  

∣

∣

∣

∣

∣

​  

5/2

−5/2

​  

∣

∣

∣

∣

∣

​  

=1

∴ Angle b/w then is tan  

−1

(1)=45  

∘

=  

4

π

​