A 64-inch board is cut into three pieces so that the second piece is twice as long as the first piece, and the third
piece is 5 times as long as the first piece. Find the length of the longest piece.

Answers

Answer 1
Answer:  40 inches

==========================================================

Explanation:

x = first piece2x = second piece, since its twice as long as the first5x = third piece, since its five time as long as the first

x is some positive real number, and the units of each are in inches.

Add up the smaller pieces and we should get 64 inches back again

x+2x+5x = 64

8x = 64

x = 64/8

x = 8

The first piece is 8 inches long.

2x = 2*8 = 16 is the length of the second piece (in inches)

The third piece is 40 inches because 5x = 5*8 = 40

--------

Summary:

first = 8 inches

second = 16 inches

third = 40 inches

Check: 8+16+40 = 64, which confirms the answer


Related Questions

find the radius of this circle.

Answers

Answer:

r = 5 units

Step-by-step explanation:

Given:

Angle subtended at the centre (∅) in radians = 2π/3

Arc length (S) = 10π/3

radius (r) = ?

Required:

Radius (r)

Solution:

Formula for arc length given the central angle in radians is:

S = r∅

Make e the subject of the formula by dividing both sides by ∅

S/∅ = r∅/∅

r = S/∅

Plug in the values

r = (10π/3) / (2π/3)

Change the operation sign to multiplication and turn the fraction by your right upside down

r = 10π/3 × 3/2π

r = (10π × 3)/(3 × 2π)

Cross out terms that can divided each other

r = 5

15 points What’s the area‼️‼️‼️‼️‼️ please help me attach work too if you can

Answers

Answer:

66

Step-by-step explanation:

5x2= 10

7x8= 56

10+56= 66

Answer:

106

Step-by-step explanation:

split the shape, so you have 2 rectangles.

Multiply 8 and 7 = 56

add 2 and 8 =10, then multiply 10 by 5. =50

add 50 and 56

therefore your answer is 106.

Help help help help help

Answers

Answer:

x2+y2−12x+4y−60=0

The center of the circle is point: C=(6,−2).

The radius of the circle is r=10.

In Problem, p is in dollars and q is the number of units.
(a) Find the elasticity of the demand function
p2 + 2p + q = 49 at p = 6.
(b) How will a price increase affect total revenue?

Answers

Answer:

-14

Explanation:

Elasticity of demand is the degree of change in demand after a change I'm price, basically demand's sensitivity to price change.

Formula for calculating price elasticity is: change in price/change in quantity =dq/dp

Since we are given p²+2p+q=49 and not initial and current amount of price and quantity, we differentiate to find demand elasticity, thus:

2p+2+dq/dp=0

dq/dp=-2p-2

Given p =6, we substitute:

dq/dp=-2×6-2

dq/dp=-12-2

dq/dp=-14

With a demand elasticity of -14 there is an inverse relationship between price and demand. While price increases, demand falls.

what percentage of the appies are yellow?

Answers

5*6=30
6 yellow apples
6/30=.2
.2*100=20
20%

Answer:

20%

Step-by-step explanation:

6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.

1.
What is the slope of the line through the points (-2, -1) and (8, -3)?

Answers

Answer:

The slope of the line is [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

Step-by-step explanation:

To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

For finding the slope of this line with the points (-2,-1) and (8,-3), start by writing down the information given from the question.

[tex]y_{2}= -3[/tex]

[tex]y_{1}=-1[/tex]

[tex]x_{2}=8[/tex]

[tex]x_{1}= -2[/tex]

Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(-1)}{8-(-2)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-2}{10}= -\frac{1}{5}[/tex]. The final answer will be [tex]-\frac{1}{5}[/tex]  in fraction form or -0.2 in decimal form.

The table represents the equation y= 8x what y= value is missing from the table?

Answers

Answer:

24

Step-by-step explanation:

y=8(3)= twenty four

you just fill in the x

The height of the saddle off horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height of the horse's saddle above the base ofthe carousel

Answers

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]

Solve each equation.

2p = 2 p = _____

q - 3 = 7 q = _____​

Answers

p=1
q= 10
p=1 because 2x1 equals 2
q= 10, because 10 minus 3=7(just add 7+3)

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]2p=2[/tex]

[tex]\frac{2p}{2}=\frac{2}{2}[/tex] [tex]\hookleftarrow \mathrm{Divide\:both\:sides\:by\:}2[/tex]

[tex]=1[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{P=1}}}}}[/tex]

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

[tex]q - 3 = 7[/tex]

[tex]q-3+3=7+3[/tex] [tex]\hookleftarrow \mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]

[tex]=10[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{q=10}}}}}[/tex]

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

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

DFGI is a trapezoid with midsegment EH. What is DI?
D
8 cm
F
7 cm
EH = 6.00 cm
FG = 4.00 cm
5 cm
G
6 cm
H

Answers

Answer:

a. 8 cm

Step-by-step explanation:

Given:

EH = 6 cm

FG = 4.00 cm

Based on the mid-segment theorem of a trapezoid, we have:

EH = ½(FG + DI)

Plug in the values

6 = ½(4 + DI)

Multiply both sides by 2

6*2 = 4 + DI

12 = 4 + DI

12 - 4 = 4 + DI - 4

8 = DI

DI = 8 cm

The net of a rectangular prism is shown.
8 in.
2 in.
2 in.
8 in.
2 in.,
1
1
1
6 in.
1
2 in. :

Answers

1

is the correct answer lol ez stuff

an electric guitar costs $790 with a 235 full replacement warranty if the manufacturer sells 500 and 98,274 warranties and has to honor 11% of them, how much profit did the manufacturer gain from the warrenties

Answers

Answer:

i got Profit = $125,129,007.1

Step-by-step explanation:

For how many minutes did Lynn run at a greater speed
than Kael?
0 12
O 17
O 23
O 28

Answers

12-40=28 so the answer to this is D

Answer:

D. ✔ 28

Step-by-step explanation:

E 2021

Multiple choice math problem

Answers

Answer:

ok so its a triangle with one side being

11

on side being

2

and one side is x

so we just use the formula

11^2+2^2=c^2

11^2+2^2=125

125 squared is 25

so

3 times the square root of 13 is 10.8166538264

so no

5 times the square root of 5 is 11.1803398875

so the answer i guess might be a?

Hope This Helps!!!

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6. Donna adds 400 ml (milliliters) of water to 100 ml of coffee. What percentage of Donna's drink is coffee?

Answers

9514 1404 393

Answer:

  20%

Step-by-step explanation:

100 mL of the drink is coffee

The total amount of drink is 100 mL +400 mL = 500 mL. Then the fraction that is coffee is ...

  coffee/total = (100 mL)/(500 mL) = 1/5 = 1/5 × 100% = 20%

20% of Donna's drink is coffee.

Mr. Smith wants to know if he can fit 4 trapezoid tables like the one shown below into a room. What is the total area of 4 trapezoid tables? Answer without units. NUMBER ONLY!

Answers

Answer:

(1/2)(2)(5+3)

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The area of a trapezoid is:

( a + b ) ÷ 2 x h

Where a & b are the bases, and h is the height.

Use formula with the given measurements:

(3 + 5) ÷ 2 x 2

= 8 ÷ 2 x 2

= 4 x 2

= 8

Hope this helps

A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
10h
3
31
34

Answers

Answer: Choice C) 31

==============================================

Explanation:

The recursive rule

f(n+1)=f(n)-3

can be rearranged to

f(n) = f(n+1)+3

after adding 3 to both sides

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

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

f(3) = 22+3

f(3) = 25

Repeat for n = 2

f(n) = f(n+1)+3

f(2) = f(2+1)+3

f(2) = f(3)+3

f(2) = 25+3

f(2) = 28

Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

Use the diagram shown to find 4 ÷ 1/3

Answers

Answer:

12

Step-by-step explanation:

Since there is no diagram. I will just tell you the answer. first convert into multiplcation keep everything but the 1/3. Change 1/3 into 3/1 (3). Multiply 4*3=12.

Sorry if I don't have a graph.

Hope this helps!

Expand and simplify (b+6)(b-4)

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: {b}^{2} + 2b - 24}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex] \: (b + 6)(b - 4)[/tex]

➼[tex] \: b \: (b - 4) + 6 \: (b - 4)[/tex]

➼[tex] \: {b}^{2} - 4b + 6b - 24[/tex]

Combining like terms, we have

➼[tex] \: {b}^{2} + 2b - 24[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

6. Roll a pair of dice. What is the probability that a total of 12 will be face up?

Answers

Answer:

The Probability would be 2.78%

Step-by-step explanation: Hope this helps :)

in a triangle the angle with the smallest measure is always the opposite the​

Answers

Answer:

in a triangle, the angle with the smallest measure is always opposite the shortest side.

Step-by-step explanation:

write cos2x as sinx
please help with this ​

Answers

Answer:

[tex]\cos(2\, x) = 1 - 2\, (\sin(x))^2[/tex].

Step-by-step explanation:

Angle sum identity for cosine: [tex]\cos(a + b) = \cos(a) \, \cos(b) - \sin(a) \, \sin(b)[/tex].

Pythagorean identity: [tex](\cos(a))^{2} + (\sin(a))^{2} = 1[/tex] for all real [tex]a[/tex].

Subtract [tex](\cos(x))^{2}[/tex] from both sides of the Pythagorean identity to obtain: [tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex].

Apply angle sum identity to rewrite [tex]\cos(2\, x)[/tex].

[tex]\begin{aligned}&\cos(2\, x)\\ &= \cos(x + x) \\ &= \cos(x) \, \cos(x) - \sin(x)\, \sin(x) \\ &= (\cos(x))^{2} + (\sin(x))^{2}\end{aligned}[/tex].

[tex](\sin(a))^{2} = 1 - (\cos(a))^{2}[/tex] follows from the Pythagorean identity. Hence, it would be possible to replace the [tex](\cos(x))^{2}[/tex] in the previous expression with [tex](1 - (\sin(x))^{2})[/tex].

[tex]\begin{aligned}&(\cos(x))^{2} - (\sin(x))^{2}\\ &= \left[1 - (\sin(x))^{2}\right] - (\sin(x))^{2} \\ &= 1 - 2\, (\sin(x))^{2} \end{aligned}[/tex].

Conclusion:

[tex]\begin{aligned}&\cos(2\, x) \\ &= (\cos(x))^{2} + (\sin(x))^{2} \\ &=1 - 2\, (\sin(x))^{2}\end{aligned}[/tex]

11x+7y=17
solve for y

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: y = \frac{17 - 11x}{7} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]\\11x + 7y = 17[/tex]

[tex] \\➺ \: 7y = 17 - 11x[/tex]

[tex]\\➺ \: y = \frac{17 - 11x}{7} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Pls Helppppp meeeeee!!​

Answers

Answer:

G

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplifying the radicals in the expression

[tex]\sqrt{52}[/tex]

= [tex]\sqrt{4(13)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]

= 2[tex]\sqrt{13}[/tex]

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

[tex]\sqrt{117}[/tex]

= [tex]\sqrt{9(13)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]

= 3[tex]\sqrt{13}[/tex]

Then

[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]

= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]

= 5[tex]\sqrt{13}[/tex] → G

Problem:-

[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]

[tex]\small\bf{F.} \: \sf{13} [/tex]

[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]

[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]

[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]

Solution:-

[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]

[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]

Answer:-

So, the correct option is D.

=======================

#Hope it helps!

(ノ^_^)ノ

Which compound inequality could be represented by the graph?
–4 ≤ x ≤ 4
–2 ≤ x ≤ –1
x ≤ –1 or x ≥ 0
x ≤ 3 or x ≥ –1

Answers

Answer:

It is D.

Step-by-step explanation:

x ≤ 3 or x ≥ –1

Answer:

D) X <_ 3 or X _> -1

Whole Unit Test Review Answers:

1) D

2)D

3)B

4)C

5)D

6)A

7)B

8)C

9)A

10)B

11)D

12)D

13)B

14)B

15)D

(I got a 100%, and these were my answers, hope they help!)

(The pic below is a screenshot of the 100%, for reassurance)

Find the value of n?

Answers

Answer:

[tex]n^{2} -3=39.2=78\\n^2=78+3=81\\n=\sqrt{81} \\n=9[/tex]

Step-by-step explanation:

what values of x makes -6x =12 true

Answers

Answer:

=> —6x = 12=> —x = 12/6=> —x = 2

=> x = —2

Step-by-step explanation:

hope it's helpful :-)

-6x=12

12 /-6 = -2

therefore, -2 make the value of x true

A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 95% confidence interval for the proportion of employees who prefer plan A: (0253.0553). Identify the point estimate for estimating the true proportion of employees who prefer that plan.
a. 0.403
b. 0.253
c. 0.553
d. 0.15

Answers

Answer:

a. 0.403

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

Confidence interval of (0.253,0.553)

The bounds are 0.253 and 0.553, so the point estimate is:

[tex]p = \frac{0.253 + 0.553}{2} = 0.403[/tex]

This means that the correct answer is given by option A.

Find the correct algebraic representation of the dilation shown below.




a- (1/2x,1/2y)
b-(2/7x,2/7y)
c-(7/2x,7/2y)
d-(7x,7y)

Answers

Given:

The diagram of triangle DEF and triangle D'E'F' on a coordinate plan.

To find:

The algebraic representation of the dilation.

Solution:

The vertices of triangle DEF are D(0,7), E(7,-7) and F(-7,-7).

The vertices of triangle D'E'F' are D'(0,2), E(2,-2) and F(-2,-2).

We know that, the dilation factor is:

[tex]k=\dfrac{x\text{ or }y\text{ coordinate of the dilated point}}{x\text{ or }y\text{ coordinate of the corresponding original point}}[/tex]

For point D' the y-coordinate is 7 and for point D the y-coordinate is 2. So,

[tex]k=\dfrac{2}{7}[/tex]

The rule of dilation is:

[tex](x,y)\to \left(kx,ky\right)[/tex]

[tex](x,y)\to \left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex]

The algebraic representation of the dilation is [tex]\left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)[/tex].

Therefore, the correct option is b.

If Sarah turns 15 on august 27 and her graduation year is 2024 how old will she be when she graduates high school?

Answers

Answer:

She will be 17

Step-by-step explanation:

My sister is like that but she's graduating in 22'

It sort of depends where Sarah lives -.-  

But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.

So 15 plus 3.

Sarah will be 18 when she graduates high school.

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