A box has a volume of 135 feet3. The length is same as the height, and the width is 5 times the length. What are the dimensions of the box?

Answers

Answer 1

let the length be x ft, width=5x ft, height=x ft
thus the volume will be:
volume=length*width*height
thus
135=x×x×5x
135=5x³
solving for x we get:
27=x³
getting the cube root of both sides:
∛27=x³
x=3 ft
thus
length=3 ft, height=3ft, width=3×5=15 ft

Answer 2

Final answer:

The dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.

Explanation:

This is a classic problem of volume where we need to consider the volume formula of a box, which is length × width × height. The question states that the box has a volume of 135 cubic feet, with the length being the same as the height, and the width being 5 times the length.

To find the dimensions of the box, we can set up the equation: length × 5 ×length × length = 135. Simplifying, we get that the length is the cube root of 135/5, which equals to 3. Thus, the dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.

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Related Questions

What is cos (x)?

A) 48/58

B) 58/48

C) 26/58

D) 58/26

Answers

Remark
In order to solve for the Cos(x), you need to find the missing side. You can do that by finding the Sin(x) first and then the Cos of x or you can just use the Pythagorean theorem. I'm going to do the latter.

Formula
a^2 + b^2 = c^2

Givens
a = ???
b = 32
c = 58

Sub and solve
a^2 = ???
b^2 = 1024
c^2 = 3364

a^2 + 32^2 = 58^2
1024 + a^2 = 3364 Subtract 1024 from both sides.
a^2 = 3364 - 1024
a^2 = 2340 Take the square root of both sides.
sqrt(a^2) = sqrt(2340) Break a into its prime factors.
a = sqrt(2 * 2 * 5 * 3 * 3 * 13)

Rule
For every pair of equal factors, one can be brought outside the root sign and the other is discarded.
a = 2 * 3 * sqrt(5*13)
a = 6 sqrt(65)

The cos of an angle = opposite / hypotenuse.
Cos(x) = 6*sqrt(65) / 58 <<<<< This should be the answer
If you are offered choices, you should list them

Another choice would be 6*8.0623 / 58 = 0.8340 <<<<< Answer

13. Which theorem or postulate proves the two triangles are similar? The diagram is not drawn to scale.
A. AA Postulate
B. AS Postulate
C. SSA Theorem
D. SSS Theorem

Answers

The Answer is the AA Postulate

Answer:

A) AA postulate

Step-by-step explanation:

This postulate used to prove the two triangles are similar.

If two angles in a triangle are congruent to two angles in other triangle, then the two triangles are called similar.

Hope this will helpful.

Thank you.

Consider the following set of equations:

Equation A: y = −x + 5
Equation B: y = 6x − 2

Which of the following is a step that can be used to find the solution to the set of equations?

−x = 6x + 2
−x − 2 = 6x + 5
−x + 5 = 6x – 2
−x + 5 = 5x

Answers

Since Y equals BOTH (-X+5) and (6X-2), you can set the two equations equal to eacher other; therefore, the answer is: C: -X+5=6X-2

Based on the graph, which statement BEST describes what is happening to the temperature over time?

A.The temperature rises 10 degrees over 3 hours.
B.The temperature rises 10 degrees over 6 hours.
C.The temperature rises 40 degrees over 3 hours.
D.The temperature rises 50 degrees over 6 hours.

Answers

I am pretty sure that the right answer is A.

What are the coordinates of the image of vertex P after a reflection of rx-axis(x, y)? P'( , )

Answers

Answer: (-7, 4)

Step-by-step explanation:

The hypotenuse of a right triangle is 5 m long. The longer leg is 1 m longer than the shorter leg. Find the side lengths of the triangle.

Answers

The shortest side is 3 m and the other side is 4 m. If you put all these numbers in the Pythagorean Theorem it checks out. (3^2+4^2=5^2)

Final answer:

The Pythagorean theorem is used to determine the lengths of a right triangle's sides. When we know the hypotenuse length and the fact that one leg is 1m longer than the other, we can solve for the lengths to be approximately 3m and 4m.

Explanation:

The subject of your question is related to the geometric concept of right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this problem, we know the hypotenuse = 5m and the longer leg is 1m longer than the shorter leg. Let's denote the shorter leg as 'x' m. Consequently, the longer leg is 'x+1' m. Applying the Pythagorean theorem, we get: (x)² + (x+1)² = 5².

Solving this equation, we find x~3m (shorter leg) and x+1~4m (longer leg). These are the lengths of the sides of your right triangle.

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A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.

What is the vertical clearance 7 m from the edge of the tunnel?

15.4 m
0.3 m
15.7 m
0.6 m

Answers

Vertex at the origin and opening down → y=ax^2
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4

y=ax^2→y=-(1/4)x^2

7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4

Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m

Please, see the attached file.

Answer: Third option 15.75 m

the basic formula of a parabola is;

y -k= 4a (x-h)^2

Solving for this, the vertical clearance 7m forom the edge of the tunnel must be

15.7m

Hope this helps! Goodluck!

All log graphs contain the points (1,0), (a,1), and (1/a,-1).

True .
False.

Answers

The correct answer is: True

Explanation:
1. [tex]log_a1 = 0[/tex] (Straightforward)
2. [tex]log_aa = 1 [/tex] (log to base of itself is always 1)
3. [tex]log_a \frac{1}{a} = log_aa^{-1} = -1(1) = -1[/tex] (Using log power property)

Hence the correct option is True.

Can someone help me solve this ??

Answers

The external angle at the intersection of two secants is half the difference of the intercepted arcs. That is

∠E = (1/2)(4x° -2x°) = x°

The given measure of arc AB tells you

... 4x° = 56°

... x° = 14°

The appropriate choice is ...

... B. 14°

A relay team ran a race. Each team member ran #1/4# of the distance. The whole race was #8/9# mile. How far did each team member run?

Answers

Each member ran 2/9 miles

MANY POINTS!!

When adding fractions, make sure the ______ are the same, and then add the _______.

Answers

denominators and numerators

When adding fractions make sure the denominators are the same, and then add the numerators.

I hope this helps :)

Compare the functions shown below:

f(x)

cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1
g(x)

x y
−6 −11
−5 −6
−4 −3
−3 −2
−2 −3
−1 −6
0 −11
h(x) = 2 cos x + 1

Which function has the greatest maximum y-value?

a. f(x)
b. g(x)
c. g(x) and h(x)
d. f(x) and h(x)

Answers

We can find the local maxima and minima of any -continous- function by first finding where the slope is 0, as at this point maxima or minima exist.

Given an arbitrary function '[tex]f(x)[/tex]' we find the point of slope 0 by taking its first derivative and equaling to 0 ('[tex] \frac{d}{dx}f(x)=0 [/tex]').

Lets, first, find the local extremes of the first function:
[tex]f(x)=cos(x)[/tex]
[tex] \frac{d}{dx} f(x)=\frac{d}{dx}cos(x)=-sin(x)=0[/tex]
[tex]x=sin^{-1} (0)=0[/tex]

So our first function has a maxima at '[tex]x=0[/tex]' or at '[tex]y=f(0)=cos(0)=1[/tex]'.

Now we get the extremes for the second function:
[tex]h(x)=2cos(x)+1[/tex]
[tex]\frac{d}{dx} h(x)=\frac{d}{dx}[2cos(x)+1]=-2sin(x)=0[/tex]
[tex]x=0[/tex]

So our second function has a maxima at '[tex]x=0[/tex]' or at '[tex]y=h(0)=2cos(0)+1=3[/tex]'.

Clearly, '[tex]h(0)=3\ \textgreater \ f(0)=1[/tex]', this means the second function '[tex]h(x)[/tex]' has the largest maxima -y value-.

Answer:

f(x) and h(x)

Step-by-step explanation:

f(x) and h(x) have the greatest maximum y-value because if you graph out all the equations you can determine by graph which ones have the greatest y-value. When you graph the equations you find that f(x) and h(x) both have a greatest y-value of 3! While g(x) has a greatest y-value of -2.

*Please note that it is looking for the greatest y-VALUE not the greatest y-INTERCEPT.

A laptop company has discovered their cost and revenue functions for each day: c(x) = 3x2 − 10x + 200 and r(x) = −2x2 + 100x + 50. if they want to make a profit, what is the range of laptops per day that they should produce? round to the nearest number which would generate profit.

Answers

Given that:
c(x) = 3x2 − 10x + 200
and
r(x)=−2x2 + 100x + 50

Profit is given by:
P(x)=r(x)-c(x)

P(x)=(−2x2 + 100x + 50)-(3x2 − 10x + 200)
P(x)=-5x^2+110x-150
thus:
at maximum profit P'(x)=0
thus:
P'(x)=-10x+110=0
hence:
x=11
thus the number of units required for one to make profit is 11 units

Tina is growing sunflowers in her garden. The flowers are currently 6 inches tall each week x, they will double in size . Which equation best represent how tall the sunflower will b in x weeks

Answers

For this case we have an equation of the form:
y = A (b) ^ x
Where,
A: initial height
b: growth rate
x: time
Substituting values we have:
y = 6 (2) ^ x
Answer:
An equation that best represent how tall the sunflower will b in x weeks is:
y = 6 (2) ^ x

Write an equation for the line that passes through (0, -9) and (3, 0).

A. y = 3x + 9
B. y = -9x + 3
C. y = 3x + 3
D. y = 3x - 9

Answers

First find the slope of the line:-

= (0- - 9) / (3 - 0) = 9/3 = 3

Now use the point slope form of the equation to plug in the point (3,0):-
y - y1 = 3(x - x1)
y1 = 0 and x1 = 3:-
y - 0 = 3(x - 3)

y = 3x - 9 is the answer Its D.

Help quick please!!! Find the value of x

Answers

Hello!

First you have to find the missing angle in the triangle

The angles in a triangle add to 180°

180 - 97 - 30 = 53

The angle we just found and angle x form a straight line meaning they add to 180°

180 - 53 = 127

The answer is 127°

Hope this helps!

Hi!

X is part of a straight angle, which should add up to 180°.

So first we need to figure out what the other side of this straight angle is. Since the other side is inside the triangle, it should be easy.

All angles in any triangle always add up to exactly 180°. To figure out what the last angle is in the triangle, we just need to add the two existing angle measurements together and subtract the sum from 180.

97 + 30 = 127

180 - 127 = 53

So the last angle in the triangle is 53°.

Now, we can figure out the value of x. Since x is part of a 180° straight angle, and we know that half of said angle is 53°, we can find x by subtracting 53 from 180.

180 - 53 = 127

x = 127

Hope this helps :)

Find the sum or difference: 2.8 - -5.1

Answers

2.8-(-5.1)

-(-5.1)=5.1

2.8+5.1= 7.9

Is this what you were asking?

Subtracting means adding the opposite.Subtracting -5.1 means adding the opposite of -5.1 which is +5.1.
2.8 - (-5.1) = 2.8 + (+5.1) = 2.8 + 5.1 = 7.9

Kevin owes $4,645 on a credit card with a 19.7% interest rate compounded monthly. What is the monthly payment he should make in order to pay off this debt in 12 months, assuming he does not charge any more purchases with the card?

$387.08

$84.34

$429.62

$1,034.65

**Please help with steps too, please.

Answers

The "steps" are to enter the data into the appropriate places in a financial calculator. (PV=4645, i=19.7/12, n=12) Then PMT = -429.62.

Alternatively, and somewhat more slowly, you can make use of the amortization formula.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where A is the monthly payment,
P is the current balance (4645),
r is the annual rate (.197),
n is the number of compoundings per year (12), and
t is the number of years (1).

Filling in the numbers, you have
A = 4645*(.197/12)/(1 -(1 +.197/12)^-12)
A ≈ 429.62 . . . . . corresponds to the 3rd choice

Which of the following steps could be used as a shortcut method to multiply 12 by 50

Answers

do 12 times 5 then add a zero to it

You can take the zero off 50 and do 12 times 5=60 and add the zero on and get =600

Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.
9
7
8
6.6

Answers

Hello!

You have to find out happened between triangles

6 / 3 = 2
10 / 5 = 2

They multiplied the first triangle by 2 to get the second

Apply this to find the missing side

4 * 2 = 8

The answer is 8

Hope this helps!

Answer:

The correct option is: 8

Step-by-step explanation:

Suppose, the missing side length in second triangle is [tex]x[/tex]

So, the side lengths of first triangle: [tex]3, 4, 5[/tex]

and the side lengths of second triangle: [tex]6, x, 10[/tex]

As two triangles are similar, that means their corresponding side lengths will be proportional.

So,

[tex]\frac{3}{6}=\frac{4}{x}\\ \\ 3x= 4*6\\ \\ 3x= 24\\ \\ x=\frac{24}{3}=8[/tex]

So, the missing side length in second triangle is 8.

Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).

Answers

Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
y−1=34(x+2)
the equation above can be written in the form of y=ax+b, as follows:
y-1=34x+68
y=34x+69
the slope of the line is a=34
the slope of the perpendicular line will be:
m=-1/34
thus the equation of the perpendicular line cutting through (-4,-2) will be:
m(x-x1)=y-y1
thus
-1/34(x-(-4))=y-(-2)
-1/34x-4/34=y+2
y=-1/34x-36/17
Answer: y=-1/34x-36/17

Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).

A crowd of 50,000 fans is expected to attend the homecoming football game. if the typical vendor can serve 1,500 customers per hour and the game will last for four hours, how many vendors are needed to ensure that each fan can be served during the game? (round to the nearest whole number.) a) 9 b) 10 c) 8 d) 1

Answers

Since every hour, a vendor sells to 1500 customers, we multiply by hours, like this:

1500 * 4 = 6000.

Then we divide 50000/6000, and that would give us 8.33333333, and we round that to the next number which is 9, and that's the answer.

Answer: 9 vendors.

Hope this helped! c:

Using Multiplication, There are 9 vendors are needed to ensure that each fan can be served during the game.

What is Multiplication?

Multiplication is to "increase a number by the number of times mentioned".

According to the question,

Number of fans expected to attend a football game = 50,000

Number of customer to be served = 1,500per hour

To find number of customer to be served for 50,000 fans

The game has to be last for 4 hours.

Formula : 1 vendor is to sell 1,500 customer per hour

4*1500 = 6000

A vendor has to sell 6000 customers in 4 hours.

In order to find the number of vendors have to sell 50,000 customers in 4 hours

Let 'x' be the number of vendors

To find the number of vendors only if we divide 50,000 by 6000

=[tex]\frac{50,000}{6000}[/tex] = 8.333 ≈ 9

Hence, there are 9 vendors are needed to ensure that each fan can be served during the game.

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The baseball team has sold tickets to a spaghetti dinner. forty-eight student tickets have been sold at $1.50 each. if the baseball team has made $149 total from the sale of all tickets, and adult tickets cost $3.50, how many adult tickets were sold?

Answers

Let the number of adults be x
number of students is 48
Amount collected from students=48*(1.5)=$72
Amount collected from adults=3.5*x=3.5x

Total amount collected will be:
72+3.5x=149
solving for x we have:
3.5x=149-72
3.5x=77
thus
x=77/3.5
x=22
thus the number of adults was x =22

find the volume of the composite figure. round your answer to the nearest hundredth

Answers

611.08

Be sure to treat the two shapes as completely different figures, then add their totals together

The correct answer is 590.77mm3.

The cost of fertilizing a lawn is $0.25 per square foot. find the cost to fertilize the triangular lawn whose base is left parenthesis 14 plus startroot 17 endroot right parenthesis feet and altitude is startroot 68 endroot feet.

Answers

To Calculate the cost of The cost of fertilizing, we need to Calculate first the Area of the Triangle.

the Area of the Triangle = 1/2 x base x altitude = 1/2 x (14+√17) x 68 = 524.08 square foot

The cost of fertilizing = the cost of the square foot x the total area = 0.25x524.08 = 131 $

A farmer planted corn in a square field.one side of the field measures 36 yards. what is the area of the cornfield

Answers

Area = 36 x 36 = 1296 yd²

Answer: 296 yd²

Answer:

1,296 ik im late but yeah

Step-by-step explanation:

The sides of a rectangle are in a 3:4 ratio. What is the length of the shorter sides of the rectangle if it's perimeter is 42cm

Answers

Final answer:

Given a rectangle with sides in a 3:4 ratio and a perimeter of 42 cm, the length of the shortest side is 9 cm.

Explanation:

We are given that the sides of the rectangle are in a 3:4 ratio and that the perimeter is 42 cm. The rectangular perimeter is calculated by the formula 2*(length + width). In this case, because the sides are in a 3:4 ratio, we can say 2*(3x + 4x) = 42, where 'x' represents the length of the shortest side.

Solve this equation, 2*(7x) = 42, we find that 'x' is 3. So the length of the shorter side, 3x, is 9 cm. Applying the same 3:4 ratio, the longer side, 4x, is 12 cm.

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Final answer:

To find the length of the shorter side of a rectangle with sides in a 3:4 ratio and a perimeter of 42cm, we set up an equation using the ratio values as coefficients and the known perimeter. Solving this equation shows that a unit in the ratio equals 3cm and the shorter side is 9cm.

Explanation:

In this mathematics problem, we are trying to find the length of the shorter side of a rectangle, knowing that the sides are in a 3:4 ratio and that the perimeter is 42cm. The perimeter of a rectangle can be found by using the equation [tex]P=2L+2W[/tex] (Perimeter equals twice the length plus twice the width).

If we represent the shorter side as 3x and longer side as 4x, we can establish the following equation based on the given perimeter:[tex]2*(3x)+2*(4x)=42c[/tex]m. Simplifying this equation gives 14x=42cm. Solving for 'x', we find x=3. Therefore, each unit in the ratio corresponds to 3cm, and the length of the shorter side, represented by 3x, is [tex]3*3=9[/tex]cm.

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Express answer in exact form.

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)

Answers

we know that
the regular hexagon can be divided into 6 equilateral triangles

area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²

area of a circle=pi*r²

in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²

the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
[ (3/2)*pi in²-(9/4)*√3 in²]

the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]

Solve the equation. Check for extraneous solutions

please help!!!

Answers

!z!=a→z=a or z=-a; z=4x+3, a=9+2x

!4x+3!=9+2x
1) 4x+3=9+2x
Solving for x:
4x+3-3-2x=9+2x-3-2x
2x=6
2x/2=6/2
x=3

Checking for extraneous solution:
!4x+3!=9+2x
x=3→!4(3)+3!=9+2(3)
!12+3!=9+6
!15!=15
15=15 Ok, then x=3 is not a extraneous solution

2) 4x+3=-(9+2x)
Solving for x:
4x+3=-9-2x
4x+3-3+2x=-9-2x-3+2x
6x=-12
6x/6=-12/6
x=-2

Checking for extraneous solution:
!4x+3!=9+2x
x=-2→!4(-2)+3!=9+2(-2)
!-8+3!=9-4
!-5!=5
5=5 Ok, then x=-2 is not a extraneous solution

Answer:
x = -2 or 3

Solve 4/7=x+3/21 need help ASAP

Answers

4/7 = x+3/ 21

21 (4/7 = x+3)

3 *4=x+3

x= 9

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