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1. A student is helping a family member build a storage bin for their garage. They would like for the bin to have a volume of 240 ft3. If they already have the length measured at 8 feet and the width at 6 feet, what is the height needed to reach the desired volume?

2. The volume of a rectangular prism is 6,142.5 cm3. If the height is 16.25 cm and the length is 28 cm, what is the value of the width?

3. If the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m, what is the value of B, the area of the base?

4. What is the volume of a rectangular prism with a length of 15 yards, a width of 8 yards, and a height of 5 yards?

5. A teacher purchased a fish tank for her classroom. The dimensions of the tank are 36 inches by 60 inches by 48 inches. What is the maximum amount of water that the tank can hold?

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

An expression that represent the sum of  (7x-y) and (5x+3y) in simplest terms is 12x + 2y

The given expressions are  (7x-y) and (5x+3y)

The applying the addition property of equality we have

= (7x - y) + (5x + 3y)

= 7x - y + 5x + 3y

collecting like terms

= 7x + 5x - y + 3y

= 12x + 2y (in simplest terms)

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The number makes the expression equivalent is m = 0.2584.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 12(- 1.4m + 0.4) = m + 0.2.

- 16.8m + 4.8 = m + 0.2.

- 16.8m - m = 0.2 - 4.8

- 17.8m = - 4.6.

m = (-4.6/-17.8).

m = 0.2584.

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Answer: 7

Step-by-step explanation:

The value of x is 1.2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

6-4x = 6x-8+2

group the variable and constant terms

6 +8 -2 = 6x +4x = 10x

12= 10x

=> x= 12/10 = 1.2

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Answer:x=1/2

Step-by-step explanation:

[tex]5^{2x+1} =5^{2}[/tex]

2x+1=2

2x=1

x=1/2

Answer:

180-81=

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

390/3=130, 130x4=520

Step-by-step explanation:

Step 1: 2x²--7x²=9x²

Step 2: 2x--7x=9x

Step 3: -7-+2=-9

Overall answer: 9x²+9x-9

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The altitude of the balloon found using Pythagorean Theorem is 40·√3 feet, the best correct option is option C)

C) 40·√3 ft

The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is the same as the sum of the square of each of the two legs of the right triangle.

15) The parameters in the question includes;

Horizontal distance of the flag pole from the point the rope is staked down = 40 feet

Length of the rope to which the balloon is secured = 80 feet

Location of the balloon = directly above the flag pole

Therefore, the altitude of the balloon, the length of the rope, and the horizontal distance from the flag pole from the point the rope is staked form a right triangle, with the length of the rope representing the hypotenuse side.

Let h represent the altitude of the flag pole, using Pythagorean Theorem, we get;

80² = 40² + h²

Therefore; h² = 80² - 40² = 4800

The altitude of the balloon, h = √(4800) = 40·√3

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Answer:

Step-by-step explanation:

Dan drove for 1.6 hours.

64 miles per hour (mph) is the unit rate so divide by 102.4 by 64 and you get 1.6

Answer:

A.  x = 3

B.  A = (3, 2)

C.  V = (-1, 2)

D.  Left

E.  See below.

F.  p = -4

[tex]\textsf{G.} \quad x=-\dfrac{1}{16}(y-2)^2-1[/tex]

H.  See attachment.

[tex]\textsf{J.} \quad x=\dfrac{1}{4}(y-3)^2+3[/tex]

     [tex]x=-\dfrac{1}{12}(y+1)^2+5[/tex]

Step-by-step explanation:

The given focus of the parabola is F (-5, 2).

The equation for a vertical line is x = a.

Therefore, a vertical line that is 8 units to the right of the focus is:

[tex]\implies x=-5+8=3[/tex]

Therefore:

A line that is perpendicular to the directrix is a horizontal line.

The equation for a horizontal line is y = a.

As the horizontal line passes through the focus:

The point of intersection, A, of the axis of symmetry and the directrix is:

The vertex of the parabola is the point that is halfway between the focus and the directrix.

Therefore:

The parabola will open sideways as the axis of symmetry is horizontal.

As a parabola never touches its directrix, this parabola will open to the left.

The absolute value of p is the distance between the vertex and the focus, and the distance between the vertex and the directrix.

For a sideways parabola, if p > 0 the parabola opens to the right, and if p < 0 the parabola opens to the left.

Since the focus and directrix are 8 units apart, and the parabola opens to the left:

Vertex form of a sideways parabola:

[tex]\boxed{x=\dfrac{1}{4p}(y-k)^2+h}[/tex]

Given:

Substitute the values into the formula:

[tex]\implies x=-\dfrac{1}{16}(y-2)^2-1[/tex]

See attachment.

Rearrange the equation of the parabola shown in the attachment:

       [tex]y^2+16x-4y=-20[/tex]

[tex]\implies 16x=-y^2+4y-20[/tex]

[tex]\implies 16x=-(y^2-4y+4)-16[/tex]

[tex]\implies 16x=-(y-2)^2-16[/tex]

[tex]\implies x=-\dfrac{1}{16}(y-2)^2-1[/tex]

This matches the equation in vertex form in part G.

Given:

Therefore:

Therefore, the equation of the parabola with the given parameters is:

[tex]\boxed{x=\dfrac{1}{4}(y-3)^2+3}[/tex]

Given:

Therefore:

Therefore, the equation of the parabola with the given parameters is:

[tex]\boxed{x=-\dfrac{1}{12}(y+1)^2+5}[/tex]

Answer:

-4 acceleration

Step-by-step explanation:

: )

The number of students who like the book is 64 students.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

Given: Total students in English class = 100

Nine twenty-fifths of the class did not like the book.

Thus, the number of students did not like the book = 9/25 × 100

= 36

Therefore, the number of students like the book =Total students- students did not like the book will be:

= 100-36

= 64 students.

The number of students is 64.

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Complete question

After reading a book for English class, 100 students were asked whether or not they enjoyed it. Nine twenty-fifths of the class did not like the book. How many students liked the book?

The inequality for the annual family income is:

y < 1240x + 48,200

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Let x=0 be the year 2006

The inequality is:

y < 1240x + 48,200

Graphing:

Consider equal sign in place of < symbol

Take random values for x, find corresponding y values and plot them

Mark it as dashed line as shown in the graph because of the inequality symbol "< "

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Answer: 5.66

Step-by-step explanation:

The perimeter of the square being 32, the sides are 8 units. The diameter of the circumscribing circle is the diagonal of the square which is 8 sec 45 = 11.3 units. Hence, the radius of the circle = 5.66 units.

The expression equivalent to 7x³ × (x⁸) × 2 is  14x¹¹.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are the same.

Therefore,

7x³ × (x⁸) × 2

Using the law of indices,

[tex](x^{a}) (x^{b} ) = x^{a+b}[/tex]

Hence,

7x³ × (x⁸) × 2 = 7x³ × 2x⁸

7x³ × 2x⁸ = 14x¹¹

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The expression that shows the number of miles he drove and trips he made to San Diego is; 3850 + yb

Let a round trip to Los Angeles be denoted by the variable; x

Let the number of miles in a round trip to Los Angeles be denoted by the variable a

Let a round trip to San Diego be denoted by the variable: y

Let the number of miles in a round trip to San Diego be denoted with the variable: b

This means that our algebraic equation representing the number of miles driven in all to be: xa + yb

Since the truck driver made 5 round-trips to Los Angeles, then it means that, we have the equation;

5a + yb as the total miles driven in all.

However, from the table attached, a round trip to  Los Angeles  is 770 miles. Thus;

Total miles driven = 5(770) + yb = 3850 + yb

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Answer:

5/3 is the slope

Step-by-step explanation:

Use the slope formula

m = y2 - y1/ x2 -x1

Answer:

Slope = 5/3

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Now the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 7)/(5 - 2)

→ [ m = 5/3 ]

Hence, required slope is 5/3.

Answer:

b = 40 , c = 70

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 5x² + bx + c ← is in standard form

with a = 5 and b = b , then

x = - [tex]\frac{b}{10}[/tex]

equating to the given x- coordinate of the vertex , that is - 4

- [tex]\frac{b}{10}[/tex] = - 4 ( multiply both sides by - 10 )

b = 40

then

y = 5x² + 40x + c

substitute (- 4, - 10 ) into the equation and solve for c

- 10 = 5(- 4)² + 40(- 4) + c

- 10 = 5(16) - 160 + c

- 10 = 80 - 160 + c

- 10 = - 80+ c ( add 80 to both sides )

70 = c

then b = 40 and c = 70

Answer:

  (a)  $479.50

Step-by-step explanation:

You want to know how much the friend with the smaller bedroom will pay for rent if they split the $975 cost based on the square footage of each bedroom. The two bedrooms in the 1225 square foot property are 130 and 150 square feet.

Apparently, the cost of the non-bedroom area is to be split evenly. That common area is ...

  1225 ft² -(150 +130) ft² = 945 ft²

Then the proportion due from the occupant of the smaller bedroom is ...

  (945/2 +130)/1225 = 241/490 ≈ 0.49184

That fraction of the rent is ...

  0.49184 · $975 = $479.54

The nearest answer choice is $479.50.

__

Additional comment

If we were to assume the split is based only on bedroom size, then the rent paid for the 130 ft² space would be (13/28)($975) ≈ $452.68. This would be equivalent to splitting the rent for the common area in the same proportion as for the bedrooms.

We note that half the rent is $487.50, a number less than either of the last two answer choices. Those can be rejected for that reason. (The smaller bedroom is expected to pay less than half of the rent.)

Answer:

Step-by-step explanation:

n=3+d

n -d = 3

5n -5d = 15

5n +10d = 135

5n - 5d   = 15

     15d  = 120

        d= 8 dimes

       n =  11 nickels

5x11 + 8x10 = 55 + 80=  135

Answer:

The correct answer is 514.90

Step-by-step  

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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a) The ball reaches a maximum height of 182.25 feet.

b) The ball has a travel time of 6 seconds.

In this case we find a kind of uniform accelerated motion known as free fall, in which a particle is accelerated uniformly by gravity and any effect of other forces are neglected. The height of the ball in terms of time is described by a quadratic equation, whose definition is shown below:

h(t) = h' + v' · t + 0.5 · g · t²

Where:

First, write the complete the equation of the height of the ball:

h(t) = - 16 · t² + 84 · t + 72

a) Second, clear the expression on one side and use the discriminant of the quadratic formula:

- 16 · t² + 84 · t + [72 - h(t)] = 0

84² - 4 · (- 16) · [72 - h(t)] = 0

7056 + 64 · [72 - h(t)] = 0

7056 + 4608 - 64 · h(t) = 0

11664 - 64 · h(t) = 0

h(t) = 729 / 4 ft

h(t) = 182.25 ft

The maximum height of the ball is 182.25 feet.

b) Third, use the quadratic formula to determine the roots of the quadratic equation:

t = - 84 / [2 · (- 16)] ± [1 / [2 · (- 16)]] · √[84² -  4 · (- 16) · 72]

t = 2.625 ± (1 / 32) · 108

t₁ = 6 s and t₂ = -0.75 s

The travel time of the ball is 6 seconds.

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The main differences between the place value of the whole number and the decimal is given below

What is decimal ?

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.

A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Decimals can be classified as non-recurring (as in not repeating or ending), recurring (as in repeating or not terminating), and decimal fractions (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

The whole number part of the decimal number is the part that lies strictly to the left of the decimal point, and the place value of each digit in the whole number part is given .

The fractional part of the decimal number is the part that lies strictly to the right of the decimal point.

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I guess it sort of depends on whether you are folding the rectangle in half "long-ways" or "short-ways", however, if the rectangle is folded "long-ways", then the length of the new long side would be 5.5, with the shorter end being 4.25, or just 4.2.

Hope this helps!

Answer:

see below

Step-by-step explanation:

A

The hypotenuse is ALWAYS the longest side of a right triangle, and located Directly Across from the Right Angle: c = √79

Pythagorean Theorem:  a² + b² = c²

a = 2√5

b = ?

c = √79

(2√5)² + b² = (√79)²

20 + b² = 79

b² = 59

√b² = √59

b = √59 = KJ

B

tan=opposite side / adjacent side

From I, KJ is opposite;  and IK is adjacent

tan(I) = √59/(2√5) ≈ 1.72

C

cos=adjacent side / hypotenuse

From J, KJ is adjacent;  and IJ is the hypotenuse

cos(J) = √59/√79 ≈ 0.86