how many cubic inches will a rectangular pyramid hold if its 15 in height by 12 inches base

Answer:

21

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

h is the height of the pebble after a certain amount of time has gone by. Since we are told to find that time when the pebble is on the ground, we say that h = 0 since the height of something on the ground has no height at all. Then factor the quadratic.

\(-16t^2+12t+1900=0\)

Throw that into the quadratic formula or however you were taught to factor irrational quadratics (maybe completing the square?) to get that

t = 11.27869 sec and t = -10.52869 sec

Since we all know that time will never carry a negative value, we will disregard it and go with 11.27869 seconds. Not sure to where you are told to round.

Answer:

Slope: 10

Y-intercept: +9

Step-by-step explanation:

An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.

The surface areas for each figures are:

1. The surface area of the cuboid is:

Top and bottom: 2(10 ft x 4 ft) = 80 ft²

Front and back: 2(10 ft x 5 ft) = 100 ft²

Sides: 2(4 ft x 5 ft) = 40 ft²

Total surface area = 80 + 100 + 40 = 220 ft²

2. The surface area of the cuboid is:

Top and bottom: 2(18 cm x 5 cm) = 180 cm²

Front and back: 2(18 cm x 5 cm) = 180 cm²

Sides: 2(5 cm x 5 cm) = 50 cm²

Total surface area = 180 + 180 + 50 = 410 cm²

3. The surface area of the prism is:

Top and bottom: 2(5 cm x 14 cm) = 140 cm²

Front and back: 2(5 cm x 12 cm) = 120 cm²

Sides: 2(12 cm x 14 cm) = 336 cm²

Total surface area = 140 + 120 + 336 = 596 cm²

4. The surface area of the stacked cuboids is:

Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²

Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²

Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²

Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²

Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²

Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²

Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²

Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²

5. The surface area of the cylinder is:

Top and bottom: 2π(6 mm)² = 72π mm²

Side: 2π(6 mm)(5 mm) = 60π mm²

Total surface area = 72π + 60π = 132π mm²

6. The surface area of the cylinder is:

Top and bottom: 2π(1 ft)² = 2π ft²

Side: 2π(1 ft)(10 ft) = 20π ft²

Total surface area = 2π + 20π = 22π ft²

7. The surface area of the cylinder stacked on a cube is:

Top and bottom of cylinder: 2π(5 m)² = 50π m²

Side of cylinder: 2π(5 m)(8 m) = 80π m²

Surface area of cube: 6(10 m x 13 m) = 780 m²

Total surface area = 50π + 80π + 780 = (130π + 780) m²

8. The surface area of the cylinder is:

Top and bottom: 2π(9 in)² = 162π in²

Side: 2π(9 in)(4 in) = 72π in²

Therefore, the total surface area of the cylinder is:

2(162π in²) + 72π in² = 396π in²

So the surface area of the cylinder is 396π square inches.

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Image transcribed:

Find the surface area of each figure.

10 ft

18 cm

5 cm

4 ft

5 ft

3.

4.

6 cm

7 cm

2 cm

5 cm

12 cm

14 cm

4 cm

10 cm

8 cm

Find the surface area of each cylinder. Leave your answer in terms of π.

5.

6 mm

6.

1 ft

5 mm

10 ft

7.

5 m

8.

4 in.

8 m

10 m

9 in.

13 m

11 m

247

Journal and Practice Workbook

Geometry

18.39 is 5.58% of 329.64.

We have to find that 18.39 is what percent of 120?

First, make the assumption that 329.64 is 100% as it is our output value.

We next represent the value we seek with x, therefore

100% = 329.64                  

And, x% = 18.39                

Now, we get pair of simple equations

100% = 329.64                  ........(1)

x% = 18.39                         ........(2)

Now by simply dividing equation 1 by equation 2 and note of the fact that the LHS of both equations have the same unit (%);

100% / x% = 329.64 / 18.39

Taking the reciprocal of both sides, we get

x% / 100% = 18.39 / 329.64

or x = 5.58%

Hence, 18.39 is 5.58% of 329.64.

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Answer:

j = 139.99 + 139.99 * 0.08625

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: 4 if i believe

Answer: To find the absolute value of the expression 1 1/2 - 2/31, we first need to convert the mixed number 1 1/2 into an improper fraction.

1 1/2 can be written as (2 * 1 + 1) / 2, which is equal to 3/2.

Now we can subtract 2/31 from 3/2:

3/2 - 2/31 = (3 * 31 - 2 * 2) / (2 * 31) = (93 - 4) / 62 = 89/62.

The absolute value of a fraction is the positive value without considering its sign. So, the absolute value of 89/62 is 89/62.

Therefore, the absolute value of 1 1/2 - 2/31 is 89/62.

Answer:

There's no images attached

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer:

To determine the classification of a triangle based on its side lengths, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

For this particular triangle with side lengths 6 cm, 10 cm, and 12 cm, we can apply the Pythagorean theorem to determine whether the triangle is acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is equal to 90 degrees).

Using the Pythagorean theorem, we find:

6^2 + 10^2 = 136

12^2 = 144

Since 136 is less than 144, we know that 6 cm, 10 cm, and 12 cm are the side lengths of a triangle that is obtuse (one angle is greater than 90 degrees), because the longest side (the hypotenuse) is greater than the sum of the squares of the lengths of the other two sides.

Therefore, the correct answer is: obtuse, because 6^2 + 10^2 < 12^2.

Answer:

ancient greek invented math

Answer:

sorreyyyy mateeeeee dont know the answer

a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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Answer:

C  126 sq. units

Step-by-step explanation:

A = 1/2(b)(h)

A = 1/2(21)(12)

A = 1/2 × 252

A = 126 sq. units

Answer:

-0.6x+2.2

Step-by-step explanation:

I graphed it in desmos

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

The measure of the arc opposite to 189° is 136°.

Secant lines are lines that intersect a curve at two distinct points. They are used to approximate the slope of the curve by measuring the change in the y-coordinate of the two points divided by the change in the x-coordinate of the two points.

The measure of the angle opposite to 189° is x.

To solve for x, we can use the property of alternate interior angles.

The sides of the two secant lines that intersect outside the circle form alternate interior angles whose measures are equal.

Therefore, the two angles formed by the secant lines inside the circle must have the same measure.

Therefore, 53° + x° = 189°.

Subtracting 53° from both sides, we get x° = 136°.

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Answer:

simplified: 4x−28

Step-by-step explanation:

The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.

Answer:

\(600, 900, 1350\)

Step-by-step explanation:

Given

\(a = 400\) -- initial subscribers

\(b = 1.5\) -- growth factor

Required

Determine the number of subscribers in the next three months

To do this, we make use of:

\(y = ab^x\)

In this case:

x is the number of months

y is the number of subscribers

So:

when x = 1;

\(y = ab^x\)

\(y = 400 * 1.5^1\)

\(y = 400 * 1.5\)

\(y = 600\)

when x = 2

\(y = 400 * 1.5^2\)

\(y = 400 * 2.25\)

\(y = 900\)

when x= 3

\(y = 400 * 1.5^3\)

\(y = 400 * 3.375\)

\(y = 1350\)

So, the next three number of subscribers is:

\(600, 900, 1350\)

Answer:

Step-by-step explanation:

AB=√[(4+2)²+(6-11)²]=√61

BC=√[(-1-4)²+(0-6)²]=√61

AC=√[(-1+2)²+(0-11)²]=√122

AC²=AB²+BC²

So it is a right angled triangle.

The area of the triangle is (8/5)sqrt(1199) square units.

We are given that;

Coordinates= A=(-2,11) B = (4.6) C=(-1,0)

Now,

we can plug in one point on line AB, such as A(-2, 11), and solve for b:

y = mx + b 11 = (-5/6)(-2) + b 11 = (5/3) + b b = 11 - (5/3) b = (28/3)

Hence, the equation of line AB is:

y = (-5/6)x + (28/3)

Now we can set y equal to 0 (the y-coordinate of C) and solve for x:

y = (-5/6)x + (28/3)

0 = (-5/6)x + (28/3) (-5/6)

x = -(28/3)

x = -(28/3)/(-5/6)

x = (56/15)

Therefore, point D has coordinates (56/15, 0). To find the height of the triangle, we need to find the distance between points A and D using the distance formula:

\(h = AD = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) h = sqrt((56/15 - (-2))^2 + (0 - 11)^2) h = sqrt((136/15)^2 + 121) h = sqrt(18496/225 + 121) h = sqrt(45121/225) h = (3/15)sqrt(5024)\)

Now we can plug in the values of b and h into the area formula and simplify:

\(A = (1/2)bh A = (1/2)(sqrt(61))((3/15)sqrt(5024)) A = (1/10)sqrt(61)sqrt(5024) A = (1/10)sqrt(307584) A = (1/10)(16)sqrt(1199) A = (8/5)sqrt(1199)\)

Therefore, by the given triangle answer will be (8/5)sqrt(1199) square units.

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(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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Since t = 0 corresponds to the initial launch, the cannonball hits the ground after 4 seconds.

An equation is a mathematical statement that shows the equality between two expressions, often with one or more variables. It consists of two sides separated by an equal sign. An equation may have one or more solutions, which are values of the variables that make both sides of the equation equal. Equations are commonly used in many branches of mathematics, as well as in physics, engineering, and other sciences, to model relationships between quantities and to solve problems.

Here,

To find the height of the cannon before it is launched, we can look at the equation h(t) = −4.9t² + 19.8t + 58 and plug in t=0:

h(0) = −4.9(0)² + 19.8(0) + 58

= 58 meters

To find when the cannonball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a parabola:

x = -b/2a, where a=-4.9 and b=19.8.

Plugging in these values, we get x = -19.8/(2*(-4.9))

= 2.02 seconds

To find the maximum height of the cannonball, we can plug in the value of t we just found (t=2.02 seconds) into the original equation and solve for h:

h(2.02) = −4.9(2.02)² + 19.8(2.02) + 58

≈ 65 meters

To find how long it takes the cannonball to land on the ground, we can look at the equation h(t) = −4.9t² + 19.8t + 58 and set h(t) = 0 (since the cannonball hits the ground when its height is 0):

−4.9t² + 19.8t + 58 = 0

Solving for t using the quadratic formula, we get t ≈ 4 seconds.

If we launch the cannonball from the ground instead (hi=0), the initial height term in the equation disappears and we get:

h(t) = −4.9t² + 19.8t

To find the new equation of the cannonball's path if launched from the ground, we simply remove the initial height term hi from the original equation:

h(t) = −4.9t² + 19.8t

To find the new maximum height of the ball and how long it takes to hit the ground, we can use the same methods as before, but with the new equation.

The x-coordinate of the vertex is x = -b/2a

= -19.8/(2*(-4.9))

= 2.02 seconds.

Plugging this into the new equation, we get:

h(2.02) = −4.9(2.02)² + 19.8(2.02)

≈ 64 meters

To find the time it takes to hit the ground, we set h(t) = 0 and solve for t: −4.9t² + 19.8t = 0, which gives t = 0 or t = 4 seconds (the same as before).

However, since we know the cannonball was launched from the ground, we can ignore the solution t=0, and conclude that the cannonball hits the ground after approximately 4 seconds.

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