A square pyramid has a base with an area of 225 centimeters squared if the volume is 300 centimeters cubed how tall is the pyramid

The value of x when the secant intersect is 5.

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.

Therefore,

(4 + 5)4 = (x - 2 + x + 4)(x - 2)

9(4) = (2x + 2)(x - 2)

36 = 2x² - 4x + 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

x² - x - 20 = 0

x² - 5x + 4x  - 20 = 0

x(x - 5) + 4(x - 5) = 0

(x + 4)(x - 5) = 0

(x - 5)(x + 4) = 0

x = 5 or x = -4

Therefore,

x = 5

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The number of triangles that are displayed can be found to be 216 triangles.

Each rectangular tile has a decorative pattern of 3 equal-sized squares, and each square is divided into 2 same-sized triangles. Therefore, each tile has 3 squares * 2 triangles per square = 6 triangles.

Marnie uses 36 of these tiles on the wall behind her kitchen stove. To find the total number of triangles displayed, multiply the number of triangles per tile by the total number of tiles:

Total triangles = 6 triangles per tile x 36 tiles = 216 triangles

So, there are 216 triangles displayed on the wall behind Marnie's kitchen stove.

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Answer:

176

Step-by-step explanation:

To do this question, we can simplify it even further.

If x=25 when y=110, it is in the ratio 25:110.

If we divide by five on both sides, the ratio becomes:

5:22.

Then, if we multiply by eight on both sides,

it becomes 40:22x8 which means y is equal to 176.

Answer:

40 plus 19/ 9-3=40

The requreid, as per the given percentage condition Mia tips the movers $80.

To find the amount of the tip, we need to calculate 16% of the total cost of the services, which is $500.

16% of $500 = 0.16 x $500 = $80

Therefore, Mia tips the movers $80.

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Answer:

Step-by-step explanation:

(3n³ + 2n)² = 9n^6 + 12n^4 + 4n^2

(4k² + 2k³) = 2k²(2 + k)

(3y²-y')' = 6y-y''

(4c+30) = 2(2c+15)

(2b² * b)² = 4b^6

(2gh²)* = 2gh^2

(6w³)² = 36w^6

The best response to Raina's comment will be that technology is good but handouts still serve the useful purpose of being a hard copy that speakers can use in case technology fails.

To respond to Raina, the best thing to do will be to acknowledge the fact that technology is good but handouts are still important because, unlike technology that can trip off by some sudden technical faults, handouts can be depended upon.

So, while responding to Raina, we will not discard her point but will let her know that technology is good but handouts still have their benefits.

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Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A = (-3, 3 + 3) = (-3, 6)

B = (0, 7 + 3) = (0, 10)

C = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A(-3, 6), B'(0, 10), and C(-3, 3).

So the correct answer is: A(−3, 6), B(0, 10), C(−3, 3).

The volume of the triangular prism as shown in the attached image is 30 cm³.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the height of the prism.

The area of the triangular base can be found using the formula:

Area = (1/2) × base × height

In this case, the base is 5 cm and the height is 4 cm, so the area of the triangular base is:

Area = (1/2) × 5 cm × 4 cm = 10 cm²

The height of the prism is 3 cm.

Therefore, the volume of the triangular prism is:

Volume = Area of triangular base × height

= 10 cm² × 3 cm

= 30 cm³

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a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

b) The number of squares that will fit on the land is 61773.

Explain square

A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.

According to the given information

(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.

To find the GCD, we can use the Euclidean algorithm:

GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3

Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.

(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:

735 * 756 = 555960 square meters

The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:

555960 / 9 = 61773.333...

Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.

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F(x) is an antiderivative of f(x) because F'(x) = f(x)

An anti-derivative is the integral of a function

To verify that F is an antiderivative of f where

F(x) = √(3x² - 4) and f(x) = 3x/√(3x² - 4)

This means that F(x) = ∫f(x)

This implies that F'(x) = f(x)

So, we verify as follows

F(x) = √(3x² - 4)

Taking the derivative with respect to x, we have that

dF(x)/dx = d√(3x² - 4)/dx

Let u = 3x² - 4

So, dF(x)/dx = d√u/dx

= d√u/du × du/dx

= 1/(2√u) × du/dx

Now,du/dx = d(3x² - 4)/dx

= 6x

So,

dF(x)/dx  = 1/(2√u) × du/dx

= 1/(2√(3x² - 4)) × 6x

= 1/(√(3x² - 4)) × 3x

= 3x/(√(3x² - 4))

= f(x)

So, F(x) is an antiderivative of f(x) because F'(x) = f(x)

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The two numbers given by the algebraic expressions are x = 5 and y = 2.

A system of equations is a set of two or more equations that are to be solved simultaneously. In other words, a system of equations represents multiple relationships between variables that need to be solved for at the same time. A system of equations can be solved using various methods, such as substitution or elimination. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. One common method for solving systems of linear equations is called Gaussian elimination, which involves manipulating the equations in the system to eliminate one variable at a time until a solution is found.

Let us suppose the numbers as x and y.

From the given statement the mathematical expression can be set as:

y = 2x - 8

x + y = 7

Now. substituting the value of y in equation we have:

x + (2x - 8) = 7

3x - 8 = 7

3x = 15

x = 5

Now, for x = 5 the value of y is:

y = 2(5) - 8

y = 2

Hence, the two numbers are x = 5 and y = 2.

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The complete question is:

The number y is 8 less than 2 times another number x, their sum is 7. Find the number.

The values of t for which the height of the ball is of 26 feet are given as follows:

t = 0.57 s and t = 2.18 s.

The quadratic function that models the height of the ball after t seconds is given as follows:

h(t) = -16t² + 44t + 6.

The height of the ball is of 26 feet when:

h(t) = 26

Hence:

-16t² + 44t + 6 = 26

16t² - 44t + 20 = 0.

The coefficients are given as follows:

a = 16, b = -44, c = 20.

Using a quadratic function calculator, the solutions to the quadratic equation are given as follows:

t = 0.57 s and t = 2.18 s.

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Answer:

142 ft square

Step-by-step explanation:

Face 1: 3(10)=30 ft square

Face 2: 4(10)=40 ft square

Front: 2(6)=12/2=6 ft square

Back: Same as front

bottom: 6(10)=60 ft square

Total: 30+40+6(2)+60=142 ft square

() means multiply in case don't know

The amount that Marcus will receive when he redeems the CD at the end of the 19 years, which is described as the compounded future value, is $37,255.14.

The future value is the present investment or value compounded at an interest rate.

The future value can be determined using the FV formula or an online finance calculator as follows:

N (# of periods) = 228 months (19 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $37,255.14

Total Interest: $28,255.14

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Using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².

The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics.

Formally speaking, the size of an object is the visible outcome of an ordering—of the class of objects to which it belongs.

The most frequent way to gauge an earthquake's size is through its magnitude.

It is a gauge for the magnitude of an earthquake's sole source.

As a result, it is the same regardless of how or where you view it, and the following computation can be made:

So, in the given situation we will be using the formula:

M = 2/3 log E/E₀

Where E is the power released in Joules and x, the minimal measure released by such an earthquake shall be allotted to.

Assuming 5.5, the same magnitude is given when the above equation is used:

M = 2/3 log E/E₀

5.5 = 2/3 log (E/10⁴°⁴)

8.5 = log (E/10⁴°⁴)

10⁸°⁵ = E/10⁴°⁴

E = 10⁴°⁴ * 10⁸°⁵

E = 4.5 * 10¹²

Therefore, using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².

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Correct question:

The magnitude, M, of an earthquake, is represented by the equation M=23logEE0 where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?

On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Let's use "x" to symbolise box A's weight. Then, we could type:

Given that box B weighs 5 kg more than box A, its weight is "x + 5".

Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".

We can write: Since we are aware that the combined weight of the three boxes is 51 kg:

[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]

Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:

17.67 kg (x + 5) is the estimated weight of Box B.

The approximate weight of Box C is 25.67 kg (x + 8).

Therefore, none of the answers to the question's assertions are true.

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The solution set is {(x, y) | x = y + 2}, which represents a straight line with a slope of 1 passing through the point (2, 0).

Therefore, the correct answer is option 2, infinite solutions.

Equations of the form ax2 + bx + c = 0, where a, b, and c are real numbers, and a 0, are known as polynomial equations in the variable x. Any equation that has the formula p(x) = 0, where p(x) is a polynomial of degree 2 with a single variable, is actually a quadratic equation.

The equation has the following form: ax2 + bx + c = 0, where x is the unknown variable and a, b, and c are constants, with "a" not equal to 0.

Numerous strategies, including factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations.

To solve the system of equations:

x - y = 2 ---(1)

-3x + 3y = -6 ---(2)

We can use the first equation to isolate x in terms of y:

x = y + 2

-3(y + 2) + 3y = -6

Simplifying the equation, we get:

-3y - 6 + 3y = -6

Solving for y, we get:

0 = 0

For all values of y this equation is true-

So,the equations has infinite solutions.

To find the solution set, we can substitute the value of y into the expression for x:

x = y + 2

x = y + 2, for all values of y

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Answer:

y^2 - 4

Step-by-step explanation:

We are given the statement,'The square of y decreased by the quotient of 28 and 7'. i.e. Subtracting the quotient 28/7 = 4 from y^2 . i.e. y^2 - 4

Hence, the expression which represents the given statement is y^2 - 4 .

A) The area of the walls is 700 ft²

B) The area of the doors, windows, and rectangular opening is 226ft²

C) The area that Kamrie will paint is 474 ft², and she will need to purchase 2 cans of paint.

Part A:

The area of each of the short walls is

10 ft x 15 ft

= 150 sq ft.

So, the total area of the four walls is:

2(200 sq ft) + 2(150 sq ft)

= 700 sq ft

Part B:

The area of the three windows along the long wall is

3 ft x 8 ft

= 24 sq ft each, so their total area is

3(24 sq ft)

= 72 sq ft

The area of the two windows along the short wall is also

3 ft x 8 ft = 24 sq ft each,

so their total area is

2(24 sq ft)

= 48 sq ft

The area of the rectangular opening along the other long wall =

7 ft x 8 ft = 56 sq ft.

So, the total area of the doors, windows, and rectangular opening is

72 sq ft + 48 sq ft + 56 sq ft

= 176 sq ft

Part C:

To determine the area that Kamrie will paint, we need to subtract the area of the doors, windows, and rectangular opening from the total area of the walls

700 sq ft - 176 sq ft

= 524 sq ft

To determine how many cans of paint Kamrie needs to buy, we divide the area to be painted by the coverage per can

524 sq ft ÷ 415 sq ft/can

≈ 1.26 cans

So Kamrie needs to buy at least 2 cans of paint to cover the entire living room.

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Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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Answer: To find the area of a triangle, we can use the formula:

Area = (base x height) / 2

However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.

To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:

s = (a + b + c) / 2

Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.

So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:

s = (94 + 188 + 168) / 2 = 250

Next, we can use Heron's formula to find the area of the triangle:

Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet

Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:

Cost = 7329.53 x $3 = $21,988.59

Therefore, the approximate cost of the triangular lot is $21,988.59.

Step-by-step explanation:

The average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.

Based on the survey results of 1500 adults, we can be 95% confident that the true mean number of hours worked in the previous week for the entire population of the country lies between 38.4 hours and 43.5 hours.

This means that if we were to repeat this survey multiple times, 95% of the time the sample mean would fall within this range. Therefore, we can conclude that the average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.

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Answer:

Step-by-step explanation:

The perimeter of a square is the sum of its sides and they are all equal, so to obtain the length of each of them we divide the perimeter of the first fence between 4:

[tex]\text{P1}= \dfrac{\text{64 feet}}{\text{4 sides}}[/tex]

[tex]\text{P1}= 16 \ \text{feet}[/tex]

Then, the length of each side of the second fence will increase 2 feet at each end, as shown in the figure. We have then that the perimeter of the second fence is:

[tex]\text{P2 = 20 feet} \times \text{4 sides}[/tex]

[tex]\text{P2 = 80 feet}[/tex]

The sum of the perimeters of both fences is:

[tex]\text{PT = P1 + P2}[/tex]

[tex]\text{PT = 64 feet + 80 feet}[/tex]

[tex]\text{PT = 144 feet}[/tex]

Total cost = $1.26 x 144 feet

Total cost = $181.44

The total cost of the fences was $181.44

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

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With this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

To solve this problem, we will need to find the time of flight and the horizontal velocity. We can use the following kinematic equations:

Vertical motion:

Maximum height: h = (v^2 * sin^2(angle)) / (2 * g)

Time of flight: t = 2 * v * sin(angle) / g

Horizontal motion:

Range: R = v * t * cos(angle)

Given:

Initial velocity (v) = 20 m/s

Angle = 45 degrees

Acceleration due to gravity (g) = 9.81 m/s²

Calculations:

Convert angle to radians: 45 degrees = 45 * (π/180) = 0.785 radians

Calculate time of flight: t = 2 * 20 * sin(0.785) / 9.81 = 2.04 seconds

Calculate horizontal range: R = 20 * 2.04 * cos(0.785) = 28.98 meters

So, with this strategy, the ball will travel approximately 28.98 meters horizontally before it hits the ground.

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A ball is thrown with an initial velocity of 20 meters per second at an angle of 45 degrees with respect to the horizontal. How far does the ball travel horizontally (range) before it hits the ground? Assume no air resistance.

The perimeter of the given shape in terms of pi is 22 cm + 25 pi cm.

The circumference of the rectangle is equal to the sum of the lengths of its four sides. It is simple to do this because there are two of each side length; all that is needed is to sum the length and width and multiply the result by two.

By multiplying half of the semicircle's circumference by the diameter's length, one can determine the semicircle's perimeter. Thus, the semicircle's perimeter is as follows:

Perimeter of semicircle = 6 cm + (1/2) x pi x 6 cm

Perimeter of semicircle = 6 cm + 3 pi cm

Each quarter circle has a perimeter that is just one-fourth of its circumference. Consequently, the 14 cm quarter circle's perimeter is as follows:

Perimeter of quarter circle with radius 14 cm = (1/4) x 2 pi x 14 cm

Perimeter of quarter circle with radius 14 cm = 7 pi cm

And, the perimeter of the quarter circle with radius 30 cm is:

Perimeter of quarter circle with radius 30 cm = (1/4) x 2pi x 30 cm

Perimeter of quarter circle with radius 30 cm = 15 pi cm

Therefore, the total perimeter of the given shape is:

Perimeter = Perimeter of semicircle + Perimeter of quarter circle with radius 14 cm + Perimeter of quarter circle with radius 30 cm

Perimeter = (6 cm + 3 pi cm) + (7 pi cm) + (15 pi cm)

Perimeter = 22 cm + 25 pi cm.

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