A student constructs a regular square pyramid with a base that has sides of 13. 2 cm and a

slant height of 6 cm. Find the surface area of the pyramid. Find the surface are of the pyramid

The answer choice which represents a number line for the intersection of the given intervals is; (4, ∞).

The answer choice which represents a number line for the union of the given intervals is; (-3, ∞).

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-3, ∞) and (4, ∞)

It follows that the intersection of both intervals is the interval; (4, ∞).

Also, the interval which represents the union of both intervals is; (-3, ∞).

Hence, the image which represents both scenarios is attached.

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Geometrically there are 16 different routes from A to B that use each road exactly once.

What is geometry?

The area of mathematics known as geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. Geometry comes from the Ancient Greek terms "geo" and "metron," which both imply "measuring."

Keep in mind that cities C and E can be excluded from the count of paths because there is only one road that can lead out of either city if a path enters it. The geometric diagram is shown below.

Now move on to the casework. It's important to keep in mind that there are two routes from A to D, D to A, B to D, and D to B.

Case 1: A⇒D: If the path from D leads back to A, the subsequent path must go to B⇒D⇒B. The path ADABDB has 2×1×2=4 possible outcomes. The path must continue with either BDAB or BADB if it leads from B to D. There are 8 possibilities as 2×2×2=8. Therefore, there are 4+8=12 potential outcomes in this scenario.

Case 2: A⇒B: BDADB must be the next step on the path. There are 2×2=4 options in this situation.

Combining the two situations results in 12+4=16.

Therefore, there are 16 different routes.

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The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.

To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.

It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.

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The value of a is -1 When we put the value of x as zero all the terms which include x become zero then only constant terms are remaining.

The given question is in the form of an equation.

let's try to understand what is an equation.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance,

the equation 4x + 56 = 14 consists of the two equations 4x + 56 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

There are so many types of equations present linear equations, quadratic equations, and cubic equations.

According to the degree of the equation so many different types of equations.

2x^2 + x -a + 4  = 5 put x = 0.

2*0 + 0 - a + 4  = 5

-a + 4 = 5

-a = 5 - 4

-a  = 1

a  = -1.

So the value of a is -1.

Given Question is incomplete complete question here

What should be the value of a if the value of  2x^2 + x -a + 4  equals to  5 when x =0.

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1. The area of two concentric circles with radii 28 cm and 18 cm is 460π cm^2.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle is 2 units.

What are concentric circles?

Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words.

The radii of two concentric circles are 28 cm and 18 cm.

The bigger circle has a radius of r1=28 cm and the smaller circle has the radius of r2=18 cm.

Area of two concentric circles is -

A = π[(r1)^2-(r2)^2]

A = π[(28)^2-(18)^2]

A = π[(28+18)(28-18)]

A = π[46 × 10]

A = 460π cm^2

Therefore, the area of concentric circle is 460π cm^2.

The formula for perimeter of the circle is 2πr, and the formula for the area of the circle is πr^2, where r is the radius of the circle.

Now, according to the data given the perimeter and area of the two circles are equal.

So, the equation will be 2πr = πr^2.

2πr = πr^2

2π = πr

r = 2 units

Therefore, the radius is 2 units.

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1. If radii of two concentric circle are 28 cm and 18 cm respectively. Find the area of the concentric circles.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle​.

Answer:

25

Step-by-step explanation:

By the Pythagorean Theorem, the sum of the squares of the leg lengths is equal to the square of the hypotenuse:

[tex]a^2+b^2=c^2\\20^2+15^2=c^2\\400+225=c^2\\625=c^2\\25=c[/tex]

Hence, the hypotenuse has a length of 25

Answer:

Step-by-step explanation:

2

Diana's savings will be 280 dollars after four weeks.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

300 - 5x

Where x represents the number of the week.

We have to determine Diana's savings after four weeks

As per the question, we have

⇒ 300 - 5x

Substitute the value of x = 4 in the above expression

⇒ 300 - 5(4)

⇒ 300 - 20

⇒ 280

This means her savings will be 280 dollars after four weeks.

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The question seems to be incomplete the correct question would be:

Diana's savings at the end of each week can be described by the expression 300-5x where x represents the number of the week.

What is her savings after four weeks?

No, 8, 15, 17 are not Pythagorean triples.

No, 8 15 17 are not Pythagorean triples. A Pythagorean triple is a set of three positive integers a, b, and c such that a2 + b2 = c2. In other words, the sum of the squares of two integers must equal the square of the third integer.

In the case of 8 15 17, if we calculate the sum of the squares of the two smaller integers, 8 and 15, we get

[tex]8^2 + 15^2 = 64 + 225 = 289[/tex].

This does not equal the square of the third integer,

[tex]17^2 = 289,[/tex]

so 8 15 17 are not Pythagorean triples.

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Answer:

$22

Step-by-step explanation:

27.50 20 present off so you get 5.5 substract and u get 22

4366 softballs will fit inside of a storage.

What is volume ?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Diameter of softball = 8.3 in

Radius of softball = 4.15 in

                              = 0.345 ft

Volume of sphere = 4/3 π r³

                = 4/3 π (0.345)³

                = 4/3 * 0.1289

                = 0.1718

Volume of cuboid = l * b * h

                              = 15 * 10 * 5

                              = 750

Number of softballs that can fit inside the storage = 750 / 0.1718

                                                                      = 4366

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Señor Ochoa draws the perimeter of the garden with actual length of the vertical and horizontal legs of his triangular garden 3 meters as 6cm in his initial drawing with 18.5cm third side. Then new drawing with the vertical and horizontal legs of 18 cm

A scale drawing is a representation of an object or space that is reduced or enlarged in proportion to the actual size. To make a new scale drawing of Señor Ochoa's garden with the new dimensions of 18 centimeters for the vertical and horizontal legs of the triangle, you would need to apply a scale factor of 18/6 = 3 to the original drawing.

So, you would multiply each original dimension by 3 to get the new dimensions for the scale drawing.

The new scale drawing would be:

6cm × 3 = 18cm

6cm × 3 = 18cm

8.5cm × 3 = 25.5cm

The new scale is

= scale dimension/ original dimension

= 18cm/ 3m

= 18cm/ 300cm

= 3/ 50

It is also worth noting that as you are changing the scale, the measurement of the hypotenuse of the triangle would be affected, which is the square root of 3 meters, that would be approximately 25.5cm, which is the same as the original measurement on the original drawing.

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Step-by-step explanation:

x^4-9x^2-8x^2+72

x^2(x^2-9)-8(x^2-9)

(x^2-8)(x^2-9)

(x^2-8)(x+3)(x-3)

Answer:

Step-by-step explanation:

A 30-60-90 triangle is a right triangle where the three interior angles are 30°, 60°, and 90°.

Let, the shorter leg of a 30 60 90 triangle is equal to a. Then:

If we know the shorter leg length, we can find out that:

In the 30 60 90 triangles :

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The formula for vector direction is: Direction = arctan (y/x) , Where x is the x component of the vector and y is the y component of the vector.

1. Find the x and y components of the vector

2. Divide the y component by the x component

3. Calculate the arctan (inverse tangent) of the result

4. The result is the direction of the vector in radians (or degrees if you prefer).

If you want to convert the result from radians to degrees, you can use the following formula:

(in degrees) = arctan (y/x) * (180/π)

Where π (pi) is approximately equal to 3.14.

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The expressions that represent this week's price of gasoline per gallon =g+0.05g.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Here, we have,

the price of a gallon of gasoline was `g` dollars.

the price of gasoline per gallon increased by `5%`.

So, the expressions that represent this week's price of gasoline per gallon

=g + g*5%

=g+0.05g

Hence, the expressions that represent this week's price of gasoline per gallon =g+0.05g.

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The Equation of line F is y= -9/2x  + 59/2.

The Equation of line G  is y = 1/10 x .

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

For Line F:

slope = -9 /2

and, Equation of line F as

y - (-2) = -9/2 (x -(7))

y + 2= -9/2( x- 7)

y = -9/2x + 63/2 -2

y= -9/2x  + 59/2

For Line G:

Slope = (0 -(1))/ ( 0-(10))

slope = 1/10

and, Equation of line G as

y - (1) = 1/10 (x -10)

y-1 = 1/10 x - 1

y = 1/10 x

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Answer:

44

Step-by-step explanation:

If there are 22 people running and they each want two energy drinks, then Jerome needs to make 44 cups. 22 times 2 is 44

Answer:

Step-by-step explanation:

from the graph we konw the ∠ABD=∠DBC, because ∠DBC=20, so ∠ABD=20

The number of concrete masonry units needed to construct a foundation wall is 102.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, a foundation wall 104" high with a 120" perimeter.

Since, perimeter of square =  4 * side

120 = 4 * side

side  = 30"

Hence area of the foundation wall = side²

area of the foundation wall = 30² = 900

volume of the foundation wall  = area * height

the volume of the foundation wall  = 104 * 900 = 93,600"

The volume of the concrete masonry whose length, width, and depth are 16, 8, and 8 respectively is

Volume of masonry = 8 * 8 * 16

The volume of masonry = 1024

since 10 % of masonry goes to waste.

Thus the effective volume of the masonry  = 1024*0.9 = 921.6

total masonry required = 93600/ 921.6 = 101.56

therefore, To build a foundation wall, 102 concrete masonry units are required.

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The probability of picking a yellow sweet tart three times in a row is 0

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here, There are  4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts. P(yellow ball three times in a row) = 2/12 ×1/11 ×0/10

                                                                             = 0

Hence, The probability of picking a yellow sweet tart three times in a row is 0

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Answer:

Step-by-step explanation:

The ratio of the volume of the pyramid to the volume of the prism is 1.so, the option A. is correct.

Let the base of  the base of a prism is b and the height of the prism is h.

so, the volume of the prism-

                                    V= [tex]b^{2}[/tex] h

also, given that base of the given pyramid is also b and the height of the pyramid is three times the height of the prism.

                                     h'=3h

so, the volume of the square pyramid-

                                    V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex]h'

                                    V'=[tex]\frac{1}{3}[/tex][tex]b^{2}[/tex](3h)

                                    V'=[tex]b^{2}[/tex]h

so, now-

                                  [tex]\frac{V'}{V}[/tex]=[tex]\frac{b^{2}h }{b^{2}h }[/tex]

                                   [tex]\frac{V'}{V}[/tex]= 1

  so. the ratio of the volume of the pyramid to the volume of the prism is 1.                                

The value of AB after solving the triangle is 10√3.

Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,

We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that

We can then square both sides of this equation to get

Since we know that BC/AB = 3/4, we can substitute this value into the equation

AB^2 = 100 + BC^2 to get

AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.

Solving this equation for AB, we get AB = 10√3

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Answer:

x = 4, y = 12

Step-by-step explanation:

xy = -16

y = x + 8

substitute y = x + 8 into xy = -16

x(x + 8) = -16

x^2 +8x + 16 = 0

x = 4

sub x = 4 into y = x + 8

y = 4 + 8

y = 12

Explain how the Distributive Property can be used to solve the equation 3(x+4)=36. Multiply the first term in the parentheses by 3, then add 3 to the second term in the parentheses. Then solve the equation using inverse operations.

Answer:

ITS 64 degrees

Step-by-step explanation:

Answer:

116

Step-by-step explanation:

hope this helps:)..........

The triangles can be proved congruent by SAS theorem.

Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.

To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.

Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;

Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.

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If the freight elevator lifts goods the same height in 2 minutes and 30 seconds, it will travel at a pace of 6.4 feet per second.

Speed is the pace at which an item moves along a route in time, whereas velocity is the rate and direction of movement. In other words, velocity is a vector, whereas speed is a scalar number. The sign for speed is v (italic), whereas the symbol for velocity is v. (boldface). A bar is placed over the symbol to represent average values. Speed is defined as the rate at which distance changes over time. It has a distance by time dimension. Thus, the SI unit of speed is defined as a combination of the fundamental units of distance and time. As a result, the SI unit of speed is the metre per second.

Here,

Given that a passenger elevator in the sears tower in Chicago can lift people 960 feet in 1 minute and 30 seconds (1.5 minutes). This means that the lift is travelling with a speed of:

=960/1.5

=640 ft/min

If the elevator lifts cargo through the same height in 2 minutes and 30 seconds (2.5 minutes), then the speed is given by:

=640/2.5

=384 ft/min

=384/60

=6.4 ft/second

The freight elevator be traveling at the speed of 6.4 ft/second if it lifts cargo the same height but in 2 minutes and 30 seconds.

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