A right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. a right pyramid with square base has a base edge length of 24 feet and slant height of 20 feet. what is the height of the pyramid?

The general terms for the given arithmetic sequences are given as follows:

1. [tex]a_n = -2 -3(n - 1)[/tex]

2. [tex]a_n = 22 - 2(n - 1)[/tex]

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The general term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

For sequence 1, given by -2, -5, -8, -11, the first term and the common ratio are given as follows:

[tex]a_1 = -2, d = -3[/tex]

Hence the general term that defines sequence 1 is presented below:

[tex]a_n = -2 -3(n - 1)[/tex]

For sequence 2, represented by 22, 20, 18, 16, the first term and the common ratio are given as follows:

[tex]a_1 = 22, d = -2[/tex]

Hence the general term that defines sequence 2 is presented below:

[tex]a_n = 22 - 2(n - 1)[/tex]

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Answer: A

Step-by-step explanation:

We can rewrite the expression as

[tex]\frac{\log_{3} 3}{\log_{3} m}[/tex]

Using the change of base formula, we get [tex]\log_{m} 3\[/tex]

Answer:

C. 4≤x≤6

Step-by-step explanation:

First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.

Hope that helps! Have a fantastic day!

Answer:

D

Step-by-step explanation:

This function passes the vertical line test.

The vertical line test test is done by drawing a vertical line anywhere on the graph. If the line goes through two points or more then it isn't a function.

Answer:

The ribbon is 5m long.

The length of the piece = 3 ^ 4 / 5 m.

The length of the remaining piece.

We can simply solve this mathematical problem by using the following mathematical process.

First of all, we have to convert the length of the cut piece into simple decimal value.

Length of cut piece =3^ 4 / 5 = (3 * 5 + 4) / 5 = 19/5 = 3.8m

Length of the remaining ribbon = Intital length cut length = 5 - 3.8 = 1.2m = 12/10 - m = 6/5 * m = 1 1/5 m

Answer: 1 1/5

Step-by-step explanation:

5 - 3 = 2 - 4/5 = 1 1/5

Answer:

6%- 457 Million

Step-by-step explanation:

w=241(1.06)^11=457 million

The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word more will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

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The inequality that describes this graph is y ≥ x+5

From the given graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≥

Hence, the inequality that describes this graph is y ≥ x+5

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The pH of the solution is 12.2.

Molarity (kon) = No. of moles of FoH x 1000

Mckor, 7:12 × 10-4 moles x Looo 50.0 mL.

Volume of solution (m²), McKong = 1.424x102M, [on] =1.424×102M POH = -log [on] pOH =

-log [1.424x102] pon = 1.85.

pH + pOH = 14

PH = 14-pOH = 14-1.85 pH = 12.15.)

12.2.

pH is a measure of the concentration of hydrogen ions in water. Specifically, pH is the negative logarithm of the hydrogen ion (H+) concentration (mol/L) in an aqueous solution. pH = -log10(H+) This term indicates the basicity or acidity of a solution from 0 to 14 where pH 7 is neutral.

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(A) Algorithms are mathematical formulas placed in software that performs an analysis on a data set.

Therefore, (A) algorithms are mathematical formulas placed in software that performs an analysis on a data set.

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The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

6x - 5y = -8

6x - 5y = -8

Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8

6x - 5y = -8

- 6x - 5y = -8

----------------------

0 = 0

This in other words means that the difference between both equations is 0

When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions

Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

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Answer: The answer is D for those who don't like to read extra long expert answers (no offense to experts, just shorten answers to the direct answer pls)

Step-by-step explanation: Edge 2022

[tex]\displaystyle\\Answer:\theta=\frac{\pi }{2}+\pi n.[/tex]

Step-by-step explanation:

[tex]\displaystyle\\7*cosec^2\theta-9*cot^2\theta=7\\7-7*cosec^2\theta+9*cot^2\theta=0\\7-\frac{7}{sin^2\theta}+9*\frac{cos^2\theta}{sin^2\theta} } =0\\\frac{7*sin^2\theta-7+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*(1-sin^2\theta)+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*cos^2\theta+9*cos^2\theta}{sin^2\theta} =0\\\frac{2*cos^2\theta}{sin^2\theta}=0\\[/tex]

[tex]2*cot^2\theta=0\\Divide\ the\ right\ and\ initial\ parts\ by\ 2:\\cot^2\theta=0\\cot\theta=0\\\theta=\frac{\pi }{2}+\pi n\ \ \ (n=0,\ 1,\ 2,\ 3\ ...).[/tex]

The graph which represents Charlies distance from her car at different times is indicated as attached. The schedule of her movement is also attached.  This type of graph is called Distance Time Graph.

A distance-time graph can show the distance traveled while an item moves in a straight line.

The gradient of the line in a distance-time graph is equal to the object's speed. The item is travelling more quickly the steeper the line and the larger the gradient.

See the attached for Charlies Distance - Time movements visualized in a graph.

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Step-by-step explanation:

Given,

s=5

t=8

solution,

= 3st² - s²

= 3*5*8² - 5²

= 3*5*64 - 25

= 960 - 25

= 935

The median of this box and whisker plot is 73

A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.

From the given data, following can be inferred

which is demonstrated in the box and whisker plot below

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Answer: GET BRAINLY PLUS FOR VERIFIED ANSWERS NOW

Step-by-step explanation:

NOW

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.

Quadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.

From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.

For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown

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Answer:

680

Step-by-step explanation:

x = total number

.6x  = bus riders = 408              (.6 is decimal for 60%)

.6x = 408

x = 408/.6 = 680

With the aid of the attached diagrams in the question, we have;

1- Linear relation

2- W = 8•P + 80

3- Please find attached the graph created using a graphing calculator.

4- a) The initial value is the mass of the vase

b) The slope is the mass of each pebble

5- The initial value is lesser than 80

6- 1.2 kilograms

7- 53 pebbles

8- a)

b) (0, 80)

c) The masses are the same

9- Trapezoid area, A = 14•x² - 4•x

10- Tanya and Leah are 18 and 6 years old respectively

1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.

From the table we have;

The relationship between the x and y-values in the table is therefore;

2. The slope, m, of the linear function is found as follows;

m = (360 - 280)/(30 - 20) = 8

The equation is therefore;

W - 360 = 8•(P - 30)

W = 8•P - 240 + 360 = 8•P + 80

3. Please find attached the graph drawn with a graphing calculator.

4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.

Therefore;

y = 8×0 + 80 = 80

a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases

b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble

5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.

6- The weight, W, of 112 pebbles is therefore;

W = 10 × 112 + 80 = 1,200

7- 504 = 8•P + 80

Which gives;

504 - 80 = 8•P

P = 424 ÷ 8 = 53

8- Wilma's equation is; W = 10•P + 80

a) Please find the second graph showing the graphs of the two equations combined.

b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80

2•P = 0

P = 0

Therefore, at the point of intersection, W = 80

The coordinates of the point of intersection is therefore;

c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.

9. The area of the trapezoid, A, can be expressed as follows;

A = 4•x × ((2•x + 5)+(5•x - 7))/2

A = 2•x × (7•x - 2) = 14•x² - 4•x

10. Let T represent Tanya's age now and let L represent Leah's current age, we have;

T = L + 12

T - 3 = (L - 3) × 5

Solving gives;

L + 12 - 3 = (L - 3) × 5 (Substitution property)

L + 9 = 5•L - 15

4•L = 9 + 15 = 24

L = 24 ÷ 4 = 6

T = L + 12

Therefore;

T = 6 + 12 = 18

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Step-by-step explanation:

it is a line, so that is 1 point, where it cuts the x-axis.

in general that means y = 0.

so,

0 = 4x - 3

4x = 3

x = 3/4

the point, where the line cuts the x-axis is

(3/4, 0)

If the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.

Given that the value of determinant a is 3, determinant b is 5.

We are required to find the value of determinant ab.

Determinant of a matrix is the scalar value computed for a given square matrix.It means the matrix which is not square does not have a determinant value.  It is denoted by IAI.

We know that,

IaI*IbI=IabI

So we have to just put the values in the above formula to get the determinant of ab.

IabI=3*5

=15

Hence if the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.

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Answer:

Step-by-step explanation: The earth rotates 34 km every 32 seconds. We can simplify this by dividing both sides by 32. Now, we have 34/32 km every 32 seconds. Now, to further simplify this, we need to convert 34/32 to a mixed number 34/32 = 1 2/32 which then can be simplified to 1 1/16. So, near the equator, the speed of Earth's rotation is 1 1/16 km per second.

The volume of the cylinder and the cone is equal

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where

r is the radius

h is the height

For the cylinder

r = 8/2 = 4 in

h = 5

Substitute

V = π(4)²*5
V = 80π cubic inches

For the cone

r = 4 in

h = 15in

Substitute

V = 1/3πr^2h

V = 1/3(π)(4)^2 * 15

V = 80π cubic inches

Hence the volume of the cylinder and the cone is equal

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The Area of the kite with the given diagonals is: 125 square meters.

A kite can be described as a quadrilateral having four (4) sides, which can be categorized into two pairs of congruent sides, each of them is adjacent to the other. A kite has two diagonals that intersect, where by the longer diagonal divides the smaller diagonal into equal halves.

An example of a kite is shown in the image attached below, where:

JL and KM are the diagonals of the kite.

The formula for finding the area of a kite is given as:

Area = 1/2 × (product of the lengths of the diagonals)

Given the following:

Length of diagonal 1 = 10 meters

length of diagonal 2 = 25 meters

Area = 1/2 × (product of the lengths of the diagonals) = 1/2 × (10 × 25)

Area of kite = 1/2 × (250)

Area of kite = 1/2 × (250)

Area of kite = 125 square meters.

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The cost of one yard of black fabric is $4.

The cost of one yard of red fabric is $5.

2r + b = 14 equation 1

2r + 4b = 26 equation 2

Where:

r = cost of one yard of red fabric

b = cost of one yard of black fabric

Subtract equation 1 from equation 2

3b = 12

b = 12 / 3

b = 4

Substitute for b in equation 1

2r + 4 = 14

2r = 14 - 4

2r = 10

r = 10 / 2

r = $5

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Answer:

See below

Step-by-step explanation:

REMEMBER  sec = 1/cos ...so the left side is

[1/cos -1]   /  [1/cos  +1 ]    

  get common denominator for numerator and denominator

[ (1 -cos) /cos  ]  /  [ (1+cos) / cos ]    

 now flip the bottom fraction and multiply to get

[(1-cos/cos) ]  *  [ cos / (1+cos) ]    which simplifies to   ( the 'cos' term cancels)

(1-cos) / (1+cos)              done !

The 32° measure of arc CB, and m<BCD which is 52° gives m<BAC and m<ACB as 16° and 90° respectively, from which we have;

First part;

Given;

Angle subtended by arc CB = 32°

m<BCD = 52°

Based on circle theory, we have;

Therefore;

Arc CB = 2 × m<BAC

Which gives;

Arc CB = 32° = 2 × m<BAC

m<BAC = 32° ÷ 2 = 16°

Angle subtended by the diameter at the circumference is 90°.

Therefore;

m<ACB = 90°

In triangle ∆ABC, we have;

m<ACB + m<BAC + m<CBA = 180°

m<CBA = 180° - (m<ACB + m<BAC)

Therefore;

m<CBA = 180° - (90° + 16°)

m<CBA = 180° - (90° + 16°) = 74°

Second part;

The arc subtending m<ACD is AB which is also the diameter.

Angle formed by the diameter, which is a straight line = 180°

Therefore;

Angle subtended at the center by arc AB = 180°

Angle subtended at the circumference, m<ACB is therefore;

m<ACB = 180° ÷ 2 = 90°

A

m<ACB = m<ACD + m<BCD (Angle addition property)

Therefore;

90° = m<ACD + 52°

m<ACD = 90° - 52° = 38°

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