Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid? Question 4 options: A) Cutting off one of the bottom corners B) A cut parallel to the vertical axis, directly through the vertical axis C) A cross section cut parallel with the bottom D) A cut parallel to the vertical axis, but off the vertical axis

The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)

Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.

we have given a polynomial,

(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)

Take LHS

⇒  (x-1/x)(x^4/3+x^2/3)

⇒  (x^2-1/x)×(x^4 + x^2/3)

⇒  (x^2-1/x) x^2(x^2+1/3)

⇒  x^2/3x (x^2-1)(x^2+1)

⇒​x^2/3x(x^4-1)                                  ∴(a^2-b^2 = (a+b)(a-b))

multiply numerator and denominator by x

⇒x^3/3 (x^4-1/x^2)

⇒x^3/3(x^2- 1/x^2) = RHS

Hence, given problem has solved.

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The future value of the annuity investment is expressed in option A

The future value formula is used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).

The formula can be expressed as

FV = [MP(1 + r/n)^nt - 1] / [r/n]

We can substitute the values into the equation;

FV = 250[(1 + 0.062/12)^12 * 30] / 0.062 /12

The answer to this question is option A

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The equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

Damian bought a new game station for $774 using the stores zero interest finance plan. He will pay $43 a month for 18 months.

We can represent the equation he can use to found out how much money he still owes using a straight line as follows -

y = 774 - 43x

y = - 43x + 774              [x] is the number of month

Therefore, the equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

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Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

A semicircle has 1 line of symmetry.

Step-by-step explanation:

Answer: an=4n+5

Step-by-step explanation:

a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...

A formula for the nth term of the arithmetic sequence:

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

where: a₁ - is the first term of the arithmetic sequence

            d - is the difference between the terms of the arithmetic sequence

d=a₂-a₁=a₃-a₂=a₄-a₃= ...

d=13-9=17-13=31-17= ...

d=4

             n - is the number of the arithmetic sequence term

[tex]a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5[/tex]

Step-by-step explanation:

Square has perimeter 4a because every side is equal,

so :

if a=√8 , then 4a = 4*√8 or 11.313708499

and the number is rational

Eve's data is a random sampling since she picked the participants randomly.

A simple random sample is a subset of a population chosen at random. This sampling strategy gives each person of the population an exact equal chance of being chosen, reducing the likelihood of selection bias.

To be considered a truly random sample, every subject in your target demographic must have an equal chance of being chosen. Conducting a study to estimate the length of time college students workout at your campus each week is an example of breaking this assumption.

In this case, Eve needed to collect the eye color of 50 random people for a high school statistics project and she felt more comfortable collecting the data from 20 arbitrary classmates, 12 arbitrary neighbors, and 18 arbitrary members of her bible study group. In this case, she picked them randomly. In Adam's case, it doesn't necessarily have to be strangers.

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Answer:

whats the problem

Step-by-step explanation:

Lois’ pay before the tax had been deducted is £660.

Given:

Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers.

22% = 514.80

divide by 22 on both sides

22%/22 = 514.80/22

1%= 23.4

= 514.8/0.78

= 5148/10/78/100

= 5148*100/10*78

= 66*100/10

= 66*10

= £660.

Therefore Lois’ pay before the tax had been deducted is £660.

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Answer:

A square is an sqaure.

Step-by-step explanation:

circle is a circle. :) happy to help

Line AD and line EG are parallel line, Transversal CH < ABC and EFH  are same side exterior angles

The presence of two parallel lines and a transversal line leads to some important theorem used in geometry

Some of the theorems include

The exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include

The exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.

The question is asking  of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are

Hence < EFH and < ABC are same side exterior angles

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The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

According to the question,

We have the following information:

The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.

We will find the 13.6% of 42,000 to find the decrease in the price of the next model:

(13.6*42000)/100

$5712

Now, the price of next model will be:

42000-5712

$36288

Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.

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Answer:

Your question is missing some parts

and the degree seems off is it 90⁰

As per the system of linear equations concept, the solution of x is -1.282

Linear equations:

Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given,

Here we have the equations -4x - 1 = 5ˣ + 4

Now, we need to find the value of x by using the graph.

In order to plot the graph for the given linear equation,

First, we have to split the equation into two,

Like the following:

y = -4x - 1

y = 5ˣ + 4

Now, we plot the graph of both equations

Then we get the graph like the following.

Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.

While we looking into the graph, we have identified the solution is,

x = -1.282

Therefore, the solution of x is -1.282

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Answer:

Evaluating the function [tex]f(x)=2x^2[/tex] for the first five positive integers of [tex]x[/tex]:

[tex]f(1)=2(1)^2=2(1)=2[/tex]

[tex]f(2)=2(2)^2=2(4)=8[/tex]

[tex]f(3)=2(3)^2=2(9)=18[/tex]

[tex]f(4)=2(4)^2=2(16)=32[/tex]

[tex]f(5)=2(5)^2=2(25)=50[/tex]

The answer of the given multiplication is 19.2, 1.7, 15.93 and 0.0512 respectively.

To find the answer, we will simply multiply the given numbers.

i) 3.2 × 6 = 19.2

ii) 8.5 × 0.2 = 1.7

iii) 2.7 × 5.9 = 15.93

iv) 0.32 × 0.16 = 0.0512

Hence, the answers is 19.2, 1.7, 15.93 and 0.0512 respectively.

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The value of x in the given triangle is x = -8  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of first angle is 51°

the measure of second angle is 83°

the measure of third angle is (x + 54)°

So , By Angle sum property ,

we get

first angle [tex]+[/tex] second angle [tex]+[/tex] third angle [tex]=[/tex] 180°

substituting the values of angles

we get

51° +  83° + (x + 54)° = 180°

134 + x + 54 = 180

188 + x = 180

x = 180 - 188

x = -8

Therefore , the value of x in the triangle is -8  .

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The cost of each ticket of the amusement park is $15.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two student groups went to an amusement park on the same day.

Group 1 bought 9 tickets and received a $120 discount.

Group 2 bought 3 tickets and received a $30 discount.

Let x be the amount of one ticket and y be the total amount.

According to the question:

We have system of equation,

y = 9x - 120    equation1

y = 3x - 30    equation 2

Subtract the equation 2 to equation 1.

So, 6x = 90

x = 15

Therefore,  $15 is the cost of each ticket.

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The cost of the sales tax in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The sales tax percentage in Texas = 5 %

                                                          = 5 / 100

                                                          = 0.05

The cost of 1 bag of dog food in Houston = $ 52

Now ,

The sales tax cost is calculated by the equation ,

The sales tax cost =
Sales tax percentage in Texas x cost of 1 bag of dog food in Houston

The sales tax cost = $ 52 x 0.05

                              = $ 2.60

And , the total cost of 1 bag of dog food = cost of 1 bag of dog food in Houston + sales tax cost

Total cost of 1 bag of dog food = $ 52 + $ 2.60

                                                   = $ 54.60

Therefore , the sales tax cost is $ 2.60

Hence , the sales tax cost to pay in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

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Answer: 2 Adult 3 Kid

Step-by-step explanation:

5.10 x 2 = 10.2

3.60 x 3 = 10.8

10.8 + 10.2 = 21

The value of f after solving the expression, 2-f/4 = f-3f/4+3, is -2.

According to the question,

We have the following expression:

2-f/4 = f-3f/4+3

We know that to find the value of f we will have to move the terms with the same variable on one side. Now, moving f and 3f/4 from the right hand side to the left hand side will result in the change of their signs.

3f/4-f/4-f +2 = 3

Moving 2 from the left hand side to the right hand side:

3f/4-f/4-f = 3-2

Taking the least common factor as 4:

(3f-f-4f)/4 = 1

(-2f)/4 = 1

Using the cross multiplication method:

-2f = 4

f = -4/2

f = -2

Hence, the value of f for the given expression is -2.

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The solution of the linear equation:

3x+4x+5x=4(x+2)

is x = 1

Here we need to solve the following linear equation:

3x + 4x + 5x = 4*(x + 2)

First, we should expand the right side to get:

3x + 4x + 5x = 4x + 8

Now we group like terms:

3x + 4x + 5x - 4x = 8

Taking x as a common factor in the left side:

(3 + 4 + 5 - 4)*x = 8

(3 + 5)*x = 8

8x = 8

x = 8/8

x = 1

The solution is x = 1.

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Answer: A

Step-by-step explanation:

The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.

The trigonometric ratios for angle A are measured below.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a right angled triangle as shown in the image attached.

The six trigonometric ratios are -

sin (A) = 10/√116

cos (A) = 4/√116

tan (A) = 10/4

cosec (A) = √116/10

sec (A) = √116/4

cot (A) = 4/10

Therefore, the trigonometric ratios for angle A are measured above.

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The valid equations are written below. Then the correct options are C, D, and E.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The sum of the two interior angles is equal to the exterior angle of the third angle.

The sum of the supplementary angle will be 180°.

From the diagram, the equations are written as,

m∠5 + m∠6 = 180°               (Supplementary angle)

m∠2 + m∠3 = m∠6              (Exterior angle)

m∠2 + m∠3 + m∠5 = 180°   (Angle sum of triangle)

Then the correct options are C, D, and E.

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The complete question is attached below.