A word problem made out of the equation 1/4+3-7/8x<-2

Answer:

Step-by-step explanation:

Simplifying

px + 5 = -4x + q

Reorder the terms:

5 + px = -4x + q

Reorder the terms:

5 + px = q + -4x

Solving

5 + px = q + -4x

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-5' to each side of the equation.

5 + -5 + px = q + -5 + -4x

Combine like terms: 5 + -5 = 0

0 + px = q + -5 + -4x

px = q + -5 + -4x

Reorder the terms:

px = -5 + q + -4x

Divide each side by 'x'.

p = -5x-1 + qx-1 + -4

Simplifying

p = -5x-1 + qx-1 + -4

Reorder the terms:

p = -4 + qx-1 + -5x-1

The equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser.

Consider that Kevin has p people sponsoring him, Mika has one more than Kevin, and Cheryl has one more than Mika.

Kevin = p

MIka = m

Cheryl = c

Then m = 1 + p

c = 1 + m

Or

m = c - 1

Now solve both equation;

m = 1 + p = c - 1

p = c - 1 -1

p = c + 2

p = m -1

p = c + 2

Then m - 1 = c + 2

m = c + 3

Hence, the equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.

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so the domain is

Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph. Therefore, the graph for the given equation is plotted below.

The given equation is 4x + 5y = -40.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Put x=0, 1, 2, 3, 4, 5,.....in the given equation and solve for y

When x=0, 4(0)+5y=-40

⇒ 5y=-40

⇒ y=-8

When x=1, 4(1)+5y=-40

⇒ 5y=-44

⇒ y=-8.8

When x=2, 4(2)+5y=-40

⇒ 5y=-48

⇒ y=-9.6

Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph

Therefore, the graph for the given equation is plotted below.

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The factorial expression 26! has a value of 4.032914600e+26

The expression is given as

26!

The above expression is a factorial expression

And the factorial of a number n where n >= 0 and n is not a decimal number is calculated using

n! = n x (n - 1) x (n - 2) x ..... x 1

This means that

n = 26

So, we have

26! = 26 x 25 x 24 x  23 x ..... x 1

Evaluate the products

26! = 4.0329146e+26

Approximate

26! = 4.032914600e+26

Hence, the value of the expression is 4.032914600e+26

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If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.

Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:

The monthly rent m is given by:

The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:

Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700

The monthly revenue with this monthly rent is:

Answer: 4p^3(7p^2q^3+6

Step-by-step explanation: Im pretty sure.

Step 1:

What are congruences?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Step 2:

JH is congruent to HI

Final answer

JH is congruent to HI

There is no shortage of units in this market with a $5 price ceiling and the size of shortage is 0 units.

Given: On this market, the government imposes a $5 price ceiling.

We need to find the size of the shortage in this market.

From the given table, we can see that the quantity demanded for $5 price ceiling is 4 units and the quantity supplied is 8 units.

So, the demand is satisfied and an extra 4 units are also provided.

Therefore, there is no shortage of units in this market a $5 price ceiling and the size of shortage = 0 units.

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Answer:

13x + 7x = 180 (corresponding angles, sum of adjacent angles on a straight line=180)

20x = 180

x = 9

Substitute x into angle measures to find values.

13x° = 13(9)

= 117°

7x° = 7(9)

= 63°

Step-by-step explanation:

Consider the Cartesian equation,

2

x+3

=

4

y−5

=

2

z+6

Now,

a

=−3

i

+5

j

−6

k

b

=2

i

+4

j

+2

k

Vector equation,

r

=

a

+λ.

b

=−3

i

+5

j

−6

k

+λ(2

i

+4

j

+2

k

)

This is the required equation

The simplification of the given expression would be; 4x/7 + 2y /7 + 5.

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given an expression as  5/7 x + 2/7 y − 2 − 1/7 x + 7

Thus,

5/7 x + 2/7 y − 2 − 1/7 x + 7

Combine the like terms first;

5/7 x  − 1/7 x + 2/7 y − 2+ 7

Then solve the like terms;

(5 -1)x/7 + 2y /7 + 5

4x/7 + 2y /7 + 5

Therefore, the simplification of the given expression would be; 4x/7 + 2y /7 + 5.

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Cartesian coordinates are- 4.2426

The horizontal component of the Cartesian coordinate system is denoted by the letter x, whereas the vertical component is denoted by the letter y. In this coordinate system, equations for lines will need to include both the x and y variables.

Given

(r,θ) = (6,π/4)

x= r cosθ =6 x cos(π/4)
= 6√2 = 3√2

≈  4.2426

y= r sinθ = 6 x sin(π/4)

= 6√2 = 3√2

≈ 4.2426

Hence the answer is 4.2426

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The solution to the system of equations in problem 13 is (0, -4).

The solution to the system of equations in problem 14 is (-6, -1).

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Given:

(2x+5) is one of the factor.

By taking the factors equal to zero then we get the values of x.

Therefore, the zeros of the polynomial are

Answer: you cant but here are some ways to practice:)

Find the greatest common divisor of both the numerator and the denominator. This can be done either with prime factor trees or another method.

Divide both the numerator and the denominator with the greatest common divisor.

The result is a simplified fraction. hope this helps and sorry.

The equation of the parabola for the given points is y = -3x² + 7x + 1

Equation of the parabola

The standard form of the equation of a parabola is expressed as

y = f(x) = ax² + bx + c

where a, b, and c are constants and a ≠ 0.

Given,

Here we have the points (0, 1), (1, 5), (2, 3).

Now, we have to find the equation of the parabola.

Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.

In order to find the values of a, b and c we need to formulate three equations using the three given points.

Since for the three unknowns a, b, and c, we will require three equations.

For that we have to take the Point (0,1) i.e. x = 0 and y = 1

Substituting the values of x and y in the standard parabola equation, then we get,

1 = a(0)² + b(0) + c

1 = 0 +  0 + c

c = 1 -------------------(1)

Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5

Substituting the values of x and y in the standard parabola equation, then we get,

5 = a(1)² + b(1) + c

5 = a +  b + c

It can be written as,

a + b + c = 5 -----------------------------(2)

Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3

Substituting the values of x and y in the standard parabola equation, then we get,

3 = a(2)² + b(2) + c

3 = 4a +  2b + c

It can be written as,

4a + 2b + c = 3 -----------------------------(2)

Apply the value of c as 1 in equation (2), then we get,

a + b + 1 = 5

a + b = 4 ---------------------(4)

Similarly, apply the value of c on the equation (3), then we get,

4a + 2b + 1 = 3

4a + 2b = 2

Divide the equation by 2 on both sides, then we get,

2a + b = 1 --------------------(5)

Subtract equation (5) from equation (4),

(2a - a) +(b - b) = 1 - 4

a = -3

Apply the value of a in the equation (4) to get the value of b,

(-3) + b = 4

b = 7

Therefore, the equation of the parabola is

y = -3x² + 7x + 1

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The data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.

Any data, including numbers, alphabets, amounts, lengths, etc., are arranged in descending order from highest to lowest.

In other terms, anything is considered to be in descending order when it is arranged from a higher value to a lower value. It is possible to arrange numbers in descending order, including whole numbers, natural numbers, integers, fractions, and decimals.

For example 7, 3, 9, 2 in decreasing order, for instance. Starting with the biggest number, we'll work our way down to the lesser ones one at a time. When these numbers are listed in descending sequence, they are written as 9, 7, 3, and then 2.

Given data:

9.5, 9 3/8, 9.125, 9 3/4

Now, simplifying the mixed fraction as

9 3/8

=75/8

= 9.375

9 3/4

=39/4

= 9.75

Thus, we have the data in decimal form

9.5, 9.375, 9.125, 9.75

Hence, the data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.

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The given triangle is a right angled triangle. Therefore, by Pythagoras theoram,

From the figure,

Hence, Option D is the right answer.

The equation that can be used to determine the total cost, y, in dollars for Albert to play any number of games, x, is Y = 18x/2 or 9x.

An equation is a mathematical statement expressing the equality that two values or expressions share.

Equations are generally represented using the equation sign (=).

The cost of 2 games of laser tag = $18

The cost of 1 game of laser tag = $9 ($18/2)

The cost of x laser tag games = $9x or 18x/2

Thus, we can represent the equation of the total cost as y = 9x.

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we can use cross multiplication

where x is the number of fan boats

the number of fan boats to 54 sailboats is 90

The value of (f·g)(x) from the given function is -2x³ - x².

The given functions are f(x) = 2x +1 and g(x) = -x².

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

(f·g)(x) = f(x) × g(x)

= (2x +1) × (-x²)

= 2x × (-x²) + 1 × (-x²)

= -2x³ - x²

Therefore, the value of (f·g)(x) from the given function is -2x³ - x².

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"Your question is incomplete, probably the complete question/missing part is:"

If f(x) = 2x +1 and g(x) = -x², then find (f·g)(x).

Answer:

1/6

Step-by-step explanation:

1/2 1/3

lcd(least common denomitator)=6

there fore it is 1/6

The value of C is 7.68 units and the value of angle A and B is 23° and 66° respectively.

As we can see,

This is a right angled triangle.

We can use Pythagoras theorem to find the value of third side,

It says, Square of hypotenuse side H is equal to square of Base side B plus square of Perpendicular side.

H² = P² + B².

The value of perpendicular here is 3.

The value of base here is 7.

Putting the values,

H² = (7)²+(3)²

H² = 49 + 9

H² = 58

H = √58

H = 7.68

Now, using trigonometric ratios,

For angle B,

Sin(B) = Perpendicular/Hypotenuse = P/H

Sin(B) = 7/7.68

Sin(B) = 0.91

Sin(66°) = 0.91

The value of B in degree is 66°.

For angle A,

Sin(A) = Perpendicular/Hypotenuse = P/H

Sin(A) = 3/7.68

Sin(A) = 0.39

Sin(23°) = 0.39

The value of A in degree is 23°.

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The amount which needs to be replayed if the loan is unsubsidized, as opposed to being subsidized is $59,295.86.

The monthly payment amount formula on a loan of P at rate r for t years is A = P(r ÷ 12) ÷ (1 -[tex]\frac{(1 +r)}{12} ^{-12t}[/tex])

For the normal compensation plan, T = 25. The P = $90,000 and r = 0.625, so the formula is,

A = $90,000(0.625 ÷ 12) ÷ (1 - (1 +[tex](\frac{1 +0.625}{12} )^{(-300)}[/tex])

A = $90,000(0.625) ÷ (1 - [tex](1.135)^{(-300)}[/tex])

A = $90,000(0.625) ÷ (1.832)

A = $(90,000 × 0.625) ÷ (1.832)

A = $30704.14

Payments under the extended repayment plan last for 25 years. The amount which needs to be replayed is $90,000 - $30704.14 = $59,295.86.

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Answer:

It is a rate of change that is not the same at all points - in time or space.

Step-by-step explanation:

The quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5).

What do math quadrilaterals mean?

If a point (x, y) is rotated 90 degrees counterclockwise with respect to the origin, the rotational rule is:

(x, y) → (-y, x) (-y, x)

Consequently, the image point's coordinates following rotation will be (-y, x).

According to this rule, the quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5)

We may obtain the graph of the picture quadrilateral A'R'M'Y' by graphing the image points.

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In statistics, there are ways of analyzing data and these include measures of "central tendency" and "measures of dispersion."

This question is focused on "measures of dispersion," that is, an analysis of how well the data set is being spread away from the centre. The centre is most commonly denoted as the mean (average), and the SPREAD is an analysis of how farther away the observed data is from the centre.

The Mean, Median and Mode are basically measures of "central tendency" and therefore, options A, B and C do not measure the SPREAD of a distribution.

The Quartiles and Standard deviation actually measure how well (either very close or very far) the data set move away from the distribution.

The Quartiles basically examine the data set from all four quarters of the entire set, the 1st, 2nd, 3rd and 4th quarters. This measure of spread measures how well the data is from the distribution depending on which quartile it falls. The Standard deviation measures how far the mean deviates (or drifts away) from the data set.

The correct answer therefore is option D.

==========================================================

Explanation:

Draw a vertical number line. Plot point R at -18 which is 18 units below 0.

Then move up 6 units to arrive at -12 which is one potential location of point S. The distance from R = -18 to R = -12 is RS = 6 units.

Now go back to point R = -18. This time move down 6 units to arrive at -24 as the other possible location of S.

See the diagram below.