Find the value of each variable in the following parallelogram

The m ∠SPR of the rhombus with sides PQRS is 65, option C.

Only the opposite angles of a rhombus are equal. A rhombus's diagonal angle is 90 degrees.

There are two ways to find the angle SPR of the rhombus, PQRS;

If ∠PQR = 50°  then, ∠PQR = ∠PSR (opposite sides)

∠OSR = 1/2 x 50° = 25° where SQ bisects ∠PSR

∠ORS + ∠ROS + ∠OSR = 180°

∠ORS + 25° + 90°  = 180°

∠ORS = 180° - 115°

∠ORS = 65°

Also, it can be calculated thus:

Because rhombus adjacent sides are supplementary, it can be written as; ∠QRS + ∠PQR = 180°

∠QRS = 180° - ∠PQR

∠QRS = 180° - 50°

∠QRS = 130°

Even though a rhombus' diagonal is an angular bisector, the ∠PRS is half of the ∠QRS.

Therefore ∠SPR = ∠QRS/2

∠SPR = 130°/2

∠SPR = 65°

The value of ∠SPR is half the angle because the opposite angles are equal therefore each side has 65°.

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Answer:y ≥ 15 − 5x

Step-by-step explanation:

Answer: (x-5)(x)(x+9)(x+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

factors of 8

Answer:

F- of a 8* i think

Step-by-step explanation:

Answer:

Irrational, Rational, and Complex Roots

Step-by-step explanation:

Irrational roots cannot be written as a fraction, for example, √2 is an irrational root because 2 is not a square number

Rational roots can be written as a fraction. For example, √4 is a rational root because it can be either -2 or 2 which are both rational.

Complex/imaginary roots take the form of [tex]a+bi[/tex] where "a" is the real part and "b" is the imaginary part. For example, √(-1) = i which is complex/imaginary.

Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = [tex]2^{4}[/tex], where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

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Sarah will make 6 baskets in her next 6 shots.

If Sarah made a basket on one of her first shots in a basketball game, and she continues to make baskets at the same rate, we can use that information to predict the number of baskets she will make in her next 6 shots.

Since we know that Sarah made a basket on one of her first shots, we can assume that the probability of her making a basket on any given shot is 1/1 or 100%.

If the probability of Sarah making a basket on any given shot is 100%, then we can expect her to make a basket on all 6 of her next shots. Therefore, Sarah will make 6 baskets in her next 6 shots.

Therefore, Sarah will make 6 baskets in her next 6 shots.

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Answer:

the answer to your question is 3.

Answer:

x = 3.25

Step-by-step explanation:

Answer:

Just subtract the answer to what your adding:

7.50 - 4.25 = 3.25

Step-by-step explanation:

Hope it helps! =D

The quotient is the number that is generated when we perform division operations on two numbers, and the result of the division is called the quotient.

There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient, and remainder.

The number is divided by another number to get a different number as an output.

Dividend = Quotient × Divisor + Remainder

If the remainder is equal to 0, then;

Dividend = Quotient × Divisor

Therefore,

Quotient = Dividend ÷ Divisor

Dividend: The number which is required to be divided

Divisor: The number which divides the given dividend

Remainder: The number which is left after the division method. When a number is completely divided then the remainder is zero.

Consider an example 25/5=5-----quotient.

where 25 is the dividend

5 is the divisor.

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Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

A relationship that explains how two variables relate to one another is represented by the word "functions," which is frequently used in mathematics. There are three: a variable, which can be any type of input, and predictor variables, which are the results of the function or equation.

Here,

A quadratic function's "width" can be calculated using the coefficient before the variable.

The graph will be narrower than the parent graph if the coefficient is more than one (f(x)=x2), and

wider if the coefficient is less than one. Thus, from widest to narrowest:

f(x)=0.5x²

f(x)=3x²

f(x)=-5x²

Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.

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He must work for 10 hours a day to complete the job in 10 days. 10 hours per day is the optimal amount of time to finish the job in 10 days

1. Begin by setting up an equation. Let x be the number of hours worked.

2. 8 hours x 12 days = 96 hours

3. We want to finish the job in 10 days, so 10x = 96

4. Solve for x. 10x = 96, x = 9.6

5. Since we can't work partial hours, round up to 10 hours. Therefore, the man must work 10 hours a day to complete the job in 10 days.

To finish the job in 10 days, the man must work for a total of 100 hours. This means he must work for 10 hours a day to complete the job in the allotted time. Working 8 hours a day would take 12 days, and working 9 hours a day would take 11.11 days. Therefore, 10 hours per day is the optimal amount of time to finish the job in 10 days.

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Option b is correct monthly payment = $163.07

A loan of $7,500 with an 11% interest rate compounded monthly over a time period of 5 years.

Monthly Payment = Amount / Discount factor

Discount factor [tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

where,

Amount = $7500

Rate= 11%=0.11

[tex]i = \frac{0.11}{12} = 0.0091[/tex] ( by using division)

Time = 5 years

Time (n) = 5 × 12 = 60

Now, put i and n in the Discount factor,

[tex]D = \frac{1-(1+i)^{n} }{i}[/tex]

[tex]D = \frac{1-(1+0.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{1-(1.009)^{-60} }{0.009}[/tex]

[tex]D = \frac{0.421 }{0.009}[/tex]

D = 46.77

Monthly payment (M),

[tex]M = \frac{Amount}{Discout factor} = \frac{A}{D}[/tex]

[tex]M = \frac{7500}{46.77}[/tex] ( by using division)

Monthly payment = 163.07

Therefore, Option b is the correct monthly payment = $163.07.

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The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). To find the factor of a polynomial using the Remainder Theorem, you can use the following steps:

Example:

P(x) = x^3 + 3x^2 + 2x -6

Factor = (x-2)

P(2) = 8 + 12 + 4 - 6 = 0

So, the factor of P(x) is (x-2)

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Answer: graph a and d

Step-by-step explanation:

The mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

The sample distribution of the proportions is used to measure the proportion with which success is achieved. The chance of an event taking place is the proportion computed by dividing the number of successes by the size of the sample.

Given that, You intend to draw a random sample of size n = 580 from a population whose parameter is p = 0.31, we are asked to find the mean of the distribution of sample proportions and standard deviation of the distribution of sample proportions.

Under the sampling distribution of the proportions, the mean and standard deviation are calculated by :

a) The mean is given as ;

μ = nP

Where, n is the sample size

P is the population proportion

Therefore,

μ = 580(0.31)

μ = 179.8

b) The standard deviation is given as follows :

δ = [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]

δ = [tex]\sqrt{\frac{0.31(1-0.31)}{580} }[/tex]

δ = 0.019

Hence, the mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

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To solve the problem, we must first find the slope of the line containing (4, -2) and (x, -6). The slope of a line is calculated as the change in y-coordinates divided by the change in x-coordinates, or (y2 - y1) / (x2 - x1). In this case, the slope of the line containing (4, -2) and (x, -6) is (-6 - (-2)) / (x - 4) = -4 / (x - 4)

Since the line containing (4, -2) and (x,-6) is perpendicular to the line containing (-2,-9) and (3,-4), we know that the product of the slopes of these two lines is -1. We can use that information to find the slope of the second line: -1 = (-4 / (x - 4)) * m, where m is the slope of the second line. Solving for m, we get m = -1 / (-4 / (x - 4)) = (x - 4) / 4.

We can now use the point-slope form of a linear equation to find the equation of the line containing (-2,-9) and (3,-4). The point-slope form is y - y1 = m(x - x1). In this case, we can use (-2,-9) as (x1, y1) and (x - 4) / 4 as m:

y - (-9) = (x - 4) / 4 * (x + 2)

Simplifying we get y = (x-4)/4 + (-9) = (x-4)/4 - 9

Now we can substitute x = -2 and y = -9 to check if it belongs to this line:

-9 = (-2 - 4)/4 - 9

-9 = -2/4 - 9

-9 = -0.5 - 9

-9 = -9.5

It match so this line is the correct one.

The value of x that satisfies the given conditions is x = -2

You can graph this line on a separate sheet of paper by plotting the point (-2, -9) and using the slope (x-4)/4 to find additional points on the line.

A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

It is referred to as being unfair when two terms are joined by a sign like "not equal to," "more than," or "less than." The inequality illustrates the relationship between variables and numbers in terms of greater than and less than.

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality'. So, a lack of balance results in inequality.

Given that a rental car company charges $50 per day to rent a car and $0.15 for every mile driven.

The equation of inequality will be written as,

C ≥ [tex]0.15m + 50x[/tex]    

Here, C is the total cost, m is the number of miles, and x is the number of days.

C ≥ [tex]0.15m + 50x[/tex]    

C ≥ ( [tex]0.15*100[/tex] ) + [tex]50x[/tex]

130 ≥ 19.5 + [tex]50x[/tex]

130 - 19.5 ≥ [tex]50x[/tex]

[tex]50x[/tex] ≤ 110.5

x ≤ 110.5 / 50

x ≤ 2.21 days

Therefore,

A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

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Answer:

656

Step-by-step explanation:

Two triangles will be better than one half times five times thirteen. We'll also have a single rectangular piece. It measures 12 by 10. 20 times 2 equals 40. 13 divided by 2 divided by 2 is equal to 4. I am capable of 44 times two times two. 13 is 52 One is equal to 10 x 2 x 1/2. 12 times 10 is 120, and 5 times 13 is 65. Consequently, the area is 297 square feet (40 plus 52 plus 20 plus 65 plus 120).

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Answer: 297 ft.2

Step-by-step explanation:

The perimeter of the rectangle, given that the rectangle has an area of 40 ft² and a length of 8 ft is 26 ft

We'll begin by obtaining the width of the rectangle. The width of the rectangle can be obtained as follow:

Area = Length × Width

40 = 8 × Width

Divide both sides by 8

Width = 40 / 8

Width = 5 ft

Finally, we shall determine the perimeter of the rectangle. Details below:

Perimeter = 2(Lenght + Width)

Perimeter = 2(8 + 5)

Perimeter = 2(13)

Perimeter = 26 ft

Thus, we can conclude that the perimeter is 26 ft

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The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

The cost of adult ticket be x and child ticket be y respectively.

Now as per sum ,

(i) 5x + 13y = 59 and,

(ii) 5x + 9y = 47

Subtracting equation (ii) from (i) we get,

13y - 9y = 59 - 47

⇒ 4y = 12

⇒ y = 3

putting y = 3 in equation (ii) we get

5x + 9*3 = 47      ⇒ x = 20/5 = 4

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

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Function has one y for one x. if you pass line through x = 7 it cuts graph on different values of y

it is not function

The equivalent expression is  -1.9b + 7.8.

There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Combine similar phrases now:

The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.

When we combine the term b's coefficient, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

By condensing the equation, we obtain

= (- 1.9) +b + 7.8

= −1.9b + 7.8

There is a condensed equivalent formula of -1.9b + 7.8.

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Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It's worth noting that if we multiply our answer by itself, we get the original polynomial.

A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

Here,

Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial.

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Answer:

x = 11

Step-by-step explanation:

We'll have to get X alone by doing the opposite of what the current equation is showing

67 = 7x-10. I usually turn the numbers around cause it looks better...

7x-10 = 67

We see it's subtracting 10, so we'll add 10 on both sides

7x = 67 + 10

7x = 77

Since 7x is being multiplied, we'll divide on both sides

x = 77/7

x = 11

Answer: -11

Step-by-step explanation:

rearrange it so it's -7x-10=67

add 10 to itself and 67

then you get -7x=77

then divide 77 by -7

and you get -11

i hope this was right :)

The required dimensions of the dilated kitchen is 8.5 inch by 13.09.

The scale factor is defined as the ratio of modified change in length to original length.

Here,
Current dimension of the graph = 8.5 inch by 11 inch
Final dimension of the graph = 24 inch by 36 inch

Now,
Dilated dimension of the kitchen
Length = 24 / 8.5 × 3 = 8.5 inch

Width = 36/11 × 4 = 13.09

Thus, the required dimensions of the dilated kitchen is 8.5 inch by 13.09.

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Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation: