Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

The sides 7cm , 24cm and 25cm ; forms a right angled triangle because the condition of Pythagoras Theorem is satisfied .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of hypotnuse (longest sides) is equal to the sum of the square of the other two sides .

The sides are given as ⇒ 7cm , 24cm and 25cm ;

here the longest side (hypotnuse) is = 25 cm ;

According to Pythagoras theorem ,

⇒ [tex]25^{2} =24^{2} +7^{2}[/tex] ;

⇒ [tex]625=576+49[/tex] ;

⇒ [tex]625 = 625[/tex] ;

The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Angled Triangle .

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The sum of all the elements of set S is -(220/7).

To express the function (x^2+5x +y)/(x^2+7x - 44) as a quotient of two linear functions, the denominator must be a factor of the numerator. In other words, (x^2+7x - 44) must divide (x^2+5x +y) without leaving any remainder. To find the sum of the elements of S, we can set the numerator equal to the denominator multiplied by a constant and solve for y.

x^2+5x +y = c(x^2+7x - 44)

The constant c is a scalar value.

x^2+5x +y = cx^2 +7cx - 44c

we can now equate the coefficients of x^2 and x.

1 = c

and, 5 = 7c

now we can solve for c:

c = 5/7

Now we can substitute the value of c back into the equation:

x^2+5x +y = (5/7)(x^2+7x - 44)

=> x^2+5x +y = (5/7)x^2 + (35/7)x - (220/7)

we can now equate the constant terms:

y = -(220/7)

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Answer

212

because I added the 98,4,100,10

Answer:

This question is based on the concept of mean. Therefore, the scores for the four games were 97, 98, 98, 107.

Given:

Sue played four games of golf. For these games her modal score was 98 and her mean score was 100. Her range of scores was 10.

According to the question,

If the modal score is 98 then, there must be two games where she scored 98.

The mean is the total of all of her scores divided by the number of games,

We get,

98+98+x+y=400

x+y= 204

As it is given that, the range is 10 and x is the lowest and y is the highest we can say that:

As we know that, her range of scores was 10,

97+10= 107

Therefore, the scores for the four games were 97, 98, 98, 107.

For the given system of equations the value of x is 0.27 and the value of y = 2.7.

A system of equations in algebra consists of two or more equations and looks for common answers. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.

The given equations are:

-8x + 6y = 14 and

-5x + 2y = -7

For the equation -5x + 2y = -7 isolate the value of x:

-5x = 7 - 2y

x = - (7 - 2y) / 5

Substitute the value of x in the equation -8x + 6y = 14.

[tex]-8 (\frac{7-2y}{5} ) +6y =14\\\\-11.2 + 3.2y + 6y =14\\\\9.2y = 14 + 11.2\\\\y = 2.7[/tex]

Substitute the value of y in any one of the equations:

-8x + 6(2.7) = 14

-8x = 14 - 16.2

x = 0.27

Hence, the value of x is 0.27 and the value of y = 2.7.

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Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

Total investment in two accounts = $20,000

The simple interest rate for account one, x = 8%

The simple interest rate for account two, y = 10%

Total interest for a year = $1,920

Let account one = x and account two = y

x + y = 20,000 ... Equation 1

0.08x + 0.1y = 1,920 ... Equation 2

Multiply Equation 1 by 0.08

0.08x + 0.08y = 1,600 ... Equation 3

Subtract Equation 3 from Equation 2:

0.08x + 0.1y = 1,920

-

0.08x + 0.08y = 1,600

0.02y = 320

y = 16,000

= $16,000

In Equation 1, x + y = 20,000, Substitute y = 16,000:

x + 16,000 = 20,000

x = 4,000

= $4,000

Check:

From Equation 2:

0.08x + 0.1y = 1,920

0.08(4,000) + 0.1(16,000) = 1,920

320 + 1,600 = 1,920

Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.

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Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?

First account:

Second account:

Answer:

C. No; you would need to know that each pair of diagonals is perpendicular.

Step-by-step explanation:

It is not sufficient to establish that MNOP and TQRS are congruent parallelograms given that MO=TR and NP=QS. Parallelograms that are congruent have the same size and form. A common method for demonstrating that two parallelograms are congruent is to use one of the following criteria:

SSS (Side-Side-Side) : If all three pairs of corresponding sides are congruent.

SAS (Side-Angle-Side): If two pairs of corresponding sides and the included angle are congruent

ASA (Angle-Side-Angle): If two pairs of corresponding angles and the included side are congruent

HL (Hypotenuse-Leg): If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle

CPCTC (Corresponding parts of Congruent Triangles are Congruent)

Given that we only know that MO=TR and NP=QS, we do not have enough information to prove that the parallelograms are congruent. It is missing information about the angles and the diagonals of the parallelograms.

In addition to that, we need to know that the diagonals of the parallelograms bisect each other. If this is the case, then we can use HL to prove that the parallelograms are congruent.

The required product are as follows,
A: -4p²q²-3pq = 4c²[1 - 3c²]     B: 4c²-12c⁴ = 4c²[1 - 3c²]    
C: 3m²+9m³ = 3m²{1 + 3m}       D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
(a)
Given expression,
-4p²q²-3pq = -pq (4pq + 3)

Similarly,
B: 4c²-12c⁴ = 4c²[1 - 3c²]

C: 3m²+9m³ = 3m²{1 + 3m}

D: c³+c⁷ = c³[1 + c⁴]

E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]

Thus, the required products has be illustrated above.

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After Ms. Wilson pays her federal taxes, D. She will receive a refund of $ 258.

A tax refund is given when an individual or business overpays their taxes to the government during the year. It happens when the taxes that an individual or business paid through the year (withholding taxes or estimated taxes) are more than their actual tax liability for the year.

Going by the table, Ms. Wilson at her Single filling status was meant to pay the tax amount of $ 5, 086 in federal taxes and instead paid $ 5, 344. She will therefore get a refund of :

= 5, 344 - 5, 086

= $ 258

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Aubree's car used 1 gallon to travel 30 miles.

The car used 4 gallons to travel 120 miles. We need to calculate the distance car can travel with 1 gallon of gas.

By unitary method;

The distance car can travel = (120/4)*1 =30

Aubree's car used 1 gallon to travel 30 miles.

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On 1 gallon of gas, Aubree`s car can go 30 miles.

This is a question of the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, [by dividing] and then finding the necessary value by multiplying the single unit value.

Aubree`s car used 4 gallons of gas to travel 120 miles. So, to find the miles it travelled on 1 gallon of gas. We can simply just divide the total miles the car travelled by the total litres of gas it used.

Therefore, 120/4=30 miles.

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Check the picture below.

Answer:

Step-by-step explanation:

(14,2) is the point  lies on the slope-intercept form, line .

What does the slope intercept form mean?

The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

                   In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. We can observe that the line's slope is 3 from our equation, y = 3 x + 5.

All lines passing thru the origin should have a slope of y = mx + c

In this case, since the slope is 1/7 ,  the line will be  y = 1/7x

Thus, it could observe which is the only point  that satisfies this equation of the line out of all the points.

For choice "E" when x= 7  and y = 14  m = 1/7 and put the value in y = mx + c  it will give 14 = 2 , which is wrong.

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On solving the provided question, we can say that by equation so he has to play 10 games at each arcade,  to spend the same amount of money at each arcade

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation that we can create here is

Kabir paid an entrance of $5 plus an additional 0.75 per game at a local arcade.

he and a friend went to another arcade where kabir paid $1.25 per game, but there was no entrance fee

let kabir played 10 games.

then at arcade 1 he spends $5 + (10*0.75) = 5 + 7.5 = $12.5

now at arcade 2 = 12.5/1.25 = 10 to spend the same amount of money at each arcade

so he has to play 10 games at each arcade,  to spend the same amount of money at each arcade

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Answer:

f(x) = (1/5)x - (2/5)

Step-by-step explanation:

The linear function can be written in the form of f(x) = mx + b, where m is the slope and b is the y-intercept.

To find the rule for the linear function when x=-10, y=-1, when x=0, y=1 and when x=10, y=3, we can use the two points method.

We can start by finding the slope (m) of the function using the following formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are two points on the line.

Using the point (-10, -1) and (10, 3) we get:

m = (3 - (-1)) / (10 - (-10)) = 4/20 = 1/5

Now that we know the slope, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

Plug in one of the points and the slope that we found:

y - (-1) = (1/5)(x - (-10))

y = (1/5)x - (2/5)

So the equation of the linear function is f(x) = (1/5)x - (2/5)

This is the rule of the linear function when x=-10, y=-1, when x=0, y=1 and when x=10, y=3.

ANSWER:

STEP-BY-STEP EXPLANATION:

We must interpret each sentence mathematically, just like this:

Less then would be a subtract

Product would be a multiplication

No more than would be equal or less than

Answer:        

.2n-7≤95

.2n≤102

n≤510

hope this helps

Answer:

The prime factors of 12 are 2 x 2 x 3.

So the composite factors of 12 are:

1, 2, 3, 4, 6 and 12.

[tex]dy/dt[/tex] for each pair of functions is [tex]4t^3 + 28t[/tex].

[tex]y[/tex] = [tex]x^2 - 2x[/tex]

[tex]x[/tex] = [tex]t^2 + 8[/tex]

[tex]y[/tex] = [tex](t^2+8)^2 - 2(t^2+8)[/tex]

[tex]dy/dt[/tex] = [tex]2(t^2+8)(2t) - 2(2t)[/tex]

         = [tex]4t^3 + 32t - 4t[/tex]

[tex]dy/dt[/tex] = [tex]4t^3 + 28t[/tex]

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.

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To calculate measure of the angle of a given triangle apply cosine rule :

c² = a² + b² - 2abcos C

b² = a² + c² - 2ac cos B

a² = c² + b² - 2cbcos A and by comparison find the smallest and the largest angle.

As given in the question,

Consider a triangle ABC to determine the smallest and the largest angle of the triangle,

Side opposite to angle A = BC

Side opposite to angle B = AC

Side opposite to angle C = AB

Let

side AB = c

side AC = b

side BC = a

To determine the measure of the angle using side measurement apply

cosine rule :

c² = a² + b² - 2abcos C

b² = a² + c² - 2ac cos B

a² = c² + b² - 2cbcos A

Calculate measure of all the angles and compare them to determine smallest and largest angle of the triangle.

Therefore, to find the measure of the angle of a triangle use cosine rule and by comparison determine the smallest and the largest angle.

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maximum degree f(x) = x2 + bx + c g(x) = x3 + wx2 + yx + z [f(x)]3 - [g(x)]2 + f(x) - 1 (x2+bx+c)3 - (x3+wx2..for the given polynomial

What is a polynomial class 9?

Polynomial Definition. Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. An algebraic expression p(x) = a0xn + a1xn-1 + a2xn-2 + … an is a polynomial where a0, a1, ………. an are real numbers and n is non-negative integer.

Find the value of f(–9) and g(1) if f(x) = 8x + 6 and g(x) = 9x + 20x−2

polynomial f(x) = 8x + 6

f(–9) = 8(-9) + 6 = -66

g(x) = 9x + 20x − 2

g( 1 ) = 9( 1 ) + 20( 1 ) − 2 = 27

None of the given choices were correct (unless there's a typo error for  — it's supposed to be g( 1 ) = 27 instead of 29?) because the value are: f(–9) = -66 and g( 1 ) = 27

f(–9) and g(–1) if f(x) = –3x – 2 and g(x) = 3x³ – 24x

f(x) = –3x – 2

f(–9) = –3(–9) – 2 = 25

g(x) = 3x³ – 24x

g(–1) = 3(–1)³ – 24(–1) = 21

Therefore, : f(–9) = 25, g(–1) = 21

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Please find attached herewith the solution of your question.

Hope it helps

Answer: 10 liters

Step-by-step explanation:

Let the number of liters of 10% solution be [tex]x[/tex].

[tex]0.10x+5(0.25)=0.15(x+5)\\\\0.10x+1.25=0.15x+0.75\\\\1.25=0.05x+0.75\\\\0.05x=0.50\\\\x=10[/tex]

The answer to the simplification is 56.

The order of precedence is the hierarchical order in which calculations are conducted. The simplest example of this is the way you always multiply before you add numbers.

In mathematics, you have BODMAS

B = Bracket

O = of

D = Division

M = Multiplication

A = Addition

S = Subtraction

From the equation;

7 x (-7 +15)

Removing the bracket

7 x (8)

Multiplying

56

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Answer:

85 Millimeters

Step-by-step explanation:

1 centimeter is equal to 10 millimeters. Hope this helped!

Answer:i had to

Step-by-step explanation: mb

The graph of the linear equation can be seen in the image at the end.

I assume that you want to graph the linear equation:

x + 2y = 3

To do so, you just need to find two points that lie on that line, to find them, just evaluate the linear equation in two different values of x (or y)

Remember that the point notation is (x, y)

if we use x = 0

0 + 2y = 3

2y = 3

y = 3/2 = 1.5

So we have the point (0, 1.5)

if x = 1

1 + 2y = 3

2y = 3 - 1

2y = 2

y = 2/2

y = 1

So the point is (1, 1)

Now that you have these two points, you can graph them on a coordinate axis, and connect them with a staright line.

The graph can be seen below.

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Patrice needs to consume more than 1200 calories, but less than 1600 calories.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250.

From the first inequality

2450 < 2x + 50

2400 < 2x

x > 1200

From the second inequality

2x + 50 < 3250.

2x < 3200

x < 1600

Therefore, x > 1200 and x < 1600; Patrice needs to consume more than 1200 calories, but less than 1600 calories.

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Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

A graph illustrating the correlation between two extra variables is the most common way to present data using a chart. It is also permitted to use diagrams that were manually or digitally drawn. starting at the origin, go 3 units up, then 2 units to the right. It is necessary to display the numbers for the positions 2, 3, and 4 on the reference system. Make your points really clear. 2.3 is represented by the pinkish dot with letter P. For each value in a data collection, you must first create a number line before you can create a line chart.

Here,

The boxplot, in its most basic version, visualizes five sample statistics: the minimum, the smallest value, the mean, the upper quartile, and the maximum.

The plot's box is a rectangle with ends at each quartile that encloses the sample's middle half. Therefore, the box's length represents the sample's interquartile range.

Nothing specific is represented by the box's other dimension. At the sample median, a line is drawn from across box.

Up until they hit the sampling maximum and minimum, whiskers extend from the box's two ends.

Each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

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Answer:

$240

Step-by-step explanation:

To calculate the interest, you need to multiply the principal (the amount financed, $4,000.00) by the interest rate (2%) and the number of years (3).

So, the interest would be: $4,000.00 x 0.02 x 3 = $240.00

The contractor would pay $240.00 in interest over the course of the 3-year financing.

The given algebraic expression when solved to the nearest tenth is 5.6

2.7 - 6.8x = - 6.8 - 5.1x

collect like terms

2.7 + 6.8 = -5.1x + 6.8x

9.5 = 1.7x

divide both sides by 1.7

x = 9.5/1.7

x = 5.6

Therefore, the algebraic expression is given by x = 5.6

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