Need help on algebra

The height is 31.51 inches.

From the question, we have

Let height= h

width = h+6

diagonal = 49 inches

Using Pythagoras Theorem

49²  = h²  + (h+6)²

2401 = h² +h² +36+12h

2401 = 2h² +36+12h

2h²+12h-2365 = 0

Solving this, we get

h=−3+1/2√4766

h=31.51 inches

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The inequality using variables x and y which satisfy the points are; y>-3x+3.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the points (2,5) and (-3,-5) lie on the boundary line.

The system of inequality is given by:

y>-3x+3-

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies the inequality.

a)  (6, 5)

when x=6 and y= 5

then we have:

y>-3x+3

6 > -3×5 + 3

6>- 15+3

5 > -12

This means that the point will lie in the solution set.

Also, (-2, -3) when x= -2 and y= -3

then we have:

5 > -3×(-2) + 3

5> 6 + 3

5> 9

Hence, the inequality using variables x and y which satisfy the points are; y>-3x+3.

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The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Children under 12: free

Kids aged 12-17: $3

Adults aged 18-64: $8

Senior citizens 65 and over: $4

The function for the above can be written as,

C(n) = 0 for 0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function  C(x) is {0, 3, 4, 8}

Thus,

The piecewise-defined function that gives the cost C(n) for a museum visitor who is n years old is C(n) = 0 for  0≤ n ≤ 12

Cn) = 3 for 12 ≤ n ≤ 17

C(n) = 8 for 18 ≤ n ≤ 64

C(n) = 4 for 65 ≤ n

The range of the function is {0, 3, 4, 8}.

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Answer:

Although square roots are generally taken to be positive, a square root can be negative as a negative number multiplied by a negative number is always positive.

Step-by-step explanation:

In general, when someone is asking for a square root, they are seeking the positive value. This is called the principal square root. However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the principal square root, but the negative version. The negative square "squared" will give the same positive result as the principal square root, for instance,

3⋅3=9 and −3⋅−3=9.

Answer: The correct answer is 0. Negative numbers don't really have any square roots since a square cannot be negative it can only be positive or a 0.

Step-by-step explanation: I hope this helps!

The measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

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

We have been given the angles as;

(12x + 18)° and (8x +10)

We need to solve the value of x by an alternate interior angle;

(12x + 18)° = (8x +10)

Solving;

(12x - 18)° = (8x +10)

(12x - 8x)° = (18 +10)

4x = 28

x = 7

The value of x is 7.

Thus, (12x + 18)° = 102 degree

(8x +10) = 66 degree

Hence, the measure of angle (12x + 18)° is 102 degrees and the measure of angle (8x +10) ° is 66 degrees.

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Answer: You can find a right degree angle of a triangle when it’s a 90 degrees or if you can see it makes like a square.

The rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

What is rational function equation?

A rational equation can be defined as an equation that involves at least one rational expression

A rational function is a function of the form f( x )=P( x ) / Q( x ) ,

f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.

A rational function f ( x )=P( x ) / Q( x )

f( x ) = P( x ) / Q( x ) may have a vertical asymptote

The domain is the set of all real numbers for which Q( x ) ≠ 0

Given data ,

The function has vertical asymptote at x = 5 and x = -5

So , the denominator of the fraction of rational function contains the terms (x - 5) and (x + 5)

The x intercept is at ( 2 , 0 ) and ( -1 , 0 )

The y intercept is at ( 0 , 4 )

So , the numerator of the fraction of the rational function contains the terms

( x- 2 ) and ( x + 1 )

So , the rational function is of the form

f ( x )=P( x ) / Q( x )

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

Now , we have the y intercept at ( 0 , 4 )

So , f ( 0 ) = 4

Substituting the value of f ( 0 ) in the above equation , we have

4 = A ( 0 + 1 ) ( 0 - 2 ) / ( 0 - 5 ) ( 0 + 5 )

4 = A ( -2 ) / ( -25 )

4 = 2A / 25

Multiply 25 on both sides , we get

2A = 100

Divide by 2 on both sides , we get

A = 50

Therefore , the rational function becomes

f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

Hence , the rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )

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Answer:

12

Step-by-step explanation:

(5+7)/7=12/7.

Green box = 12.

The  interpretation of the y-intercept is that the sales made in Year 2 is 20 million

A graph y-axis and x-axis. The y-axis is the vertical axis while x-axis is the horizontal axis. In this case, the y-axis is the Sales and the x-axis is the Year

The y-intercept is the point where the graph touches the y-axis. In this case, the y-intercept is 20. If you trace to the x-axis (Year), the value there is 2. The interpretation is that the sales made in Year 2 is 20 million

The point can be interpreted as the sales made in Year 8 is 40 million

The output value of this graph when the input value is 4 i.e. Year 4. The output value is the sales made in Year 4 which is 30 million (it is approximately halfway between 20 and 40)

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The cost of the hotel for 1 night is $130 using the ratio concept.

If b is not equal to 0, an ordered pair of real numbers a and b, represented as a / b, is a ratio. An equation that balances two ratios is called a proportion. For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 male and 3 girls. The formula a: b or a/b can be used to compare any two values.

However, the percentage formula is represented as a:b::c:d or a:b=cd.

There are three types of proportion. They are:

1) Direct Proportion.

2) Inverse Proportion.

3) Compound Proportion.

4) Continued Proportion

Given,

Cost for four rental nights = $520

The cost for one rental night is given by

x = 520/4

x = $130 per night

Therefore, the cost of the hotel for 1 night is $130.

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The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, considering the graph, in thousands of kilometers, is of:

50.

The approximate difference between the maximum and minimum distances of the Earth from the Sun in thousands of kilometers, is obtained by the subtraction of the maximum value and the minimum value of the graph.

From the graph shown at the end of the answer, these parameters are presented as follows:

Hence the difference between these two values is obtained as follows:

25,000 - (-25,000) = 25,000 + 25,000 = 2 x 25,000 = 50,000 km.

In thousands of km, the difference is:

50000/1000 = 50.

The graph is given by the image shown at the end of the answer.

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The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

Given that,

We have to find the Find the average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table below.

x           f(x)

1           90

4           87

7           84

10          81

We have to find the slope of the 2 points.

The points are (4,87) and (7,84)

The slope point is rise/run

Rise is y₂-y₁

Run is x₂-x₁

So,

Slope = (84-87)/(7-4)

Slope = (-3)/(3)

Slope = -1

Therefore, The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

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Answer:

Step-by-step explanation:

Ok: It me again!

1. Since Greg earned 53$ for washing cars, he said he earned twice as much than mowing as a equation that would be:

2*m=53$ he made in total

So:

2. Answer: 2m=53$

Based on the mentioned information, each birthday card costs $2.2.

Forming the equation based on the mentioned variables. The equation will be formed as -

Cost of birthday cards × number of cards + cost of thank-you notes × number of notes = total cost

Equation for package a

3x + 2y = 9.60 : Equation 1

Equation for package b

8x + 6y = 26.60 : Equation 2

Multiplying equation 1 with 3

9x + 6y = 28.8 : Equation 4

Now subtracting equation 2 from equation 4

9x + 6y = 28.8

-8x (-)+ 6y = (-) 26.60

The result will be :

x = 2.2

Thus, the cost of birthday card is $2.2

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Answer: When you are simplifying exponential terms raised to another exponent, the way to simplify them is to multiply the exponents together.

Step-by-step explanation:

Answer:

r=-40

Step-by-step explanation:

[tex]\frac{-0.4r}{-0.4} = \frac{16}{-0.4}[/tex]

r=-40

Wyatt has to drive more than 50 miles to save his earnings after spending it.

Given,

The cost for training and license = $500

The cost for gas and insurance = $4 per mile

The amount paid for the first delivery = $400 + $6 per miles

We have to find the total cost he spends and earns;

Here,

x be the distance he drives in mile

Then,

The amount he spends = $500 + $4x

The earnings of him = $400 + $6

Then,

Equate this;

500 + 4x ≥ 400 + 6x

500 - 400 ≥ 6x - 4x

100 ≥ 2x

x ≥ 100/2

x ≥ 50

That is,

Wyatt has to drive more than 50 miles to save his earnings after spending it.

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Answer: X = 1.12

Y = 1.75

Step-by-step explanation:

8/10 = 5/X +5

5(10) = 8(X + 5)

CROSS MULTIPLY AND DIVIDE

50 - 40 = 8X + 40 -40

10 = 8X

10/8 = 8X/8

1.25 = X

8/10 = 7/7 +Y

CRPSS MULTIPLY AND DIVIDE

7(10) = 8(7 +Y)

70 = 56 + 8Y

70 -56 = 56 -56 + 8Y

14 = 8Y

14/8 = 8Y/8

1,75 = Y

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{4 +5}{6 +6} \implies \cfrac{ 9 }{ 12 } \implies \cfrac{3 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{3 }{ 4 }}(x-\stackrel{x_1}{(-6)}) \implies y +5 = \cfrac{3 }{ 4 } ( x +6) \\\\\\ y+5=\cfrac{3 }{ 4 }x+\cfrac{9}{2}\implies y=\cfrac{3 }{ 4 }x+\cfrac{9}{2}-5\implies {\Large \begin{array}{llll} y=\cfrac{3 }{ 4 }x-\cfrac{1}{2} \end{array}}[/tex]

Answer:

[tex]\displaystyle \boxed{ y=\frac{3}{4}x-\frac{1}{2} }[/tex]

Step-by-step explanation:

      First, we will find the slope. This is done by finding the change in y over the change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }= \frac{4--5}{6--6} =\frac{4+5}{6+6}=\frac{9}{12}=\frac{3}{4}[/tex]

      Next, we will find the equation. We will create a point-slope equation and simplify into slope-intercept form.

y - 4 = [tex]\frac{3}{4}[/tex](x - 6)

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{9}{2}[/tex] + 4

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{1}{2}[/tex]

4 shirts ∝ 31

4 = 31k

7 shirts ∝ 54.25

7 = 54.25k

Where k is the constant of proportionality

The constant of proportionality is k = 0.13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Timberlee buys 4 shirts for $31 and Riley buys 7 shirts for $54.25.

In proportionality terms, we can write as,

4 shirts ∝ 31 _____(1)

7 shirts ∝ 54.25 _____(2)

(1) can be written as,

4 shirts = 31K

7 shirts = 54.24k

Where k is the constant of proportionality.

Now,

The value of k.

From (1)

4 = 31k

k = 4/31

k = 0.13

From (2)

7 = 54.24k

k = 7/54.24

k = 0.13

Thus,

The constant of proportionality is k = 0.13.

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Using scientific notation, the number can be expressed as 1.73 * 10⁻²

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.

Scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10. For example:

20000 = 2 x 10⁴, where 4 is the positive exponent.

When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10. For example:

0.0002 = 2 x 10⁻⁴, where -4 is the negative exponent.

From the above, we can now approach the problem and convert 0.0173 into scientific notation.

This will result into a negative exponent and can be expressed as

0.0173 = 1.73 * 10⁻²

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The measure of angles are

The length of the hypotenuse of the right triangle = 11 inches

The length of the one leg = 10 inches

Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square

Then the equation will be

The length of the other leg = [tex]\sqrt{11^2-10^2}[/tex]

= [tex]\sqrt{121-100}[/tex]

= 4.58 inches

Therefore AC = 11 inches

AB = 10 inches

BC = 4.58 inches

The angle B = 90 degrees

Consider the angle A

cos θ = Adjacent side / hypotenuse

cos θ = 10 /11

θ = 24.61 degrees

Consider the angle C

cos θ = Adjacent side / Hypotenuse

cos θ = 4.58 / 11

θ = 65.39 degrees

Hence, the measure of angles are

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The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).

Equation of circle:

Equation of the circle refer the position of a circle on a cartesian plane.

Given,

C is a circle with center the origin.

A tangent to C passes through the points (-20, 0) and (0, 10)

Here we need to find the equation of the circle C.

In order to find the equation of our line:

We have to identify the y-intercept which is (0,10).

Now, we need to find the gradient of our line which is:

Than can be calculated by,

=> (10 - 0) / (0- (-20))

=>  10/20 = 0.5

Now, the equation of our line is written as,

y = 0.5x + 10

But, here we know the center of our circle is the origin:

Which is in the following form:

=> x² + y² = r²

where r refers the radius

So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.

Then the equation of the circle is written as,

=> x² + (0.5x + 10)² = r²

When we simplify it, then we get,

=> x² + (0.5x + 10)(0.5x + 10) = r²

Now, we can expand and simplify the brackets to leave us with:

=> 1.25x² + 10x + 100 = r²

=> 1.25x² + 10x + 100 - r² = 0

Here we know that this is a tangent and so it only meets the circle at one point.

So, this equation should only have one solution.

Then it can be written as,

=> b² - 4ac = 0

=> 10² - 4(1.25)(100 - r²) = 0

When we simplify this one then we get the value of

=> r² = 90

Therefore the equation of the circle is x^2 + y^2 = 80.

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The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. f(x) = 3x+8

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.

The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. For example, the graph of the function f(x) = x2 + 3 is generated by simply pushing the graph of the function g(x) = x2 up by 3 units.

Therefore,

f(x) = |x|

y = f(x) + C C < 0 moves it down

y = |x| 8  for  shifting down 8

y = f(x + C) C > 0 moves it left

y = Cf(x)  C > 1 stretches it in the y-direction

y = 3x+8  to stretch it 2 vertically

y = −f(x)  Reflects it about x-axis

y = 3x+8

Hence, The graph's curve "moves to the left/right/up/down," "expands or compresses," or "reflects" when a function is transformed. f(x) = 3x+8

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The market price of the watch after a discount of 10% is  $3500   .

In the question ,

it is given that

the price at which the trader sold the wrist watch = $3150

the amount of discount given by trader = 10% ,

we need to find the market price of the watch ,

let the market price of the watch be "x" .

so , the formula that can be used to calculate the market price is

selling price = market price - (discount percent)×(market price)

Substituting the values , we get

3150 = x - 10% of x

3150 = x - 0.10x          ....because 10% = 0.10

(1 - 0.10)x = 3150

0.90x = 3150

Dividing both sides by 0.90 , we get

x = 3150/0.90

x = 3500

market price is $3500  .

Therefore , The market price of the watch after a discount of 10% is  $3500   .

The given question is incomplete , the complete question is

A trader sold a wrist watch for $3150 after giving a 10% discount. Find the marked price of the watch ?

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The angles x of the right angle triangle is 36.87 degrees.

A right angle triangle is a triangle that has one angle as 90 degrees. The angles of a right angle triangle can be found using trigonometric ratios.

Therefore, let's find the angle M(x)

sin x = opposite / hypotenuse

where

Therefore,

sin x = 6 / 10

sin x = 0.6

x = sin⁻¹ 0.6

x = 36.8698976458

x = 36.87 degrees.

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Answer:

5m-19

Step-by-step explanation:

distribute

4(2m-1)-3(m+5)

8m-4-3m-15

Combine like terms

8m-3m-4-15

5m-19

Hopes this helps please mark brainliest

Answer:

5m-19

Step-by-step explanation:

thank me later :)

Steps to Solving:

1) Distribute

2) Distribute the products again

3) Subtract the numbers

4) Combine like terms

Their down payment of $22,500 is 15% of the purchase​ price.

A $7500 down payment​ is 5% of the purchase​ price.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A family buys a studio apartment for 150,000.

They pay a down payment of $22,500.

∴ Their down payment is (22500/150000)×100% of the purchase​ price which is,

= 15% of the purchase​ price.

Let x be the percentage of $7500 downpayment in a purchase of 150000.

∴ (x/100)×150000 = 7500.

1500x = 7500.

x = 75/15.

x = 5%

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The total charge for this job is $12131.04.

Charge per square yard to remove old carpet = $5.99

Charge per square yard to install the new carpet = $4.50

Charge for carpet and pad they selected per square yard = $16.99 and $3.00

Dimension of the living room = 17 1/2 by 20 feet

⇒ 35/2 by 20 feet

Dimension of the hall = 4 by 12 feet

The living room and the hall is in the shape of rectangular.

The formula of the area of the rectangle is

A= length x width

the total area of the living room and the hall is

⇒ (35/2) x 20 + (4 x 12)  

⇒ 398 square feet.

The total cost is

⇒ 5.99 + 4.50 + 16.99 + 3. 00

⇒30.48

Thus, the total charge for this job is

⇒398 x 30.48

⇒$12131.04

Total cost (TC) in that is the overall economic cost of production and is made of variable cost, which varies in step with the amount of a terrific produced and includes inputs together with exertions and raw materials, plus fixed cost, which is unbiased of the quantity of an amazing produced and includes inputs that cannot be various in the brief term including homes and machinery, which include probably sunk prices.

Total cost in economics includes the full possibility price (blessings received from the next-nice alternative) of every issue of production as part of its constant or variable prices.

The additional total cost of one additional unit of manufacturing is known as marginal cost.

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