9. The perimeter and the ratio of the
length to the width of a rectangle are
given. Find the length and width of the
rectangle.
Perimeter: 132 cm 1:w = 7:4

The area of trapezoid ABCD is 37.5 units^2.

Trapezoid is a type of quadrilateral with at least one pair of parallel sides. The area of trapezoid is given by:

Area = ½(a + b)*h

Where a and b are the length of two parallel sides and h is the perpendicular length between the length of two parallel sides.

In the given trapezoid ABCD, which is defined by coordinates of A, B, C, and D, the distance of each side is given by: √((x2 – x1)^2 + (y2 – y1)^2)

The length of a (DA) = √((x2 – x1)^2 + (y2 – y1)^2) = √((-3 – 0)^2 + (2 – (-2))^2) = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5 units

The length of b (BC) = √((x2 – x1)^2 + (y2 – y1)^2) = √((7 – 1)^2 + (-3 – 5)^2) = √((6)^2 + (-8)^2) = √(36 + 64) = √(36 + 64) = √(100) = 10 units

The length of h (AB) = √((x2 – x1)^2 + (y2 – y1)^2) = √((1 – (-3))^2 + (5 – 2)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √(25) = 5 units

Hence, the area of trapezoid:

Area = ½ (5 + 10) * 5 = 7.5 * 5 = 37.5 units^2

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The equation in terms of log(x) and log(z) is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

What is logarithmic expression?

A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.

Consider, the given logarithmic expression,

[tex]logx\sqrt{z}[/tex]

By using the logarithmic rule: log(ab) = log(a) + log(b)

So,

[tex]logx\sqrt{z} = log(x) + log\sqrt{z}[/tex]           ..(1)

Replace [tex]\sqrt{z}[/tex] by [tex]z^\frac{1}{2}[/tex].

So,

[tex]log\sqrt{z} = logz^\frac{1}{2}[/tex]

Apply the rule: [tex]loga^b = b log(a)[/tex]

Therefore, [tex]log(\sqrt{z}) = \frac{1}{2}log(z)[/tex]

Substitute this value in equation (1).

[tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

Hence, the expression in terms of x and z is, [tex]logx\sqrt{z} = logx + \frac{1}{2} log(z)[/tex].

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Answer:10 blocks

Step-by-step explanation: East And West are in a straight line

Answer:

9

How I got the Answer:

We have,        

  p = 0.30        

   q = 1 - p = 0.70          

    n = 449

Here,

npq = 4449*0.3*0.7 = 9

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Answer:

y = 100x + 400

Step-by-step explanation:

What we know:

     - You started with 400

     - You get 100 a week

What we need to find out:

 - The equation or rate to know how much money acquired in specific time

Step 1 ( of 1 ): Equation

-   if you let y represent the total of money you acquire then the equations starts as

y=

-  Then we know that we get 100 a week so let x represent the amount of weeks so

y = 100x

-  Lastly we know that we started with 400 so then we just add that to the equation to make it

y = 100x + 400

Answer:

1323.3

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

The number never changes when you divide by 1. So -1/1=-1.

-Hope this helped

Answer:

the slope is 1

Step-by-step explanation:

x1,y1=(3,-1)

x2,y2=(-3,-5)

[tex]m = y2 - y1 \div x2 - x1[/tex]

-5--1/-3-3

-6/-6

m=-6/-6

simplify the fraction -1/-1

since 2 negatives = positive

m=1/1

simplify

m=1

Step-by-step explanation:

we know, the area of a rectangle is

length × width

so, we have here

length × (x - 5) = x² - 7x + 10

therefore,

length = (x² - 7x + 10) / (x - 5)

so, just by looking at it (with experience) I see that length is (x - 2).

but let's do the actual polynomial division, which seems to be the desired exercise here.

x² - 7x + 10 ÷ x - 5 =

it is very similar to actual number divisions.

we go from left to right.

we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).

x² / x = x

that is already our first term of the result (quotient) :

x² - 7x + 10 ÷ x - 5 = x

now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x

and now we pull down the next term from the dividend :

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x + 10

and we repeat the process with that new dividend :

-2x / x = -2

that is our next term of the quotient.

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

- -2x + 10

-------------

0 0

there is no remainder, and there is no more term to pull down. we are finished.

the result of the division is (as expected) : x - 2

the expression to describe the length is therefore

x - 2

The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.

Let's assume that x times 3/8 are in 5/4.

So, calculating a division equation for the value of x.

x * 3/8 = 5/4

=> x = 5/4 * 8/3

=> x = 40/12

Dividing the numerator and denominator by 4.

We get, the value of x equal to

=> x = 10/3

Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.

For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.

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A) The interval(s) on which f is increasing is; (1,3) ∪ (4,6).

B) The interval(s) on which f is decreasing is; (0,1) ∪ (3,4).

(C) The interval(s) on which f is concave upward is; (0,2) ∪ (3,5).

A) A function is said to be increasing on an interval if for every point on that interval we see that the first derivative is positive. Thus, from the attached graph, we see that the function is increasing on the intervals (1,3) and (4,6).

B) If the value of the derivative f' (x) ≤ 0 of the function, then we can say that the interval is a decreasing interval. From the graph, we can say that the function is decreasing on intervals (0,1) and (3,4).

C) The graph is concave upward on the intervals (0,2) and (3,5).

D) The graph is concave downward which means convex on the interval (3,4).

e) The points of inflection are defined as the points located on a smooth plane curve that the curvature changes sign. In this graph, the points of inflection are x=3 and x=5.

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The solution of the expression -3√7r³-6√7r² is -3√7r²(r+3)

Expression:

An expression also known as the algebraic expression consists of unknown variables, numbers and arithmetic operators.

Given,

Here we have the expression -3√7r³-6√7r²

Now, we have to solve this expression step by step.

In order to solve this expression, we have to write the given expression as,

=> - 3√7r³- 6√7r²

Here the value √7 is common, so we have to take it as the common term and then rewrite the given expression as,

=> √7(-3r³-6r²)

Now, we have to take the number -3, as the common term then we get he expression like the following,

=> -3√7(r³+3r²)

Now we have to take the variable r² as the common term, then we get,

=> -3√7r²(r+3)

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By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.

In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,

The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]

Then, the distance (D) between them is given by :

[tex]D = \sqrt{(x_{1} -x_{2} )^{2} -(y_{1} -y_{2} )^{2} }[/tex]

Now, the given points are  (−6, −3) and (0, 5).

Putting these values in the distance formula, we have

[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]

Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.

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Answer: 10 units

Step-by-step explanation: i took the test and got it right

Answer:

it would be 66.75 for one day if ella plans to drive for 1 day with 50 miles, and if you need how much money she has left it is 63.25

Step-by-step explanation:

hope it helped:)

Answer:

1) The new price would be $595

2 )The discount is $105 off

Step-by-step explanation:

1) 700 x 0.85 = 595

2) 700 x 0.15 = 105

From the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

As given in the question,

Let x represents the number of nickels

And y represents the number of quarters

Total number of nickels and quarters are 35

Total value of given coins = $2.50

Required equation for the given condition is:

x + y = 35   ___(1)

1 nickel = 0.05 dollars

1 quarter = 0.25 dollars

0.05x + 0.25y <2.50 ___(2)

Substitute x = 35 - y in (2) we get,

0.05 ( 35 - y ) + 0.25y < 2.50

⇒1.75 - 0.05y + 0.25y < 2.50

⇒ 0.2y < 2.50 - 1.75

⇒ 0.2y < 0.75

⇒ y < 3.75

Maximum number of quarters for the given condition is equal to 3.

Therefore, for the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

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Answer: x = -2

Step-by-step explanation:

[tex]\frac{1}{6x^2} =\frac{1}{2x} +\frac{7}{6x^2}[/tex]

[tex]\frac{1}{6x^2} = \frac{3x}{6x^2} + \frac{7}{6x^2}[/tex]  (work with common denominators)

[tex]\frac{1}{6x^2} = \frac{3x+7}{6x^2}[/tex]

[tex]1 = 3x + 7[/tex] (remove the 6x^2 because they'll cancel out when you cross multiply)

[tex]-6 = 3x[/tex]

[tex]-2 = x[/tex]

Using equation, the number of math assignment is 69 .

Brianna has 113 assignments in the history, science, and art sections combined. The rest of her assignments are in the math section. Brianna has 182 assignments in total.

Using equation, the number of assignments in the math section of Brianna's binder can be calculated as follows:

She has 113 assignments in the history, science, and art sections combined.  

Let x be the number of assignments that are in math section.

There are 182 assignments in total.

Therefore,

x + 113 = 182

subtract 113 from both sides of the equation

x + 113 = 182

x + 113 - 113 = 182 - 113

x = 69

Therefore, the number of math assignment is 69.

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Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 and crosses the y- axis at (0, - 7 ) ⇒ c = - 7

that is the y- intercept c = - 7

A variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.

According to the question,

We have the following information:

Each person performed for the same amount of time. Kira sang three solos and played a piano piece. Hector sang 2 solos and played a piano piece that lasted twice as long as Kira's. Each of the solos Kira and Hector sang was 3.5 minutes long.

Now, let's take time for solos to be x min and time for Kira's piano to be y min and that for Hector is z min.

So, we have the following equations:

Kira:

3x+y

Hector:

2x+z

Now, z = 2y

x = 3.5 minutes

Time is equal:

3x+y = 2x+z

3x+y = 2x+2y

3x-2x = 2y-y

x = y

y = 3.5 min

z = 2*3.5

z = 7 min

Hence, a variable can be any number or alphabet that may constantly vary and the equation to represent the given situation for Kira is (3x+y) and for Hector is (3x+z) where x is the time for solos and y and z are times for piano. The value of x and y is 3.5 minutes and that of z is 7 minutes.

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Answer:

320 pounds sterling

Step-by-step explanation:

All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!

Answer:

2.543%

Step-by-step explanation:

295x1.02543=$302.50

295+2.543%=302.50

Answer:

  0.4 m = 40 cm

Step-by-step explanation:

You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.

The scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.

This lets us write a proportion for the height of the model tower:

  [tex]\dfrac{h}{40\text{ m}}=\sqrt[3]{\dfrac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^{-6}}=\boxed{0.40\text{ m}}[/tex]

Logan should make his tower 0.4 meters, or 40 cm high.

Answer:

The coordinates of B are (4, 2)

Step-by-step explanation:

The coordinates of B can be calculated as follows ?

The midpoint of line AB is M(3,-3)  is derived from the formula

[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]

Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B

Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.

Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is

[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]

Substitute 2 for [tex]x_{1}[/tex], then it follows that

[tex]\frac{2+x_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]

Simplify both sides of the equation

[tex]2+x_{2}=6[/tex]

Substract 2 from both sides of the equation

[tex]2-2+x_{2}=6-2[/tex]

Simplify the equation

[tex]x_{2}=4[/tex]

Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is

[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]

Substitute -8 for [tex]y_{1}[/tex], then it follows that

[tex]\frac{-8+y_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]

Simplify both sides of the equation

[tex]-8+y_{2}=-6[/tex]

Add 8 to both sides

[tex]-8+8+y_{2}=-6+8[/tex]

Simplify the equation

[tex]y_{2}=2[/tex]

Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).

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The amount owed by the debtor is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer: -1

Step-by-step explanation:

Answer:

By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.

-4/4 = -1

So, the slope is -1

Answer:

oof try adding dem

Step-by-step explanation:

hope you git 20 points

The value of n is 22.

In this question, we have been given the parallel lines HE and AD are

cut by transversal BF at points G and C, respectively.

Consider the following diagram.

If m∠HGF = 5n and m∠BCD = 2n +66, we need to find n.

∠HGF and ∠BCD are alternate exterior angles.

We know that  alternate exterior angles are congruent.

So, m∠HGF = m∠BCD

5n = 2n +66

5n - 2n = 66

3n = 66

n = 66/3

n = 22

Therefore, the value of n is 22.

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Answer:

[tex]m= -2\frac{1}{13}[/tex]

Step-by-step explanation:

2m-27/3=5m

x3.             x3

2m-27=15m

-2m.     -2m

-27=13m

/13.   /13

-27/13=m

-2 1/13=m

Hopes this helps please mark brainliest