Gordon types 1,820 words in 26 minutes. Find the unit rate.

Answer:

1. a²-b²

2.4b² + 5ab/2

Step-by-step explanation:

1:. it's a formula of a²-b² so, it can be solved like this and

2: I'm not sure about 2nd one

Given :-

To Find :-

Solution:-

Taking the given equⁿ :

\(\bf \implies30=\dfrac{5}{6}y\)

\(\bf \implies 30\times 6=5y\)

\(\bf\implies y=\dfrac{\cancel{30}\times6}{\cancel5}\)

\(\underline{\boxed{\red{\bf{\longmapsto \qquad y \qquad = \qquad 36 \qquad}}}}\)

\(\boxed{\green{\bf\pink{\dag}\: Hence\:the\:value\:of\:y\:is\:36.}}\)

Some rules :-

On transposing numbers or variables,

The answer of  the given question based on finding each measure of a circle the answer is , (a)  m(MNP) = 12.5° degrees , (b) m(KL) = 102.5° degrees , (c)  m(KJ) = 52.5° degrees , (d)  m(JN) = 102.5° degrees , (e)  m(JLM) =  12.5° degrees.

In geometry,  arc is a portion of  curved line that can be thought of as  segment of  circle. It is defined by two endpoints on  circle and the arc itself is the part of  circle between those two points. An arc can be measured in degrees, and its measure is equal to  central angle subtended by  arc. The length of  arc can also be calculated using the formula L = rθ, where L is  length of  arc, r is radius of  circle, and θ is  angle (in radians) subtended by  arc at center of circle.

Using the properties of angles and arcs in circles:

a. Angle MNP is inscribed in arc MP, so m(MNP) = 1/2m(MP) = 1/2(25) = 12.5° degrees.

Since angles NPM and MPK are vertical angles, we have m(MPK) = m(NPM) = m(MNP) = 12.5° degrees. Then, m(MN) = m(MPK) + m(KPM) = 12.5 + 40 = 52.5° degrees.

b. Angle LKP is inscribed in arc LP, so m(LKP) = 1/2m(LP) = 1/2(25) = 12.5° degrees.

Since angles PKL and LKN are vertical angles, we have m(PKL) = m(LKN) = m(LKP) = 12.5° degrees. Then, m(KL) = m(PKL) + m(PKC) = 12.5 + 90 = 102.5° degrees.

c. Angle PKJ is inscribed in arc PJ, so m(PKJ) = 1/2m(PJ) = 1/2(25) = 12.5° degrees.

Since angles LPK and LPJ are vertical angles, we have m(LPK) = m(LPJ) = m(PKJ) = 12.5° degrees. Then, m(KJ) = m(LPK) + m(LPJ) = 12.5 + 40 = 52.5° degrees.

d. Angle JNM is inscribed in arc JM, so m(JNM) = 1/2m(JM) = 1/2(25) = 12.5° degrees.

Since angles KJM and KJN are vertical angles, we have m(KJM) = m(KJN) = m(JNM) = 12.5° degrees. Then, m(JN) = m(KJM) + m(MJN) = 12.5 + 90 = 102.5° degrees.

e. Angle JLM is an inscribed angle that intercepts arc JM, so m(JLM) = 1/2m(JM) = 1/2(25) = 12.5° degrees.

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Step-by-step explanation:

if u want it by step by step thn tell me i will do that..

The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer:

87/10

is already in the simplest form. It can be written as 8.7 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 87 and 10 is 1

Divide both the numerator and denominator by the GCD

87 ÷ 1

10 ÷ 1

Reduced fraction:  

87 /10

Therefore, 87/10 simplified to lowest terms is 87/10.

Hope this helps!

Answer:

40

Step-by-step explanation:

the width is 2x and the length is x.

2x+2x+x+x=120

6x=120

x=\(\frac{120#\\}{6}\)

x=20

2*20= width

width is 40 feet.

Adam's balance at the end of June is $627.27

The adjusting balance method is used to determine the interest that would be paid by a credit card owner. The interest that would be paid is determined at the end of a period after all transactions have been adjusted for.

For example, if I have $100 in my credit card. If I buy a shoe worth $50 and deposit $20. My balance at the end of the month would be ($100 + $50 - $20) = $130.

Adam's balance can be determined by adding the amount he spent on purchases to the beginning balance and subtracting the payments he made.

$626.45 + $37.41 + $44.50 - $65.5 +$24.89 - $104.77 +$23.60 + $15 + $51.85 = $605.23

The balance at the end of the month would be the sum of the interest and the amount in his balance

Interest earned = balance x interest rate

Interest rate = 14.63% / 4 = 3.66%

Interest earned = $605.23 x 0.0366 = $22.14

Balance = $22.14 + $605.23 = $627.37

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Answer:

C

Step-by-step explanation:

627.27. Just had it on my test

According to the given area of rectangle, the length and width of the rectangle is 7 and 21 respectively.

Area of rectangle

The standard form of calculating the area of the rectangle is written as,

A = l x w

where l refers the length and w refers the width of the rectangle.

Given,

Here we have given that the area of a rectangle is 147 square feet. And we need to determine the length and width if the length is three times the width.

Let us consider length of rectangle is n,

Then the width of rectangle is 3n.

Here we have to remember that the area of a rectangle is

=> A = n x 3n = 3n²

Here we are told that the area,

=> 3n²=147

Then the value of n² = 49

Therefore, the length is 7 and the width is 21.

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Answer:

135 degree

Step-by-step explanation:

180 - 45 = 135 degrees for the larger angle.

The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is

a(x)= -13

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:

a(x) = [f(b) - f(a)]/(b - a)

where,

a(x) = Average Rate of Change

f(a) = Function Value at a

f(b) = Function Value at b

Given,

g (x)=-2x³ +5x² from x=2 to x = 3

Average rate of change is a(x)

g (x)=-2x³ +5x²

Put x=2 in the above equation

g(2)= -2(2)³+5(2)²

= -16+20

=4

g(2)=4

Now, put x=3 in the above equation

g(3)= -2(3)³+5(3)²

= -57+45

= -9

We know that,

Average rate of change a(x)= (g(b)-g(a))/(b-a)

a(x)= g(3)-g(2)/(3-2)

a(x)= (-9-4)/1

a(x)= -13

Therefore, the average rate of change a(x)= -13

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Answer:

48g-40h+64

Step-by-step explanation:

multiply the 8 by each term inside the parenthesis

Player A was named MVP for 3 times , player B was named MVP for 4 times and player C was named MVP for 7 times.

It is given that player A was named MVP for one time less than player B and Player C was named MVP for four more than half the times of player B.

We have to find the no. of times each of players named MVP if , they together were named  MVP for 13 times.

Solve the expression (x - 1) + x + (x/2) + 4 = 13 for the value of x.

The value of x will be 2x - 2 + 2x + x + 8 = 26 or 5x + 6 = 26 or 5x = 20 or x = 4.

As per the question ;

Player A was named MVP for one time less than player B.

Player C was named MVP for four more than half the times of player B.

Let' assume player B was named MVP for x no. of times.

So,

No. of times player A was MVP = x - 1

and

No. of times player B was MVP = (x/2) + 4

Also ;

The sum of three players named MVP = 13

so ;

(x - 1) + x + (x/2) + 4 = 13

multiplying by 2 on both sides , we get ;

2x - 2 + 2x + x + 8 = 13 × 2

5x + 6 = 26

5x = 20

x = 20/5

x = 4

So ,

No. of times player A was MVP = x - 1

= 4 - 1

= 3

No. of times player B was MVP = x

= 4

No. of times player C was MVP = (x/2) + 4

= (6/2) + 4

= 3 + 4

= 7

Thus , player A was named MVP for 3 times , player B was named MVP for 4 times and player C was named MVP for 7 times.

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the counting number just before C5F16 is 3,072.

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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Answer:

arithmetic sequence formula: first term + (n - 1)common difference

9 + (n - 1)-2

9 + -2n + 2

= -2n + 11

The scale factor is 4/5.

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

To find the scale factor, we can compare the ratios of the corresponding side lengths of the congruent triangles.

Scale factor = (corresponding side length in triangle FQX) / (corresponding side length in triangle CVI)

Let's first identify the pairs of congruent angles:

Angle FQX = angle CVI (both are right angles)

Angle XQF = angle ICV (corresponding angles)

Angle FXQ = angle CVI (corresponding angles)

Now let's write the ratios of the corresponding side lengths in a proportion:

FQ / CV = QX / VI = XF / IC

Substituting the given values, we have:

28 / 35 = 36 / 45 = 24 / 30

Simplifying each fraction, we get:

4 / 5 = 4 / 5 = 4 / 5

Therefore, the scale factor is 4/5.

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The values of the missing sides are;

1. q = 4. 1, p = 11. 3

2. y = 56. 6, x = 35. 6

3. b = 16. 7, a = 9.1

Using the sine and cosine identities, we have;

sin θ = opposite/ hypotenuse

cos θ = adjacent/hypotenuse

We have that;

sin 20 = q/12

find the values

q = 4. 1

Also

cos 20 = p/12

p = 11. 3

For the second triangle

cos 39 = 44/y

cross multiply

y = 44/0. 7777

y = 56. 6

Also,

sin 39 = x/56.6

x = 35. 6

For the third triangle

sin 57 = 14/b

cross multiply

b = 16. 7

Also,

cos 57 = a/16. 7

cross multiply

a = 9. 1

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

the 2nd to last one................

From the problem, we have :

The common denominator will be the product which is 3 x 6 = 18.

Using the multiplication rule for equivalent fractions, it will be :

The add the results,

Estimate : 8 9/18

Next is to simplify the fraction.

The numerator 9 and the denominator 18 can be divided by 9

So this will be :

The answer will be : 8 1/2

Answer: 43.75 miles per day.

Step-by-step explanation: All you have to do is divide 350 by 8, when you divide you basically just split the number evenly 8 times, which is what 350 divided by 8 is. He will have to drive 43.75 miles a day.

Answer:

A

Step-by-step explanation:

You know that you can simplify 6/9 because both the numerator (top number) and denominator (bottom number) can be divided by 3. Therefore, you divide them by 3 to get 2/3. 2/3 cannot be simplified anymore. 2/3 is equal to 2/3. Therefore, the answer is A.

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Answer:

2

Step-by-step explanation:

2

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

Answer:

\((A)m\angle 2=125^\circ\\(C)m\angle 8=55^\circ\\(E)m\angle 14=100^\circ\)

Step-by-step explanation:

The diagram of the problem is drawn and attached.

Given that:

\(m\angle 9 =80^\circ\\m\angle 5 =55^\circ\)

\(m\angle 5+ m\angle 6=180^\circ\\55^\circ+ m\angle 6=180^\circ\\m\angle 6=180^\circ-55^\circ\\m\angle 6=125^\circ\\$Now:\\m\angle 6 = m\angle 2 $(Corresponging angles)\\Therefore m\angle 2=125^\circ\\\)

\(m\angle 5= m\angle 8=55^\circ $(Vertically Opposite Angles)\)

Also

\(m\angle 9+ m\angle 10=180^\circ\\80^\circ+ m\angle 10=180^\circ\\m\angle 10=180^\circ-80^\circ\\m\angle 10=100^\circ\\$Now:\\m\angle 10 = m\angle 14 $(Corresponging angles)\\Therefore m\angle 14=100^\circ\\\)

The angle measures that are correct are m<2 = 125degrees, m<8 = 55 degrees and m<14 = 100 degrees

Given the following angles from the diagram;

From the diagram

Hence;

55 + m<2 = 180

m<2 = 180 - 55

m<2 = 125degrees

Also;

Hence;

80 + m<14 = 180

m<14 = 180 - 80

m<14 = 100 degrees

Hence the angle measures that are correct are m<2 = 125degrees, m<8 = 55 degrees and m<14 = 100 degrees

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