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Answer: 1. C

2. B

Step-by-step explanation:)

The rotation rule describes the rotation about the origin in mathematics. The new coordinates of a point (x, y) after rotation can be determined using trigonometric functions. The angle of rotation can be calculated using the arc length formula.

In mathematics, the rule that describes rotation about the origin is referred to as the rotation rule or the radian rule. When a point (x, y) is rotated about the origin, the new coordinates (x', y') can be determined using the following formulas:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

The angle of rotation can be calculated using the arc length formula:

Angle = (Arc Length / Circle Circumference) * 360 degrees

For example, if the arc length separating the two hands of a clock is 1.0 meter and the radius of the clock is 0.70 meters, the angle of rotation can be calculated as follows:

Angle = (1.0 / (2 * pi * 0.70)) * 360 = 81 degrees

Step-by-step explanation:

since both objects and sides are similar, you can set each side equal, then you cross multiply, and do subtraction, then find x.

Final answer:

To find the value of x in similar polygons, justify the similarity, write an equation relating the sides, algebraically solve for x, calculate, and then check that the result is reasonable.

Explanation:

The subject of this question is Mathematics, and it is likely at the high school level, as it involves finding a missing length in similar polygons, which requires knowledge of ratios and properties of similar figures, often covered in high school geometry courses.

Steps to find the value of x:

Justify that the triangles are similar: This can typically be done by verifying that the triangles meet the criteria of similarity, such as having identical angles or corresponding sides in proportion.

Write an equation that relates the sides of the triangles: Utilize the properties of similar triangles to write ratios that compare the lengths of corresponding sides.

Algebraically isolate the unknown quantity x.

Plug in numbers and calculate the answer.

Check the answer to ensure it seems reasonable.

It's also important to remember that if two triangles are similar, their corresponding lengths are proportional, which you can express algebraically with a statement such as AB/CD = EF/GH where AB, CD, EF, and GH are corresponding sides of the similar triangles.

Answer:

NOTE THIS IS AN EXAMPLE:

Step-by-step explanation:

Let W = # white marbles and Y = # yellow marbles

W + Y = 44

W = 3Y -  8

W - 3Y  = -8

Subtract

4Y = 52

Y = 13

W =31

Answer:

Exact Form:

x = 6 5 , 6

Decimal Form:

x = 1.2 , 6

Mixed Number Form:

x = 1  1 /5 , 6

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

The value of x to this equation are as follows:

x = 6 or 6 /5

5x² - 36x + 36 = 0

-b ± √b² - 4ac / 2a

Using quadratic formula,

where,

a = 5

b = -36

c = 36

Therefore,

x = 36 ± √(-36)² - 4 × 5 × 36 / 2 × 5

x = 36 ± √1296 - 720 / 10

x = 36 ± √576 / 10

x = 36 ± 24 / 10

x = 36 + 24 / 10 or 36 - 24 / 10

x = 60 / 10  or 12 / 10

x = 6 or 6 / 5

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Answer:

Each subtraction expression represents the length of one leg of a right triangle with a hypotenuse of length

Step-by-step explanation:

Each subtraction expression x2 - x1 or y2 - y1 represents the length of a side of a right angled triangle. These length of sides are then used to calculate the resulting hypotenuse side using the Pythagorean theorem. In this case, the resulting hypotenuse is the length calculated.

Answer:

the answer is A)Each subtraction expression represents the length of one leg of a right triangle with a hypotenuse of length.

Step-by-step explanation:

took it on edge

Answer:

from original question:

Step-by-step explanation:

To determine the future value for the 401(k), we need to determine the amount contributed annually. It is stated that the amount the employee contributes to the fund is 9% of $45,624. $45,624(0.09) = $4,106.16 The employer contributes a maximum of 3% of the employee contribution. Therefore: $45,624(0.03) = $1368.72. Therefore, the total annual contribution is $5,474.88, giving a future value of $196,302.40. For the Roth IRA, the monthly contributions are $352.45 giving a future value of $152,636.09. Therefore, the 401(k) has a greater future value by $43,666.31.

The 401(k) has a greater future value by $43,666.31.

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV).

To determine the future value for the 401(k), we need to determine the amount contributed annually.

It is stated that the amount the employee contributes to the fund is 9% of $45,624. $45,624(0.09) = $4,106.16

The employer contributes a maximum of 3% of the employee contribution. Therefore:

$45,624(0.03) = $1368.72.

Therefore, the total annual contribution is $5,474.88, giving a future value of $196,302.40.

For the Roth IRA,

the monthly contributions are $352.45 giving a future value of $152,636.09.

Therefore, the 401(k) has a greater future value by $43,666.31.

To learn more about the future value;

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Answer:

The likelihood that the professor's socks matched his pants on both days is 0.5625

Step-by-step explanation:

Total no. of pair of socks = 24

No. of black pairs = 18

We are given that  he selects one pair of socks on Monday and one on Tuesday. Since he has lots of clean socks in the drawer he does not do laundry.

So, It is  a case of replacement

He always wears black pants.

We are supposed to find he likelihood that the professor's socks matched his pants on both days i.e. Black socks both days.

So ,Probability of wearing black socks on Monday = [tex]\frac{18}{24}[/tex]

So ,Probability of wearing black socks on Tuesday =[tex]\frac{18}{24}[/tex]

So,the likelihood that the professor's socks matched his pants on both days = [tex]\frac{18}{24} \times \frac{18}{24}=0.5625[/tex]

Hence the likelihood that the professor's socks matched his pants on both days is 0.5625

Final answer:

The probability that the professor picks black socks on both Monday and Tuesday is 9/16.

Explanation:

The question asks about the probability that a professor will pick black socks on two consecutive days without doing laundry in between. With 24 pairs of socks, of which 18 pairs are black and 6 pairs are brown, we will calculate the likelihood of the professor picking black socks on both Monday and Tuesday.

First, the probability of picking black socks on Monday (first pick) is 18 black pairs divided by 24 total pairs, which simplifies to:

Since the socks are not washed between Monday and Tuesday, the number of socks available remains the same. Therefore, the probability of picking black socks again on Tuesday (second pick) is also 3/4.

To find the overall probability that the professor picks black socks on both days, we must multiply the probability of the first event by the probability of the second event. In this case:

The probability that the professor's socks matched his pants (picked black socks) on both days is 9/16.

Answer:

36 ft^2

Step-by-step explanation:

3^2*3^3=9+27=36

Answer:

36 ft^2

Step-by-step explanation:

To solve this, you need to isolate/get the variable "r" by itself in the equation:

-1 = -3r + 2r       Combine like terms(terms that have the same variable and power/exponent.)  The only like terms you can combine are -3r and 2r

-1 = -r       Divide -1 on both sides to get "r" by itself

[tex]\frac{-1}{-1} =\frac{-r}{-1}[/tex]   (two negative signs cancel each other out and become positive)

1 = r   or   r = 1

Answer:R=-1

Step-by-step explanation: You would have to first do the math for the equation, then you would have to work in the "R" and given the answer is smaller than the equation itself we can tell that the "R" is a negative. So, if we add the -3 and the 2 we get 1,so we can say that the "R" are both equal to -1 then we put it in the equation. We get -1=1 we add the "R's" then get -1

Answer:

x = -6

Step-by-step explanation:

x - 4  = -10

x = -6

Can I get brainliest

Answer:

x = -6

Step-by-step explanation:

you just add 4 to the other side in order to isolate the x

check

-6 - 4 = -10

Answer:

It will take 0.8333h for the mustang to catch up to the grand am.

The two cars will have traveled 66.664 miles on the turnpike

Step-by-step explanation:

The position for each car can be modeled by equations in the following format:

[tex]S(t) = S(0) + vt[/tex]

In which S(t) is the position t hours after the last car(the Ford Mustang) has left, S(0) is the position of each car when the Ford Mustang left and v is the speed of each car, in miles per hour.

Pontiac

Traveling at 50 mph, which means that [tex]v = 50[/tex].

The Ford Mustang leaves half an hour after the Pontiac. The Pontiac travels at 50 mph, which means that in this interval, the Pontiac will have traveled 0.5*50 = 25 mph. This means that S(0) = 25. So

[tex]S_{P}(t) = 25 + 50t[/tex]

Ford Mustang

Leaves from position 0, so S(0) = 0.

Travel in the same distance at 80 mph, so [tex]v = 80[/tex]. So

[tex]S_{M}(t) = 80t[/tex]

How long would it take for the mustang to catch up to the grand am ?

This is t when

[tex]S_{M}(t) = S_{P}(t)[/tex]

[tex]80t = 25 + 50t[/tex]

[tex]30t = 25[/tex]

[tex]t = \frac{25}{30}[/tex]

[tex]t = 0.8333[/tex]

It will take 0.8333h for the mustang to catch up to the grand am.

When it catch up how far will the two cars have traveled on the turnpike

This is either [tex]S_{M}(0.8333)[/tex] or [tex]S_{P}(0.8333)[/tex], since they will be in the same position. So

[tex]S_{M}(t) = 80t[/tex]

[tex]S_{M}(0.8333) = 80*0.8333 = 66.664[/tex]

The two cars will have traveled 66.664 miles on the turnpike

The Ford Mustang will catch up to the Pontiac Grand Am in 18.75 minutes and they will have traveled a total of 25 miles on the turnpike.

To find out how long it takes for the Ford Mustang to catch up to the Pontiac Grand Am, we need to determine the time it takes for the Mustang to cover the same distance that the Grand Am has already traveled. The Grand Am has a head start of half an hour at a speed of 50 mph, so it has covered a distance of:

Distance = Speed x Time = 50 mph x 0.5 hr = 25 miles

Now, we can calculate the time it takes for the Mustang to cover this distance:

Time = Distance / Speed = 25 miles / 80 mph = 0.3125 hr = 18.75 minutes

Therefore, it will take the Mustang 18.75 minutes to catch up to the Grand Am.

When the two cars catch up, they will have traveled a total distance of 25 miles, which is the distance covered by the Grand Am in the half-hour head start.

A constant term is the whole number in an expression!

They are always easy to identify

5x + 14 ....

14 is the constant term!

80y - 2

-2 is the constant term!

I hope I helped :)

[tex]\huge\boxed{\sf{Hello\;there! :)}}[/tex]

A constant term is a number in an algebraic expression or equation.

A constant doesn't have any variables next to it.

For example, in the equation

4x²-2x=24, 24 is the constant.

[tex]\huge\boxed{\text{Hope\;it\;helps\;you!}}[/tex]

[tex]\huge\bold{\underline{\underline{Good\;luck!}}}[/tex]

[tex]\huge\rm{StillEnjoyingLife :)[/tex]

Answer:

Step-by-step explanation:

Let x represent the number of hours for which you can rent the truck.

truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented. It means that the cost of renting the truck for x hours would be expressed as

50.75 + 8.25x

You have at most $125.00 to spend on a truck rental. Therefore, the inequality that describes the number of hours you can rent the truck is

50.75 + 8.25x ≤ 125

Final answer:

To write the expression 6(-5r-4)-2(r-7s-3) in standard form, distribute the numbers outside the parentheses across the terms within and combine like terms to get -32r + 14s - 18.

Explanation:

To write the expression 6(-5r-4)-2(r-7s-3) in standard form, we must distribute the numbers outside the parentheses to each term inside the parentheses and then combine like terms.

Distribute the 6: 6 × (-5r) = -30r and 6 × (-4) = -24, giving us -30r - 24.

Distribute the -2: -2 × r = -2r, -2 × (-7s) = +14s and -2 × (-3) = +6, giving us -2r + 14s + 6.

Combine the two resulting expressions: -30r - 24 - 2r + 14s + 6.

Combine like terms: The terms -30r and -2r combine to -32r, and the constants -24 and +6 combine to -18.

The standard form of the expression is -32r + 14s - 18.

Check the answer to see if it is reasonable.

The lateral area of the rectangular prism is calculated to be 208m² using the formula for lateral area of a prism. Assuming the width is the same as the length, the surface area is calculated to be 240m² using the formula for surface area of rectangular prism.

In mathematics, the lateral area and surface area of a rectangular prism can calculated using specific formulas. To calculate the lateral area of a rectangular prism, which is the area excluding the base and the top, you use the formula: Lateral area = Perimeter of the base x Height. Given the base length is 4m, and the height is 13m, the perimeter of the base is 4 x 4m = 16m. So, the lateral area = 16m x 13m = 208m².

The surface area of a rectangular prism is calculated using the formula: Surface area = 2lw + 2lh + 2wh. where l is the length, w is the width, and h is the height. In this case, the width is not given. Assuming it's the same as the length (since it's also 4m in the given figure), the surface area = 2*(4m*4m) + 2*(4m*13m) + 2*(4m*13m) = 32m² + 104m² + 104m² = 240m².

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Answer:

1.5 gm per cubic cm

Step-by-step explanation:

Volume of pyramid is given by formula = 1/3(area of base * height)

Given in problem

base area = 100 sq. cm

height= 6cm

therefore volume of the pyramid = 1/3(100*6) = 200 cubic cm

Formula of density is = mass of the body/ volume of the body

minimum weight of required paperweight = 300 gm

minimum density of paperweight = 300/200 = 1.5 gm per cubic cm

Answer:

The answer is 6 cups.

Step-by-step explanation:

If 20 cookies are 2 cups, that means that 10 cookies are 1 cup. If you see the pattern, the answer would easily be 6 cups.

Answer:

432 square meters

Step-by-step explanation:

The lateral area means the area that's not the bases. We have to add up all the lateral faces.

2(big rectangle area) + 2(small rectangle area) = total lateral area

2(144) + 2(72) = total lateral area

total lateral area = 432 square meters

Answer:

432

Step-by-step explanation:

432

Answer:

Clare account balance after one year will be $164.80

Step-by-step explanation:

Interest = PRT/100

Principal P = $160, Rate r = 3%, and time t = 1 year

Interest = (160*3*1)/100

Interest =480/100

= $4.80

The total balance in Clare's account after 1 year will be $160 + $4.80

= $164.80

Answer:

6 hours

Step-by-step explanation:

Please refer to the attached image for explanations

Answer:

Answer letter D

Step-by-step explanation:

-3x + 3y = 9

2x - 7y = -14

Let's start by simplifying both equations:

-3x + 3y = 9 (divide everything by 3)

2x - 7y = -14 (divide everything by 2)

We will then have:

-x + y = 3

x - [tex]\frac{7}{2}[/tex]y = - 7

Then we sum both equations, eliminating x and isolating y to find its value!

y + (- [tex]\frac{7}{2}[/tex]y) = 3 + (- 7)

[tex]\frac{2}{2}[/tex]y + (- [tex]\frac{7}{2}[/tex]y) = - 4

Summing the fractions of y we have

- [tex]\frac{5}{2}[/tex] y = - 4 .: y = [tex]\frac{8}{5\\}[/tex] .: y = 1 [tex]\frac{3}{5}[/tex](we found y!)

Now we substitute y in one of the previous equations to find x:

-3x + 3 × ( [tex]\frac{8}{5\\}[/tex] ) = 9

-3x + [tex]\frac{24}{5\\}[/tex] = 9

-3x = 9 - [tex]\frac{24}{5}[/tex]

-3x = [tex]\frac{45}{5}[/tex] - [tex]\frac{24}{5}[/tex]

-3x = [tex]\frac{21}{5}[/tex]

x = [tex]\frac{21}{5}[/tex] ÷ -3 (this is tricky, but it's the same as [tex]\frac{21}{5}[/tex] × -[tex]\frac{1}{3}[/tex] )

x = - [tex]\frac{7}{5}[/tex] .: x = - 1 [tex]\frac{2}{5}[/tex](finally found x!)

Bringing everything together we have:

x = - 1 [tex]\frac{2}{5}[/tex]

y = 1 [tex]\frac{3}{5}[/tex]

I hope it helps :)

To convert the word form of the time to decimal form, add 10.00 and 0.62 to get the final number representation of 10.62 seconds.

To write the time of ten and sixty-two hundredths seconds as a number, we need to convert the word form into decimal form. The word form tells us that there are ten whole seconds and sixty-two hundredths of a second. To convert this to decimal form, we write 10 as 10.00 and 62 hundredths as 0.62. Then, we add the two decimal numbers together to get the final result: 10.00 + 0.62 = 10.62. Therefore, the number representation of the given time is 10.62 seconds.

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There are 120 possible combinations of phone models, colors, and calling plans.

To calculate the number of possible combinations of phone models, colors, and calling plans, we need to multiply the number of choices for each category together. In this case, there are 4 phone models, 6 colors, and 5 calling plans. So the total number of combinations is 4 x 6 x 5 = 120.

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Final answer:

To write a coordinate geometry proof, first choose and plot your figures in a coordinate system, then use properties of the system to express geometric properties, apply Euclid's geometric axioms, perform algebraic manipulations, and compile these into a logical proof sequence.

Explanation:

Writing a coordinate geometry proof involves several logical steps that combine geometry with algebra. The aim is to use the properties and axioms of geometry, expressed in a coordinate system, to prove a geometric statement. Here's a simplified process:

Choose a coordinate system and plot the given geometric figures using the appropriate coordinates.

Use the properties of the chosen coordinate system to write expressions for geometric properties such as the lengths of sides, slopes of lines, and coordinates of midpoints or centroids.

Apply geometric axioms, such as those from Euclid's geometry, to relate different parts of the figure.

Carry out algebraic manipulations to show that a certain property holds, such as proving two sides are congruent or two angles are equal.

Compile the findings into a logical sequence to form the proof, stating clearly how the coordinate geometry demonstrates the property or theorem in question.

Throughout your proof, ensure you reference the correct coordinate systems and datum points, and be prepared to convert between coordinate systems if necessary, which can be crucial when applying different geometric axioms or properties.

Answer:

After 10 seconds

Step-by-step explanation:

In this problem, the height of the object after t seconds is described by the function

[tex]h(t)=-16t^2+144t+160[/tex]

where

160 ft is the initial height of the object at t = 0

+144 ft/s is the initial velocity

[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)

Here we want to find the time at which the object hits the ground, so the time t at which

[tex]h(t)=0[/tex]

Therefore we can write

[tex]-16t^2+144t+160 =0[/tex]

Simplifying (dividing each term by 16), we get

[tex]-t^2+9t+10=0[/tex]

This is a second-order equation in the form

[tex]ax^2+bx+c=0[/tex]

Which has solutions given by the formula

[tex]t_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] (2)

Here we have:

a = -1

b = 9

c = 10

Substituting into (2) we find the solutions:

[tex]t_{1,2}=\frac{-9\pm \sqrt{9^2-4(-1)(10)}}{2(-1)}=\frac{-9 \pm 11}{-2}[/tex]

Which gives:

[tex]t_1=10 s\\t_2 =-1 s[/tex]

Since time cannot be negative, the only solution is

t = 10 seconds

Answer:

The answer to your question is $84.15

Step-by-step explanation:

Data

cost of the meal = $76.50

tip 10%

total cost = ?

Process

1.- Calculate the 10% of $76.50 using proportions and cross multiplication.

             $76.50 --------------- 100%

                   x     -----------------  10%

                      x = (10 x 76.5) / 100

                      x = 765/100

                      x = 7.65

2.- Calculate the total cost

Total cost = cost of the meal + tip

-Substitution

Total cost = $76.50 + $7.65

-Result

Total cost = $84.15

Answer:

0.9032

Step-by-step explanation:

Given that:

mean (μ) = 146 grams and standard deviation (σ) = 2.3 grams

The z score is a measurement used in statistics to calculate how far a value is from the mean in a normal distribution. The z score is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For the baseball not to weigh more than 149 grams i.e x = 149 g

[tex]z=\frac{x-\mu}{\sigma}=\frac{149-146}{2.3} =1.30[/tex]

From the probability distribution table, P(x < 149) = P(z < 1.30) = 0.9032 = 90.32%

Final answer:

To calculate the unit rate of candy per person, divide 7/8 pounds by 6 people, which results in 7/48 pounds per person. This is the unit rate in its simplest form.

Explanation:

To find the unit rate in pounds per person, we divide the total amount of candy, which is 7/8 pounds, by the number of people, which is 6.

Step 1: Determine the total weight of the candy: 7/8 pounds.

Step 2: Determine the number of people: 6 people.

Step 3: Divide the total weight by the number of people to get the unit rate:

   (7/8) pounds ÷ 6 = (7/8) ÷ (6/1) = 7/8 ÷ 6/1 = 7/8 ÷ 6 = 7/48 pounds per person.

Step 4: Simplify the fraction, if possible. In this case, the fraction 7/48 is already in simplest form.

The unit rate of candy per person is 7/48 pounds.

Final answer:

7/48 pounds per person is the simplest form for the unit rate of candy per person.

Explanation:

The student is asking how to determine the unit rate of candy distributed per person if 7/8 pounds of candy were split among 6 people.

Calculation of Unit Rate:

To find the unit rate, divide the total amount of candy by the number of people:

This is already the simplest form, so the unit rate is 7/48 pounds per person.

Answer:

X=72

Step-by-step explanation:

216/3= 72

Answer: 3 and 240

Step-by-step explanation:

Edg 2020

Answer:

The triangular prism has

✔ 3

lateral faces.

The triangular prism has a lateral area of

✔ 240

square inches.

Step-by-step explanation: