Mathematics High School

The scale factor of a figure and its enlargement is 6. What is the new length of the enlarged figure if the original length is 3 cm?
3 cm
6 cm
18 cm
36 cm

Answers

Answer 1

You multiply three times six.

3 x 6 = 18

Answer 2

Answer:

The new length of the enlarged figure will 18 cm.

Step-by-step explanation:

A scale factor is a number which scales, or multiplies the original figure by some quantity.

In the equation [tex]y = Cx[/tex], C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.

As the given length is 3 cm, so with a scale factor of 6, the length of the enlarged figure will be [tex]3\times 6=18[/tex] cm

Therefore, the new length of the enlarged figure will 18 cm.

Related Questions

Express in exponential form log(2)16 = 4

Answers

[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad % exponential notation 2nd form a^y= b\implies log_a b=y \\\\ -------------------------------\\\\ log_2(16)=4\qquad \qquad \implies \qquad 2^4=16[/tex]

A rhombus has diagonals 500 yd and 800 yd in length. Find the area in square miles.

Answers

To find the area of a rhombus with diagonals of 500 yards and 800 yards, use the formula (d1 * d2) / 2 and convert the result to square miles.

Given: The diagonals of the rhombus are 500 yards and 800 yards.

Formula: The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the diagonals of the rhombus.

Calculation: Area = (500 * 800) / 2 = 200,000 square yards.

Conversion: To convert square yards to square miles, divide the area by 3,097,600 (number of square yards in a square mile).

Final Result: The area of the rhombus is approximately 0.0646 square miles.

0.032 divided 4 = ___

Answers

0.008. Hope this helps in any way.

Luis bought stock at $66.80. The next day, the price increased $13.85. This new price changed by −2 3 /4 % the following day. What was the final stock price, rounded to the nearest cent? ?

Answers

we know that
1) Luis bought stock at ---------------> $66.80
2) The next day, the price increased $13.85--------> $66.80+$13.85=$80.65
3) This new price changed by −2 3 /4 % the following day
2 3/4%----> (2*4+3)/4----> 11/4 %----> 2.75%
so
(100%-2.75%)-----> 97.25%
the final stock price is $80.65*0.9725-----> $78.43

the answer is
$78.43

The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students? a0 What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr. Smith's students? a1

Answers

Answer: The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.

Step-by-step explanation:

Mr Smith's math class scores : 61, 67, 81, 83, 87, 88, 89, 90, 98, 100

Number of terms,N = 10

[tex]Mean=\mu =\frac{\text{sum of all the terms}}{\text{total number of terms}}[/tex]

[tex]\mu =\frac{61+67+81+83+87+88+89+90+98+100}{10}=\frac{844}{10}=84.4[/tex]

Standard deviation of the sample:

[tex]\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{10}(1364.4)}=11.68[/tex]

Standard deviation for the population:

[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{9}(1364.4)}=12.31[/tex]

The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.

Hey y'all I REALLYYYY need help with this!!
!Calculate the distance between the points K= (1, -5) and J= (8,-9) in the coordinate plane. Give exact answer (not decimal form)

Answers

Hello,
[tex]|KJ|=\sqrt{(1-8)^2+(-5+9)^2}=\sqrt{65}[/tex]

Given f(x)=x-7 and g(x)=x2 find g(f(-1))

Answers

[tex]f(x)=x-7\\\\f(-1)=-1-7=-8\\\\g(x)=x^2\\\\g(f(-1))=g(-8)=(-8)^2=64[/tex]

$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.

Answers

So, what we have to do is split 10000
0.04(2500) + 0.05(7500)
Multiply:
100 + 375 = 475
$475 is made in one year

Solve using the quadratic formula

Answers

The answers are -16 and 9. Hopefully this helps :D

Answer:

x = - 16, x = 9

Step-by-step explanation:

[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]

Ignore the "A" ^

v² + 7v - 144 = 0

a = 1, b = 7, c = - 144

[tex]x=\frac{-7±\sqrt{7^{2} -4(1)(-144)} }{2(1)}[/tex]

[tex]x=\frac{-7±\sqrt{49 +576} }{2}[/tex]

[tex]x=\frac{-7±\sqrt{625} }{2}[/tex]

[tex]x=\frac{-7+25}{2}[/tex] and [tex]x=\frac{-7-25}{2}[/tex]

[tex]x=\frac{18}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex]

x = 9 and x = - 16

Identify the radius of the circle whose equation is (x - 2)2 + (y - 8)2 = 16.

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r}\\\\ -------------------------------\\\\ (x-\stackrel{h}{2})^2+(y-\stackrel{k}{8})^2=16\implies (x-2)^2+(y-8)^2=\stackrel{r}{4^2}[/tex]

The radius is 4.

That equation is in center-radius form. When that’s the case, the radius is the square root of the number in the right of the equals sign. Square root of 16 is 4.

Suppose you have an unfair coin that comes up heads 60% of the time and tails 40% of the time. you play a game where you flip the coin a single time and you lose $2 if you get heads and you win $3 if you get tails. what is the expected value of your outcome?

Answers

The expected value is that you lose 2$ because you come up with heads 60% of the time, which is the most likely outcome, and if you come up with heads then you lose 2$.

Find the volume of the cylinder. Use 3.14 for pie

Answers

volume of a cylinder formula is
[tex]v = \pi {r}^{2} \times h[/tex]
[tex]v = 3.14 \times {3}^{2} \times 12[/tex]

How could the relationship of the data be classified? scatter plot with points scattered going up to the right

A fairly strong positive correlation
A fairly strong negative correlation
A fairly weak negative correlation

Answers

Answer:

The correct answer is A. A fairly strong positive correlation

Step-by-step explanation:

Scatter Plot : A graph of plotted points that show the relationship between two sets of data.

Now, the points of the scatter plot are going up this shows the increase in the data points so we can say the correlation is positive.

Now, the direction of the scatter plots is to the right. So, we can say that the correlation is strong correlation.

Hence, the correct answer is A. A fairly strong positive correlation

Answer:

the Correct Option is A : fairly strong positive correlation

Step-by-step explanation:

Scatter Plot is a graph that is graphed using points and which shows the relationship between two sets of data. Only used to show correlation.

As given the points of the scatter plot are going up this implies the increment in one set of data with respect to other so we can say here correlation is positive. And the direction of the scattered points is to the right. So, it reflects that the correlation is strong correlation.

Thus, the Correct Option is A : fairly strong positive correlation

Use the verbs in the word bank to complete the sentences. Remember that you will need to put the verb in the correct form. Watch out for irregulars and stem changers! Do NOT write the sentence. ONLY fill in the verb in its correct form.

Word Bank:

ser comer jugar estar ir estudiar

1. Carlos _____ muy inteligente.

2. Mi hermana y yo ______ al museo.

3. Yo ________ al fútbol todos los sábados.

4. ¿Qué ______ tú cuando vas al restaurante mexicano?

5. Ustedes _________ los verbos en español. ¿No?

Question 1 options:
Blank # 1

Blank # 2

Blank # 3

Blank # 4

Blank # 5

Answers

1.es
2. fuimos
3. juego
4.comes
5. saben

*100% CORRECT ANSWER WERE

1) es

2) vamos

3) juego

4) comes

5) estudian

URGENT 50 POINTS!!!

Plan A has a $700 yearly premium with a $3,000 deductible.
Plan B has a $1,200 yearly premium with a $1,000 deductible.

Water damage (from broken pipes, overflows, etc.) results in approximately 12% of claims overall, with an average claim being $5,200. What is the expected value (loss or gain) to Acasa for every customer who chooses plan A?

A.)$-1,060
B.)$ 436
C.)$ -360
D.)$ -100

Answers

oh no my answer i tooooooooooo short ok bye
its not c.
answer- b

Answer:

The answer is B

Step-by-step explanation:

I got it right on plato

Juan had $5.25 in nickels and quarters. if he had 15 more nickels than quarters, how many quarters did he have?

Answers

We will need to have a model for this problem to easily solve it.
First, let us say x is the number of nickels Juan had, and y is the number of quarters Juan had.

Now, we all know that a nickel is worth 5 cents and a quarter is worth 25 cents. The given said Juan had a total amount of nickels and quarters equal to $5.25 and that there should be 15 more nickels than quarters - we need a second model: $5.25 = $0.05x+$0.25y, but x = y+15 => $5.25 = $0.05(y+15)+$0.25y. Simplifying, we have $5.25 = $0.05y+$0.25y+$0.75 or $0.3y+$0.75.

Isolating the unknown, we have $5.25-$0.75 = $0.3y, or $4.50 = $0.3y.
Divide both sides by $0.3, we have y = 15. Therefore, x = 15+15 or 30.
Check the solution, 30($0.05)+15($0.25) = $5.25.

Therefore, Juan had 15 quarters.

Juan had 15 quarters. To solve this, we created a system of equations representing the total value of the coins and the relationship between the number of nickels and quarters. Calculations led to the conclusion that there were 15 quarters in total.

The question requires us to solve a system of equations to find out how many quarters Juan had if he had $5.25 in nickels and quarters, with 15 more nickels than quarters. Let's denote the number of quarters as q and the number of nickels as n. Remember, a quarter is worth $0.25 and a nickel is worth $0.05.

Based on the given information, we can establish the following equations:

0.25q + 0.05n = $5.25 (the total value equation)n = q + 15 (the number of coins equation)

We can substitute the second equation into the first to find the value of q.

0.25q + 0.05(q + 15) = $5.25

Solving for q:

0.25q + 0.05q + 0.75 = $5.25

0.30q + 0.75 = $5.25

0.30q = $4.50

q = $4.50 / 0.30

q = 15

Therefore, Juan had 15 quarters.

Can someone explain this to me???

Answers

The question requires us to explain the different exponential graphs:
Exponential functions are given by:
f(x)=a(b)^x
when:
a is negative, the graph will be reflected along y-axis
b>1 the graph will be an exponential growth
b<1 the graph will be an exponential decay
1] a]
y=3(2)^x
y-intercept:
at y-intercept x=0 thus
y=3(2)^0
y=3(1)=3
thus y intercept is at y=3

c] since there is no asymptote

d] Domain:
All real numbers

e] Range:
[0,∞)

That all positive real numbers.

2]
a] f(x)=2(0.25)^x
a=2
b=0.25
b<1
thus the function is exponential decay

b] The horizontal axis is at y=0.

c] Domain:
The domain is all real numbers.

d] Range:
The range are all positive values.

e] y-intercept
f(x)=2(0.25)^x
at y-intercept , x=0 thus
y=2(0.25)^0
y=2(1)
y=2

3] y=-5(2)^x

a] This is a decay function since a=-5

b] y-intercept
f(x)=-5(2)^x
f(x)=-5(2)^0
f(x)=-5

C] the asymptote is y=0

d] Domain are all real numbers

e] Range
Range are all negative real numbers

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049

Answers

The correct answer is: a. The population will fall below 1,200,000 around the year 2024.

To determine when the city's population will fall below 1,200,000, we need to use the formula for exponential decay:

[tex]P(t) = P_0 \cdot (1 - r)^t[/tex]

where:

- P(t) is the population at time t .

- P₀ is the initial population.

- r is the rate of decrease (expressed as a decimal).

- t is the number of years.

Given:

- Initial population, P₀ = 1,405,233

- Rate of decrease, r = 1.1% = 0.011

- Final population, P(t) = 1,200,000

We need to find t such that:

[tex]1,200,000 = 1,405,233 \cdot (1 - 0.011)^t[/tex]

First, we divide both sides by 1,405,233:

[tex]\frac{1,200,000}{1,405,233} = (0.989)^t[/tex]

Next, we calculate the left-hand side:

[tex]\frac{1,200,000}{1,405,233} \approx 0.854[/tex]

So we have:

[tex]0.854 = (0.989)^t[/tex]

To solve for t , we take the natural logarithm of both sides:

[tex]\ln(0.854) = \ln((0.989)^t)[/tex]

Using the properties of logarithms, we can bring down the exponent:

[tex]\ln(0.854) = t \cdot \ln(0.989)[/tex]

Now, solve for t :

[tex]t = \frac{\ln(0.854)}{\ln(0.989)}[/tex]

Let's calculate this:

[tex]\ln(0.854) \approx -0.157 \\\\ \ln(0.989) \approx -0.011 \\\\ t = \frac{-0.157}{-0.011} \approx 14.27[/tex]

Since 14.27 years from 2010 is approximately in 2024:

[tex]2010 + 14.27 \approx 2024[/tex]

So the population will fall below 1,200,000 around the year 2024.

The correct answer is: a. 2024

You have decided to buy a new home and the bank offers you a 10 year fixed loan at 5.0% on a balance of $275,325. Use the table provided to determine the monthly payments.a.$183,147c.$185,350b.$184,789d.$186,523

Answers

Answer:

ita A

Step-by-step explanation:

Final answer:

You can calculate the monthly payments for a 10-year fixed loan at 5.0% on a balance of $275,325 by plugging the values into the amortization formula: M = P [r(1+r)^n] / [(1+r)^n – 1]. Perform the calculations and compare the result to the answer choices.

Explanation:

This question falls under the category of financial mathematics, specifically loan repayment calculations. When calculating a fixed loan, we typically use an amortization formula to find our monthly payment. The formula we use is: M = P [r(1+r)^n] / [(1+r)^n – 1], where M is our monthly payment, P is the principal loan amount (in this case $275,325), r is our monthly interest rate (annual rate of 5% divided by 12), and n is the number of payments (or the number of months, in this case, 10 years or 120 months).

Plugging in these numbers, we get M = $275,325[0.004167(1+0.004167)^120] / [(1+0.004167)^120 – 1].

After performing these calculations, you will get the monthly payment for this 10-year fixed loan. Compare this number to the choices given to get your answer.

Learn more about Loan Repayment Calculation here:

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Below are the heights of the players on the University of Maryland women's basketball team for the 2017-2018 season and the heights of the players on the women's field hockey team for the 2018 season.
Note: it is typical for a women's field hockey team to have more players than a women's basketball team would.

Field Hockey Player Heights (inches) Basketball Player Heights (inches)
Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Field Hockey Player Heights (inches) Basketball Player Heights (inches)
66 in. 60 in. 67 in. 68 in. 75 in. 72 in.
68 in. 64 in. 63 in. 63 in. 72 in. 74 in.
67 in. 69 in. 66 in. 66 in. 68 in. 75 in.
65 in. 64 in. 65 in. 70 in. 73 in.
66 in. 68 in. 66 in. 68 in. 72 in.
60 in. 66 in. 65 in. 69 in.
64 in. 66 in. 67 in. 72 in.

1. Field Hockey Players:
Find the Measures of Center and Variability for Field Hockey Players Heights.
Mean (Round to Nearest Whole Number):

Mode:

Median:

Range:

2. Basketball Players:
Find the Measures of Center and Variability for Basketball Players Heights.
Mean (Round to Nearest Whole Number):

Mode:

Median:

Range:

3. a. How many of the 10 basketball players are shorter than the tallest field hockey player?

b. List the heights that overlap in the dot plot?

Answers

Answer:

for the first and second questions the answers are

Field hockey players basketball players

mean:66 mean:72

mode:66 mode:72

median: 66 median:72

range:10 range:7

Step-by-step explanation:

1. For the Field Hockey Players

The mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.

2. For the Basketball Players:
The mean is approximately 67 inches, the median is 67 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches

3. All 10 basketball players are shorter than the tallest field hockey player.

3b. the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.

How to find the measures of center and variability

Field Hockey Players:

The data is sort as follows

60, 60, 64, 64, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 68, 68, 68, 68, 69, 69, 70, 72, 72, 72, 73, 75, 75.

Now let's calculate the measures of center and variability:

Mean (Average): Add up all the heights and divide by the total number of heights. We then round the answer to the nearest whole number.

Mean

= (60 + 60 + 64 + 64 + 65 + 65 + 65 + 66 + 66 + 66 + 66 + 66 + 66 + 66 + 67 + 67 + 67 + 68 + 68 + 68 + 68 + 69 + 69 + 70 + 72 + 72 + 72 + 73 + 75 + 75) / 30

= 2040 / 30

= 68 inches (rounded to the nearest whole number).

Mode: This is the height that occurs most frequently.

From the sorted list, we can see that 66 inches appears 8 times, which is more than any other height, so Mode = 66 inches.

Median: This is the middle height when all the heights are listed in ascending order. If there is an even number of heights, as in this case, the median is the average of the two middle heights.

Here, the 15th and 16th heights are both 66 inches, so Median = (66 + 66) / 2 = 66 inches.

Range: This is the difference between the tallest (maximum) and shortest (minimum) players.

Range = Maximum - Minimum = 75 inches - 60 inches = 15 inches.

So, for the field hockey players, the mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.

Basketball Player Heights

The data is sort as follows

63, 63, 64, 64, 66, 67, 68, 72, 72, 74.

Mean (Average): The mean is calculated by adding all the numbers together and then dividing by the number of numbers.

Mean

= (63 + 63 + 64 + 64 + 66 + 67 + 68 + 72 + 72 + 74) / 10

= 673 / 10

= 67.3 inches.

Median: The median is the middle number in a sorted, ascending list. If there are an even number of observations, the median is the average of the two middle numbers.

In our list, since we have 10 numbers, an even number, the median is the average of the 5th and 6th numbers.

Median = (66 + 67) / 2 = 66.5 inches.

Mode: The mode is the number that appears most frequently in a data set.

From our list, we can see that the numbers 63 and 72 both appear the most (2 times each). So, this data set has two modes: 63 inches and 72 inches.

The range is calculated by subtracting the smallest number in a set from the largest number.

In your data set, the smallest number (the minimum) is 63 inches and the largest number (the maximum) is 74 inches.

So, Range = Maximum - Minimum = 74 - 63 = 11 inches.

So, for this data set, the mean is approximately 67.3 inches, the median is 66.5 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches.

3. First, let's identify the tallest field hockey player. Considering all heights given for field hockey players, the tallest field hockey player is 75 inches.

Now, let's look at the basketball player heights. We have 10 basketball player heights in total: 68 in., 64 in., 63 in., 63 in., 72 in., 74 in., 60 in., 66 in., 65 in., and 69 in.

From this, we can see that all 10 basketball players are shorter than 75 inches. So, all 10 basketball players are shorter than the tallest field hockey player.

3b. The overlapping heights are those that appear in both basketball and field hockey teams. Looking at both sets, the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.

Learn more about measures of center and variability at

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Find the balance after 8 years

Answers

Here’s the equation: 3000+0.03(3000)
But because it is 8 years:
3000+0.24(3000)
We can make it simpler:
1.24(3000)
3720
Your balance will be $3720

(y + 5)(y – 9) = 0
need help asap!!

Answers

Set each equation equal to zero.

y + 5 = 0

Subtract 5 from both sides.
y = 0 - 5
y = - 5

y - 9 = 0

Add 9 to both sides
y = 0 + 9
y = 9

y = - 5, 9

$80 is divided Between two men such that 1/4 of one persons share is equal to 1/6 Of the other how much will each man receive

Answers

x + y = 80
y/4 = x/6

6y = 4x

4x + 4y = 320
6y + 4y = 320
10y = 320
y = 32

6(32) = 4x

x = 48

Answer: The amounts are $32 and $48.

Final answer:

To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share, each man will receive $40 and $60, respectively.

Explanation:

To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share:

Let x be one person's share and y be the other person's share.

Set up the given ratio: 1/4x = 1/6y.

Solve the ratio equation to find x and y: 1/4x = 1/6y can be simplified to x = $40 and y = $60.

Kevin owes $4,645 on a credit card with a 19.7% interest rate compounded monthly. What is the monthly payment he should make in order to pay off this debt in 12 months, assuming he does not charge any more purchases with the card?

$387.08

$84.34

$429.62

$1,034.65

**Please help with steps too, please.

Answers

The "steps" are to enter the data into the appropriate places in a financial calculator. (PV=4645, i=19.7/12, n=12) Then PMT = -429.62.

Alternatively, and somewhat more slowly, you can make use of the amortization formula.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where A is the monthly payment,
P is the current balance (4645),
r is the annual rate (.197),
n is the number of compoundings per year (12), and
t is the number of years (1).

Filling in the numbers, you have
A = 4645*(.197/12)/(1 -(1 +.197/12)^-12)
A ≈ 429.62 . . . . . corresponds to the 3rd choice

Explain how you find a unit rate when given a rate.

Answers

This can be illustrated with an example:-

A car travels 100 miles in 2 hours
rate = 100 miles per 2 hours
unit rate = number of miles per ONE hour

so the unit rate in this case = 100/2 = 50 miles per hour.

Unit rate is the distance travelled in unit time. In this case the unit is an hour.

Mike saw 4 times and Many birds as Gigi. Mike saw 28 birds. Which equation can be used to find how many birds Gigi saw? a. 4x28=n b. 28-4=n c. 4+28=n d. 28+4=n

Answers

Hello there, and thank you for posting your question here on brainly.

Short answer: A. 4 x 28 = n

Why?

You can use context clues. So, Gigi saw n birds, Mike saw 4 times as many birds as Gigi. Times is often referred to as multiplication. What is the only equation that shows times, or multiplication? That'd be A. 4 x 28 = n

Hope this helped you! ♥

PLEASE HELP!! All I need to finish off my year! WILL BRAINLIEST AND VOTE!
1. How would you prove that circles are similar?
3.Find the center and the radius for the circle, given the equation:
x^2-14x+y^2+8y=16

Answers

Part 1)
we know that
All circles are similar. Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. In our attempt to prove all circles are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another

Part 2)
a) ∡BAD=128°-----------> by central angle

b) ∡BCD
The inscribed angle measures half of the arc it comprises.
so
∡BCD=128°/2----> 64°

c) ∡BED
The measure of the external angle is the semi difference of the arcs that it covers.
arc BCD=360°-128°=232°
∡BED=(1/2)*[232-128]-----> 52°

d) What is the relationship between BA and BE?
in the right triangle ABE
∡BEA=∡BED/2-----> 52°/2-----> 26°
tan (∡BEA)=BA/BE------> tan 26°=BA/BE----> BA/BE=0.4877

Part 3) Find the center and the radius for the circle, given the equation:
x²-14x+y²+8y=16

Group terms that contain the same variable

(x²-14x)+(y²+8y)=16

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

(x²-14x+49)+(y²+8y+16)=16+49+16

Rewrite as perfect squares

(x-7)²+(y+4)²=81

(x-7)²+(y+4)²=9²

a) the center is the point (7,-4)

b) the radius is 9

Juan Ramirez sells suits in a major department store on weekends. He earns a commission of 5% on the first 10 suits he sells. If he sells more than 10, he earns another 3% on the additional suits. Last weekend Juan sold 13 suits priced at $250 each. What was his commission?

A. $185.00
B. $260.00
C. $147.50
D. $210.40

Answers

C. $147.50
the first 10 suits would sell at 250 each totaling 2500 which means he earns 5% of $2500, which is 0.05 x 2500 = $125. The next 3 suits which also sold at 250 which totals $750, he makes 3% of that amount which is 0.03 x 750 = $22.50. Together is makes 125 + 22.50 = $147.50 in commission.

N english instructor asserted that students' test grades are directly proportional to the amount of time spent studying. lisa studies 6 hr for a particular test and gets a score of 79. at this rate, how many hours would she have had to study to get a score of 92?

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You can simply use the cross method, so you will have
[tex]x = \frac{92 \times 6}{79} = 6.9[/tex]
which means she has to study approximately 7 hours to get score of 92.

Hope this helps.

In three more years, miguel's grandfather will be six times as old as miguel was last year. when miguel's present age is added to his grandfather's present age, the sum is 68. how old is each one now?

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Grandfather is 57 and Miguel is 11 .Therefore, 57 + 11 =68 Miguel was 10 last year. In 3 years grandfather will be 60. 10 x 6= 60

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The scale factor of a figure and its enlargement is 6. What is the new length of the enlarged figure if the original length is 3 cm?
3 cm
6 cm
18 cm
36 cm