Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]

Final answer:

The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).

Explanation:

The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).

The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.

Answer:

b

Step-by-step explanation:

Answer:

in 20 years Sam = 32 = same as Mary so 20 years before Mary was 12 and Sam was 4 times older when she was 48. Sam is now 48 and Mary is 48.  

Step-by-step explanation:

Answer:9/7+5/8=72/56+35/56

Step-by-step explanation:9/7 times 8 by both 9 and 7 and times 7 by both 5   and 8 and you will get your answer

Answer:

[tex]1\frac{51}{56}[/tex]

Step-by-step explanation:

In order to find the answer to this question you will have to find the common denominator, (CD) multiply the denominators by the amount it takes to receive the common deliminator then do the same with the numerators without finding the common numerator, and then add the two numerators together and reduce if needed.

[tex]\frac{9}{7} +\frac{5}{8}[/tex]

Find the common denominator:

[tex]CD=56[/tex]

[tex]9\times 8 =72[/tex]

[tex]7 \times 8 = 56[/tex]

[tex]= \frac{72}{56}[/tex]

Do the same with the second fraction:

[tex]5\times7=35[/tex]

[tex]8\times7=56[/tex]

[tex]=\frac{35}{56}[/tex]

Then you would have:

[tex]\frac{72}{56} +\frac{35}{56}[/tex]  

Add the numerators:

[tex]72+35=107[/tex]

[tex]=\frac{107}{56}[/tex]

Turn the improper fraction into a mixed number:

[tex]\frac{107}{56} = 1\frac{51}{56}[/tex]

You get this by dividing 107 by 56 which should give you 1 with the remainder of 51 and you keep the denominator the same.

[tex]=1\frac{51}{56}[/tex]

Hope this helps.

Answer:

(a):  9x + 45

Option A, 9(x + 5) because it distributes into 9x + 45

Option B, 9 * x + 9 * 5 because it multiplies into 9x + 45

(b):  13 + 9y - 3 - y

Option D, 8y + 10 because it combines into this number

Answer:

1) { 2,3,4,6,8,9,10,12,15} , {2,4,8,10}, { 2,4,8,10}

Step-by-step explanation:

£ = [ 1,2,3,4,6,8,12,16,24 48}

A = { 2,4,6,8,10}

B = { 3,6,9,12,15}

1) AUB = all members in A and B

= { 2,3,4,6,8,9,10,12,15}

2) AnB' = members in A not in B

{2,4,8,10}

3) A - B = take away members of B in A that is B from A

= { 2,4,8,10}

I hope this was helpful, please mark as brainliest

Answer:

Gaby do not need to borrow money and they are left with $39.5      

Step-by-step explanation:

We are given the following in the question:

Total money = $50

Cost of a Cobb salad = $8.95

Cost of a drink = $1.55

Order: A Cobb salad and a drink

Cost of order =

[tex]= 8.95 + 1.55\\=\$10.5[/tex]

Thus, the total cost of order is $10.5

Money left =

= Total money - Order bill

[tex]=50 - 10.5\\=\$ 39.5[/tex]

Thus, Gaby do not need to borrow money and they are left with $39.5.

Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).

Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).

The initial values and rates of change for Mr. Allen's and Mr. Jessup's payment plans can be compared based on the given information.

1. Initial Values:

  - Mr. Allen's initial amount S: $560

  - Mr. Jessup's initial amount: $400

  Difference in initial values: $560 - $400 = $160

  Mr. Allen's initial value is $160 more than Mr. Jessup's.

2. Rates of Change:

  - Mr. Allen's rate of change: $80 per month

  - Mr. Jessup's rate of change: $40 per month

  The rate of change represents the amount by which the owed amount decreases each month. Mr. Allen's rate of change is greater because he pays off $80 per month, while Mr. Jessup pays off $40 per month.

In summary:

Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).

Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).

Complete question:

Mr. Allen bought a new computer. His monthly payment plan is shown in the table.

Month                                      0        1     2         3        4       5      6     7

Amount Mr. Allen Owes (S)  560 480   400  320   240  160  80    0

Mr. Jessup buys a new computer for $400. He makes monthly payments of $40 until the computer is paid for. Compare the initial values and rates of change of each function.

You can graph both functions to show that the amount Mr. Allen owes starts at $560 and decreases $80 per month. The amount that Mr. Jessup owes starts at $400 and decreases $40 each month.

Mr. Allen's initial value is $160 more than Mr. Jessup's. Mr. Allen's rate of change is greater than Mr. Jessup's rate of change.

To calculate Peter's monthly expenses, add up the amounts in row 5 of the table. Compare the total expenses with different salaries to determine if Peter can meet them. Advise Peter to create a budget and prioritize expenses if he wants to move out.

To calculate Peter's monthly expenses, we need to add up all the amounts in row 5 of the table. Assuming each amount represents a monthly expense, we can sum them up to get the total monthly expenses. To determine if Peter can meet his expenses with different salaries, we compare the total expenses with each salary. If the salary is greater than or equal to the total expenses, Peter can meet his expenses. If the salary is less than the total expenses, Peter cannot meet his expenses.

If Peter wants to move out of his parent's house, I would advise him to create a budget and prioritize his expenses. He should also consider finding ways to increase his income or reduce his expenses to make moving out more affordable.

Answer:

b) When the temperature is 70°F, the park can expect 42 visitors.

Step-by-step explanation:

Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:

y = 42 + 15x

The general equation of a straight line plotted y against x with an intercept(c) on the y-axis and a slope(m) is given by the equation:

y = mx + c

comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.

This means that at temperature 70°F, x is 0.

therefore y = 42 + 15(0) = 42

Therefore when the temperature is 70°F, the park can expect 42 visitors.

Answer:

5 or 3

Step-by-step explanation:

The median is is the midpoint of the data. This means half is below 50 and half is above 50.

The answer would be they handle less than 50 accounts.

50% of sales managers at Force Inc. manages fewer than 50( = the median given) number of accounts.

Given that:

[tex]Min = 35\\Q_1 = 45\\Median = 50\\Q_3 = 65\\Maximum = 85[/tex]

These 5 numbers summary tells the partition of data or quartiles with endpoints as minimum and maximum.

The median is a point for which the counts of data lying above it is equal to the counts of data lying below it.

Since the question asks about :

50% Sales managers manage < ? number of accounts

and since 50% of data lie below and above the median which is 50 given in the table.

Thus we have:

50% of the Sales manager at Force Inc. managing fewer than 50(the median given) number of accounts.

Learn more here:

https://brainly.com/question/300591

Answer:

6 yards

Step-by-step explanation:

Perimeter of a rectangle:  2a + 2b

2(33) + 2(75)

66 + 150

216 inches

216/12 gives us feet

18/3 gives us yards

6 yards

Answer:  6 yards

Option A:

The shortest distance Mark can cover to reach home early is 54.7 miles.

Solution:

Towards North  = 35 miles

Towards West = 42 miles

Using Pythagoras theorem,

In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x be the hypotenuse.

[tex]x^2=35^2+42^2[/tex]

[tex]x^2=1225+1764[/tex]

[tex]x^2=2989[/tex]

Taking square root on both sides, we get

[tex]\sqrt{x^2}=\sqrt {2989}[/tex]

x = 54.67

x = 54.7

The shortest distance Mark can cover to reach home early is 54.7 miles.

Option A is the correct answer.

Answer:

Dog: 9 pounds

Cat: 18 pounds

Step-by-step explanation:

x + y= 27

y = 2x

2x + x = 27

3x = 27

x = 9

y = 2x = 18

ye boi its A | SMART BOIS

Answer:

Hi I am cool

Step-by-step explanation:

Answer:

Don't you just divided that by 3?

Step-by-step explanation:

The error in the amount of change she was 25.28%.

Step-by-step explanation:

Given,

The actual price = 15.65$

The amount Luna gives to cashier = 20$

The change she receives = c = 3.25$

The actual amount of changes = x = total amount - actual price:

20$ - 15.65$ = 4.35

The percentage of error can be found using: [tex]\frac{x-c}{x}[/tex]

By putting the values in equation, we get

=> [tex]\frac{4.35 - 3.25}{4.35} * 100[/tex]

=> [tex]\frac{1.10}{4.35} * 100[/tex]

=> 25.28  %

Hence, the error in the amount of change she was 25.28%.

The percent error in the amount of change Luna was given is:

[tex]\[\boxed{25.29\%}\][/tex]

To determine the percent error in the amount of change Luna was given, we need to compare the actual change received to the correct change she should have received.

Step 1: Calculate the Correct Change

Luna gave the cashier $20 for a shirt that costs $15.65. The correct amount of change should be:

[tex]\[\text{Correct Change} = 20 - 15.65 = 4.35 \, \text{dollars}\][/tex]

Step 2: Calculate the Error

The cashier gave Luna $3.25 instead of $4.35. The error in the change given is:

[tex]\[\text{Error} = \text{Correct Change} - \text{Actual Change Given} = 4.35 - 3.25 = 1.10 \, \text{dollars}\][/tex]

Step 3: Calculate the Percent Error

Percent error is given by the formula:

[tex]\[\text{Percent Error} = \left( \frac{\text{Error}}{\text{Correct Change}} \right) \times 100\][/tex]

Substitute the values into the formula:

[tex]\[\text{Percent Error} = \left( \frac{1.10}{4.35} \right) \times 100\][/tex]

Perform the division:

[tex]\[\frac{1.10}{4.35} \approx 0.2529\][/tex]

Convert to a percentage:

[tex]\[0.2529 \times 100 \approx 25.29\%\][/tex]

The percent error in the amount of change Luna was given is:

[tex]\[\boxed{25.29\%}\][/tex]

Answer:

becouse the value of the exponential function cant go negative... there is no exponent that makes a number negative if the base is positive..

Step-by-step explanation:

Basic exponential functions have a horizontal asymptote at y = 0 because as the input x increases, the output of the function approaches zero but never touches it due to exponential decay.

Basic exponential functions always have a horizontal asymptote at y = 0 because as the value of x becomes very large, the value of the exponential function approaches zero. This is due to the nature of exponential decay, where the function's rate of change decreases exponentially. Exponential functions are of the form f(x) = a^x, where a is a positive constant different from 1. When a is less than 1, the function represents exponential decay, and as x approaches infinity, f(x) approaches zero, but never actually reaches it, hence creating a horizontal asymptote at y = 0.

Answer: The answer would be the third option 4/4 x 6 = 6

Answer:

4/4 x 6 = 6

Step-by-step explanation:

This is the answer because 4/4 is one which means 1 x 6 = 6 so they are the same.

Answer:

[tex]2304 \ in^3[/tex]

Step-by-step explanation:

Given the surface dimensions of the garden as 24 inches by 48 inches:

#Calculate surface area of the garden's top:

[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]

Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:

[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]

Hence, the amount of soil used is 2304 cubic inches.

Answer: those are right!

Hope this helps ❤️

For the given rectangles, [tex]f=4[/tex] cm and [tex]g = 6[/tex] cm.

Step-by-step explanation:

Step 1:

The area of a rectangle is calculated by multiplying its length with its width. Both the rectangles APQD and PBCQ have the same width.

The second rectangle PBCQ has a length of 9 cm. Its area is determined by subtracting the area of APQD from the area of ABCD.

The area of the rectangle PQBC [tex]= 60 - 24 = 36[/tex] [tex]cm^{2}[/tex].

Step 2:

The length of rectangle PBCQ is 9 cm and the area is 36 [tex]cm^{2}[/tex] so the width can be determined.

[tex]Width = \frac{area}{length} = \frac{36}{9} = 4[/tex] cm. So [tex]f=4[/tex] cm.

Step 3:

The width of the rectangle APQD is also 4cm.

The width of the rectangle APQD is 4 cm and the area is 24 [tex]cm^{2}[/tex].

[tex]length = \frac{area}{width} = \frac{24}{4} = 6[/tex] cm. So [tex]g = 6[/tex] cm.

first off let's convert the mixed fraction to an improper fraction and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{3}{7}~~}{\frac{7}{6}}\implies \cfrac{3}{7}\cdot \cfrac{6}{7}\implies \cfrac{18}{49}[/tex]

Answer:

{x,y,z}={-8,-3,4}

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Area of a circle = πr^2

64π / π = πr^2 / π

sqrt(64) = sqrt(r^2)

8 = r

Answer:  8

Option D:

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

Solution:

Given expression is [tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex].

To find the product of the expression:

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex]

Multiply each term of the first term with each term of the 2nd term.

           [tex]=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)[/tex]

Using the exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

           [tex]=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)[/tex]

           [tex]=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7[/tex]

Arrange the terms with same power.

           [tex]=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7[/tex]

           [tex]=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

Hence option D is the correct answer.

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

The test has 35 multiple-choice questions and 3 open-ended questions.

To solve this, we can set up a system of linear equations. Let x represent the number of multiple-choice questions and y represent the number of open-ended questions.

Equation 1: x + y = 38 (total questions)

Equation 2: 4x + 20y = 200 (total points)

By solving this system of equations, we can find the values of x and y. First, multiply equation 1 by 4 and subtract it from equation 2:

4(x + y) = 4(38) => 4x + 4y = 152

4x + 20y = 200 - (4x + 4y = 152) gives: 16y = 48 or y = 3.

Substituting y = 3 into equation 1 gives: x = 38 - 3 = 35.

Therefore, there are 35 multiple-choice questions and 3 open-ended questions on the test.

Answer: 9+x

Step-by-step explanation:

If you have x apples, and you need nine more, you would need to ADD 9 and "x".