Variable b is 7 more than variable c. Variable b is also 1 less than variable c. Which pair of equations best models the relationship between b and c? (1 point) Group of answer choices c = b − 7 c = b − 1 c = b + 7 c = b − 1 b = c − 7 b = c + 1 b = c + 7 b = c − 1

Let the adding value be x

ATQ

\(\\ \sf\longmapsto \dfrac{2+x}{5+x}=\dfrac{5}{6}\)

\(\\ \sf\longmapsto 6(2+x)=5(5+x)\)

\(\\ \sf\longmapsto 12+6x=25+5x\)

\(\\ \sf\longmapsto 6x-5x=25-12\)

\(\\ \sf\longmapsto x=13\)

Answer:

The answer is below

Step-by-step explanation:

The formula m = (12,000 + 12,000rt)/12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years. Keri decides that she can afford, at most, a $275 monthly car payment. Give an example of an interest rate greater than 0% and a loan length that would result in a car payment Keri could afford. Provide support for your answer.

Answer: Let us assume an annual interest rate (r) = 10% = 0.1. The maximum monthly payment (m) Keri can afford is $275. i.e. m ≤ $275. Using the monthly loan payment formula, we can calculate a loan length that would result in a car payment Keri could afford.

\(m=\frac{12000+12000rt}{12t}\\ but\ m\leq275, \ and \ r=10\%=0.1\\275= \frac{12000+12000(0.1)t}{12t}\\275= \frac{12000}{12t} +\frac{12000(0.1)}{12t}\\275= \frac{1000}{t} + 100\\275-100= \frac{1000}{t} \\175= \frac{1000}{t} \\175t = 1000\\t= \frac{1000}{175}\\ t=5.72\ years\)

The loan must be at least for 5.72 years for an annual interest rate (r) of 10%

Here's the keywords you need! :)

example of an interest rate and a loan length that costs under $275/month (example: 4-year loan at 2% interest)

monthly payment for the loan you described (example: 4-year loan at 2% interest is $270/month)

statement that the monthly payment for the loan you described is less than or equal to $275 (example: $270/month payment is less than $275)

Just got it right on edge 2020, hope this helps!! :)

Answer:

slope = - 7, y- intercept = (0, 5 )

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 )

y = - 7x + 5 ← is in slope- intercept form

with slope m = - 7 and y- intercept c = 5 ⇒ (0, 5 )

Answer:

\(\frac{\partial f}{\partial x} = -70+7\cdot y\), \(\frac{\partial f}{\partial y} = 12+7\cdot x\), \(\frac{\partial f}{\partial x} (1,-1) = -77\), \(\frac{\partial f}{\partial y}(1,-1) = 19\)

Step-by-step explanation:

Let \(f(x,y) = 9000-70\cdot x +12\cdot y +7\cdot x \cdot y\), then the first partial derivatives of this multivariate function are, respectively:

\(\frac{\partial f}{\partial x} = -70+7\cdot y\) (1)

\(\frac{\partial f}{\partial y} = 12+7\cdot x\) (2)

Now we evaluate the partial derivatives at \((x,y) = (1, -1)\):

\(\frac{\partial f}{\partial x}(1,-1) = -70+ 7\cdot (-1)\)

\(\frac{\partial f}{\partial x} (1,-1) = -77\)

\(\frac{\partial f}{\partial y}(1,-1) = 12+7\cdot (1)\)

\(\frac{\partial f}{\partial y}(1,-1) = 19\)

a) The monthly payment for this fully amortising mortgage is approximately $10,331.25.
b) The monthly payment for this interest-only mortgage is approximately $14,360.33.

c) The new monthly payment after the interest rate increase is approximately $9,090.70.

d) The remaining loan balance is approximately $625,014.72.

A) To calculate the monthly payment of a fully amortising mortgage, we can use the formula:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments

For the given question, the loan amount is 81% of $1,175,378, which is $952,622.38. The annual interest rate is 11.6%, so the monthly interest rate would be 11.6% / 12 = 0.9667%. The mortgage term is 21 years, which means a total of 21 * 12 = 252 payments.

Plugging these values into the formula, we can calculate the monthly payment:

M = 952,622.38 * (0.009667 * (1+0.009667)^252) / ((1+0.009667)^252 - 1)

The monthly payment for this fully amortising mortgage is approximately $10,331.25.

B) To calculate the monthly payment of an interest-only mortgage, we can use the formula:

M = P * r

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate

For the given question, the loan amount is 80% of $1,495,863, which is $1,196,690.40. The annual interest rate is 14.4%, so the monthly interest rate would be 14.4% / 12 = 1.2%.

Plugging these values into the formula, we can calculate the monthly payment:

M = 1,196,690.40 * 0.012

The monthly payment for this interest-only mortgage is approximately $14,360.33.

C) To calculate the new monthly payment after an interest rate increase, we can use the same formula as in part A:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

For the given question, the remaining loan balance is $700,134. The current interest rate is 14.5% per annum, and the loan term is 12 years.

To calculate the new interest rate, we need to add 1% to the current interest rate, which gives us 15.5% per annum, or 15.5% / 12 = 1.2917% as the monthly interest rate.

Plugging these values into the formula, we can calculate the new monthly payment:

M = 700,134 * (0.012917 * (1+0.012917)^144) / ((1+0.012917)^144 - 1)

The new monthly payment after the interest rate increase is approximately $9,090.70.

D) To calculate the remaining loan balance, we can use the formula:

B = P * ((1+r)^n - (1+r)^p) / ((1+r)^n - 1)

Where:
B = Remaining loan balance
P = Loan amount
r = Monthly interest rate
n = Total number of payments
p = Number of payments made

For the given question, the monthly payment is $8,364. The annual interest rate is 12.4%, so the monthly interest rate would be 12.4% / 12 = 1.0333%. The remaining loan term is 10 years, which means a total of 10 * 12 = 120 payments have been made.

Plugging these values into the formula, we can calculate the remaining loan balance:

B = P * ((1+0.010333)^120 - (1+0.010333)^360) / ((1+0.010333)^360 - 1)

The remaining loan balance is approximately $625,014.72.

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1. To identify the surface S, we need to analyze the given equation. However, it seems that the equation is missing, as only "z" is mentioned. Please provide the complete equation for a more accurate identification.

2. Once the equation for surface S is provided, we can find the tangent plane at the point (1, 0, 3). To find the tangent plane, we need the gradient of the surface equation.

The gradient of the surface equation gives the direction of the normal vector to the surface at any point. The equation of the tangent plane can then be written as:

(x - x1)(∂f/∂x) + (y - y1)(∂f/∂y) + (z - z1)(∂f/∂z) = 0,

where (x1, y1, z1) is the given point and (∂f/∂x), (∂f/∂y), and (∂f/∂z) are the partial derivatives of the surface equation with respect to x, y, and z, respectively.

To find the tangent plane at (1, 0, 3), we need the equation of the surface S. Please provide the equation so that we can proceed with the calculation.

Please let me know if you have any further questions or if there's anything else I can assist you with.

a) The area of a circle is given by the formula:

Where A is the area, π=3.14 and d is the diameter=8 ft.

By replacing values:

b) The circumference of a circle is given by:

Where C is the circumference, π=3.14 and d is the diameter=8 ft.

By replacing values:

Answer: do you have a picture

Step-by-step explanation:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The area in the first quadrant between the given circles is 2π.

The given equation of circles are:

x²+y²=16,

x²+y²=16,

x²−4x+y²=0

To evaluate the integral, we'll need to convert the equations into polar coordinates.

The first circle, x² + y² = 16.

In polar coordinates,

x = rcosθ

y = rsinθ.

Substituting these into the equation,

we get r²cos²θ + r²sin²θ = 16.

Simplifying this equation, we have r² = 16,

which simplifies further to r = 4.

The second circle, x² - 4x + y² = 0.

Converting this into polar coordinates, we have

(rcosθ)² - 4(rcosθ) + (rsinθ)² = 0.

Simplifying this equation, we get

r² - 4rcosθ = 0,

Which leads to r = 4cosθ.

To find the area in the first quadrant between these two circles,

Integrate the area element dA over the given region.

The area element in polar coordinates is given by

dA = 1/2 (r² dθ).

Now, set up the integral to evaluate the area:

\(A = \int\limits^{\frac{\pi}{2}}_0 {(\frac{1}{2} r^2)} \, d\theta\\ =\frac{1}{2} \int\limits^{\frac{\pi}{2}}_0 {4cos^2\theta} \, d\theta \\= 8 \int\limits^{\frac{\pi}{2}}_0 {cos^2\theta} \, d\theta\)

Using trigonometric identities,

We can simplify this integral further:

\(= 8 \int\limits^{\frac{\pi}{2}}_0 {(1+cos2\theta)/2} \, d\theta\)                                 [∵ cos2θ = 2cos²θ - 1]

= (1/2) [(8(π/2) + 4sin(2(π/2))) - (8(0) + 4sin(2(0)))]

= (1/2) [(4π + 0) - (0 + 0)]

= 2π

Hence,

The area in the first quadrant between the given circles is 2π.

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Answer:

you got it right

Step-by-step explanation:

Answer:

Tom is 30 years old. Danny is 31 years old, Pablo is 32 years old, and Adam is 36 years old.

90 cubic feet  is the volume of the rectangular prism.

A polyhedron with two congruent and parallel bases is a rectangular prism.

It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.

It is referred to as a prism because of the length of its cross-section. The study of shapes and the arrangement of objects is known as geometry.

The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms.

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces).

The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.

According to our question-

V = Base x Height is the formula for a rectangle prism.

V = 18 x 5 square feet.

V = 90 cubic feet

Hence, 90 cubic feet  is the volume of the rectangular prism.

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Answer:

The expression required to find perimeter of square is: 4n-16

Step-by-step explanation:

Length of side of square = n-1.5

We need to find Perimeter of Square

The formula used is: \(Perimeter\: of\: square=4(Length\:of\:Side)\)

Putting values and finding perimeter

\(Perimeter\: of\: square=4(Length\:of\:Side)\\Perimeter\: of\: square=4(n-1.5)\\Perimeter\: of\: square=4n-6\)

So, the perimeter of square is: 4n-16

Since the options are not given, I cannot choose the best answer.

But the expression required to find perimeter of square is: 4n-16

Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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Answer:

-29, -34, -39

Step-by-step explanation:

the numbers are going down by five each time.

-24-5=-29

-29-5=-34

-34-5=-39

Hope this helps!

Answer:

-29

Step-by-step explanation:

because -14 and -19 is minus 5

Answer:

$7500

Step-by-step explanation:

Let's say she sells x dollars in terms of goal sales

base salary + goal commission = goal total salary

1000 + goal commission = 2500

1000 + 20% commission of total goal sales = 2500

1000 + 20% of x = 2500

1000 + 0.2x = 2500

subtract 1000 from both sides to isolate x and its coefficient

0.2x = 1500

multiply both sides by 5 to find x

x = 7500

Answer:

x+6.3

Step-by-step explanation:

x+6.3

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

Answer:

164 in squared

Step-by-step explanation:

Find area of faces and multiply by 2 because there is another one.

10 x 3 x 2=60

3 x 4 x 2=24

10 x 4 x 2=80

Answer:

164 in^2

Step-by-step explanation:

3*4=12*2=24 in^2

4*10=40*2=80 in^2

3*10=30*2=60 in ^2

24+80+60=164 in^2

Answer:

C. Functional

Step-by-step explanation:

I hope I helped you,

Alex Martin :)

√32 or 4√2 is the missing length of the right angle triangle whose other 2 legs measure 4 by 4 units.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Given the data in the diagram;

To determine the missing length, plug the given values into the formula above and solve for c.

c = √( a² + b² )

c = √( (4)² + (4)² )

c = √( 16 + 16 )

c = √( 32 )

Hypotenuse c = √32 or 4√2

Therefore, the missing length of the right angle triangle is √32.

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\(2x-5y=10\\\\\implies 5y = 2x-10\\\\\implies y =\dfrac{2x-10}5 = \dfrac{2}5 (x-5) = \dfrac{2x}5 - 2\)

Answer:

(D) \(y = - \frac{2x}{5} - 2\)

Step-by-step explanation:

The problem consist in isolate the \(y\) variable

The steps are below:

\(2x -5y = 10\\-5y = 10 - 2x\\y = \frac{10 - 2x}{5}\)

Know the trick is in separate the fraction in two others as this example:

\(\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}\)

So in our case we have:

\(y = -\frac{10}{5} - \frac{2x}{5}\\y = -2 -\frac{2x}{5}\)

That correspond to D

The function shows that the cost of hotdogs is 1.75 and the cost of hamburger is 1.5.

Let hotdogs = h

Let hamburger = x

The expression will be:

h + x = 3.25

h + 7x = 12.25

Subtract the functions

6x = 9

x = 1.5

Therefore, hot dogs will be:

= 3.25 - 1.5

= 1.75

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At a concession stand, one hot dog and one hamburger cost $3.25; one hot dog and seven hamburger cost $12.25. Find the cost of one hotdog and the cost of one hamburger.

Answer:

24 pieces of glass

Step-by-step explanation:

Answer:

x= 7

Step-by-step explanation:

add (12x+1) and (5x-3) which becomes 17x-2 and then set that equal to 117 and solve. move the 2 to the right side of the equation which becomes 17x=119 and then divide 119 by 17 which x equals 7.

plug in 7 for x to make sure you get 117

Saad and Hamid can build a 4 feet by 3 feet hen house using the 12 square feet of plywood they bought.

Saad and Hamid purchased 12 square feet of plywood to make a hen house in the backyard of their house. Let's assume they want to construct a rectangular hen house.

To find the dimensions of the hen house, we need to consider the area of the plywood. Let's represent the length and width of the hen house in feet as L and W, respectively.

The area of a rectangle is given by the formula A = L * W. In this case, the area is given as 12 square feet. Therefore, we have the equation L * W = 12.

Now, let's consider the constraints. Typically, a hen house should have a minimum length and width to accommodate the hens comfortably. Let's assume the minimum length is 2 feet and the minimum width is 1 foot.

We can solve the equation L * W = 12 by trying different combinations of L and W that satisfy the minimum constraints. One possible solution is L = 4 feet and W = 3 feet.

Therefore, Saad and Hamid can construct a hen house with dimensions 4 feet by 3 feet using the 12 square feet of plywood they purchased.

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Answer:

the answer is -60........

Answer:

-60! 1560 divided by 26 is 60, but any negative divided by a positive is a negative, so the product will be negative as well.

Step-by-step explanation:

Hope it helps! =D

Answer:

.2 Cm

Step-by-step explanation: