CONSUMER MATH!!
Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% APR. You agree to the loan but require your friend to pay you interest of 3.6% APR on the loan and your friend agrees.

How much interest does your friend save compared to the credit card at the end of the first month?

Answer:

  y = tan(x +π/2)

Step-by-step explanation:

It can be helpful to start with a simple sketch of the function you have and of the tangent function. Then, you can see the relationship.

The tangent function is always rising, has vertical asymptotes at -π/2 and π/2, and has a zero crossing at x=0.

The function we want is always rising, has vertical asymptotes at x=0 and x=±π, and a zero crossing at x=-π/2.

We can create the function we want by shifting the tangent function to the left by π/2. The formula that does that is ...

  y = tan(x +π/2)

Answer:

-i

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope of line perpendicular to x=4 is 0

reqd. eq. of line is y=-5

Answer:

π(6²)

Step-by-step explanation:

The base of the cone is a circle with area (A) calculated as

A = πr² ← r is the radius

Here diameter = 12 , hence r = 12 ÷ 2 = 6, thus

A = π(6²)

Answer:number 3

Step-by-step explanation:

Answer:

[see pdf]

Step-by-step explanation:

The graph makes a straight line, not a curve, so it is linear.

However, the graph has only points, not a full line, so it's also discrete.

(also yes I meant of instead of on in the pdf)

Answer:

A. discrete, C. linear

Step-by-step explanation:

By analysing the graph, it is evident that model is discrete since there is only information of certain points and shows a linear behavior, as there is a constant rate between dependent and independent variable. So, the right choices are A and C.

Answer:

were is the diagram

Step-by-step explanation:

Answer:

The length of the ladder is 9.2m

Step-by-step explanation:

Answer: 14.9 years, approximately 15years.

Step-by-step explanation:

Formular for finding the amount of a compound interest

A = P ( 1 + r/100 )n

From the question given,

A = $14,000; P = $4,000; n = ? (year)

Rate = 8.75%.

Substitute for these values in the above equation, we therefore have

14,000 = 4,000(1+ 8.75/100)n (is raised to the power of n)

Divide both side by 4,000

14,000/4,000 = 4,000(1+8.75/100)n/4,000.solving the one in bracket fractionally

3.5 = {(100 + 8.75)/100}n

3.5 = (108.75/100)n

3.5 = 1.0875n( raised to the power of n).In order to solve for 'n' to know the number of years, we take the logarithm of both side.

Log.3.5 = Log(1.0875)n

Going by the law of logarithm,

Log 3.5 = nLog1.0875

Checking your log table, log 3.5 =0.5441 and log1.0875 = 0.0364

Equating both and solve for n

0.5441 = 0.0364n

Divide through by the coefficient of n,

n = 0.5541/0.0364

n = 14.9 years

Approximately 15 years

Hence it will take $4,000 at 8.75% rate to amount to $14,000 a period of 14.9 years approximately 15years.

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slope = difference in y/difference in x

Substitute values in:

slope = (1 - 9)/(-2- (-9)

slope = -7/7

slope = -1

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Answer:

a=[tex]17\sqrt{2}[/tex]

Step-by-step explanation:

As we have 2 of the angles, we can find the third. The measure of the third angle is 45 degrees.

As this is the same measure as the other, that means that the side length will be the same.

Now was have two side lengths of 17 in a right triangle, so we can use the Pythagorean theorem to find a.

Recall that the pythagorean theorem states: [tex]a^2+b^2=c^2[/tex]

In this case, a is 17, b is 17, and c is a

Knowing this, we can input our value into this formula and solve for a.

[tex]17^2+17^2=a^2\\\\289+289=a^2\\\\a=\sqrt{578} \\\\a=17\sqrt{2}[/tex]

Answer:

17sqrt2

Step-by-step explanation:

45 45 90 triangles side: hypotenuse  a:a*sqrt2

17*sqrt2=17sqrt2

Answer:

See below table

Step-by-step explanation:

[tex]\begin{array}{cccccccc}p&q&r&\sim q&\sim q\rightarrow p&r\vee(\sim q\rightarrow p)&\sim p&[r\vee (\sim q\rightarrow p)]\rightarrow \sim p\\ \\ \\ \\T&T&T&F&T&T&F&F\\ \\T$&T&F&F&T&T&F&F\\ \\T&F&T&T&T&T&F&F\\ \\T&F&F&T&T&T&F&F\\ \\ \\ \\F&T&T&F&T&T&T&T\\ \\F&T&F&F&T&T&T&T\\ \\F&F&T&T&F&T&T&T\\ \\F&F&F&T&F&F&T&T\end{array}[/tex]

Answer:

?

Step-by-step explanation:

Answer:

7 hours, 30 minutes

Step-by-step explanation:

90 seconds times 300 = 27,000 seconds. Divided by 60 equals 450 minutes. Divided by 60 equals 7 hours, 30 minutes

Answer:

it will take 7 hours and 30 minutes to complete her invitations

Step-by-step explanation:

time taken for one envelope= 90 secs

time taken for 300 envelopes= 90*300= 27000 secs

Converting it into minutes = 27000/60= 450 minutes

Converting 450 minutes to hours = 450/60= 7.5 hours

Answer:

$50.95

Step-by-step explanation:

2(11.99)+3(8.99)=50.95

Answer:

Part 1) The radius is [tex]r=17\ units[/tex]

Part 2) The points (-15,14) and (-15,-16) lies on the circle

Step-by-step explanation:

The correct question is

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

The radius of the circle is  ____units.

The point (-15,

?) ) lies on this circle

step 1

Find the radius of the circle

we know that

The distance from the center to any point on the circumference is equal to the radius.

we have

[tex](-7,-1),(8,7)[/tex]

Find the distance

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute

[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}\\r=\sqrt{(8)^{2}+(15)^{2}}\\r=\sqrt{289}\\r=17\ units[/tex]

step 2

The point (-15,y) lies on the circle

we know that

If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle

The equation of the circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

The center is (-7,-1) an the radius is 17 units

substitute

[tex](x+7)^{2}+(y+1)^{2}=17^{2}\\(x+7)^{2}+(y+1)^{2}=289[/tex]

substitute the x-coordinate of the point and solve for the y-coordinate

For x=-15

[tex](-15+7)^{2}+(y+1)^{2}=289\\(-8)^{2}+(y+1)^{2}=289\\64+(y+1)^{2}=289\\(y+1)^{2}=289-64\\(y+1)^{2}=225[/tex]

square root both sides

[tex](y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16[/tex]

therefore

The points (-15,14) and (-15,-16) lies on the circle

see the attached figure to better understand the problem

The question relates to the properties of a circle in a coordinate system, where the circumference and area can be calculated using the radius. The circumference of a circle is found using C = 2πr, and the area is A = πr². Without a given radius, these formulas are a guide for any calculations that may be done once the radius is known.

The question asks about the properties of a circle given its center and radius, which fall under the topic of Geometry in Mathematics. No specific value for the radius is provided, so the answer should include an explanation of how one might calculate various properties of a circle, such as the circumference or area, given a radius.

Understanding the Circle

A circle with its center located at (-7, -1) means it is positioned on a coordinate system at that point. If a radius was provided, the circumference of the circle would be calculated using the formula C = 2πr and the area using A = πr², where 'r' represents the radius of the circle and 'π' (pi) is approximately 3.14159. For example, if r = 1.2 m, the area calculated to two significant figures would be A = 4.5 m².

For a circle to fit perfectly inside a square, its diameter should be equal to the side of the square; this implies that a = 2r. The area of the square is a² = 4r², and a circle inside this square would have an area of approximately three-quarters of the square, or near πr². The perimeter (circumference) of the circle is somewhat close to 6r as the perimeter should be 2πr.

Answer:

50

Step-by-step explanation:

Answer:

50

Explanation:

Answer:

Area = [tex]4x^6+12x^5+8x^4[/tex]

Step-by-step explanation:

The Complete Question:

A rectangle has height  [tex]4x^3[/tex]  and width  [tex]x^3+3x^2+2x[/tex]. What is the area of the rectangle in terms of x?

Solution:

The formula for the area of a rectangle is:

Area = Height * Width

Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:

[tex]A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4[/tex]

This is the area of the rectangle.

Answer:

y = 110°

x = 55°

Step-by-step explanation:

The line is a transversal.

∠Y = 110°, according to the rule of transversals.

Also, 2X = Y, since in a transversal the vertical angles are equal.

Vertical angles are the ones that are at the intersection of the parallel line and the transversal.

So, 2X = Y = 110°

⇒ X = 55°

Hence, X = 55° and Y = 110°.

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

θ= 30° or θ= 60°

Step-by-step explanation:

Please see attached picture for full solution.

Since √ 3/2 is positive, look at first 2 quadrant. (CAST diagram)

Answer:

92 are the value of x I think

Answer:

6.09864679092 minutes

Step-by-step explanation:

Mach 27= 33076.19km/h

3,362, at 33076.19km/h

3,362/33076.19

0.101644113182 hours

6.09864679092 minutes

Answer:

Around 6 minutes

Or in other words, fast

Answer:

12.75 + 0.75v = t

Step-by-step explanation:

12.75 is the fee she has to pay to join so you would add that to the cost of videos she rented. Since 0.75 is the cost of one and you don't know how many she rented you would put a variable which in this case would be "v". So if she payed the fee and rented 2 videos it would be 12.75 + 0.75(2) = 14.25

The correct equation to represent the total amount Sierra pays to rent videos is:

[tex]\[ t = 0.75v + 12.75 \][/tex]

Where [tex]\( t \)[/tex] represents the total cost, [tex]\( v \)[/tex] represents the number of videos Sierra rents, [tex]\( 0.75 \)[/tex] is the cost per video, and [tex]\( 12.75 \)[/tex] is the initial fee Sierra paid to join the video rental club. The term [tex]\( 0.75v \)[/tex] calculates the total cost of renting [tex]\( v \)[/tex] videos, and adding [tex]\( 12.75 \)[/tex] accounts for the initial fee. This equation allows us to determine the total cost [tex]\( t \)[/tex] for any number of videos [tex]\( v \)[/tex] that Sierra rents.

Answer:

Part 1) [tex]f(g(x))=3(x^2)+2[/tex]

Part 2) [tex]g(f(5))=289[/tex]

Step-by-step explanation:

we know that

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function

we have

[tex]f(x)=3x+2[/tex]

[tex]g(x)=x^{2}[/tex]

Part 1) Determine f(g(x))

To find f(g(x)) substitute the function g(x) as the variable in function f(x)

so

[tex]f(g(x))=3(x^2)+2[/tex]

Part 2) Determine g(f(x))

To find g(f(x)) substitute the function f(x) as the variable in function g(x)

so

[tex]g(f(x))=(3x+2)^2[/tex]

For x=5

[tex]g(f(5))=(3(5)+2)^2[/tex]

[tex]g(f(5))=289[/tex]

Answer:

The initial height from which the ball was dropped = 7.90 meters

Step-by-step explanation:

The correct question is:

In the video, I drop a ball off a three-story balcony. We know that objects in free fall follow the equation for height h, in meters, [tex]h = -4.9t^2 + c[/tex], where [tex]t[/tex] is time in seconds, and [tex]c[/tex] is the initial height. A student timed the drop at 1.27 seconds.

Use this to determine the height from which the ball was dropped, to at least 2 decimal places.

Solution:

The height [tex]h[/tex] of the free falling ball is represented by the equation as:

[tex]h=-4.9t^2+c[/tex] where [tex]t[/tex] is time in seconds, and c is the initial height.

To determine the initial height from which the ball was dropped.

The drop was timed at 1.27 seconds, we will plugin [tex]t=1.27[/tex] in the given height function to find [tex]h(1.27)[/tex]

[tex]h(1.27)=-4.9(1.27)^2+c[/tex]

[tex]h(1.27)=-7.90+c[/tex]

Since, the drop is timed at 1.27 seconds, so in the given time the ball will reach the ground, making [tex]h(1.27)=0[/tex]

So, we have.

[tex]0=-7.90+c[/tex]

Adding both sides by 7.90 to solve for [tex]c[/tex].

[tex]0+7.90=-7.90+7.90+c[/tex]

[tex]7.90=c[/tex]

∴ [tex]c=7.90\ m[/tex]

Thus, the initial height from which the ball was dropped = 7.90 meters

Answer:

The answer is C, r = -0.83

Step-by-step explanation:

The graph has a negative slope, and the correlation between the points isn't super spread out. Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.

The correlation coefficient best matches the graph. The answer is C,

r = -0.83.

We have given that,

A) r = 0.91

B) r = 0.34

C) r = -0.83

D) r = -0.25

We have to determine the best matches graph.

The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.

The graph has a negative slope, and the correlation between the points isn't super spread out.

Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.

To learn more about the correlation coefficient visit:

https://brainly.com/question/4219149

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Answer: 4,900,000

Step-by-step explanation:

5 million - 100 thousand = 4.9 million

Answer:

NM and FG

Step-by-step explanation:

To make sure the triangles are congruent by SAS, Ebony needs to compare the lengths of two sides and the measure of the included angle of the triangles.

In order to make sure the triangles are congruent by SAS (Side-Angle-Side), Ebony would need to compare the lengths of two sides and the measure of the included angle of the triangles.

Specifically, Ebony would need to compare:

If the length of segment EF is equal to segment ON and the measure of ∠MON is equal to ∠GEF, then the triangles will be congruent by the SAS postulate.

https://brainly.com/question/22062407

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