Meg borrows $8650 to buy a car at 4.5% interest.
years?
How much interest will she pay after 5 years

Answer:

8.2

Step-by-step explanation:

1. Since AD is equal to DB, we will need to set 3x-11 equal to 5x-29. When you solve the equation you will get 9 for x.

2. Plug the 9 in for x in DB (you could plug it in for AD instead if you want since DB and AD are equal to each other). You should get 16.

3. Take a look at the smaller triangle DBP which is part of triangle ABC. We will need to use the Pythagorean Theorem. Square the legs of the triangle and set it equal to the hypotenuse squared. One of the legs, DP, is unknown so we will just have it as x. The other leg is DB, which is 16.

* PB is the hypotenuse and has a value of 18. Remember that P is the circumcenter, which means it is equidistant to each vertex and each angle bisector is equal to each other. As a result PC is equal to PB which happens to be 18.

You should have it something like this:

16^2 + x^2 = 18^2

Now do all the squaring and stuff and you should eventually get x^2 = 68

4. Square root x^2 = 68 and you will get a long decimal. You will need to round it to the tenths place.

5. After rounding you will finally get 8.2

The measurement of DP is 8.2 units.

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Given that, P is the circumcenter △ ABC, and AD = 3x - 11, DB =5x - 29,

PC = 18

Since, DP bisects AB, so, AB = DP

3x-11 = 5x-29

x = 9

DB = 5*9 - 29 = 16

Since, P is the circumcenter, then PB = PC = PA = 18

Using Pythagoras theorem in Δ BPD

PB² = DB² + DP²

DP² = PB² - DB²

DP² = 18² - 16²

DP² = 324 - 256

DP² = 68

DP = 8.2

Hence, The measurement of DP is 8.2 units.

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Answer:

2

Step-by-step explanation:

2 seems to be the only one that is correct

Correct Statements: (modified the statements that are incorrect)

1. The coordinates of point A are (-3, 3)

2. Already correct

3. The coordinates of point C are (-2, -2)

4. Point B is the closest to the y-axis (only one away)

5. Point A is 3 away and Point B is 1 away

(sorry if this is confusing but this is what I got)

Answer:

6.93 meters

Step-by-step explanation:

Use similar triangles to solve

if the tree shadow is 26.05m  long and she stands 20.6 meter away from the tree, so her shadow meets the tip, her shadow is 26.05-20.6 = 5.45

height of Emily divided by shadow of Emily must equal height of tree divided by shadow of Tree

1.45 /5.45=x/26.05

26.05 x (1.45/4.45)=x

x= 6.93

Answer:

Step-by-step explanation:

The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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Answer: 28

Step-by-step explanation: Im taking the same class here is a photo of the work, divide 56/2 than you get 28

Answer:

x=75.66

Step-by-step explanation:

+47  180+47

3x=227

divide 3 on each side

x=75.66

Answer:568.888888888 or 568 and 8/9

Step-by-step explanation:proportional to the radius squared and then divide by 8. 640*64/(9*8)

Answer:

csctheta= \(\frac{\sqrt{13} }{3}\)

Step-by-step explanation:

answer is provided on top

The value of the \(\rm cosec \theta = \frac{\sqrt{13} }{3}\). Cosec is found as the ratio of the hypotenuse and the perpendicular.

The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle

The given data in the problem is;

\(\rm cot \theta = \frac{2}{3}\)

The \(cot \theta\) is found as;

\(\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\\)

From the phythogorous theorem;

\(\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\\)

The value of the cosec is found as;

\(\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}\)

Hence the value of the \(\rm cosec \theta = \frac{\sqrt{13} }{3}\).

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We have the following functions:

We need to find g(8) + f(-3). The expression g(8) is equivalent to replace 8 in the place of x, that is,

Similarly, f(-3) is given by

which gives

Therefore, g(8)+f(-3) is given by

so the answer is 25

The length of the original square must be equal to 3 inches.

To find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.

Since the new length is stretched by 5in, the new length would be.

\(l = (x + 5)in\)

The area of a square is given as

\(A = l^2\)

But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.

\(A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\\)

Solving the quadratic equation above;

\(x^2 + 10x - 39 = 0\\x = 3 or x = -13\)

Taking the positive root only, x = 3.

The side length of the original square is equal to 3 inches.

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Answer:

The dimensions of the rooms in the blueprint will be Living room (), Kitchen (), Office (), Bedroom (), Bedroom (), Bathroom ().

Given information:

A house blueprint has a scale of 1 in : 4 ft.

The length and width of each room in the actual house are shown in the table below:

 Living room  Kitchen  Office  Bedroom  Bedroom     Bathroom

Length  20             16    8              8                      20                6

width 8             16    16              16              20                8

The scale factor is of 1 in: 4 ft. So, 4 ft of actual length is equivalent to 1 inch in the blueprint.

So, the length and width of the different rooms in te house in the blueprint will be,

 Living room  Kitchen  Office  Bedroom  Bedroom       Bathroom

Length(in) 5             4            2              2                      5                        1.5

width(in)   2             4            4              4                      5                          2

Therefore, the dimensions of the rooms in the blueprint will be Living room (), Kitchen (), Office (), Bedroom (), Bedroom (), Bathroom ().

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Step-by-step explanation:

hope this helps

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

\(sin^2x=1-cosx\)

Now use the Pythagorean identity that says

\(sin^2x =1-cos^2x\) and make the replacement:

\(1-cos^2x=1-cosx\). Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

\(1-cos^2x+cosx-1=0\) and then simplify to

\(cosx-cos^2x=0\)

Factor out the common cos(x) to get

\(cosx(1-cosx)=0\) and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

\(x=\frac{\pi }{2},\frac{3\pi}{2}\)

The second equation simplifies to

cos(x) = 1

Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.

So, in the end, your 3 solutions are

\(x=\frac{\pi}{2},\pi,\frac{3\pi}{2}\)

Answer:

B

Step-by-step explanation:

product means multiplication, but there isn't any multiplication happening

The true statements are;

1) AB + BC = AC

Length of BC = |6 - 1|

2) ∠JMK = 50°

∠KML = 35°

1) From the given number line interval, we can deduce the interpretation as follows;

AB + BC = AC

Length of BC = 5 units or |6 - 1|

Length of B = 3 Units

2) We can see that ∠JML is an angle triangle. Thus, ∠JML = 85°. Thus;

6x + 2 + 4x + 3 = 85

10x + 5 = 85

10x = 85 - 5

10x = 80

x = 80/10

x = 8°

Thus;

∠JMK = 6(8) + 2

∠JMK = 50°

∠KML = 85° - 50°

∠KML = 35°

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

sin²x = 1 - cos²x and cos²x = 1 - sin²x

Consider the left side

\(\frac{(1-sinA)(1 + sinA)}{(1+cosA)(1-cosA)}\) ← expand numerator/denominator using FOIL

= \(\frac{1-sin^2A}{1-cos^2A}\)

= \(\frac{1-(1-cos^2A)}{1-(1-sin^2A)}\)

= \(\frac{1-1+cos^2A}{1-1+sin^2A}\)

= \(\frac{cos^2A}{sin^2A}\)

= cot²A = right side , thus proven

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

20 calories per Cheetos

Step-by-step explanation:

hope it helped

Answer:

9/10

Step-by-step explanation:

0.90 = 0.9 = 90/100 = 9/10

If my answer is incorrect, pls correct me!

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

-Chetan K

Answer:

The answer is on the image.

Hope it helps!

For this case, the first thing we should do is write the linear function that best suits the table.

In this case we have the following function:

y = 7.5x - 5

C = 7.5t-5

For C = 100 we have:

100 = 7.5t-5

We clear the time:

t = (100 + 5) / (7.5)

t = 14

Answer:

it did take the pizza to reach 100 degrees Celsius about 14 minutes

Answer:

Imma say C...It makes the most sense!

Step-by-step explanation:

Have a good night!

The volume of each pyramid is exactly √3/6 cubic feet.

To find the volume of each pyramid, we need to first find the volume of the cube and then divide it by three. So, the volume of each pyramid is:

V = (1/3) Bh

We know that the base of each pyramid is a square with side length s, where s is half of the length of a side of the cube. So, s = 1 foot. Therefore, the area of the base of each pyramid is B = s² = 1² = 1 square foot.

To find the height of each pyramid, we need to use the Pythagorean theorem. Let's call this distance d. Then, using the Pythagorean theorem, we have:

d² + (1/2)² = s²

d² + 1/4 = 1

d² = 3/4

d = √(3)/2

Now that we know the height of each pyramid, we can calculate its volume:

V = (1/3) Bh = (1/3)(1)(√(3)/2) = √(3)/6 cubic feet

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Applying the given operation, the resulting matrix is given by:

\(\left[\begin{array}{ccc}7&\frac{9}{2}&-6\\-6&-3&12\end{array}\right]\)

The matrix given in this problem is:

A=[ 4 3 0 ]; [-6 -3 12] (; represents new row).

Hence:

The operation is:

R1 -> R1 - 0.5R2

Meaning that row 2 is kept constant, while row 1 is changed according to the operation.

Then:

The resulting matrix is given by:

\(\left[\begin{array}{ccc}7&\frac{9}{2}&-6\\-6&-3&12\end{array}\right]\)

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Answer:

6x^2+4xy

Step-by-step explanation:

You distribute the 2x by multiplying it with each term
2x(3x)+ 2x(2y)

6x^2+4xy

hopes this helps please mark brainliest

Answer:

370

Step-by-step explanation:

nearest ten would be 370

Answer:

370

Step-by-step explanation:

just round the 9 into a 10

if your looking for the square root of this rounded its 19.20 (sorry if that's not what you needed I was confused)

Step-by-step explanation:

The frequency and the time period is related by the formula as follows :

\(f=\dfrac{1}{T}\)

Here, f is frequency and T is time period

Now, we need to solve T in terms of f.

Firstly, cross multiplying the above equation,

\(f\times T=1\)

Now dividing both sides by T.

\(\dfrac{f\times T}{T}=\dfrac{1}{T}\\\\f=\dfrac{1}{T}\)

Hence, this is the required solution.

Answer:

T= 1/f

Step-by-step explanation:

T= one OVER f