Triangle ABC is the preimage of a transformation that consists of a reflection across x -axis followed by a reflection across the y -axis. Which of the triangles is the image of △ABC under this transformation? Select the triangle that corresponds to the image △A′B′C′ .

Answers

Answer 1

The image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.

The preimage triangle ABC undergoes a reflection across the x-axis followed by a reflection across the y-axis.

To determine the image triangle △A'B'C', we need to understand the effects of these transformations.

Reflection across the x-axis flips the points of the preimage vertically, while reflection across the y-axis flips the points horizontally.

When both reflections are applied successively, the resulting image will be a reflection across the origin (0,0).

Given that, the image triangle △A'B'C' will be the reflection of triangle ABC across the origin.

In this case, the x-coordinate and y-coordinate of each point in triangle ABC will be negated to obtain the corresponding point in △A'B'C'.

Let's consider the points of triangle ABC:

A(x₁, y₁), B(x₂, y₂), C(x₃, y₃)

To obtain the corresponding points in △A'B'C', we negate the x and y coordinates:

A'(-x₁, -y₁), B'(-x₂, -y₂), C'(-x₃, -y₃)

Therefore, the image triangle △A'B'C' is formed by reflecting triangle ABC across the origin, resulting in each point's coordinates being negated.

Note: It's important to note that without the actual coordinates of triangle ABC, it's not possible to determine the specific shape or size of the image triangle △A'B'C'.

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Related Questions

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer: 127

Step-by-step explanation:

360 - 70 - 36 = 254

254/2 = 127

D = 127

side length of titles are 2ft. Rachel tiled the whole floor with 6 rows of 4 tiles
what is the area of the kitchen floor

Answers

The area of the rectangular shaped kitchen floor is A = 96 feet²

Given data ,

The side length of each tile is 2ft, then the area of each tile is:

Area of a tile = side x side = 2ft x 2ft = 4 sq ft

Since there are 6 rows of tiles, each row has 4 tiles, therefore the total number of tiles is:

Total number of tiles = 6 x 4 = 24 tiles

So, the total area covered by the tiles is:

Total area covered by tiles = Area of a tile x Total number of tiles

= 4 sq ft/tile x 24 tiles

= 96 sq ft

Hence , the area of the kitchen floor is 96 feet²

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Please help I am struggling thank you, have a great day

Answers

Answer:

24

Step-by-step explanation:

For this problem, substitute the value -3 for x and solve. It would look like this:

[tex]4(-3)^2+2(-3)-6[/tex]

Using the order of operations (PEMDAS) we solve the exponent first.

[tex]-3^2=9[/tex]

Then solve the multiplication parts.

[tex]4(9)+2(-3)-6\\4*9=36[/tex]and        [tex]2*(-3)=-6[/tex]

Finally subtract to get the answer.

[tex]36-6-6=24[/tex]

Idaho gets out and closes the door behind her. She is in a room with one exit, and the lock requires a key. There's a table with a briefcase that is also locked. It has a three-digit combination. The first part of the combination is on a wheel with all 10 digits. The second wheel has only 5 digits, and the third has 3 digits. How many combinations are possible?

Answers

Answer:

150

Step-by-step explanation:

To determine the number of possible combinations for the briefcase, we need to multiply the number of options for each wheel.

The first wheel has 10 digits, so there are 10 possibilities.

The second wheel has 5 digits, so there are 5 possibilities.

The third wheel has 3 digits, so there are 3 possibilities.

To calculate the total number of combinations, we multiply the possibilities for each wheel:

10 × 5 × 3 = 150

Therefore, there are 150 possible combinations for the briefcase.

Answer: 150

Step-by-step explanation:

I’m not completely sure, but this is going by my logic. The first one has ten digits and any of those ten digits could go with 1 digit from the 5 wheel, and 1 digit from the 3 wheel, so (I think) you have to multiply 10x5x3 to get the amount of possible combinations.

But, if this is wrong, please correct me! I love puzzles and just though this would be fun to try and figure out, I don’t want to spout out any mis or disinfo to anyone

But, in the case my answer’s right, hope this helped :D

Could someone help me with this? Thank you

Answers

The values for the determinants of the matrices are:

|A| = -3

|B| = -2

|AB|= -6

How to determine the determinant of A, |A|?

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

If the matrix Z is given as:

[tex]Z = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]

The determinant will be:

|Z| = (a * d) - (b * c)

Thus:

|A| = (-1 * 3) - (0 * 0) = -3

|B| = (2 * (-1)) - (0 * 0) = -2

AB = A * B

[tex]AB = \left[\begin{array}{ccc}-1&0\\0&3\end{array}\right] * \left[\begin{array}{ccc}-2&0\\0&-1\end{array}\right][/tex]  

Calculations for the product (multiply each row by each column):

[-1 * (-2)] + [0 * 0] = 2

[-1 * 0] + [0 * (-1)] = 0

[0 *  (-2)] + [3 * 0] = 0

[0 * 0] + [3 * (-1)] = -3

[tex]AB = \left[\begin{array}{ccc}2&0\\0&-3\end{array}\right][/tex]

Thus,

|AB| = (2 * (-3)) - (0 * 0) = -6

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Select the matrix that represents the parallelogram

Answers

The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 270 degrees counterclockwise, the new coordinates would be:

Answers

After rotating the triangle counterclockwise by 270 degrees, the new coordinates of the vertices would be (3, -1), (-4, 2), and (3, 5).

How to Find the New Coordinates of a Triangle after a Rotation?

To rotate a point counterclockwise around the origin by 270 degrees, we can use the following transformation rules:

[tex]New_x = -y[/tex]

[tex]New_y = x[/tex]

Let's apply these rules to each vertex of the triangle and find the new coordinates:

For the first vertex (-3, 1):

[tex]New_x = -1[/tex]

[tex]New_y = -(-3) = 3[/tex]

So, the new coordinates for the first vertex after rotating counterclockwise by 270 degrees are (3, -1).

For the second vertex (2, 4):

[tex]New_x = -4[/tex]

[tex]New_y = 2[/tex]

The new coordinates for the second vertex after rotating counterclockwise by 270 degrees are (-4, 2).

For the third vertex (5, -3):

[tex]New_x = -(-3) = 3[/tex]

[tex]New_y = 5[/tex]

The new coordinates for the third vertex after rotating counterclockwise by 270 degrees are (3, 5).

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Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m

Answers

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

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Suppose theta is an angle in the third quadrant and cos theta = 5/7. What is the value of sin(theta)
3√8
√24
24
2√12

Answers

The value of sinθ is √24/7 meanwhile the correct answer is not in the option provided or perhaps option (b) is meant to be √24/7 instead.

Understanding Quadrant in Trigonometry

In the third quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) of the angle are negative.

Given that

cosθ = 5/7

we can determine the value of sinθ using the Pythagorean identity:

sin²θ + cos²θ = 1

sin²θ + (5/7)² = 1

sin²θ + 25/49 = 1

Now, let's solve for sinθ:

sin²θ = 1 - 25/49

sin²θ = 49/49 - 25/49

sin²θ = 24/49

Taking the square root of both sides, we find:

sinθ = √(24/49)

Simplifying further:

sinθ = √24 / √49

sinθ = √24 / 7

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Can someone help me find the surface area of these 2 prisms?

Answers

Step-by-step explanation:

1) the 1-st prism is cube. Then its surface area can be calculated as:

A=5*5*6=150 [ft²];

2) A=[Perimeter of triange]*height+2*[Area_of_triangle];

according to the formula above height=3; Perimeter of triangle=9+12+15=36; Area of triangle=12*9*0.5=54;

Finally, A=36*3+2*54=108+108=216 [cm²].

How do I solve this help me pls now I need it pls I’ll give lots of points help me I put a picture here

Answers

The radius of cylinder is 31.5 cm.

We have,

LSA of Cylinder. = 693 cm²

Height = 11 cm

We know the formula

Lateral Surface Area of Cylinder = 2πrh

So, LSA of cylinder = 639π

2πh= 693π

2rh = 693

r = 693 / 2h

r =693 / 2 x 11

t = 63/2

r = 31.5  cm

Thus, the radius of cylinder is 31.5 cm.

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Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 820 defective panels?

Answers

Answer:

  16000

Step-by-step explanation:

You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.

Setup

Let b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...

  0.05(b -6000) +0.02b = 820

Solution

Simplifying the equation, we have ...

  0.07b -300 = 820

  0.07b = 1120

  b = 16000

Plant B produced 16000 panels.

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$16,000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the account after 4 years? Round to the nearest cent.

Answers

The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Understanding Compound Interest

Recall the compounding formula:

A = P * [tex]e^{rt}[/tex]

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * [tex]e^{0.02 * 4}[/tex]

Using a calculator, we can calculate:

A = $16,000 * [tex]e^{0.08}[/tex]

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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Kyle's current credit card balance is $3,109.87 with a minimum payment of $159.00. Over the next month he spends $532.42. If the APR is 27.99% (billed monthly), what will Kyle's new balance be, with interest? (4 points) $3,404.65 $3,564.54 $3,606.84 $3,789.03

Answers

Answer:

  (b)  $3564.54

Step-by-step explanation:

You want the new balance showing on a credit card statement if the APR is 27.99%, the old balance is $3109.87, a payment of $159 was made, and purchases were made totaling $532.42.

Subtotal

Apparently, the new balance is computed by subtracting payments, and adding new charges to the old balance, then computing and adding the finance charge on this sum.

  balance before finance charge: $3109.87 -159.00 +532.42 = $3483.29

Finance charge

The finance charge is 1 month's interest at the annual rate:

  I = Prt = $3483.29×0.2799×(1/12) = $81.25

New Balance

The new balance is the subtotal above, with the finance charge added:

  new balance = $3483.29 +81.25 = $3564.54

Kyle's new balance will be $3564.54.

__

Additional comment

This is a very expensive credit card. Not only is the interest rate of 27.99% very high, but also finance charges are charged on new purchase in the month they are purchased.

Some cards these days have interest rates of 12.75% or lower, with no finance charge for purchases made during the month. Some cards offer a rebate of up to 1.5% of purchases, so a net "negative" finance charge if you pay off the card every month.

What is the x of 4(40)-10

Answers

Answer: x= 150

Explanation: Multiply 4 by 40 and subtract 10. PEMDAS

of tennis balls is shaped like a cylinder with the dimensions shown
r= 4 cm
What is the approximate surface area of the can? Use 3.14 for. Use the formula for the surface area of a cylinder SA= 2mth + 2rr²
527 cm²
100 cm²
628 cm²
525 cm²
21 cm
Previous
Next >

Answers

The formula for the surface area of a cylinder SA= 2mth + 2rr² is 525 cm².

To find the surface area of the cylindrical can, we need to use the formula:

SA = 2π[tex]r^2[/tex]+ 2πrh

where r is the radius of the circular base of the can, h is the height of the can, and π is a mathematical constant approximately equal to 3.14.

From the given dimensions, we know that the radius of the can is 4 cm. However, we do not have the height of the can. Therefore, we cannot accurately calculate the surface area of the can.

Based on the answer choices provided, we can approximate the surface area of the can by using the given value of r = 4 cm and an estimated value for the height.

For example, if we assume the height of the can is approximately 10 cm, then we can use the formula to calculate the surface area:

SA = 2π([tex]4^2[/tex]) + 2π(4)(10)

SA = 100.48 + 251.2

SA ≈ 351.68 [tex]cm^2[/tex]

     ≈525 cm²

This value is closest to the fourth answer choice of 350 [tex]cm^2[/tex]. However, it is important to note that this answer is an approximation based on estimated values, and may not be entirely accurate.The  correct answer is 525 cm².

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A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement? Answer by looking at the images below!

Answers

Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.

The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.

Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.

Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.

For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.

Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.

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The complete question is:

A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.

a) Are the four different colour outcomes equally likely? Explain.

b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)

c) Find the sum of their probabilities.

You are given a map with a number scale 1:60 you must measure a length on the map of 10cm

Answers

The measure of a length of 10cm on the scale is 1/6 units

How to determine the measure of a length on the map of 10cm

From the question, we have the following parameters that can be used in our computation:

Scale = 1 : 60

For a length of 10 cm, we have

Actual length = 10 cm

This means that

Scale ; 10 cm = 1 : 60

Express as fraction

So, we have

Scale/10 cm = 1/60

When evaluated we have

Scale = 1/6 units

Hence, the measure of a length of 10cm on the scale is 1/6 units

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How many variables are in the expression.
8d²+2bc+ 10ab

1
2
3
4

Answers

There are 4 variables in the expression 8d² + 2bc + 10ab

How to determine the number of variables in the expression

From the question, we have the following parameters that can be used in our computation:

8d²+2bc+ 10ab

Express properly

So, we have

8d² + 2bc + 10ab

Consider an expression ax + by where the variable is a and b are constants

The variables in the expression are x and y

Using the above as a guide, we have the following:

The variables in the expression 8d² + 2bc + 10ab are a, b, c and d

This means that there are 4 variables in the expression

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Use angle diagram to name each one of the angles.

Answers

The angles in the parallel lines are solved

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Given data ,

Let the two parallel lines be represented as a and b

where the transversal line is m

Now , from the given figure , we can deduct that

We can conclude some factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Now , the angles are

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Hence , the angles are solved

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During the repair, the mechanics will need to
connect a cable between chairs B and J, and then
continue that cable to chair G. What is the angle
formed by the cable?

Answers

The angle formed by the cable between chairs B and J, and then

continue chair G is

75 degrees

How to determine the angle

The angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle

Assuming each chair is equal distance apart, then they will subtend equal angle.

The number of chairs for A to L is 12

angle per chair = 360 / 12 = 30 degrees

number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees

Inscribed angle = 1/2 * intercepted arc

Inscribed angle = 1/2 * 150

Inscribed angle = 75 degrees

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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!

Answers

Answer:

∆SMK is similar to ∆RMT by AA.

Help me please answer is not A

Answers

Answer:

B) 16.47

Step-by-step explanation:

In order to find the mean of grouped data with intervals, we use the formula

(∑f * m) / (∑f)

where (∑f * m) is the sum of the product of each frequency (f) and the corresponding midpoint (m) for its interval and (∑f is the sum of each frequency

Step 1:  First, we need to find the sum of the frequencies: ∑f = 2 + 3 + 8 + 4 = 17

Step 2:  Next, we need to find the midpoint (m) of each interval.  We do this by averaging the end points of each interval

m of first interval:  (9.5 + 12.5) / 2 = 11

m of second interval:  (12,5 + 15.5) / 2 = 14

m of third interval:  (15.5 + 18.5) / 2 = 17

m of fourth interval:  (18.5 + 21.5) / 2 = 20

Step 3:  Now, we multiply the frequency for each interval by its corresponding midpoint and add them together to find the sum

f * m for first interval: (2 * 11) = 22

f * m for second interval:  (3 * 14) = 42

f * m for third interval:  (8 * 17) = 136

f * m for fourth interval:  (4 * 20) = 80

Sum of f * m for each interval:  22 + 42 + 136 + 80 = 280

Step 4:  Finally, we divide the sum of f * m for each interval by the sum of f to find the mean:

280 / 17 = 16.47058824 = 16.47

NO LINKS!! URGENT HELP PLEASE!!

O is the center of the regular nonagon below. Find its area. Round to the nearest tenth if necessary.

Answers

Answer:

471.1 square units

Step-by-step explanation:

A regular nonagon is a 9-sided polygon with sides of equal length.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.

The side length (s) of a regular polygon can be calculated using the apothem formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Given values:

a = 12n = 9

Substitute the given values into the formula to create an expression for the side length (s):

[tex]12=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{9}\right)}[/tex]

[tex]12=\dfrac{s}{2 \tan\left(20^{\circ}\right)}[/tex]

[tex]s=24 \tan\left(20^{\circ}\right)[/tex]

The standard formula for an area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:

[tex]A=\dfrac{9 \cdot 24 \tan(20^{\circ}) \cdot 12}{2}[/tex]

[tex]A=1296\tan(20^{\circ})[/tex]

[tex]A=471.705423...[/tex]

[tex]A=471.7\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.

6 sin =5 solve to the nearest 0.1

Answers

Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

please help me thank you so much

Answers

Answer:

1)

7+9-15 = add 7 and 9, then subtract 15

2)

15-(7+9) = The sum of 7 and 9 subtracted from 15

3)

15-(7+9) =  subtract 7 from 15, then add 9

Step-by-step explanation:

Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient

Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.


Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $20.50
10 $25.00
15 $32.50


What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.

For every additional mile the cab travels, the total fee increases by $1.50.

When the cab travels 0 miles, the total fee will be $1.50.

When the cab travels 0 miles, the total fee will be $10.00.

Answers

Answer:

When the cab travels 0 miles, the total fee will be $10.00.

Step-by-step explanation:

We Know

2 miles = $13.00

5 miles = $17.50

3 miles = 17.50 - 13.00 = $4.50

1 mile = 4.50 / 3 = $1.50

So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.

What does the y-intercept mean in this situation?

It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).

So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.

Question 1 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. x=-8, y = 2
OB. More than 1 solution
OC. No solution
OD. x= 12, y = 3
3y-12x = 18
2y-8x = 12

Answers

The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]

To do this, we can rearrange each equation to solve for y in terms of x:

[tex]3y = 12x + 18\\\\y =4x + 6[/tex]

For the second equation.

[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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.3185 degrees = minutes and seconds

Answers

The conversion of 3185 degrees to minutes and seconds is 19 minutes and 6.6 seconds

How to convert the 3185 degrees to minutes and seconds

From the question, we have the following parameters that can be used in our computation:

Degrees = 0.3185

By definition, there are 60 minutes in a degrees

So, we have

Minutes = 0.3185 * 60

Evaluate the product

Minutes = 19.11

The decimal part of the product above represents the number of seconds

So, we have

Minutes = 19

Seconds = .11 * 60

Evaluate

Seconds = 6.6

Hence, .3185 degrees is 19 minutes and 6.6 seconds

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50 POINTS!!!
Math...Money...Interest...
Please give the correct answers and show the steps. I will report your account if I find an error. Thank you for your help.

Answers

Answer:

2.

Quarterly:

100000 = 60000(1 + 0.075/4)^4tt ≈ 6.87466382 years

Monthly:

100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 years

Continuously:

100000 = 60000e^0.075tt ≈ 6.811008 years

3.

Twice a year:

300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 years

Eight times a year:

300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 years

Continuously:

300 = 100e^0.1025tt ≈ 10.718169 years

Step-by-step explanation:

The formula for compound interest is:

A = P(1+r/n)^nt

The formula for compounded continuously is:
A = Pe^rt

Where:

A = the future value of the investment

P = the principal balance

r = the annual interest rate (decimal)

n = number of times interest is compounded per year

t = the time in years


Using that we can plug the formula in for each question:

2.

Quarterly:

100000 = 60000(1 + 0.075/4)^4tCompounded quarterly means in a year, it is compounded 4 timesNote that the question is asking to find how much time it takes so t is the thing we need to solve fort ≈ 6.87466382 years

Monthly:

100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 years

Continuously:

100000 = 60000e^0.075tWe are now using the compounded continuous formulat ≈ 6.811008 years

3.

Twice a year:

Since the question does not give us a starting amount but it gives us a goal of tripling the money, we can substitute any amount of money for P and A as three times PFor now, let's say P is 100 and A is 3 times 100 so A is 300300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 years

Eight times a year:

We will continue to place hold P as 100 and A as 300300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 years

Continuously:

We will now use the compounded continuous formula300 = 100e^0.1025tt ≈ 10.718169 years





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