What is the reflection image of (4, -1) across line y=x?

a
(-1,4)
b
(-1,-4)
c
(1,-4)
d
(-4,1)

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Answer:

3/4:1

Step-by-step explanation:

the ration is 3/4:1 bc you beat 1 egg for 3/4 of a cup of milk

After answering the given query, we can state that  the parabola equation expands upwards, and the apex is (4, 4.5).

Using the equals sign (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical formulas through a mathematical assertion. The equal symbol, for example, puts a space between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two lines that are printed on opposite sides of a letter. Most of the time, the emblem and the particular program match. e.g., 2x - 4 = 2 is an example.

P equals 1/2, meaning that the distance between the apex and the focus is equal to the distance between the directrix and the focus.

As a result, the parabola's equation is:

\((x - 4)^2 = 4(1/2)(y - 1.5)\\(x - 4)^2 = 2(y - 1.5)\)

The left half of the equation is expanded as follows: x2 - 8x + 16 = 2(y - \(1.5) x2 - 8x + 13 = 2y\\y = (1/2)x^2 - 4x + 13/2\)

The problem can also be expressed in vertex form by filling in the cube as follows:

\((x - 4)^2 = 2(y - 1.5)\\(x - 4)^2 = 2(y - 1.5) + 6\\(x - 4)^2 = 2(y - 4.5)\\(x - 4)^2/8 = (y - 4.5)\\\)

Therefore, the parabola expands upwards, and the apex is (4, 4.5).

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

\(\huge\boxed{x=9}\)

Step-by-step explanation:

We know that ∠A and ∠B are the same exact length. Since one of the angles is given to us in an exact length, we can set the measures equal to each other.

\(4x + 9 = 45\)

Let’s solve for x.

\(4x +9-9=45-9\\\\4x=36\\\\x=9\)

Hope this helped!

Answer:

Please check the explanation.

Step-by-step explanation:

                                                      Part a)

Given the table

Year             Value ($)

1                    18,000

2                   15,300                

3                   13,005

Let us check the sequence

18000, 15300, 13005,...

Let us find the common ratio 'r' of all the adjacent terms to check whether the sequence represents the geometric sequence or not, using the formula such as:

\(\:r=\frac{a_{n+1}}{a_n}\)

\(\frac{15300}{18000}=\frac{17}{20},\:\quad \frac{13005}{15300}=\frac{17}{20}\)

As the ratio of all the adjacent terms is the same, so

\(r=\frac{17}{20}\)

Therefore, the given sequence is a geometric sequence

                                                  Part b)

Given the sequence

18000, 15300, 13005,...

The nth term of the geometric sequence is

\(a_n=a_1\cdot r^{n-1}\)

here

\(a_1=18000\)

\(r=\frac{17}{20}\)

so

\(a_n=18000\left(\frac{17}{20}\right)^{n-1}\)

In order to determine the car worth in the 15th year, substitute n = 15

\(a_{15}=18000\left(\frac{17}{20}\right)^{15-1}\)

\(a_{15}=18000\frac{17^{14}}{20^{14}}\)

\(a_{15}=18000\times \:\:0.10276\)

\(a_{15}=1850\) $

Therefore, the worth of a car in the 15th year will be: $1850

Answer:

\(sin(90) = 1\)

\(sin( - 90) = - sin(90) = - 1\)

\(so \: \sin(90) > \sin( - 90) \)

....hope this helps:)

Answer:

0.0

Step-by-step explanation:

To find 0.007 divided by 0.498, we can perform the following calculation:

0.007 / 0.498 ≈ 0.0141

Rounding this to the nearest tenth gives:

0.0141 ≈ 0.0

Therefore, the result, rounded to the nearest tenth, is 0.0.

Answer:

EAFI

Step-by-step explanation:

Since we know ∠A + ∠D = 90°, we can add the two equations together to get

90 = 7x + 6

Subtract 6 from both sides

84 = 7x

Divide both sides by 7 to get x = 12

Plug back into the equation to get ∠A = 36

Repeat for number 3, but this time the angles equal 180

Using the same steps as before, y = 3 and ∠C = 126

Put the letters together to get EAFI

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer: B. Angle FGD.

Answer:

4b^4

Step-by-step explanation:

Work backwards, multiply 4b^5 to 2b, get 8b^6, divide by 2b^2 and get 4b^4

Answer:

A.

92%

Step-by-step explanation:

Step-by-step explanation:

Hypotenuse² = (Leg 1)² + (Leg 2)²

= (8)² + (15)² = 289

Hence the hypotenuse is 17cm.

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

4x+25

I hope this helped ;)

Tthe probability that the first card is a 2 and the second card an ace is 4/663

In a standard deck of cards, we have the following values

Sample size i.e. number of cards = 52

Ace = 4

Number of 2 = 4

The first card is the card number 2

So, we have

P(2) = 4/52

The card is not replaced

So, we have

P(Ace | 2) = 4/51

The probability is

P = 4/52 * 4/51

Evaluate

P = 4/663

hence, the probability is 4/663

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Answer:

25% chance of winning.

Step-by-step explanation:

The approximate volume of the astroid is 2.57 * 10^9 m^3

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

Radius = 8.5 × 10^2 m.

Using the formula 4/3 π r^3 for the volume, we get

Volume = 4/3 * (22/7) * (8.5 × 10^2)^3

Evaluate

Volume = 2.57 * 10^9 m^3

Hence, the volume is 2.57 * 10^9 m^3

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In a trial run the cutoff time should be 58.78 minutes.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.

Given a normal distribution:

Mean = 62.9 minutes

Standard deviation = 6.1 minutes

To cut the bottom 25% riders

Using the relation:

Z score = (score - mean) / standard deviation

Z score for the bottom 25% corresponds to

- 0.674(using tables or calculator)

Hence,

-0.674 = (score - 62.9) / 6.1

-0.674 * 6.1 = score - 62.9

-4.1114 = score - 62.9

-4.1114 + 62.9 = score

Score = 58.78

Hence, in a trial run the cutoff time should be 58.78 minutes.

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Answer:

Step-by-step explanation:

i guess u shud make the ratio into x ie 3x:7x

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

$28 per hour

Step-by-step explanation:

Let's first find out how much extra Victoria was paid during the week she worked overtime.

Without overtime, Victoria's weekly paycheck would be $550. However, she received $690 that week. The difference between the two amounts is the extra pay for overtime:

Extra pay = Total pay - Regular pay = $690 - $550 = $140

Now, we know that Victoria worked 5 hours of overtime. To find her overtime pay per hour, we can divide the total overtime pay by the number of overtime hours:

Overtime pay per hour = Total overtime pay / Overtime hours = $140 / 5 = $28

Victoria's overtime pay is $28 per hour.

Hope this helps!

Answer:

Victoria is paid $28 per hour of overtime.

Step-by-step explanation:

Get the difference of Victoria's paycheck with and without overtime.

Difference = $690 - $550

Difference = $140

The difference is the amount that she was paid for the overtime.

Since she worked for 5 hours then we can just divide the amount over the time.

Rate = $140/5hours

Rate = $28/hr

Answer:

10 010 10 10 10 10 101 01 mo1

Step-by-step explanation:

Answer:

perpendicular lines

Step-by-step explanation:

We have:

Total assets

Total liabilities

Stockholders equity

Retained earnings

Answer: $104,600