The image of A (7, 4) after a reflection across a line is A'(1, 4). Find the equation of the
line of reflection.

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

B) 352

Step-by-step explanation:

45% = 0.45

640 x 0.45= 288

288 is how many students walked to school

So to find how many took the bus to school

640- 288= 352

Answer:

Your answer is.....

Child ticket = 9$

adult ticket =16$

Mark it as brainlist answer . follow me for more answer.

Step-by-step explanation:

The slope of the line will be equal to -4/3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

Given that the two points are (2,3) and (8,-5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -5 - 3 ) / (  8 - 2 )

Slope = -8 / 6

Slope = -4 / 3

Therefore, the slope of the line will be equal to -4/3.

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Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

Answer:

C.) Sometimes

Step-by-step explanation:

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

The word that correctly fills the blank is sometimes, the correct option is C.

Rational Numbers are numbers that can be written in the form of p/q, q≠0.

The sum of two irrational number is sometimes a rational number.

For example the summation of the irrational number with its additive inverse, the sum will be 0, which is a rational number and a whole number.

Therefore, the word that correctly fills the blank is sometimes, the correct option is C.

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

If the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

To predict the percent of seeds that sprout if the plant produces 53 seeds, we can try to establish a relationship between the number of seeds produced and the sprout percentage based on the given data points.

We can create a scatter plot of the given data points to visualize the relationship.

Seeds Produced: 65, 55, 56, 70, 44, 63, 51

Sprout Percent: 51, 54, 67.6, 49, 70.4, 49.8, 72.6

Based on the scatter plot, we can see if there is a clear pattern or trend. Let's assume that there is a linear relationship between the number of seeds produced and the sprout percentage.

Using the data points provided, we can perform linear regression to estimate the relationship and predict the sprout percentage for 53 seeds produced.

After performing linear regression on the given data points, the estimated equation for the relationship between the number of seeds produced (x) and the sprout percentage (y) is:

y = -0.3933x + 79.2133

Using this equation, we can plug in x = 53 to predict the sprout percentage for 53 seeds produced:

y = -0.3933 * 53 + 79.2133

Calculating this expression, we find:

y = 57.5

Therefore, if the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

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Cost of the health insurance is $11657.14

What is cost?

A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.

14% of x = 68

x = 68 x 100/14

  = $485.71

Total cost = $485.71 x 24 months = $11657.14

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Step-by-step explanation:

there are many possibilities, 4 of them really easy.

the endpoint of a diameter is simply a point on the circle arc.

the easy options are to assume that the center of the circle is on the x- or the y-axis.

let's go with the x-axis (we only need 2 circles : one with the center left, and one with the center right of the origin).

we know the radius is 3.

so, the center of either circle is 3 units away from the origin.

so, center of circle1 = (-3, 0), center of circle2 = (3, 0).

the equation for a circle is

(x - h)² + (y - k)² = r²

r is the radius, (h, k) is the center point.

equation for circle1 :

(x - -3)² + (y - 0)² = 3²

(x + 3)² + y² = 9

equation for circle2 :

(x - 3)² + (y - 0)² = 3²

(x - 3)² + y² = 9

you see ?

the other 2 easy options would be to put the centers on the y-axis : (0, -3) and (0, 3)

Answer:

26.8875

Step-by-step explanation:

Answer:

You will spend $26.98875 on gasoline

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer:

What am i supposed to be solving please give more description

Step-by-step explanation:

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Tanya swims 56 laps each month.

If Tanya swims a total of 672 laps in a year, we can find out how many laps she swims each month by dividing the total number of laps by the number of months in a year.

There are 12 months in a year, so we can divide 672 by 12 to get:

672 / 12 = 56

Therefore, Tanya swims 56 laps each month.

This assumes that Tanya swims the same number of laps every month. If she does not swim the same number of laps each month, then we would need more information to determine how many laps she swims each month.
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Answer:

F

Step-by-step explanation:

Simplify then graph it, find the x-intercept.

y = 3.75 + 1.5 (x - 1)

y = 1.5x + 2.25

When graphed, the x-intercept is 1.5

So it is, $1.50 per mile

Answer:

F. $1.50 per mile

Step-by-step explanation:

In order to solve this, you can first change it to slope-intercept form to find the slope, or rate of change, easier:

y = 3.75 + 1.5(x - 1) (given)

y = 3.75 + 1.5x - 1.5 (multiply 1.5 by each term in the parenthesis)

y = 2.25 + 1.5x (subtract 1.5 from 2.25)

y = 1.5x + 2.25 (order the terms by exponent value)

In slope-intercept form, the m (slope) of this equation is 1.5, so the rate of change is $1.50 per mile (with an initial fee of $2.25).

Answer:

8+18+20x16 ,

Step-by-step explanation: yeah .

The slope of the line represents the speed in miles per hour

The y intercept represents the initial distance

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

The graph

Where, we have

x = time in hours

y = distance in miles

The slope is

slope = change in y/x

So, we can conclude that the slope is the speed

By definition, the y intercept is the initial value of the graph

In this case;

y intercept = initial distance

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Answer:

(y+10)(y-4)

Step-by-step explanation:

-40y^2

/ \

10y -4y

If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.

We are required to find the cost after all the rebates and envelopes provided.

The cost can be calculated as under:

Cost=109.99-10.00+0.35+0.41

=$100.75

Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.

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Answer:

72

Step-by-step explanation:

2*5=10

3*6=18

6*8=54

8*9=72

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer: b=-2

Step-by-step explanation:

3(b+3)-4(-2+b)=19

3b+9+8-4b=19

-b+17=19

-b=19-17

-b=2

-b/-1=2/-1

b=-2

Answer:

dependent

Step-by-step explanation:

the probability of drawing the blue marble was changed when you drew the red marble and did not put it back

Answer:

25%

Step-by-step explanation:

percent error is found by the equation(measured-real)/real x 100

20 is the measured value and 16 is the real value

(20-16)/16 x 100

4/16 x 100

0.25 x 100

25

hope this helps!

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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The value of dy/dx is -27/8 for 1=5x³+2y²+4xy  at (-1,3).

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

The equation is 1=5x³+2y²+4xy

We need to differentiate the given equation

5.3x²+4ydy/dx+4(xdy/dx+y)=0

15x²+4ydy/dx+4(xdy/dx+y)=0

15x²+4ydy/dx+4xdy/dx+4y=0

15x²+dy/dx(4y+4x)+4y=0

dy/dx(4y+4x)=-15x²-4y

dy/dx=-15x²-4y/4y+4x

Now plug in x =-1 and y=3

dy/dx=-15(-1)²-4(3)/4(3)+4(-1)

=-15-12/12-4

=-27/8

Hence, the value of dy/dx is -27/8 for 1=5x³+2y²+4xy  at (-1,3).

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