describe how to map line p onto line q

The coordinates of the point on the directed line segment from (-10, 2) to (-3,-5) that partitions the segment into a ratio of 4 to 3 is (-6,-2).

Given:

we have two points :

(-10, 2) to (-3,-5)

and the ratio which partitions the segment is:

4:3

we are asked to determine the coordinates of the point.

Let the given points (-10,2) be (x₁, y₁) and (-3,-5) be (x₂, y₂) and the ratio be m:n.

Using section formula to find the coordinates:

x = (mx₂ + nx₁)/(m+n)

= {4(-3) + 3(-10)} /(4+3)

= -12-30/7

= -42/7

= -6

y = (my₂ + ny₁)/(m+n)

= {4(-5) + 3(2)} / (4+3)

= -20+6/7

= -14/7

= -2

Therefore, the required point is (-6,-2)

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The value of x is 1.1913

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

5[tex]x^5[/tex] = 9+3

5[tex]x^5[/tex] =12

[tex]x^5[/tex]=12/5

Take 5th root on both sides

[tex]x=\sqrt[^5]{12/5}[/tex]

x= 1.1913

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As gradients multiplied we get [tex]\frac{-4}{3}[/tex] the line segments AB and BC are not perpendicular

How to find lines are perpendicular?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

To find whether the line segments are perpendicular we have to first find the gradient of AB and BC

Finding the gradient of AB

A(1,3) and B(2,1)

[tex]m_{AB}[/tex]=(1-3)/(2-1)

       = [tex]\frac{-2}{1}[/tex]

       =-2

Finding the gradient of BC

B(2,1) and C(5,3)

[tex]m_{BC}[/tex]=(3-1)/(5-2)

      =[tex]\frac{2}{3}[/tex]

When we multiply the two gradients if we get -1 then the two line segments are perpendicular.

[tex]m_{AB}X m_{BC} = -2X\frac{2}{3}[/tex]

                  = [tex]\frac{-4}{3}[/tex]

As the gradient is not equal to -1 the line segments AB and BC are not perpendicular

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The graph of the inequality, y ≤ -2/5x - 4, is shown below

From the question, we are to graph the given linear inequalities.

The given linear inequalities is y ≤ -2/5x - 4.

To graph the linear inequality,

First, we will draw the line of the equation y = -2/5x - 4

To draw the line, we will use the x-intercept and y-intercept.

y-intercept

When x = 0

y = -2/5x - 4

y = -2/5(0) - 4

y = 0 - 4

y = -4

Thus, the coordinate of the y-intercept is (0, -4)

x-intercept

When y = 0

y = -2/5x - 4

0 = -2/5x - 4

4 = -2/5x

4 × 5 = -2x

20 = -2x

x = 20/-2

x = -10

Thus, the coordinate of the x-intercept is (-10, 0)

Now, using the coordinates of the x and y-intercepts, the line of the graph is shown.

Since the sign of the inequality is less than or equal to (≤), the line is a solid line and the solution is below the line.

The graph of the inequality is shown below.

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Answer:

yesss

Step-by-step explanation:

Answer:

$656.25

Step-by-step explanation:

The formula for simple interest is:

[tex]A=Prt[/tex]

Where A is the final amount, P is the principal, r is the rate, and t is the time in years.

The question does not specify whether the interest rate is annual or not, but I will assume it is! To convert 15 months to years, divide it by 12 months!

[tex]\frac{15}{12}=\frac{5}{4}=1.25[/tex]

I also need the percent to be a decimal. To convert a percent to a decimal, divide by 100.

[tex]7.5/100 = 0.075[/tex]

Now, plug the values into the formula!

[tex]A=7000*0.075*1.25\\A=656.25[/tex]

The total amount after 15 months is $656.25

Answer:

12

Step-by-step explanation:

480 tomatoes/40 baskets = 12 per basket

The three geometric mean between 2 and 512 are

The first term = 2

Consider the common ratio as r

Then the second term = 2r

The third term = [tex]2r^2[/tex]

The fourth term is = [tex]2r^3[/tex]

The fifth term is given that 512

The fifth term = [tex]2r^4[/tex]

Then the equation will be

[tex]2r^4[/tex] = 512

[tex]r^4[/tex] = 512 / 2

[tex]r^4[/tex] = 256

r = ±4

When r = 4

The three geometric mean between 2 and 512 are

2r = 2×4 = 8

[tex]2r^2[/tex] = 2×4×4 = 32

[tex]2r^3[/tex] = 2×4×4×4 = 128

When r = -4

The three geometric mean between 2 and 512 are

2r = 2×-4 = -8

[tex]2r^2[/tex] = 2×-4×-4 = 32

[tex]2r^3[/tex] = 2×-4×-4×-4 = -128

Hence, the three geometric mean between 2 and 512 are

The complete question is :

Find the three geometric means between 2 and 512.

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Answer:

Answer and explanation in image

Step-by-step explanation:

The angle with cosine value of 1/7​ is 81.79°

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Given that: the cosine value of the angle is 1/7​

Let the angle be θ. Then we can write that:

cos θ = 1/7

θ = cos⁻¹ (1/7)           (Take the inverse of cosine on both sides)

θ = 81.79°

Note: To get cos⁻¹ on your calculator, press the shift button followed by the cos button

Therefore, the angle is 81.79°

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Answer:

Willis paid 1.774 dollars a pound

Step-by-step explanation:

Assuming there was no tax in the purchase, you can divide 8.87/5 to get your price per pound.

Answer:

Step-by-step explanation:

The average rate of change between two points is the slope of the line between those points.

The points are:

The slope is:

The points are:

The slope is:

Answer:

[tex]\textsf{Average rate of change of the golf ball}=\dfrac{9}{2}\; \sf m/s[/tex]

[tex]\textsf{Average rate of change of the baseball}=\dfrac{9}{4}\; \sf m/s[/tex]

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\boxed{\dfrac{f(b)-f(a)}{b-a}}[/tex]

To find the average rate of change from 3 to 7 seconds:

Therefore, use the formula:

[tex]\implies \dfrac{f(7)-f(3)}{7-3}[/tex]

Golf Ball

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&14\\\cline{1-2} 7&32\\\cline{1-2} 9&24\\\cline{1-2} 12&2\\\cline{1-2}\end{array}[/tex]

From inspection of the table:

Substitute these values into the formula to find the average rate of change of the golf ball from 3 seconds to 7 seconds:

[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{32-14}{7-3}=\dfrac{9}{2}\; \sf m/s[/tex]

Baseball

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&6\\\cline{1-2} 7&15\\\cline{1-2} 9&13\\\cline{1-2} 12&0\\\cline{1-2}\end{array}[/tex]

From inspection of the table:

Substitute these values into the formula to find the average rate of change of the baseball from 3 seconds to 7 seconds:

[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{15-6}{7-3}=\dfrac{9}{4}\; \sf m/s[/tex]

The general rule for the dimensions will be 4d and (d + 2) after taking d = 1, the dimensions are 4 and 3 feet

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is given that:

A park is planning a rectangle-shaped koi pond with an area given by the expression 4d² + 8d square feet.

= 4d(d + 2)

The dimensions could be 4d and (d + 2)

Let d = 1

The dimensions are 4 and 3 feet

Thus, the general rule for the dimensions will be 4d and (d + 2) after taking d = 1, the dimensions are 4 and 3 feet

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Using the scale size, the actual length of the paramecium is 0.253.

In the given question we have to find the actual length of the paramecium.

Under a 750:1 magnification microscope, a paramecium has a length of

19 mm.

Using the microscope length of paramecium = 19 mm

Magnification microscope = 750:1

So the actual length of paramecium = microscope length of paramecium× scale size

The actual length of paramecium = 19× 1/750

The actual length of paramecium = 19/750

The actual length of paramecium = 0.253

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The suitable for blank is 2099.43 approximately.

Let the principle be P.

Time (t) = 19 years and 6 months = 19.5 years

Compound is semiannually.

Rate of Interest (r) = 4.5%

Amount will be (A) = $5000

So, suitable equation is given by,

[tex]A=P\left(1+\frac{r}{200}\right)^2t\\5000=P\left(1+\frac{4.5}{200}\right)^{2\times19.5}=P\left(1+\frac{9}{400}\right)^{39}\\\\P\approx2099.43[/tex]

Hence the suitable for the blank is 2099.43.

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Answer:

T

Step-by-step explanation:

Answer:

T

Step-by-step explanation:

T because it is the same position and Q therefore being congruent to each other, a way visualize it is to flip it and aline the lines together and see which one is the same angle as Q.

The value of the underlined digit is 600.

What is the place value strategy?

The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.

We must determine the values of each integer in order to calculate the value of the underlined digit (6) in the equation.

In 5,678.321, the first digit, 5, is 1,000 in the thousands of places.

The second digit, 6, is in the hundreds (100) place.

So the value is 600.

Hence the answer is, the value of the underlined digit is 600.

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We need to determine the length per year, so take the ratio of 450/9 and simplify it.

r = 450cm/9yr
r = 50cm/1yr
r = 50cm

50cm/100cm = 1/2

So, the coastline recedes 1/2 meters every year.

Answer:0.50 meters

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

[tex]\frac{16}{20} =\frac{4(4)}{4(5)}=\frac{4}{5}=0.8[/tex]

Answer: 0.8

Step-by-step explanation:

16/20=4/5, which is the equivalent to 0.8

Los capitales depositados en las cuentas de 2 %, 3 % y 4 % son 630.000, 420.000 y 315.000, respectivamente.

En este problema tenemos el caso de una suma de dinero distribuida y depositada en tres cuentas con tres tasas de interes simple distintas. Existe una tasa de interés simple cuando el interés generado sobre el capital no es acumulativo en el tiempo. El modelo de interés simple es descrito por la siguiente fórmula:

C' = C · (1 + r / 100)

Donde:

A continuación, describimos la ganancia registrada en cada cuenta tal que produce la misma ganancia:

Cuenta al 2 %:

z = x · (2 / 100)

z = 0.02 · x

0.02 · x - z = 0

Cuenta al 3 %:

z = y · (3 / 100)

z = 0.03 · y

0.03 · y - z = 0

Cuenta al 4 %:

z = (1.365.000 - x - y) · (4 / 100)

z = 54600 - 0.04 · x - 0.04 · y

0.04 · x + 0.04 · y + z = 54600

La solución de este sistema de ecuaciones lineales se obtiene mediante métodos numéricos:

(x, y, z) = (630.000, 420.000, 12.600)

Finalmente, el capital depositado en la cuenta al 4 % es:

c = 1.365.000 - 630.000 - 420.000

c = 315.000

Se deposita capitales de 630.000, 420.000 y 315.000 en las cuentas de 2 %, 3 % y 4 %, respectivamente.

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Answer:

solve    9 = -6/-7(14) + b this is not the answer but when you solve it that will be your answer

Step-by-step explanation:

m = y2 - y1                    y = mx + b

      x2 - x1                     9 = -6/-7(14) + b

m = 3 - 9

      7 - 14

3 - 9 = -6

7 - 14 = -7

m = -6/-7

For given function f(x-3) = x^2- 2x+ 7, the value of f(-1) is 10

For given function f(x-3) = x^2- 2x+ 7 we need to find the value of f(-1)

i.e., we get an equation,

x - 3 = -1

x = -1 + 3

x = 2

Substitute x = 2 in given function,

f(-1) =  (-1)^2- 2(-1) + 7

f(-1) = 1 - (-2) + 7

f(-1) = 1 + 2 + 7

f(-1) = 10

Therefore, for given function f(x-3) = x^2- 2x+ 7, the value of f(-1) is 10

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The ordered pair (13, 41) simply means a daily usage fee of $41 would be charged to use the Body for Life gym for 13 days.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Based on the information provided, a linear equation which models the situation is given by:

y = 2x + 15

For the ordered pair (13, 41), we have:

y = 2x + 15

y = 2(13) + 15

y = 26 + 15

y = $41.

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Answer:

10u^2 - 2u - 2

Step-by-step explanation:

Combine like terms:

4u^2 + 3 + 6u^2 - 2u - 5

10u^2 - 2u - 2

Answer:

79.73

Step-by-step explanation:

Answer:79.73

Step-by-step explanation: because if you take 6.14 and add it to 73.59 you get 79.73

The height of the goalpost is 16.45 m.

Given, Anand uses a mirror on the ground to measure the height of his school’s football goalpost.

He walks a distance of 14.75 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center.

He then steps 1.3 meters to the other side of the mirror, until he can see the top of the goalpost clearly marked in the X.

His partner measures the distance from his eyes to the ground to be 1.45 meters.

we are asked to determine the height of the goalpost = ?

As per the rule of reflection in physics,

Angle of incidence = Angle of reflection

As we can see in the picture attached, both the angles (θ) are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

AB/ED = CB/CD

1.45/ED = 1.3/14.75

ED = 14.75×1.45/1.3

ED = 16.45 m

Hence the height of the goal post is 16.45 m

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Answer: m<BCA = 57°

Step-by-step explanation:

180-(10x-37)°

180-(10x(16)-37)°

180-123

57°

Answer:

153.86

Step-by-step explanation:

to get the area of the circle you take the radius to the power of 2 and then multiply with π
when the radius of circle S is half the radius of circle L and circle L has radius 14 inch, then the radius of S is 7.
area = radius² * π = 7² * π = 49 * π
π is approximately 3.14
so 49*3.14 = 153.86