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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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Answer:

Nepali=17 English=18

Step-by-step explanation:

first in Nepali,

Answer: m<BCA = 57°

Step-by-step explanation:

180-(10x-37)°

180-(10x(16)-37)°

180-123

57°

The sample size will be needed to estimate the mean time to spoilage with an accuracy of one day is 166

The formula for the margin of error is given as

[tex]E = Z*\frac{sd}{\sqrt{n} }[/tex]

The standard deviation is given as sd = 5 days

We have to find the critical value of Z at the confidence level of 99 %

This value is given as 2.576

E = 1 day because the accuracy has been said to be within one day.

We have to insert the values in the formula that we have here

[tex]1 = 2.576*\frac{5}{\sqrt{n} }[/tex]

√n = 12.88

square both sides to get rid of the square root sign

n = 12.88²

n = 165.89

n ~ 166

The sample size would be 166

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The recursive equation for the nth term is aₙ = -4aₙ₋₁

The definition of the functions is given as

a₂ = 2

a₅ = -384

Sequence type = Geometric sequence

The nth term of a geometric sequence is represented as

aₙ = arⁿ⁻¹

So, we have

a₂ = ar = 6

a₅ = ar⁴ = -384

Divide the equations

r³ = -384/6

Evaluate

r³ = -64

Take the cube roots

r = -4

The recursive equation for the nth term is represented as

aₙ = aₙ₋₁ * r

So, we have

aₙ = -4aₙ₋₁

Hence, the equation is aₙ = -4aₙ₋₁

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Answer:

  B. The graph of K has a greater y-intercept

  D. The graph of J has a greater slope.

Step-by-step explanation:

Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.

The y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.

We see from the equation for function K that the constant is 8. This is the value of y when x=0.

Function K has the greater y-intercept (8 vs. 2).

The slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.

The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.

Function J has the greater slope (5 vs. 3).

Additional comment

Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.

The solution of the inequalities is x < - 3 / 2 or x > 48 / 5

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Inequality expression always have the symbols <, >, ≤ and ≥.

Therefore, let's solve the inequalities.

12x + 7 < - 11 or 5x - 8 > 40

12x + 7 < - 11

subtract 7 from both sides of the inequalities.

12x + 7 - 7 < - 11 - 7

12x < - 18

divide both sides by 12

x < - 18 / 12

x < - 3 / 2

5x - 8 > 40

add 8 to both sides of the inequalities

5x - 8 + 8 > 40 + 8

5x > 48

divide both sides by 5

x > 48  / 5

x > 48 / 5

Therefore,

x < - 3 / 2 or x > 48 / 5

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The y-intercept is (0, 400), which represents the amount of money the radio station originally had. The x-intercept is (8, 0), which represents the number of weeks it will take for the radio station to have $0 left.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Similarly, the x-intercept can be defined as the point at which the graph of any function crosses the x-coordinate and the value of "y" is equal to zero (0).

For the y-intercept, x = 0 and we have the following:

y = 400 - 50x

y = 400 - 50(0)

y = 400.

For the x-intercept, y = 0 and we have the following:

y = 400 - 50x

0 = 400 - 50x

50x = 400

x = 400/50

x = 8.

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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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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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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 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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Answer:its  10,00 more than it so one

Step-by-step explanation:

10^4=10,000

10,000x4=40,000

10000x5=50,000

Answer:

1 × 10^4

Step-by-step explanation:

5 × 10 ^ 4 = 5 × 10000

= 50,000

4 × 10 ^ 4 = 4 × 10000

= 40,000

Therefore; 50,000 - 40,000

= 10,000 or 1 × 10 ^ 4

Hence 5 × 10^4 is bigger than 4 ×10^4 by

1 × 10^4

Answer:

a = 108°

b = 72°

c = 48°

d = 48°

Step-by-step explanation:

• ∠a and the 72° angle are on a straight line. Therefore they add up to 180°:

∠a + 72° = 180°

⇒ ∠a = 180 - 72°

⇒ ∠a = 108°

• ∠b and the 72° angle are corresponding angles (the angles make an F-shape). Therefore, they are equal:

∠b = 72°

• ∠d and the 48° angle are alternate angles (the angles make a z-shape). Therefore they are equal:

∠d = 48°

• ∠c and ∠d are vertically opposite angles. Therefore, they are equal:

∠c = ∠d

⇒ ∠c = 48°

The solution to the initial value problem in this problem is given as follows:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

The initial value problem is given as follows:

y''-4y'-5y = 0.

The first step is finding the roots of the characteristic equation, which is given as follows:

r² - 4r - 5.

The equation can be factored as follows:

r² - 4r - 5 = (r - 5)(r + 1).

Applying the inverse Factor Theorem, the roots are given as follows:

These roots are real, hence the format of the solution is given as follows:

[tex]y = Ae^{5x} + Be^{-x}[/tex]

Considering the initial condition at x = 1, we have that:

Ae^(5) + Be^(-1) = 0

Considering the initial condition of the derivative at x = 1, we have that:

5Ae^(5) - Be^(-1) = 2.

Adding the two equations, the condition A is obtained as follows:

6Ae^(5) = 2.

A = 2/(6e^5)

A = 0.0022.

Hence the condition B is:

B = -0.0022e^(5)/e^(-1)

B = -0.8853.

Hence the solution is:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

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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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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:

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]

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.

Answer:

C) 20

Step-by-step explanation:

The absolute value of -20 is 20, because absolute value just keeps the same number, but makes positive.

Hope this helped!

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:

Answer and explanation in image

Step-by-step explanation:

Answer:

+8 or -8

Step-by-step explanation:

Both can be the qrt of 64 because   -8 * -8 = + 64

Answer:

21.5

Step-by-step explanation:

geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]

where An is nth term

A is first term

r is common ratio

given [tex]A_{99}[/tex] = 48

A=12

we find r

48=12 *[tex]r^{99-1}[/tex]

48/12=[tex]r^{98}[/tex]

[tex]\sqrt[98]{4}[/tex]=r

r=1.014

so to find 50th term

[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]

[tex]A_{50}[/tex]=21.53

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

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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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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Answer:

First we convert the sentence to an equation so:

[tex] \frac{3}{4} x = 24[/tex]

Now to isolate x divide by the recuprical of 3 over 4 which is 4/3

[tex] \frac{3}{4} \times \frac{4}{3} = 24 \times \frac{4}{3} [/tex]

24x4= 96 and 3 remains.

[tex]x = \frac{96}{3} [/tex]

Now we can simplify by 3 and we will get the final answer which is

[tex]x = 32[/tex]