Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?

The shape that we have here is sued to show the infinite geometric progression.

This is the sequence of numbers that has all the other values in the sequence gotten by the multiplication of a certain factor

In this question or the shape we can see that the triangle is made up of smaller other triangles embedded in it.

The area of the traingle that is in the red color is seen to have been made up of 1/3 of the total triangles that we have in the shape. This can be seen to be similar as the triangles that are represented by the green and the blue color.

Putting a  lot of triangles inside one big triangle gives up a pictorial diagram on how to add infinite amount of things up.

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[tex]y = - 5x + n \\ [/tex]

[tex] - 2 = - 5( - 1) + n \\ - 2 = 5 + n \\ n = - 7[/tex]

[tex]y = - 5x - 7 \\ 5x + y = - 7[/tex]

Answer:

○ [tex]5x + y = -7[/tex]

Step-by-step explanation:

The formula for forming the equation of a line given a point and a slope is:

[tex]\boxed{y- y_1 = m(x - x_1)}[/tex],

where:

m = slope (-5)

[tex]y_1[/tex] = y-coordinate of point (-2)

[tex]x_1[/tex] = x-coordinate of point (-1).

Substituting these values into the formula:

[tex]y - (-2) = -5(x - (-1))[/tex]

⇒ [tex]y + 2 = -5(x + 1)[/tex]

⇒ [tex]y + 2 = -5x -5[/tex]      [expanding the brackets]

⇒ [tex]y = -5x -5 - 2[/tex]      [subtracting 2 from both sides]

⇒ [tex]y = -5x - 7[/tex]

⇒ [tex]5x + y = -7[/tex]            [adding [tex]5x[/tex] to both sides]

This means that the second option is correct.

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A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.

Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.

A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).

An equidistant locus is one that is at the same distance to a reference point or a line.

In question 14, the required locus should be at the same distance to points A, B, C, and D.

In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.

The required construction is herewith attached to this answer.

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TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

A. Let assume the two are linear relationship

Let y represent juice made

Let x represent the concentrate remaining

Hence:

Slope=600-200/200-280

Slope=400/-80

Slope=-5

y=-5x+b

Where:

x=200

y=-5(200)+b=600

y=-1000+b=600

b=1600

Thus,

y=-5x+1600

y=0.  -5x+1600=0

        -5x=-1600

divide both side by 5x

x=-1600/-5

x=320 ounces

B. x=0

y=1600 ounces

Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

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Answer:

y ≤ 2.5x + 5

Step-by-step explanation:

first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = 2.5x + 5 ← equation of line

since the line is solid then inequality will be ≤

the solution to the inequality is the blue region below the line , then

y ≤ 2.5x + 5 ← inequality represented by graph

Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.

The future value formula is given by:

[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]

In which:

For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:

P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.

Hence the amount available is given by:

[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]

[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]

F = $100,336.67

The amount deposited was:

15 x 4 x $1000 = $60,000.

Hence the amount earned in interest was:

$100,336.67 - $60,000 = $40,336.67

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Answer:

1. Given

2. Definition of Congruent Angles

3. Triangle Interior Angle Sum Theorem

4. Transitive Property of Equality

5. Substitution Property of Equality

6. Definition of Congruent Angles

The analogous equation for the square will be; (x-10)²=87.

Algebraic equations with equivalent solutions or roots are called equivalent equations.

Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;

Using the original equation as a starting point as;

-20x+ x² + 13 = 0

Now x² - 20x = -13.

We need to take the "x" term's coefficient, or b, to complete the square.

Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,

B = -20

b/2 = -10

(b/2)² = 100

x² - 20x +100 = -13 + 100

On the left side,

LHS: (x + b/2)² = (x-10)2

RHS: -13 + 100 = 87

(x-10)² = 87

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Answer:

8√3

I hope this helps you

Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.

A linear equation is represented by ax + b = 0. The solution for this equation is

ax + b = 0

⇒ ax = -b

⇒ x = -b/a

The given equation is

7/8 + x = 1/4

On simplifying,

x = 1/4 - 7/8

⇒ x = -5/8

Therefore, the solution of the given equation is -5/8.

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If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

Given that arc has measure of 7π/4.

We are required to convert the measure from radian to degree measure.

Converting means chaning of units from one to another.

To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.

7π/4=7*180/4

=7*45

=315 degrees

Now we have to convert 60 degrees into radians.

60 degrees=60*π/180

=π/3

Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

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Answer:

-5/3

Step-by-step explanation:

Do PEMDAS

8 - 11 = -3

-3 ^ 3 = -27

-(-27) = 27

I-14I = 14

3 x 14 = 42

27 - 42 = -15

2^4 = 16

16 - 7 = 9

-15/9 = -5/3

The value of P such that P*3=1 is 4

The set of Real numbers, R is given as

m*n=(√m +√n) (√m-√n).

The values of P, if P*3=1 is represented as:

P * 3=(√P +√3) (√P-√3).

The result of this operation is 1.

So, we have:

(√P +√3) (√P-√3) = 1

Apply the difference of two squares

P - 3 = 1

Add 3 to both sides

P = 4

Hence, the value of P such that P*3=1 is 4

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The time it will take the thermometer to hit the ground is 22 seconds

From the question, we are to determine the how long it would take the thermometer to hit the ground

From the given information,

The equation for the height as a function of time is

h(t) = -16t² + initial height

From the given information,

The thermometer falls from a weather balloon at a height of 7744 ft

∴ Initial height = 7744 ft

When the thermometer hits the ground, h(t) = 0

Thus, we get

0 = -16t² + 7744

16t² = 7744

t² = 7744/16

t² = 484

t = √484

t = 22 seconds

Hence, the time it will take the thermometer to hit the ground is 22 seconds

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The general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

According to the given question.

We have a differential equation

[tex]12y^{"} -5y^{'} -3y = 0[/tex]

The above equation can be written as

[tex](12D^{2} -5D -3)y = 0[/tex]

The auxillary equation for the above differential equation is

[tex]12m^{2} -5m-3 = 0[/tex]

[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]

⇒ 3m(4m - 3) +1(4m - 3) = 0

⇒ (3m + 1)(4m -3) = 0

⇒ m = -1/3 or 3/4

Therefore,

[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]

Here, P.I = 0

As we know that the general solution of the differential equation is given by

y = PI + CF

Thereofre, the general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

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Answer:

3

Step-by-step explanation:

- 4x³y² + 6

the x is raised to the power of 3 , that is exponent of x is 3

The probability distribution of X when X~B(1,1/25) is (Option A)

See the explanation below.

Given X~B(n,p)

P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)

Thus, X~B [1, 1/25]

1/25 = 0.04

hence, p(x=0)

= C⁰₁ * 0.04⁰ (1 - 0.04)¹

= 0.96

P (x=1)

=  C¹₁ 0.04¹ (1-0.04)⁰

= 0.04

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Answer:

Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.

Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.

m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB

m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO

m<ABO + m<ACO = m<BOC - m<BAC

The equation of the halfpipe is  Option A , (0, 20); Y equals one over eighty times x squared plus 20.

The equation of the halfpipe is  Y = X²/80 +20.

What is parabola ?

The equation of parabola is given by  

(X-h)² = 4p(Y-k)²

In this case h = 0

So we get  

Y = X²/4P +k

Focus point is (h, p+k) , (p+k) = 40

Hence h, k = (0,20)

P = 40-k = 20

Equation Y = X²/80 +20

Therefore, the equation of the halfpipe is  Y = X²/80 +20

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The complete question is -

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 20); y equals one over eighty times x squared plus 20

(0, 20); y equals one over eighty times x squared minus 20

(0, 10); y equals one over forty times x squared plus 10

(0, 10); y equals one over forty times x squared minus 10

The following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

If the measuring has a level of precision of 0.01 ml, this means that the measured quantities are only sensible to the smallest hundreths. Any change less than 0.01 ml and any decimal less than a hundreths are "invisible" for measuring processes.

Hence, the following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

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Answer:

B,D,E

Step-by-step explanation:

From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°

The lines ZY and ZW are tangents to the attached circle which is centered at x.

From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.

From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;

∠WZY = 360° - (90° + 90° + 109°)

∠WZY = 360° - 289°

∠WZY = 71°

Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°

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Answer:  B. 71°

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!! :)

I got it right!

The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.

There are four methods of solving quadratic equation. Namely;

0 = -2x² + 5x - 3

x = -b ± √b² - 4ac / 2a

where,

x = -b ± √b² - 4ac / 2a

x = -5 ± √5² - 4(-2)(-3) / 2(-2)

= -5 ± √25 - (24) / -2

= -5 ± √1 / -2

= -5/2 ± 1/2

= -5/2 - 1/2 or x = -5/2 + 1/2

= -5-1 / 2 or -5+1/ 2

x = -6/2 or -4/2

x = -3 or -2

Therefore, the solution to the quadratic equation is x = -3 or -2

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The height from the ground to the base of the window is 16 inches.

The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.

In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.

XY / XZ = WY / VZ

(8 / 24) = WY / 48

WY = (8 X 48) / 24 = 16 inches

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Horizontal asymptote of c(x) is 450.

A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

Thus, the following formula represents the average cost to produce x refrigerators:

C(x) = (200000 + 450x)/x

Horizontal asymptote of c(x) would be

= 450x/x

= 450

Hence, Horizontal asymptote of c(x) is 450

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Answer:

numbers

Step-by-step explanation:

numbers

Answer:

Step-by-step explanation:

The probability that the person is over 40 and prefers cola exists at 1.3725.

The probability of an event exists in the ratio of the size of the event space to the size of the sample space.

The size of the sample space exists the entire number of possible outcomes.

The event space exists the number of outcomes in the event you exists interested in.

So, P = size of the event space/size of the sample space

To estimate the probability that the person exists over 40 years.

Size of the sample size = 255

Size of the event space = 85

P = 85/255

P = 1/3

To estimate the probability that they drink cola.

Size of the sample size = 255

Size of the event space = 95

P = 95/255

P = 19/51

To estimate the probability that the person exists over 40 years of age or that they drink cola

So, P = (1/3) + (19/51)

[tex]$P = (51*3+3*19)/153[/tex]

P = 1.3725

Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.

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