Find the coordinates of point P along the directed line segment AB, from A(1,6) to B(-2,-3), so that the
ratio of AP to PB is 5 to 1.
The coordinates are P().

The formula for the area of a circle is given as follows:

A = πr².

The area of a circle of radius r is given by the multiplication of the number π and the square of the radius, according to the equation presented as follows:

A = πr².

Hence, for example, for a circle of radius of 5 units, the area is given as follows:

A = π x (5 units)² = 25π units².

The diameter of a circle is twice the radius, hence the radius is half the diameter, and as a function of the diameter, the area will be given as follows:

A = 0.25πd².

As the diameter in the context of this problem is:

r² = (0.5d)² = 0.25d².

The problem is incomplete, hence the area of the circle was explained in general terms.

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Answer: 56 miles

Step-by-step explanation:

Tristan ran 7 miles, multiply by 4 because Kimberly ran 4 times as many miles as Tristan. 7x4=28

Next, 28x2=56 because Dominic ran 2 times as many miles as Kimberly, which is 28 times 2.
So Dominic ran 56 miles in total.

The equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0 and the slope of the line is 1/8

Slope of the line that passes through the points (9,9) and (1, 8)

The equation of the line is

y -y₁ = ((y₂ - y₁)/ (x₂ - x₁)) (x - x₁)

y - 9 = ((8 - 9)/(1 - 9)) (x - 9)

y - 9 = (1/8) (x - 9)

8y - 72 = x - 9

8y - x - 63 = 0

8y = 1/8 (x + 63)

Therefpre, the equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0

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Answer:

140

Step-by-step explanation:

It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.

The best course grade your friend can earn is 88%.

The minimum score your friend needs to have on the final to earn a 75% for the course is 35%.

If the final counts for 20% of the course grade, it means that the average of 85% counts for 80% (100 - 20%) of the total score.

The linear expression that can be used to determine the best course grade your friend can earn is:

(average that has already been accumulated x 80%) + (score on the finals x 20%)

(85% x 80%) + (20% x 100%)

(85% x 0.80) + (0.2 x 100%)

68 + 20 = 88%

The linear equation that can be used to determine the minimum score that can be earned on the final to have75% in the course is

Final grade = (total average before the final x 80%) + (score on the final x 20%)

75% = (85% x 80%) + (f x 20%)

75% = (85% x 0.80) + (0.20 x f)

75% = 68% + 0.20f

75% - 68% = 0.20f

7 =  0.20f

f = 7% / 0.20

f = 35%

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Answer:

okay so step by step explanation,

first multiply  7[tex]x^{2}[/tex] with 5[tex]x^{2}[/tex] and -[tex]y^{2}[/tex]

35[tex]x^{4}[/tex]-7[tex]x^{2}[/tex][tex]y^{2}[/tex]

then do the second one

20[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]

take the sum of those,

35[tex]x^{4}[/tex]+13[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]

good luck<3!

Answer:

B

Step-by-step explanation:

This is correct because it is the only one in proper set notation.

Hope it helps!

A standard lot is an amount of currency which is the same as 100,000 units of a base currency .

There are three lot sizes;

In finance, a lot indicates a measure or increment of a commodity that can be transacted. Products are bought and sold using different lot sizes. Products such as spot forex are sold in lots of 100,000, 10,000, 1,000, or 100 units.

Competition and brokerage online has resulted in the introduction of various lot sizes and forms.

A change of $10 corresponds to a pip movement of a standard lot.

By buying $100,000 at ¥110.00 and the price increases to ¥110.50, which indicates a 50 pip movement and a gain of $500 and vice versa.

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The number of times that the cube will land on 5 if the number cube was rolled 500 times is 83 times.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

It should be noted that in a number cube, we hage numbers from 1 to 6. The probability of getting a 5 is 1/6.

Therefore, when it's rolled 500 times, the possible number will be:

= 1/6 × 500

= 83 times.

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Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.

617/50
600/50 = 12
617/50 = 12 17/50

Answer: 88

Step-by-step explanation:

For every 7 grey goats there are 4 white goats. 160/7=22  4*22=88

The amount of tax that the executive would pay on his income is; 20000 GBP

Tax is defined as a compulsory payment that is levied on the income or on the sales of specific goods and services. Tax is usually imposed by the government to get a variety of macroeconomic objectives.

Now, income tax is the tax that is levied on the income of an individual. There are different types of taxes, such as progressive tax which levies a higher tax percentage on those that earn higher incomes This means invariably that the tax rate increases as income increases.

We are given;

Gross Amount executive earns = 50,000 GBP.

We are told that any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%.

Thus;

Tax that would be paid = tax rate * gross income

Tax that would be paid = 50000 * 0.4 = 20000 GBP

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Answer: 11,000

Step-by-step explanation:

The person earns 50,000 GBP, so they will stop at the tier 3 level of tax.

The first 11,500 GBP is tax free. They will be taxed 20% on (33,500−11,500)=22,000 GBP, and they will be taxed 40% on (50,000−33,500)=16,500 GBP. Hence the total tax (in GBP) they need to pay is

Total Income Tax=11,500×0%+22,000×20%+16,500×40%=0+22,000×20100+16,500×40100=0+4,400+6,600=11,000

Answer:

4/3/2/7-8= -7

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Graphing the equation shows local max volume at x = 4  of 1024 cm^3

1024 cm^3  * RM . 30 / cm^3 = RM 307.2

Answer:

42.2 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.

We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Substituting θ = 32° and H = 75 into the ratio, we get:

[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]

[tex]\textsf{O}=75\sin 32^{\circ}[/tex]

[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]

The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.

In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.

[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]

Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).

Answer:

x = 15 , y = 4

Step-by-step explanation:

If 3 or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally. then

[tex]\frac{x}{5}[/tex] = [tex]\frac{18}{6}[/tex] = 3 ( multiply both sides by 5 )

x = 15

and

[tex]\frac{12}{y}[/tex] = 3 ( multiply both sides by y )

12 = 3y ( divide both sides by 3 )

4 = y

Answer:

7. what are the fold down options for this question exactly?

1. C and E

3. B and D

Step-by-step explanation:

7.

1. function 1 has a slope of 2/3 and function 2 has a slope of 3 so they are both positive rates of change, and the y intercept (the value that y has when it passes through x = 0) for function 1 is -6 while the y intercept for function 2 is -3.

3. K has a y intercept of 8 compared to the 3 that J has, and J has a slope of 5 compared to the 3 that K has.

Numbers between 2.6×10^-1 and 29.5% are

2.6 × 10^-1 in exponential form written in decimal as 0.26

29.5% in percentage written in decimal as 0.295

2/7 in fraction written in decimal as 0.2857

2.8%  in percentage written in decimal as 0.028

0.2875 already in decimal form

the problem asks of numbers from 0.26 to 0.295

comparing the numbers shows that the numbers in this range are

0.2875 and 2/7

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The area of the rectangular land is 208,607 square meters,

A rectangle is defined as a quadrilateral whose opposite sides are equal and parallel

How to find the area of a rectangle?

The lengths of a rectangle are denoted by L and W

where: L=length

            w=width

Area of the land (A)= Area of the larger land  minus Area of the smaller land carved out

A= (LW) - (lw)

A=(513x466.5)-(267x113)

A=239,312-30705

A=208.607 meters square

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Using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

For instance, 12 inches equals one foot when converting between inches and feet.

So, 64 inches in cm is:

We know that:

1 inch = 2.5 cm

Then, 64 inches is:
64 inches = 2.5 × 64

64 inches = 160

Therefore, using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.

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Correct question:
Valerie is 64 inches tall. About how many centimeters tall is Valerie?

(1 inch -2.5 centimeters)

A. 25.5

B. 30.6

C. 160

D. 180

The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.

In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:

D = b² - 4 · a · c

Where a, b, c are real coefficients of the quadratic equation.

There are three possibilities for the results of the discriminant:

First, write the quadratic equation:

6 · x² + 13 · x + 6 = 0

Second, collect the real coefficients of the polynomial:

(a, b, c) = (6, 13, 6)

Third, calculate the discriminant:

D = 13² - 4 · 6²

D = 169 - 144

D = 25

The quadratic equation has two roots that are real and different.

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The slope-intercept form of the given line be,

y = -(9/8)x + 7

Given, a line is passing from two points (0 , 7) and (8 , -2)

we have to find the slope-intercept form of the equation of the line passing from the given points.

Using the slope-intercept form, we get

(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)

(y - 7)/(x - 0) = (7 - (-2))/(0 - 8)

(y - 7)/(x - 0) = 9/-8

-8(y - 7) = 9x

-8y + 56 = 9x

9x + 8y = 56

Slope-intercept form of the equation is,

y = -(9/8)x + 7

Hence, the slope-intercept form of the given line be, y = -(9/8)x + 7

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-> 2j.

-> 15+2j.

15+2j.

It is very easy, we just have to take the square root as it tells us in the problem:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]

You may ask ¿why 21?

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \longmapsto \orange{21} [/tex]

5.1 The amount of money received by the man at the end of 4 years is

$10,217.39

5.2 The rate of interest per annum is 94.56%/year.

Given:

P=5000

r = 18%

t= 4 years.

5.1 First, convert R as a percent to r as a decimal

r = R/100

r = 18/100

r = 0.18 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.18/12)(12)(4)

A = 5,000.00(1 + 0.015)(48)

A = $10,217.39

5.2 Given:

P = 3700

A = 8360,34

t = 7 years.

r =?

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 2 × [(836,034.00/3,700.00)1/(2)(7) - 1]

r = 0.945604

Then convert r to R as a percentage

R = r * 100

R = 0.945604 * 100

R = 94.56%/year

Hence we get the required answer.

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The rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

We know that the rate of change of a function is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given;

[tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex]

We need to find the rate of change of function for x = 4 and x = 9.

Let us find the value of y or f(x) for the given value of x.

For x = 4, [tex]f(x) = \sqrt{4} - \frac{1}{\sqrt{4}}[/tex]   = 2 - 1/2 = 4 - 1 / 2 = 3 / 2

For x = 9, [tex]f(x) = \sqrt{9} - \frac{1}{\sqrt{9}}[/tex]   = 3 - 1/3 = 9 - 1 / 3 = 8 / 3

Put the values of x and y in the slope formula, we will get;

Slope = (8 / 3 - 3 / 2) / (9 - 4) = 7 / 6*5 = 7 / 30

So, the rate of change of function is 7 / 30.

Thus, the rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

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Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.

Information is defined as the content of a message which is passed from a source to its receiver.

The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2

The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.

To calculate for one hour for both would be addition of the derived fractions;

= 1/2 + 1/3

= 3+2/6

= 5/6

When converter to minutes, multiple by 60;

= 5/6 × 60

= 300/6

= 50 minutes.

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The point slope form of equation is y- 3 = -4/3( x- (-3)).

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points= (-3, 3) and (9, -13)

Now,

slope= (-13 - 3)/ (9 - (-3))

slope= -16 / 12

slope= -4/3

Now, the point slope form

y- [tex]y_1[/tex] = m (x- [tex]x_1[/tex])

y- 3 = -4/3( x- (-3))

y- 3= -4/3x - 4

y= -4/3x - 1

Hence, the point slope for of equation is y- 3 = -4/3( x- (-3)).

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