(7x² + 4y²)(5x² - y²)

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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The amount in the account after 25 years be $ 84,216.11

Given, an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously.

We have to find the amount in the account after 25 years.

Now, on using the compound interest amount formula, we get

Amount = P(1 + r/100)^t

Amount = 18500(1 + 6.25/100)^25

Amount = 18500(1.0625)^25

Amount = 18500(4.55)

Amount = 84,216.1137

Hence, the amount in the account after 25 years be $ 84,216.11

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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 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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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 value of ∠A in triangle ABC is 40°

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given triangle ABC,

∠A=7x-16°, ∠B=81°

By alternate segment theorem,

∠C=4x+27°

The sum of all the angle of a triangle is 180°.

∠A+∠B+∠C=180°

⇒7x-16+81+4x+27=180

11x=180-92

11x=88

x=8

So the value of ∠A=7×8-16 = 40°

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Answer:

The value of ∠A in triangle ABC is 40°

Pretty much the same as the person that posted before.

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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Answer:

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

Step-by-step explanation:

Answer:

4 4/9

is the time it will take

-> 2j.

-> 15+2j.

15+2j.

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:

[tex]-x^{3}+6x^{2} +5x-7[/tex]

Step-by-step explanation:

-x^3-x+6x^2+6x-7

Order the polynomial from exponent order to make it easier

-x^3+6x^2+6x-x-7

-x^3+6x^2+5x-7

Hopes this helps please mark brainliest

Answer:

-x^3+6x^2+5x-7

Step-by-step explanation:

open parentheses, collect like terms.

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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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).

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]

Answer:

B

Step-by-step explanation:

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

Hope it helps!

Answer: 88

Step-by-step explanation:

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

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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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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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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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 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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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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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:

All of them

Step-by-step explanation:

A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.