Sue is n years old. Her sister is 7 years old and her brother is twice Sue's age. All three siblings have a total age of 31.
Write an equation to represent this.

[tex]3/x - 2 -5/2 -4/x - 2[/tex] is equivalent to [tex](-15x + 40)/2(x-2)(x-2)[/tex]

[tex]3/x - 2 - 5/2 - 4/x - 2[/tex] can be simplified by finding a common denominator:

LCD = 2(x-2)

So we need to multiply the first fraction by 2/2 and the second fraction by (x-2)/(x-2):

[tex]3/x - 2 * 2/2 - 5/2 - 4/x - 2 * (x-2)/(x-2)[/tex]

[tex]= (6 - 2(x-2))/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14)/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14 - 5(x-2) - 2(4x-8))/2(x-2)(x-2)\\= (-2x + 14 - 5x + 10 - 8x + 16)/2(x-2)(x-2)\\= (-15x + 40)/2(x-2)(x-2)[/tex]

Therefore, [tex]3/x - 2 -5/2 - 4/x - 2[/tex] is equivalent to [tex](-15x + 40)/2(x-2)(x-2).[/tex]

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The area of the triangle is 120 square centimeters.

A = 120 cm².

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle = 1/2 x base x height.

Given:

The height h of the triangle is 8cm greater than its corresponding base.

That means

the height = 20 + 8 = 20 cm.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 12 x 20

= 120 square centimeters.

Therefore, the area is 120 square centimeters.

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Unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms.

In 10 years, an individual's earned and unearned income may vary greatly depending on their career and investment choices, economic conditions, and personal circumstances.

Some individuals may see increases in earned income as they gain more experience or take on higher-paying positions, while others may see fluctuations or decreases in earned income due to changes in the job market.

Similarly, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Hence, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

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In the curve of the sinusoidal curve when x = -2 y = 2

A sinusoidal curve, also known as a sine wave, is a type of waveform that is commonly used to describe oscillations or periodic phenomena in various fields such as physics, engineering, mathematics, and electronics.

A sinusoidal curve is a graph of a function that oscillates between an upper value and a lower value, and repeats itself over a period of time.

In order to find the value of y when x = -2, from the x-axis at x = -2 trace it to touch the curve and then trace to the y-axis to get the y value (Check the attached).

Therefore, when x = -2, y = 2

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The rational function for the graph is defined as follows:

y = -8(x - 3)/(x² - x - 12)

A rational function is a function in which the variable x appears in both the numerator and the denominator of the function.

The function in this problem has a zero at x = 3, hence the numerator is given as follows:

a(x - 3).

In which a is the leading coefficient.

The function has vertical asymptotes at x = -3 and x = 4, hence the denominator is given as follows:

(x + 3)(x - 4) = x² - x - 12.

Hence the function is defined as follows:

y = a(x - 3)/(x² - x - 12)

When x = 0, y = -2, hence the leading coefficient a is obtained as follows:

-2 = 3a/12

3a = -24

a = -8.

Hence the function is defined as follows:

y = -8(x - 3)/(x² - x - 12)

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Answer:

6.67%

Step-by-step explanation:

The formula for accrued value A on a deposit P for t years compounded n times annually at i% APR is
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

where r = i/100 i.e the interest rate as a decimal

We are given
P = $12,000

i = 6.5%

r = 6.5/100 = 0.065

n = 4 since interest is compounded annually

t = 1 year since we are interested in the annual yield

[tex]\begin{aligned}A &= 12000\left(1 + \dfrac{0.065}{4}\right)^{4\cdot 1}\\& = 12000(1 + 0.01625)^4\\&= 12000(1.01625)^4\\& = \$12,799.22\end{aligned}[/tex]

Effective Annual Interest = 12,799.22 - 12,000 = $799.22
This works out to an annual  yield of 799.25/12000

= 0.0667

= 6.67%

To find the weight of a baby at age 5 months, we can substitute x=5 in the given function:

f(5) = 1.5(5) + 7

f(5) = 7.5 + 7

f(5) = 14.5

Therefore, the weight of a baby at age 5 months is 14.5 pounds. Answer: D.

Answer:

The period of a spring-mass system is the time it takes for the weight to complete one full cycle of motion (i.e., go up and down once).

In this problem, we are told that the weight goes up and down 60 times in 90 seconds. Therefore, the time it takes for the weight to complete one cycle of motion is:

90 seconds / 60 cycles = 1.5 seconds/cycle

To find the period of the motion in minutes, we need to convert the time per cycle from seconds to minutes:

1.5 seconds/cycle * 1 minute/60 seconds = 0.025 minutes/cycle

Therefore, the period of the motion is 0.025 minutes/cycle or 25 milliseconds/cycle. In this case, it is 1/40 minutes.

Answer: i think B.1/40 minutes

Step-by-step explanation: hope this helps0^0

As per measurement, 30 inches is equivalent to 2.5 feet.

Measurement is an essential aspect of our daily life, and it helps us to quantify things precisely. The measuring units are used to determine the size, weight, or any physical quantity of an object. It is essential to know the conversions between the measuring units to make the necessary calculations accurately.

In this context, let's discuss the conversion of inches to feet.

Inches and feet are two common units of measurement used for length or distance. Inches are the smaller unit, and feet are the larger unit. One foot is equivalent to 12 inches. Therefore, to convert inches to feet, we divide the given number of inches by 12.

Let's consider we need to convert 30 inches to feet.

30 inches / 12 inches per foot = 2.5 feet

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The required conversion of 10 miles per hour to kilometers per hour is given by 16.0934 kilometers per hour.

Conversion of miles to kilometer is :

One miles is equal to 1.60934 kilometers

Now substitute the required value we get,

10 miles = ( 10 ) × ( 1.60934 ) kilometers

⇒ 10 miles = ( 10 × 1.60934 ) kilometers

⇒ 10 miles = 16.0934 kilometers

Required conversion is :

10 miles per hour = 16.0934 kilometers per hour

Therefore, converted value of 10 miles per hour is equal to 16.0934 kilometers per hour .

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Answer:

False, it took her 2 hours and 24 minutes

Step-by-step explanation:

The equation 12h = 5 is not correct because it would mean that Helen completed her run in 5 hours, which is not possible since she only ran 12 miles.

To find the correct number of hours, we can use the formula:

Distance = rate x time

Where distance is the total distance Helen ran (12 miles), rate is her speed (5 miles per hour), and time is the number of hours it took her to run.

We can rearrange the formula to solve for time:

Time = distance / rate

Plugging in the values we have:

Time = 12 miles / 5 miles per hour

Simplifying, we get:

Time = 2.4 hours

Therefore, it took Helen 2.4 hours (or 2 hours and 24 minutes) to complete her run.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

The formula of linear interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]

The formula to calculate linear interpolation is:

Linear Interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]

where,

It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.

Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.

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60 INCH TV MATE 60

the answer is 60 inch its a trick question just find out the inches there trying to trick you its 60 inch mate enjoy <3 Mark me brainliest

Answer:

1. Tv Length: 12 in

2. Tv Width: 5 in

3. Sorry I don't understand 3

4. I have a 60-inch Tv.

Hope this helps!

I

The value of tan V as a fraction in its simplest terms is 4/3.

The figure in the image is a right triangle.

First, we determine side UT using pythagoras theorem

UT = √( 35² - 21² )

UT = √784

UT = 28

Hence, using trigonometric ratio

Tangent = Opoosite / Adjacent

tanV = UT / UV

tanV = 28/21

tanV = 4/3

Therefore, the value of tanV is 4/3.

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Note that:

The vertical angles are given as follows:

∠CFB vs ∠AFD

∠CFA vs ∠DFB

The complimentary pair of angles is :

∠CFE vs ∠EFA.

Complementary angles are a pair of two angles whose sum equals 90 degrees. In other words, when two angles are complementary, one angle is said to be the complement of the other.

For example, if angle A and angle B are complementary, then A + B = 90 degrees.

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Full Question:

See the attached

Another name for a regression line is Least squares line

Answer:Best-Fit-Line

Step-by-step explanation:

--Or line of best fit

HOP THIS HELPS!!!

We can convert Kilometer to feet by using the relation 1Km = 3280.83 ft.

A Kilometer is used as a standard unit of measuring distance between any two bodies.

As per the standard unit conversion rates 1 km is equal to 3280.83 ft.

So if we want to convert any quantity in km to feet. We can follow the above mentioned unit conversion rate in order to do so.

Let us say for example, we have to km and we have to converted into feet.

2 kilometer = 2 × 3280.83 ft

2 kilometer = 6561.66 ft.

So, we can convert any kind of distance given in kilometer to feet by using the same method as above.

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Answer:

a) r = 2

b)
GP a₆ = 384

AP a₆ = 32

Step-by-step explanation:

First term a₁ = 12 for both progressions

r = common ratio, d = common difference

nth term of geometric progression = a₁ x rⁿ⁻¹
nth term of arithmetic progression = a₁ + (n - 1)d

Second term of GP = Fourth term of AP

=> 12r¹ = 12 + 3d

==> 12r = 12+ 3d  (1)

Third term of GP = 10th term of AP

=> 12r² = 12 + 9d (2)

3 x (1) => 3(12r = 12 + 3d) => 36r  = 36 +  9d (3)

(2) - (3) gives12r² -36r = 12 - 36
12r² - 36r = 12 + 9d - (36 + 9d)

12r² -36r = -24

12r² -36r + 24 = 0

Dividing by 12 gives
r² - 3r + 2= 0

We can factor r² - 3r + 2 as (r - 1)(r-2)

r² - 3r + 2= 0
=>  (r - 1)(r-2) = 0

=> r = 1 or r = 2

r cannot be 1 since all terms of the GP will be equal with a common ratio of 1

Therefore r = 2  (Part a)

Using equation (1) we get:
12r = 12+ 3d
12 x 2 = 12 + 3d

24 = 12 + 3d

3d = 24 - 12 = 12

d = 12/3 = 4

So the common ratio, r,  is 2. Common difference d = 4

6th term of GP =12 x r⁵ =  12 x 2⁵ = 12 x 32 = 384

6th term of Ap = 12 + 5d = 12 + 5(4) = 12 + 20 = 32

Answer: 1st 133

Step-by-step explanation: Hope this helps!

When computing the correlation​ coefficient, the effect of changing the order of the variables on​ r is option (A) It has no effect on r

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.

Changing the order of the variables has no effect on the correlation coefficient, It has no effect on r.

This is because the correlation coefficient measures the degree of association between two variables, regardless of which variable is designated as the dependent variable or independent variable. The formula for the correlation coefficient is symmetrical, meaning that it yields the same result regardless of the order in which the variables are entered into the formula.

Therefore, the correct option is (A)  It has no effect on r

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Answer: 131.39

Step-by-step explanation:

Ans x/2 = 22/4

A word problem is a few sentences describing a "real-life" scenario where a problem needs to be solved using math.

To answer the question above, we equate the amount of cake mix initially to the amount of water needed to make a mug cake

4  tablespoons of cake mix = 2 tablespoons of water

we then equate the amount of cake mix in the final moment to the amount of water needed to make a mug cake

22  tablespoons of cake mix = X tablespoons of water

Now we divide both and these will give us the answer.

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David has drawn a total of 177 cm of lines.

We can use the Pythagorean theorem, which tells us that in a right triangle, the square of the length of the hypotenuse (the diagonal line) is equal to the sum of the squares of the lengths of the other two sides (the lines along the long edge and the width).

In this case, the length of the hypotenuse is the distance from the starting corner to the end of the diagonal line, which we can calculate as follows:

d = √(77² + 36²) ≈ 85.99 cm

Therefore, David has drawn a total of 77 cm + 36 cm + 85.99 cm = 198.99 cm of lines. However, we should subtract the length of the starting corner to the end of the first line, which is 77 cm, since it was counted twice (once as part of the diagonal line and once as part of the line along the long edge).

So, the total length of lines that David has drawn is 77 cm + 36 cm + 85.99 cm - 77 cm = 177 cm.

Pythagoras' theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

This can be expressed as:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

Pythagoras' theorem can be used to solve a variety of problems involving right triangles, such as finding the length of a missing side or determining whether a triangle is a right triangle. It is also the basis for the distance formula in two and three-dimensional Euclidean space.

Pythagoras' theorem has applications in many fields, including physics, engineering, and computer graphics, and it is one of the most important and widely used theorems in mathematics.

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The number 19 have only two factors. They are 1 and 19. So it is a prime number. The statement is true.

Prime numbers are the numbers having only two factors, 1 and the number itself. There are some conditions that should be satisfied if they are counted as prime numbers.

It must be greater than 1.

It must be a natural number, not a decimal fraction or negative number.

It must have only two factors.

It must not be a product of any two numbers other than 1 and the number.

So a number which is not divisible by any other number than 1, can be called a prime number. All other numbers are composite numbers.

So 19 is not divisible by any other numbers. So it is a prime number.

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Department of Education is usually determined by the sales tax rate and the amount of the purchase.

The main sources of funding for the Department of Education come from income taxes and sales taxes.

The amount of income taxes collected by the Department of Education is usually determined by the tax code and the amount of income earned.

In addition to income taxes and sales taxes, the Department of Education also collects taxes from other sources. These include inheritance taxes, property taxes, and excise taxes. Inheritance taxes are taxes collected on the transfer of property from one person to another upon death.

Property taxes are taxes collected on the value of real estate, such as land and buildings. Excise taxes are taxes collected on the purchase of certain items, such as cigarettes and alcohol.

By understanding how taxes work, you can locate the Department of Education funding in your tax breakdown.

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Work Shown:

-7/2 = -3.5

The two given points are (-2,-3.5) and (4,-4)

Let's use the slope formula.

[tex](x_1,y_1) = (-2,-3.5) \text{ and } (x_2,y_2) = (4,-4)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-4 - (-3.5)}{4 - (-2)}\\\\m = \frac{-4 + 3.5}{4 + 2}\\\\m = \frac{-0.5}{6}\\\\m = \frac{-1/2}{6}\\\\m = \frac{-1/2}{6/1}\\\\m = \frac{-1}{2}\div\frac{6}{1}\\\\m = \frac{-1}{2}*\frac{1}{6}\\\\m = -\frac{1}{12}[/tex]

The slope is -1/12

It means "go down 1 unit, then go to the right 12 units".

You can use a tool like GeoGebra to confirm the answer is correct.

5.75 hours long to consume 33450 watt hours

The time it takes for a lightbulb to consume 3450 watt hours can be calculated using the formula: time = energy/power. In this case, the energy is 3450 watt hours and the power is 600 watts.

To find the time, we can plug the values into the formula:

time = 3450 watt hours / 600 watts

time = 5.75 hours

Therefore, it takes 5.75 hours for the lightbulb to consume 3450 watt hours.

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Answer:

x² + y² = z²

Step-by-step explanation:

The side of the bottom square is y.

The side of the left square is x.

The side of the right square is z.

These sides are also the legs and hypotenuse of the right triangle.

We use the Pythagorean Theorem.

x² + y² = z²

The inequality that represents the value of x is x ≥ -10.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y ≤ -6 (x - 18) - 2

Substitute y = 46

So,

46 ≤ - 6 (x - 18) - 2

46 ≤ - 6x + 108 - 2

46 ≤ 6x + 106

46 - 106 ≤ 6x

-60 ≤ 6x

-10 ≤ x

Thus,

The inequality of x is x ≥ -10.

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Answer:

Para encontrar el ancho del arco en su base, necesitamos encontrar las dos raíces de la ecuación cuadrática y = -x^2 - 6x + 16, que corresponden a los puntos donde la altura del arco es igual a cero.

Vaina

y = -x^2 - 6x + 16

0 = -x^2 - 6x + 16

x^2 + 6x - 16 = 0

Podemos resolver esta ecuación usando la fórmula cuadrática:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

donde a = 1, b = 6 y c = -16.

x = (-6 ± sqrt(6^2 - 4(1)(-16))) / 2(1)

x = (-6 ± sqrt(100)) / 2

x = (-6 ± 10) / 2

Esto nos da dos soluciones posibles:

x1 = (-6 + 10) / 2 = 2

x2 = (-6 - 10) / 2 = -8

La base del arco se extiende desde x = -8 hasta x = 2, por lo que el ancho del arco en su base es:

ancho del arco = 2 - (-8) = 10

Por lo tanto, el ancho del arco en su base es 10.

Step-by-step explanation:

espero te sirva, si no puedes español traducelo