5) At West High School, 362 students take
Spanish. This number has been increasing
at a rate of 20 per year. The number of
students taking French is 259 and has been
decreasing at a rate of 3 per year. At these
rates, when will there be two times as
many students taking Spanish as taking
French?
Please help

The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that specific  number whose logarithm you are trying to determine. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number.

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Answer:

51mm

Step-by-step explanation:

Equilateral triangles have same length sides so divide the perimeter (153) by 3 to get 51mm

Answer:

whats?

Step-by-step explanation:

Answer:

a)\(a_{n}\) =−2n+14

b)\(a_{n}\)  = − 5 n + 30

-8 to 8

Step-by-step explanation:

f(x) is the same as y when discussing functions. Therefore we look for the places where the line is above or touching the x axis

The average rate of change for the function between the given values is approximately 8491275.888.

To find the average rate of change for a given function, we will use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where f(a) and f(b) are the values of the function at points a and b, respectively, and (b-a) represents the change in the independent variable over the interval from a to b.

Using the given function f(x) = x² + 4x and the interval from 6 to 84818129/2, we can calculate the average rate of change as follows:

Let a = 6 and b = 84818129/2, then we can calculate the function values at a and b:

f(a) = f(6) = 6² + 4(6) = 36 + 24 = 60

f(b) = f(84818129/2) = (84818129/2)² + 4(84818129/2) = 360020447540116.5.

The change in the independent variable over the interval from a to b is:

b - a = (84818129/2) - 6 = 42409058.5

We can now substitute these values into the formula for the average rate of change:

average rate of change = (f(b) - f(a)) / (b - a)= (360020447540116.5 - 60) / 42409058.5≈ 8491275.888

Therefore, the average rate of change for the function between the given values is approximately 8491275.888.

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Answer:

2219.4

Step-by-step explanation:

All you have to do is 6% of 36990 = 0.06 * 36990 = 2219.4

Answer: 1/27

Step-by-step explanation:

(1/3)^3 = 1/27

The distance the cheetah would have covered when sprinting at maximum speed can be expressed as 1.1667t miles. The distance the cheetah covered in terms of t minutes running at maximum speed can be represented by the equation:

Distance = Rate × Time.

To determine the rate in miles per minute, we need to use the conversion information provided in the warm-up. Once we have the rate in miles per minute, we can substitute it into the equation along with the given time to calculate the distance the cheetah would have traveled.

To represent the distance the cheetah covered in terms of time, we can use the equation: Distance = Rate × Time. In this case, we need to determine the rate in miles per minute. The conversion information from the warm-up is required to establish the rate.

Let's assume the conversion information states that the cheetah's maximum speed is 70 miles per hour. To convert this rate to miles per minute, we divide it by 60 (since there are 60 minutes in an hour): 70 miles per hour ÷ 60 minutes = 1.1667 miles per minute (rounded to four decimal places).

Now, we can substitute the rate of 1.1667 miles per minute into the equation along with the given time (t minutes) to calculate the distance the cheetah would have traveled.

Therefore, The equation becomes : Distance = 1.1667 miles per minute × t minutes = 1.1667t miles. The distance the cheetah would have covered when sprinting at maximum speed can be expressed as 1.1667t miles.

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Answer:

C

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc, so

arc DE = 2 × ∠ DFE = 2 × 18° = 36°

DF is a diameter of the circle , then

arc DEF = 180° , then

arc EF = 180° - 36° = 144°

Now

mEF and m DE lies in one line hence supplementary

mEF:-

Answer:

The second one

Step-by-step explanation:

Answer:

I am not good in maths but I think it is

A 1/4

A model's scale ratio is the ratio of linear dimensions. The scale factor of the triangle is (1/2).

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

The scale ratio of the triangle can be found by taking the ratio of any one side of the dashed triangle to the solid triangle. Therefore, the scale ratio will be,

\(\rm Scale\ ratio = \dfrac{\text{Length of the dashed line}}{\text{Length of the solid line}}\\\\ Scale\ ratio = \dfrac{2}{4} = \dfrac{1}{2}\)

Hence, the scale factor of the triangle is (1/2).

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The inverse function, given the function f(x) = 5(x+4) - 6, can be found to be A. 1.

First, we need to find the inverse function of f(x). To do this, we'll switch the roles of x and y (we'll use y to represent f(x)) and then solve for y.

Given the function f(x) = 5(x + 4) - 6, let's replace f(x) with y:

y = 5(x + 4) - 6

x = 5(y + 4) - 6

x = 5y + 20 - 6

x = 5y + 14

x - 14 = 5y

y = (x - 14) / 5

Now we have the inverse function, f^(-1)(x) = (x - 14) / 5. To find the value of the inverse function when x = 19, plug in 19 for x:

f^(-1)(19) = (19 - 14) / 5

f^(-1)(19) = 5 / 5

f^(-1)(19) = 1

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Answer: \(0.076\) and \(1\overline{0}000\)

Step-by-step explanation:

The question asks you to go to two significant figures.

\(0.076499\) to two significant figures is \(0.076\) because leading zeros are insignificant. Any number from 1 to 9 is always significant. If the digit next to the 6 was 5 or greater, then it would be \(0.077\), but because it is 4 or less, it is not the case.

\(10100\) to two significant figures is \(1\overline{0}000\) because the zeros represent placeholders unless a decimal is present after the final zero. However, what we have is a 0 sandwiched in between a 1 and a 1. Zeros in between numbers that are between 1 and 9 are always significant. Because the second zero is considered significant, we draw a line over it to signify it as such. The remaining zeros are insignificant and are simply placeholders.

The approximate diameter of the sphere with a surface area of 95π inches is approximately 9.74 inches.

The surface area of a sphere is given by the formula:

A = 4πr²

where A is the surface area and r is the radius of the sphere. We can solve this equation for r to get:

r = √(A / 4π)

Substituting A = 95π, we get:

r = √(95π / 4π)

 = √(95/4)

 ≈ 4.87

Therefore, the radius of the sphere is approximately 4.87 inches. The diameter of the sphere is twice the radius, so the approximate diameter of the sphere is:

d ≈ 2r ≈ 2(4.87) ≈ 9.74

Therefore, the approximate diameter of the sphere is approximately 9.74 inches.

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Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Answer:

I think its true..................

A conversation with your friend explaining the symmetry you observe in nature is given below.

Me: Hey, have you ever noticed how symmetrical nature can be?

Friend: What do you mean?

Me: Well, think about things like snowflakes, leaves, and flowers. They all have a certain amount of symmetry to them.

Friend: Yeah, I guess I've noticed that before. But why is that?

Me: It's actually because of the way that nature grows and develops. The growth of these things is guided by physical laws and processes that tend to produce symmetrical shapes.

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Answer:

\( \frac{x - 4}{x - 7} \)

Step-by-step explanation:

\( \frac{ {x}^{2} + 2x - 24 }{ {x}^{2} - x - 42 } \\ \frac{(x + 6) (x - 4)}{(x - 7)(x + 6)} \:the \: term \: will \: be \: simplified (x + 6) \\ and \: we \: will \: be \: left \: with \: \frac{x - 4}{x - 7} \)

Answer:

Step-by-step explanation:

x² + 2x - 24 = x² + 6x  - 4x - 4 * 6

                   = x(x + 6) - 4(x + 6)

                   = (x + 6) (x - 4)

x² - x - 42 = x² -7x + 6x - 6 * 7

                = x(x - 7) + 6(x - 7)

               =  (x - 7) (x + 6)

\(\frac{x^{2}+2x-24}{x^{2}-x-42}=\frac{(x + 6)*(x-4)}{(x+6)(x-7)}\\\\\\=\frac{x-4}{x-7}\)

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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The statement is true. If a function f is differentiable at a point a, then the line tangent to f at x = a can be used to approximate values of f near x = a.

The line tangent to f at x = a is the best linear approximation to the function f at x = a. It is the line that passes through the point (a, f(a)) and has a slope equal to the derivative of f at x = a, denoted f'(a). This line is also known as the linearization of f at x = a.

To approximate the value of f at a nearby point x = a + h, where h is a small number, we can use the equation of the tangent line:

y = f(a) + f'(a) * (x - a)

Substituting x = a + h into this equation gives:

y = f(a) + f'(a) * (a + h - a)

y = f(a) + f'(a) * h

Therefore, an approximation for the value of f at x = a + h is given by f(a) + f'(a) * h. This is known as the linear approximation or tangent line approximation of f at x = a.

However, it is important to note that this approximation is only accurate when h is small, and the function f is differentiable at x = a. If h is large or the function is not differentiable at x = a, the approximation may not be accurate.

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Answer:

The line between 1 5/8 and 1 7/8 is exactly 1 3/4.

Step-by-step explanation:

1 3/4 = 1 6/8

Since the lines are every 1/8 of a cup, there are a total of 16 lines indicating 1/8 of a cup for a total of two full cups.

1/8 less than 1 6/8 is 1 5/8.

1/8 more than 1 6/8 is 1 7/8.

The line between 1 5/8 and 1 7/8 is exactly 1 3/4.

Answer: 7238.28

Step-by-step explanation:

Answer:

well if you are a boy and don't like long hair then sure... but if you are a girl then don't cut... I mean I like long hairs... but it's your choice so.. ok

In every triangle the addition of all internal angles is always 180 degrees.

So this means we can build this equation

5x + 35 + 60 = 180

now separate x values and numerical values

5x = 180 - 60 - 35

x= (180 - 60 - 35)/ 5 = 85/5 = 17

The solutions to the quadratic  equation 3x² + 8x - 50x = 42 correct to 2 decimal places are approximately x = 12.07 and x = 1.93.

What exactly are quadratic equations?

A quadratic equation in algebra is a second-degree polynomial equation of the form: ax² + bx + c = 0, where a, b, and c are constants and x is the variable. For the equation to be quadratic, the coefficient a must not be equal to zero.

Now,

To solve the equation 3x² + 8x - 50x = 42 algebraically, we can follow these steps:

3x² - 42x = 42

Move all the terms to one side of the equation, so that the equation equals 0:

3x² - 42x - 42 = 0

Divide both sides of the equation by the common factor of 3 to simplify it:

x² - 14x - 14 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = -14, and c = -14, so we can substitute these values into the formula:

x = (-(-14) ± √((-14)² - 4(1)(-14))) / 2(1)

= (14 ± √(232)) / 2

≈ 12.07 or 1.93

Therefore, the solutions to the equation 3x² + 8x - 50x = 42 correct to 2 decimal places are approximately x = 12.07 and x = 1.93.

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Right question:-

Solve this equation algebraically. Give your solutions correct to 2 decimal places. 3x² + 8x - 50 x = 42.

Answer:

\(v = \frac{n+y+16}{2}\)

Step-by-step explanation:

2(v-8) = n+y

Distribute

2v-16 = n+y

Move -16 to the other side

2v = n+y+16

Divide everything by 2

\(v = \frac{n+y+16}{2}\)

Answer:

\(v = \frac{n+y}{2} +8\)

Step-by-step explanation:

To find the expression that represents v, we have to isolate v. Our first step is distributing the 2 to both v and 8.

(2(v) - 2(8))

2v - 16 = n + y

Now add 16 to both sides.

2v = n + y + 16

Now divide both sides by 2, this will isolate v and give us the initial value of it.

\(v = \frac{n+y}{2} +8\)