If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (sºt)(-7)?

Answer:

5

Step-by-step explanation:

The radius is 5.

All I do was think of the center-radius form a circle

(x-h)^2+(y-k)^2=r^2

x^2     + y^2    =25

(x-0)^2+(y-0)^2=5^2

The center is (0,0) and the radius is 5.

So a point on the circle (x,y) has a distance of 5 from the center

and the center's case here is (0,0).

Answer:

Step-by-step explanation: The most important step to do is to simplify the equations down. We do this by finding common variables.

Common Variables are pairs such as 12x and 32x, and not 12x and 32y or 12 and 32.

1. [tex]12 -3y - 2x + x + 2x = 12 - 3y + x[/tex]

2. [tex]3x + 2y - 2x + y + 12 = 12 + 3y + x[/tex]

3. [tex]x + 3y + 2x - 3x + 7 + 5 = 12 + 3y[/tex]

4. [tex]12+ 3y[/tex] cannot be simplified any further.

5. [tex]12-3y+x[/tex] cannot be simplified any further.

6. [tex]5 + 2y + 7x - 4x + 3y - 17 = -12 + 5y + 3x[/tex]

7. [tex]4y + 3y + 3x - 6y - 10 - 2= -12+3x+y[/tex]

8. [tex]-12 +  3x + y[/tex] cannot be simplified any further.

9. [tex]12+ 3y + x[/tex] cannot be simplified any further.

Now, we start to match the equations.

Equation 1 is the same as Equation 5

Equation 2 is the same as Equation 9

Equation 3 is the same as Equation 4

Equation 6 is the same as none of them.

Equation 7 is the same as Equation 8.

And there you are have it!

Answer:

[tex]-\dfrac{1}{2}[/tex]

Step-by-step explanation:

In the given graph of straight line to find the slope of the line.

First we choose two points on line and then using formula to find the slope.

Formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Point on line from graph: (2,-1)  and (-2,1)

[tex]x_1\rightarrow 2[/tex]

[tex]y_1\rightarrow -1[/tex]

[tex]x_2\rightarrow -2[/tex]

[tex]y_2\rightarrow 1[/tex]

Substitute the points into formula

[tex]m=\dfrac{1+1}{-2-2}[/tex]

[tex]m=-\dfrac{1}{2}[/tex]

Hence, The slope of the line is [tex]-\dfrac{1}{2}[/tex]

The slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.

The slope of a line is a measure of its steepness or incline. It determines how much the line rises or falls for each unit of horizontal change. Mathematically, the slope is defined as the ratio of the vertical change (the difference in y-coordinates) to the horizontal change (the difference in x-coordinates) between any two points on the line.

The slope is typically denoted by the letter "m" and can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two distinct points on the line.

The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line is upward-sloping from left to right, a negative slope indicates a downward-sloping line, a zero slope indicates a horizontal line and an undefined slope indicates a vertical line. The magnitude of the slope represents the steepness of the line.

To find the slope (m) of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:

m = (y2 - y1) / (x2 - x1)

In this case, the points are (-2, 1) and (2, -1). Let's substitute the values into the formula:

m = (-1 - 1) / (2 - (-2))

= (-2) / (2 + 2)

= (-2) / 4

= -1/2

Therefore, the slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.

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The equation which is correct for the given function is:

           D.   [tex]y+2=2(x+3)^2[/tex]

By looking at the graph we observe that the graph of the function passes through the point (-4,0) , (-2,0)  , (-3,-2)

A)

         [tex]y=(x+4)(x+2)[/tex]

when x= -3 we have:

[tex]y=(-3+4)(-3+2)\\\\y=1\times (-1)\\\\y=-1\neq -2[/tex]

Hence, option: A is incorrect.

B)

     [tex]y=x^2+3x-2[/tex]

when x= -2 we have:

[tex]y=(-2)^2+3\times (-2)-2\\\\y=4-6-2\\\\y=-4\neq 0[/tex]

Hence, option: B is incorrect.

C)

    [tex]y+2=-2(x+3)^2[/tex]

when x= -2 we have:

[tex]y+2=-2(-2+3)^2\\\\y+2=-2[/tex]

[tex]y=-4\neq 0[/tex]

Hence, option: C is incorrect.

D)

   [tex]y+2=2(x+3)^2[/tex]

We see that the graph of this equation matches the given graph of the function.

Answer:

D. y + 2 = 2(x+3)^2

Step-by-step explanation:

Answer:

The answer is y = -12x - 42

Step-by-step explanation:

First distribute -12 into the paranthesis.

y - 6 = -12x - 48

Then add 6 to both sides.

y = -12x - 42

That's your final answer. I hope this helps love! :)

Answer:

[tex]x = \frac{ - 1}{12} y + \frac{ - 7}{2} \\ c. \: y = - 12x - 42[/tex]

Step-by-step explanation:

[tex] 1. \: - 12x - 48 = y - 6 \\ 2. \: - 12x = y + 42 \\ 3. \: \frac{12x}{ - 12} = \frac{y + 42}{ - 12} \\ x = \frac{ - 1}{12} y + \frac{ - 7}{2} [/tex]

1 pound

Step-by-step explanation:

15+10=25

25÷6=24.1

For this case we must indicate the result of the following expression:

[tex]\frac {2x ^ 3-3x + 5} {x + 3}[/tex]

We must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Answer:

See the attached image

Option A

Answer: Choice A

Step-by-step explanation:

The true statement is the graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97

The function is given as:

[tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]

See attachment for the graph of [tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]

From the attachment, we have the following highlights

Hence, the true statement is (b) above

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Answer:

Yes, this is a good statistical question because a variety of answers are given.

Step-by-step explanation:

A question can be called a good statistical question because of the variety of the answers it can bring to data. The answers to the same question will be different for different people.

Hence,

Yes, this is a good statistical question because a variety of answers are given ..

Answer:

C

Step-by-step explanation:

Did Unit Test Review B)

Answer:

1). sin x  and csc x

2). cos x and sec x

3).tan x and cot x

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Csc θ = Hypotenuse /Opposite side

Sec θ = Hypotenuse /Adjacent side

Cot θ = Adjacent side/Opposite side

To find the correct answers

From the above points we get reciprocal of functions are,

1). sin x  and csc x

2). cos x and sec x

3).tan x and cotx

ANSWER

The answer is B.

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

EXPLANATION

The graph represents a rational function.

This rational function has a hole at x=1 and a vertical asymptote at x=-3.

This implies that the denominator of the rational function in factored form is

[tex](x + 3)(x - 1)[/tex]

When we expand this, we get:

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

This tells us that the answer must be option B.

This graph also has a horizontal asymptote at y=1.

The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.

Therefore the function is actually

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

Answer:

Desiree and Justin have the same ratio, Justin's is just simplified.

Step-by-step explanation:

Take Desiree's ratio and divide both sides by 5

24:6

24/6 : 6/6

4:1

This is the same ratio as Justin

Both ratio's are the same

Answer:

Both are correct

Step-by-step explanation:

Check the picture below.

since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.

let's find the hypotenuse first.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}[/tex]

The value of Sin θ for a given circle and given condition is (2√5)/5.

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). Any interval joining a point on the circle to the center is called a radius.

Here, let the horizontal side be x.

         vertical side be y

then as per the given condition

Vertical distance = 2 X horizontal distance

      y = 2x

By Pythagoras Theorem,

      r = [tex]\sqrt{x^2+y^2}[/tex]

      1 = [tex]\sqrt{x^2+(2x)^2}[/tex]

      1 = x² + 4x²

      5x² = 1

       x² = 1/5

      x = 1/√5

then, y = 2/√5

Now, Sin θ = perp. / Hypo.

         Sin θ = y/1

           Sin θ  = 2/√5

or        Sin θ  = (2√5)/5

Thus, the value of Sin θ for a given circle and given condition is (2√5)/5.

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Answer:

C. √xy\y

Step-by-step explanation:

Multiply the denominator and the numerator by the conjugate of the numerator to arrive at your answer.

Answer:

y=1/4 x +11

Step-by-step explanation:

So this is a word problem but it isn't too bad to figure what they want:  They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).

So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.

The given equation has a slope of -4

The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.

So we know our equation is in the form of y=1/4 x+b

Now we are given that this line should go through (-4,10) so plug it in to find b.

10=1/4 * (-4)+b

10=-1+b

11=b

So the equation is y=1/4 x+11

Answer: [tex]y=\frac{1}{4}x+11[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Given the equation of the line [tex]y= -4x - 6[/tex], you can identify that the slope is:

[tex]m=-4[/tex]

By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation  of the line that represents the new path which will be built perpendicular to other path, is:

[tex]m=\frac{1}{4}[/tex]

Knowing that the path will intersect at the point (-4 ,10), you  need to substitute the slope and this point into  [tex]y=mx+b[/tex] and solve for "b":

[tex]10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11[/tex]

Therefore, the equation that represents the new path is:

 [tex]y=\frac{1}{4}x+11[/tex]

Answer: %150

Step-by-step explanation:

Percent increase = New Value - original value/ original value * 100

15 - 6/6 * 100

9/6 * 100

1.5 * 100

150

A. You would just get a lot of names back from people, thinking they have the most time playing instruments.

B. This question is not a statistically accurate question if you would like statistical answers back.

Statistical question definition:

A statistical question is one that can be answered by collecting data and where there will be variability in that data. For example, there will likely be variability in the data collected to answer the question,

The question to ask to get statistical answers back would be: How many hours do you play the instrument a day?

Each student would answer and you would see who has the most hours.

Final answer:

Minnie should collect quantitative data on the hours spent playing instruments by her classmates to determine who spends the most time. The original survey question is not statistical because it does not allow for analysis of a group trend, but changing the question to inquire about the typical number of hours spent by students each week would make it statistical.

Explanation:

Part A: Expected Data Collection

The data Minnie would expect to collect from her survey question would consist of quantitative information. Specifically, she should gather the number of hours each classmate spends playing musical instruments per week. This data allows her to determine which student spends the most time practicing.

Part B: Statistical Question Analysis

The question, "Which student spends the most time playing musical instruments?" is not a statistical question because it seeks a singular answer rather than understanding a trend, variation, or distribution within a group. To make it statistical, the question could be modified to: "How many hours do students typically spend playing musical instruments each week?" This revised question allows for the collection, analysis, and interpretation of data, which can lead to conclusions about the musical habits of Minnie's classmates.

Answer:

last choice

Step-by-step explanation:

So the y-intercept is -2 and the slope is -2/3

The only choices I'm going to look at is first and last because they go through -2 on y-axis.

Now -2/3 is the slope that means the graph should be going down reading it left to right so the last choice,

The increase in price of the stock is $37.50. To find the percent increase, divide the increase (37.50) by the original price (12.50) and multiply by 100, giving a percent increase of 300%.

The question requires us to find the percent increase in the price of a stock. First, to find the increase, we subtract the initial price from the final price. We get $50 - $12.50 = $37.50. This is the increase in price. To find the percentage increase, we divide this increase by the initial price and multiply by 100 to convert it into percent. Therefore, the percentage increase = ($37.50 / $12.50) x 100 = 300%. Therefore, there is a 300% increase in the stock price.

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Answer:

[tex]\large\boxed{m=\dfrac{5}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation of a line:}\ y=-\dfrac{2}{5}x+\dfrac{4}{5}\to m_1=-\dfrac{2}{5}.\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{2}{5}}=\dfrac{5}{2}[/tex]

Answer:

The answer is 57 degrees Fahrenheit

Step-by-step explanation:

The  temperature in degrees Fahrenheit is 57.2°F

The Fahrenheit temperature scale is used in the United States; the Celsius, or centigrade, scale is employed in most other countries and for scientific purposes worldwide.

The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) representation is:

°F = (9/5 × °C) + 32.

Given:

temperature= 14 C

using formula,

F=9/5C+32,

F= 9/5 * 14+32

F= 126/5+32

F= 25.2+32

F= 57.2

Hence, the temperature in degrees Fahrenheit is 57.2°F.

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Answer:

Part 1) The amount invested at 4% was $2,000

Part 2) The amount invested at 9% was $3,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x------> the amount invested at 4%

5,000-x ----> the amount invested at 9%

in this problem we have

[tex]t=1\ year\\ P=\$5,000\\I=\$350\\r1=0.04\\r2=0.09[/tex]

substitute in the formula above

[tex]350=x(0.04*1)+(5,000-x)(0.09*1)[/tex]

[tex]350=0.04x+450-0.09x[/tex]

[tex]0.05x=450-350[/tex]

[tex]0.05x=100[/tex]

[tex]x=2,000[/tex]

so

[tex]5,000-x=5,000-2,000=3,000[/tex]

therefore

The amount invested at 4% was $2,000

The amount invested at 9% was $3,000

Answer:

A-B-D-B

Step-by-step explanation:

Answer:

9/56

Step-by-step explanation:

[tex] \frac{1}{2} + \frac{2 }{7} - \frac{5}{8 } = \frac{9}{56} [/tex]

Answer:

- x² + x - 1

Step-by-step explanation:

(f / g)(x)

= [tex]\frac{x^4-x^3+x^2}{- x^2}[/tex]

divide each term on the numerator by - x²

= [tex]\frac{x^4}{- x^2}[/tex] - [tex]\frac{x^3}{-x^2}[/tex] + [tex]\frac{x^2}{-x^2}[/tex]

=  - [tex]x^{4-2}[/tex] + [tex]x^{3-2}[/tex] - [tex]x^{2-2}[/tex]

= - x² + x - [tex]x^{0}[/tex] = - x² + x - 1

Answer:

see explanation

Step-by-step explanation:

Given

2x² + 7x = 15 ( subtract 15 from both sides )

2x² + 7x - 15 = 0 ← in standard form

To factorise the left side

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = + 7

The factors are + 10 and - 3

Use these factors to split the x- term

2x² + 10x - 3x - 15 ( factor the first/second and third/fourth terms )

2x(x + 5) - 3(x + 5) ← factor out (x + 5) from each term

(x + 5)(2x - 3) ← in factored form

Answer:

215.6 m²

Step-by-step explanation:

The area (A) of a regular polygon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

perimeter = 7 × 7.7 = 53.9 m, hence

A = 0.5 × 53.9 × 8 = 215.6 m²

Answer:

215.6 meters squared

Step-by-step explanation:

The rule for nth term will  be   [tex]\rm a_n = 2\times 4^{n-1}[/tex] and the 14th term of the sequence is 134217728.

The series which can be written in the form of  

[tex]\rm a_n = a_1 \times r^{n-1}[/tex]

nth term, a₁ is the first term, and r is the common ratio.

is called geometric series/

It is given in the question that

The first term of a geometric series is 2 and the common ratio is 4.

The rule for nth term will  be

[tex]\rm a_n = 2\times 4^{n-1}[/tex]

To find the 14th term of the sequence. ​

[tex]\rm a_{14} = 2\times 4^{14-1}\\\\\rm a_{14} = 2\times 4^{13}\\\\a_{14}= 2 \times67108864 \\\\\\a_{14}= 134217728[/tex]

Therefore the 14th term of the sequence is 134217728.

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To find the nth term of a geometric series with first term 2 and common ratio 4, the formula [tex]a * r^(n-1)[/tex] is used.

For the 14th term, apply 2 * [tex]4^(13)[/tex] to get 134,217,728.

The student has asked for the rule to find the nth term of a geometric series and for the 14th term specifically. The first term is given as 2, and the common ratio is 4.

In a geometric series, the nth term is found using the formula[tex]a * r^(n-1)[/tex], where a is the first term and r is the common ratio. To find the 14th term, we would use the formula [tex]2 * 4^(14-1)[/tex].

Let's calculate the 14th term:

Therefore, the 14th term of the sequence is 134,217,728.