an angle is formed by​

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]

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:

The result of 36 divided by 3 is 12

Answer:

12 is  the answer

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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The answer is 12

a² = c² - b²

a² = 15² - 9²

a² = 225 - 81

a² = 144

a = √144

a = 12

Answer:

12 ft

Step-by-step explanation:

The diagonal divides the flag into 2 right triangles.

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse (diagonal ) is equal to the sum of the squares on the other 2 sides.

let x be the length, then

x² + 9² = 15²

x² + 81 = 225 ( subtract 81 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

The length of the flag is 12 ft

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]

Answer:

9/56

Step-by-step explanation:

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

-5

Step-by-step explanation:

We have two points.  We can find the slope m using

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

   = (8--2)/ (1-3)

      (8+2)/(1-3)

     10/-2

   -5

The slope is -5

Answer:

-5

Step-by-step explanation:

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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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).

The value of x in the triangle is 8 and the value of y is [tex]8\sqrt2[/tex]

How to determine the value of x in the triangle

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the Pythagoras theorem, we have:

[tex]x^2 = 10^2 - 8^2[/tex]

This gives

[tex]x^2 = 36[/tex]

take the square root of both sides

x = 8

How to determine the value of y in the triangle

Using the Pythagoras theorem on the second triangle, we have

[tex]y^2 = 8^2 + 8^2[/tex]

This gives

[tex]y^2 = 2(8^2)[/tex]

take the square root of both sides

[tex]y = 8\sqrt2[/tex]

Hence, the value of x is 8 and the value of y is [tex]8\sqrt2[/tex]

Answer:

y=5x+1

Step-by-step explanation:

step 1

Find the slope of the given line

we have

(0,1) and (5,0)

m=(0-1)/(5-0)

m=-1/5

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

m1=-1/5

substitute

(-1/5)*m2=-1

m2=5

step 3

Find the equation of the line with slope m=5 and y-intercept (0,1)

The equation of the line into slope intercept form is equal to

y=mx+b

we have

m=5

b=1

substitute

y=5x+1

Answer:

C

Step-by-step explanation:

Answer: 14 is 20% of 70

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

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:

no

Step-by-step explanation:

a line is better for a more constant and organized data. this data is unorganized and is scattered. this would be best for this type of dara

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]

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]d = \frac{W}{F}[/tex]

Step-by-step explanation:

To do this, we must isolate the variable d.

W = Fd

To isolate d, we must divide the variable F from both sides.

W ÷ F = Fd ÷ F

W ÷ F = d

Now that we have isolated the variable d, we have successfully solved this formula for distance.

[tex]d = \frac{W}{F}[/tex]

Answer:

d = W/F.

Step-by-step explanation:

You simply divide both sides by F:

W / F = Fd / F

W/F = d.

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:

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:

Answer:

A and B, A and C

Step-by-step explanation:

A and B touch at T same as A and C. The tangent is in between the two circles but through the touching points. B and C share the tangent but externally since at T it does not pass in between them.

Answer:

Step-by-step explanation:

A pie weighs n pounds.  How much would one serving weigh if the entire pie were to be shared equally among 12 people?

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:

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

Option (1) will be the answer.

        [tex]\frac{\text{sinA}}{a}= \frac{\text{sinB}}{b}= \frac{\text{sinC}}{c}[/tex]

        Where [tex]a,b,c[/tex] are the opposite sides of ∠A, ∠B and ∠C.

Given in the question,

Apply sine rule in the triangle given in the picture,

[tex]\frac{\text{sin(40)}^\circ}{y}= \frac{\text{sin(75)}^\circ}{25}[/tex]

   Therefore, expression given in option (1) will be the answer.

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The equation 3 • (10 • 12) = (3 • 10) • 12 is justified by the associative property of multiplication, stating that the grouping of numbers in multiplication does not change the outcome.

The equation 3 • (10 • 12) = (3 • 10) • 12 can be justified using the property of associative property of multiplication. This property states that when three or more numbers are multiplied, the way in which the numbers are grouped does not change the product. In simpler terms, no matter how we place the parentheses in a multiplication equation, the result will always be the same.

For example, let's take three numbers, a, b, and c. The associative property of multiplication tells us that (a • b) • c = a • (b • c). Applying this to the given equation, 3 • (10 • 12) is the same as (3 • 10) • 12 because, according to the property, the grouping of numbers does not affect the outcome. This demonstrates why the original equation holds true.