Trigonometric Functions help. What is the length of side AB? Type the correct answer rounded to one decimal place.

Answer:

(- 5, 0) and (3, 0)

Step-by-step explanation:

Given

f(x) = x² + 2x - 15

To find the x- intercepts let f(x) = 0, that is

x² + 2x - 15 = 0 ← in standard form

(x + 5)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ← left x- intercept

x - 3 = 0 ⇒ x = 3 ← right x- intercept

Answer:

Left-most x-intercept: (-5, 0)

Right-most x-intercept: (3, 0)

Answer:

180π cm³

Step-by-step explanation:

The formula for the area of an ellipse with major axis a and minor axis b is

A = π·a·b.

Here, that area is A = π(6 cm)(4 cm) = 24π cm².

Multiplying this base area by the altitude, 7.5 cm, results in the volume:

V = (24 cm²)·π·(7.5 cm) = 180π cm³

Answer:

565,5 cm³

Step-by-step explanation:

To calculate the volume of a cylinder we have to found the area of the base and multiply by the altitude of the cylinder. As the base is elliptical, the area is given by:

[tex]A = a*b*\pi[/tex], where a is the major axis and b the minor axis. Thus:

[tex]A=6*4*\pi =75.39 cm^2[/tex]

And,

[tex]V = A*h = 75.39*7.5 = 565.48 cm^3[/tex].

Rounding to the nearest tenth: 565.5 cm³

Answer:

the answer should be f(x)=-4

Substitute x=-3 in the equation

F(x)= -2(-3)^2 -3(-3) +5

-18+9+5=-4

The answer is -4

Answer:

The required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Step-by-step explanation:

From the given graph it is clear that the related line passes through the points (-3,-3) and (3,1).

If a line passes through two points, then the equation of line is

[tex]y-y_1=\frac{y-y_1}{x-x_1}(x-x_1)[/tex]

The equation of related line is

[tex]y-(-3)=\frac{1-(-3)}{3-(-3)}(x-(-3))[/tex]

[tex]y+3=\frac{4}{6}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x+3)[/tex]

[tex]y+3=\frac{2}{3}(x)+2[/tex]

Subtract 3 from both the sides.

[tex]y=\frac{2}{3}(x)+2-3[/tex]

[tex]y=\frac{2}{3}(x)-1[/tex]

The equation of related line is [tex]y=\frac{2}{3}(x)-1[/tex]. The related line is a dotted and the shaded region is below the line. So, the sign of inequality is <.

The required inequality is

[tex]y<\frac{2}{3}(x)-1[/tex]

Therefore the required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].

Answer:

A [tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

Step-by-step explanation:

The equation [tex]12x^3-5x=2x^2+x+6[/tex] have in both sides expressions [tex]12x^3-5x[/tex] and [tex]2x^2+x+6.[/tex]

Therefore, the system of two equations

[tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

has the solution (x,y), where x is the solution of the equation above.

ANSWER

[tex]y = 12 {x}^{3} - 5x[/tex]

{

[tex]y= 2 {x}^{2} + x + 6[/tex]

EXPLANATION

The given equation is

[tex]12 {x}^{3} - 5x = 2 {x}^{2} + x + 6[/tex]

To find the system of equations, we just have to equate each side of the equation to y and form two different equations.

The left sides gives one equation,

[tex]y = 12 {x}^{3} - 5x[/tex]

The right side also gives,

[tex]y= 2 {x}^{2} + x + 6[/tex]

Hence the correct choice is A

Hence  margin of error for population proportion is option c which is 0.6

MoE refers to estimated point value that tells us how much difference is there from actual value.

critical value * SD of population

Given max sample proportion =0.28 and min sample proportion=0.16

Hence we can directly calculate MOE by subtracting both = 0.28=0.16=0.6

which is option no. c

Hence option c is 0.6 which is correct.

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Answer:

0.6 is the answer

Answer:

It is unlikely

Step-by-step explanation:

The probability of a sticky dart landing in the green section of the board, assuming that it lands on the board is possible but very unlikely.

The green section of the board has the least area compare to an other section of the board. Therefore, the dark is unlikely to land in this section.

Answer:

it is unlikey

Step-by-step explanation:

the possibility of the sticky dart landing on the green part is unlikley

Answer:

9% + 5%

Step-by-step explanation:

Answer:

$1644.

Step-by-step explanation:

We have been a typical household in the United States has an average after-tax income of $41,100. We are asked to find how much more is spent on insurance/pensions than on health care.

We have been given that 5% is spent on health care and 9% is spent on insurance/pensions. This means that 4% (9%-5%) is more on insurance/pensions than on health care.

Now, we need to find 4% of $41,100.

[tex]\text{Amount more spent on insurance/pensions than on health care}=\frac{4}{100}\times \$41,100[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=4\times \$411[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=\$1644[/tex]

Therefore, $1644 is more spent on insurance/pensions than on health care.

Answer:

He correctly determines that she has 300 nickels and 330 dimes.

Step-by-step explanation:

I'll first explain how Mark got that system of equations. Then I'll solve the system of equations to find the numbers of coins.

Moira has a collection of nickels and dimes. We don't know the number of nickels and the number of dimes she has.

First, we define two variables to represent the unknowns in this problems, the numbers of coins.

Let n = number of nickels.

Let d = number of dimes.

The sum of the numbers of coins is n + d. We are told she has 630 coins, so the first equation is

n + d = 630

Since we have two unknowns, we need two equations. Now we write an equation based on the values of the coins. A nickel is worth $0.05. A dime is worth $0.1. n nickels are worth 0.05n, and d dimes are worth 0.1d. The total value of the coins is 0.05n + 0.1d. We are told the value of the coins is $48. Now we can write the second equation.

0.05n + 0.1d = 48

Our system of equations is:

n + d = 630

0.05n + 0.1d = 48

These are the same equations Mark got.

Now we solve the system of equations. We will use the substitution method. First, we solve one equation for one variable. Then we substitute that into the other equation.

Let's solve the first equation for n:

n + d = 630

Subtract d from both sides:

n = 630 - d

Now that we know that n is the same as 630 - d, we replace n of the second equation with 630 - d.

0.05n + 0.1d = 48

0.05(630 - d) + 0.1d = 48

Distribute the 0.05:

31.5 - 0.05d + 0.1d = 48

Combine the terms in d:

0.05d + 31.5 = 48

Subtract 31.5 from both sides.

0.05d = 16.5

Divide both sides by 0.05.

d = 330

Now that we know d is 330, we substitute d with 330 in the first original equation and solve for n.

n + d = 630

n + 330 = 630

Subtract 330 from both sides.

n = 300

Since we let n = the number of nickels, and d = the number of dimes, now we can fill in the blanks.

n = number of nickels = 300

d = number of dimes = 330

Answer: He correctly determines that she has 300 nickels and 330 dimes.

*******************************************************************

The question is already answered, but we can check with the given information to confirm that our answer is correct.

We check the number of coins:

300 nickels + 330 dimes = 630 coins (the number of coins checks out.)

Now, we check the value of the coins:

300 * $0.05 + 330 * $0.1 = $15 + $33 = $48 (the value of the coins checks out.)

Since both the number of coins and the value of coins check correctly, our answer, 300 nickels and 330 dimes, is correct.

To find the number of nickels and dimes Moira has, start by simplifying the system of equations and solve for the variables. The solution to the given system of equations reveals that Moira has 300 nickels and 330 dimes.

The subject of this question is about solving a system of equations. The system in this case is given as {n+d=630 & 0.05n+0.10d=48}, where n represents the number of nickels Moira has and d represents the number of dimes she has.

First, we clear the decimals in the second equation by multiplying every term by 100, which gives us 5n + 10d = 4800. This can be simplified to n + 2d = 960 after dividing each term by 5.

Now, we have a new system of equations: {n + d = 630 & n + 2d = 960}. Subtraction of the first equation from the second will give us d = 330. Substituting d = 330 into the first equation will give us n = 300. Therefore, Moira has 300 nickels and 330 dimes.

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Answer:0.1

Step-by-step explanation:

Solve the inequality for x:

5x - 3 ≤ 7x +7

Subtract 7x from each side:

-2x -3 ≤ 7

Add 3 to each side:

-2x ≤ 10

Divide both sides by -2, also when dividing  both sides of an inequality you flip the direction of the inequality sign:

x ≥ -5

The dot will be on -5, because the inequality includes equal to, the dot is solid and is greater than, the arrow will point to the right.

The correct answer is D.

The force used by Randy is 40 N.

When a force moves anything over a distance, it is said to be doing work.

Work = Force * Displacement

Work done given in the question = 200 N.m

Distance moved by the piano = 5m

W = F * d

200 = F * 5

F = 40N

Hence, the force used by randy is 40N.

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When you raise something to the power of -1, all that happens is that thing turns upside down.

For example: (x^3 / y^4)^-1 will become (y^4 / y^3), basically the same fraction but just swap the numerator and denominator.

In your example, the first exponent is 4 and the second exponent is 3.

Answer: y^4 and x^3

the point estimate typically is in the middle of the interval, so it would be at (1/2)(0.52+0.80) or 0.66.

No. Asher figured that just subtracting 4 from 4x, which is 64, would get him the value of x. However, since 64=4x, one needs to divide 64 by the number of x's to get x's value. 64/4= 16, which is the value of x.

The method of solving the equation by asher is; Incorrect because she is supposed to divide directly and not subtract.

We are told that she wants to solve the equation;

4x = 64

Now, she decided to subtract 4 from both sides to get the value of x. That will not be correct because she is meant to divide both sides by the coefficient of x to get the value of x.

4x = 64

x = 64/4

x = 16

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Find the volume of the lake:

37 x 30 x 2 = 2,220 cubic miles.

Now find 65% of the total volume:

2,220 x 0.65 = 1,443 cubic miles

Divide the number of fish by the volume of the lake:

115, 200 fish / 1,443 cubic miles = 79.83 fish per cubic mile.

Rounded to the nearest fish = 80 fish per cubic mile.

Answer:

80 fish per cubic mile.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x-4y=4\\x+2y=18&\text{multiply both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x-4y=4\\2x+4y=36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=40\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=8}\\\\\text{Put the value of x to the second equation:}\\\\8+2y=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}[/tex]

[tex]\text{Put the values of x and y to the expression}\ x^2+y^2+xy:\\\\8^2+5^2+(8)(5)=64+25+40=129[/tex]

For this case we have that by definition of trigonometric relations of a rectangular triangle, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. While the tangent of the same angle is given by the leg opposite the angle on the leg adjacent to the angle.

Then, according to the figure we have:

[tex]sin (B) = \frac {7} {25} = 0.28\\tg (B) = \frac {7} {24} = 0.2917[/tex]

Answer:

[tex]sin (B) = \frac {7} {25}\\tg (B) = \frac {7} {24}[/tex]

Answer:

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Step-by-step explanation:

We have been given a right triangle. We are asked to find the [tex]\text{sin}(B)[/tex] and [tex]\text{tan}(B)[/tex] for our given triangle.

We know that sine relates opposite side of right triangle to its hypotenuse.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

We can see that AC is opposite side to angle B and  AB is hypotenuse of the given triangle.

[tex]\text{sin}(B)=\frac{AC}{AB}[/tex]

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

We know that tangent relates opposite side of right triangle to its adjacent.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

We can see that AC is opposite side to angle B and  BC is adjacent side of the angle B.

[tex]\text{tan}(B)=\frac{AC}{BC}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Answer:

The graph  attached below is for r=2+ 2sin θ where θ=pi

Step-by-step explanation

The coordinates in a polar equation are written as (r,θ)

r= radius and θ is the angle

⇒⇒⇒ so this mean we rotate θ radians and of the size r units

In our case assume θ=[tex]\pi[/tex] where 0≤θ≤2[tex]\pi[/tex]

Answer:

No, because each group of n items does not have an equal chance of being selected.

Step-by-step explanation:

Answer:

45 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  We have a reference angle, which is the angle made between the ground and the belt, of 32 degrees.  The height up the side of the barn, which is the side across from the reference angle, is 24 feet.  Which of our trig ratios relates side opposite to the hypotenuse?  It's the sin ratio, so let's set it up and solve for the length of the belt, which is the hypotenuse of the right triangle.

[tex]sin(32)=\frac{24}{x}[/tex]

Doing some algebraic acrobatics that with we get

[tex]x=\frac{24}{sin(32)}[/tex]

Plug that into your calculator in degree mode and you'll get 45.28991.  Rounded to the nearest foot is 45 feet.

The length of the conveyor is approximately 45 feet.

The subject of the question is Mathematics, and it deals with determining the length of a conveyor belt that makes an angle with the horizontal. This type of problem involves trigonometry, specifically the use of sine, cosine, or tangent functions to find the length of the hypotenuse of a right-angled triangle.

To find the length of the conveyor belt, we consider the belt as the hypotenuse of a right-angled triangle, with the vertical height of the barn door as the opposite side, and the angle given as the angle between the belt (hypotenuse) and the ground (adjacent side).

The height of the barn door is 24 feet, and the angle between the belt and the ground is 32 degrees. We can use the sine function (sin) since we have the opposite side and need to find the hypotenuse (length of the conveyor belt).

The formula to find the length (L) of the conveyor belt is:

L = height / sin(angle)

L = 24 feet / sin(32 degrees)

L = 24/0.5299

L = 45.29 feet

Answer:

  the associative property

Step-by-step explanation:

The associative property of addition lets you move the parentheses without changing the order of the operands.

Answer:

see explanation

Step-by-step explanation:

Using the coefficients of the polynomial and evaluating for h = - 3

- 3 | 1   - 4   - 9   36

      ↓   - 3   21   - 36

      -------------------------

       1   - 7   12   0 ← remainder

Since remainder is 0 then (x + 3) is a factor, so

y = (x + 3)(x² - 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)

The factors are - 4 and - 3, since

- 4 × - 3 = + 12 and - 4 - 3 = - 7, then

x² - 7x + 12 = (x - 4)(x - 3), and

y = (x + 3)(x - 4)(x - 3)

Answer:

an = 15 (1/5)^(n-1)

Step-by-step explanation:

In a geometric series, each term is multiplied by a common ratio to get the next term.  Such that:

an = a₁ (r)^(n-1)

Here, the first term, a₁, is 15.  The common ratio, r, is 1/5, because each term is divided by 5 to get the next term.  So:

an = 15 (1/5)^(n-1)

Your answer is correct, well done!

I think this is an example of it

Answer:

Option B.

Step-by-step explanation:

we have

[tex](x-3)^{2}=5[/tex]

take square root both sides

[tex](x-3)=(+/-)\sqrt{5}[/tex]

[tex]x=3(+/-)\sqrt{5}[/tex]

11125 ft2. I hope i got it right

Answer:

  B.  s = 0.85r

Step-by-step explanation:

The sale price is 15% off the regular price. In equation form, that is ...

  s = r - 15%×r

  s = r(1 - 0.15) = 0.85r

The equation that can be used to calculate the sale price is s = 0.85r.

A half life means that half the sample decays.

If the sample size is 1 , then after one half life there would be x  * 1/2 =  1/2 of the sample left.

For the 2nd half life, multiply 1/2 by 1/2 to get 1/4.

So after 2 half lives, there is 1/4 of the sample left, which means 3/4 of the sample decayed.

The answer is 3/4

Answer:

y = 3.4

Step-by-step explanation:

Given 2 secants and a tangent drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the external part of the secant to the entire secant.

Using the secant with measure y + 11, then

y(y + 11) = 7²

y² + 11y = 49 ( subtract 49 from both sides )

y² + 11y - 49 = 0 ← in standard form

with a = 1, b = 11 and c = - 49

Using the quadratic formula to solve for y

y = ( - 11 ± [tex]\sqrt{11^2-4(1)(-49)}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{121+196}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{317}[/tex] ) / 2

y = [tex]\frac{-11-\sqrt{317} }{2}[/tex] or y = [tex]\frac{-11+\sqrt{317} }{2}[/tex]

y = - 14.4 or y = 3.4

However y > 0 ⇒ y = 3.4 ( nearest tenth )

Answer:

2 : 3

Step-by-step explanation:

Calculate the ratio of corresponding sides

AB : LM = 4 : 6 = 2 : 3

AD : LO = 2 : 3

DC : ON = 4 : 6 = 2 : 3

CB : NM = 2 : 3

The ratio of corresponding sides is 2 : 3