The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it down three units. Which function is representative of this transformation?

Answer:

  32. -30°

  33. 45° or 135°

  34. 90°

Step-by-step explanation:

The table below shows a short list of trig function values.

32. -tan(x) = tan(-x)

33. -cos(x) = cos(180°-x)

34. sec(x) = 1/cos(x). 1/0 is "undefined".

The values shown above are the ones that are in the range of the inverse trig functions: arctan (-90°, 90°), arccos [0°, 180°], arcsec [0°, 90°)∪(90°, 180°].

[tex]32.\quad tan\theta=-\dfrac{\sqrt3}{3}\\\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\\\\\text{Since there is no "3" on the Unit Circle, un-rationalize the denominator:}\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\bigg(\dfrac{\sqrt3}{\sqrt3}\bigg)\implies \dfrac{sin\theta}{cos\theta}=-\dfrac{3}{3\sqrt3}=-\dfrac{1}{\sqrt3}\\\\\implies sin\theta =\pm\dfrac{1}{2}\quad and \quad cos\theta = \pm\dfrac{\sqrt3}{2}\quad and \text{ coordinate is in Quadrant 2 or 4}[/tex]

[tex]\text{Look on the Unit Circle (below) for coordinates }\bigg(\dfrac{-\sqrt3}{2},\dfrac{1}{2}\bigg)\ and\ \bigg(\dfrac{\sqrt3}{2},\dfrac{-1}{2}\bigg)\\\\\bold{Answer:}\large\boxed{150^o\ and\ 330^o\implies \dfrac{5\pi}{6}\ and\ \dfrac{11\pi}{6}}[/tex]

[tex]33.\quad cos^2\theta=\dfrac{1}{2}\\\\\\.\qquad \sqrt{cos^2\theta}=\sqrt{\dfrac{1}{2}}\\\\\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\\\\\\\text{Rationalize the denominator:}\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\implies cos\theta=\pm\dfrac{\sqrt2}{2}\\\\\\\text{Look on the Unit Circle to find when }cos\theta=\dfrac{\sqrt2}{2}\ and\ \dfrac{-\sqrt2}{2}[/tex]

[tex]\bold{Answer:}\large\boxed{45^o, 135^o, 225^o, 315^o\implies \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}}[/tex]

[tex]34.\quad sec\theta=\text{unde fined}\implies sec\theta=\dfrac{1}{0}\\\\\\.\qquad \dfrac{1}{cos\theta}=\dfrac{1}{0}\implies cos\theta=0\\\\\\\text{Look on the Unit Circle to find when }cos\theta=0\\\\\bold{Answer:}\large\boxed{90^o\ and\ 270^o\implies\dfrac{\pi}{2}\ and\ \dfrac{3\pi}{2}}[/tex]

11125 ft2. I hope i got it right

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:

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:

(- 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

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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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:

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:

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:0.1

Step-by-step explanation:

[tex]a = \frac{b \times h}{2} [/tex]

33.6 × 2 = b×h

67.2 = b×h

h=4

67.2÷4 =b

16.8=b

answer: b=16.8inches

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

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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The answer is:

The correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

To solve the problem, we need to remember the product of powers with the same base property, the property is defined by the following relation:

[tex]a^{m}*a^{n}=a^{m+n}[/tex]

If we are multiplying two or more powers with the same base, we must keep the base and add/subtract the exponents.

So, we are given the expression:

[tex]4^{3}*4^{4}[/tex]

We can see that both powers have the same base (4), so solving we have:

[tex]4^{3}*4^{4}=4^{4+3}=4^{7}[/tex]

Hence, we have that the correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

Have a nice day!

Answer:

The correct answer is option C

4^7

Step-by-step explanation:

Points to remember

Identities

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

x⁻ᵃ = 1/xᵃ

To find the correct option

It is given that,

4^3 * 4^4

⇒ 4³ * 4⁴

By using identities we can write,

4³ * 4⁴  = 4⁽³ ⁺ ⁴)

 = 4⁷

Therefore the correct option is option C.  4^7

Answer:

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

Step-by-step explanation:

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:

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)

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

Answer:

Step-by-step explanation:

Let's calculate the probability of selecting a blue shirt from a total of 10 shirts:

It's 5/10, or 0.5, which stems from there being 5 blue shirts among the 10 Jeremy owns.  50/50 is not a standard way of expressing probability; 0.5 is proper.

Answer:

8% difference I think.

Step-by-step explanation:

72 - 64 = 8.

The temperature increase from 64 degrees to 72 degrees represents a 12.5% increase. You calculate this by dividing the difference in temperature by the original temperature and then multiplying by 100.

To calculate the percent increase in temperature from 64 degrees to 72 degrees, you subtract the original temperature from the new temperature and divide by the original temperature. Then, multiply the result by 100 to get the percentage.

Here is the calculation:

Percent Increase = ((New Temperature - Original Temperature) / Original Temperature) × 100

Percent Increase = ((72 - 64) / 64) × 100

Percent Increase = (8 / 64) × 100

Percent Increase = 0.125 × 100

Percent Increase = 12.5%

Therefore, the temperature has increased by 12.5%.

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:

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]

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]

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:

  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.

Answer:

B

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2

where F is faces, V is vertices and E is edges

Substitute the values given and solve for F, that is

F + 13 - 26 = 2

F - 13 = 2 ( add 13 to both sides )

F = 15 → B

The correct option is (B) 15

Euler's formula states the relationship between the number of Faces, Edges and Vertices of any polyhedron. It is given as

[tex]F+V=E+2[/tex]

where

[tex]F=\text{number of faces}\\V=\text{number of vertices}\\E=\text{number of edges}[/tex]

From the question

[tex]V=13,E=26[/tex]

so

[tex]F+V=E+2\\F+13=26+2\\F=26+2-13=15[/tex]

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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:

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

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.