one of the acute angles in a right triangle has a measure of 36.6°. What is the measure of the other acute angle?
A. 145.4°
B. 34.6°
C. 55. 4°
D. 90°​

The best describes the resulting line M is that Line m and line k are intersecting but not perpendicular.

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Dilation called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

Given that point P lies on line K.

Thus, dilation of line K is performed with center P and scale factor 5.

We can conclude that the Line m and line k are intersecting but not perpendicular.

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The complete question is

Which best describes the resulting line m?

A. Line m and line k are intersecting but not perpendicular..

B. Line m and line k are parallel.

C. Line m and line k are identical.

D. Line m and line k are perpendicular.

Answer:

-32 + 2i.....

yan po Ang sagot ko jan

Answer:

\(\text{g}^{-1}(x)=\boxed{\dfrac{x-13}{2}}\)

\(\left(\text{g}^{-1} \circ \text{g}\right)(-4)=\boxed{-4}\)

\(h^{-1}(9)=\boxed{-3}\)

Step-by-step explanation:

To find the inverse of function g(x) = 2x + 13, begin by replacing g(x) with y:

\(y=2x+13\)

Swap x and y:

\(x=2y+13\)

Rearrange to isolate y:

\(\begin{aligned}x&=2y+13\\\\x-13&=2y+13-13\\\\x-13&=2y\\\\2y&=x-13\\\\\dfrac{2y}{2}&=\dfrac{x-13}{2}\\\\y&=\dfrac{x-13}{2}\end{aligned}\)

Replace y with g⁻¹(x):

\(\boxed{\text{g}^{-1}(x)=\dfrac{x-13}{2}}\)

\(\hrulefill\)

As g and g⁻¹ are true inverse functions of each other, the composite function (g⁻¹ o g)(x) will always yield x. Therefore, (g⁻¹ o g)(-4) = -4.

To prove this algebraically, calculate the original function g at the input value x = -4, and then evaluate the inverse function of g at the result.

\(\begin{aligned}\left(\text{g}^{-1} \circ \text{g}\right)(-4)&=\text{g}^{-1}\left[\text{g}(-4)\right]\\\\&=\text{g}^{-1}\left[2(-4)+13\right]\\\\&=\text{g}^{-1}\left[5\right]\\\\&=\dfrac{(5)-13}{2}\\\\&=\dfrac{-8}{2}\\\\&=-4\end{aligned}\)

Hence proving that (g⁻¹ o g)(-4) = -4.

\(\hrulefill\)

The inverse of a one-to-one function is obtained by reflecting the original function across the line y = x, which swaps the input and output values of the function. Therefore, (x, y) → (y, x).

Given the one-to-one function h is defined as:

\(h=\left\{(-3,9), (1,0), (3,-7), (5,2), (9,6)\right\}\)

Then, the inverse of h is defined as:

\(h^{-1}=\left\{(9,-3),(0,1),(-7,3),(2,5),(6,9)\right\}\)

Therefore, h⁻¹(9) = -3.

If we randomly select a student who works part-time, the probability of that student also driving themselves to school is 1 or 100%.

To find the probability of randomly selecting a student who drives and works part-time, we need to use the formula for conditional probability. This formula states that the probability of event A given event B is equal to the probability of both events A and B occurring together, divided by the probability of event B.

In this case, event A is selecting a student who drives to school, and event B is selecting a student who works part-time. To find the probability of both events occurring together, we need to find the intersection of sets A and B, which is the group of students who both drive and work part-time. According to the Venn diagram, this group has a size of 3.

Therefore, the probability of selecting a student who drives and works part-time is:

P(A|B) = P(A and B) / P(B)

= 3 / 3

= 1

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Answer:

Step-by-step explanation:

57.6

Answer:

The angle in C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The Volume of the Cylindrical Silo is 88000 cubic feet

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.

Solution:

Given:

Height of the Container = 70 feet

Circumference of the Base = 125.7 feet

To Find: Volume of the Container

Volume = πr²h

Circumference = 2πr

125.7 = 2 * 3.14 * r

r = 20.01

Volume = 3.14 * 20.01 * 20.01 * 70

Volume = 88007.94 cubic feet

Volume = 88000 cubic feet (approx)

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Answer: $48.

Step-by-step explanation:

Since each slice of pizza is $2 and Wyatt bought 14 slices of pizza, you would multiply 14 by 2 then add it onto the cost of the membership.

14 * 2 = 28

20 + 28 = 48

The monthly cost for 14 slices of pizza is $48.

Answer:

X= -b+c+8

X= b-c+8

solutions

Answer:

Jeff bought a canoe for $333.75. The sales tax was 5%. What was his total cost?

Step-by-step explanation:

The total cost of jeff  purchase was approximately $351.27.

Step-by-step explanation:

10+2x=y, where x is less than or equal to 800.

To find the graph, plug the equation into a graphing calculator.

Answer:

C

Step-by-step explanation:

Since the lines make a linear pair,

(5x+10)+(2x-5)=180

7x+5=180

7x=175

x=25

now, we just plug in

5(25)+10

125+10

135

Therefore, m = 7.5454... (rounded to four decimal places) and n = 0.5455...

What is Simultaneous Equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

1) 3p + 4q = 23

10p + 12q = 74

Subtracting 3 times the first equation from the second equation, we get:

10p + 12q - 3(3p + 4q) = 74 - 3(23)

10p + 12q - 9p - 12q = 5

p = 5

Substituting p = 5 in the first equation, we get:

3(5) + 4q = 23

4q = 8

q = 2

Therefore, p = 5 and q = 2.

2) 4s + 2t = 20

11s + 4t = 49

Multiplying the first equation by 2 and subtracting it from the second equation, we get:

11s + 4t - 2(4s + 2t) = 49 - 2(20)

11s + 4t - 8s - 4t = 9

3s = 9

s = 3

Substituting s = 3 in the first equation, we get:

4(3) + 2t = 20

2t = 8

t = 4

Therefore, s = 3 and t = 4.

3) 3a + 4b = 34

12a + 5b = 59

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

12a + 5b - 3(3a + 4b) = 59 - 3(34)

12a + 5b - 9a - 12b = 17

3a - 7b = 17

Multiplying the first equation by 5 and subtracting it from the second equation, we get:

12a + 5b - 5(3a + 4b) = 59 - 5(34)

12a + 5b - 15a - 20b = -61

-3a - 15b = -61

a + 5b = 20

Adding the equations 3a - 7b = 17 and a + 5b = 20, we get:

4a = 37

a = 9.25

Substituting a = 9.25 in the equation a + 5b = 20, we get:

9.25 + 5b = 20

5b = 10.75

b = 2.15

Therefore, a = 9.25 and b = 2.15 (rounded to two decimal places).

4) 6m + 5n = 48

18m + 4n = 78

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

18m + 4n - 3(6m + 5n) = 78 - 3(48)

18m + 4n - 18m - 15n = -6

-11n = -6

n = 0.5455...

Substituting n = 0.5455... in the first equation, we get:

6m + 5(0.5455...) = 48

6m = 45.2727...

m = 7.5454...

Therefore, m = 7.5454(rounded to four decimal places) and n = 0.5455.

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Answer:

Volume of cone = 40 in³

Step-by-step explanation:

Given:

Volume of cylinder = 120 in³

Height of cylinder = Height of cone

Radius of cylinder = Radius of cone

Find:

Volume of cone

Computation:

Volume of cylinder = πr²h = 120 in³

Volume of cone = (1/3)πr²h

So,

Volume of cone = (1/3)(120)

Volume of cone = 40 in³

Answer:

9

Step-by-step explanation:

triangles always = 180 degrees

we know there is a 90 degree angle so 180-90=90

we know the other angle is 20 degrees so you do 90-20 which equals 70

now we know that the angle with x equals 70

so then you do 70-16 which equals 54

now just divide 54 by 6 and you get 9

so x=9

hope this helped ;)

We fail to reject the null hypothesis and conclude that the claim is not supported by the data.

To test the claim that the percentage of orange marbles is at most 11%, we can use the critical value method and a 7% significance level. Step 1: State the null and alternative hypotheses. Null Hypothesis (H0): The percentage of orange marbles is equal to or greater than 11%. Alternative Hypothesis (Ha): The percentage of orange marbles is less than 11%. Step 2: Determine the test statistic. Since we are comparing a sample proportion to a hypothesized value, we can use the z-test statistic. The formula for the z-test statistic is: z = (p - P) / sqrt(P(1-P)/n). where: p is the sample proportion, P is the hypothesized proportion, n is the sample size. In this case, p = 11/142 = 0.0775 (sample proportion), P = 0.11 (hypothesized proportion), and n = 142 (sample size). Step 3: Determine the critical value. Since the alternative hypothesis is one-sided (less than), we need to find the critical value corresponding to a 7% significance level.

Looking up the z-table, the critical value for a 7% significance level is approximately -1.645. Step 4: Calculate the test statistic.  Using the formula for the z-test statistic, we get: z = (0.0775 - 0.11) / sqrt(0.11(1-0.11)/142) ≈ -1.0407. Step 5: Compare the test statistic with the critical value. Since the test statistic (-1.0407) is greater than the critical value (-1.645), we do not reject the null hypothesis. Step 6: Draw the conclusion.  Based on the test, there is not enough evidence to support the claim that the percentage of orange marbles is less than 11% at a 7% significance level. Therefore, we fail to reject the null hypothesis and conclude that the claim is not supported by the data.

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Answer:

\( 5^{-3} = \dfrac{1}{125} \)

Step-by-step explanation:

Rule of negative exponents:

\( a^{-n} = \dfrac{1}{a^n} \)

This problem:

\( 5^{-3} = \dfrac{1}{5^3} = \dfrac{1}{5 \cdot 5 \cdot 5} = \dfrac{1}{125} \)

Answer:

\(\boxed{\frac{1}{125}}\)

Step-by-step explanation:

\(5^{-3}\)

Apply rule:

\(\displaystyle a^{-b}=\frac{1}{a^b}\)

\(\displaystyle 5^{-3}=\frac{1}{5^3}= \frac{1}{125}\)

Answer:

495

Step-by-step explanation:

The possible solutions to the equation tan²(a) + tan(a) = 0 on the interval (0, 2) are a = 0, 3π/4, π, 5π/4, 2π, etc.

The equation to be solved is:

tan²(a) + tan(a) = 0

To find the solutions on the interval (0, 2), we can factor the equation:

tan(a) * (tan(a) + 1) = 0

This equation will be satisfied if either tan(a) = 0 or tan(a) + 1 = 0.

1) For tan(a) = 0:

We know that tan(a) = sin(a)/cos(a), so tan(a) = 0 when sin(a) = 0. This occurs at a = 0, π, 2π, etc.

2) For tan(a) + 1 = 0:

tan(a) = -1

a = arctan(-1)

a = 3π/4

To solve the equation, we first factor it by recognizing that it is a quadratic equation in terms of tan(a). We then set each factor equal to zero and solve for the values of a. For tan(a) = 0, we know that the sine of an angle is zero at the values a = 0, π, 2π, etc. For tan(a) + 1 = 0, we find the value of a by taking the arctangent of -1, which gives us a = 3π/4. Thus, the solutions on the interval (0, 2) are a = 0, 3π/4, π, 5π/4, 2π, etc.

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To determine the number of receptacles required for the bathroom counter space, we need to refer to the electrical code guidelines. The specific requirements may vary depending on the country or region, as well as the local electrical codes in place.

In the United States, according to the National Electrical Code (NEC), at least one 20-ampere-rated branch circuit is required to serve the bathroom receptacles. The code specifies that this circuit should be dedicated solely to the bathroom receptacles and should not serve any other areas.

The NEC also states that at least one receptacle outlet is required on the bathroom countertop. This receptacle should be located within 3 feet of the outer edge of the countertop and should be installed above the countertop surface. This means that a receptacle needs to be placed within reach of the bathroom counter space.

Considering the given information that the bathroom counter space is seven feet, including the sink, we need to install at least one receptacle outlet on the countertop within 3 feet of the outer edge. Depending on the specific layout and size of the counter space, additional receptacles may be required to meet the code's requirements for accessibility and convenience.

To ensure compliance with local electrical codes and safety standards, it is advisable to consult with a licensed electrician or refer to the specific electrical codes applicable in your area. They will be able to provide accurate guidance based on the local requirements and regulations.

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(a) The graph of the linear functions is as attached.

(b) The equation of the linear function in slope-intercept form is; y = x

(c) The equation of the transformed function in slope-intercept form is;

y = x + 2 and y = x - 3

Functions are defined as the relationship between sets of values. For example, in the function; y = f(x), for every value of x there exists a set of y values.

x is the independent variable.

y is the dependent variable.

If the linear function is; y = x,

The equation of the transformation in slope-intercept form is given as;

For translation of 2 units up, we have;

y = x + 2

For a translation of 3 units down, we have;

y = x - 3

Thus, the required graph has been attached and the solution is determined.

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Answer:

$1350.

Step-by-step explanation:

If Justin files a claim for $2100, he will pay the first $750 toward the claim, and his insurance company will pay the remaining costs.

So, Justin will pay $750.

And, the insurance company will pay $2100 - $750 = $1350.

Using the given integral property and definitions, we evaluated the integrals to find: a) -32, b) -32/3, c) -192, d) -96.

a. We know that ∫0^4 3x(4−x)dx = 32. To find ∫4^0 3x(4−x)dx, we can use the property ∫b^a f(x)dx = -∫a^b f(x)dx.

So, ∫4^0 3x(4−x)dx = -∫0^4 3x(4−x)dx = -32.

b. To evaluate ∫0^4 x(x−4)dx, we can expand the expression inside the integral:

x(x - 4) = x^2 - 4x

Now we can integrate term by term:

∫0^4 x(x−4)dx = ∫0^4 (x^2 - 4x)dx = ∫0^4 x^2 dx - ∫0^4 4x dx

Integrating each term separately:

∫0^4 x^2 dx = [x^3/3] from 0 to 4 = (4^3/3) - (0^3/3) = 64/3

∫0^4 4x dx = 4 ∫0^4 x dx = 4[x^2/2] from 0 to 4 = 4(4^2/2) - 4(0^2/2) = 32

Therefore, ∫0^4 x(x−4)dx = 64/3 - 32 = 64/3 - 96/3 = -32/3.

c. Using the linearity property of integrals, we can split the integral:

∫0^4 6x(4−x)dx = 6 ∫0^4 x(4−x)dx - 6 ∫0^4 x^2 dx

From part (b), we know that ∫0^4 x(4−x)dx = -32/3.

From part (b), we also know that ∫0^4 x^2 dx = 64/3.

Plugging these values back into the expression:

∫0^4 6x(4−x)dx = 6(-32/3) - 6(64/3) = -64 - 128 = -192.

d. To evaluate ∫0^8 3x(4−x)dx, we can split the integral using the linearity property:

∫0^8 3x(4−x)dx = 3 ∫0^8 x(4−x)dx - 3 ∫0^8 x^2 dx

From part (b), we know that ∫0^8 x(4−x)dx = -32/3.

From part (b), we also know that ∫0^8 x^2 dx = 64/3.

Plugging these values back into the expression:

∫0^8 3x(4−x)dx = 3(-32/3) - 3(64/3) = -32 - 64 = -96.

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Answer:

0,0

Step-by-step explanation:

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

Below

Step-by-step explanation:

A line with a slope of 0 is a HORIZONTAL line

 to include the point (-6,4)   the equation would just be

      y = 4

Answer:

it would be 14.70

Step-by-step explanation:

Answer:

Table N 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx

Verify the table 4

For x=1, y=2

so

y/x=2/1=2

For x=2, y=4

so

y/x=4/2=2

For x=3, y=6

so

y/x=6/3=2

therefore

The constant of proportionality k is equal to 2 and the equation is equal to

y=2x

The table 4 represent a direct variation, therefore is a possible ratio table for ingredients X and Y