if 3x was the opposite of -5, what is the value of x?

We can use the sine ratio to solve this problem and the value of x would be 8.604.

What are trigonometric ratios?

Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.

Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we have given the hypotenuse of the triangle, and  an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x

sin35°= x/15

To solve for x, we can use the following steps:

Multiply both sides of the equation by 15 to isolate x:

sin 35° = x/15

15 * sin 35° = x

Use a calculator to approximate sin 35°:

sin 35° ≈ 0.5736

Substitute the approximation into the equation and solve for x:

x = 15 * 0.5736

x ≈ 8.604

Therefore, x is approximately equal to 8.604.

Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.

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First clear the bracket of the inner fraction's numerator. This would allow you to reduce the inner fraction to lowest terms.

Given the expression

\((\frac{(2r^2t)^3}{4t^2})^2\)

In order to simplify, note that the numerator and denominator of the fraction

\(\frac{(2r^2t)^3}{4t^2}\)

have common factors. So, we would first remove the bracket in the numerator. This would allow us to reduce the fraction to lowest terms.

To clear the numerator's bracket, note that

\((2r^2t)^3=(2r^2t)\times(2r^2t)\times(2r^2t)\\=(2\times2\times2)\times(r^2\times r^2\times r^2)\times(t\times t\times t)\\=8\times r^6 \times t^3=8r^6 t^3\)

that was long. The shorter way was to do the following

\((2r^2t)^3=2^3\times r^{2\times3}\times t^3=8r^6t^3\)

so back to the original question, to simplify

\((\frac{(2r^2t)^3}{4t^2})^2\)

we would do

\((\frac{(2r^2t)^3}{4t^2})^2=(\frac{2^3r^{2\times3}t^3}{4t^2})^2\\\\=(\frac{8r^6t^3}{4t^2})^2\)

Now that we have removed the bracket from the numerator, we can now accomplish the step of reducing the fraction to lowest terms

\((\frac{8r^6t^3}{4t^2})^2=(\frac{8}{4}\times r^6\times \frac{t^3}{t^2})^2\\=(2\times r^6\times t^{3-2})^2\\=(2\times r^6\times t^1)^2\\=(2r^6t)^2\)

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The formula of the function when the graph is analyzed will be y =1.5sin[(pi/4)x] - 3.

From the graph, the mid line is y = -3 and the amplitude will be:

= -1.5 - (-3)

= 1.5

From the mean line to the max is ¼ of a cycle. Therefore, the period will be:

= 4 × 2 = 8

Number of cycles in 2pi will be:

= 2pi/8

= pi/4

Hence, the formula of the function will be y= 1.5sin[(pi/4)x] - 3.

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Answer:

f(x)=1.5sin (pie/4 x)-3

Step-by-step explanation:

Kahn academy aproved

The three main examples of parallel lines are railway track, sidewalk edges and ladder rails

Given,

Parallel lines;-

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

We have to the examples of parallel lines;

Here,

Examples of parallel lines in real life are railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, and eraser

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Based on the number of colored pencils packaged, the rulers, and the glue sticks, the smallest number of each supply you will need to make the kits are not have any supplies left over are:

To find the smallest number of each supply that can go into making kits such that there is no leftover over, divide each of the quantities by their highest common factor.

The highest common factor of 4, 12, and 30 is 2.

The smallest quantities of each are:

Colored pencils:

= 12 / 2

= 6 colored pencils

Rulers:

= 30 / 2

= 15 rulers

Glue sticks:

= 4 / 2

= 2 glue sticks

The total number of items needed to make the kits is:

= 6 + 15 + 2

= 23 items

Full question is:

The parents teachers association at your school donated school supplies to help increase student creativity and student success in the classroom. Your teacher would you to create kits that include one package of colored pencils, one glue stick, and one ruler. When you receive the supplies, you notice the colored pencils are packaged 12 boxes to a case, the rulers are packaged 30 to a box, and glue sticks are packaged 4 to a box.

What is the smallest number of each supply you will need in order to make kits and not have supplies left over?

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Answer:

B

Step-by-step explanation:

20 × 2/5 = 8

15 × 2/5 = 6

5 × 2/5 = 2

p/s : the pic is for question no 7. i thought that you want the number 7 so i solved it first. then i reread your question. then i realized u actually want number six. so...

yeah, your welcome :)

Answer:

39.9 ft

Step-by-step explanation:

We solve using the Trigonometric function of Tangent

The formula for angle of elevation =

tan θ = Opposite/Adjacent

θ = Angle of elevation = 35°

Adjacent = 57 feet

Height = Opposite = x

Hence,

tan 35 = x/57 ft

Cross Multiply

x = tan 35 × 57 ft

x = 39.911829678 ft

Approximately the height of the building = 39.9 ft

Answer:

put it on the dots for the x-axis and the y-axis

Step-by-step explanation:

we have that

The double angles formula is equal to

and remember that

therefore

substitute in the original expression

therefore

To calculate the remaining balance on Welham's loan today, we need to determine the outstanding principal after 96 payment periods.

First, we calculate the monthly interest rate by dividing the annual interest rate by 12:

r = 4.25% / 12 = 0.04208333

Next, we calculate the number of remaining payment periods:

n = 20 years * 12 months/year - 96 payment periods = 144 - 96 = 48 payment periods

Using the formula for the monthly payment on a fixed-rate mortgage, we can calculate the monthly payment amount:

P = $326,500

r = 0.04208333

n = 20 years * 12 months/year = 240 payment periods

monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

After calculating the monthly payment amount, we can use the remaining balance formula for a fixed-rate mortgage:

remaining balance = monthly payment * ((1 + r)^n - (1 + r)^p) / r

where p is the number of payments made (96 payment periods in this case).

Substituting the values into the formula, we can calculate the remaining balance on the loan today.

Please note that the exact calculations require precise values for the interest rate and the number of remaining payment periods. Make sure to use the actual values provided in the problem statement to obtain an accurate result.

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Answer:

SA = [2π(1.4)² + 2.8π(4.2)] ft²   (Answer B)

Step-by-step explanation:

d = 2.8 ft; r = 1.4 ft

h = 4.2 ft

SA = area of 2 circular bases + lateral area

SA = 2πr² + 2πrh

SA = 2π(1.4)² + 2π(1.4)(4.2)

SA = 2π(1.4)² + 2.8π(4.2)

-----------------------------

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer:

D.

Step-by-step explanation:

The last one has the correct variables and amounts in the right order.

12x + 9y = 120

6x + 14y = 136

For two events A and B in a sample space (a) Pr(AUB) = 1.0000000000001. (b) Pr(AIB) = 0.7840058543652 (c) Pr(BIA) =0.0280920459043 (d) Pr(A') = 1 - Pr(A) = 0.00769999999999996. (e) Pr(A) = 0.9923. (f) Pr(B') = 0.96443. (g) Pr((AUB)') = -1.11022302462516 x 10^-16.

Let A and B be two events in a sample space for which Pr(A) - 0.9923, Pr(B) = 0.0355700000000001 and Pr(AB) 0.02787 then :

a. To find Pr(AUB), we use the formula: Pr(AUB) = Pr(A) + Pr(B) - Pr(AB)
Plugging in the given values, we get: Pr(AUB) = 0.9923 + 0.0355700000000001 - 0.02787 = 1.0000000000001

b. To find Pr(AIB), we use the formula: Pr(AIB) = Pr(AB)/Pr(B)
Plugging in the given values, we get: Pr(AIB) = 0.02787/0.0355700000000001 = 0.7840058543652

c. To find Pr(BIA), we use the formula: Pr(BIA) = Pr(AB)/Pr(A)
Plugging in the given values, we get: Pr(BIA) = 0.02787/0.9923 = 0.0280920459043

d. Pr(A') = 1 - Pr(A) = 0.00769999999999996.

e. Pr(A) is given as 0.9923.

f. Pr(B') = 1 - Pr(B) = 0.96443.

g. To find Pr((AUB)'), we use the formula: Pr((AUB)') = 1 - Pr(AUB)
Plugging in the value we found in part (a), we get: g. Pr((AUB)') = 1 - Pr(AUB) = -1.11022302462516 x 10^-16.
Note that this result is not a valid probability since probabilities must be between 0 and 1.

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To find the critical value that corresponds to a confidence level of 95% for estimating a population mean, we can use the t-distribution since the sample size is small (n = 4) and the population is assumed to have a normal distribution.

The critical value is obtained by considering the desired confidence level and the degrees of freedom, which is equal to the sample size minus 1 (df = n - 1 = 4 - 1 = 3). Since we are looking for a 95% confidence level, the remaining 5% is divided equally into two tails (2.5% in each tail). Therefore, we need to find the critical value that leaves 2.5% in the upper tail. Using a t-distribution table or statistical software, the critical value for a confidence level of 95% and 3 degrees of freedom is approximately 3.182.

Therefore, the critical value that corresponds to a confidence level of 95% for estimating a population mean with a sample size of 4 is approximately 3.182.

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Answer:

5a + 2

Step-by-step explanation:

To find h(a + 1), substitute x = a + 1 into h(x), that is

h(a + 1) = 5(a + 1) - 3

            = 5a + 5 - 3

            = 5a + 2

Answer:

m= \(-\frac{1}{3}\)

Explanation:

Formula is Y=mx+b

m equals the slope (rise/run each point).

x stays for an ongoing function.

b is the y intersect(You'll see that the line crossed +4 on the vertical line).

Looking at the line from left to right, it starts from the top to the bottom instead of button to top. If this slope goes down, it is negative.

\(y=-\frac{1}{3}x+4\)

That is why \(m=-\frac{1}{3}\) instead of \(m=\frac{1}{3}\)

Answer:

I think the value of x =50

Answer:

\(a_{n}=2+3(n-1)\)

Step-by-step explanation:

Step 1. To find the equation that describes the pattern, we use the arithmetic sequence formula:

\(a_{n}=a_{1}+d(n-1)\)

Where a_n is the n'th terms and d is the common ratio between the numbers.

Step 2. The sequence we have is:

2 5 8 11

The first term is:

\(a_{1}=2\)

And the common ratio or the difference between consecutive numbers is:

3 2+3=8 5+3=8  8+3=11

This will be the value of d:

d=3

Step 3. Substituting a_1 and d into the formula:

\(a_{n} =a_{1}+d(n-1)\\a_{n}=2+3(n-1)\)

This is the equation that represents the number pattern, it represents that we add three each time to the previous number in the sequence.

Hence, the correct answer is \(a_{n}=2+3(n-1)\)



Answer:

I am not sure if this is correct but I think it is A

Step-by-step explanation:

Answer:8755

Step-by-step explanation:100%+3%=103% in decimal form 1.03

8500x1.03=8755

Answer:

it is equallaterial.

Step-by-step explanation:

it id that because all of the side are the same

Answer:

Step-by-step explanation:

If -5x + 7 = -2x - 3, then x =

-5x + 2x = -3 -7

-3x = -10

x = 10/3

------------------

The equation of the regression line is:

y = -3.76x + 99.93

This equation represents the relationship between the number of classes missed (x) and the predicted final exam score (y) based on the given data.

x y

10 54

11 41

12 37

14 36

15 29

16 28

18 28

19 26

22 19

25 19

26 18

Based on the scatter plot, we can observe the relationship between the number of classes missed (x) and the final exam score (y). To analyze this relationship quantitatively, we can calculate the correlation coefficient and fit a regression line.

Calculating the correlation coefficient (r):

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we want to calculate the correlation coefficient (r) between x (number of classes missed) and y (final exam score).

Using the following formula:

r = [Σ((x - mean(x)) * (y - mean(y)))] / [sqrt(Σ(x - mean(x))^2 * Σ(y - mean(y))^2)]

Here's the calculation:

Step 1: Calculate the means of x and y:

mean(x) = (10 + 11 + 12 + 14 + 15 + 16 + 18 + 19 + 22 + 25 + 26) / 11 = 18.27

mean(y) = (54 + 41 + 37 + 36 + 29 + 28 + 28 + 26 + 19 + 19 + 18) / 11 = 31.27

Step 2: Calculate the differences from the means:

x - mean(x): -8.27, -7.27, -6.27, -4.27, -3.27, -2.27, -0.27, 0.73, 3.73, 6.73, 7.73

y - mean(y): 22.73, 9.73, 5.73, 4.73, -2.27, -3.27, -3.27, -5.27, -12.27, -12.27, -13.27

Step 3: Calculate the products of the differences:

(-8.27 * 22.73) + (-7.27 * 9.73) + (-6.27 * 5.73) + (-4.27 * 4.73) + (-3.27 * -2.27) + (-2.27 * -3.27) + (-0.27 * -3.27) + (0.73 * -5.27) + (3.73 * -12.27) + (6.73 * -12.27) + (7.73 * -13.27) = -432.41

Step 4: Calculate the sums of the squared differences:

Σ(x - mean(x))^2 = 113.41

Σ(y - mean(y))^2 = 891.91

Step 5: Calculate the square root of the product of the sums of squared differences:

sqrt(Σ(x - mean(x))^2 * Σ(y - mean(y))^2) = sqrt(113.41 * 891.91) = 322.02

Step 6: Calculate the correlation coefficient:

r = -432.41 / 322.02 = -1.34 (approximately)

The correlation coefficient (r) is approximately -1.34. ItIt indicates a strong negative linear relationship between the number of classes missed and the final exam score.

Fitting a regression line:

To fit a regression line, we need to calculate the slope (b) and the y-intercept (a) using the following formulas:

b = r * (SD(y) / SD(x))

a = mean(y) - b * mean(x)

where SD(y) is the standard deviation of y and SD(x) is the standard deviation of x.

Calculating the slope (b):

First, we need to calculate the standard deviations of x and y.

SD(x) = sqrt[Σ(x - mean(x))^2 / (n - 1)]

SD(y) = sqrt[Σ(y - mean(y))^2 / (n - 1)]

where n is the sample size.

Using the previously calculated values:

SD(x) = sqrt(113.41 / 10) = 3.37

SD(y) = sqrt(891.91 / 10) = 9.45

Now, let's calculate the slope:

b = -1.34 * (9.45 / 3.37) = -3.76 (approximately)

Calculatin

g the y-intercept (a):

a = mean(y) - b * mean(x)

= 31.27 - (-3.76 * 18.27)

= 31.27 + 68.66

= 99.93 (approximately)

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The area of one of the six congruent faces of the cube after the hole is drilled can be determined by subtracting the area of the drilled hole from the original face area of the cube.

First, let's find the area of the drilled hole. The hole is cylindrical, and its radius is given as 1. The formula for the area of a cylinder is A = πr^2, where r is the radius. Therefore, the area of the drilled hole is π(1^2) = π square units.

Next, we need to find the original face area of the cube. Since the cube has side length 3, each face is a square with side length 3. The formula for the area of a square is A = side^2, so the original face area is 3^2 = 9 square units.

Finally, to find the area of one of the six congruent faces of the cube after the hole is drilled, we subtract the area of the drilled hole from the original face area. Thus, the area is 9 - π square units.

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\(( {t + 8})^{3} = {t}^{3} + 3 \times ({t})^{2} \times( 8) + 3 \times (t) \times ( {8})^{2} + {8}^{3} \\ \)

So :

\( ({t + 8})^{3} = {t}^{3} + 24 {t}^{2} + 192t + 512\)