A store pays $49.14 for an easel. The Store markes up the price by %50. What is the amount the make-up

Answer:

Kerri should draw the two cities 4.2" or 4 1/5" apart.

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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The interquartile range of the stem and leaf plot is 6.

The table given is a stem and leaf plot. A stem and leaf plot is a table that divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the unit digit.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1) = 61

First quartile = 1/4 x (n + 1) = 55

Interquartile range = 61 - 55 = 6

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The area of the semicircle is A = 1187.9 cm².

The area of a circle with a radius of r is A = πr².

Given that, the diameter of the semicircle is 55 cm.

The radius of the semicircle is,

r = 55/2

The area of a semicircle is given by,

A = (1/2)πr²

Substitute the values,

A = (1/2)π(55/2)²

A = 1187.9

Hence, the area of the semicircle is A = 1187.9 cm².

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Answer:

nothing actually Iteursitskysjtskydjtsitsitsitskgditdkgd elhsitdlhclufluclydlhcogogjdy

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Sum of the interior angles of any triangle equal 180° .

Thus ;

The angle which facing to the side 4 is 45°.

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Hint :

In a right triangle, the side facing the 45° angle is √2 / 2 times the hypothenuse .

Thus ;

\( \frac{ \sqrt{2} }{2} x = 4 \\ \)

Multiply sides by 2

\(2 \times \frac{ \sqrt{2} }{2} x = 2 \times 4 \\ \)

\( \sqrt{2} x = 8 \\ \)

Divide sides by √2

\( \frac{ \sqrt{2}x }{ \sqrt{2} } = \frac{8}{ \sqrt{2} } \\ \)

\(x = \frac{4 \times 2}{ \sqrt{2} } \\ \)

\(x = \frac{4 \times \sqrt{2} \times \sqrt{2} }{ \sqrt{2} } \\ \)

\(x = 4 \sqrt{2} \\ \)

\(x = hypothenuse = 4 \sqrt{2} \)

Done...

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Answer:

x=-3.5

Step-by-step explanation:

14/-4 = -3.5

Answer:

If you're asking how -4x could equal 14, here's how:

Substitute -3.4 for x, so -4x-3.5, which would equal 14.

Answer:

here are 117,600 ways the runners can finish first, second, and third in the race.

Step-by-step explanation:

The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.

The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.

For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.

Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.

To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.

Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.

Answer:

x = -7

y = 47

Step-by-step explanation:

Given the system of equation

y = −8x − 9 ... 1

y = −6x + 5 ...2

Equating both expressions

-8x - 9 = -6x + 5

Collect like terms

-8x + 6x = 5 + 9

-2x = 14

x = 14/-2

x = -7

Substitute x = -7 into equation 1.

From 1: y = −8x − 9

y = -8(-7) - 9

y = 56 - 9

y = 47

Hence the solution to the system of equations (x, y) is (-7, 47)

Answer:

'

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Write the sample space and tell how many possible outcomes there are.

What structure did you use to write all of the outcomes (list, table, tree, something else)? Explain why you chose that structure.

What is the probability that:

You get a white card and a red card (in either order)?

You get a black card (either time)?

You do not get a black card (either time)?

You get a blue card?

You get 2 cards of the same color?

You get 2 cards of different colors?

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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The difference between the maximum and the minimum values of the trigonometric function is 6.

We have to determine the difference between the maximum and the minimum values of the trigonometric function.

The function is y = -3cos(2x) + 8

The maximum and the minimum value of cos can be defined at the value of 0 and 1.

As we know that, the value of cos0 = 1 and the value of cos90 = 0

Now the value of the function at x = 0

y = -3cos(2×0) + 8

y = -3cos(0) + 8

y = -3×1 + 8

y = -3 + 8

y = 5

Now the value of the function at x = 90

y = -3cos(2×90) + 8

y = -3(-1) + 8

y = 3 + 8

y = 11

The difference between the maximum and the minimum values of the trigonometric function = 11 - 5

The difference between the maximum and the minimum values of the trigonometric function = 6

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Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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Answer:

24

Step-by-step explanation:

12 + 12 =24

Hah thats all i got to say lolololol

Answer:

1 adult = 16 students

a = 16x

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

as x goes up by 1 y goes up by 4

Answer:

True

Step-by-step explanation:

If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots

If the discriminant \(D=b^2-4ac > 0\), then there are two real roots

If the discriminant \(D=b^2-4ac=0\), then there is only one real root

Answer:

The answer is

Step-by-step explanation:

(6)(-1)(-3)(10)(-2)

Multiply the terms in the bracket

That's

(6)(-1) = - 6

(-3)(10) = - 30

So we have

(-6)(-30)(-2)

= 180( - 2)

= - 360

Hope this helps you

Given the numbers;

We can find the GCF and LCM using the prime factors method below;

Part A: GCF

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainders.

In this case, we would compare the common prime factors that we get.

Thus;

By comparison, the value common across all three numbers is 2(once) and 31(once). Therefore the GCF is

Answer A:

Part B: LCM

The Least Common Multiple ( LCM ) . For three integers a,b,c denoted LCM(a,b,c), the LCM is the smallest positive integer that is evenly divisible by both a, b and c.

In this case, we would list all the prime numbers found, as many times as they occur most often for anyone given number, and multiply them together to find the LCM.

Therefore the LCM would give;

Answer B:

Answer:

4x²=2(x-4)

2x²=x-4

2x²-x+4=0​

x=1+√31​/ 4, 1-√31​/4

Step-by-step explanation:

1. Cancel log on both sides

2. Divide both sides by 2

3. Move all terms to one side

4. Use the quadratic formula

Answer:

the answer is -5

-4(-5)-13=7

The measure of angle x on the straight line is 130 degrees.

The sum of interior angles in a triangle equals 180 degrees.

To determine the value of x, we first determine its suplemetary angle x .

Hence:

40 + 90 + ( suplemetary angle of x ) = 180

Solve for the suplementary angle:

130 + ( suplemetary angle of x ) = 180

Suplementary angle of x = 180 - 130

Suplemetary angle of x = 50 degree

Now, we can find the measure of  angle x.

Note that, sum of angles on a straight line equals 180 degree.

Hence:

x + ( suplemetary angle of x )  = 180

x + 50 = 180

Solve for x

x = 180 - 50

x = 130 degrees.

Therefore, the value of x is 130 degrees.

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Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°