what is 12×=4-y^2+4

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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tax will be = 50 x 5% = $2.5

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

Answer is E hope this helps :)

Step-by-step explanation:

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

3 A'(-1,2) B'(4,3) C'(-2,5)

Step-by-step explanation:

The rule for a 270-degree rotation: When rotating a point 270-degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, we switch x and y and make x negative.

 3 A'(-1,2) B'(4,3) C'(-2,5)

Answer:

13%

Step-by-step explanation:

I really don’t know if it’s right

The algebric expression \(cot(sin^{(-1)}\sqrt{(x^2}\)simplifies to sqrt(1 - |x|^2) / |x|.

The expression "cot(sin^(-1)(sqrt(x^2)))" involves trigonometric and square root functions. Let's break it down step by step to simplify the expression.

Inside the square root: x^2.

The square root of x^2 is |x| (the absolute value of x), as the square root eliminates the square and keeps the positive value.

The expression sin^(-1)(sqrt(x^2)) is equivalent to arcsin(sqrt(x^2)).

Since we already know that the square root of x^2 is |x|, we can rewrite the expression as arcsin(|x|).

Now, we have cot(arcsin(|x|)).

The cotangent (cot) of an angle is equal to the reciprocal of the tangent (tan) of the same angle.

So, cot(arcsin(|x|)) can be written as 1 / tan(arcsin(|x|)).

Using the inverse trigonometric identity, tan(arcsin(x)) = x / sqrt(1 - x^2), we can simplify further.

In our case, x = |x|.

Therefore, tan(arcsin(|x|)) = |x| / sqrt(1 - |x|^2).

Substituting this result back into the expression, we have 1 / (|x| / sqrt(1 - |x|^2)).

To divide by a fraction, we multiply by its reciprocal.

Hence, the final simplification of the expression is sqrt(1 - |x|^2) / |x|.

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Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Answer:

(1,0)

Step-by-step explanation:

Given

\(H = (-2,2)\)

\(I = (4,3)\)

\(J = (4,-2)\)

\(K = (-2,-3)\)

Required

The midpoint of the diagonals

Midpoint is calculated as:

\(M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

For H and J, the midpoint is:

\(M = (\frac{-2+4}{2},\frac{2-2}{2})\)

\(M = (\frac{2}{2},\frac{0}{2})\)

\(M = (1,0)\)

For I and K, the midpoint is:

\(M = (\frac{4 - 2}{2},\frac{3-3}{2})\)

\(M = (\frac{2}{2},\frac{0}{2})\)

\(M = (1,0)\)

The midpoint of both diagonal is: (1,0)

Answer:

option C

Step-by-step explanation:

The order of set of numbers {-415%, -√17, -4.1, -4.08} from least to greatest is {-415% < -√17 < -4.1 < -4.08}

Order of set of numbers:

Numerical order is a way of arranging a group of numbers into a sequence. This could be ascending or descending.

When we arrange numbers in ascending order, we arrange them from small to big, and when we arrange numbers from big to small, it is called descending order.

Given,

=> {-415%, -√17, -4.1, -4.08}

Here we need to convert the numbers into decimal for to arrange it,

First, we have to convert the value -415% into decimal,

=> -415%

=> -415/100

=> -4.15

Next, √17 is equal to,

=> -√17

=> -4.12

How we have to arrange them in order,

=> { -4.15< -4.12 < -4.1 < -4.08}

Which is equal to,

=> {-415% < -√17 < -4.1 < -4.08}

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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The solution of the system of equations are x = 7 and y = 77

Given data

y = 9x + 14

y = 6x + 35

solving using substitution method to solve the simultaneous equation we have

y = 9x + 14  equation 1

y = 6x + 35  equation 2

equating the both equations will give

9x + 14  = 6x + 35

9x - 6x = 35 - 14

3x = 21

x = 7

plugging x = 7 into equation 1

y = 9x + 14

y = 9 * 7 + 14

y = 63 + 14

y = 77

The solution of the system of equations are x = 7 and y = 77

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the photo is not loading ok this is your photo open this and see now that address now because you are so

The five number summary, based on the given box plot would be:

Minimum value is the left-most point or the left end of the left whisker of the box plot. In the box plot, the minimum value is 1. Q1 is the left edge of the box. It represents the value below which 25% of the data falls.

Median is the line inside the box that divides it into two parts. It represents the value below which 50% of the data falls, or the 50th percentile. The median is 7. Q3 is the right edge of the box. It represents the value below which 75% of the data falls. In your given summary, Q3 is 9.

Maximum value is the right-most point or the right end of the right whisker of the box plot.

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Answer:

You need to watch 18 movies

and both the plans will cost $99

Step-by-step explanation:

x= the amount of movies watched

y= total amount

The first plan equation: y = 5.50x

The second plan equation: y = 36 + 3.50x

You have to set both equations to equal each other

    Step 1:  5.50x = 36 + 3.50x

    Step 2: subtract 3.50x on both sides: 2x=36

    Step 3: isolate the x by dividing 2: x=18

Then plug the 18 in both equations

5.50(18)= 99

36 + 3.50(18)=99

Answer:

The correct answer is choice C.

Step-by-step explanation:

To find the area of the arrow, we must add together the areas of the rectangle and the triangle that make up the arrow.  The rectangle has a length of 10 inches and a width of 4 inches, and the triangle has a base of 8 inches and a height of 2 inches.  Using this information, we can plug numbers into the following formula:

Area of arrow = area of rectangle + area of triangle

Area of arrow = (10*4)+(1/2*8*2)

Area of arrow = 40 inches squared + 8 inches squared

Area of arrow = 48 inches squared

Therefore, the correct answer is option C, 48 square units (in this case, inches).

Hope this helps!

The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).

C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, we calculate the sample proportion:

Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324

Next, we need to calculate the margin of error.

Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:

Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)

Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.

Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015

Finally, we can construct the confidence interval:

Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)

Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).

Now, let's interpret the results.

The correct answer is:

C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.

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Answer:

Expression is; 29 - x = 16

I've attached an image showing the number line

Step-by-step explanation:

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

I've attached an image showing the number line

Answer:

26 2/5 feet

Step-by-step explanation:

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

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Answer:

Step-by-step explanation:

First, you have to find the combine like terms use the distributive property.

Distributive property:

Add the numbers from left to right.

\(\sf{9q^2+4q^2=13q^2}\)

\(\Longrightarrow \boxed{\sf{7p^2+13q^2-4p}}}\)

Therefore, the final answer is 7p²+13q²-4p.

I hope this helps, let me know if you have any questions.

Simplification of polynomials

Polynomials are mathematical expressions made up of many terms.

To simplify a polynomial as much as possible, we group all the terms like terms and rearrange them from lowest to highest power.

Since to solve this polynomial, we place the similar terms very well and add them, then

In this polynomial only 9q² + 4q² are like terms, so we add them.

Answer:

Step-by-step explanation:

Answer:

9pi/4 and 17pi/4

Step-by-step explanation:

Using the unit circle, we can easily find coterminal angles that coincide with a given angle. This includes across the y-axis and the x-axis, making sure to stay within the guidelines of [-2pi, 2pi]. The reference angle for 29pi/4 is pi/4. Coterminal angles are found my making a full rotation around the circle (by adding 2pi). In this case, make sure to have a common denominator before adding. These coterminal angles should not surpass -2pi or 2pi. pi/4+8pi/4=

9pi/4 +

8pi/4=17pi/4

. 9pi/4 and 17pi/4 are coterminal angles.

Answer:

12

Step-by-step explanation:

14/7 = 2

So, 6 x 2 = 12.

Answer:

p =12

Step-by-step explanation:

6:7

The second number is 14  so 14/7 =2

Multiply each part by 2

2*6 : 2*7

12 : 14

p =12

Answer:

21.63 m

Step-by-step explanation:

Given :

Hypotenus = 42 m

Base = 36 m

Hence, using Pythagoras rule :

Opposite = √hypotenus² - Adjacent²

Height = √42²-36²

Height = √1764 - 1296

Height = √468

= 21.63 m