Figure Q was rotated about the origin (0,0) by 270 degrees counterclockwise.

Answer:$728

Step-by-step explanation: 4 percent increase= 104% which is x1.04

=700*1.04  

Answer:

Step-by-step explanation:

prime factorization of 60= 2*2*3*5 = [tex]2^{2} * 3^{1} * 5^{1}[/tex]

prime factorization of 150 = 2*3*5*5 = [tex]2^{1} * 3^{1} * 5^{2}[/tex]

greatest (highest) common factor (divisor), calculated

HCF = 2*3*5 = 30

For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to

LCM = [tex]2^{2} * 3^{1} * 5^{2}[/tex]=300

Answer:

There are 17 chickens and 23 cows

Step-by-step explanation:

Assuming every chicken has 1 head and 2 legs and every cow has 1 head and 4 legs, let us set up a system of equations for this proble

Let
x = number of chickens
y = number of cows

x chickens will have x heads
y cows will have y heads

Total number of heads = x + y = 40

x chickens will have 2x legs
y cows will have 4y legs
Total legs = 2x + 4y = 126

We have two equations:

x + y = 40       (1)

2x + 4y = 126  (2)

Multiply: (1) x 2
=> 2(x + y) = 2(40)
=> 2x + 2y = 80  (3)

Subtract: (2) - (3)

2x + 4y - (2x + 2y) = 126 - 80

2x + 4y -2x - 2y = 46

4y - 2y = 46

2y = 46

y = 23

Since y = 23 and x + y = 40
x + 23 = 40
x = 40 - 23 = 17

There are 17 chickens and 23 cows

Answer:

y = 4x + 3

Step-by-step explanation:

See picture below :)

The function graphed above is:

Increasing on interval: (-3 0.5),

Decreasing on interval(s): (-∞ -3) and (0.5 ∞)

What is decreasing and increasing interval?

Real number intervals with growing and decreasing real-valued functions are referred to as increasing and decreasing intervals.

We apply the first-order derivative test to examine the sign of the derivative in each interval and identify the growing and decreasing intervals.

For the graph attached, the decreasing interval is

from negative infinity to -3 and

0.5 to positive infinity

While the increasing interval is from -3 to 0.5

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The area of the triangular sail in the sail model is 42 square inches.

The area of a triangular sail is given by the formula:

Area = (1/2)bh

where b is the length of the base and h is the height.

Substituting b = 12 inches and h = 7 inches, we get:

Area = (1/2)(12 inches)(7 inches) = 42 square inches

Therefore, the area of the triangular sail in the sail model is 42 square inches.

The area of a triangle is given by the formula:

Area = (1/2) * base * height

where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.

To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.

Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.

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Answer:

24

Step-by-step explanation:

N/A

Answer:

x = -2

Step-by-step explanation:

The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).

Therefore, the equation of the line is simple:

x = -2

This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.

Answer:

Step-by-step explanation:

The equation of the line that models the cost of renting a kayak in slope-intercept form is: y = 5x + 10

The slope and y-intercept of the line that predicts the price of renting a kayak must be identified in order to formulate the equation for the line.

We can observe from the provided graph that the line traverses points (0, 10) and (6, 40). We may determine the slope of the line using these two points:

Slope = (Y Change/X Change) = (40 - 10)/(6 - 0) = 30/6 = 5

The equation of a line can also be expressed in the slope-intercept form, which is as follows:

y = mx + b

where m denotes the line's slope and b its y-intercept.

The slope of the line is previously known to be 5. One of the points the line passes through can be used to determine the y-intercept, for instance (0, 10). When we enter these numbers into the equation, we obtain:

10 = 5(0) + b

If we simplify, we get:

b = 10

Thus, the slope-intercept form equation of the line that represents the cost of renting a kayak is as follows:

y = 5x + 10

where x represents the duration of the kayak rental and y represents the entire cost.

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Answer: 3.14 ft

Step-by-step explanation:

★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet

★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet

Hence , the circumference is 3.14 ft.  

Answer:

Step-by-step explanation:

To determine which pairs satisfy the equation 2y - 8x = 6, we need to find values of x and y that make the equation true. One way to do this is to solve for y in terms of x:

2y - 8x = 6

2y = 8x + 6

y = 4x + 3

Now we can substitute different values of x into this equation and see what values of y we get. For example:

When x = 0, y = 3

When x = 1, y = 7

When x = -1, y = -1

When x = 2, y = 11/2

When x = -2, y = -5

So the pairs that satisfy the equation 2y - 8x = 6 are:

(0, 3), (1, 7), (-1, -1), (2, 11/2), (-2, -5)

In each of these pairs, when we substitute the values of x and y into the equation, we get a true statement

The solution is, the length of MP = 9.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

from the given figure we get,

MPN is a right angled triangle,

by using Pythagorean theorem, we get,

here, height = 12

hypotenuse = 15

so, base = MP

              = √15²  - 12²

              =√81

              =9

Hence, The solution is, the length of MP = 9.

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Answer:

f = 648

Step-by-step explanation:

[tex]\frac{f}{24} =27[/tex]

Multiply both sides by 24

[tex]f=648[/tex]

a. The exact value of tan(cos⁻¹(-16/19)) in simplified radical form is -3/16.

b. sin⁻¹(tan(2π/3)) is undefined and does not have an answer.

a. We know that cos(cos⁻¹(x)) = x and hence cos(cos⁻¹(-16/19)) = -16/19.

Let θ = cos⁻¹(-16/19), then we have

cos(θ) = -16/19 and

sin(θ) = √(1 - cos²(θ))

= √(1 - (16/19)²)

= 3/19 (using the Pythagorean identity).

Now, we can use the identity tan(θ) = sin(θ)/cos(θ) to find the value of tan(cos⁻¹(-16/19)):

tan(cos⁻¹(-16/19))

= sin(θ)/cos(θ)

= (3/19) / (-16/19)

= -3/16.

Therefore, the exact value of tan(cos⁻¹(-16/19)) is -3/16 in simplified radical form.

b. The range of the function tan(x) is (-∞, ∞), which means that it can take any value. However, the range of the function sin⁻¹(x) is [-π/2, π/2], which means that it can only take values between -π/2 and π/2. In particular, sin⁻¹(x) is not defined for |x| > 1, since there is no angle whose sine is greater than 1 or less than -1.

Let's consider sin⁻¹(tan(2π/3)). We know that tan(2π/3) is undefined, since the tangent function has vertical asymptotes at odd multiples of π/2 (including 2π/3).

Therefore, sin⁻¹(tan(2π/3)) is also undefined and does not have an answer.

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Let's call the position of the plane "P", and the positions of clearing A and clearing B "A" and "B", respectively. We want to find the distance from the plane to clearing A.

First, draw a diagram. The angle of depression to clearing A means that the line from the plane to clearing A makes a 32 degree angle with the horizontal. Similarly, the angle of depression to clearing B means that the line from the plane to clearing B makes a 56 degree angle with the horizontal. We know that the distance between clearings A and B is 5.7 km.

Now, we can use trigonometry to find the distance from the plane to clearing A. Let's call this distance "d". We can set up the following equation:

tan(32) = d/x

where x is the horizontal distance from the plane to clearing A. We can rearrange this equation to solve for d:

d = x tan(32)

Similarly, we can set up an equation for the distance from the plane to clearing B:

tan(56) = (x + 5.7) / d

We can rearrange this equation to solve for d:

d = (x + 5.7) / tan(56)

Now we can set the two expressions for d equal to each other and solve for x:

x tan(32) = (x + 5.7) / tan(56)

x tan(32) tan(56) = x + 5.7

x (0.6561) = x + 5.7

0.6561 x = x + 5.7

-0.3439 x = 5.7

x = -5.7 / 0.3439

x ≈ -16.57

Since the distance from the plane to clearing A is a positive distance, we can ignore the negative solution. Therefore, the distance from the plane to clearing A is approximately:

d = x tan(32) ≈ (-16.57) tan(32) ≈ 9.18 km

Rounding this to the nearest hundredth of a kilometer gives:

d ≈ 9.18 km

Therefore, the distance from the plane to clearing A is approximately 9.18 km.

:)?

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Yes, it is a function.

The reason is that the values on each row all align in a manner that shows the graph is moving in a clear direction. This is consistent with the behavior expected from the standard function, with all of the values on each row being the same distance from the origin.

The age of Sadie is 6 years.

Two or more expressions with an Equal sign is called as Equation.

Let x be the age of Sadie

x+1 be the age of Guadalupe

The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.

x² +5(x+1)=71

x² +5x+5=71

x² +5x-66=0

Factor out the expression.

x²+11x-6x-66=0

x(x+11)-6(x+11)=0

(x-6)(x+11)=0

x=6 and x=-11

Hence, the age of Sadie is 6 years.

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The required measure of the unknown side in similar triangles is 4.

Similar triangles are two triangles that have the same shape but are not necessarily the same size. More specifically, two triangles are similar if their corresponding angles are congruent (i.e., have the same measure), and the corresponding sides are proportional (i.e., have the same ratio).

Here,
Two similar triangles are given in the figure,

Let the unknown side be x
For a similar triangle, the ratio of the corresponding sides are equal So,
a / 8 = 6 / 12
a = 8/2
a = 4

Thus, the required measure of the unknown side in similar triangles is 4.

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The possible measure of the side AB is 9.09 cm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The sum of all the interior angles in a triangle is 180°.

So, The measure of angle 'f' = 180° - (72 + 59)°.

f = 49°.

We also know the cosine rule for a triangle ABC is, cosA = (b² + c² - a²)/2bc.

cos49° = (49 + 144 - m²)/168.

110.22 = 193 - m².

m² = 82.78.

m = 9.09.

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Step-by-step explanation:

study by the University of London found that participants who multitasked during cognitive tasks, experienced an IQ score decline similar to those who have stayed up all night. Some of the multitasking men had their IQ drop 15 points, leaving them with the average IQ of an 8-year-old chil

Answer:

x = 13 or x = 1

Step-by-step explanation:

To solve the equation (x - 7)^2 = 36, we can take the square root of both sides:

(x - 7)^2 = 36

sqrt((x - 7)^2) = sqrt(36)

x - 7 = ±6

Solving for x, we get:

x - 7 = 6 or x - 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.

The correct calculation of the average is given as 0.2546

The average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.

The calculation of the average would be gotten by the number of hits / by the total bats that he had

This is given as

151 / 593

= 0.2546

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Function with the domain of [-3, 3] is f(x) = [tex]x^2[/tex]

A function is a mathematical formula that gives each input value in a set an individual output value. The domain and range are two sets that relate to one another in such a way that each element in the domain has a unique association with the elements in the range.

An equation or collection of rules that indicate how the output is determined depending on the input constitutes a function, which is often denoted by a symbol like f. The independent variable is the value of the inputs, and the dependent variable is the value of the outputs.

Here's an example of a function with the domain of [-3, 3]:

f(x) = [tex]x^2[/tex]

This function maps each value in the interval [-3, 3] to its square. For example, when x = -3, f(x) = [tex](-3)^2[/tex] = 9, and when x = 3, f(x) = [tex](3)^2[/tex] = 9. The graph of this function is a parabola that opens upward and has its vertex at the origin (0,0).

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The perimeter of a triangle is the sum of the lengths of its three sides.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.

The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.

The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.

In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.

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Answer:

Step-by-step explanation:

[tex]\frac{x+6}{x^2(x^2+2)} =\frac{A}{x} +\frac{B}{x^2} +\frac{Cx+D}{x^2+2} \\x+6=Ax(x^2+2)+B(x^2+2)+(Cx+D)x^2\\equating~co-efficients ~of~same~powers~of~x\\0=A+C (of~x^3)\\0=B+D (of~x^2)\\1=2A (of~x)\\A=1/2\\6=2B (constant~term)\\B=6/2=3\\C=-A=-1/2\\D=-B=-3\\\frac{x+6}{x^2(x^2+2)} =\frac{1}{2x} +\frac{-3}{x^2} +\frac{-\frac{1}{2} x-3}{x^2+2}[/tex]

Answer:

w = 105° because 180 - (45 + 60) = 75 and 180 - 75 = 105.

Step-by-step explanation:

To find w, we first need to find z.

We can find z by setting up an equation. As we know, all angles in a triangle will add up to 180, we can say that z + 45 + 60 = 180.

We can also rewrite this as 180 - 45 - 60 = z, or 180 - (45 + 60) = z.

Solving this, we get z = 75.

We can also see that w and z are supplementary angles, meaning they will add up to 180.

Therefore, we can come to the conclusion that w + 75 = 180, or 180 - 75 = w.

Solving this we get:

w = 105

Therefore, w = 105°.

Answer:

they are

Step-by-step explanation:

divide 12*4=3

9*3=3

same ratio

Therefore , the solution of the given problem of equation  comes out to be 454 adult tickets and 733 student tickets were sold.

The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. Despite the fact that the previous line represents distinct components, the phrase "math equation blending several variables" is frequently used to describe it. In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b, usually known as mx+b, presents an easy-to-understand set of equations.

Here,

Let x be the number of adult tickets sold, and y be the number of student tickets sold.

The total number of tickets sold is 1,187: x + y = 1187.

The total amount of money collected is $3,003: 5x + 1y = 3003.

We can use the first equation to solve for x in terms of y: x = 1187 - y.

Substituting this expression for x into the second equation, we get:

5(1187 - y) + y = 3003

Simplifying and solving for y, we get:

5935 - 4y = 3003

-4y = -2932

y = 733

So 733 student tickets were sold. To find the number of adult tickets sold, we can use either of the original equations. Let's use x + y = 1187:

x + 733 = 1187

x = 454

So 454 adult tickets were sold.

Therefore, 454 adult tickets and 733 student tickets were sold.

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The function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

What are functions?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.

Given a function as follows:

[tex]y = -\sqrt[3]{11+8x}[/tex]

Consider two functions, f(x) and g(x).

Let f(x) = -∛x

g(x) = 11+8x

Then f(g(x) = f(11+8x) = [tex]-\sqrt[3]{11+8x}[/tex]

Therefore the function  [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) =  -∛x and g(x) = 11+8x.

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