Does 5, square root of 50, 5 make a right triangle?

Answer:

The graph relates the temperature change

y

(in degrees Fahrenheit) to the altitude change

x

(in thousands of feet).

a. Is the relationship proportional? Explain.

b. Write an equation of the line. Interpret the slope.

c. You are at the bottom of a mountain where the temperature is

74\F

. The top of the mountain is 5500 feet above you.

What is the temperature at the top of the mountain?

Step-by-step explanation:

The quantities in a ratio usually expressed in the x : y are called the terms of ratio.

For instance ; given the the ratio of boy to girls in a class as 2 : 3. The values of x and y are 2 and 3 respectively.

Since they make up the values in the ratio expression, they are called the terms of ratio.

Therefore, the quantities x and y in a ratio are called terms of ratio.

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Answer:

Ans:

Step-by-step explanation:

AB+BC=AC

AB=BC

It is the centroid for both the endpoints

Value of the iterated integral is 64.

To make it clearer, I'll rewrite the integral using proper notation:

∫(from 0 to 2) ∫(from 0 to 2x) ∫(from 0 to y) 3xyz dz dy dx

To evaluate the iterated integral, follow these steps:

1. Evaluate the innermost integral with respect to z:

∫(from 0 to 2) ∫(from 0 to 2x) [(3xyz²)/2] (from 0 to y) dy dx

2. Plug in the limits of integration for z:

∫(from 0 to 2) ∫(from 0 to 2x) [(3xy³)/2 - 0] dy dx

3. Evaluate the next integral with respect to y:

∫(from 0 to 2) [(3x²y⁴)/8] (from 0 to 2x) dx

4. Plug in the limits of integration for y:

∫(from 0 to 2) [(3x²(2x)⁴)/8 - 0] dx

5. Simplify the expression:

∫(from 0 to 2) [(3x¹⁰)/8] dx

6. Evaluate the outermost integral with respect to x:

[(3x¹¹)/88] (from 0 to 2)

7. Plug in the limits of integration for x:

[(3(2)¹¹)/88 - (3(0)¹¹)/88]

8. Simplify the expression:

(3 * 2048) / 88 = 6144 / 88 = 64

So the value of the iterated integral is 64.

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The values for \(\theta (0 \le \theta \le 2\pi)\) that satisfy the equation are\(\dfrac{4\pi} {3}, \dfrac{5\pi} {3}\). The correct option is a.

The trigonometric function \(sin \theta\)  is a continuous and periodic function. The relationship between the sides and the angles of the right angle triangle are denoted by trigonometric functions.

The values for\(\theta (0 \le \theta \le 2\pi)\)  that satisfy the equation are calculated as:

\(3sin \theta = sin\theta \sqrt{3}\)

This can be solved as:

\(3sin \theta = sin\theta \sqrt{3}\)

Subtract \(sin \theta\) from both sides of the equation:

\(2sin\theta = -\sqrt{3}\)

Divide both sides by 2:

\(sin\theta = -\sqrt\dfrac{3}{2}}\)

From the unit circle or trigonometric ratios, we know that \(sin \theta\) that corresponds to two angles are \(\dfrac{\pi}{3}\) and \(\dfrac{5\pi}{3}\).

Therefore, the values for\(\theta (0 \le \theta \le 2\pi)\) that satisfy the equation are \(\dfrac{4\pi} {3}, \dfrac{5\pi} {3}\)

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The solution to the trigonometric equation 3sinθ = sinθ - √3 for values of theta between 0 and 2π is θ = π/3 , 5π/3 (option d).

First, let's start by consolidating the trigonometric equation on one side. So, 3sinθ - sinθ = √3. This simplifies to 2sinθ = √3.

Now, we can divide both sides by 2 to solve for sinθ, so sinθ = √3/2.

Looking at the unit circle, the values of theta (0≤θ≤2π) that make sinθ = √3/2 are π/3 and 5π/3. Therefore, the solution to the equation 3sinθ = sinθ - √3 within the given domain is θ = π/3 , 5π/3.

This corresponds to option (d) in the given multiple choice responses.

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Answer:

Ok, at the beginning the distance between the trains is 200km:

IPa(0s) - P(0s)I = 200km.

where Pa is the position of train A, and Pb is the position of train B.

Now, the speed of train A is:

Sa = 50km/h

Sb = 65km/h

Now, remember the relation:

Distance = Speed*time.

So, in one hour, the displacement of train A is:

Distance = 50km/h*1h = 50km

The displacement of train B is:

distance  = 65km/h*1h = 65km.

Now, if at the beginning train A is 200km ahead of train B, then we have:

Pa - Pb = (Pa(0s) + 50km) - (Pb(0s) + 65km)

= (Pa(0s)  - Pb(0s)) + (50km - 65km) = 200km - 15km = 185km.

Now, if train B was 200km ahead of train A, we have:

Pb - Pa = (Pb(0s) + 65km) - (Pa(0s) - 50km) =

(Pb(0s) - Pa(0s)) + (65km - 50km) = 200km + 15km = 215km

Answer:

\(2y - 8x = 3\)

Step-by-step explanation:

\(y - 4x = 9\)

\(2y - 8x = 18\)

So 2y - 8x = 3 is parallel to y - 4x = 9.

Answer:

7.81%

Step-by-step explanation:

First, you have to calculate the net earnings by calculating the 80% of the gross income:

gross income= $2,400

net earnings= $2,400*80%= $1,920

Then, you have to calculate the percentage that represents the utility bills spending from the net earnings by dividing $150 by the net earnings and multiplying for 100:

($150/$1,920)*100= 7.81%

According to this, the answer is that 7.81% of Terry's net earnings are spent on utilities.

Answer:

7.8

Step-by-step explanation:

Answer:

1. -2x + 6y - 4

2. -6y - 1

3. -10x - 2y - 7

4. -2x - 6

5. 2x - 12y - 4

Step-by-step explanation:

1. 2x+3y-6-4x+3y+2

(2x-4x) + (3y+3y) + (-6+2)

-2x + 6y - 4

2. 4x-3y-3-4x-3y+2

(4x-4x) + (-3y-3y) + (-3+2)

-6y - 1

3. -8x+2y-8-2x-4y+1

(-8x-2x) + (2y-4y) + (-8+1)

-10x - 2y - 7

4. -X+Y-3-X-Y-3

(-x-x) + (y-y) + (-3-3)

-2x - 6

5. 4x-8y-6-2x+4y+2

(4x-2x) + (-8y-4x) + (-6+2)

2x - 12y - 4

Answer:

137°

Step-by-step explanation:

Basically, its the reverse of question 1.

With angle x, you can find out that the opposite angle is 360 - 106 = 254°

the angle is twice the size of angle y as said in the corcle theorems.

254 divided by 2 = 137°

(please correct me if im wrong, i feel like im missing something)

If you draw all diagonals of a regular hexagon you have 5⋅6=30 possible triangles, but 5 of those are the same (the equilateral triangles) so we have 30−5=25 possible triangles.

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.

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The distance that the spring compresses is:

\(v\sqrt{m/k}\)

So, by  kinetic and elastic potential energy

Kinetic and Elastic Potential Energy

The kinetic energy of an object of mass m traveling at a speed v is:

\(K = 1/2 mv^{2}\)

The elastic potential energy of a spring of constant k that compresses a distance x is:

\(E = 1/2kx^{2}\)

The block of mass m is moving at a speed v when compresses a spring of constant k. The kinetic energy will eventually transform into elastic energy, but before that, both energies will be equal. It happens when:

\(1/2mv^{2} = 1/2kx^{2}\)

Simplifying:

\(mv^{2} = kx^{2}\)

Dividing by k:

\(x^{2} = mv^{2} / k\)

Taking square root:

\(x = \sqrt{mv^{2} /k\\\\\)

= v\(\sqrt{m/k}\)

The distance that the spring compresses is

\(v\sqrt{m/k}\)

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By concepts of functions, the inverse of the rational function f(x) = (2 · x + 1)/(x - 4) is f⁻¹(x) = (4 · x + 1)/(x - 2), whose value at being evaluated at x = 3 is equal to 13.

In this question we must determine the inverse of a given function and evaluate the resulting expression at a given value. First, we apply the following substitution:

f⁻¹(x) = x

x = f(x)

x = (2 · f⁻¹(x) + 1)/(f⁻¹(x) - 4)

Then we clear f⁻¹(x) within the expression:

x · (f⁻¹(x) - 4) = 2 · f⁻¹(x) + 1

x · f⁻¹(x) - 4 · x = 2 · f⁻¹(x) + 1

x · f⁻¹(x) - 2 · f⁻¹(x) = 4 · x + 1

f⁻¹(x) · (x - 2) = 4 · x + 1

f⁻¹(x) = (4 · x + 1)/(x - 2)

Lastly, we evaluate the function at x = 3:

f⁻¹(3) = (4 · 3 + 1)/(3 - 2)

f⁻¹(3) = 13

By concepts of functions, the inverse of the rational function f(x) = (2 · x + 1)/(x - 4) is f⁻¹(x) = (4 · x + 1)/(x - 2), whose value at being evaluated at x = 3 is equal to 13.

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No, g is not differentiable at x = 7. To explain why, let's examine the definition of differentiability at a point. A function is differentiable at a point if the derivative exists at that point. In other words, the function must have a unique tangent line at that point.

In this case, we have two different definitions for g depending on the value of x. For x ≤ 7, g(x) = 2x^10, and for x > 7, g(x) = -x + 11. At x = 7, the two definitions meet, but their derivatives do not match. The derivative of 2x^10 is 20x^9, and the derivative of -x + 11 is -1.

Since the derivatives of the two parts of the function do not coincide at x = 7, the function g is not differentiable at that point. The function has a "break" or discontinuity in its derivative at x = 7, indicating that the tangent line is not well-defined at that point. Therefore, we can conclude that g is not differentiable at x = 7.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85\)

Answer:

Step-by-step explanation:

Since T is in Quadrant II, sinT > 0 and cosT < 0.

cotT = -5/12

The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Answer:

900%

Step-by-step explanation:

The missing information for parts 4 and 5 will be the definition of midpoint and AH ≅ AH respectively.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that, ΔMAT is isosceles and point H is the midpoint of the MT.

The statement with their valid reasons is explained below,

As we know that in an isosceles triangle two sides are the same.As a result,

MA = TA

As H is the midpoint of the MT.

MH=TH

From the reflex property of congruence, AH≅AH

Thus, the missing information for parts 4 and 5 will be the definition of midpoint and AH ≅ AH respectively.

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Answer:

Step-by-step explanation:

Divide 27 by 0.3 to get your answer

Answer:

27.30 because your basically adding 30 as in cents.

Step-by-step explanation:

Katie will pay $1.10 for shipping and handling.

The cost of shipping refers to the amount of money that is charged for the transportation of goods or products from one location to another.

To calculate how much Katie will pay for shipping and handling, we first need to find 10% of $11.

To do this, we multiply $11 by 0.10 (which is the decimal equivalent of 10%).

$11 x 0.10 = $1.10

Therefore, Katie will pay $1.10 for shipping and handling on top of the $11 she paid for the set of spoons.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

7/8 or 1/2

Step-by-step explanation:

Because if the siblings ate 1/8 and u simplify 1/8 and u will get 1/2

A statement that best identifies the slope of an equation of a line of best fit for the data in the table and its meaning in the context of the problem is: C.) The slope is $2.24/pound, and it represents the cost for each pound of grapes.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (13.44 - 8.96)/(6 - 4)

Slope (m) = 4.48/2

Slope (m) = 2.24.

Based on the table, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.24.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

If A be a 5 × 4 matrix and let b and c be two vectors in \(R^5\) and we are told that Ax = b is inconsistent, then the number of solutions for A * x = c could be unique, infinite, or none, based on the given information.

Since A is a 5x4 matrix and b and c are vectors in \(R^5\), we know that A * x = b and A * x = c are systems of linear equations with x being a 4x1 vector.
We are given that A * x = b is inconsistent, which means it has no solutions. Now, let's analyze the system A * x = c.
1. If A * x = c has a unique solution, it would mean that there is a vector x for which the system A * x = b is inconsistent but A * x = c is consistent. This is possible.
2. If A * x = c has infinitely many solutions, it would mean that the system A * x = c has a free variable and there are infinitely many combinations of x that satisfy the equation. This is also possible.
3. If A * x = c has no solution (inconsistent), then both systems A * x = b and A * x = c would be inconsistent, which is also possible.
Therefore, the number of solutions for A * x = c could be unique, infinite, or none, based on the given information.

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the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Step 1

Remove full rotations of 360 degrees until the angle is between 0 and 360 degrees

Step 2

Hence, we find sin 120 using reference angles in the first quadrant

Therefore,

Answer sin 480 =(√3)/2

Answer:

Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice. If we roll n dice then there are 6n outcomes.

We can also consider the possible sums from rolling several dice. The smallest possible sum occurs when all of the dice are the smallest, or one each. This gives a sum of three when we are rolling three dice. The greatest number on a die is six, which means that the greatest possible sum occurs when all three dice are sixes. The sum of this situation is 18.

When n dice are rolled, the least possible sum is n and the greatest possible sum is 6n.

There is one possible way three dice can total 3

3 ways for 4

6 for 5

10 for 6

15 for 7

21 for 8

25 for 9

27 for 10

27 for 11

25 for 12

21 for 13

15 for 14

10 for 15

6 for 16

3 for 17

1 for 18