Mr. Edwards is 3 times as old as his daughter. The sum of their ages is 80. How old was Mr. Edwards when his daughter was born?

The slope of the line y = -2x + 7 is -2

So, any line paralell to this line, will have the same slope (-2)

Answer: -2

Answer:

B) x <= -3

Step-by-step explanation:

B is the only answer that shows x being less than -3.

all of the other answers show x being greater than -3.

Answer:

y= 1/6x + 8

Step-by-step explanation:

\(\text{Given that,}\\\\x -6y = -48 \\\\\implies x +48 = 6y\\\\\implies y =\dfrac{x +48}6\\\\\implies y =\dfrac x6 + \dfrac{48} 6\\\\\implies y = \dfrac 16 x + 8\\\\\text{This is the slope-intercept form of the given equation(y =mx +b)}.\)

Answer:

6x -4

Step-by-step explanation:

(4x-5)+(2x+1)

Combine like terms

4x+2x   -5 +1

6x -4

Answer:

6x + 10

Step-by-step explanation:

3x + 5 + 3x + 5

6x + 10

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answer:

c.

Step-by-step explanation:

From the last row in the matrix z = 1.

From the second row:

y + 5z = -4

y = -4 -5(1) = -9.

From the first row:

x + -1 = -3

x = - 3 + 1

x = -2.

Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.

In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.

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Answer:

6o×40=2400

area 1/4=2400÷4=600

area 1/6=600÷6=100

(d)=100 ft2

Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.

An algorithm in math is a procedure, a description of a set of steps that can be used to solve a mathematical computation.

Now,

Hence, Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.

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Answer:

16

Step-by-step explanation:

The location of the values square root of 11, square root of 8, and twenty two ninths on the number line is illustrated below.

It should be noted that a number line simply means a straight line that serves as an abstraction for real numbers.

As square root of 12 will be 3.4641.

The square root of 15 is 3.872 and twenty two ninths on the number line will be around 20.22.

So, we can conclude that Point A is twenty-two ninths, point B is square root of 12, and point C is square root of 15.

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Given:

Vertex: (-3, 3)

Focus: (-3, 2)

Let's find the distance from the point (x, y) to the focus of the parabola and the directrix.

To find the distance, apply the distance formula:

Thus, we have:

Distance from (x, y) to the focus:

Where:

(x1, y1) ==> (x, y)

(x2, y2) ==> (-3, 2)

Thus, we have:

Therefore, the distance from the point (x, y) to the focus is:

• The distance from the point to the directrix.

From the graph, the directrix is:

y = 4

Now, to find the distance, subtract the y-coordinate of the point from y = 4.

The distance is the absolute value of the result.

Thus, we have:

ANSWER:

Distance from the point to the focus:

Distance from the point to directrix:

Answer:

Yes I will help

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the curves y = 5/6\(x^{2}\) and y = 11/6 - \(x^{2}\)about the x-axis is (242/15)π cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. First, we need to determine the points of intersection between the curves. Setting the equations equal to each other, we have:

5/6\(x^{2}\) = 11/6 - \(x^{2}\)

Multiplying both sides by 6, we get:

5\(x^{2}\) = 11 - 6\(x^{2}\)

Bringing all terms to one side, we have:

11\(x^{2}\) + 5\(x^{2}\) = 11

Simplifying,

16\(x^{2}\) = 11

Dividing both sides by 16,

\(x^{2}\) = 11/16

Taking the square root of both sides,

x = ±√(11/16)

Since we are rotating about the x-axis, we need to integrate from x = -√(11/16) to x = √(11/16) to obtain the volume.

Using the formula for the volume of a solid of revolution by cylindrical shells, the volume V is given by:

V = ∫[a,b] 2πx(f(x) - g(x)) dx

where f(x) and g(x) are the equations of the curves, and [a, b] is the interval of integration.

Substituting the given equations, we have:

V = ∫[-√(11/16), √(11/16)] 2πx((11/6) - \(x^{2}\) - (5/6)\(x^{2}\)) dx

Simplifying,

V = ∫[-√(11/16), √(11/16)] 2πx(11/6 - (11/6 + 5/6)\(x^{2}\)) dx

V = ∫[-√(11/16), √(11/16)] 2πx(11/6 - 16/6\(x^{2}\)) dx

V = ∫[-√(11/16), √(11/16)] 2πx(11 - 16\(x^{2}\))/6 dx

Integrating and evaluating the integral, we get:

V = [(242/15)π] cubic units

Therefore, the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is (242/15)π cubic units.

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The answer to the given question is the angular acceleration of the wheel is 0.7742 rad/s².

We can use the formula for rotational dynamics:

τ = Iα

where τ is the torque applied, I is the moment of inertia, and α is the angular acceleration.

Rearranging this equation, we get:

α = τ / I

Plugging in the given values, we have:

α = 48 Nm / 62 kg⋅m²

Simplifying, we get:

α = 0.7742 rad/s²

Rotational dynamics deals with the motion of objects that are rotating around an axis. The key concept in rotational dynamics is torque, which is a measure of how much a force can cause an object to rotate. The moment of inertia is another important quantity in rotational dynamics, and it describes an object's resistance to rotational motion. The moment of inertia depends on the distribution of mass around the axis of rotation. The angular acceleration of a rotating object is directly proportional to the torque applied and inversely proportional to the moment of inertia. Therefore, a greater torque or a smaller moment of inertia will result in a greater angular acceleration. These concepts are used in a variety of applications, from the motion of planets to the operation of engines and turbines.

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Given,

The statement is

"The square of any side of a triangle is equal to the sum of the squares of the other two sides minus the product of these sides and the cosine of their included angle."

Required

The law which define the above statement.

The law of cosine states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus the product of these sides and the cosine of their included angle.

Hence, option A is correct.

The total number of students that are on the team is e. 210 if the ratio of  freshmen to sophomores to juniors to seniors is 1:3:4:6

As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;

Freshmen = 1x

Sophomores = 3x

Juniors = 4x

Seniors = 6x

As the number of juniors on the team is 60, therefore;

4x = 60

To determine the value of x we divide both sides by 4;

4x/4 = 60/4

x = 15

Now the total number of students can be found by substituting the value of x;

1x + 3x + 4x + 6x

1(15) + 3(15) + 4(15) + 6(15) = 210

Hence, the total number of students on the team is 210.

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Answer: x = 8

Step-by-step explanation:

because x + 7 = 15, you can subtract 7 from both sides to get x = 8.

Hope it helps <3

Answer:

8

Step-by-step explanation:

x + 7 = 15

x = 15 - 7

x = 8

Thus, the value of x is 8

Types of quadrilaterals are parallelograms, rectangles, squares, rhombi, trapezoids, kites, and isosceles trapezoid.

A polygon having four sides and four angles are called a quadrilateral. Quadrilaterals come in a wide variety of forms, each with its own set of qualities and attributes.

Some of the most typical varieties are listed below:

Parallelogram - A quadrilateral has opposing sides that are equally long and parallel.

Rectangle - A parallelogram with all angles at 90 degrees is referred to as a rectangle.

Square - A rectangle with equally long sides.

Rhombus - A parallelogram with equal-length sides is referred to as a rhombus.

Trapezoid - A quadrilateral with just one set of diagonally opposed sides is called a trapezoid.

Kite - A quadrilateral has two sets of adjacent sides that are of equal length or a kite.

Isosceles trapezoid - An isosceles trapezoid is one with equally long non-parallel sides.

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Answer:

Answer is 28.

Step-by-step explanation:

and thanks for free points.

Answer: 28

Step-by-step explanation:

Answer:

(1, -6)

Step-by-step explanation:

After reflecting over y axis: (1, 6)

After reflecting (1, 6) over x axis: (1, -6)

I think you made a typo in your question. I think you meant "x-axis" instead of "r-axis"

Answer:

5

Step-by-step explanation:

49/9 = 5

Answer:

f(t) = 80 + 120 e^(-0.08 t)

Step-by step explanation:

The exponent is negative, so this is an example of exponential decay.  As t increases, the exponent becomes more and more negative.  So e^(-0.08 t) gets closer and closer to 0.  Meaning f(t) gets closer and closer to 80.

Using the law of syllogism, the conclusion is given as follows:

c. if a quadrilateral is a square, then it is a rectangle.

The Law of Syllogism is a logic axiom which states that if the conditional statements p -> q and q -> r are true, the conditional statement p -> r is also true, basically applying the transitive property.

In the context of this problem, the statements are given as follows:

Hence the conclusion is:

p -> r

Read as:

If p then r.

Replacing the statements, we have that:

If a quadrilateral is a square, then it is a rectangle.

Which means that option c is correct.

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To summarize, a perfectly egalitarian society has a Gini index of 0, and a perfectly totalitarian society has a Gini index of 1.

The Gini index (G) measures how much the income distribution differs from absolute equality.

On the other hand, a perfectly totalitarian society (where a single person receives all the income) will have a Gini index of 1. This means that there is a huge inequality between individuals, with the single person receiving all of the income.

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Answer:

m∠ZHS = 72°

Explanation:

We have the following diagram:

Now, the green angles are called corresponding angles. These angles have the same measure. So, ∠HEY and ∠ZHS are corresponding angles. It means that if the measure of ∠HEY is 72°, the measure of ∠ZHS is also 72°

Therefore, m∠ZHS = 72°

Answer:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

15

Step-by-step explanation:

Hope it is helpful....

Answer:

The Square root of 225 is 15