EFG and GFH are a linear pair, mEFG = 2n +17, and mGFH = 4n +31. What are mEFG and mGFH?​

Solution:

The question will be represented below as

To figure out the horizontal component (x), we will use the trigonometric ratio below

By substituting the values, we will have

Step 2:

To figure out the vertical component (y), we will use the trigonometric ratio below

By substituting the values, we will have

Hence,

The horizontal component is = 63.1 km/h

The vertical component is = 90.1 km/h

If the sum of two terms = 0, then the 2 terms must have the same value but different signs

That means x and y must have the same value but different signs

Look at the given answers

The 1st, 2nd, and 4th answers are wrong because the solution of this equation must have a value of x and a value of y together

In the 3rd answer

x = 1 and y = -1

Both have the same value and different signs

Then 3rd answer is a solution

In the 5th answer

x = -2 and y = -2

They have the same value with the same signs

The 5th answer is not a solution

In the last answer

x = 0 and y = 0

They have the same value but the zero has no sign

Then substitute them in the equation to check if it is solution or not

2(0)+2(0) = 0

0 + 0 = 0

The 2 sides of the equation are equal, then

The last answer is a solution

The answer is the 3rd and last answers

Step 1

From the question;

We are required to find how many months it will take him to read 90 books

Step 2

We will use the ratio below to solve the problem.

Answer; It will take Bobby 9months to read 90 booj

The proportional relationship graph that represents the table of values given would look like the graph shown below.

A proportional relationship graph always passes through the point of origin, (0, 0). The slope of the graph of a proportional relationship is also called the constant of proportionality, k, which can be calculated by using the coordinates of any point on the line, (x, y).

Constant of proportionality, k = y/x.

The equation for a proportional relationship is given as y = kx.

Given the table of values above which represents a proportional relationship, the graph of the table of values will go through the points below:

(0, 0)

(14, 7)

(6, 3)

(26, 13)

Therefore, the graph of the proportional relationship would look like the graph attached below which passes through:

B. (0, 0) and continues through the point (14, 7).

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The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b - 6.9.

Given expression:

3(−4.5b − 2.1) − (6b + 0.6)

To simplify the expression open the brackets and multiply the terms,

-13.5b − 6.3 − 6b - 0.6

Now, combine the like terms together and add them,placing a negative sign in front of the terms

-13.5b − 6b - 0.6 - 6.3

-19.5b - 6.9

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~ 399.3 $ / w

. The average for the 2 highest-salaried quarters:

(17 500 $ + 18 300 $ ) / 2 = 35 800 $ / 2 = 17 900$

. The 58% compensation representing the total amount Barry will be compensated:

17 900 * 58 / 100 = 10 382 $

. The weekly compensation:

10 382 $ / 26 week ~= 399.307692 $ / w

Distance Between Two Points

We are given two points on the graph attached to the question.

The red point has coordinates (7,3) and the origin is at (0,0)

I'll work out the graph to show the required distance.

The required distance (in the red drawing) is the hypotenuse of a right triangle of lengths 7 and 3, thus the distance is calculated as:

Calculating, we get d is approximately 7.62

Given the following table of values, k'(-1) is 3.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. finding a function's derivative, or rate of change, in mathematics. Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables.

Given Data

k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]

k(x) = -3h'(x) + 4 [tex]\frac{4x^{3}g(x)-x^{4}g'(x) }{gx^{2} }[/tex]

k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g'(-1)}{g(-1^{2}) }[/tex]

k'(-1) = -3(-1) + 4(0)

k(-1) = 3 + 0

k'(-1) = 3

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Answer:

The answer is the third one.

Step-by-step explanation:

They show the points plotted correctly.

If the half-life is 15 hours and there are 18 g, it means that after 15 hours,

18/2 grams would decay, leaving behind 18/2 grams

This means that 9 grams would be left.

After another 15 hours (making a total of 30 hours), 9/2 grams would decay leaving behind 9/2 grams (i.e 4.5 grams.

After another 15 hours (making a total of 45 hours), 4.5/2 grams would decay leaving behind 4.5/2 grams. Hence 2.25 grams are left

After another 15 hours (making a total of 60 hours), 2.25/2 grams would decay leaving behind 2.25/2 grams.

Hence after 60 hours, only 1.125 grams would be left

The mean (or average) is given as:

where xi is the value of each data and n is the total number of data. In this case we have:

Therefore the average is 1 hour 4 minutes and the answer is B.

7 + 3 × (2 × 8) is the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 × (2 × 8) + 7.

Given, 3 × (2 × 8) + 7

Following the application of the Commutative property of addition, which stipulates that altering the order of addends does not affect the result.

The expression will be,

7 + (2 × 8) × 3

Then, using the associative principle of multiplication, which states that how elements are arranged in a multiplication issue does not affect the product.

The expression will be,

7 + 3 × (2 × 8)

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the Given

We are asked to find the x-intercept of the linear equation. This can be seen below.

Explanation

To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.

From the graph, we can determine the x-intercept as

Answer: (2,0)

If function f(x) = √(x + 1) - 5 is translated three (3) units to the right and two (2) units up, the equation which represents g(x) is: D. f(x) = √(x - 2) - 3

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Translating f(x) = √(x + 1) - 5 three (3) units to the right and two (2) units up, we have:

f(x) = √(x + 1) - 5

f(x) = √(x + 1 - 3) - 5 + 2

f(x) = √(x - 2) - 3

In Geometry, g(x - 3) simply means shifting a graph three (3) units to the right while adding two (2) to the function simply means moving the graph up.

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 3 units to the right and 2 units up.

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For the constant speed, it take 5 minutes 3 seconds after you depart JBLM will you be the closest to Mt. Rainier.

Speed:

Speed means a rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM.

Here we need to find the time taken after you depart JBLM will you be the closest to Mt. Rainier for the constant speed of 800 km/hr.

Let us consider +x direction is east, and the -y direction is south.

We know that, JBLM is at the origin (0, 0). All distance units are presented in kilometers.

While we consider that, you are flying on line

165x + 152y = 0

We know that the slope of the line

ax + by = c

is given by -a/b, which suggests we can form the equation of a perpendicular line by swapping x and y coefficients and negating one of them.

Then, we get the equation as,

152x - 165y = c

That is perpendicular to the flight path.

Now we need to find c so that this is true at the coordinates of Mt. Rainier.

The perpendicular line through (56, -40) is

152x - 165y - (152(56) - 165(-40)) = 0

When we expand it then we get,

152x - 165y - (8512 + 6600 ) = 0

152x - 165y - 15112 = 0

We know that the distance in km from JBLM (0, 0) to this line is given by

So, when we apply the value of (x,y) as (0,0) then we get,

=> | 152(0) - 165(0) - 15112 |/√(152²+165²)

=> 15112/√50329

=> 15112/224.34

≈ 67.362

Therefore at the constant speed of  800 km/hr, you will have flown that 67. 362 km.

Then for one km you would take,

=> 62.076/800 hr ≈ 0.0842 hr

When we convert this then we get,

=> 0.0842 = 5 minutes 3 seconds.

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Step-by-step explanation:

so,

h(x) = f(x) × g(x)

h'(x) = f'(x) × g(x) + f(x)×g'(x)

with f(x) = -2x + 6

f'(x) = -2

so,

h'(-2) = -2 × g(-2) + (-2×-2 + 6) × g'(x) =

= -2 × -4 + 2 × 5 = 8 + 10 = 18

The value of g for the given conditions is obtained from linear equations as 2000.

A linear equation in one variable has only one variable of order 1. It has the formula ax + b = 0, where x is a variable. There is only one solution to this equation.

The initial amount is given as g.

400 pounds is added.

2 times 600 pounds is taken out.

The remaining amount is 1200 pounds.

Form a linear equation from the given constraints.

g+400-2(600)=1200

Solve the linear equation using basic mathematical functions.

g+400-1200=1200

g=2400-400

g=2000

So, the value of g is obtained using the linear equation as 2000.

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Here is the meaning of each statement:

The percentage of households that have the internet in 2007 is 61.7%

The percentage of households that have the internet in 1984 is k%.

The percentage of households that have the internet in 2017 is greater than the percentage of households that have the internet in 2000.

The sum of the percentage of households that have the internet in 1997 and 2001 is approximately equal to the percentage of households that have the internet in 2009.

Percentage is the fraction of an amount expressed as a number out of 100. In order to change a number to percentage, multiply the number by 100. The sign that represent percentage is %.

A function is an expression or rule that defines the relationship between the independent variable and the dependent variable. A function could be a linear function or an exponential function.

In this question,

x = is the number of years after 1980

and the independent variable is the percentage of households that use the internet after 1980.

H(27) = 61.7

1980 + 27 = 2007

This means that 61.7% households use the internet 27 years after 1980 or 61.7% households use the internet in 2007

H(4) = k

1980 + 4 = 1984

This means that k% households use the internet 4 years after 1980 or k% households use the internet in 194

H(37) > H(30)

This means that the percentage of households that use the internet 37 years after 1980 is greater than the percentage of households that use the internet 30 years after 1980

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Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph

The first thing we need to note here is the shape of the parabola.

This in the sense that if the parabola opens up or faces down

On the graph we can see that the parabola faces the positive x-direction

Generally, the equation of a quadratic graph is usually in the form below;

So by identifying the values of a,b and c, we can get the complete equation of the graph

The above form is called the standard form while the form we have in the options is referred to as the vertex form

The vertex form can be written as;

Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6

At this point, the value of x is 0

The vertex (h,k) represents the center point of the parabola

In the case of this question, the point is (-2,2)

so h =-2 and k is 2

What is left is to get a

we can obtain this from the value of y = 6 and x = 0

Thus;

6 = a(0-(-2))^2 + 2

6 = a(2)^2 + 2

6 = 4a + 2

4a = 6-2

4a = 4

a = 4/4 =1

So the equation in the vertex form is f(x) = (x + 2)^2 + 2

The exponential equation that represents the growth of the flying squirrels is F = 350 X 3^t.

An exponential equation can be described as an equation with exponents. The exponent is usually a variable. An exponential equation exhibits a compound growth rate.

The general form of exponential function is f(x) = [tex]e^{x}[/tex]

Where:

The population of the bird = present population x (1 + growth rate)^number of years

350 x (1 + 2)^t

F = 350 X 3^t

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Graph the inequality by finding the boundary line, then shading the appropriate area.

y < −x −3

The perimeter of a figure or shape is the distance around it.

The perimeter of the given path would be

9x + 10x^2 - x^3 + 4x^2 - 7x + 8 - x^2 + 9x + 12

We would collect like terms. It becomes

- x^3 + 10x^2 + 4x^2 - x^2 + 9x + 9x - 7x + 8 + 12

= - x^3 + 13x^2 + 11x + 20

The correct option is C

If we consider a, b and c all positive constants and b > 1, a exponential growth in general is represented by a function like:

In otherwise, a exponential decay can be represent by:

Now we can check whose functions are similar to one of these:

h(x) = 3x + 1.3 is a linear function, therefore, this is neither exponential growth or decay;

f = 3*(4.2^x) is an exponential growth;

y = (5/6)*(7^x) is an exponential growth;

T = 0.6*(1.3^x) is an exponential growth;

W(x) = (1/8)*[(3/5)^x] is an exponential decay, since in this case we have 3/5 < 1.

K = 4.2*(0.28^x) is an exponential deacay by the same argument.

ANSWER

EXPLANATION

We want to find the number of different combinations of colors possible if both spinners are spun at once.

To do this, we have to find the product of the number of colors on each spinner.

That is:

The answer is option B.

Solution:

Given the graphed polygon below:

To determine the coordinates of the vertices after reflection over the x-axis,

step 1: Give the coordinates of DEFG.

Thus, we have

step 2: Give the reflection formula, over the x-axis.

For reflection over the x-axis, we have

step 3: Give the coordinates after reflection over the x-axis.

From the formula in step 2,

we thus have

SOLUTION

The probability of an event occuring is found using the formula

There is only "one" 4, in a die, out of a total of "six" numbers labelled 1 to 6.

So, possible outcome = 1

Total possible outcome = 6, since the die was tossed once.

Probability becomes

Hence the answer is

(vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. Q. The number of zeroes at the end of a perfect square is always odd.

I hope it will be helpful for you.

The absolute value function y = 3|x + 1| + 9 is y ≥ (x + 4)/3 when x ≥ 0 and

y > - (x - 2)/3 when x < 0.

The absolute value function always outputs a positive value irrespective of the input.

Given we have to write the absolute value function as a piecewise function.

We know | x | = a implies x ≥ a and - x < a.

y = 3| x + 1 | + 9.

y - 9 = 3| x + 1|.

(y - 9)/3 = | x+ 1 |.

∴ (y - 9)/3 ≥ x + 1.

y/3 - 3 ≥ x + 1.

y/3 ≥ x + 4.

y ≥ (x + 4)/3.

OR

(y - 9)/3 = | x+ 1 |.

- (y - 9)/3 < x + 1.

-y/3 + 3 < x + 1.

-y/3 < x - 2.

-y < (x - 2)/3.

y > - (x - 2)/3.

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GIVEN:

We are told that a baseball fan is sitting at a point where his eyes are 350 feet vertical distance from the ground. When the fan is looking at the home plate the angle of depression is 30 degrees.

Required;

Find the horizontal distance from the fan to the home plate.

Step-by-step solution;

We begin by making a sketch of the scene to determine the shape and angles formed. This is shown below;

From the sketch above we can see the that the baseball fan has effectively formed a right triangle with the home plate from his position and the dimensions, that is, angles and sides, have been labeled.

We have the reference angle given as 60 degrees and the opposite is x (horizontal distance from the fan to home plate). That means the adjacent side is 350.

We can now use the following trig ratio;

We now cross multiply;

A second way to determine this distance is by using the triangle formed by the angle 30 degrees, in which case the horizontal distance will be the green line as shown in the sketch above. In that case, the vertical distance of 350 feet will be the opposite while the horizontal distance will be the adjacent while the reference angle will be 30 degrees.

For the second scenario, the straight line distance between both sets of eyes is 300 feet, and the angle of depression is 48 degrees. Note that the second fan is being watched at an angle of depression of 48 degrees which means he is at a lower level.

Now we are required to determine the vertical distance between the field level and the eyes of the second fan.

Let us begin by calculating the value of x as indicated in the triangle.

We shall use the trig ratio of;

Now we cross multiply;

Observe carefully that the distance calculated as x (222.9 ft) is the vertical distance between both fans. If we subtract this value from 350 feet we will now derive the vertical distance from the second fan to the field level.

Therefore,

ANSWER:

Gina's books has 349 fewer pages than Terri's, if Gina's books has 597 pages, Terri's books have 946 pages. In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.

In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.

The most commonly studied operations are the binary operations (i.e., the operations of arity 2), such as addition and multiplication, and the unary operations (i.e., the operations of arity 1), such as additive inverse and the multiplicative inverse. An operation of arity zero, or nullary operation, is constant. The mixed product is example of operation of arity 3, also called ternary operation.

Generally, arity is taken to be finite. However, the infinitary operations are sometimes considered, in which case "usual" operations of finite arity are called finitary operations.

A partial operation is defined similarly to operation, but with partial function in place of a function.

Gina's book = 597 pages

Terri's book= (597+349) pages

                   = 946 pages

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