What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point negative 1, negative 4.

Answer:

Given the data, the pool has a diameter of 20 feet, so, R=10ft.

The pool cover expands 12 inches beyond the pool, so, 12in.= 1 foot

Therefore, the radius of the pool cover will then be: 10+1= 11ft.

ANSWER A (pool cover)) r² π = 11² π = 121 π ft²

A.)= 121 π ft²

ANSWER B (rope)) l = 2 r π = 2 · 11 π = 22 π ft.

B.)=  22 π ft

Step-by-step explanation:

I got a 100% on it on founders edtell

Final answer:

The provided sequence is a geometric sequence that converges to 0 because its common ratio's absolute value is less than 1.

Explanation:

The sequence provided is 48, 12, 3, 3/4, suggesting a pattern where each term is divided by 4 to get the next term (this is a common ratio r = 1/4). This type of sequence is known as a geometric sequence, and to determine if it converges, we can apply the ratio test.

In a geometric sequence, successive terms approach zero if |r| < 1. Since the absolute value of the common ratio here is less than 1, the terms of the sequence will get progressively smaller and approach zero. Therefore, we can conclude that this geometric sequence converges, and the limit is 0.

Answer:

The answers are:

345 dollars

34500 cents

Step-by-step explanation:

In order to determine the answers, we have to know about the percentage notation. For any "x" value that is expressed as x%, it is the same that:

x%=[tex]\frac{x}{100}[/tex]

So, first we determine the value in dollars and then we determine the value in cents, where:

1 dollar=100 cents

In dollars $:

=5.75%*$6000

=[tex]\frac{5.75}{100}[/tex]*$6000

=$345.00

In cents c:

=5.75%*6000*100

=[tex]\frac{5.75}{100}[/tex]*6000*100

=34500.00 cents

Answer:

2400

Step-by-step explanation:

Given : The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each.

To Find: If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?

Solution:

No. of faces of first die = 6

No. of faces of second die = 4

No. of faces of third die = 10

No. of faces of fourth die = 10

Now we are supposed to find the the number of possible outcomes exist.

So, Number of possible outcomes if all the dice are thrown together :

= [tex]6 \times 4 \times 10 \times 10[/tex]

=[tex]2400[/tex]

Hence there are 2400 possible outcomes if all the dice are thrown together and their combination dictates a certain outcome of the game.

We are given the two functions:

f(x) = 2x + 7

g(x) = 6x – 5

Part A. Find (f + g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 2 x + 7 + 6 x – 5

(f + g)(x) = 8 x + 2

Part B. Find (f ⋅ g)(x)

(f ⋅ g)(x) = f(x) ⋅ g(x)

(f ⋅ g)(x) = (2 x + 7) (6 x – 5)

(f ⋅ g)(x) = 12 x^2 – 10 x + 42 x – 35

(f ⋅ g)(x) = 12 x^2 + 32 x – 35

Part C. Find f[g(x)]

f[g(x)] = 2 (6 x – 5) + 7

f[g(x)] = 12 x – 10 + 7

f[g(x)] = 12 x - 3

Sample Response:

Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

Answer:

(D)[tex]96^{\circ}=(arc)BC[/tex]

Step-by-step explanation:

It is given from the figure that m∠BAC=48° and arcAC=110°.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Now, using the above property, we have

[tex]m{\angle}BAC={\frac{1}{2}}(arc)BC[/tex]

Substituting the given values, we get

[tex]48^{\circ}=\frac{1}{2}(arc)BC[/tex]

[tex]96^{\circ}=(arc)BC[/tex]

Thus, the measure of the arc BC is 96 degrees.

Hence, option D is correct.

The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is [tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on and this can be determined by using the arithmetic operations.

Given :

Polynomial Equation -- [tex]2x^3+5x^2-8x-20=0[/tex]

The following steps can be used in order to determine the rational roots of the given polynomial equation:

Step 1 - Write the given polynomial equation.

[tex]2x^3+5x^2-8x-20=0[/tex]

Step 2 - The coefficient of [tex]x^3[/tex] is 2. So the factors of 2 are [tex]\pm[/tex]1, [tex]\pm[/tex]2.

Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are  [tex]\pm[/tex]1,  [tex]\pm[/tex]2,  [tex]\pm[/tex]5,  [tex]\pm[/tex]10,  [tex]\pm[/tex]20.

Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,

[tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on.

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Based on the labor force participation rate, the number of unemployed people is 1.5 million people.

The unemployed rate is based on the labor force participation rate and not the adult population.

The labor force is 60% and in absolute value this is:

= 60% x 50 million people

= 30 million people

The unemployment rate is 5% of this:

= 5% x 30 million

= 1.5 million people

In conclusion, there are 1.5 million unemployed people

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To use the linear combination method and addition to eliminate the y-terms, the second equation should be multiplied by 4.

An equation is like a relationship between two or more variables. It is expressed in equal to form. Equation of two variables looks like: ax+ by=c.

It is solved to find the value of variables.

The given equations are 7x+16y= -2 and 9x-4y=22 and we have to solve using linear combination method.

First we have to change  -4y to -16y because after we have to do addition so we will multiply the second equation by 4 which makes the equation as under:

36x-16y=88

Adding equation 1 and 2

7x+16y+36x-16y=-2+22

42x=20

x=20/42

x=10/21

Put the value of x in 7x+16y=-2

7(10/21)+16y=-2

10/3+16y=-2

16y=-2-10/3

16y=-16/3

y=-1/3

Hence to solve the equations we need to first multiply second equation by 4 which is option D.

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The given statement is a false statement.            

Collinear Points--

Two or more points are said to be collinear if they lie on a straight line.

Coplanar--

Set of points are said to be coplanar if they lie on the same plane.

If the set of points are collinear then we may get a line such that it will contain all these points and as we know that line always lie in a plane also there may be infinite number of planes which may contain the same line.

So, all the points on the line will also lie in the same plane.

Yes, collinear points are necessarily coplanar.

Answer:

Option B is correct.

(1 , -5) lies on the graph.

Step-by-step explanation:

Given the points (4,1) and (-2 , -11)

First find the linear equation for the given points.

Equation of line for two points [tex](x_1, y_1)[/tex] and  [tex](x_2, y_2)[/tex]

is given by:   [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]

Substitute the given points (4,1) and (-2 , -11)  in above equation to find the equation of line:

[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]

or

[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]

or

[tex]y-1=2(x-4)[/tex]

Using distributive property on RHS ( i.e,  [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )

we have;

y -1 = 2x-8

Add 1 to both sides of an equation;

y-1+1 = 2x-8+1

Simplify:

y = 2x -7

Therefore, the equation of line for the given point is: y =2x - 7     ....[1]

To find which points lies on the graph ( i.e, Line)

Substituting the given options in equation [1] we have;

A . (1,1)

Put x =1 and y =1

[tex]1 = 2\cdot 1 -7 = 2-7[/tex]

1 = -5 which is not true.

Similarly

B. for (1, -5)

[tex]-5= 2\cdot 1 -7 = 2-7[/tex]

-5 = -5 which is true.

C. for (1, 2)

[tex]2= 2\cdot 1 -7 = 2-7[/tex]

2 = -5 which is not true.

And

D.  For (1 , -7)

[tex]-7= 2\cdot 1 -7 = 2-7[/tex]

-7 = -5 which is also not true.

Therefore, the only point which lies on the  line graph [1] is; (1 ,-5)

Answer:

6^2 + x^2 = 9^2

36 + x^2 = 81

81-36= 45

square root of 45 is approximately 6.71 miles

Step-by-step explanation:

Using the theram theroy is very important to know the fulma and steps

In mathematics, an exclamation point represents a factorial, meaning the product of an integer and all the positive integers below it. For example, 5 factorial, or 5!, is 5 x 4 x 3 x 2 x 1 = 120. Unlike exponentials, factorials involve consecutive multiplication of integers.

In mathematics, the exclamation point is used to represent a factorial. Factorial indicates the product of an integer and all the positive integers below it. For instance, 5! would be 5 x 4 x 3 x 2 x 1 =  120. This calculation method is a significant concept especially in exponential arithmetic.

Contrary to exponential notation, factorials do not deal with the concept of powers or repeated multiplication of the same number. Instead, they focus on consecutive multiplication of descending positive integers. For example, 3! is evaluated as 3 x 2 x 1 = 6, instead of 3 x 3.

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