Given this equation in slope-intercept form…
y = 2x + 5
Identify or solve for the following:
Slope
y-intercept
x-intercept
Independent variable
Dependent variable
Domain
Range

Answer:

There can be three solution sets of linear equalities. They can have one solution, or they can have no solutions or they can have infinitely many solutions. System of linear inequalities that have many or infinite solutions are called ” dependent”.

Step-by-step explanation:

Answer:

the answer is no solutions

Step-by-step explanation:

the solution is found at the point in which the two lines intersect.

in this case they do not intersect because the lines are parallel. if you rearrange  2x – y = 7   you will get y = 2x - 7.  the slope is 2x

the slope of the second equation is 2x as well. when slopes are the same they are parallel and therefore never cross.

For this case we have the following system of equations:

[tex]2x-y = 7\\y = 2x + 3[/tex]

To solve, we substitute the second equation in the first:

[tex]2x- (2x + 3) = 7\\2x-2x-3 = 7\\-3 = 7[/tex]

As noted, equality is not fulfilled. Thus, the system has no solution.

It can also be observed that the equations are:

[tex]y = 2x + 3\\y = 2x-7[/tex]

That is, they have the same slope, [tex]m = 2[/tex], so the lines are parallel. If the lines are parallel, they never intersect.

Answer:

The system has no solution

Answer:

1st, 3rd, and 6th

Step-by-step explanation:

Let's look at each statment...

1.) Correct

Explanation: 10 percent of the students at the school participate in soccer. If 140 is 10% of the number of students at the school, there is more than 140 students at this school.

2.) Incorrect

Explanation: We've already established that the # of students at the school is more than 140.

3.) Correct

Explanation: 10% as a decimal is 0.1 Divide 140 by 0.1 and you get 1,400. So, the total number of students is 1,400.

4.) Incorrect

Explanation: We've already established that the number of students is 1,400, not 290.

5.) Incorrect

Explanation: We've already established that the number of students is 1,400, not 150.

6.) Incorrect

Explanation: If the percent was a ratio, it would be 10:100 or 10/100. This is because a whole percent is 100% and the percent of students who play soccer is 10%.

7.) Correct

Explanation: We've already established that the ratio would be 10:100 or 10/100. Thus, this is correct.

I hope this helps! :)

Answer:

B) (-⁷/₂, ³/₂)

Step-by-step explanation:

Midpoint equation: ( (x₁ + x₂)/2, (y₁ + y₂)/2 ), when the two points are (x₁, y₁) and (x₂, y₂).

Plug in: ( ⁽⁻⁶ ⁺ ⁻¹⁾/₂, ⁽⁻² ⁺ ⁵⁾/₂ )

Add: (-⁷/₂, ³/₂)

Answer:

B

Step-by-step explanation:

Using the midpoint formula

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 6, - 2) and (x₂, y₂ ) = (- 1, 5)

midpoint = [ [tex]\frac{1}{2}[/tex](- 6 - 1), [tex]\frac{1}{2}[/tex](- 2 + 5)]

              = (- [tex]\frac{7}{2}[/tex], [tex]\frac{3}{2}[/tex] ) → B

Answer:

y=-4x

Step-by-step explanation:

You can graph it.. It might be easier for you to count than to use the formula for slope. We are counting from (0,0) to (2,-8)... I'm doing rise/run... I have to go down from (0,0) 8 units so the rise is -8 and the run is 2. So the slope is -8/2=-4.

We know the y-intercept is (0,0)... so the equation is y=-4x+0 or just y=-4x

Maybe you seen that this was proportional because it was a straight diagonal line going through the origin which we knew then that the line was already in the form of y=kx

Then you can look at the point (2,-8) and see what you need to do 2 to get -8 multiplication-wise.

2(-4)=-8

so

x(-4)=y

or

y=-4x

Answer:

Step-by-step explanation:

Use the half angle identity for cosine:

cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)

I'm going to figure out the sign part first for cos(x/2)...

so x is in third quadrant which puts x between 180 and 270

if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)

cosine is negative in the second quadrant

so we know that

cos(x/2)=-sqrt(1+cos(x))/sqrt(2)

Now we need cos(x)... since we are in the third quadrant cos(x) is negative...

If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.

So let's plug it in:

cos(x/2)=-sqrt(1+4/5)/sqrt(2)

No one likes compound fractions (mini-fractions inside bigger fractions)

Multiply top and bottom inside the square roots by 5.

cos(x/2)=-sqrt(5+4)/sqrt(10)

cos(x/2)=-sqrt(9)/sqrt(10)

cos(x/2)=-3/sqrt(10)

Rationalize the denominator

cos(x/2)=-3sqrt(10)/10

Answer:

supplementary angle sum = 180°

EOG + EOF = 180°

71° +EOF = 180°  

EOF = 180° -71°

EOF = 109°

Step-by-step explanation:

Answer:

m<EOF = 109 deg

Step-by-step explanation:

Definition of supplementary angles:

Two angles are supplementary if the sum of their measures is 180 degrees.

Angles EOF and EOG are supplementary, so the sum of their measures is 180 degrees.

m<EOF + m<EOG = 180

We are given the measure of <EOG: m<EOG = 71 deg.

We substitute that measure in our equation and solve the equation for m<EOF.

m<EOF + 71 deg = 180 deg

Subtract 71 deg from both sides.

m<EOF = 109 deg

Answer:

17.325 liters

Step-by-step explanation:

Given

Muriatic acid needed by one hot tub = 165 ml

Total hot tubs: 105

So, in order to find the total quantity of muriatic acid, the quantity for one tub will be multiplied by total tubs

So,

Total quantity of muriatic acid: 105 * 165

= 17325 ml

Since we have to find the answer in liters.

1 liter contains 1000 milliliters.

So,

for 17325 ml

= 17325 / 1000 = 17.325 liters

Hence, Apollo Spas needs 17.325 liters of muriatic acid for all of the hot tubs ..

Answer:

17.325 liters

Step-by-step explanation:

Number of Apollo Spas Services= 105 hot tubs

Each hot tub needs Muriatic acid= 165 ml

We have to find the total liters of muriatic  acid

Total number of liters required = Number of hots cups× 165 ml

Total number of liters required= 105×165 ml

Total number of liters required= 17,325 ml

1ml = 1/1000 liters

Total number of liters required= 17.325 liters

Hence, the correct answer is 17.325 liters

Answer:

D.

Step-by-step explanation:

The conclusion that can be drawn from the given statements is that " events E and F are independent".

Two events such as A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B. I.e.,

P(A ∩ B) = P(A)×P(B)

If A and B are two events in a sample space S, then the probability of event B after event A has occurred is called the conditional probability and it is denoted by P(B|A) = [P(A ∩ B)]/P(A).

Given that E and F are two events.

P(E|F) = 0.3

P(E) = 0.3

So, the conditional probability is written as,

P(E|F) = P(E ∩ F)/P(F)

If E and F are independent events, then the probability P(E ∩ F) = P(E) × P(F).

On substituting,

P(E|F) = P(E) × P(F)/P(F)

          = P(E)

Therefore, P(E|F) = P(E) = 0.3

Hence, events E and F are independent.

Learn more about independent events here:

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Answer:

The system has one solution

Step-by-step explanation:

we have

[tex]y=(0.5)^{x}[/tex] ----> equation A

[tex]y=6[/tex] -----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

There is only one  point of intersection

therefore

The system has one solution

see the attached figure

Answer: w = 4

Step-by-step explanation:

Subtract 1w from each side of the equation to get 5w = 20.

Divide both sides of the equation by 5 to get w = 4.

Hello!

Answer:

[tex]\boxed{w=4}\checkmark[/tex]

Answer should be positive sign.

Step-by-step explanation:

First, you subtract by w both sides of an equation.

[tex]6w-w=w+20-w[/tex]

Simplify.

[tex]5w=20[/tex]

Then, you divide by 5 both sides of an equation.

[tex]\frac{5w}{5}=\frac{20}{5}[/tex]

Finally, simplify and then solve.

[tex]20\div 5 = 4[/tex]

[tex]\boxed{w=4}[/tex], which is our final answer.

Hope this helps!

Thanks!

Have a nice day! :)

Answer:

Yes

Step-by-step explanation:

Any relation is said to be a function , if and only if

i) every element of first ordered pair is mapped with some element of second ordered pair.

ii) every element in first ordered pair is mapped to only singe element from the ordered pair.

Here in this case we see that there is some value of y for every value of x Hence first condition satisfies.

Also , none of the value of x is mapped or resulting into a two different values of y

Hence both the conditions are fulfilled , there for it is a function.

Answer:

7,680

Step-by-step explanation:

I did 12% x 5 years and got 60

Then I decreased 19,200 by 60% to get 7,680

Hope this helps!

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}1&26&7\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right] \times\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right]\\\\=\left[\begin{array}{ccc}(-1)(3)+(2)(2)+(4)(0)&(-1)(6)+(2)(4)+(4)(6)&(-1)(1)+(2)(0)+(4)(2)\end{array}\right]\\\\=\left[\begin{array}{ccc}-3+4+0&-6+8+24&-1+0+8\end{array}\right] \\\\=\left[\begin{array}{ccc}1&26&7\end{array}\right][/tex]

Option B [1 26 7] is the product of given matrix.

What is matrix multiplication formula?

Consider matrix A which is a × b matrix and matrix B, which is a b ×c matrix.

Then, matrix C = AB is defined as the A × B matrix.

An element in matrix C, Cxy is defined as Cxy = Ax1By1 +….. + AxbBby =

AxkBky  for x = 1…… a  and y= 1…….c

How to multiply given matrix?

[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right][/tex]×[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right][/tex]

=[ -1×3+2×2+4×0   -1×6+2×4+4×6   -1×1+2×0+4×2  ]

=[-3+4+0   -6+8+24   -1+0+8]

=[1  26 7 ]

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Answer:

B AND C

Step-by-step explanation:

Collinear Points: points that lie on the same line.

Coplanar Points: points that lie in the same plane.

Answer:

X=1

Step-by-step explanation:

Subtract by 2 from both sides of equation.

6x+2-2=9x-1-2

Simplify.

1-2=-3

6x=9x-3

Then subtract by 9x from both sides of equation.

6x-9x=9x-3-9x

Simplify.

-3x=-3

Divide by -3 from both sides of equation.

-3x/3=-3/-3

Simplify, to find the answer.

-3/-3=1

X=1 is the correct answer.

Answer:

x=1

Step-by-step explanation:

Answer:

Answer: A (first option)

Step-by-step explanation:

E2020

The angles formed by the diagonals and sides of the rhombus are

x + y = z.

Option A is correct.

As, When the diagonals of a rhombus are perpendicular, the angle z must be exactly 90 degrees (z=90).

Any triangle's interior angles must add up to 180 degrees.

Using Angle Sum Property

x + y + z = 180°

(x+y+z)=180°

x+y+z=180

As, z=90

x + y + 90 = 180

x + y = 90

So, the angles formed by diagonals is x + y = z.

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Answer:

C. 4x+5y

Step-by-step explanation:

Lets start by factorizing the expression 16x²+40xy+25y²

Consider the expression ax²+bx+c

During factorization, two numbers picked should add up to b while the product should be=ac

We find two numbers that when added give 40 and when multiplied = 16×25=400

These numbers are 20 and 20

Therefore the expression will be broken into:

16x²+20xy+20xy+25y²

4x(4x+5y)+5y(4x+5y)

(4x+5y)(4x+5y)

The expression is a perfect square.

Answer:

c

Step-by-step explanation:

a p e x

Option: C is the correct answer.

The ordered pair which will be found in the graph of the inverse function is:

C.  (0,-2) , (4,-1) , (8,0) , (12,1) , (16,2)    

We are given a table of values as:

       x                f(x)

     -2                 0

     -1                  4

      0                  8

      1                   12

      2                  16

i.e. the domain of the function is: {-2,-1,0,1,2}

and range of the function is: {0,4,8,12,16}

We now that for any function f(x) and it's inverse function the x and y value get interchanged i.e. the domain of the function f(x) becomes the range of its inverse function and the range of the function f(x) becomes the domain of the inverse function.

Hence, for any function with given ordered pair the inverse function will have ordered pair with x and y-value getting swapped.

i.e. if (-2,0) is an ordered pair of f(x)

then (0,-2) will be an ordered pair in the inverse function of f(x).

Hence, similarly all the ordered pairs could be obtained.

            The answer is:

             Option: C

Answer:

b and c

Step-by-step explanation:

i think its b and c

Answer:

A, D, and E

Step-by-step explanation:

They all have ten 0.1 square which equals 1.

Answer:

F(x)=4x and g(x) =3x

Step-by-step explanation:

We will have to check each pair of functions one by one

So,

For f(x)=3-4x and g(x)=16x-3

For composition we have to put g(x) in place of x in f(x)

(fog)(x)=3-4(g(x))

= 3-4(16x-3)

=3-64x+12

=-64x+15

So first pair doesn't give 12x.

Now for,

F(x)=6x2 and g(x)= 2/x

(fog)(x)= 6(g(x))^2

=6(2/x)^2

=6*(4/x^2)

=24/x^2

For the last pair:

F(x)=4x and g(x) =3x

(fog)(x)=4(g(x))

=4(3x)=12x

So for the last pair of functions (fog)(x) is 12x ..

Answer:

d

Step-by-step explanation:

on edge

Step-by-step explanation:

The answer to the question

Answer:

8,680 years old

Step-by-step explanation:

The fossil is 8,680 years old if 35% of its carbon-14 remains.

Your answer asks to find the median of the given numbers.

To find the median, you would need to sort of the numbers from least to greaters.

The given numbers we have:

12, 8, 5, 6, 1, 10, 13, 11

Now, just sort them from least to greatest.

1, 5, 6, 8, 10, 11, 12 ,13

What you would do next is eliminate the numbers on the side, one by one, in order to get your median.

[tex]1, 5, 6, 8, 10, 11, 12 ,13\\\\5, 6, 8, 10, 11, 12\\\\6, 8, 10, 11\\\\8, 10[/tex]

We ended up with two numbers, 8 and 10. Since we didn't end up with one number, we're going to have to add those numbers, and then divide it by two.

[tex]8+10=18\\\\18\div2=9[/tex]

You should get 9.

Therefore, the median would be 9.

B). 9 should be your FINAL answer

Answer:

The correct answer is option B.  9

Step-by-step explanation:

Median:

Median of a data set means that, the central data when arrange all the in ascending or descending order

It is given a data set ,

12, 8, 5, 6, 1, 10, 13, 11

To find the median of data set

Here there are 8 items, median is average of 4th and 5th terms

Ascending order,

1, 5, 6, 8, 10, 11, 12, 13

Median = (8 + 10)/2 = 18/2 = 9

The correct answer is option B.  9

First add 3 to both sides (what you do on one side you must do to the other). Since 3 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the right side and bring it over to the left side.

1 > s - 3

1 + 3 > s - 3 + 3

4 > s

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

4 > s OR s < 4

aka 4 is greater then s OR s is less then 4

This means that the graph will have an empty circle and the arrow will go to the left of 4. Look at image below.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

8/12+8/11 needs to be converted, so the denominator (the bottom number) is the same. To do that, you can multiply them, so 12 x 11= 132

Now since you multiplied the bottom, you need to multiply the top of each equation.

88/132+96/132=184/132 or as a decimal, 1.3939393939....

Or a faster way is to just insert into a calculator 8 divided by 12 then add 8 divided by 11.

Answer:

16/23

Step-by-step explanation:

I added 12 and 11 and then I added 8 and 8

The graph is attached.

To solve the problem, we need to look for the characteristics of the line.

We can see that:

- The line has a positive slope since the coefficient of the linear term is a positive number (2).

- Since the line has a positive slope, the line is increasing.

From the line we can calculate the axis intercepts:

For the x-axis intercept, making "y" equal to 0, we have:

[tex]y=2x+1\\\\0=2x+1\\\\x=-\frac{1}{2}=-0.5[/tex]

We have that the x-axis interception point is located at the point (-0.5,0)

For the y-axis intercept, making "x" equal to 0, we have:

[tex]y=2x+1\\\\y=2*0+1\\\\y=1[/tex]

We have that the y-axis interception point is located at the point (0,1)

Also, we have a "less" symbol for the inequality, meaning that the shade that represents the solution of the inequality is located under the pointed line.

The graph of the inequality is attached.

Have a nice day!

Answer:

(x + 5)=0 or (x - 17)=0

x=-5 or x=17

Discard the negative value

x=17 is considered.

Michael is 17yrs old

Answer:

Step-by-step explanation:

          Let x = Michael's age.

     Then x² = the square of his age

and x² - 12x = the square of his age – 12 times his age

and x² - 12x = 85

We must solve the quadratic for x.

1. Subtract 85 from each side.

x² - 12x - 85 = 0

2. Multiply the leading coefficient and the constant

1 × 85 = 85

3. Find two numbers that multiply to give -85 and add to give -12.

Possible pairs are 1, 85; 5, 17

Start with the numbers near the end of the list.

By trial and error, you will find that 5 and -17 work:

5 ×(-17) = -85  

and 5 -  17 = -12

4. Rewrite -12x as 5x -17x

x² + 5x – 17x - 85 =0

5. Factor by grouping the first two and the last two terms

x(x + 5) - 17(x + 5) =0

(x  + 5)(x - 17) = 0

6. Find the zeroe

[tex](x + 5)(x - 17) = 0\\\\\begin{array}{rlrl}x + 5 & = 0 &  x - 17 & =0\\x & = -5 & x & = 17\\\end{array}\\\text{Michael can't have a negative age, so } \boxed{\textbf{he is 17 years old.}}[/tex]

Check:

[tex]\begin{array}{rcl}(-17)^{2} + 12(-17) & = & 85\\289 - 204 & = & 85\\85 & = & 85\\\end{array}[/tex]

OK.

Answer:

a=1 or a=5/6

Step-by-step explanation:

I'm going to attempt to factor 6a^2-a-5

a=6

b=-1

c=-5

Find two numbers that multiply to be a*c and add to be b.

a*c=-30                                   =-6(5)

b=-1                                          =-6+5

So replace -a with -6a+5a in the expression we started with

6a^2-6a+5a-5

now we factor by grouping

6a(a-1)+5(a-1)

(a-1)(6a-5)

Now let's solve the equation:

(a-1)(6a-5)=0

So a=1 or a=5/6