If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (Wºr) (x)
(-∞,0]
(-∞,2]
[0,∞)
[2,∞)

Answer:

(2,-1)

(-2,1)

(0,1)

Step-by-step explanation:

Let's plug in the points given and see which satisfy it (make it true).

2x+3y>=-1

Test (2,-1)

2(2)+3(-1)>=-1

4    + (-3)>=-1

           1>=-1  This is true 1 is greater than -1 so (2,-1) works!

Test (-6,0)

2(-6)+3(0)>=-1

-12   +  0  >=-1

         -12 >=-1 This is not true. -12 is not greater than -1.

Test (-2,1)

2(-2)+3(1)>=-1

-4   +  3 >=-1

         -1 >=-1  This is true. -1 does equal -1.

Test (0,1)

2(0)+3(1)>=-1

 0  +  3 >=-1

         3>=-1  This is true.  3 is greater than -1.

Test (0,-1)

2(0)+3(-1)>=-1

0   + (-3)>=-1

         -3>=-1  This is false.  -3 is not greater than -1.

To determine which ordered pairs are solutions to the inequality 2x + 3y ≥ -1, we need to substitute the x and y values from each ordered pair into the inequality and check if the inequality holds true.
Let's go through each ordered pair step by step:
1. Check the ordered pair (2, -1):
Substitute x = 2 and y = -1 into the inequality:
2(2) + 3(-1) ≥ -1
4 - 3 ≥ -1
1 ≥ -1
The inequality holds true, so (2, -1) is a solution.
2. Check the ordered pair (-6, 0):
We don't need to evaluate this one because it is not a solution according to the results we are considering.
3. Check the ordered pair (-2, 1):
Substitute x = -2 and y = 1 into the inequality:
2(-2) + 3(1) ≥ -1
-4 + 3 ≥ -1
-1 ≥ -1
The inequality holds true, so (-2, 1) is a solution.
4. Check the ordered pair (0, 1):
Substitute x = 0 and y = 1 into the inequality:
2(0) + 3(1) ≥ -1
0 + 3 ≥ -1
3 ≥ -1
The inequality holds true, so (0, 1) is a solution.
5. Check the ordered pair (0, -1):
We don't need to evaluate this one because it is not a solution according to the results we are considering.
Therefore, the ordered pairs that are solutions to the inequality 2x + 3y ≥ -1 are:
(2, −1)
(−2, 1)
(0, 1)

Answer:

We can find the answer to your question by using a computational tool or any similar software

The equation is

-8/2*y - 8 = 5/y + 4 -7y + 8/y^2 - 18

-4*y + (- 8-4 + 18) = 5/y  -7y + 8/y^2

-4*y + 6 = 5/y  -7y + 8/y^2

-4*y + 7y + 6 = 5/y  + 8/y^2

3y + 6 = 5/y  + 8/y^2

We multiply by y^2

3y^3 + 6y^2 = 5y  + 8

3y^3 + 6y^2 -5y - 8 = 0

See image below for result of the equation

Answer:

She need a interest rate of 6.25%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=16\ years\\ P=\£8,000\\ A=\£8,000*2=\£16,000\\r=?[/tex]

substitute in the formula above  and solve for r

[tex]16,000=8,000(1+16r)[/tex]

[tex]16r=2-1[/tex]

[tex]r=1/16[/tex]

[tex]r=0.0625[/tex]

Convert to percentage

[tex]r=0.0625*100=6.25\%[/tex]

Answer:

(1,1)

Step-by-step explanation:

We have the following system:

[tex]y=x^2-x+1[/tex]

[tex]y=x[/tex]

We are going to plug the 2nd equation into the 1st eqaution giving us:

[tex]x=x^2-x+1[/tex]

Now time to solve [tex]x=x^2-x+1[/tex].

[tex]x=x^2-x+1[/tex]

Subtract x on both sides:

[tex]0=x^2-2x+1[/tex]

Now this actually not too bad.  This a perfect square trinomial.  That is it is of the form [tex]a^2x^2+2abx+b^2[/tex] which equals [tex](ax+b)^2[/tex].

So solving [tex]0=x^2-2x+1[/tex] is equivalent to solving [tex]0=(x-1)^2[/tex]

In order to solve  [tex]0=(x-1)^2[/tex], we just need to know when x-1=0 which is at x=1.  I got by adding 1 on both sides of x-1=0

Now remember y=x means we have the solution (1,1).

Okay, I'm going to leave all of this algebra here.  I'm going to graph this without a graphing calculator.

[tex]y=x[/tex] is a line with slope 1 and y-intercept 0.

[tex]y=x^2-x+1[/tex] is a parabola.  The vertex isn't obvious to me right now without the algebra but I do know the parabola is open up because the coefficient of x^2 being positive.

So let's find the vertex.

I'm going to start with the x-coordinate which is -b/(2a).

Compare [tex]x^2-x+1[/tex] to [tex]ax^2+bx+c[/tex] and you should see that [tex]a=1,b=-1,c=1[/tex].

So [tex]-\frac{b}{2a}=-\frac{-1}{2(1)}=\frac{1}{2}[/tex]

So the vertex occurs when the x-coordinate is 1/2.

To find the correspond y-value just use the equation that relations x and y.

That is use [tex]x^2-x+1[/tex].

Replace x with 1/2.

[tex](\frac{1}{2})^2-(\frac{1}{2})+1[/tex]

[tex]\frac{1}{4}-\frac{1}{2}+1[/tex]

Find a common denominator.

[tex]\frac{1}{4}-\frac{2}{4}+\frac{4}{4}[/tex]

[tex]\frac{1-2+4}{4}[/tex]

[tex]\frac{3}{4}[/tex]

So the vertex is at (1/2,3/4) and the parabola is open up.

When you plug in 0 into [tex]x^2-x+1[/tex] you get [tex]0^2-0+1=1[/tex] so the ordered pair (0,1) is on the parabola.

Using symmetry about the line x=1/2 we know that (1,1) is also on this graph.

Let's use this information to produce a graph now.

Now our answer appears to be (1,1) in the graph.

We can check this answer by plugging in (1,1) into our system and see if both equations check out:

[tex]y=x[/tex]  gives us 1=1 which is true.  So we are good there.

[tex]y=x^2-x+1[/tex] gives us [tex]1=1^2-1+1[/tex] which is true. So we are good there.

The work for showing [tex]1=1^2-1+1[/tex].

[tex]1^2-1+1[/tex]

[tex]1-1+1[/tex]

[tex]0+1[/tex]

1

So the point (1,1) checks out for both of our equations which means it is a common point amongst the equations given.

Answer:

your slope is 3/4

Step-by-step explanation:

when finding the slope you find two points to go by.  

when you find the point for x you count back until you line up with your y point.  like on this graph you start at -3 and count back on the graph until you are in line with your next point which is 5.  

so -3 count back to 5

which is going to be 4

then you count how many spaces there is until you get to five which is 3 spaces so then you just put y over top of x and you have your slope.  

which on this graph your slope will be 3/4

Answer:

y=2.4

Step-by-step explanation:

9y-2+y=5y+10

(combine like terms)

10y-2=5y+10

(subtract 5y from both sides)

5y-2=10

(add 2 to both sides)

5y=12

(divide both sides by 5)

y=2.4

Answer:

y = 2 when x= 4

y=3 when x = 8

y = 4 when x=12 ....

Step-by-step explanation:

The given rule is:

y=1/4x+1

We have given the values of x. We have to find the values of y by substituting the values of x in the given rule:

y=1/4x+1

x=4

Substitute the value of x in the rule:

y=1/4 * 4+1

y=4/4 +1

By taking L.C.M of the denominator:

y= 4+4/4

y=8/4

Cancel out 8/4 by the table of 4

y= 2

y = 2 when x= 4

y=1/4x+1

x=8

Substitute the value in the given rule:

y= 1/4 * 8+1

y= 8/4 +1

By taking L.C.M we get,

y = 8+4/4

y= 12/4

Cancel out 12/4 by the table of 4

y= 3

y=3 when x = 8

Then,

y=1/4x+1

x= 12

Substitute the value in the given rule:

y = 1/4*12+1

y= 12/4+1

By taking L.C.M we get,

y=12+4/4

y=16/4

Cancel out 16/4 by the table of 4

y =4

y = 4 when x=12 ....

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x-----> the total number of guests

y -----> the amount of meat

we know that

The inequality that represent this situation is equal to

[tex]y\geq \frac{1}{3}x-2[/tex]

Note The inequality is "greater than or equal" because the given statement say "at least"

The solution of this inequality is the shaded area above the solid line [tex]y=\frac{1}{3}x-2[/tex]

The slope of the solid line is positive

The y-intercept of the solid line is -2  

The x-intercept of the solid line is 6

therefore

The graph in the attached figure

Remember that

The values of x an y cannot be a negative number

Answer:

4th graph

Step-by-step explanation:

Answer:

V = π(12²)(15) = 2,160π units³

The correct answer is D.

Answer:

-2

Step-by-step explanation:

6^2 = 36

5 x 6 = 30

36 - 30 - 8 = -2

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{y}=0.64\to\dfrac{x}{y}=\dfrac{64}{100}\\\\25<y<100\Rightarrow\dfrac{x}{y}=\dfrac{64:2}{100:2}\\\\\dfrac{x}{y}=\dfrac{32}{50}\to x=32[/tex]

Answer:

4/10 or 40%

Step-by-step explanation:

Their is 10 marbles in all and their is 4 black marbles so,

4/10 or 40%

Hope my answer has helped you and if not i'm sorry.

[tex]|\Omega|=10\\|A|=4\\\\P(A)=\dfrac{4}{10}=\dfrac{2}{5}=40\%[/tex]

Answer:

Mean Absolute Deviation = 3.

Step-by-step explanation:

The mean = (2 + 9 + 1 + 7 + 8 + 9) / 6

= 36/6

= 6.

Subtract  6 from each  number:

2 - 6 = -4 Absolute value = 4

9 - 6 = 3

1 - 6 = -5 Absolute value = 5

7 - 6 = 1

8 - 6 = 2

9 - 6 = 3

Total = 4 + 3 + 5 + 1 + 2 + 3 = 18

Mean Absolute Deviation = 18 / 6 = 3.

Answer:

B: 3

Step-by-step explanation:

First you will take the numbers and add them. The equation would be 2 + 9 + 1 + 7 + 8 + 9. That equals 36.

Then, you may divide that by 6 (how many numbers there were) and that is your mean (also 6).

Next, you find the how far each number is from the mean using absolutes. Those values are 4, 3, 5, 1, 2, and 3.

Finally, add those together to get 18, then divide by how many numbers there were (6) that to get the mean absolute deviation (3).

Hope this helped! :)

Answer:

-6 goes inside ( ) since G(-6)=10.

Step-by-step explanation:

It looks like you are looking for a number such that when you put in the ( ) of G(  ) you get 10 as a result.

So let's say you are trying to solve G(b)=10 for b.

Well G(x)=-3x-8 so G(b)=-3b-8.

I just replaced all the x's with b's to find G(b).

Now we are trying to solve G(b)=10 for b.

G(b)=10

-3b-8=10

Add 8 on both sides:

-3b=10+8

Simplify:

-3b=18

Divide both sides by -3:

  b=18/-3

Simplify:

  b=-6

So G(-6)=10!

Check:

-3(-6)-8

18-8

10

G(-6)=10 is confirmed.

-6 goes inside the G( )=10.

answer g(-6)=−3x−8=10

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is where all the points are in the form (positive, negative).

The center and radius of [tex](x-h)^2+(y-k)^2=r^2[/tex] is (h,k) and r, respectively.

Let's look at the centers and the radius of each of these choices:

A) This one has center (4,-2) and radius [tex]\sqrt{32} \approx 5.7[/tex].

If you add 5.7 to -2 you get a positive number and we needed it negative.

Not this choice; moving on.

B) This one has center (-3,2) and radius [tex]\sqrt{25}=5[/tex].

The center is not even in quadrant 4; moving on.

C) This one has a center (3,-4) and radius 1.

Add 1 to 3 you get 4.

Subtract 1 from 3 you get 2.

Those x's are positive so that looks good so far.

Add 1 to -4 you get -3.

Subtract 1 from -4 you get -5.

Those y's are negative so that looks good.

This circle is in quadrant 4 and doesn't go outside it.

D) This one has center (5,-7) and radius 4.

Add 4 to 5 you get 9.

Subtract 4 from 5 you get 1.

Positive x's is good.

Add 4 to -7 you get -3.

Subtract 4 from -7 you get -11.

Those are negative so that looks good.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

Quadrant IV: The fourth quadrant is in the bottom right corner of the plane. In this coordinate X has positive values and y has negative values.

According to the question

We have to find the circles lie completely within the fourth quadrant.

Observing the below graph, These two circle lie  completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex]

[tex](x-5)^{2} +(y+7)^{2} =16[/tex]

These circles lie bottom right corner of the plane.

From the given graphs below Option C and D lie completely within the fourth quadrant.

[tex](x-3)^{2} +(y+4)^{2} =1[/tex], [tex](x-5)^{2} +(y+7)^{2} =16[/tex] lie completely within the fourth quadrant.

Find out more information about fourth quadrant here

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Answer:

False

Step-by-step explanation:

In order to circum a circle about a triangle the circles center don't have to be placed at the triangle.

Final answer:

The statement regarding a vector forming a right angle triangle with its components is true, and the Pythagorean theorem can indeed be used to calculate the length of the resultant vector from two perpendicular vectors.

Explanation:

The initial question regarding the center of the circle to circumvent a triangle seems to be incomplete or incorrect. Instead, delving into vector mathematics, which is the relevant context provided, will yield a more informative response.

True or False: A vector can form the shape of a right angle triangle with its x and y components.
This statement is true. A vector in two dimensions has an x-component and a y-component. When these components are drawn from the tail of the vector, they form the legs of a right-angle triangle with the vector itself being the hypotenuse.

Furthermore, it is also true that the Pythagorean theorem can be used to calculate the length of the resultant vector when adding two vectors that are at right angles to each other. The formula used is a² + b² = c², where 'c' is the length of the resultant vector, and 'a' and 'b' are the magnitudes of the original vectors.

Answer:

No solution

Step-by-step explanation:

-3x + 3y = 4

-x + y = 3

Solve the equation for x:

Move the variable to the right side and change its sign

-x + y = 3

-x = 3 - y

Change the signs on both sides of the equation

-x = 3 - y

x = -3 + y

Substitute the given value of x into the equation -3x + 3y = 4

-3x + 3y = 4

x = -3 + y

-3(-3+y)+3y=4

Solve the equation for y

-3(-3+y)+3y=4

y = 0

There is no solution for y.

And since there's no solution for y, the system has no solution.

Answer:

[tex]\large\boxed{x=3\dfrac{3}{4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3}{4x}=\dfrac{1}{5}\qquad\text{cross multiply}\\\\(4x)(1)=(3)(5)\\\\4x=15\qquad\text{divide both sides by 4}\\\\x=\dfrac{15}{4}\\\\x=3\dfrac{3}{4}[/tex]

Answer:

its 4/15 because u will get the answer i got 100% for that

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (4, 2)

m = [tex]\frac{2-1}{4-2}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\huge\boxed{\frac{1}{2}}[/tex]

We can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope, where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.

Plug in the values. [tex]\frac{2-1}{4-2}[/tex]

Subtract. [tex]\frac{1}{2}[/tex]

Answer:

The correct answer is option a.  400

Step-by-step explanation:

Points to remember

Area of square = a²

Where 'a' is the side length of square

To find the area of square

It is given that, the side length of square is 20 inches.

Here a = 20 inches

Area = a²  

 = 20²

 = 400

Therefore the correct answer is option a.  400

Answer:

A) x² + 7x - 9

Step-by-step explanation:

Deduct\Add each like-term to arrive at your answer.

Answer:

C. 60,000

Step-by-step explanation:

Given

Three times as many bought tickets

24,000 * 3 = 72,000

one-sixth of them cancelled their tickets

72,000 * 1/6 = 12,000

Subtract

72,000 - 12,000 = 60,000

Answer

60,000 people are attending this week

This week, 60,000 fans are attending the football match.

To find the number of fans attending the football match this week, we need to start with the number of fans who bought tickets. This week, three times as many fans bought tickets as last week, so there were 3 * 24,000 = 72,000 fans who bought tickets. However, one-sixth of them cancelled their tickets, which means 1/6 * 72,000 = 12,000 fans cancelled. Therefore, the number of fans attending the match this week is 72,000 - 12,000 = 60,000.

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Answer:

[tex]-\frac{25}{3}[/tex]

Step-by-step explanation:

To isolate for x, start by multiplying both sides by 2.5.

[tex]\frac{25}{3} =-x[/tex]

Next, divide both sides by -1.

[tex]\frac{-25}{3} =x[/tex]

Answer:

x = -25/3

Step-by-step explanation:

10/3 = x / (-5/2)

Multiply each side by (-5/2) to isolate x

-(5/2) * 10/3 = -5/2 * (x / (-5/2))

-50/6 = x

Divide the top and bottom by 2 on the left hand side

-25/3 =x

Changing to a mixed number ( if required)

3 goes into 25  8 times ( 3*8=24)   with 1 left over(25-24=1)

x = -8 1/3

(9x^2 + 8x) – (2x^2 + 3x)

Subtract like terms:

9x^2 - 2x^2 = 7x^2

8x - 3x = 5x

The difference is 7x^2 + 5x

Answer:

2.5

Step-by-step explanation:

The positive factors of 12 are 1,2,3,4,6,12

The positive prime factors of 12 are 2 and 3.

(Primes are integer numbers only divisible by themselves and one.)

The arithmetic mean or average of 2 and 3 is (2+3)/2.

(2+3)/2=5/2=2.5

Answer:

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Step-by-step explanation:

The given complex number equation is:

[tex]\frac{1-2i}{2+i}+\frac{4-i}{3+2i}=x+yi[/tex]

We simplify the LHS and compare with the RHS

We collect LCD on the left to get:

[tex]\frac{(1-2i)(3+2i)+(4-i)(2+i)}{(2+i)(3+2i)}=x+yi[/tex]

[tex]\frac{3+2i-6i+4+8+4i-2i+1}{6+4i+3i-2}=x+yi[/tex]

Simplify to get:

[tex]\frac{16-2i}{4+7i}=x+yi[/tex]

Rationalize the LHS:

[tex]\frac{(16-2i)(4-7i)}{(4+7i)(4-7i)}=x+yi[/tex]

Expand the numerator using the distributive property and the denominator using difference  of two squares.

[tex]\frac{64-112i-8i-14}{16+49}=x+yi[/tex]

Simplify to get:

[tex]\frac{50-120i}{65}=x+yi[/tex]

[tex]\frac{10-24i}{13}=x+yi[/tex]

[tex]\frac{10}{13}-\frac{24}{13}i=x+yi[/tex]

By comparing real parts and imaginary parts; we have;

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

For this case we must multiply the following expression:

[tex](2x-6) (3x ^ 2-4x-5)[/tex]

Applying distributive property we have:

[tex](2x) (3x ^ 2) - (2x) (4x) - (2x) (5) - (6) (3x ^ 2) + (6) (4x) + (6) (5) =[/tex]

By definition of multiplication of powers of the same base, we have to put the same base and add the exponents:

[tex]6x ^ 3-8x ^ 2-10x-18x ^ 2 + 24x + 30 =[/tex]

Adding similar terms:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

[tex]6x ^ 3-26x ^ 2 + 14x + 30[/tex]

Answer:

Trapezoid- A.

Answer:

A. Trapezoid

Step-by-step explanation:

The proper name of this quadrilateral is a trapezoid.

The picture might look confusing because the trapezoid is upside down.

However, it still counts as a trapezoid.

Answer:

(0,5)

Step-by-step explanation:

-2x+6y=30

5x+2y=10

I'm going to use elimination.

I'm choosing this method because both equations are in the same form.

They are in the form ax+by=c.  

So in order to use elimination, I need one of my columns that contain the variables to contain opposites. Neither one of my columns with the variables have that.  Example -2x and 5x are not opposites and 6y and 2y are not opposite.

I'm going to multiply both sides of equation 2 by -3.  This will help me to achieve the opposites in a column.

So the system becomes:

-2x+6y=30

-15x-6y=-30

---------------------If we add the columns you will see that the variable y get's eliminated. Let's do that.

-2x+6y=30

-15x-6y=-30

-------------------Adding!

-17x+0y=0

-17x     =0

    x      =0

So using one of the equations (you choose; doesn't matter which one you pick) along with x=0, I'm going to find y.

I choose equation 2.

That is I choose 5x+2y=10 along with x=0 to find y.

5x  +2y=10 with x=0

5(0)+2y=10

0   +2y =10

       2y=10

         y=10/2

         y=5

The solution is (x,y)=(0,5).

Answer:

[tex] \sqrt{37} [/tex]

or 6.08276253