Which can be the first step in finding the equation of the line that passes through the points 5,-4 and -1,8 in slope-intercept form?

Answer:

13. Let's say Jason's age is x, Omar's age is y and Henry's age is z. Then we have:y = 3x (Omar is three times as old as Jason) z = x + 5 (Henry is five years older than Jason) x + y + z = 80 (Their total age is 80) Now replace y and z in the last equation with the two other equations and you get: x + 3x + (x + 5)= 80 Calculate brackets: x + 3x + x + 5 = 80 Move 5 over and add up the x:  5x = 75 x = 75/5 = 15 So Jason is 15. Now we put x = 15 into the other equations and we get: Omar's age: y = 3*15 = 45 Henry's age: z = 15 + 5 = 20 So Omar is 25 years older than Henry.

14.

Let c = chickens and d = ducks, then:

c = 2d

c - 272 = 1/2 (d - 16)

We can rewrite the expression in terms of one variable, d:

2d - 272 = 1/2 (d - 16)

2d - 272 = 1/2d - 8

3/2d = 264

d = 176

c = 2 * 176 = 352

She had 352 chickens in the beginning.

15.

11-shirts

Answer:

-2

Step-by-step explanation:

6^2 = 36

5 x 6 = 30

36 - 30 - 8 = -2

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:

4.8cm ^3

Step-by-step explanation: just finished quiz.... good luck

Answer: (C) 4.8cm3

Just did it on edge

Answer:

V = π(12²)(15) = 2,160π units³

The correct answer is D.

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:

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:

[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

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:

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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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:

See explanation

Step-by-step explanation:

You have to graph the system of inequalities presented as

[tex]\left\{\begin{array}{l}y<4x-2\\y\ge -\frac{5}{2}x-2\end{array}\right.[/tex]

Part A:

1. Draw a dotted line [tex]y=4x-2[/tex] (dotted because the sign < is without notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:

[tex]0<4\cdot 0-2\\ \\0<-2[/tex]

Since this inequlity is false, the origin doesn't belong to the shaded region, so you have to shade that part which doesn't contain origin (red part in attached diagram).

2. Draw a solid line [tex]y=-\frac{5}{2}x-2[/tex] (solid because the sign ≥ is with notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:

[tex]0\ge -\frac{5}{2}\cdot 0-2\\ \\0\ge -2[/tex]

Since this inequlity is true, the origin belongs to the shaded region, so you have to shade that part which contains origin (blue part in attached diagram).

The intersection of these two regions is the solution area.

Part B:

Plot point (-2,-2). Since this point doesn't belong to the solution area, this is not a solution of the system of two inequalities. You can check it mathematically - substitute x=-2 and y=-2 into the system:

[tex]\left\{\begin{array}{l}-2<4\cdot (-2)-2\\-2\ge -\frac{5}{2}\cdot (-2)-2\end{array}\right.\Rightarrow \left\{\begin{array}{l}-2<-10\\-2\ge 3\end{array}\right.[/tex]

Both inequalities are false, so (-2,-2) doesn't belong to the solution area.

Answer:2/14 or 1/7

Step-by-step explanation:

Add the student together to get the number of students

10+4

14

Divide the girls by half

4/2

2

2/14 is your answer reduced is 1/7

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:

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:

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:

A) x² + 7x - 9

Step-by-step explanation:

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

Answer:

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

or 6.08276253

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:B

Step-by-step explanation:i just did it! c:

The situation that is most likely to have a constant rate of change is the length of a brick path compared with the number of rows of bricks. That is option B.

Rate of change of a variable is the change in its value over a defined period of time. But rate of change can be calculated if one variable increases and the other variable which it is compared with decreases.

But in a scenario where both the variables are not changing, a constant is reached. For example, the length of a brick path compared with the number of rows of

bricks.

The length of the brick path is constant which forms the number of the rows of the bricks which are equally constant.

Therefore, the situation that is most likely to have a constant rate of change is the length of a brick path compared with the number of rows of bricks.

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Answer:

D. 18 units

Step-by-step explanation:

This is because . . .

C = 2 * pi * r

Since r = 3 . . .

2 * 3 * 3.1415926 . . .

2 * 3 * 3 = 18 units

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For any questions, please comment!!

Answer: D . 18 units

Step-by-step explanation:

We know that the circumference of the circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

Given : The radius of  the circle = 3 units

Then , the circumference of the circle will be :-

[tex]C=2\pi (3)[/tex]

We know the the value of [tex]\pi =3.14[/tex], we estimate the value of  [tex]\pi =3[/tex]

[tex]C=2(3) (3)=18[/tex]

Hence, the the best estimate of the circumference of this circle is 18 units.

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.

[tex]-np-80<60\\\\-np<140\\\\n>-\dfrac{140}{p}[/tex]

Answer:

n > -140/p.

Step-by-step explanation:

-np - 80 < 60

-np  < 60 + 80

-n < 140/p

n > -140/p.

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:

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:

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:

(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:

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:

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