A box contains 7 plain pencils and 3 pens. A second box contains 3 color pencils and 3 crayons
One item from each box is chosen at random. What is the probability that a pen from the first
box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form.
​

The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.

The slope of a line given by

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.

The equation is y = -4x - 3

On comparing the equation with the slope-intercept form y = mx + c,

m = -4 and y-intercept c = -3.

Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.

The graph at option 3 has a line with two points (2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0-2}[/tex]

   = 4

Thus, it is not the same as the slope of the given equation.

The graph at option 4 has a line with two points (-2, 5) and (0, -3)

So, the slope is

m = [tex]\frac{-3-5}{0+2}[/tex]

   = -4

Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.

Therefore, the graph at option 4 is the correct representation of the given equation.

Learn more about the graph of an equation in a slope-intercept form here:

https://brainly.com/question/19440459

#SPJ2

Answer:

y - 1/3 = 3/4(x - 4)

Step-by-step explanation:

We know that the general equation of a line is the following:

y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.

Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

They tell us as data that:

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

Now the equation is:

[tex]y = \frac {3} {4} x + b[/tex]

We substitute the point to find "b":

[tex](4, \frac {1} {3})[/tex]

[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]

[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]

Finally the equation is:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

In point-slope form the equation is:

[tex]y- \frac {1} {3} = \frac {3} {4} (x-4)[/tex]

Answer:

[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]

Answer:

x^2=5-x

x^2+x-5=0

x=-1± √(1)^2-4(1)(-5)   /2(1)

-1± √21   /2

Step-by-step explanation:

Answer:

The answer will be A.  -1± √21   /2

Step-by-step explanation:

I hope it helps

Answer:

umm his friends each got 1/8

Step-by-step explanation:

hernando ate 2/8 meaning 8-2=6= 6/8

6/8 / 6 = 1/8

:D

I guess this what you want

After Hernando ate  [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with  [tex]\frac{1}{8}[/tex] of the pizza

Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6

First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate  [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:

[tex]1- \frac{1}{4} =\frac{4-1}{4} = \frac{3}{4}[/tex]

The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:

[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]

Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.

Answer:

[tex]{\huge \boxed{x=-2}[/tex]

Step-by-step explanation:

First you do is add and subtracting numbers from left to right.

-5+6=1

-9x+1=19

Then subtract by 1 from both sides of equation.

-9x+1-1=19-1

Simplify.

-9x=18

Divide by -9 from both sides of equation.

-9x/-9=18/-9

Simplify, to find the answer.

18÷-9=-2

x=-2 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

x=-2

Step-by-step explanation:

-9x -5+6=19

Combine like terms

-9x +1 = 19

Subtract 1 from each side

-9x +1-1 = 19-1

-9x = 18

Divide by -9

-9x/-9 = 18/-9

x = -2

Answer:

a + 2

Step-by-step explanation:

Given

[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator

= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]

Cancel the factor (a + 1) on the numerator/denominator

= a + 2 ← quotient

Alright (so what I did was type this into desmos and it was the exact same line but it was the other way around so it is) C

Changing from y = -3x + 5 to y = 2x + 5 would make the slope steeper.

The slope of the new graph would become steeper.

When changing from y = -3x + 5 to y = 2x + 5, the original slope of -3 increases to 2, making the new graph steeper.

Therefore, the correct answer is D. The slope of the new graph would become steeper.

Answer:

The circumference is:

[tex]C = 43.98\ ft[/tex]

The area is:

[tex]A=153.94\ ft^2[/tex]

Step-by-step explanation:

The circumference of a circle is calculated using the following formula

[tex]C = \pi d[/tex]

Where C is the circumference and d is the diameter of the circle.

In this case we know that

[tex]d = 14\ ft[/tex]

Therefore the circumference is:

[tex]C = \pi *14[/tex]

[tex]C = 43.98\ ft[/tex]

The area of a circle is calculated using the following formula

[tex]A=\pi(\frac{d}{2})^2[/tex]

Where d is the diameter of the circle.

Then

[tex]A=\pi(\frac{14}{2})^2[/tex]

[tex]A=\pi(7)^2[/tex]

[tex]A=49\pi[/tex]

[tex]A=153.94\ ft^2[/tex]

The circumference of the flower bed is approximately 43.96 feet and the area is approximately 153.86 square feet.

The gardener's circular flower bed has a diameter of 14 feet. The formula to calculate the circumference of a circle is C=πd where 'd' represents the diameter. Therefore, by substituting the given diameter, we get C = 3.14 * 14 = 43.96 feet approximately.

The area of the circle can be calculated by using the formula A=πr², where 'r' represents the radius of the circle. The radius is half of the diameter, that is 14/2 = 7 feet. So, A = 3.14 * 7² = 153.86 square feet approximately.

https://brainly.com/question/35150964

#SPJ12

Answer:

44.238

Step-by-step explanation:

50.441-6.203=44.238

Answer:C 13/2

Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2

Answer:

[tex]\frac{13}{2}[/tex]

Step-by-step explanation:

When you have a whole number, you gotta add a denominator, so just add 1 underneath:

[tex]\frac{13}{1}[/tex]

Then you have

[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]

Multiply straight across and you get

[tex]\frac{13}{2}[/tex]

f(x) is the total number of hours overall that he has worked out.

x would be the number of weeks he works out.

You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).

Answer:

In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.

Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.

It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.

Answer:

The correct answer option is C. (0, c).

Step-by-step explanation:

We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.

Z is a point on the middle of one of the sides of the trapezoid.

Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.

Z (0, c)

==============================================

Explanation:

Note how the point (a,0) mirrors over the y axis to land on (-a,0)

A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.

The x coordinate changes from positive to negative. The y coordinate stays the same.

The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)

Apply the midpoint formula to find where Z is located.

Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0

Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c

So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.

Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.

Answer:

(-1, 0)

Step-by-step explanation:

Jim, please use the symbol " ^ " to indicate exponentiation:

y = x^3 + 3x^2 – x – 3.  Thanks.

A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa).  To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.

Given y = x^3 + 3x^2 – x – 3,

          dy/dx = 3x^2 + 6x - 1

           d²y

          ------ = 6x + 6            and this is zero at x = -1.

           dx²

We can easily show that the 2nd derivative changes sign at x = -1.

Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).

Answer: (-2,3) and (0,-3)

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

When the graph of the given function is flipped over the line [tex]y=x[/tex], the coordinates will swap.

The mapping for a reflection in the line [tex]y=x[/tex] is [tex](x,y)\to(y,x)[/tex].

We can observe that one portion of the graph is in the first quadrant [tex](x,y)[/tex]. When we flip this part we will get [tex](y,x)[/tex], which is still in the first quadrant.

Also, when we flip the portion of the graph in the second quadrant (-x,y), we will obtain (y,-x), which is standing for all coordinates in the fourth quadrant.

The image is shown in the attachment.

Answer:

- (- 10)

Step-by-step explanation:

Point A is positioned at - 10 on the number line.

The opposite is the negative of the value

That is the opposite of - 10 is - (- 10)

1.

Cubic Polynomial--

A cubic polynomial is a polynomial of degree three.

2.

End behavior--

The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.

3.

Irreducible--

A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.

4.

Leading coefficient--

It is the coefficient of the highest degree term existing in the expression.

5.

Leading term--

It is the term with the highest degree.

6.

quartic polynomial-

A quadratic polynomial is a polynomial of degree 4.

7.

Zeros of polynomial--

The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.

Answer:

A and D

Step-by-step explanation:

The remainder after division is 8, that is the 8 at the end of 2 - 4 8

Given f(x) divided by (x + h)

Then if (x + h) is a factor the remainder = 0

Hence (x + 7) is not a factor since remainder is 8

and f(- h) = remainder

that is f(- 7) = 8 → D

A and D are the correct statements.

In option  A f(-7) is the remainder which gives the value 8.

So, option A is correct.

When we put x = 7 in the function it is coming 99

So, option B and C are wrong.

So options D is correct

So, option E is wrong.

Find more about "Division of functions" here:

https://brainly.com/question/25289437

#SPJ2

ANSWER

The system consists of parallel lines. Both lines have the same slope.

EXPLANATION.

The first equation is

[tex]y = \frac{1}{3} x - 4[/tex]

This equation is in the slope-intercept form.

The second equation is

[tex]3y - x = - 7[/tex]

We write this one too in slope-intercept form so that we can make comparison.

[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]

We can see that both equations have slope

[tex]m = \frac{1}{3} [/tex]

This means the two lines are parallel.

The two lines have different y-intercepts.

Two parallel lines with different y-intercepts will never meet.

The lines will never intersect.

Answer:

The true statements are:

- The system consists of parallel lines

- Both lines have the same slope

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   y = 1/3 x - 4 ⇒ (1)

   3y - x = -7 ⇒ (2)

- Lets put equation (1) in the form of equation (2)

∵ y = 1/3 x - 4 ⇒ multiply both sides by 3

∴ 3y = x - 12 ⇒ subtract x from both sides

∴ 3y - x = -12

∴ Equation (1) is 3y - x = -12

∵ Equation (2) is 3y - x = -7

∵ The coefficients of x and y in the two equation are equal

∵ The numerical terms in the two equations are not equal

∴ The equations have no solution because their lines are parallel

∵ The parallel lines have same slope

* The true statements are

- The system consists of parallel lines

- Both lines have the same slope

Answer:

C

Step-by-step explanation:

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]

Answer:

6.06 x [tex]10^{9}[/tex]

Step-by-step explanation:

(5.25 x [tex]10^{5}[/tex] ) / (8.7 x [tex]10^{-5}[/tex] )

= (5.25 x [tex]10^{5}[/tex] ) x( [tex]10^{5}[/tex] )/ (8.7 )

= (5.25 x [tex]10^{5 + 5}[/tex] )/ (8.7 )

= 0.606 x [tex]10^{10}[/tex]

= 6.06 x [tex]10^{9}[/tex]

Each line on the graph is one unit.

AB = 15 units long

Answer:

15 units

Step-by-step explanation:

Since A and B are along the same horizontal line, we count count the number of units to determine the distance

The horizontal distance from A to B is 15 units

y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

Two or more expressions with an Equal sign is called as Equation.

Given that Ryan throws a tennis ball straight up into the air.

The ball reaches its maximum height at 2 seconds.

The approximate height of the ball x seconds after being thrown is shown in the table.

We need to find the equation of the motion of the ball.

Let us take a point (0, 4) from the table.

The right equation is the point in which the equation satisfies.

y=-17(0)(0-4)

4=0

So y = –17(x)(x – 4) is false.

y = –16(x – 2)² + 68

4=-16(4)+68

The point (0, 4 ) satisfies the equation y = –16(x – 2)² + 68

Hence, y = –16(x – 2)² + 68 is the equation which models the motion of the ball.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ7

Answer:  84

Step-by-step explanation:

Set up a proportion as follows: [tex]\dfrac{\text{students that practice everyday}}{\text{total students}}[/tex]

[tex]\dfrac{7}{12}=\dfrac{x}{144}[/tex]

Cross multiply: 12x = 7 × 144

Divide by 12:         x = 7 × 12

Simplify:                x = 84

To find the area of a rhombus, multiply the two diagonals together then divide by 2.

Area = 20 *15 = 300 / 2 = 150 sq. units.

Power = Current *Voltage  

You already have the current, but not the voltage.  

But you are given resistance, and you know that  

Voltage=Current*Resistance  

Therefore  

V=I*R=4*12=48V  

So you have 48V  

Now you can figure out the Power  

P=I*V=4*48=192W  

Therefore you have 192W.

hope this helps

The total power in a circuit is 192W.

Power exists at the time rate of excess or absorbing energy. The power delivered or absorbed by an element exists as the product of the current flowing through the component and the voltage across the element. Power exists estimated in watts. If the power exists positive then it exists absorbed by the component and if it exists negative then it is supplied by the element.

Power = Current [tex]*[/tex] Voltage

We have the current, but not the voltage.

But you are given resistance, and you know that

Voltage = Current [tex]*[/tex] Resistance

Therefore,

[tex]V=I*R=4*12=48V[/tex]

So you have 48V

Thus, we get the Power

[tex]P=I*V=4*48=192W[/tex]

Therefore, the total power in a circuit is 192W.

To learn more about  power

https://brainly.com/question/20910042

#SPJ2

Slope formula: y2-y1/x2-x1

Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope

For this case we have by definition, the slope of a line can be found by the following formula:

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

Two points are needed through which the line passes.

According to the data we have:

[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]

Substituting we have:

[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]

ANswer:

The slope is [tex]\frac {15} {14}[/tex]

Answer:

about A+=+2000%281%2B+0.023%2F1%29%5E%281%2A18%29+=+2000%2A1.023%5E18= $3,011.56 thats my math

Step-by-step explanation:

Answer:

$3,698.50

Step-by-step explanation:

When making a compound interest rate this means that the interests generated are taken into consideration when creating new interests in the next period, now there are 4 quarterly periods on a year, this means there are 88 periods in the 22 years that the account will grow, you just have to do the math:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where n is the number of cycles per year and nt is the number of cycles over the years.

We just have to put the values into the formula:

[tex]A=500(1+\frac{.092}{4})^{22*4}[/tex]

[tex]A=500(1+\frac{.092}{4})^{88}[/tex]

[tex]A=$3,698.50[/tex]

Answer:

66

Step-by-step explanation:

We know x = -4. To solve, we just need to plug in -4 for x.

6 (-4 + 15) =

6 (11) =

66

Answer:

66

Step-by-step explanation:

x= -4  

6(x + 15)

Substitute x =-4 into the second equation

6(-4+15)

6(11)

66