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:

x = 5/2

x = 2 1/2

x = 2.5

Step-by-step explanation:

3x - 1 - (x + 3) = 1

3x - 1 - x - 3 = 1

2x - 1 - 3 = 1

2x - 4 = 1

2x = 1 + 4

2x + 5

2x = 5

x = 5/2 → 2 1/2 → 2.5 ( can be written in any of these forms depending on what you need to do)

Hope this helped! :)

Answer:

Step-by-step explanation:

3x−1−(x+3)=1

First remove the bracket

That's

3x - 1 - x - 3 = 1

Group the constants at the right side of the equation

That's

3x - x = 1 + 1 + 3

Simplify

We have

2x = 5

Divide both sides by 2

That's

2x / 2 = 5/2

Hope this helps you

Answer:

Step-by-step explanation:

[tex]A=\begin{bmatrix}0 &0 &5 \\ 0 &0 &-3 \\ 0 &0 &3 \end{bmatrix}[/tex]

[tex]B=\begin{bmatrix}8 &-12 &5 \\ 7 &19 &5 \\ 0 &0 &0 \end{bmatrix}[/tex]

A.B = A × B

[tex]A.B=\begin{bmatrix}0 &0 &0 \\ 0 &0 &0 \\ 0 &0 &0 \end{bmatrix}[/tex]

Dimension of the resultant matrix is (3 × 3)

Answer:

1. JG (Jim gets first prize, George gets second prize)

2. JH (Jim gets first prize, Helen gets second prize)

3. JM (Jim gets first prize, Maggie gets second prize)

4. GH (George gets first prize, Helen gets second prize)

5. GJ (George gets first prize, Jim gets second prize)

6. GM (George gets first prize, Maggie gets second prize)

7. MJ (Maggie gets first prize, Jim gets second prize)

8. MG (Maggie gets first prize, George gets second prize)

9. MH (Maggie gets first prize, Helen gets second prize)

Step-by-step explanation:

The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.

The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.

Hey there! :)

Answer:

Last choice. a= 6.

Step-by-step explanation:

Starting with:

-6(2 + a) = -48

Distribute the -6:

-6(2) -6(a) = -48

Simplify:

-12 - 6a = -48

Add 12 to both sides:

-12 + 12 - 6a = -48 + 12

-6a = -36

Divide both sides by -6:

a = 6. Therefore, the last choice is correct.

Answer:

a = 6

Step-by-step explanation:

Solve the one-variable equation using the distributive property and properties of equality.

–6(2 + a) = –48

What is the value of a?

a = –6

a = –3

a = 5

a = 6

Answer:

x=-1

Step-by-step explanation:

8/x+2=2/x-4

8/x=2/x-6

8=2-6x

6=-6x

-1=x

Answer:

x=6

Step-by-step explanation:

8/x+2=2/x-4

Using cross products

8*(x-4) = 2 (x+2)

Distribute

8x - 32 = 2x+4

Subtract 2x

8x-2x -32 = 2x-2x+4

6x-32 = 4

Add 32

6x-32+32 = 4+32

6x = 36

Divide by 6

6x/6 = 36/6

x = 6

Answer:

1

Step-by-step explanation:

We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1

Answer:

  35.98

Step-by-step explanation:

Fill in the numbers and do the arithmetic.

  y = a + bx . . . . . . a=4.95, b=0.29, x=107

  y = 4.95 + 0.29(107) = 35.98

The predicted price is 35.98.

Answer:

4

Step-by-step explanation:

Since there are 4 columns of x and y values the answer is 4.

Answer:

How many points should appear in Kelsey’s graph   Option B

(B) 4

Step-by-step explanation:

Answer:

192 m^2.

Step-by-step explanation:

We can split this up into 3 rectangles:

Area of the bottom rectangle = 27 * (9-3)

= 27 * 6 = 162 m^2.

Area of rectangle on the left = (18-6)*2

= 24 m^2

Area of small rectangle on the right = 3*2

= 6 m^2

Total area = 162+24+6

192 m^2.

Answer:

4/11

Step-by-step explanation:

The probability of winning a new TV is the number of times you will win a TV over the total number of times you try to win a TV. In this case, the odds of winning a new TV are 4/7, or 4 wins every 7 loses. (Odds are probability of success to failure) Therefore, there are 4 wins for every 4 + 7 raffles, or 4/11.

hope it helps uh.......

Answer:

40 miles per hr.

Step-by-step explanation:

alll u have to do is divide the number of miles by the hrs.

ex.80/2=40

140/3.5=40

200/8=40

300/7.5=40

Answer:

31 units

Step-by-step explanation:

I just did it

The length of segment AD must be 31 units for ABCD to be a parallelogram.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Now, When the figure is a parallelogram, opposite sides have the same measure:

That is,

⇒ AD = BC

Plug the given values we get;

⇒ 3x +7 = 5x -9

⇒ 16 = 2x

⇒  8 = x

Hence, Use this value of x in the expression for AD to find its required length:

 AD = 3(8) +7 = 24 +7

 AD = 31 . . . . units

Thus, The length of segment AD must be 31 units for ABCD to be a parallelogram.

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Answer:

9 pounds of deluxe

42 pounds of regular

Step-by-step explanation:

given data

Deluxe coffee mix with regular coffee = 51

mix contains deluxe coffee = 9 pounds

Deluxe coffee costs ​$5

regular coffee costr = ​$3

solution

we consider here

deluxe coffee = x lbs

regular coffee = y lbs

and

x+ y ≥ 52

and mixture contains at least 9 pounds of deluxe coffee

so  x ≥ 9

and

cost equation will be

cost C = 5x + 3 y

deluxe costs more than regular

and here we want to use as possible as to minimize the cost

so least amount

x + y = 51

x  = 9

y = 51 - 9

y = 42

Answer:

Radius = 6.5cm

Diameter = 13cm

Step-by-step explanation:

The diameter is given (13)

Radius is half the diameter (13/2=6.5)

Answer:

Explanation

The straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.

The chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

The second is correct

f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)

Answer:

C. 120 m²

Step-by-step explanation:

The surface area is equal to the area of 4 rectangles + area of 4 triangles + area of base.

Area of 4 rectangles:

4(5 × 4)

4(20) = 80

Area of 4 triangles:

4(3 × 4 × 1/2)

4(6) = 24

Area of base:

4² = 16

Add the areas.

16 + 24 + 80

= 120

The surface area of the composite solid is 120 m².

The surface area of this composite solid would be, 136 m². Hence, option D is true.

Used the formula for the surface area of the cuboid and the surface area of the 4 triangles,

The surface area of the cuboid = 2 (LW + LH + HW)

And, The surface area of the 4 triangles = 4 (1/2 × Base × Height)

Given that,

In a triangle,

Base = 4 m

Height = 3 m

And, In a Cuboid,

Length = 4 m

Width = 4 m

Height = 5 m

Hence, we get;

The surface area of the 4 triangles = 4 (1/2 × Base × Height)

= 4 (1/2 × 4 × 3)

= 4 × 6

= 24 m²

The surface area of the cuboid = 2 (LW + LH + HW)

= 2 (4 × 4 + 4 × 5 + 5 × 4)

= 2 (16 + 20 + 20)

= 112 m²

Therefore, The surface area of this composite solid would be,

24 m² + 112 m² = 136 m²

So, Option D is true.

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Answer:

[tex]\frac{19}{4}=Rs 1[/tex]

[tex]Rs. 1 = 100 paise[/tex]

[tex]\frac{19}{4}=100 paise[/tex]

[tex]4.75=100 paise[/tex]

[tex]\frac{4.75}{100}=paise[/tex]

[tex]0.0475=paise[/tex]

i hope this will help you :)

=1,075

Therefore,

\frac{43}{4} =1,075

Hope it helps you!!!

Plz Mark me as a brailiest

Step-by-step explanation:

Answer:

The x-intercepts as shown on this graph are: (-3,0), (1,0), and (3,0). The y-intercept as shown on this graph is: (0,2).

Step-by-step explanation:

The intercepts refer to where the function intersects with either the x-axis or y-axis. Since the line crosses the y-axis at (0,2), that's the y-intercept. The same thing applies to the x-intercepts. On this graph, it's easier to identify because the intercepts are marked with dots.

Answer:

[tex]\frac{dA}{dt} = 7200\pi t[/tex]

a) [tex]\frac{dA}{dt} = 7200\pi\ cm^2/s[/tex]

b) [tex]\frac{dA}{dt} = 21600\pi\ cm^2/s[/tex]

c) [tex]\frac{dA}{dt} = 36000\pi\ cm^2/s[/tex]

We can conclude that the area of the circle increases faster when the time increases.

Step-by-step explanation:

First let's write the equation for the area of the circle:

[tex]A = \pi*r^2[/tex]

The rate that the radius of the circle increases is 60 cm/s, so we have:

[tex]\frac{dr}{dt} = 60[/tex]

[tex]dr = 60dt \rightarrow r = 60t[/tex]

To find the rate that the area increases, let's take the derivative of the equation of the area in relation to time:

[tex]\frac{dA}{dt} = \pi*\frac{d}{dt} r^2[/tex]

[tex]\frac{dA}{dt} = \pi *\frac{dr^2}{dr} \frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt} = \pi *2r *\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt} = 2\pi *(60t) *60[/tex]

[tex]\frac{dA}{dt} = 7200\pi t[/tex]

a)

Using t = 1, we have:

[tex]\frac{dA}{dt} = 7200\pi *1 = 7200\pi\ cm^2/s[/tex]

b)

Using t = 3, we have:

[tex]\frac{dA}{dt} = 7200\pi *3 = 21600\pi\ cm^2/s[/tex]

c)

Using t = 5, we have:

[tex]\frac{dA}{dt} = 7200\pi *5= 36000\pi\ cm^2/s[/tex]

We can conclude that the area of the circle increases faster when the time increases.

Answer:

Critical value: b. 2.33

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

The significance level is 0.01.

The sample 1 (women), of size n1=150 has a proportion of p1=0.62.

The sample 2 (men), of size n2=200 has a proportion of p2=0.24.

The difference between proportions is (p1-p2)=0.38.

[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]

The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).

As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.

Answer:

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Step-by-step explanation:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Permutations of four letters from a set of 12 letters. So

[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]

11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet

Answer: it’s 11,880

not 11800

Answer:

D

Step-by-step explanation:

Answer:

c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.

Answer:

32.5861

Step-by-step explanation:

I interpreted it this way:

20 - stop at n = 20 (inclusive)

1 - start at n = 1

4(8/9)^(n - 1) - geometric expression

Answer:

  Rn ≈ 0.6345

  Ln ≈ 0.7595

Step-by-step explanation:

The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.

It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:

  x = -1, -.25, 0.50, 1.25, 2

Of course, the spreadsheet can easily compute the sum of products for you.

__

The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:

  Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)

  Rn ≈ 0.6345

__

The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:

  Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)

  Ln ≈ 0.7595

_____

It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

[tex]\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|[/tex]

We have the constraints:

[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

Answer: Left column x- axis

Right column : Tournament round

Left column: y-axis.

Right column: number of teams remaining

Step-by-step explanation:

You expect the y -value, teams remaining to decrease as you go from the first round to the last round in the x-values.

After the first round only 32 teams will left.

After the second round 16 teams will left.

After the third round 8 teams will left.

After the fourth round only 4 teams will left.

After the fifth round only 3 teams will left.

After the sixth round only 1 team will left.

If x and y are two variables in an algebraic equation and every value of x is linked with any other value of y, then 'y' value is said to be a function of x value known as an independent variable, and 'y' value is known as a dependent variable.

An exponential function is a mathematical function in the form f(x) = [tex]a^{x}[/tex] where x is a variable, and a is a constant called the base of the function.

According to the given question

We have an exponential function

[tex]f(x) = 64(\frac{1}{2} )^{x}[/tex]

And y-axis  represents the teams remaining and x axis represents the tournaments round

Since, here the values of x are independent variables and values of y are dependent variables.

Now for the

Tournament round 1 ,

y = f(1) = [tex]64(\frac{1}{2} )=32[/tex]

⇒ 32 teams are remaining

Tournament round 2

[tex]y = f(2) = 64(\frac{1}{2}) ^{2}[/tex]

⇒ y = 16, only 16 teams are remaining

For round 3

[tex]y = f(3) = 64(\frac{1}{2}) ^{3} =8[/tex]

For round 4

[tex]y = f(4) = 64(\frac{1}{2} )^{4}= 4[/tex]

⇒ Only 4 teams are remaining

For round 5

[tex]y = f(5) = 64(\frac{1}{2} )^{5} = 2[/tex]

⇒ only 2 teams are remaining

For round 6

[tex]y = f(6) = 64(\frac{1}{2}) ^{6}=1[/tex]

⇒ only one team is remaining

By using these parameters we will plot a graph for tournament rounds .

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