Simplify the following.


I need to see a step by step answer on both questions to see how it actually works.

Answer:

So that it can run faster

Answer:

[tex]a = change \: in \: v \div time[/tex]

Step-by-step explanation:

Change in V =28-0

=28

time =4 sec

Therefore acceleration =28 ÷4

7m/s^-2

Step-by-step explanation:

just multiply the 2 together to get the area

it would just be

[tex](5x) \times (2{x}^{2} - 4x + 13)[/tex]

use the distributive property

[tex]10 {x}^{3} - 20 {x}^{2} + 65[/tex]

unless you want to simplify the answer, this would be the answer

simplified, it would be

[tex]5(2{x}^{3} - 4 {x}^{2} + 13)[/tex]

Answer:

y=-1/4x+9/4

Step-by-step explanation:

Get slope of the line first (to find slope that is perpendicular, get the negative reciprocal)

4 turns into -1/4

To get the y-intercept, plug in the given coordinate values into this formula:

y=mx+b

3=-3(-1/4)+b

3-3/4=b

b=9/4

b is our y-intercept

9/4 is our y-intercept

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = 4 + x\implies y = \stackrel{\stackrel{m}{\downarrow }}{1}x+4\qquad \impliedby \begin{array}{|c|ll}\cline{1-1}slope-intercept~form\\\cline{1-1}\\y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}}\\\\\cline{1-1}\end{array}[/tex]

so therefore

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies\cfrac{1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{1}\implies -1}}[/tex]

so we're really looking for the equation of a line whose slope is -1 and passes through (-3 , 3)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-3=-(x+3)\implies y-3 = -x-3\implies y = -x[/tex]

Answer:

5

Step-by-step explanation:

A=a+b/2 x h

4 = a

5 = b

8 = h

4 + 5 / 2 = 4.5

4.5 x 8 = 36

So the other base length is 5

1. The equation in slope-intercept form is: y = -3/2x + 7/2

2. y = -3/2x - 18

3. Both lines have the same slope, they are therefore parallel.

Two lines that are parallel will have the same slope (m), and is represented by the equation in slope-intercept form as, y = mx + b.

1. Rewrite 3x + 2y = 4 in slope-intercept form:

2y = -3x + 4

y = -3x/2 + 4/2

y = -3/2x + 2

The slope is -3/2. Therefore, the slope (m) of the line that passes through (-1, 5) would be -3/2.

Substitute m = -3/2, and (a, b) = (-1, 5) into y - b = m(x - a):

y - 5 = -3/2(x - (-1))

y - 5 = -3/2(x + 1)

Rewrite in slope-intercept form:

2(y - 5) = -3(x + 1)

2y - 10 = -3x - 3

2y = -3x - 3 + 10

2y = -3x + 7

y = -3x/2 + 7/2

y = -3/2x + 7/2

2. The slopes of perpendicular lines are negative reciprocal to each other.

Rewrite 2x + 3y = 4

3y = -2x + 4

y = -2/3x + 4/3

The slope of the ine that passes (-2, 15) would be -3/2.

Substitute (a, b) = (-2, 15), and m = -3/2 into y - b = m(x - a):

y - 15 = -3/2(x - (-2))

y - 15 = -3/2x - 3

y = -3/2x - 3 - 15

y = -3/2x - 18

Therefore, the equation in slope-intercept form of the line that passes through (-2, 15) is: y = -3/2x - 18.

3. Given the equations, 2x – y = −1 and 4x – 2y = 6:

Rewrite in slope-intercept form and find their slope

2x - y = -1

-y = -2x - 1

y = 2x + 1 (slope if 2)

4x - 2y = 6

-2y = -4x + 6

y = -4x/-2 + 6/-2

y = 2x - 3 (slope is 2)

Both lines are therefore, parallel.

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Answer:

1) {y,x}={-3,-23}

2) {x,y}={7,-9/2}

Step-by-step explanation:

Required:

1) y - x = 20, 2x - 15y = -1

Equations Simplified or Rearranged :

[1]    y - x = 20

  [2]    -15y + 2x = -1

Graphic Representation of the Equations :

x + y = 20        2x - 15y = -1  

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = x + 20

// Plug this in for variable  y  in equation [2]

  [2]    -15•(x +20) + 2x = -1

  [2]     - 13x = 299

// Solve equation [2] for the variable  x

[2]    13x = - 299

  [2]    x = - 23

// By now we know this much :

  y = x+20

   x = -23

// Use the  x  value to solve for  y

   y = (-23)+20 = -3

Solution :

{y,x} = {-3,-23}

2) 25-x=-4y,3x-2y=30

Equations Simplified or Rearranged :

  [1]    -x + 4y = -25

  [2]    3x - 2y = 30

Graphic Representation of the Equations :

   4y - x = -25        -2y + 3x = 30  

Solve by Substitution :

// Solve equation [1] for the variable  x

  [1]    x = 4y + 25

// Plug this in for variable  x  in equation [2]

 [2]    3•(4y+25) - 2y = 30

  [2]    10y = -45

// Solve equation [2] for the variable  y

  [2]    10y = - 45

  [2]    y = - 9/2

// By now we know this much :

  x = 4y+25

   y = -9/2

// Use the  y  value to solve for  x

  x = 4(-9/2)+25 = 7

Solution :

{x,y} = {7,-9/2}

Answer:

12 3/8

Step-by-step explanation:

6 1/2 + 5 7/8 =

= 6 4/8 + 5 7/8

= 11 11/8

= 11 + 8/8 + 3/8

= 11 + 1 + 3/8

= 12 3/8

Answer:

d. multiply the second equation by 4

Answer:

80.5

Step-by-step explanation:

The number of ways to elect a Chair and a Vice Chair is 156.

Given that the Board of directories has 13 members, to determine how many ways are there to elect a Chair and a Vice-Chair, the following calculation must be made:

As the rule does not affect, because in the two years that have elapsed a different election will be held, the number of ways to elect a Chair and a Vice Chair is 156.

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Answer:The number of ways to elect a Chair and a Vice Chair is 156.

Step-by-step explanation:

Answer:

Less than(<)

55% of 60 is 33

60% of 65 is 39

when solving problems with percentage, always multiply x, your decimal form of the percentage, by y, the often whole number part you are multiplying the percentage by.

[tex]0.55 * 60 = 33\\0.60 * 65 = 39[/tex]

note that if the percentage is for example 30%, it will be 0.3, while if it were 3%, it would be 0.03 to avoid confusion.

That said, the answer is less than.

Answer:

A. Answer is 2263.

Checkpoint 1 is -86 Checkpoint 4 is 2177

Subtract -86 from 2177....2177-(-86)   

=2263

2263 is how much higher checkpoint 1 (-86) is from checkpoint 4 (2177)

B. 239 FEET.

the altitude of the hill must be subtracted by the depth of the ckeckpoint(2)(-189)

therefore the altitude of the hill comes out to be 428-189=239feet.

therefore,the actual altitude of the hill is 239 feet.

Answer:

[tex]\sqrt{51[/tex]

Step-by-step explanation:

6^2 + 8^2 = y^2 (Pythag)

100 = y^2

10 = y

7^2 + x^2= 10^2

49+ x^2 = 10^2

x^2 = 51

Answer:

1905.9 cubic feet

Step-by-step explanation:

Use the formula for a volume of a cone - 1/3 * pi * radius^2 * height

Find volume of a cone - 1/3 * pi * 14.3^2 * 8.9 = 1905.8587024733 cubic feet

Round to nearest tenth - 1905.9 cubic feet

:)

Answer:

AB is chord

GF is tangent

DE is diameter

HJ is secant

C is center of the circle

DC is radius

K is point of tangency

AB is arc

Step-by-step explanation:

Answer:

x= 2, x= -12

Step-by-step explanation:

cuz i said so

first move the 24 to the other side of the equation by subtracting it from both side's

now the equation looks like this

x^2+10x-24

then find values that add to equal 10 and that also multiply to equal -24

this works out to (x-2) (x+12)

which means that x is equal to 2 and -12

Answer:

yes

Step-by-step explanation:

4:8 and 3:6 when simplified gives the same result which is 1:2

Answer:

A.) Yes, they do catch fish at the same rate.


Daniel:
4 : 8


Lester:
3 : 6



Both of these ratios have a rate of 1 catfish for every 2 trout. Daniel has just caught 1 more catfish and 2 more trout.

4 - 1 = 3
8 - 2 = 6

Both have a rate of catching 1 catfish for every 2 trout.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

452.16 in^3

Step-by-step explanation:

Volume of a cone = 1/3 pi r^2 h

                               = 1/3 (3.14)(6^2) (12)

Answer:

the question is asking what it is the segment between HB,HG and CG

Step-by-step explanation:

The points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on graph.

Table is a way to represent the data of the two or more variable. To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005.

The table gives the number of tickets sold for each concert. Select the points that represent this data.

The graph which represent the data in the data is attached below year wise.

For the first point, select the value 10 on graph vertically at year 2000. Similarly, select all the points on the graph for the table.

Thus, the points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on the graph.

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Answer:

[tex]\textsf{Slope of line q}: \quad 3[/tex]

[tex]\textsf{Slope of line p}:\quad -\dfrac{1}{3}[/tex]

[tex]\textsf{Equation of line p in slope-point form}: \quad y+5=-\dfrac{1}{3}(x-6)[/tex]

[tex]\textsf{Equation of line p in slope-intercept form}: \quad y=-\dfrac{1}{3}x-3[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:  [tex]y = mx + b[/tex]

(where m is the slope and b is the y-intercept)

Given:

Therefore, the slope of line q is 3.

As line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q.

Therefore, the slope of line p is -1/3

Equation of line p, using the point-slope form, the slope of -1/3 and the point (6, -5):

[tex]\begin{aligned}y-y_1 &=m(x-x_1)\\\implies y-(-5) &=-\dfrac{1}{3}(x-6)\\y+5 &=-\dfrac{1}{3}(x-6)\end{aligned}[/tex]

Simplify to slope-intercept form:

[tex]\implies y=-\dfrac{1}{3}x-3[/tex]

Slope of q:-

Perpendicular line's have slopes negative reciprocal to each other

Slope of p

Passes through (6,-5)

Equation in point slope form

[tex]~~~~x^2-6xy=z-9y^2\\\\\implies x^2- 2\cdot x\cdot 3y + (3y)^2 - (3y)^2 = z-9y^2\\ \\\implies (x-3y)^2 -9y^2 = z-9y^2\\\\\implies (x-3y)^2 = z\\\\\implies x - 3y =\pm\sqrt z\\\\\implies x = 3y\pm\sqrt z[/tex]

Answer:

0.04

Step-by-step explanation:

3÷80.81= 0.037

to the nearest whole number = 0.04

Answer:

30

Step-by-step explanation:

[tex] - 6(x - 16) = - 84[/tex]

[tex]x - 16 = 14[/tex]

[tex]x = 30[/tex]

Answer:

Equation B is the same as Equation A + 2

Step-by-step explanation:

To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.

Equation B: 5x+x=x-4.

Equation A: 5x-2+x=x-4.

Simplifying equation A to be in the form of equation B:

5x -2 + x = x - 4

Adding 2 to both sides:

5x + x -2 + 2 = x - 4 + 2

5x + x = x - 4 + (+2)

= equation A + 2

But 5x+x=x-4 = equation A

Therefore Equation B is the same as Equation A + 2

Answer: 1/5

Step-by-step explanation:

The root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4. To find the root of the equation 2x(x - 8) = (x + 1)(2x - 3), we need to solve for the value of "x" that makes both sides of the equation equal.

First, let's expand both sides of the equation:

2x(x - 8) = (x + 1)(2x - 3)

[tex]2x^2 - 16x = 2x^2 - x - 3x + 3[/tex]

Now, combine like terms on the right-hand side:

[tex]2x^2 - 16x = 2x^2 - 4x + 3[/tex]

Next, subtract [tex]2x^2[/tex] from both sides to get the x terms on one side:

-16x = -4x + 3

Now, bring all the x terms to one side by subtracting -4x from both sides:

-16x + 4x = 3

Simplify the left-hand side:

-12x = 3

Finally, solve for x by dividing both sides by -12:

x = 3 / -12

x = -1/4

So, the root of the equation 2x(x - 8) = (x + 1)(2x - 3) is x = -1/4.

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Answer:

175,424.02

Step-by-step explanation:

multiply 145,117 by 106%

multiply 1800 by 12 (months in a year)

add 21600 to 153,824.02