A pair of linear equations is shown:
y=-3x + 5
y = x + 2
Which of the following statements best explains the steps to solve the pair of equations graphically?
O on a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = -3, and the second line has y-intercept = 2 and slope =
1.
O on a graph, find the point of intection of two lines; the first line has y-intercept = -3 and slope = 5, and the second line has y-intercept = 1 and slope =
2.
O On a graph, find the point of intersection of two lines; the first line has y-intercept = -5 and slope = 3, and the second line has y-intercept = -2 and slope =
-1.
O On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = -5, and the second line has y-intercept = -1 and slope =
-2.

Answer:

Area of a rectangle is w • L

w = 5 while L = (b + 3)

Area is

5 • (b + 3) = 5b + 15

So answer is 2. 3. and 4. which are all similar forms of the same expression.

Step-by-step explanation:

Answer:

The correct  substitution of a, b, and c in the quadratic formula is given by

[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]

[tex]x = - \frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]

The solutions of the given quadratic equation are real and equal.

Step-by-step explanation:

The given quadratic equation is

[tex]4x^2+12x+9 = 0[/tex]

The coefficients a, b and c are as follow:

[tex]a = 4 \\\\b = 12\\\\c = 9[/tex]

The quadratic formula is given by

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

The correct  substitution of a, b, and c in the quadratic formula is given by

[tex]$ x=\frac{-12\pm\sqrt{(12)^2-4(4)(9)}}{2(4)} $[/tex]

Bonus:

The solution of this quadratic equation is given by

[tex]x=\frac{-12\pm\sqrt{(144 - 144)}}{8} \\\\x=\frac{-12\pm\sqrt{0}}{8} \\\\x=\frac{-12\pm 0}{8} \\\\x=\frac{-12 + 0}{8} \: and \: x=\frac{-12 - 0}{8}\\\\x= -\frac{ 3}{2} \: and \: x = -\frac{ 3}{2} \\\\[/tex]

Therefore, the solutions of the given quadratic equation are real and equal.

Answer:

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

Rewrite expression with bases of 4.

[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]

Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.

[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

Cancel same bases.

[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]

Subtract 3/4 from both sides.

[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]

Multiply both sides by 2.

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

2^{2*3/4} × 2^{x}=2^{4×2/5}

2^{3/2} × 2^{x}= 2^{8/5}

2^{3/2+x}=2^{8/5}

equate powers

{3+2x}/2= 2^2

5{3+2x}= 2{8}

15+10x=16

collect like terms

10x=16-15

10x=1

divide both sides by 10

x=1/10

x=0.1

Answer:

  19.45°

Step-by-step explanation:

Suppose the post is 1 unit high. Then the distance from the post to another corner of the rectangle will satisfy the relation ...

  distance/1 = tan(90° -angle of elevation)

So, for the near corner, the distance from the post is ...

  distance = tan(90° -36°) = tan(54°) = 1.37638 . . . post lengths

For the other given corner, the distance from the post is ...

  distance = tan(90° -22°) = tan(68°) = 2.47509 . . . post lengths

The Pythagorean theorem can be used to find the distance from the post to the diagonally opposite corner:

  distance^2 = 1.37638^2 +2.47509^2 = 8.02048

  distance = √8.02048 ≈ 2.83205

The relation of this to the angle of elevation is ...

  tan(angle of elevation) = 1/2.83205

  angle of elevation = arctan(1/2.83205) ≈ 19.45°

_____

In the attached diagram, we have used segments BP and CP as surrogates for the post, so we could determine distances PD and PE that are the sides of the rectangular courtyard. Then the courtyard diagonal is PF. Using PA as a surrogate for the post, we found the angle of elevation from F to A (the top of the post) to be 19.45°, as computed above.

Answer:

$1,313.3 per month

Step-by-step explanation:

A=p(1+r/n)^nt

P=principal=$75,000

r=interest rate=7.2%=0.072

t=20 years

n=12 months

A=p(1+r/n)^nt

=75,000(1+0.072/12)^12*20

=75,000(1+0.006)^240

=75,000(1.006)^240

=75,000(4.2026)

=315,195

A=$315,195

The term of Lauren's loan=20 years

20 years×12 months=240 months

Lauren's pay per month =$315,195/240

=$1,313.3125

Approximately $1,313.3 per month

Answer:

they are 16 and 4

Step-by-step explanation:

We can call the numbers x and y and we can write:

x - y = 12

x + y = 20

Adding these equations gives us 2x = 32 which means x = 16 and substituting this value into the first equation gives us y = 4.

Answer:

The numbers are 16 and 4

Step-by-step explanation:

Let the two numbers be x and y

x-y = 12

x+y = 20

Add the two equations together

x-y = 12

x+y = 20

-------------------

2x = 32

Divide by 2

2x/2 =32/2

x = 16

Now find y

x+y =20

16+y =20

Subtract 16

y = 20-16

y = 4

Answer:

paid vacation

paid medical

401k

Diagram related to the question can be found in the attached picture below :

Answer: 6 units

Step-by-step explanation:

From the diagram attached to the question:

Length AB = 17

Length DC = 8

height (h) = x

Area of trapezium = 75sq units

The Area (A) of a trapezium is given by:

(1/2) × (a + b) × h

Where ;

a and b are the upper and base lengths of the trapezium

h = height of trapezium

A = (1/2) × (a + b) × h

75 = (1/2) * (17 + 8) * x

75 = 0.5*25*x

75 = 12.5x

x = 75 / 12.5

x = 6 units

Answer:450 cm

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

After it's enlarged, the new dimensions will be 6 * 3.5 = 21 and 8 * 3.5 = 28, therefore, the new perimeter will be 2(21 + 28) = 2 * 49 = 98 and the area will be 21 * 28 = 588.

Answer:

n = 4

Step-by-step explanation:

4(2n + 3) = 44

Expand the brackets.

4(2n) + 4(3) = 44

8n + 12 = 44

Subtract 12 on both sides.

8n + 12 - 12 = 44 - 12

8n = 32

Divide both sides by 8.

(8n)/8 = 32/8

n = 4

Answer: 7.4 meters

Step-by-step explanation:

Start Mark = 3m

End mark = 25m

Total length to race = 25 - 3 = 22m

Position of both Ario and miguel = 3 meter from one side of the pool; that is 3 meters behind the START MARK

Ario's completed to remain ratio = 1:4

Total ratio = 5

Ario's Completed meters = (22/5) * 1 = 4.4m

Therefore, when Miguel starts the race, Ario will be on (4.4meters + number of meters behind the start mark)

= 4.4 meters + 3 meters = 7.4meters

The distance of Ario from the start point when miguel starts is;

7.44 m

        This means distance of line = 25 - 3 = 22 m

Miguel and his brother Ario are standing 3 m from one side of the pool.

This means that they are both 3 meters behind the start point.

Thus, ario's completed meters when Miguel will start is;

¹/₅ × 22 = 4.4 m

Distance of miguel from Ario when miguel starts = 3 + 4.4 = 7.4 m

Read more about algebra at; https://brainly.com/question/11408596

Answer:

x = 2

Step-by-step explanation:

Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:

3x – 5 + 5 = 1 + 5

Simplify: 3x=6

Divide each side by 3 to isolate and solve for x:

3x/3=6/3

Simplify: x=2

Step-by-step explanation:

One way of organizing data is by constructing a frequency distribution table. A tally mark is used to record how often a particular score or number occurs. The number of times a score or number appears is called the frequency.

To construct a frequency distribution table:

a. list the scores or numbers from highest to lowest (or lowest to highest),

b. use tally marks to record how often each score or number appears, and

c. count the marks and record it in the frequency column.

Answer:

C

Step-by-step explanation:

Line of symmetry

Answer:

y = | 2(x + 1)  - 1

Step-by-step explanation:

Given f(x) then f(x + c) represents a horizontal translation of f(x)

• If c > 0 then shift to the left of c units

• If c < 0 then shift to the right of c units

Here the shift is 1 unit to the left , thus

y = | 2(x + 1) ] - 1

Answer:

X ^3 (4x+1) (4x-1)

Step-by-step explanation:

Factor x3 out of  16x5−x3

Rewrite 16x2 as  (4x)2

Rewrite 1 as 1^2

Factor

x^3 (4x+1) (4x-1)

I hope I helped

Answer:

She can buy 3 candy bags.

Step-by-step explanation:

Let the number of bags = x.

9.5 + 3.5x = 20

3.5x = 10.5

x = 3

Answer: She can buy 3 candy bags.

Answer:

3

Step-by-step explanation:

Answer: The sum is 127

Step-by-step explanation:

A 2-digit number N = ab can be written as (where a and b are single-digit numbers)

a*10 + b.

Now, we want that:

(a + 2)*(b + 2) = a*10 + b.

So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)

We have:

(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b

a*b + 2*b - b + 4 = a*10 - a*2

a*b + 4 + b = a*8

a*b + 4 + b - a*8 = 0.

Now we can give one of the variables different values, and see if the equation has solutions:

>a = 1:

1*b + 4 + b - 8 = 0

2*b - 4 = 0

b = 4/2 = 2

Then the number 12 has the property.

> if a = 2:

2*b + 4 + b -16 = 0

3b -12 = 0

b = 12/3 = 4

The number 24 has the property.

>a = 3 is already known, here the solution is 35.

>a = 4.

4*b + 4 + b - 8*4 = 0

5*b + 4 - 32 = 0

5*b = 28

b = 28/5

this is not an integer, so here we do not have a solution.

>if a = 5.

5*b + 4 + b - 8*5 = 0

6b + 4 - 40 = 0

6b - 36 = 0

b = 36/6 = 6

So the number 56 also has the property.

>if a = 6

6*b + 4 + b - 8*6 = 0

7b + 4 - 48 = 0

7b - 44 = 0

b = 44/7 this is not an integer, so here we do not have any solution.

>if a = 7

7*b + 4 + b -8*7 = 0

8b -52 = 0

b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.

>if a = 8

8*b + 4 + b -8*8 = 0

9*b + 4 - 64 = 0

9*b = 60

b = 60/9 this is not an integer, so we here do not have any solution:

>if a = 9

9*b + 4 + b - 8*9 = 0

10b + 4 - 72 = 0

10b -68 = 0

b = 68/10 again, this is not an integer.

So the numbers with the property are:

12, 24, 35 and 56

And the sum is:

12 + 24 + 35 + 56 =  127

Answer:

Graph 4

Step-by-step explanation:

The graph of f(x) = x^3 includes point (0, 0) since f(0) = 0^3 = 0.

The exponent of x is 3. This is not a linear function.

Negative values of x cubed are negative, and positive values of x cubed are positive.

For x < 0, f(x) < 0, and for x > 0, f(x) > 0.

Answer: Graph 4.

Answer:

x-y

Step-by-step explanation:

X is greater than y so we are subtracting the smaller number from the bigger number

That means we do not need the absolute value signs since x-y will be positive

|x-y| when x> y

x-y

Using numbers

| 5-2|    5>2

5-2

Answer:

Hey there!

First, we want to find the radius of the circle, which equals the length of line segment AC.

Length of line segment AC, which we can find with the distance formula: [tex]\sqrt{25\\[/tex], which is equal to 5.

The equation for a circle, is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center of the circle, and r is the radius.

Although I don't know the center of the circle, I can tell you that it is either choice B or D, because the radius, 5, squared, is 25.

Hope this helps :) (And let me know if you edit the question)

Answer:  The equation of the circle is (x+1)²+(y+1)² = 25

Step-by-step explanation:  Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location:  A(-1,-2), B(-1,1) and C(3,1)  The sides of the triangle are AB=3, BC=4, AC=5.

Use the equation for a circle: ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center.  h is -1, k is -2  The radius 5, squared becomes 25.

Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .

When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.

We end up with the equation for the circle as specified:

(x+1)²+(y+1)² = 25

A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)

Answer:

Step-by-step explanation:

                +2d+30    +2d+30

                    ÷(-15)      ÷(-15)

my mistake it's actually d= -30/19 sometimes I forget you put them in fractions

Answer:

a.  Feelings about weight is the response (dependent) variable.  Sex is the explanatory (independent) variable.  The feelings about weight depend on the sex

b. Summary of  observed counts

                         Women   Men   Total

Overweight        38           18       56

Right weight      99          35      134

Underweight       6          25        31

Number           143           78      221

c. Percentage of the 143 women responding in each category:

1. Overweight = 38/143 = 26.6%

2. Right weight = 99/143 = 69.2%

3. Underweight = 6/143 = 4.2%

d. Percentage of the 78 men responding in each category:

1. Overweight = 18/78 = 23.1%

2. Right weight = 35/78 = 44.9%

3. Underweight = 25/78 = 32%

e. Summary of feelings about weight:

                         Women        Men

Overweight        26.6%        23.1%

Right weight      69.2%        44.9%

Underweight       4.2%         32%

Step-by-step explanation:

a) Data:

Sample size = 221

                       Women    Men   Total

Overweight        38           18       56

Right weight      99          35      134

Underweight       6          25        31

Number            143           78      221

b) To obtain the percentage of feelings about weight for each category, the number of those who feel overweight, right weight, or underweight is divided by the total number of women or men.  The value obtained, which is in decimal form, is then converted to percentage by multiplying with 100.

Answer:

10.6

Step-by-step explanation:

radius = 1.5 height = 1.5 so it's 10.6

Answer:

10.6

Step-by-step explanation:

Answer:

  20 km/hr

Step-by-step explanation:

The boat's still-water speed is the average of its speeds against and with the current:

  (15 +25)/2 = 20 . . . km/hr

__

If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.

  b - c = 15 . . . . upstream speed

  b + c = 25 . . . . downstream speed

Add these two equations, and you get ...

  (b -c) +(b +c) = (15) +(25)

  2b = 40

  b = 20 . . . . divide by 2

The speed of the boat in still water is 20 km/hr.

Answer:

20 km/hr

Step-by-step explanation:

To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.

15 +25=40

40/2=20

20km/hr!!!

Good luck on what you are doing I hope you do well! Brainliest would be great :)

Answer:

Nathan weighs 12 more pounds than Marty.

Step-by-step explanation:

If Marty weighs 64 pounds and Nathan weighs 76 pounds, we can subtract the weight of Marty from Nathan to get our answer.

[tex]76-64=12[/tex]

In case Nathan was actually 476 pounds, the answer would be 412.

Answer:

115

Step-by-step explanation:

It adds 3 every time and starts with -38. Our equation is:

a52 = -38+3(52-1);

a52 = -38 + 153

a52 = 115

Answer:

115

Step-by-step explanation:

→ First we need to work out the nth term. First we find the difference between each term

-38, -35, -32, -29... ⇔ +3

→ We know the first bit is 3n now we have to find the other section. We need to write the 3 times tables on top of each corresponding term

3 ,   6   ,  9  , 12

-38, -35, -32, -29...

→ We can see the to get from 3 to -38 we minus 41. So the nth term is

3n - 41

→ Now we substitute in 52 for n

3 × 52 - 41

→ Simplify

115