Use substitution to find the solutions to the systems.

Answer:

Step-by-step explanation:

The equation of a line which passes through (x₁, y₁) and with slope of m in point-slope form:

                              y - y₁ = m(x - x₁)

m = ¹/₃

(-2, 8)    ⇒   x₁ = -2,  y₁ = 8

Therefore,  the equation of the line which passes through (-2, 8) and with slope of 1/3 in point-slope form:

y - 8 = ¹/₃(x - (-2))

y - 8 = ¹/₃x + ²/₃                   {multiply both sides by 3}

3y - 24 = x + 2                    {subtract x from both sides}

-x + 3y - 24 = 2                     {add 24 to both sides}

-x + 3y = 26

Answer:

It cannot be modeled with a rectangle.

Step-by-step explanation:

The given expression 2x^2 + 3x +3 cannot be factored.

That means that it cannot be modeled with a rectangle.

So your answer is, It cannot be modeled with a rectangle.

Answer:

It cannot be modeled with a rectangle.

Step-by-step explanation:

Hope this helps

Answer:

2. 10 + 5 x 2                    $20

3. 10 + 5 x 3                    $25

4. 10 + 5 x 4                    $30

Hope that helps!

Step-by-step explanation:

Answer:

2) 10+5x2= 20

3) 10+5x3= 25

4) 10+5x4= 30

Step-by-step explanation:

just add 5 every time

Based on the test scores of the students, Cindy's z-score on the science test is 2.2

We start by calculating the mean of the scores using:

Mean =Sum/Count

So, we have:

Mean = (75 + 80 + 90 + 100 + 75 + 85 + 80 + 80 + 90 + 85)/10

Mean = 84

Using a statistical calculator, the standard deviation is:

Standard deviation = 7.35

The z-score is then calculated using:

z = (x - mean)/standard deviation

Cindy's score is 100.

So, we have:

z = (100 - 84)/7.35

Evaluate

z = 2.2

Hence, Cindy's z-score on the science test is 2.2

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Answer:

8 yards

Step-by-step explanation:

/\

/ \

/ \

----------

/ and \ = 8

_ = 10

Answer:

probably C

Step-by-step explanation:

The question can be written as:

8 * 1.032^n = 140 000, this can be rearranged to

140 000/8 = 17500 = 1.032^n

now we need to find n, we could do this manually with a calculator, but an easier method is to use [tex]\log_x(y)[/tex]

example of log

2^3 = 8

log2 (8) = 3

log1.032 (17500) = 310.17

The course that a rescue ship must take from port in order to reach the disabled ship is 312.4 km at a direction of 50.2⁰.

The sketch of the journey of the ship can be used to determine the course that a rescue ship must take from port in order to reach the disabled ship.

                              <-------- 200 km-------

                               |

                               | 240 km

                              ↓

The displacement of the ship from the initial position is calculated as follows;

d² = 200² + 240²

d² = 97,600

d = √97,600

d = 312.4 km

tanθ = 240/200

tanθ = 1.2

θ = tan⁻¹(1.2)

θ = 50.2⁰

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Answer:

y = 7

x = 24

Step-by-step explanation:

When two triangles are similar, the ratio of their corresponding sides are equal

For the bigger triangle we have a total 48; so for the smaller we have x

For the bigger, we have 14, so for the smaller, we have y

Mathematically;

25/x = 50/48

x * 50 = 25 * 48

x = (25 * 48)/50

x = 24

For y;

25/y = 50/14

y = (25 * 14)/50

y = 7

Answer:

Step-by-step explanation:

Answer:

Total cost = $4.08

Step-by-step explanation:

Given the following data;

Selling price = $3.4

Shipping and handling fee = 20%

To find the total cost;

First of all, we would determine the extra fee;

Extra fee = 20/100 * 3.4

Extra fee = 68/100

Extra fee = $0.68

Now, we can solve for the total cost using the formula below;

Total cost = selling price + extra fee

Total cost = 3.4 + 0.68

Total cost = $4.08

Answer: The side of the house will the ladder reached by ladder = 16.52 feet

Step-by-step explanation:

House is standing vertical on the ground.

By placing ladder, it will become a right triangle with hypotenuse as ladder.

By Pythagoras theorem,

[tex](hypotenuse)^2=(perpendicular)^2+(base)^2[/tex]

i.e.

[tex](17)^2=(Height \ of\ wall\ reached\ by\ ladder)^2+4^2\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)^2=289-16\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)^2=273\\\\\Rightarrow\ (Height \ of\ wall\ reached\ by\ ladder)=\sqrt{273}\approx16.52[/tex]

Hence, the side of the house will the ladder reached by ladder = 16.52 feet (approx)

Answer:

9

Step-by-step explanation:

If PQ || to BC

Then by BASIC PROPORTIONALITY THEOREM:

[tex] \frac{8}{40} = \frac{x}{45} \\ \\ \frac{1}{5} = \frac{x}{45} \\ \\ x = \frac{45}{5} \\ \\ x = 9[/tex]

Answer:

21.25%

Step-by-step explanation:

To find the percent decrease, take the original amount and subtract the new amount

80-63 = 17

Divide this by the original amount

17/80 =.2125

Multiply by 100 to change to a percent

21.25%

Answer:

B. 81 m²

Step-by-step explanation:

6x10 = 60

7x6 = 42

42/2 = 21

60+21 = 81

Answer:

B) 81 meters squared

Step-by-step explanation:

rectangle = 6 * 10 = 60

triangle = .5 * 6 * 7 = 21

60+21 = 81

Answer:

Step-by-step explanation:

The slope of a line that passes through two given points: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The equation of the line that passes through given point with a slope of m:  

y - y₁ = m(x - x₁)

Line A:

 [tex]m=\dfrac{-1-5}{3-(-1)}=\dfrac{-6}4=-\dfrac32[/tex]

[tex]y-5=-\frac32(x+1)\\\\y=-\frac32(x+1)+5[/tex]

Line B:

 [tex]m=\dfrac{-1-2}{6-7}=\dfrac{-3}{-1}=3[/tex]

[tex]y-2=3(x-7)\\\\y=3(x-7)+2[/tex]

Point of intersect means the same coordinates x and y.

So:

       [tex]3(x-7)+2=-\frac32(x+1)+5\\\\3x-21+2=-\frac32x-\frac32+5\\\\3x-19=-\frac32x+\frac72\\\\6x-38=3x+7\\\\6x+3x=7+38\\\\9x=45\\\\x=5\\\\y=3(5-7)+2=3(-2)+2=-4[/tex]

Question:

In triangle FGH, the measure of angle H = 90°, HG = 48, FH = 55, and GF = 73. What ratio represents the tangent of angle G?

___________________________________________________

Solution:

The triangle FGH should look like that in the attachment.

Tangent of angle G = opposite side/adjacent side

= FH/HG

= 55/48

Answer:

all i know is 6 is 72/30 because I'm busy right now sorry that I don't have the simplest form of answer

Answer:

6. 2 2/5

7. 66/145

8. 1 1/5

Step-by-step explanation:

Answer:

7.) c

8.) 5.9

9.) 8.78

10.) 8.778

if im wrong let me know

Step-by-step explanation:

Answer:

Use photo math, take a picture of the equation, and it will show everything you need to know about it!!!

Answer:

8 percent

Step-by-step explanation:

2.4/30 = 0.08 or 8%

Answer:

4 hope it helps you better

Answer:

Frx8txutxitxigxtix7fv7t8citcti

[tex]3\sqrt{x^2}[/tex][tex]=3x[/tex]

[tex]\sqrt[3]{x^2}[/tex][tex]=x^\frac{2}3}[/tex]

I do not know which one you mean but still one of them is still your answer. :)

Answer:

permiter 68ft

area 204ft²

Step-by-step explanation:

25ft+26ft+17ft=68ft

1/2×17ft×24ft=204ft²

I hope it's help

Answer:

when the dot's go left to right going upwards

Step-by-step explanation:

Answer:

80°+65°+2x+3x=360°(sum of quadrilateral is 360)

145°+5x=360°

5x=360°-145°

5X=215°

X=215°/5°

X=43°

The required value is [tex]x=43[/tex]

Given angles are,

[tex]80^{\circ}, 65^{\circ}, 2x,3x[/tex]

As we know the sum of all angles in the quadrilateral is [tex]360^{\circ}[/tex].

Then we have the relation,

[tex]80+65+2x+3x=360\\\\145+5x=360\\5x=360-145\\5x=215\\x=43[/tex]

So, the value of the x is 43.

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