Write an equation in slope-Intercept form for the line with slope 2 and y-Intercept - 1. Then graph the line.

The width of the mat around the photo is 3 inches

The combined area of the of the photo and math = 224 square inches

The combined area is represented as:

(2w +8)(2w + 10) = 224

Expand the equation using the distributive rule

[tex]4w^2+20w+16w+80=224\\\\4w^2+36w+80-224=0\\\\4w^2+36w-144=0[/tex]

Divide through by 4

[tex]w^2+9w-36=0[/tex]

Factorize the resulting quadratic equation to solve for w

[tex]w^2-3w+12w-36=0\\\\w(w-3)+12(w-3)=0\\\\(w-3)(w+12)=0[/tex]

w  -  3  =  0

w   =  3

w  +  12  =  0

w   =  -12

The width of the mat around the photo is 3 inches

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The width of the mat around the photo is 3 inches

Combined area:

2w +8)(2w + 10) = 224

where,

w = width of the mat around the photo

(2w +8)(2w + 10) = 224

open parenthesis

4w² + 20w + 16w + 80 = 224

4w² + 36w + 80 - 224 = 0

4w² + 36w - 144 = 0

divide through by 4

w² + 9w - 36 = 0

solve quadratic equation using factorization method

w² + 12w - 3w - 36 = 0

w(w + 12) - 3(w + 12) = 0

(w + 12) (w - 3) = 0

w + 12 = 0 or w - 3 = 0

w = -12 or w = 3

The width of the mat around the photo cannot be a negative value.

Therefore, the width of the mat around the photo is 3 inches

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Answer:

Step-by-step explanation:

How many Skittles is in a 4 pound bag?

Fun-size packages are perfect for parties, party favors, trick-or-treaters, gift baskets, lunch treats and on-the-go snacks. Approximately 20 individual packs per lb.

...

Skittles Fun-Size Packs, 4-Lb Box.

Answer:

50 degrees

Step-by-step explanation:

They are alternate exterior angles, so they add up to 180 degrees.

Answer:

1867

Step-by-step explanation:

What do you need it for?

Answer:

C.

Step-by-step explanation:

Pi = circumference / diameter.

Answer:

Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42.

Step-by-step explanation:

:)

Answer:

the y intercept is 5/3

the y intercept is 3/5

1. big planets and carbon dioxide

2. when god sent adam (the first human being) to earth and had a female with him they got married and gave birth to children and the children marry each other and so on.

3. yes we're the only alive humans within this universe, but outside the universe are god and his worshippers.

4. our human-shaped bodies are the way we feel, hear, look, and do lots more things!

5. when someone feels unlike normal.

6. to feel there's a side of u that can do the impossible.

7. things were passed down from generations so it's possible that "stuff" can be made back when adam came to earth but other than that there was "stuff" even before humanity.

8. yes

other than that, hope u got ur questions solved

Answer:

25.

Step-by-step explanation:

5 ft 7 in = 5.583 ft.

We have 2 similar triangles here.

If h is the height of the tree, then:

h / 5.583 = 18/4

h = 18*5.583/4

h = 25.12 ft

The height of the tree is approximately 25.12 feet.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The ratio of the shadow lengths is equal to the ratio of the object heights.

In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:

H/h = 18/4

We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.

Substituting this value into the equation above and solving for H, we get:

H = (18/4) x 5.58 feet

= 25.12 feet

Therefore, the tree is around 25.12 feet tall.

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Answer:

The ramp's horizontal distance is the distance in the x-axis. So the ramp's vertical distance I.e y-axis is 14 inches. And its length which is actually the hypotenuse ofthe right angled triangle 16 feet. But let's convert feet to inches first. 1 feet makes 12 inches Hence 16 feet makes 192 inches. From pythagoras a^2 =b^2 + c^2 where a the hypotenuse is 192 and b is 14. C is the ramp's horizontal distance. So we have (192)^2 = (14)^2 + c^2 C^2 = 192^2 - 14^2 = 36668 C = 191.48 From SOHCAHTOA. We have to use Sin So sin theta = (14/192) Theta = sin^(-1) (14/192) = 4.1815. Yes, it meets the FAC standard since the ramp's angle is less than 4.78

Step-by-step explanation:

Answer:

[tex]3(3x-5)[/tex]

Step-by-step explanation:

First, you have to rewrite 9 as 3 * 3 and 15 as 3 * 5

Finally, you have to factor out the common term 3 to get [tex]3(3x-5)[/tex]

Hope this helps!

P.S next time list the answer choices it would help alot :)

Answer:

12x + 10 feet

Step-by-step explanation:

Perimeter = 2( length + width)

= 2[ 2x + 6 + (4x -1)]

= 2( 2x + 6 + 4x - 1)

= 2( 6x + 5)

= 12x + 10

-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0   or   5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2   or   sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ   or   x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ   or   x = π + arcsin(4/5) + 2nπ

(where n is any integer)

Answer:

a₈ = 2

Step-by-step explanation:

Substitute n = 8 into the nth term rule

A(8) = - 12 + 2(8 - 1) = - 12 + 2(7) = - 12 + 14 = 2

Answer:

2.5 units

Step-by-step explanation:

I took the test and got this question right

I forgot how I did it but test your luck if you believe me

Answer:

b

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(1)

[tex]\frac{5}{60}[/tex] ( divide numerator/ denominator by 5 )

= [tex]\frac{1}{12}[/tex] ( in simplest form )

(2)

both quantities must have the same units

1 hour = 60 minutes , then

[tex]\frac{60}{40}[/tex] ( divide numerator/ denominator by 20 )

= [tex]\frac{3}{2}[/tex] ( in simplest form )

(3)

1 week = 7 days then 2 weeks = 2 × 7 = 14 days , so

[tex]\frac{14}{4}[/tex] ( divide numerator/ denominator by 2 )

= [tex]\frac{7}{2}[/tex] ( in simplest form )

(4)

[tex]\frac{8}{30}[/tex] ( divide numerator/ denominator by 2 )

= [tex]\frac{4}{15}[/tex] ( in simplest form )

(5)

[tex]\frac{9}{45}[/tex] ( divide numerator/ denominator by 9 )

= [tex]\frac{1}{5}[/tex] ( in simplest form )

Answer:

57 digress

I think 57 digress of both triangles are similar

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

1. both are acute triangles

2. both have all the angles measuring less than 90°

3.first triangle x measures 50 degrees and y measure 80 degrees respectively.

pls give brainliest

Answer:

8 feet

Step-by-step explanation:

it actually will be 8 feet

Answer:

the data that is shown represents a function

Step-by-step explanation:

the easiest way to know is by looking at the x-variable. Each y-variable needs one x-variable. the x-variable should not be seen paired with another y-variable.

Answer:

D. x=y+2z

Step-by-step explanation:

if you expand out the first equation (x) you will get: a^2+b^2+c^2+2ab+2bc+2ac

then looking at all of the choices, it can be seen that the third equation (z) needs to be multiplied by to get 2ab+2bc+2ac and then added to the second equation (y) which would result in D being the correct answer.

D. x=y+2z

πr²/2

22×7×7/7×2

77cm²

πr²/2×2

πr²

22/7×3.5×3.5

38.5cm²

77-38.5=38.5cm²

Power is the rate of doing work, and the power of the generating plant or

turbine and the duration of generation, gives the energy generated.

The correct responses are;

Reasons:

Number of homes in the town = 3,000 homes

The given capacity of the power plant = 12 MW = 12,000 kW

Power consumed by a household = 8,000 kWh per year

The price for electrical energy = $0.10 per kWh

Number of wind turbines = 10

WFWP = The West Fremont Wind Project

Capacity of each wind turbine = 1.2 MW

Cost of each wind turbine for 25 years = $3 million

(a) Number of hours of operation of the power plant = 8,000 hrs/yr

Required:

The amount of kWh of electricity produced in a year by the plant.

Solution:

The energy produced = Power × Time

∴ The energy produced = 12,000 kW × 8000 hr = 96,000,000 kWh

Therefore;

The energy produced by the plant in a year, E = 96 × 10⁶ kWh

(b) Energy consumed = Energy consumed per home × Number of homes

Therefore;

Energy consumed = 8,000 kWh/home × 3,000 homes = 24,000,000 kWh

The energy the community consumes in one year = 24 × 10⁶ kWh

(c) The cost per kWh = $0.10

The cost, C, of the energy per year is therefore

C = 24,000,000 kWh × $0.10/kWh = $2,400,000

The cost for 25 years = 25 × C = 25 × $2,400,000 = $60,000,000

The number of wind turbines = 10

Cost per wind turbine = $3 million

Total cost to operate the 10 wind turbine = $3 million × 10 = $30 million

Energy consumed = 24,000,000 kWh

Therefore;

24,000,000 kWh × 25 = $30 million

[tex]\displaystyle 1 \ kWh = \frac{\$ 30 \ million}{25 \times 24,000,000 \ kWh} = \mathbf{\$0.05/kWh}[/tex]

The cost to the community of the electricity supplied by WFWP over 25 years is $0.05/kWh.

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Answer:

C7,3=7!( 3!)( 7−3)!= 7! I think tell me if I'm wrong?

Answer:

7C3 = 7! / (7 - 3)! 3! = 7 x 6 x 5 x 4! / 4!

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

Answer:

$88.81

Step-by-step explanation:

to find tip, multiply 77.23 and .15 to get $11.58

total cost = meal + tip

total cost = 77.23 + 11.58 which equals $88.81