Prove that “The sum of the angles in a triangle is 180“.

Answer:

parallel line y = -1/2x + 12

perpendicular line y = 2x + 2

Step-by-step explanation:

slope = -1/2

perpendicular slope = 2

y = mx + b

10 = -1/2(4) + b

10 = -2 + b

12 = b

y = -1/2x + 12

10 = 2(4) + b

10 = 8 + b

2 = b

y = 2x + 2

Answer:

[tex]\huge \boxed{{10x^2 + 12x \mathrm{\ units^2 }} }[/tex]

Step-by-step explanation:

area of shaded region = area of whole rectangle - area of unshaded region

Area of a rectangle is length × width.

A = 5x(3x+2) - (x(5x-2))

Expand brackets.

A = 15x² + 10x -(5x² - 2x)

Distribute negative sign.

A = 15x² + 10x - 5x² + 2x

Combine like terms.

A = 10x² + 12x

Answer:

d = 1.4 t + 30

Step-by-step explanation:

Head start means any advantage achieved or advantage gained in any race or competition.

In the context, the runner is gained a head start of 30 meter from the starting point.

It is also given that the speed with which the runner is running is 5.0 km per hour.

Therefore, the equation that gives the distance covered by the runner from his start line at any time in seconds is given by d = 1.4 t + 30.

Answer:

60%

Step-by-step explanation:

There are only even and odd numbers.  If a number is not even, it is odd.  If the probability of spinning an even number is 0.4, or 40%, then just subtract that by the whole spinner, which is equivalent to 100%:

100% - 40%

= 60%

This means that the odds of spinning an odd number is 60%

Hope this helps!  Tell me if I'm wrong please!

Answer:

60%

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find f(g(x)) substitute g(x) into f(x) that's for every x in f (x) replace it by g (x)

We have

We have the final answer as

Hope this helps you

Answer:

65

Step-by-step explanation:

650x0.1=65

the answer is 65 dollars uwu

Answer:

$65

Step-by-step explanation:

10% of 650 is 65 because you multiply .1 and 650, or move the decimal one place to the left. because the question asks for the discount price, you would just find the discount.

Answer:

98.02

Step-by-step explanation:

Take 26 and multiply by 277%

26 * 277%

Change to decimal form

26 * 2.77

72.02

That is the amount of the increase

Now add it to the original amount

26+72.02

98.02

Answer:

98.02

Step-by-step explanation:

[tex]26 + 26 \times \frac{277}{100} \\ = 26 + 26 \times 2.77 \\ = 26 + 72.02 \\ = 98.02[/tex]

Answer:

[tex]A=73.5\text{ cm}^2[/tex]

Step-by-step explanation:

The formula for an area of a triangle is:

[tex]A=\frac{1}{2}bh[/tex]

Where b is the base length and h is the vertical height.

From the triangle, we can see that the base is 21 cm while the vertical height is 7. Thus:

[tex]A=\frac{1}{2}(7)(21)[/tex]

Multiply:

[tex]A=\frac{1}{2}(147)[/tex]

Multiply:

[tex]A=73.5\text{ cm}^2[/tex]

And that's our answer :)

The Area of triangle is 73.5 square cm.

We have from the figure,

Base of triangle = 21 cm

Height of triangle = 7 cm

side of triangle = 15 cm

We know the formula for Area of Triangle

Area of Triangle = 1/2 x base x height

Now, plugging the value of base and height in the formula we get

Area of triangle = 1/2 x  base x height

= 1/2 x 21 x 7

= 147/2

= 73.5 square cm

Learn more about Area here:

https://brainly.com/question/1631786

#SPJ6

Answer:

400 feet

Step-by-step explanation:

We just need to find h when t = 5. To do so, we can plug t = 5 into the function, which would be:

h = -16t² + 120t + 200

  = -16 * 5² + 120 * 5 + 200

  = -400 + 600 + 200 = 400 feet

Answer:

h = 400 feet

Step-by-step explanation:

given t = 5 seconds

h = -16t² + 120t + 200

just substitute t = 5

h = -16(5)² + 120(5) + 200

h = 400 feet

Answer:12

Step-by-step explanation:

Answer:

0.37 feet.

Step-by-step explanation:

The following data were obtained from the question:

Volume (V) = 4100 ft³

Height (h) = 1.8 miles

Radius (r) =?

Next, we shall convert 1.8 miles to foot.

This can be obtained as follow:

Recall:

1 mile = 5280 ft

Therefore,

1.8 miles = 1.8 × 5280 = 9504 ft

Finally, we determine the radius as follow:

Volume (V) = 4100 ft³

Height (h) = 9504 ft

Pi (π) = 3.14

Radius (r) =?

V = πr²h

4100 = 3.14 × r² × 9504

4100 = r² × 29842.56

Divide both side by 29842.56

r² = 4100/29842.56

Take the square root of both side

r = √(4100/29842.56)

r = 0.37 ft

Therefore, the radius of the hole is 0.37 feet.

Answer:

8640 square inches

Step-by-step explanation:

There are 12 inches in one foot so there would be 12 * 12 = 144 square inches in 1 square foot. Therefore, there are 144 * 60 = 8640 square inches in 60 square feet.

Answer:

Step-by-step explanation:

If XY is bisector of angle AXN then:   [tex]\dfrac{YN}{AY}=\dfrac{XN}{AX}[/tex]

[tex]\dfrac4{12}=\dfrac{XN}{18}\\\\XN=\dfrac4{12}\cdot18\\\\XN=6[/tex]                                                            

Answer:

A. Width = 25   Length = 15

Step-by-step explanation:

Length = L = Width - 10

Width = W

Perimeter of a rectangle

=> 2 (L + B) = 80

=> 2 (W - 10 + W) = 80

=> 2 (2W - 10) = 80

=> 4W -20 = 80

=> 4W -20 + 20 = 80 + 20

=> 4W = 100

=> 4W/4 = 100/4

=> W = 25

Width = 25

Length = 25 - 10 = 15

So, the answer is A.

Answer:

200 > 100

Step-by-step explanation:

154 rounded to the nearest hundred is 200 because 154 is closer to 200 than to 100. and 145 is closer to 100 than it is to 200 so we have 200 and 100 and we know that 200 is greater than 100 so we can conclude with 200 > 100

Answer:

[tex](-7,4]\text{ or }\{x|-7<x\leq 4\}[/tex]

Step-by-step explanation:

The domain is the span of x-values covered by the function.

From the graph, we can see that the graph covers all the x-values from x=-7 to x=4.

However, note that closed and open circles. There is an open circle at x=-7, which means that the domain excludes x=-7. However, the circle at x=4 is closed, meaning it is included in the domain.

Therefore, the domain is, in interval notation:

[tex](-7,4][/tex]

We use parentheses on the left because we do not include -7. And we use brackets on the right because we do include the 4.

And in set notation, this is:

[tex]\{x|-7<x\leq 4\}[/tex]

Answer:

The domain is the span of x-values covered by the function.

From the graph, we can see that the graph covers all the x-values from x=-7 to x=4.

However, note that closed and open circles. There is an open circle at x=-7, which means that the domain excludes x=-7. However, the circle at x=4 is closed, meaning it is included in the domain.

Therefore, the domain is, in interval notation:

(-7,4](−7,4]

We use parentheses on the left because we do not include -7. And we use brackets on the right because we do include the 4.

And in set notation, this is:

\{x|-7

Answer:

Step-by-step explanation:

R = 1.52

H = 2.2

π = 3.14

[tex]V=\frac13\pi R^2\cdot H\\\\V=\frac13\cdot3.14\cdot(1.52)^2\cdot2.2=5.3200810\overline6\approx5.32[/tex]

Answer:

5.05*10³

Step-by-step explanation:

Answer:

  swap 1,2; swap 3,4

Step-by-step explanation:

Put the numbers in scientific notation, with one digit left of the decimal point.

The number with the largest exponent is largest.

If exponents are equal, the number with the largest mantissa is the largest.

__

Here, the exponents are already in order, so you need only order the mantissas for each exponent. Ascending order is ...

  [tex]1.22\times10^{-8}\\3.61\times10^{-8}\\5.5\times10^{-6}\\7.49\times10^{-6}\\2.87\times10^{-5}[/tex]

Answer:

Probability that both marbles drawn will be green = 1 / 20

Step-by-step explanation:

(It is assumed that marbles are not returned in the bag)

[tex]p(1st \: marble \: drawn \: is \: green) = \frac{5}{20} [/tex]

[tex]p(2nd \: marble \: drawn \: is \: green) = \frac{4}{20} [/tex]

Multiplying theses we get :

[tex]p(both \: marbles \: drawn \: are \: green) = \frac{5}{20} \times \frac{4}{20} = \frac{1}{20} [/tex]

Answer:

y = 9/5

4th Option

Step-by-step explanation:

Step 1: Write out function f(y)

f(y) = 5y - 3

Step 2: Define variable from problem

f(y) = 6

Step 3: Replace variable

6 = 5y - 3

Step 4: Add 3 to both sides

9 = 5y

Step 5: Isolate y by dividing both sides by 5

y = 9/5

Answer:

Step-by-step explanation:

7). Since the points J, K and L are on a same line, these points are collinear.

8). Point M is a point which is on the same plane with the points J, K and L but it is not collinear as the points J, K, and L are.

9). Points J, K, L and M are on the same plane (horizontal plane) but point N is not coplanar with these points.

10). Since a plane is named using 3 points lying on it. Therefore, JKL is the appropriate name of the given plane with these points.

Answer:

JKL is the appropriate name of the given plane with these points.

Step-by-step explanation:

Hi there! Hopefully this helps!

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

5(0.3) + 2y = 20

| 5(0.3) + 2y = 20

| Multiply 5 and 0.3 to get 1.5

\/

1.5 + 2y = 20

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We subtract 1.5 from both sides.

2y = 20 - 1.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtract 1.5 from 20 to get 18.5.

2y = 18.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Divide both sides by 2.

[tex]y = \frac{18.5}{2}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Expand [tex]\frac{18.5}{2}[/tex] = 9.25 by multiplying both numerator and the denominator by 10.

[tex]y =\frac{185}{20}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Reduce the fraction [tex]\frac{185}{20} = 9.25[/tex] to lowest terms by extracting and canceling out 5.

[tex]y =\frac{37}{4}[/tex].

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{37}{4} = 9.25[/tex] in decimal form.

Answer:

Step-by-step explanation:

A^2 + b^2 = c^, 8^2 + x^2 =17^2 , 64 + x^2 = 289, 64- 64 + x^2 = 289-64, x^2 = 225, square root x and 225, Leg1 = 15

Answer:

z=2

Step-by-step explanation:

60=-5(-6-3z)

60= 30+15z

60-30=15z

30/15=15z/15

2=z

Answer:

-7+26i

Step-by-step explanation:

Use FOIL

2•4+2(3i)+5i•4+5i(3i)

Simplify by combining like terms for your answer

8+6i+20i-15

-7+26i

Answer: 46 inches

Step-by-step explanation: 184/4= 46

Question:

Daredevil Danny was cliff jumping. He jumped off a cliff that was 14.2 meters above the surface of the  water. At the end of his jump, Danny was 2.3 meters below the surface of the water.

The following equation describes this situation  14.2 + (-16,5) = -2.3 .

What does -16.5 tell us?

Answer:

The displacement between his current position and his initial position

Step-by-step explanation:

Given

[tex]Initial\ Position = 14.2m[/tex]

[tex]Final\ Position = -2.3m[/tex]

[tex]14.2 + (-16.5) = -2.3[/tex]

Required

What does -16.5 represents?

To understand this, we need to first calculate the displacement between his initial and final position

[tex]Displacement = Final\ Position - Initial\ Position[/tex]

[tex]Displacement = -2.3m - 14.2m[/tex]

[tex]Displacement = - 16.5m[/tex]

So: -16.5m is the total displacement from the start position (i.e. off the cliff) and current position (beneath the water surface)

Answer: $184,080

Step-by-step explanation:

First multiply 18% by the original budget to find how much the 18% of the budget was .

18% * 156,000  = 28080

Now add  add 28080 to the original budget to find out how much she actually spent.

156,000 + 20,080 = 184,080