A ball is dropped from a state of rest at time T = 0.The distance traveled after t seconds is s(t) = 16t^2 ft.

SOLUTION

Sum of angles in a triangle must be equal to 180°

So, since one of the angle measures 90° and the other is 42°, then

90 + 42 + y = 180°, where y is the third angle

So, 132 + y = 180

y = 180 - 132 = 48°.

Therefore, one unique triangle can be drawn because the third angle must measure 48º.

Option A is the correct answer.

solution

answer: B

12x - 9y +12 =0

To find the slope and y intercept, we want to put the equation in slope intercept form

y = mx+b where m is the slope and b is the y intercept

Solve the equation for y

Add 9y to each side

12x - 9y+9y +12 =0+9y

12x+12 = 9y

Divide each side by 9

12x/9 +12/9 = 9y/9

4/3 x + 4/3 = y

Rewriting

y = 4/3x + 4/3

The slope is 4/3 and the y intercept is 4/3

Let us break the shape into two triangles and solve for the unknowns.

The first triangle is shown below:

We will use the Pythagorean Theorem defined to be:

Therefore, we can relate the sides of the triangles as shown below:

Solving, we have:

Hence, we can have the second triangle to be:

Applying the Pythagorean Theorem, we have:

Solving, we have:

The values of the unknowns are:

ANSWER

G. 10 and -2 only

EXPLANATION

-5/4 is a fraction that can't be simplified. Therefore it is not an integer.

1.25 has decimals, so it is not an integer either.

10 and -2 are are integers.

STEP - BY STEP EXPLANATION

What to find?

Equation for a quadratic equation.

Given:

Shifts 8 unit to the left.

4 units down

Step 1

Note the following :

• The parent function of a quadratic equation in general form is given by;

• If f(x) shifts q-units left, the f(x) becomes, f(x+q)

• If f(x) shift m-units down, then the new function is, f(x) -m

Step 2

Apply the rules to the parent function.

8 units to the left implies q=8

4 units down implies m= 4

ANSWER

y= (x+8)²- 4

Let's solve the equation:

Therefore the solution of the equation is:

The triangle is shown below:

Notice how this is an isosceles triangle.

We can find the lengths of the hypotenuse by using the trigonometric functions:

Then we have:

Therefore the hypotenuse is 29.7 ft.

Coco, this is the solution to the inequality:

5 - 3x/2 ≥ 1/3

Subtracting 5 at both sides:

5 - 3x/2 - 5 ≥ 1/3 - 5

-3x/2 ≥ 1/3 - 15/3

-3x/2 ≥ -14/3

LCD (Least Common Denominator) between 2 and 3 : 6

-9x/6 ≥ -28/6

Dividing by -9/6 at both sides:

-9x/6 / -9/6 ≥ -28/6 / -9/6

x ≥ 28/9

In consequence, the correct answer is C. x ≥ 28/9

The equation is modelled by the function,

c(x) = 2.1x^2 - 12.7x + 167.4

The general form of a quadratic equation is expressed as

ax^2 + bx + c

The given function is quadratic and the graph would be a parabola which opens upwards because the value of a is positive

Since x represents the speed, the speed at which the he

Reflection over the x-axis:

(x,y)--->(x, -y)

and the question is what is not a reflection across the x-axis.

so,

the correct option is D which is:

R'(-9, 4) ----> R'(9, -4)

Because it is a reflection over the y-axis.

Given any three numbers a, b, and c.

By the distributive law, we must have:

a x (b + c) = (a x b) + (a x c)

Now to find 8 x78

8 x 78 = 8 x (70 + 8) = (8 x 70) + (8 x 8) = 560 + 64 = 624

Apply the angles sum property in the triangle ABC,

Similarly, apply the angles sum property in triangle BCD,

From triangle ABC,

From triangle BDC,

Now, consider that,

So the triangle BDE is also a right triangle, and the trigonometric ratios are applicable.

Solve for 'x' as,

Thus, the value of the angle 'x' is 57.3 degrees approximately.ang

by the distributive law x(y+z)=zy+xz, we have

Then we use the properties of inequalities, we can switch both sides, and if we add or multiply something on both sides the equality remains

we want the variables and the numbers without variables to be in different side, so, first we add 20 to both sides, note that the -20 will be cancelled

we want to left all the numbers with variable on the right side so we substract 3b (add -3b) to both sides. Same as before, the 3b will be cancellated (we can change the order in the sum)

of course, you're welcome

I was asking if you have understood my explanation so far

tell me

it doesn't matter the order, in fact, when you get used to the method you can work with both at the same time

any other question?

yes, you could substrac 3b first

For example

sadly I will need to leave since my shift is over, but if you ask another question one of my partners will help you

Have a nice evening!!!!

then we add like terms and switch both sides

And then we multiply by 1/5 both sides

Explanation

Step 1

Let's remember one propertie of the roots

hence

replacing in the expression

therefore, the answer is

I hope this helps you

C ≤ 0

The given equation is:

Make C the subject of the equation

At 32°F, substitute F = 32 into the equation above to get the corresponding temperature in °C

The inequality representing the corresponding temperature that is at or below 32°F is C ≤ 0

The midpoint for segment PQ can be calculated as:

Then, the midpoint of PQ is:

Additionally, PQ can be calculated as:

So:

It means that:

Solving for Q, we get:

Q = 8 + 2 = 10 or Q = 2 - 8 = -6

Finally, replacing these values on the initial equation for the midpoint, we get:

If Q = 10, then:

midpoint = 1 + 0.5(10) = 1 + 5 = 6

If Q = -6, then:

midpoint = 1 + 0.5(-6) = 1 - 3 = -2

The possible midpoints for PQ are 6 and -2

2/2 = 1

The answer would be 1

The arithmetic series is:

-1 + 2 + 5 + 8 + .....

The first term, a = -1

The common difference, d = 2 - (-1)

d = 3

The number of terms, n = 7

Find the sum of the arithmetic series below

Therefore, the sum of the arithmetic series = 56

you would have to do this backwards

20 times 2 would remove the /2

5c=40

40 divided by 5

is

8

C=8

Answer

The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.

Explanation

To do this, we have to first note that

So, we can then simplify the given expression

Hope this Helps!!!

Given:

We must find the equation that models the amount of medication in the bloodstream as a function of the days passed from the initial dose. The initial dose is a and we are going to use x for the number of days and M for the amount of mediaction in the bloodstream. We are going to model this using an exponential function which means that the variable x must be in the exponent of a power:

We are told that the half-life of the medication is 6 hours. This means that after 6 hours the amount of medication in the bloodstream is reduced to a half. If the initial dose was a then the amount after 6 hours has to be a/2. We are going to use this to find the parameter b but first we must convert 6 hours into days since our equation works with days.

Remember that a day is composed of 24 hours so 6 hours is equivalent to 6/24=1/4 day. This means that the amount of medication after 1/4 days is the half of the initial dose. In mathematical terms this means M(1/4)=M(0)/2:

We can divide both sides of this equation by a:

Now let's raised both sides of this equation to 4:

Which can also be written as:

Then the equation that models how much medication will be in the bloodstream after x days is:

Using this we must find how much medication will be in the bloodstream after 4 days for an initial dose of 500mg. This basically means that a=500mg, x=4 and we have to find M(4):

So after 4 days there are 0.00763 mg of medication in the bloodstream.

Now we have to indicate how much more medication will be if the initial dose is 750mg instead of 500mg. So we take a=750mg and x=4:

If we substract the first value we found from this one we obtained the required difference:

So the answer to the third question is 0.00381mg.

The expression with rational denominator is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

From the question, the fraction is given as

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1}[/tex]

To rewrite the fraction with a rational denominator, we simply rationalize the fraction

When the fraction is rationalized, we have the following equation

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{1}{\sqrt 5 + \sqrt{3} - 1} \times \frac{\sqrt 5 - \sqrt{3} + 1}{\sqrt 5 - \sqrt{3} + 1}[/tex]

Evaluate the products in the above equation

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{(\sqrt 5)^2 - (\sqrt{3} + 1)^2}[/tex]

This gives

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{5 - 10 - 2\sqrt 3}[/tex]

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3}[/tex]

Rationalize again

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3} \times \frac{- 5+2\sqrt 3}{- 5 +2\sqrt 3}[/tex]

This gives

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{(-5)^2 - (2\sqrt 3)^2}[/tex]

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{25 -12}[/tex]

Evaluate

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

Hence, the expression is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

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Step 1:

Find the depreciation

Step 2:

Total cost = $425 + $400 + $110 + $100 + $4000

Total cost = $5035

Final answer

Option D $0.50 per mile

The option that indicates the required sum when n equals 0 to 4 of 2 minus 5 times n, is 2 + (−3) + (−8) + (−13) + (−18) (Option C)

The sum of the terms of a sequence is called a series.

From the given sum of a sequence, we are to find the sum of the given sequence from n = 0 to n = 4

When n = 0

a(0) = 2 - 5(0)

a(0) = 2 - 0

a(0) = 2

When n = 1

a(1) = 2 - 5(1)

a(1) = 2 -5

a(1) = -3

When n = 2

a(2) = 2 - 5(2)

a(2) = 2 - 10

a(2) = -8

When n = 3

a(3) = 2 - 5(3)

a(3) = 2 - 15

a(3) = -13

When n = 4

a(4) = 2 - 5(4)

a(4) = 2 - 20

a(4) = -18

Hence the required sum is 2 + (−3) + (−8) + (−13) + (−18)

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The required sum is 2 + (−3) + (−8) + (−13) + (−18)  when n equals 0 to 4 of 2 minus 5 times n, which is the correct answer that would be an option (C).

The given expression is (2 - 5n)

We to determine the sum of the given sequence from n = 0 to n = 4

Let the required sum is  T₀ + T₁  + T₂ +  T₃ + T₄

Substitute the value of n = 0 in the expression (2 - 5n) to get T₀

⇒ T₀ = 2 - 5(0) = 2 - 0 = 2

Substitute the value of n = 1 in the expression (2 - 5n) to get T₁

⇒ T₁ = 2 - 5(1)  = 2 -5 = -3

Substitute the value of n = 2 in the expression (2 - 5n) to get T₂

⇒ T₂ = 2 - 5(2) = 2 - 10 = -8

Substitute the value of n = 3 in the expression (2 - 5n) to get T₃

⇒ T₃ = 2 - 5(3) = 2 - 15 = -13

Substitute the value of n = 4 in the expression (2 - 5n) to get T₄

⇒ T₄ = 2 - 5(4) = 2 - 20 = -18

Therefore, the required sum is 2 + (−3) + (−8) + (−13) + (−18)

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Answer:

20 meters

Explanation:

The formula for calculating the perimeter of a square is expressed as

perimeter = 4s

where

s is the length of each side of the square

From the information given,

perimeter = 8,000 centimeters

Recall,

1 cm = 0.01 m

8000cm = 8000 x 0.01 = 80 m

Thus,

80 = 4s

s = 80/4

s = 20

The length of each side of the square is 20 meters

Given:

The volume of the cube is 42.87 cubic inches.

The volume of a cube is given as,

The surface area of a cube is,

Answer: the surface area is 73.5 square inches ( approximately)

Given a point P = (x, y) a reflection P' alongside the y axis of that point follows the rule:

We need to multiply the x coordinates of the points by (-1)

The cordinates of the points in the problem are:

A = (2, 5)

B = (2, 4)

C = (-5, 1)

D = (-5, 0)

Then the endpoints of the reflection over the y axis are:

A' = (-2, 5)

B' = (-2, 4)

C' = (5, 1)

D' = (5, 0)

Which is the second option.