y=-2x+6x+8 how do i find the vertex

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

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:

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

Let's solve the equation:

Therefore the solution of the equation is:

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

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

2/2 = 1

The answer would be 1

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.

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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We have the following functions:

And we need to find:

Step 1. Find 3g by multiplying g(x) by 3:

Use the distributive property to multiply 3 by the two terms inside the parentheses:

Step 2. Once we have 3g, we subtract h(x) to it:

Here we have 3g and to that, we are subtracting h which in parentheses.

Simplifying the expression by again using the distributive property and multiply the - sign by the two terms inside the parentheses:

Step 4. Combine like terms:

What we just found is (3g-h)(x):

Step 5. To find what we are asked for

We need to evaluate the result from step 4, when x is equal to -3:

Solving the operations:

Answer:

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.

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)

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.

Applying the definition of similar triangles, the measure of ∠DEF = 85°.

If two triangles are similar, then their corresponding angles are all equal in measure to each other.

In the image given, since E and F are the midpoint of both sides of triangle BCD, then it follows that triangles BCD and EFD are similar triangles.

Therefore, ∠DBC ≅ ∠DEF

m∠DBC = m∠DEF

Substitute

4x + 53 = -6x + 133

4x + 6x = -53 + 133

10x = 80

10x/10 = 80/10 [division property of equality]

x = 8

Measure of ∠DEF = -6x + 133 = -6(8) + 133

Measure of ∠DEF = 85°

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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

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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Given the equation below

Step 1

Collect like terms.

Step 2

Divide both sides of the equation obtained, by the coefficient of the unknown.

Hence, the value of n in the equation is 4

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.

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

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

Answer:

  (d)  No, because 8 + 9 = 17

Step-by-step explanation:

You want to know if side lengths 8, 9, and 17 can form a triangle.

The triangle inequality requires the sum of the two short sides exceed the length of the longest side. For sides 8, 9, 17, this would require ...

  8 + 9 > 17 . . . . . . . not true; no triangle can be formed

The sum is 8+9 = 17, a value that is not greater than 17. The triangle inequality is not satisfied. So, no triangle can be formed.

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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

Let's remember what the variables mean:

F= temperature (in Fahrenheit),

v= wind speed.

A) The formula "works" when the wind speed is between 4 and 45 miles per hour. The question asks for a wind speed of 20 miles per hour. Then, we can apply the formula. Here,

Then,

Approximating, the answer is

B) This question is just about to find F in the provided equation after replacing the given v and WCI. Let's do that:

Then, the actual temperature is

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

solution

answer: B

you would have to do this backwards

20 times 2 would remove the /2

5c=40

40 divided by 5

is

8

C=8

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

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

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