How do the graphs of transformations compared to the graph of the parent function. Need the answer to this

if we have

(10^9)(10^2)

adds the exponents

10^(9+2)

10^11

If you have

10^18/ 10^7

subtract the exponents

10^(18-7)

10^11

If you have

(10^6)^2/10

First multiply the exponents

10^(6*2)/10

10^12/10

subtract exponents

10^(12-1)

10^11

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.

Answer:

Step-by-step explanation:

8 grams of 30% --> 2.4 grams of AS For 2.4 grams to be 40% --> 6 grams of solution Evaporate 2 grams of water

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.

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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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

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:

There were 1200 respondents:

400 parents wanted soccer offered

370 parents wanted tennis offered

625 parents wanted baseball/softball offered

150 parents wanted soccer and tennis offered

315 parents wanted soccer and baseball/softball offered

230 parents wanted baseball/softball and tennis offered

75 parents wanted all three sports offered

Therefore:

We have to add all the options that were mixed with different sports:

150 + 315 + 230 = 695 - 75= 620 (We subtract 75 because it's already included in the other values as we can see in the diagram)

We have to add all the parents that chose only one sport:

400 + 370 + 625= 1395

We have to subtract 620 from 1395:

1395 - 620= 775 parents who chose any sport

Now:

1200 - 775 = 425 respondents who didn't want any.

Therefore, 425 parents didn't want any of the sports offered.

The answer is D) 425.

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

9x + 5y = 10

is a linear equation because all variables are raised to exponent 1.

This equation is already written in standard form (A = 9, B = 5, C = 10)

2y + 4 = 6x​

is a linear equation because all variables are raised to exponent 1.

Subtracting 2y at both sides:

2y + 4 - 2y= 6x​ - 2y

4 = 6x​ - 2y

or

6x - 2y = 4

which is in standard form (A = 6, B = -2, C = 4)

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

Let's solve the equation:

Therefore the solution of the equation 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

We have the function:

And we need to find its value when x = -12. So, replacing x with -12, we obtain:

Notice that the product of two negative numbers is a positive number.

Therefore, the answer is -5.2.

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:

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

Yasmin bought 3 1/2 pounds of ground beef, we can express the amount that she bought as a fraction like this:

Since she bought it for $11.2, if we divide the cost by the amount that she purchased, we get the cost per pound, like this:

To divide by a fraction, we just have to invert its numerator and denominator:

Then, the cost per pound equals $3.2

Answer: you will only have enough money for the rounded tank, after buying everything you will have 9 cents left

Step-by-step explanation: two $3.69 fish, $4.19 fish food. 2x3.69=7.38+4.19=11.57

25-11.57=13.43

13.43+11.48=24.91

25-24.91=0.09

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

You have the following polynomial:

5r³ - 10r² + 3r - 6

In order to factorize the given polynomial, use synthetic division:

5 -10 3 -6 | 2

10 0 6

5 0 3 0

The remainder is zero in the previous division, then, r - 2 is a factor of the given polynomial, the other factor is formed with the coefficients of the division, just as follow:

5r³ - 10r² + 3r - 6 = (r - 2)(5r² + 3)

Hence, the factor are (r - 2)(5r² + 3)

Answer:(r-2) x (5r^2+3)

Step-by-step explanation:

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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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

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

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

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

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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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: