I'm not sure how to find the degrees for angle d

Given the function;

The leading exponent is odd and the leading coeeficient is positive, so as x tends to positive infinity, f(x) also tends to positive infinity and as x tends to negative infinity, f(x) also tends to negative infinity.

Thus, the correct answer is FALSE.

From the data sets given

(A U B) = ( 1, 2 ,3 ,4 , 7, 8 , 9)

(A U C) = (1, 2 ,3 ,4 ,6 ,8)

(A U B) n ( A U C) = ( 1 ,2, 3, 4 ,8)

Answer:

n∧4 basically its n to the power of 14

Step-by-step explanation:

your work is in the pic below check it out sorry if incorrect have a wonderful day:)

Solution

The interior angles of a quadrilateral measure to 360 degrees

Two of them are known and are 210 and 82. They add to 292 degrees.

The other two angles must sum to (360-292)=68 degrees.

They are in a ratio of 7:10

The sum of these two numbers is 17

The other two angles are 28 and 40 degrees respectively.

The sum of all 4 angles is 360 degrees.

The final answer

The other two angles are 28 and 40 degrees respectively.

95 fluid ounces or 3 quarts.

To solve htis problem, convert the ounces to quarts and compare the results.

1 ounce ----------------------- 0.03125 quart

95 ounces ------------------- x

x = (95 x 0.03125) / 1

x = 2.97 quarts

2.97 ounces < 3 quarts

Three quarts is more

The most appropriate choice for inverse of a  function will be given by-

[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]

What is inverse of a function?

At first, it is important to know about function

A function from A to B is a rule that maps to each element of A a unique element of B.

A is called the domain of the function and B is called the co domain of the function.

[tex]f^{-1}[/tex]  is said to be the inverse of [tex]f[/tex] if [tex]f[/tex] [tex]o[/tex] [tex]f^{-1}[/tex] = [tex]f^{-1} o[/tex] [tex]f[/tex] =  [tex]I[/tex], I is the identity function.

Let g(x) = y

[tex]\frac{10-5x}{2} = y\\10 - 5x = 2y\\5x = 10-2y\\x = \frac{10 - 2y}{5}[/tex]

[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]

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The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:

x = -3 or x = 9.

The equation in Step 6 is given as follows:

[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]

Simplifying the square roots, the variable x can be isolated, as follows:

Both -6 and 6 are correct results for the square root of 36, because:

His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:

From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;

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We have a initial population P(0) of 3800.

We know that the population is decreasing by 1.4% each year, so the population at year 1 (2009) we will have a population of:

We can generalize this for P(n), where n is the number of years from 2008.

From 2008 to 2013 we have 2013-2008=5 years, so for the year 2013, the value of n is n=5.

Then, the population for 2013 will be P(5) and can be calculated as:

Answer: the predicted population for the year 2013 is 3541.

Perimeter of an octagon

radius R = 19.9 cm

then To find perimeter

Multiply 8 times lenghts of octagon

with height=

internal angle is= 360/8 = 45°

Now apply rule of Sines

then sin 45/ lside = sin ( 180-45)/2/ radius

Therefore

Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm

Now multiply 8 times this lenght side to find perimeter

8x 15.23 = 121.84 cm

Answer:

7. x = 25

8. x = 28

Step-by-step explanation:

7. Alternate interior angles are congruent.

[tex]x + 25 = 2x[/tex]

[tex]x = 25[/tex]

8. Consecutive angles add up to 180°.

[tex]4x + 2x + 12 = 180[/tex]

[tex]6x + 12 = 180[/tex]

[tex]6x = 168[/tex]

[tex]x = 28[/tex]

SOLUTION:

Case: Equations

Method:

The table:

Plotting the points

Studying the points, could either be quadratic or exponential.

We will proceed to test the points but because the increase of the y values as x increases from left to right is not a fine pattern, it will most likely not be exponential.

Next, we test a quadratic model on the graph

Final answer:

Quadratic function

To be linear, you'd need a fixed increase in the y-values for a constant increase in the x-values.  As x increases by 1 in each new point, your y-values increase by 1, 3, 5, and 7 respectively.  That is not the same increase each time.  This is not linear.

To be exponential, you need a fixed percent increase in the y-values between the points.  From (-2,-16) to (-1,-15), your increase is 1/16 or 6.25%.  From (-1,-15) to (0,-12), your increase is 3/15 or 20%.  That is not a constant percent increase.

The only option left is quadratic.  

To find the function, start with c = -12, based on the point (0,-12).

This gives you f(x) = ax^2 + bx -12

Next plug in (2,0) into f(x):  0 = 4a + 2b - 12

And plug in (1,-7) into f(x):  -7 = a + b -12

You now have two equations with two unknowns.

Solve equation 2 for a:  
         5-b = a

Substitute that into equation 1

        0 = 4(5-b) + 2b - 12

        0 = 20 -4b + 2b - 12

        -8 = -2b

        4 = b

Substitute that b-value into 5-b=a

        5 - 4 = a

        1 = a

You have your three values and have your function:

        f(x) = 1x^2 + 4x - 12    or    f(x) = x^2 + 4x - 12

You can confirm that the other points also fit with this function.

Time taken to fill 3 same-size bathtubs is 3b minutes.

Its given in the question that it takes b minutes to fill Sylvia's bathtub with water.

Time taken to fill same-size bathtub as an expression = 3*b

                                                                                          = 3b minutes.

Hence, time takes to fill 3 bathtubs of the same size as of Sylvia's bathtub to fill with water is 3b minutes.

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The correct option is A

The graph has been horizontally stretched, 9 units to the right.

Given the function:

The function:

is a horizontally stretched transformation, 9 units to the right.

sin 0 = 26/30

sin 0 = 0.87

0 = 60°

Result 0 = 60°

A. The similar triangles are: B. ΔABC ~ ΔDBE

B. AC = 16

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if two angles in one triangle are congruent to two corresponding angles in the other triangles.

The side lengths of two similar triangles are proportional to each other, which means they have ratio that is equal to one another.

Part A:

In the given diagram, triangles ABC and DBE have two pairs of corresponding angles that are congruent to each other which are: angle ABC ≅ DBE, and angle BCA ≅ BED.

Therefore, based on the AA similarity theorem: B. triangle ABC ~ triangle DBE.

Part B:

Since triangles ABC and DBE are similar triangles, therefore, BC/BE = AC/DE

Substitute

12/15 = (x + 1)/(x + 5)

Cross multiply

12(x + 5) = 15(x + 1)

12x + 60 = 15x + 15

Combine like terms

12x - 15x = -60 + 15

-3x = -45

-3x/-3 = -45/-3

x = 15

AC = x + 1 = 15 + 1

AC = 16

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An exponential function in the form y=abˣ is y = 7×4ˣ .

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Write the equation of the function:

y = abˣ

For point (0 , 7)

7 = ab⁰

for point (2 , 112)

x = 2

y = 112

Substitute:

112 = ab²

Swap the sides:

ab⁰ = 7

ab² = 112

Find the quotient of the equations:

ab²/ ab⁰ = 112/7

Simplify the equations:

b² = 16

b =  ±√16

Split into two equations: b =  +√16 or b =  -√16

Simplify the radical expression:

b = 4

b = -4

Combine the results: b = 4 or  b = -4

Any fraction with a denominator of 1 is equal to its numerator:

a = 7

7 = a (±4)°

Substitute into one of the equations:

a = 7

b = ± 4

y = 7×4ˣ

Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.

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Note that;

secθ = 1/cosθ cotθ= cosθ/sinθ

substitute into into the expression

cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator

Since the triangle is a right-angled triangle, we can use SohCahToa to find x

Using the ratio

Opposite = 4ft

adjacent = x

Substituting these values yield

To find Z we use the fact that the sum of angles in a triangle is 180 degrees

so that in triangle XYZ

90 + 25 +Z = 180

Z = 180 - 115

Z= 65 degrees

We will now use Pythagoras theorem to find y

Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C

we have the equation

Remember the definition of logarithm

Applying the definition of a logarithm to this problem

we have that

Apply change of base formula

Remember that

so

therefore

The answer is

Answer: 11/92

Explanation:

Probability is expressed as

number of favorable outcomes/number of total outcomes

From the information given,

number of green marbles = 11

number of red marbles = 7

number of blue marbles = 6

Total number of marbles = 11 + 7 + 6 = 24

Probability of selecting a blue marble = 6/24 = 1/4

Since the marble is not replaced, total number of marbles left = 24 - 1 = 23

Probability of selecting a green marble = 11/23

The probability of selecting a blue marble followed by a green marble is

1/4 x 11/23

= 11/92

Answer:

70 miles an hour

Step-by-step explanation:

First, you want to know how fast bus A can go. So you want to do 125/3 since the bus travels 3 hours. you get 41.6666667. keep that number. then you want to divide 85 by 3 since bus B is going for 3 hours. you get 28.3333333. then you add those numbers to get how fast bus B is going and you get 70 miles per hour for bus B

we have

4P2

the formula is equal to

n!/(n-r)!

n=4

r=2

substitute

4!/(4-2)!

4!/2!=(4*3*2!)/2!

simplify

4*3=12

The total tip for a four-person meal at a restaurant is $122, people $8018. The percentage of the tip is 22%.

Given that,

The total tip for a four-person meal at a restaurant is $122, people $8018. What proportion of a tip is that? Four restaurant beers cost 120 each, and the group tip is $180.

We have to calculate the how much percentage  of a tip is there.

In a variety of situations, such as restaurants, hotels, salons, and other establishments in the service sector, leaving a tip is common. Knowing how to compute a tip and knowing how much to tip is crucial for a variety of reasons, including the fact that many service sector personnel, like waiters, rely heavily on gratuities for the majority of their income. This means that these experts might not be able to support themselves and their families without tips.

Percentage= tip/amount

Percentage= $180/$8018

Percentage= 22%

Therefore, the percentage of the tip is 22%

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Solution

For this case we have the following points:

(-9, 6) and (-3, 9)

and we can find the slope with this formula:

Then the solution would be:

B ) 1/2

The side lengths of the right triangle in exact form are z = (15√3)/2,   x = 15/2, y = (15√3)/4, a = 15/4 and b = 45/4.

Three out of the six functions used in trigonometry is expressed as;

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

From diagram, we solve for side z of the right triangle.

cosθ = adjacent / hypotenuse

cos( 30° ) = z / 15

Solve for z

z = cos( 30° ) × 15

z = (√3)/2 × 15

z = (15√3)/2

Next solve for side x

sinθ = opposite / hypotenuse

sin( 30° ) = x / 15

x = sin( 30° ) × 15

x = 15/2

Solve for side y

sinθ = opposite / hypotenuse

sin( 60° ) = y / 15/2

y = sin( 60° ) × 15/2

y = (15√3)/4

Solve for side a

cosθ = adjacent / hypotenuse

cos( 60° ) = a / 15/2

a = cos( 60° ) × 15/2

a = 15/4

Solve for side b

b = 15 - a

b = 15 - 15/4

b = 45/4

Therefore the length of side of b is 45/4

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Answer:

Step-by-step explanation:

In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.

...

Use a ⋅ or × sign if you see words like double, per, or product.

Twice 16 → 2 ⋅ 16.

Five per day → 5 ⋅ d or 5d. ...

The product of 8 and 20 → 8 ⋅ 20.

Using pythagoras theorem to find the distance between two points in a coordinate:

To calculate the distance between the points AB = hypotenuse

Therefore the distance between the points in the coordinate system = 4√2