The measures of the angles of a triangle
are shown in the figure below. Solve for x.
47°
103⁰
(3x-12)°

Let p(x) be the required polynomial.

we are given that p(x) has a zero 1 with multiplicity 2

in other word, this means that (x-1) occurs twice as a factor of p(x).

Expressions with polynomial functions include variables with various degrees, non-zero coefficients, positive exponents (of variables), and constants. A polynomial in "b" of degree 2 is, for instance, f(b) = 4b2 - 6.

Likewise, (x-3) appears as a factor of p(x) once.

we are also given that the degree of p(x) is 3.

So, p(x) can not have more than 3 linear factors.

Altogether,

p(x) = k(x-1)^2  (x-3), where constant k ∈ R - {0}.

We may take k = 1 and get the desired polynomial,

p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3

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The approximate value of log₈1000 is 0.30.

                [tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]

The given values are:

In 8 ≈ 2.08 and In 1000 ≈ 6.91

To find the approximate value of log₈1000,

log₈1000 =  In 8/In 1000

              = 2.08/6.91

              ≅ 0.30

Therefore, the approximate value of log₈1000 is 0.30.

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Answer:

with what?

Step-by-step explanation:

$139,450

==========================================================

Explanation:

asset = an item that is either cash or can be turned into cash

liability = something that needs to be paid back (eg: truck loan)

A = total assets

A = (homeValue) + (workEquipment) + (carValue) + (investments)

A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)

A = $284,678

B = total liabilities

B = (mortgage)+(credit card balance)+(truck loan)

B = ($76,765)+($2,055)+($66,408)

B = $145,228

C = net worth

C = A - B

C = ($284,678) - ($145,228)

C = $139,450 which points us to choice A as the final answer.

The net worth of the carpenter is $144,633.

Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.

Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities.

Here,

Net worth = Financial assets - Liabilities

= (175,742+3,365+44,346) - (76,765+2,055)

= 223,453 - 78,820

= $144,633

Therefore, the net worth of the carpenter is $144,633.

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The evaluation of the numbers (-3)^8 and (-3)^9 will be (-3)^17.

Based on the information given, it should be noted that this illustrates that the numbers are raised to power.

In this case, it should be noted that we want to multiply the powers, this illustrates that we gave to add the powers. This will be:

Evaluate (-3)^8 × (-3)^9

Note that 8 + 9 = 17. Therefore,

Evaluate (-3)^8 and (-3)^9

= -3^17.

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Evaluate (-3)^8 × (-3)^9

Answer:

110

Step-by-step explanation:

To find the measure of the exterior angle we first need to find the value of t.

The sum of interior angles in a triangle is equal to 180° so we can write the following equation:

t + 10 + t + t + 20 = 180 add like terms

3t + 30 = 180 subtract 30 from both sides

3t = 150 divide both sides by 3

t = 50

The exterior angles and the angle represented with t + 20 make a straight line

and they are supplementary angles so their sum is equal to 180

t + 20 = 70 to complete this to 180 we need 110

The function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is the following equation-

g(x) = 3/4 f(x)

Since, the functions are not given, we will assume them by ourselves. You can use the same procedure for any pair of functions of the form -g(x) = n f(x)

Assume that -

f(x) = 2x + 1

Now -

g(x) = (3/4) f(x)

g(x) = (3/4)(2x + 1)

g(x) = (3/2)x + 3/4

Now, both the graphs f(x) and g(x) are attached below. In general, g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4).

Therefore, the function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.

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(a) 65 means the car will travel 65 miles in 1 hour .

(b) The car will travel 97.5 miles in 1.5 hours .

(c) The car will take 0.4 hours to travel 26 miles at his speed .

In the question ,

it is given that

the car is traveling down a highway at a constant speed

and the equation representing is d =65*t

Part(a)

On comparing , the given equation with the equation of speed , time and distance

which is , distance = speed × time

on comparing both the equations , we get speed = 65 mph .

hence , 65 means the car will travel 65 miles in 1 hour .

Part(b)

substituting the value t = 1.5 hours in the given equation , we get

d = 65×1.5

= 97.5

hence , The car will travel 97.5 miles in 1.5 hours

Part(c)

Substituting the value of d = 26 miles in the given equation , we get

26 = 65×t

t = 26/65

t = 0.4 hours

hence , It takes the car 0.4 hours to travel 26 miles.

Therefore , (a) 65 means the car will travel 65 miles in 1 hour .

(b) The car will travel 97.5 miles in 1.5 hours .

(c) The car will take 0.4 hours to travel 26 miles at his speed .

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Answer: a = 2.2

C = 5.1,-5.1

The equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3

Given : x - 4y = 8

4y = x- 8

On dividing by 4 we get;

y= x/4 - 2

This is of the form y = mx + c

Thus m in this case on comparing we get m= 1/4

We know the formula of the slope ;

y - y₁ =m ( x - x₁ )

y - 1 = 1/4 ( x- 7)

On cross multiplying we get ;

x- 4y = 3

Thus the equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3 .

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Answer:

Step-by-step explanation:

1,3        2,6        4,8

I hope it helps, thank you!

The statement that represents the given inequality is:

The product of 8 and n decreased by 5 is less than 25.

The inequality is defined as follows:

8(n - 5) < 25.

The meaning of the expression n - 5 is given as follows:

n decreased by 5. (n is an unknown number).

The meaning of the expression 8(n - 5) is given as follows:

The product of 8 and n decreased by 5. (multiplication of two numbers is also called product).

The symbol of the inequality is given as follows:

<

Which represents the expression less than.

Considering the 25 on the other side of the inequality, the complete sentence is given as follows:

The product of 8 and n decreased by 5 is less than 25.

The complete problem is:

Sal wrote the statement below to represent the inequality 8(n - 5) < 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is ___________

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The lottery's anticipated worth is $80.

Given that,

The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.

A) EV=125*.2+100*.3+50*.5=$80

The lottery's anticipated worth is $80.

The expected value is obtained by multiplying each result by its likelihood.

The expected value of the lottery is then calculated by adding up all of these.

This is what we have: ;;

125(0.2) + 100(0.3) + 50(0.5) (0.5)

= 25 + 30 + 25 = $80

B) This is the formula for variance is shown in figure :

So, we can calculate the variance as follows:

.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975

C) A risk-neutral person would pay $80 or less to play the lottery.

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Answer:

Step-by-step explanation:

Expected value of the lottery is $83.75.

Variance of the outcome is 909.6.

A risk-neutral person would pay $83.75 or less to play the lottery.

a) The expected value is obtained by multiplying each result by its likelihood.

The expected value of the lottery is then calculated by adding up all of these.

This is,

125(0.25) + 100(0.3) + 50(0.45)

          = $83.75

b) we can calculate the variance as follows:

Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6

c) A risk-neutral person would pay $83.75 or less to play the lottery.

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Answer:

4cm..............................

Step-by-step explanation:

24/6=4

4x6=24

The most appropriate choice for velocity and accleration will be given by-  Deacceleration of a car of 15 [tex]m/s^2[/tex] is a real world situation for which the rate of change is -15

What is velocity and acceleration?

Velocity

The distance travelled by a body per unit interval of time where the direction of the motion of a body is taken into account is known as velocity.

Velocity is a vector quantity as direction of motion of body is taken into account.

If d is the displacement of body and t is the time,

Velocity = [tex]\frac{d}{t}[/tex]

Acceleration

The rate of change of velocity of a body is called acceleration.

Acceleration is a vector quantity as direction of motion of a body is taken into account.

If [tex]\Delta[/tex]v is the change of velocity and t is the time,

Acceleration = [tex]\frac{\Delta v}{t}[/tex]

If velocity decreases then it is called Deacceleration

Here

Deacceleration of a car is 15 [tex]m/s^2[/tex]

That means rate of change of velocity of a car is -15 [tex]m/s^2[/tex]

This is a real world situation for which the rate of change is -15

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Answer:

Step-by-step explanation:

Answer:

(f ⋅ g)(x) = f(g(x)) = 5·√(9 - x^2)

The domain is: -3 ≤ x ≤ 3

(g ⋅ f)(x) = g(f(x)) = √(9 - (5·x)^2)

The domain is: -0.6 ≤ x ≤ 0.6

Answer:

C≈97.39in

Step-by-step explanation:

Answer:97.39

Step-by-step explanation:

The total surface area of the triangular prism is 756 meter²

Given,

A triangular prism and its net.

We have to find the surface area of the triangular prism.

First we can consider the right angled triangle.

Height = 9 meter

Base = 12 meter

Hypotenuse = 15 meter

Area of the right angled triangle = (1/2 bh)

Here,

Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²

Now, area of right rectangle.

Area of rectangle = length × breadth

Here, the breadth of the rectangle is the height of the triangle = 9 meter

Length = 18 meter

Area = length × breadth = 9 × 18 = 162 meter²

Then, area of middle rectangle.

Length = 18 meter

Breadth = 12 meter

Area = length × breadth = 18 × 12 = 216 meter²

Next, area of left rectangle.

Length = 18 meter

Breadth = Hypotenuse of the triangle = 15 meter

Area = length × breadth = 18 × 15 = 270 meter²

Now, lets calculate the total surface area of the triangular prism.

Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²

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Answer:

ok wirrudi 123 alf8 434 21 3dis w

Answer:

y = -x - 7

Step-by-step explanation:

Perpendicular to the slope m = 1 is the slope -1/m = -1.

y = m * (x - Px) + Py

y = -1 * (x - 2) + (-9)

y = -x + 2 - 9

y = -x - 7

Answer:

Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .

The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76

The probability can be determined using the following formula;

probability = number of desired events or outcomes ÷ total number of events or outcomes

The total is known to be 45, the favorable or desired outcomes can be calculated as follows;

number of desired outcomes = number of vulnerable species + number of critically endangered species

number of desired outcomes = 12 + 22

number of desired outcomes = 34

Now we calculate the probability by using the above formula;

probability = 34 ÷ 45

probability = 0.76

Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.

Although a part of your question is missing, you might be referring to this question:

In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices

11/45

0.24

0.83

0.76

12/45

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Answer:  D

Step-by-step explanation:

A. [tex]P=2(4)-3=5[/tex]

B. [tex]P=2(0)-3=-3[/tex]

C. [tex]P=2(0)-0=0[/tex]

D. [tex]P=2(4)-0=8[/tex]

The answer is A, because if one minute corresponds to 10 gallons of water, then the amount of gallons is the minutes times 10.

Yes, it is a solution

y = -10x + - 4

The given point: (0, -4)

To know if it is a solution, we need to replace the y and x with the points given.

If the result on the left hand side is the same as the right hand side then, it is a solution

x =0, y = -4

-4 = -10(0) + -4

-4 = 0 + (-4)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

-4 = 0 - 4

-4 = -4

The left hand side is the same as the right hand side. Hence, it is a solution

Answer:

Yes it is a solution

Step-by-step explanation:

y = -10x + - 4

Point: (0, -4)

Given:

Ratio of ounces of oil to gallons of gasoline = 9 : 11

Gallons of gasoline = 55 gallons

Let's find the ounces of oil.

To find the ounces of oil, we have the equation:

Thus, we have:

Let x represent the ounces of oil.

Cross multiply:

Therefore, there are 45 ounces of oil.

ANSWER:

45 ounces of oil