Find the degree measure of each angle in the triangle

Answer:

x = 2

Step-by-step explanation:

first do distributive property

4*5 = 20

4*-2x = -8x

combine like terms

20+3 = 23

now we have: 23-8x = 7

solve for x

8-x = 7-23 = -16

divide by -8

x = -16/-8 = 2

x = 2

Answer:

2

Step-by-step explanation:

20-8x+3=7

-8x+3+20=7

-8x+23=7

-8x=7-23

-8x=-16

x=-16/-8

×=16/8

×= 2/1

x=2

\( \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } \)

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is (\(x^2 - 3x - 10\)). We need to solve the equation:

\(x^2 - 3x - 10 = 0\)

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

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Answer:

no

Step-by-step explanation:

at least I don't think so be cause it hard to explain

Answer:

Volume = 261.8 cm³

Surface area = 254.2 cm²

Step-by-step explanation:

To calculate the volume of the cone, we have to use the following formula:

\(\boxed{V = \frac{1}{3} \pi r^2 h}\),

where:

V ⇒ volume

r ⇒ radius = 5 cm

h ⇒ height = 10 cm

Using the above formula and the provided measures, we get:

V = \(\frac{1}{3}\) × π × (5)² × 10

    = \(\frac{1}{3}\) × π × 25 × 10

      = 261.8 cm³

In order to calculate the surface area of the cone, we have to use the following formula:

\(\boxed{SA = \pi r^2 + \pi r l}\)

where:

SA ⇒ surface area

r ⇒ radius = 5 cm

l ⇒ slant length = \(\sqrt{r^2+h^2}\) = \(\sqrt{5^2+10^2}\) = 5√5 cm

Using the formula,

SA = π × (5)² + π × 5 × 5√5

     = π × 25 + π × 25√5

     = 254.2 cm²

The exact measurements for the largest side is 12√10 inches. Hence option a is the correct option.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that the angles of a triangle are 30-60-90.

The smallest angle is always opposite the shortest side, and vice versa. The longest side is also opposite the largest angle, and vice versa.

The opposite side of angle 30 is the shortest side of the triangle.

The opposite side of angle 90 is the longest side of the triangle.

Sine law:

a/sin A = b/ sin B =c/sin C

a is the opposite side of angle A, b is the opposite side of angle B, c is the opposite side of angle C.

Assume that the length of the longest side is a.

Applying sine law in the given triangle:

6√10/sin 30 = a/sin 90

6√10/(1/2)= a/1

a = 12√10

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The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Answer:

\( - 27 {a}^{3} \)

Step-by-step explanation:

The solution is in the attached file

Answer:

15.7ft

Step-by-step explanation:

diameter= a2+b2=c2

(3)^2+(4)^2= 9+16=c^2

25=c^2(divide the square root)

c= 5

d=5 ft

find circumference:2(pie)r

2(3.14)(2.5)= 15.7ft

Answer:

Step-by-step explanation:

Use Pythagorean theorem:

Diameter² = 4² + 3²

                = 16 +9

               = 25

Diameter = √25 = √5*5 = 5 ft

Diameter = 5 ft

Circumference = πd

                        = 3.1428 * 5

                       = 15.714

                      = 15.71  ft

Radius = 5/2 = 2.5 ft

Step-by-step explanation:

the figure I've circled is similar to yhe figure shown because when we compare the measurements of the length and breadth of both rectangles, we can see that both the rectangles have the see me measurements, 3ft and 7ft. The only difference however, is that the figures have been rotated differently, the figure shown is kept vertically, on the other hand, the figure I've circled is rotated horizontally.

hope that helps...

In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:

For each additional city mpg, the highway value goes up by

0.9478 mpg.

And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

According to the statement

we have given that the relationship between the number of miles per gallon on the highway in the graphical representation and that in the city for some cars.

And we have to give some reasons for the given statements.

So, For this purpose, we know that the

A. In this statement we have to tell that the what is shown in the given relationship in the graph.

So, For each additional city mpg, the highway value goes up by

0.9478 mpg.

And the second statement is

B. I this we have to tell the intercept of the plane in the given Relationship.

So, It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

So, In this relationship between the number of miles per gallon on the highway and that in the city for some cars are:

For each additional city mpg, the highway value goes up by

0.9478 mpg.

And It is inappropriate to interpret the intercept because no cars get 0 mpg in the city.

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Disclaimer: This question was incomplete. Pleas find the full content below.

Question:

The figure shows the relationship between the number of miles per gallon on the highway and that in the city for some cars.

a. Report the slope and explain what it means.

b. Either interpret the intercept​ (7.792) or explain why it is not appropriate to interpret the intercept.

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Answer:

-2/5

Step-by-step explanation:

your answer is -2/5 because whenever you have two points you can go ahead and just do rise over run and the formula is y1-y2/x1-y1 now you can go ahead and label them so y1 is 2, y2 is 4, x1 is 2 and x2 is -3 and now plug everything in

2-4/2-(-3)

-2/5

Answer:

x=2

Step-by-step explanation:

-5x-x=-9-3

  -6x=-12

     x=2

Answer:

x = 2

Step-by-step explanation:

\(3 - 5x = x - 9\)

\( = > 5x + x = 9 + 3\)

\( = > 6x = 12\)

\( = > x = \frac{12}{6} = 2\)

A discount is the amount of money that is removed from the original price. The original price of the dishwasher is  $438.

A discount is the amount of money that is removed from the original price of a commodity when it is being sold.

We know that the commodity is being sold that a price of $361.35 but the discount is 17.5% and we are to obtain the original price of the commodity.

Let the original price be x

x - 17.5/100x = 361.35

82.5x/100 =  361.35

x =  361.35 * 100/82.5

x =  $438

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Answer: B

Step-by-step explanation:

You are combining like terms

12y+4y=16y

16y+2x

The maximum possible number of handshakes at the party can be calculated using the formula n(n-1)/2, where n is the number of people attending. This formula is derived from the fact that each person can shake hands with every other person except themselves.

Let's assume that there are n people attending the party. In order to maximize the number of handshakes, we want each person to shake hands with every other person except themselves.

Now, let's consider the first person. They can shake hands with (n-1) other people, as they cannot shake hands with themselves. Similarly, the second person can shake hands with (n-1) other people, but they have already shaken hands with the first person, so they can only shake hands with (n-1)-1 = (n-2) remaining people.

Following this pattern, the third person can shake hands with (n-1)-2 = (n-3) people, the fourth person can shake hands with (n-1)-3 = (n-4) people, and so on. The last person, the nth person, can shake hands with (n-1)-(n-2) = 1 person.

By summing up the number of handshakes for each person, we get (n-1) + (n-2) + (n-3) + ... + 1, which is the sum of the first (n-1) natural numbers. This sum can be calculated using the formula n(n-1)/2.

Therefore, the maximum possible number of handshakes at the party is n(n-1)/2.

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Using conversion from fraction to decimal and rational numbers, we have that:

7. The fraction that has a corresponding decimal greater than 1 is 4/3.

8. One rational number between 7 and 8 is given by option a, which is 7.83838383...

A fraction is converted to decimal dividing the numerator by the denominator.

In item 7, we consider fraction 4/3, for which:

Hence the corresponding decimal is given as follows:

4/3 = 1.333, which is the result of the division of 4 by 3, and is greater than 1.

The set of rational numbers is composed by all numbers that can be represented by fractions, such as integer, terminating decimals and repeating decimals.

In item 8, option a, we have the number 7.83, with the bar at 83. This means that 83 is the repeating decimal part, that is, the rational number is 7.83838383...

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Answer:

Step-by-step explanation:

Solution : Given that, n = 363 x = 171 = x / n =171 / 363 = 0.471 1 - = 1 - 0.471 = 0.529

Answer:

a)  \(\sqrt{69}\)

Step-by-step explanation:

this is a right triangle so you can use the Pythagorean Theorem:

the sum of the legs, squared, is equal to the hypotenuse, squared

10² + b² = 13²

100 + b² = 169

b² = 69

b = \(\sqrt{69}\)

Answer:

slope = 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 10 ← is in slope- intercept form

with slope m = 1

The angle of elevation of the hill to the horizontal plane at point A. The angle = 8.982°.

The angle of elevation of the hill to the horizontal plane at point A, we can use trigonometry. Let's break down the problem step by step:

Height of the tower = 48.7 m

Distance from the foot of the hill to the tower (measured along the hillside) = 305 m

Angle between the surface of the hill and the line of sight to the top of the tower = 8.9°

Let's denote the angle of elevation of the hill to the horizontal plane at point A as α.

1. Draw a diagram:

We can draw a right triangle to represent the situation. The vertical leg of the triangle represents the height of the tower (48.7 m), the hypotenuse represents the line of sight from point A to the top of the tower, and the horizontal leg represents the distance from the foot of the hill to the tower (305 m).

2. Identify the relevant trigonometric ratios:

In the right triangle, the tangent ratio relates the angle α to the sides of the triangle:

tan(α) = Opposite / Adjacent

In this case, the opposite side is the height of the tower (48.7 m), and the adjacent side is the distance from the foot of the hill to the tower (305 m).

3. Calculate the angle of elevation α:

Using the tangent ratio, we have:

tan(α) = 48.7 m / 305 m

Now, we can solve for α:

α = tan⁻¹ (48.7 m / 305 m)

  = 8.982°.

Therefore, the angle of elevation of the hill to the horizontal plane at point A is approximately 8.982°.

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Julie has $1,000 and wants to invest it. She has three options: 1-year Treasury note paying 4.4% interest, 1-year CD paying 3.9% interest, or money market mutual fund with an average yield of 3.7%. Pros of Treasury note are high interest rate but con is lack of flexibility. Pros of CD are lower risk and predictable return but con is lower interest rate. Pros of money market fund are liquidity and flexibility but con is lower interest rate.

The investment options available to Julie are 1-year Treasury note paying 4.4 percent interest This option offers the highest interest rate among the three options and is a low-risk investment as it is backed by the government. However, the money is locked in for one year, and there may be penalties for early withdrawal.

1-year CD paying 3.9 percent interest This option is also a low-risk investment, but the interest rate is slightly lower than the Treasury note. The money is also locked in for one year, and there may be penalties for early withdrawal.

Money market mutual fund with an average yield of 3.7 percent This option offers a slightly higher return than a savings account, but the risk level is slightly higher. The money can be withdrawn at any time without penalty, making it a more flexible option.

The pros of the Treasury note and CD options are higher interest rates and low-risk investments, while the cons are that the money is locked in for one year, and there may be penalties for early withdrawal.

The pros of the money market mutual fund are flexibility and slightly higher returns, while the cons are slightly higher risk and lower returns compared to the other two options. Julie should weigh the pros and cons of each option based on her personal financial goals and risk tolerance.

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The probability that a sample of five parts from a production process that produces 3% defective parts contains exactly two defective parts is approximately 0.2834.

To find this probability, we can use the binomial probability formula:

P(X = 2) = (5 choose 2) * 0.03^2 * (1 - 0.03)^3

Where "X" is the number of defective parts in the sample, "5 choose 2" represents the number of ways to choose 2 defective parts out of 5, and 0.03 and (1 - 0.03) represent the probabilities of selecting a defective and non-defective part, respectively.

Using a calculator, we can simplify and compute:

P(X = 2) = (5 choose 2) * 0.03^2 * 0.97^3

= 10 * 0.0009 * 0.9127

≈ 0.0081

Therefore, the probability is approximately 0.0081 or 0.81%.

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Answer:

(Biggest to smallest)

Sides: DE, FE, FD

Angles: <F, <D, <E

Step-by-step explanation:

DE = 14, FE = 10, FD = 8 (Biggest to smallest)

Each angle matches up diagonally with a side

Hope this helps!

Answer:

the center of rotation is a point about which a figure rotates . this point doesn't remove during a rotation

Answer

Question A:

The answer is Inverse

Question B:

The answer is Converse

Question C:

The answer is Contrapositive

SOLUTION

Problem Statement

The question gives us a statement and we are asked to find its inverse, converse, and contrapositive. The statement given is:

Method

To solve this question, we need to know the definitions for each of inverse, converse, contrapositive.

Given the original statement, "If p, then q"

Inverse:

Converse

Contrapositive:

With these definitions, we can solve the question.

Implementation

Let p be "today is Monday".

Let q be "tomorrow is Tuesday"

Thus, the original statement can be written as:

Question A:

If today is not Monday, then tomorrow is not Tuesday.

If p is "today is Monday" and q is "tomorrow is Tuesday"

Then, we can re-write the statement as follows:

"if not p then not q"

This corresponds to Inverse

Question B:

"If tomorrow is Tuesday, then today is Monday."

This can be re-written as:

"If q, then p"

This corresponds to Converse

Question C:

"If tomorrow is not Tuesday, then today is not Monday"

This can be re-written as:

"if not q, then not p"

This corresponds to Contrapositive

Final Answer

Question A:

The answer is Inverse

Question B:

The answer is Converse

Question C:

The answer is Contrapositive

Since there are students who play both sports, the events of playing basketball and playing soccer are not mutually exclusive.

A Venn diagram is a visual representation of sets or groups and their relationships to one another.

It consists of two or more circles or other shapes that overlap, with each shape representing a different set, and the overlap representing the elements that belong to both sets.

Looking at the diagram, we see that there is a region where the two circles overlap, which means there are elements (points) that are in both circles. Therefore, the events shown in the Venn diagram are not mutually exclusive.

In this particular case, the circles represent the events of students who play basketball and students who play soccer, respectively. The overlap represents students who play both basketball and soccer.

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The complete question is given below-

hi

A = (2x+5)(x-4)=0

A = 2x²-8x +5x-20

A = 2x² -3x -20

as a quadratic equation is  :  ax² +bx +c

then  a = 2 ;  b = -3  and c = -20

Answer:

a = 2 ; b = -3  ; c = -20

Step-by- step explanation:

Use FOIL method.

                      (2x + 5)(x - 4) = 0

2x*x+ 2x*(-4 )+ 5*x + 5* (-4) = 0

                2x² - 8x + 5x - 20 =0

Combine like terms,

                       2x² - 3x - 20 = 0

Standard form: ax² + bx + x = 0

a = 2

b = -3

c = -20

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of f(g(x)) is 6x³ + 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3x + 4 = 5 is an equation.

2x + 4x = 4 is an equation.

We have,

The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes.

The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works.

f(x) = 2x² + 4

g(x) = √(3x³)

Now,

f(g(x)):

= f(√(3x³))

= 2{√(3x³)}² + 4

= 2(3x³) + 4

= 6x³ + 4

Thus,

The value of f(g(x)) is 6x³ + 4.

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