Answer: The value of x = 5
Step-by-step explanation:
Given : ∠E and ∠F are vertical angles m∠E = 8x + 8 and m∠F = 2x + 38.
We know that the vertical angles are congruent.
It means [tex]\angle{E}\cong\angle{F}[/tex]
[tex]\Rightarrow\ m\angle{E}=\ m\angle{F}[/tex]
[tex]\Rightarrow\ 8x+8=2x+38[/tex]
Subtract 2x and 8 from both sides , we get
[tex]6x=30[/tex]
Divide both sides by 6 , we get
[tex]x=5[/tex]
Hence, the value of x = 5
Form the intersection for the following sets.
R = {10, 15, 20}
S = {20, 25}
R ∩ S =
A.{ }
B.{10, 15, 25}
C.{20}
D.{10, 15, 20, 25}
This diagram of airport runway intersections shows two parallel runways. A taxi way crosses both runways. How are 6 and 2 related?
a)corresponding angles
b) alternate interior angles
c)same side interior angles
d) none of these
Analyze the function’s graph to determine which statement is true.
Over the interval [–2.5, 0.5], the local maximum is 2.
As the x-values go to positive infinity, the function’s values go to negative infinity. The function is decreasing over the interval (–1, 0.75).
The function is negative for the interval [–2, 0]
The truth of the statements in the question can be verified by analyzing the function's graph over the stipulated intervals. Understanding concepts such as local maxima, the behavior of functions at infinity, an interval of decrease, and intervals where a function remains negative or positive are essential in this process.
Explanation:To determine which statement in the question is true, we need to analyze the function's graph. The statements included talk about specific behaviors of the function in different intervals of the x-axis.
The first statement mentions a local maximum of 2 over the interval [–2.5, 0.5]. You will need to locate this interval on the x-axis and see if 2 is indeed the highest y-value within this range. If there is a point on the function where the y-value is 2 and it is higher than all neighboring points, then this statement is true.
The second statement states that as the x-values go to positive infinity, the function's values go to negative infinity. This implies that as the function continues towards the positive direction on the x-axis, the y-values continuously decrease towards negative infinity. If the graph shows this, then this statement is true.
The third statement says the function is decreasing over the interval (–1, 0.75). This would mean that as x goes from –1 to 0.75, the y-values decrease. If you observe this on the graph, this statement is true.
The last statement asserts the function is negative for the interval [–2, 0]. If, for all x-values from –2 to 0, the corresponding y-values are below the x-axis (negative), then this statement is valid.
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B. if the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?
If a data set has an even number of data, is it true or false that the median is never equal to a value in the data set? explain.
The median is never equal to a value in the data set when the data set has an even number of data points.
The statement is true - if a data set has an even number of data points, the median will never be equal to a value in the data set. The median is the middle value in an ordered set of data. When there is an even number of points, there are two middle values, so the median is the average of those two values.
For example, if we have the data set (2, 4, 6, 8), the median would be (4 + 6)/2 = 5. As you can see, the median is not equal to any of the values in the data set.
In conclusion, the median is never equal to a value in the data set when the data set has an even number of data points.
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how is the decimal 2.4 written as a mixed number in its simplest form
The mixed number in their simplest form can be represented as
[tex]2\dfrac{2}{5}[/tex]
What are real numbers?Real numbers are defined as the value of a continuous quantity that can represent a distance along a line a real number in mathematics. Rational and irrational numbers are both real numbers. Rational numbers such as integers (-7, 0, 4), fractions(5/2,7/2, 4.2), and irrational numbers such as √5, π, etc., are all real numbers.
we have to determine the decimal 2.4 written as a mixed number in its simplest form.
Given that the decimal as:
⇒ 2.4
⇒ 2 + 0.4
Convert decimals into a fraction.
⇒ 2 + 4/10
⇒ 2 + 2/5
Thus, mixed number in their simplest form is
[tex]2\dfrac{2}{5}[/tex]
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What is the conversion factor used to convert inches to yards a.12 inches in 1 yard b.24 inches in 1 yard c.3inches in 1 yard d.36 inches in 1 yard
The conversion-factor used to convert inches to yards is : (d) 36 inches in 1 yard.
This means that for every 36 inches, there is 1 yard. By dividing the number of inches by 36, you can obtain the equivalent length in yards.
Conversion-Factors are ratios that express the relationship between different units of measurement.
In this case, using the conversion factor of 36 inches in 1 yard allows for a direct-conversion from inches to yards. It is derived from the information that there are 12 inches in a foot and 3 feet in a yard, giving a total of 36 inches in 1 yard.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
What is the conversion factor used to convert inches to yards
(a) 12 inches in 1 yard,
(b) 24 inches in 1 yard,
(c) 3 inches in 1 yard,
(d) 36 inches in 1 yard.
Point M is the midpoint of AB. What are the coordinates of B if A is (-8, 3) and if M is (-4, 2).
Jorge is 1 year younger than his brother. The sum of their ages is no less than 25 years. Enter the youngest age Jorge's brother can be. Question 10 options:
12
13
14
15
The youngest age Jorge's brother can be is 13. This is derived from the given condition that the sum of their ages is no less than 25, by assigning Jorge's brother's age as an unknown 'x' and using algebraic principles.
Explanation:The subject question is a simple algebraic problem. Let's denote Jorge's brother's age as x, so Jorge's age would be x-1. The problem states that the sum of their ages is no less than 25, which would translate algebraically into x + (x-1) ≥ 25.
Then we simplify the equation by combining like terms, it turns into 2x - 1 ≥ 25. To isolate x, you first add 1 to both sides of the equation, which gives you 2x ≥ 26, and then divide both sides by 2, resulting in x ≥ 13.
Therefore, the youngest age Jorge's brother can be is 13.
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Find four consecutive even integers such that if the sum of the first and the third is multiplied by 5 the result is 12 less than 9 times the fourth
The information below represents the cost of Cody's home ownership. What is his average monthly expenditure related to his home?
mortgage $1,255 per month
● taxes $2,881 per year
● insurance $156 per month
● HOA fees $320 per year
● utilities $475 per month
Answer:
Cody's average monthly expenditure related to his home is $2,152.75
Step-by-step explanation:
Since the question is asked for monthly expenditure. Thus our first work is to convert all given expenditure for per monthly.
Mortgage = $1,255
Taxes = $240.08
Insurance = $156
HOA fees = $26.67
Utilities = $475
Thus, Cody's average monthly expenditure related to his home is: 1,255 + 240.08 + 156 + 26.67 + 475 = $2,152.75
"More than 60% of the students scored below the mean on the last test." Can this statement be true? Why or why not?
Shaylee is determining if 6 is the solution to the equation.
42 ÷ w = 7 for w = 6
First, Shaylee must substitute ( ) for ( ).
To simplify, Shaylee must divide ( ) by ( ) .
First, Shaylee must substitute (6) for (w)
To simplify,Shaylee must divide (42) by(6)
:)
6 is the solution of the equation 42 ÷ w = 7.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Shaylee is determining if 6 is the solution to the equation
42 ÷ w = 7 for w = 6
Forty two divided by w equal to seven for w equal to six.
First, Shaylee must substitute 6 for w.
To simplify, Shaylee must divide 42 by 6
42/6=7
So 6 is the solution of the equation.
Hence, 6 is the solution of the equation 42 ÷ w = 7.
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The expression 53 ( 1 − x) gives the discounted price of a pair of shoes, where x is the percent of the discount written in decimal form.
What does 1 − x represent in the expression?
A. percent of original price being paid
B. discount price of the shoe
C. percent of discount
D. original price of shoe
What is the relationship between 5.34×105 and 5.34×10−2 ?
Answer:
5.34×105 and 5.34×10−2
Step-by-step explanation:
the first is greater than the scoend and the second is less then
What property of multiplication do we use to find equivalent fractions?
The equivalent fractions for 2/3 are 6/9, 10/15, and 12/18; the multiplicative identity is a feature of multiplication which is used to find equivalent fractions.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Given that 2/3 by multiplying by 3/3, 5/5, and 6/6.
= (2/3)(3/3)
= 6/9
= (2/3)(5/5)
= 10/15
= (2/3)(6/6)
= 12/18
The multiplicative identity is a feature of multiplication which is used to find the equivalent fractions.
Hence, the equivalent fractions for 2/3 are 6/9, 10/15, and 12/18; the multiplicative identity is a feature of multiplication which is used to find equivalent fractions.
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John and Mary Billings own a condominium with an acid value of 110000 if the tax rate is 25 meals per dollar off the valuation how much tax do they pay
A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance the ball has traveled when it hits the ground the fifth time is meters.
Zach is 23 years old. Zach's age is 3 years older than twice Maya's age. Let m represent Maya's age.
Which equation can be used to solve for Maya's age?
23 = 2m + 3
23 = 3m + 2
23 = m + 3
23 = 2m
Answer:
The correct option is A) [tex]23=2m+3[/tex].
Step-by-step explanation:
Consider the provided information.
Zach is 23 years old. Zach's age is 3 years older than twice Maya's age.
Let m represent Maya's age.
Twice of Maya's age can be written as:
[tex]2m[/tex]
3 years older than twice Maya's age can be written as:
[tex]2m+3[/tex]
It is given that Zach is 23 years old and Zach's age is 3 years older than twice Maya's age.
Thus, the above expression equal to 23.
[tex]23=2m+3[/tex]
Hence, the correct option is A) [tex]23=2m+3[/tex].
Chords AC and BD intersect at the center of circle ABCD. If the length of CP = 8, which is the length of PB?
The product of numbers on the diagonal when comparing two ratios
A weather forecast predicts that the temperature in antarctica will decrease 8 degrees fahrenheit each hour for the next 6 hours. write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36 degrees fahrenheit
It will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, you can set up an inequality. Let's call the number of hours it takes for the temperature to drop x.
Given that the temperature decreases 8 degrees Fahrenheit each hour, you can represent the temperature drop as:
8x
Now, you want this temperature drop to be at least 36 degrees Fahrenheit, so you can write the inequality:
8x ≥ 36
To solve for x, divide both sides of the inequality by 8:
x ≥ 36 / 8
x ≥ 4.5
So, it will take at least 4.5 hours for the temperature in Antarctica to drop by at least 36 degrees Fahrenheit.
Since time is typically measured in whole hours, it will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
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It will take at least 4.5 hours for the temperature in Antarctica to drop at least 36 degrees Fahrenheit.
Explanation:To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, we can write and solve an inequality:
Let x be the number of hours it takes for the temperature to drop.
The temperature decreases 8 degrees Fahrenheit each hour for the next 6 hours:
8x ≥ 36
Divide both sides of the inequality by 8:
x ≥ 4.5
Therefore, it will take at least 4.5 hours for the temperature to drop at least 36 degrees Fahrenheit.
Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?
Answer:
4:10 is smaller because when put into fraction form and making the denominators even, 12:20 comes out to be 6/10
Step-by-step explanation:
What is the measure of angle ABD in trapezoid ABCD?
A. 24°
B. 40°
C. 64°
D. 92°
Answer:
The answer is B.40
Step-by-step explanation:
What is the product written in scientific notation? (5.91×10^−3)⋅(8.7×10^10)
a) 14.61 × 10^−30
b) 5.1417 × 10^8
c) 14.61 × 10^7
d) 5.1417 × 10^7
The product written in scientific notation will be; 5.1417 × 10^8
How do scientific notations work?Scientific notations have some of the profits as Better readability due to compact representation. Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
We have been given that (5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
Required to find the product written in scientific notation;
(5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
(5.91 x 8.7) ( [tex]10^{-3}[/tex]× [tex]10^{10}[/tex])
51.417 × [tex]10^7[/tex]
which is the same as; 5.1417 × [tex]10^8[/tex]
Hence, the product written in scientific notation will be; 5.1417 × [tex]10^8[/tex]
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Thad and his four family members are going to the fair. Admission to the fair costs $8. Books of ride tickets are $15. THad has 200$. How much will he have for food and souvenirs?
Part 1: Define your variables and write an inequality that models the situatio.
Part 2: After paying for all family members to get into the fair, Thad buys books of ride tickets for 3 of them. Use the in equality from Part 1 to solve for the amount of money Thad has left for food and souvenirs. Show your work.
Answer:
Given,
Total number of members = 5,
Also, admission to the fair costs $8,
So, the total fair cost = $ 40
Part A: Let x represents the number of people who ride, and y represents the amount ( in dollars ) needed for food and souvenirs,
Since, ride cost for each person = $ 15,
So, the total ride cost = 15x dollars,
Thus, the total spending = ( 40 +15x + y ) dollars
According to the question,
The budget is of $ 200,
That is, total spending can not exceed $ 200,
⇒ 40 +15x + y ≤ 200
⇒ 15x + y ≤ 160
Which is the required inequality that represents the given situation,
Part B : If x = 3
15(3) + y ≤ 160
45 + y ≤ 160
y ≤ 115
Hence, $ 115 would left for food and souvenirs.
Find the Domain and Range (show work)
see attached picture for solutions:
Solve 4/5m = -15 show you’re work please ;)
WILL GIVE 20 POINTS
Write the expression 44(4–7)(4) using a single exponent.
A) 4^–28
B) 4^–4
C) 4^–3
D) 4^–2
Answer:
D) 4^-2
Step-by-step explanation:
Given: 4^4*4^-7*4
If the base is the same, we can add the powers.
a^m * a^n = a^(m + n)
4^4*4^-7*4 = 4^(4 - 7 + 1)
= 4^(5 - 7)
= 4^-2
Answer: D) 4^-2
Hope this will helpful.
Thank you.
Consider 7 x 10 to the third power. Write a pattern to find the value of the expression