Answer: Parallel.
Step-by-step explanation:
Given: Lines a and c intersect at point S, creating 4 angles.
To Prove: Corresponding angles are congruent.
We are given that lines a and c intersect at point S.
Translate line a down line c until point S reaches point Q.
Call the new line through Q line b.
We know that translations preserve orientation then every point on line b is equidistant from every points on line a.
Therefore, lines a and b are parallel by the definition of parallel lines.
Hence, the complete statement is Because translations preserve orientation, lines a and b are parallel.
The difference between 4 and the product 6x is 40
Find the value of the y-intercept of the line whose equation is 5x + 6y = 24
What is the unit rate of y=0.75x
Which is the completely factored form of 12x3 – 60x2 + 4x – 20?
what is the factored form of 64g^3+8?
Answer: For those in the future!
The answer to this is D: (4g+2)(16g^2minus8g+4)
Step-by-step explanation:
what is the unit rate of y=-2x
Janet took out a loan of $50,000 from Bank of America at 8% on March 19, 2015, which is due on July 8, 2015. Using exact interest, the amount of Janet's interest cost is:
The amount of Janet's interest cost from a loan of $50,000 at an interest rate of 8% from March 19 to July 8, 2015 is $1,160. The calculation is done using the simple interest formula, with time approximated as 0.29 years.
Explanation:The problem asking for the simple interest incurred on a loan taken by Janet can be solved using the formula of simple interest, which is I=PRT in financial mathematics. I is interest, P is the principal amount (initial loan), R is the interest rate, and T is the time.
P (Principal) = $50,000R (Rate of Interest) = 8% per annumT (Time) = Time interval from March 19 to July 8 that turns out to be approximately 3.5 months or about 0.29 years.Substituting these values into the formula, we get:
I = 50000 * 0.08 * 0.29
Calculating this out will give you the total interest, $1160.
So, the amount of Janet's interest cost is $1,160.
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Find the inverse of the function. f(x) = 7x - 1
The inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
The given function is:
f(x) = 7x - 1
Make x the subject of the formula
[tex]f(x) = 7x - 1\\\\7x = f(x) + 1\\\\[/tex]
Divide through by 7
[tex]\frac{7x}{7}= \frac{f(x)}{7} + \frac{1}{7}\\\\x = \frac{f(x)}{7} + \frac{1}{7}[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and replace f(x) by x:
[tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
Therefore the inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
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How can you check the answer to a decimal multiplication problem
something that relates inputs to outputs
Which expression is equivalent?
11 − 9(−2x − 3)
A) 18x + 38
B) −4x + 6
C) 18x − 38
D) −4x − 6
The expression equivalent to 11 - 9(-2x - 3) is 18x + 38 after applying the distributive property and rules for multiplying numbers with different signs. This corresponds to option A.
Explanation:To find which expression is equivalent to 11 − 9(−2x − 3), we need to apply the distributive property and the rules for multiplying numbers with different signs. The distributive property tells us to multiply the number outside the parentheses by each term inside the parentheses. So, let’s apply this to the expression:
First, distribute the -9 to both -2x and -3: -9(−2x) + -9(−3).According to the multiplication rules for signs, multiplying two negative numbers results in a positive number. So, -9(−2x) becomes +18x, and -9(−3) becomes +27.Now the expression looks like this: 11 + 18x + 27.Add the constant terms 11 and 27 to get 38. The expression is now 18x + 38.Therefore, the expression equivalent to 11 − 9(−2x − 3) is 18x + 38, which corresponds to option A.
To assess the precision of a laboratory scale, we measure a block known to have a mass of 1 gram. we measure the block n times and record the mean x¯ of the measurements. suppose the scale readings are normally distributed with unknown mean µ and standard deviation σ= 0.001 g. how large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001
For a 95% confidence interval with ±0.0001 margin of error, sample size[tex]\( n \approx 385 \)[/tex] measurements are needed.
To determine the sample size [tex]\( n \)[/tex] needed to achieve a margin of error of [tex]\( \pm 0.0001 \)[/tex] for a 95% confidence interval for the mean [tex]\( \mu \)[/tex], we can use the formula for the margin of error of a confidence interval:
[tex]\[\text{Margin of Error} = Z \times \frac{\sigma}{\sqrt{n}}\][/tex]
Where:
[tex]- \( Z \) is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to \( Z = 1.96 \)).\\- \( \sigma \) is the standard deviation of the measurements (given as \( 0.001 \) g).\\- \( n \) is the sample size.[/tex]
Given that the margin of error [tex](\( \text{MOE} \)) is \( 0.0001 \)[/tex], we can rearrange the formula to solve for \( n \):
[tex]\[n = \left(\frac{Z \times \sigma}{\text{MOE}}\right)^2\][/tex]
Substituting the given values:
[tex]\[n = \left(\frac{1.96 \times 0.001}{0.0001}\right)^2\]\[n = \left(\frac{0.00196}{0.0001}\right)^2\]\[n = \left(19.6\right)^2\]\[n = 384.16\][/tex]
Since [tex]\( n \)[/tex] must be a whole number (you can't have a fraction of a measurement), we round up to the nearest whole number. So, [tex]\( n = 385 \).[/tex]
Therefore, you would need to take at least 385 measurements to ensure that the margin of error for the 95% confidence interval of the mean [tex]\( \mu \) is \( \pm 0.0001 \) g.[/tex]
You have just received an inheritance of $28,000 and would like to invest it into an account. The bank offers two investment plans, one for 4 years at 5.8% compounded annually and another for 3 years at 7.083% compounded annually. You want to make equal annual withdrawals from the account over the life time of the loan. Which investment will yield the highest return over the duration of the loan, given that the account will be zeroed out by the end of that period?
a.
3 year account; $32,056.89
c.
3 year account; $24,130.77
b.
4 year account; $42,742.52
d.
4 year account; $32,174.36
Answer:
D
Step-by-step explanation:
edge
Solve. 25 -4x = 15 - 3x + 10 - x
Find the product. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression and include the final answer in your explanation. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
( x y 2 z)3 (-9x 2 y z)2
The product of (x y^2 z)^3 and (-9x^2 y z)^2 is found by applying the exponent to each variable inside the parentheses and then multiplying the results together, using exponent rules to simplify. The final simplified expression is 81x^7 y^8 z^5.
Explanation:To find the product of the expressions (x y^2 z)^3 and (-9x^2 y z)^2, we use the properties of exponents. First, we apply the power to each factor inside the parentheses, which means raising each base to the power outside, and then we multiply the corresponding exponents when the same base is found in both terms.
For the first expression (x y^2 z)^3, we get x^3 y^6 z^3, and for the second expression (-9x^2 y z)^2, we have 81x^4 y^2 z^2 after squaring -9 to get 81 and applying the exponent 2 to each variable.
Next, we multiply these results together: x^3 y^6 z^3 × 81x^4 y^2 z^2 = 81x^{3+4} y^{6+2} z^{3+2}, which simplifies to 81x^7 y^8 z^5. The rule of exponent addition when multiplying like bases, x^p x^q = x^{(p+q)}, is applied here to combine the variables with the same base. Our final simplified product is 81x^7 y^8 z^5.
The final answer is [tex]81 x^7 y^8 z^5.[/tex]
To find the product of the expression [tex](x y^2 z)^3 * (-9x^2 y z)^2[/tex], we can follow these steps:
1. Expand the first expression: [tex](x y^2 z)^3 = x^3 (y^2)^3 z^3 = x^3 y^6 z^3.\\[/tex]
2. Expand the second expression: [tex](-9x^2 y z)^2 = (-9)^2 (x^2)^2 y^2 z^2 = 81 x^4 y^2 z^2.[/tex]
3. Multiply the expanded expressions: [tex](x^3 y^6 z^3) * (81 x^4 y^2 z^2) = 81 x^3 x^4 y^6 y^2 z^3 z^2 = 81 x^7 y^8 z^5.[/tex]
Therefore, the final answer is [tex]81 x^7 y^8 z^5[/tex].
Which of the following gives all of the sets that contain -1/2?
the set of all rational numbers and the set of all real numbers
the set of all natural numbers and the set of all irrational numbers
the set of all integers and the set of rational numbers
the set of all natural numbers, the set of rational numbers, and the set of all real numbers
Answer:
the answer is a
Step-by-step explanation:
did it on edg 2021
Is 250% of 44 less than 100, greater than 100 but less than 150, or greater than 150? Explain reasoning
50% of 44 is greater than 100 but less than 150 because the value of 250% of 44 is 110 after applying the concept of the percentage.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
250% of 44
Let x be the 250% of 44:
The value of x can be found as follows:
x = (250/100)44
x = 2.5(44)
x = 110
110 > 100
110 < 150
Or
100 < 110 < 150
Thus, 50% of 44 is greater than 100 but less than 150 because the value of 250% of 44 is 110 after applying the concept of the percentage.
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Ratio of forks to knives in Mabel's kitchen is 4:5. There are 16 forks in a drawer how many knives are they
what is 5x5x5x5 plz tell me
Answer:
5∧5
Step-by-step explanation:
A movie theater charges \$10.50$10.50dollar sign, 10, point, 50 per ticket and \$5$5dollar sign, 5 per bucket of popcorn. You never buy the popcorn because you think it's too expensive. Is the total price you pay proportional to the number of tickets you buy? Choose 1 answer:
As per linear equation, total price is directly proportional to the number of tickets I buy.
What is a linear equation?A linear equation is an equation that has the highest power of the variable as 1.
Given, a movie theater charges $10.50 per ticket and $5 per bucket of popcorn.
I never buy the popcorn because I think it's too expensive.
Let, I buy 'n' number of tickets.
Therefore, the total price for the tickets is
[tex]P = 10.50n[/tex]
⇒ P∝ n
Therefore, total price is directly proportional to the number of tickets I buy.
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There are currently 21 frogs in a (large) pond. The frog population grows exponentially, tripling every 7 days. How long will it take (in days) for there to be 150 frogs in the pond?
It will take approximately 50 days for the frog population to reach 150 frogs.
Explanation:To find out how long it will take for the frog population to reach 150, we need to determine how many times the population needs to triple to reach that number. We start with 21 frogs and want to reach 150, so we need to triple the population 150 divided by 21, which is approximately 7.14, times. Since the population triples every 7 days, it will take approximately 7.14 times 7, or 50 days, for the population to reach 150 frogs.
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Find all complex solutions (real and non-real)
x^4+2x³+22x²+50x-75=0
A survey asked a group of students to choose their favorite type of sport from the choices of soccer, softball, basketball, and others. The results of the survey are shown in the graph. Based on the graph, how many more students in a class of 126 students would be expected to choose soccer than softball?
The first advertisement discussed in class states that the salespeople make an average of $1,000 per week. Suppose there are nine salespeople. What would the ninth person need to earn for the mean to be $1,000 if the other eight salespeople earned $550, $600, $600, $800, $950, $950, $1,000, and $1,100?
you want to buy a CD that cost $18.50. The sales-tax rate in your states is 4.5 percent. How much sales tax will you pay for this CD?
4.5% = 0.045
multiply 18.50 by 0.045 foe the amount of sales tax
18.50 * 0.045 = 0.83
they pay 0.83, which is 83 cents in sales tax
In a coin flip experiment, david decides to flip a coin 50 times. he wants to record the number of times "tails" comes up. using the language of probability, in this experiment, each coin flip is a ________, the way the coin lands is the ________. when the coin comes up "tails", this is considered a ________.
10z when z = 0.8
answers
If the given function is F(x) = 10z. When z = 0.8, the value of the function is 8.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, the given function is F(x) = 10z.
In the given function z is the independent variable while the value of the function is a dependent variable because its value depends upon the value of z.
The variable is reliant on other measurable factors. As a result of manipulating the independent variable(s) in an experiment, these variables are anticipated to change.
The value of the function is obtained by putting the value of z in the given function,
F(x) = 10z
F(x) = 10×0.8
F(x) = 8
Thus, if the given function is F(x) = 10z. When z = 0.8, the value of the function is 8.
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please help
A carpet layer is given a roll of carpet which has already been cut for a 12-ft wall. The wall measures 1.5 cm on a drawing. The length of the room is 6 iron the drawing. How far,in feet, will he cut the length of the carpet?
Answer: 48
Step-by-step explanation:
Do 12 divided by 1.5 = 8
8 * 6 = 48
so 48 is your answer
:3
PLEASE HELP NEED TO PASS MY CLASS
Can someone help me with this? I got 0.000104 but it wasn’t right.
Answer:
0.0001042
Step-by-step explanation:
You need to keep all the digits (unless you're told to round your answer).