Match the statements defined below with the letters labeling their equivalent expressions.
1. |x−4|=8
2. |x−4|≥8
3. |x−4|>8
4. |x−4|<∞
5. |x−4|≤8
A. x∈(−∞,∞)
B. x∈[−4,12]
C. x∈(−∞,−4)∪(12,∞)
D. x∈(−∞,−4]∪[12,∞)
E. x∈{−4,12}
Use the definition of absolute value to rewrite each equation or inequality.
[tex]|x| = \begin{cases} x & \text{if } x\ge0 \\ -x & \text{if }x < 0 \end{cases}[/tex]
1. (E) From the definition it follows that
[tex]x-4 \ge 0 \implies |x-4| = x-4 = 8 \implies x = 12[/tex]
[tex]x-4 < 0 \implies |x-4| = -(x-4) = 4-x = 8 \implies x = -4[/tex]
Then the solution set contains exactly 2 elements, and we write it as shown in choice (E), [tex]x\in\{-4,12\}[/tex].
2. (D) We solve the inequality in essentially the same way as in (1), we just need to keep track of the direction of the inequality.
[tex]x-4\ge0 \implies|x-4|=x-4\ge8 \implies x\ge12[/tex]
[tex]x-4<0 \implies|x-4|=4-x\ge8 \implies x\le-4[/tex]
Note the inclusion of [tex]x=12[/tex] and [tex]x=-4[/tex]. We write this as a union of two half-closed intervals, [tex]x\in(-\infty,-4]\cup[12,\infty)[/tex].
3. (C) This follows from the same steps as in (2). This time the inequality is strict, so we exclude the endpoints and with open intervals write [tex]x\in(-\infty,4)\cup(12,\infty)[/tex].
4. (A) Since [tex]|x|[/tex] always returns a non-negative number, any real number [tex]x[/tex] satisfies the inequalty [tex]|x-4|<\infty[/tex]. We write the solution set as the entire real line, [tex]x\in(-\infty,\infty)[/tex].
5. This leaves us with (B) for the last solution set. This inequality is complementary to the one in (3), which means the solution set to [tex]|x-4|\le8[/tex] is the complement of the set we found in (3). That interval removes everything between and including -4 and 12 from the real line. So the solution in this case is what we omit from the solution to (3), and we write [tex]x\in[-4,12][/tex].
A line has a slope of 1/6 and passes through the point (-9, -8). What is its equation in point- slope form?
Answer:
y+8=1/6(x+9)
Step-by-step explanation:
point slope: y - y1 = m ( x - x1 )
use the point and the slope and plug in the values in the point slope equation
Lines I and m are parallel. Find m<3 if m<5 = 38 and m<6 = 62.
100
62
80
38
Answer: 80 degrees ==> 3rd option
Step-by-step explanation:
m<5=m<2 ==> angles 5 and 2 are opposite interior angles, so they're congruent.
m<2=38 degrees
m<2+m<6+m<3=180 degrees
38+62+m<3=180
100+m<3=180
m<3=80 degrees ==> 3rd option
Judith has just become eligible to participate in her company’s retirement plan. Her company does not match contributions, but the plan does average an annual return of 12%. Judith is 40 and plans to work to age 65. If she contributes $200 per month, how much will she have in her retirement plan at retirement?
Answer:
She will have $375,769.33 in her retirement plan at the time of retirement.
Explanation:
The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return or discount rate.The higher the discount rate, the greater the annuity's future value.According to the question,
Periodic Payments(P) = $200
Rate of Return(r) = 12%(annual)
[tex]=\frac{12}{12}%[/tex]
= 1% monthly
= 0.01
Number of payments(n) = 65 - 40
= 25(annual)
= 25 × 12 monthly
= 300 monthly
Future value =?
The formula for calculating future value is:
Future Value = [tex]P[\frac{(1+i)^{n}-1 }{i}][/tex]
= [tex]200[\frac{(1+0.01)^{300}-1 }{0.01}][/tex]
= [tex]200[\frac{19.7884663-1}{0.01}][/tex]
= 200[1878.84663]
= 375,769.326
= 375,769.33
Final Answer:
Therefore, the future value of her retirement when she retires is
$ 375,769.33 .
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I need help nowwwe!! Please help asap
I will brainliest if you will
Answer:
Step-by-step explanation:
The domain of the function is [-3,5]
The range of the function is [-16,infinity)
X=3 is a zero of the function
X = -3 is a zero of the function
Evaluate 8+3e when e=2
The value of 8+3e when e=2 will be 14.
How to compute the expression?It should be noted that the equation or expression is given as:
8 + 3e
Therefore, we will put the value of E as 2 int the equation. This will be:
8 + 3e
= 8 + 3(2)
= 8 + 6
= 14
The value is 14.
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Our class planned a holiday party for disadvantaged kids. Some of us baked
cookies for the party. On the day of the party, we found we could divide the
cookies into packets of two, three, four, five, or six and have just one cookie
left over in each case. If we divided them into packets of seven, there would
be no cookies left over. What is the least number of cookies the class could
have baked?
Answer:x=1.
Step-by-step explanation:
3x-x+2=4
(30 POINTS) During the first year with a company, Finley was paid an annual salary of $59,000, with an 8% raise for each following year. Which equation represents Finley's annual salary, f (n), during the nth year?
f (n) = 59,000(1.08n – 1)
f (n) = 59,000(0.08n – 1)
f (n) = 59,000(1.08n)
f (n) = 59,000(0.92n)
Answer:
f(n) = 59,000(1.08m - 1)
Step-by-step explanation:
for all values of x, f(x)=x/5 +3
Answer:
f(g(x)) = 2x² + 4
Step-by-step explanation:
to evaluate f(g(x)) substitute x = g(x) into f(x) , that is
f(g(x))
= f(10x² + 5)
= [tex]\frac{10x^2+5}{5}[/tex] + 3
= [tex]\frac{10x^2}{5}[/tex] + [tex]\frac{5}{5}[/tex] + 3
= 2x² + 1 + 3
= 2x² + 4
FIRST PERSON TO ANSWER GETS 50 POINTS HELP ME OUT HERE
The equation has infinite solutions.
The value of x that makes the equation true is: 2. After substitution, we would have: 8 = 8
Another value of x that makes the equation true is: 3. After substitution, we would have: 10 = 10
What are Infinite Solutions of an Equation?If an equation has infinite solutions, it means that any value of the variable in the equation would make the equation true.
Given the equation, 2(x + 2) = 2x + 4, the value of x that makes the equation true is: 2.
Substitute x = 2 into the equation and simplify it would make both sides equal:
2(2 + 2) = 2(2) + 4
8 = 8
Another value of x that makes the equation true is: 3.
Substitute x = 3 into the equation and simplify it would make both sides equal:
2(3 + 2) = 2(3) + 4
10 = 10
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2. Which expression is not equal to the
number 0?
5-5
-7+7
6-(-6)
-8- (-8)
PLEASE HELP! If a factor of the denominator of a rational function cancels with a factor of the numerator and the inequality is closed, then the zero of the canceled factor should be included in the solution for the inequality.
True or False?
Answer:
False. If a factor of the denominator of a rational function cancels with a factor of the numerator, the zero of the canceled factor should not be included in the solution for the inequality.
Step-by-step explanation:
Give me Brainliest if that helped! :)
An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Just confused with the remainder
Answer:
its the first one
146 r 6
hope this helped! :)
Estimate 219÷15 by first rounding each number so that it has only 1 nonzero digit.
The estimated result of 219 ÷ 15, by first rounding each number and then dividing, we get the result as 11.
We are given the expression:
219 ÷ 15
We need to estimate the result by first rounding off the digits to nearest tens and then performing division to get the answer.
So, we will first do the round off.
219 will be rounded off to 220
15 will be rounded off to 20
So, the expression will become:
220 ÷ 20
So, now performing the division, we get that:
= 11
Therefore, the estimated result of 219 ÷ 15, by first rounding each number and then dividing, we get the result as 11.
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Alguien sabe como calcular esto de binario a decimal?
11 00 11 00 = 204
nice :)
estion 5(Multiple Choice Worth 2 points)
(Laws of Exponents with Integer Exponents LC)
Which is an equivalent expression for
•*•*
°0.0*
•*•*
°0.0*
0.0)
The equivalent expression for [tex][(\frac{5}{7}) ^{2}*(\frac{1}{3} )^{-3} ] ^{-1}[/tex] is [tex](\frac{7}{5}) ^{2}*(\frac{1}{3} )^{3}[/tex] (option D)
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Given: [tex][(\frac{5}{7}) ^{2}*(\frac{1}{3} )^{-3} ] ^{-1}[/tex] is the expession.
Now, multiplying (-1) power within the brackets,
=[tex](\frac{5}{7}) ^{-2}*(\frac{1}{3} )^{3}[/tex]
If power is in negative, fraction can be reciprocated to make the power positive. So,
=[tex](\frac{7}{5}) ^{2}*(\frac{1}{3} )^{3}[/tex]
Option D
Hence, the equivalent expression for [tex][(\frac{5}{7}) ^{2}*(\frac{1}{3} )^{-3} ] ^{-1}[/tex] can be written as [tex](\frac{7}{5}) ^{2}*(\frac{1}{3} )^{3}[/tex].
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A sample of 10 NCAA college basketball game scores provided the following data. Winning Team
The exchange rate for US dollars to Canadian dollars is 0.77. What is the value of $200 US dollars
[tex]\begin{array}{ccll} US\$&CA\$\\ \cline{1-2} 0.77 & 1\\ 200& c \end{array} \implies \cfrac{0.77}{200}~~=~~\cfrac{1}{c} \\\\\\ 0.77c=200\implies c=\cfrac{200}{0.77}\implies c\approx 259.74[/tex]
Each person in a community was asked, “what is your favorite type of pet?” The pie chart below summarizes their responses
From pie chart, responses of community for each category is
a. One fourth of community chosen by cat category.
b. Approximately 30% of community chosen cat or other.
c. If 6% chosen None then dog was chosen by approximately 18%.
As given,
From pie chart ,responses of community for each category is
Bird>cat>dog>fish>none>other
Fish+ none +other +cat=Approximately 50%
a. Cat chosen by approximately 25%.
b. Cat or Other= Approximately 30%
c. If 6% chosen None then dog
Approximately three times of none=6×3
= 18%.
Therefore, from pie chart
a. One fourth of community chosen by cat category.
b. Approximately 30% of community chosen cat or other.
c. If 6% chosen None then dog was chosen by approximately 18%.
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The long hand of a clock turns from 2:00pm to 2:15pm. What part of a turn did the long hand make?
Answer: A quarter turn
Step-by-step explanation:
what are the ordered pairs of y=3x-5
Infinitely many others are possible.
=================================================
Explanation:
Replace x with 0 and simplify to get...
y = 3x-5
y = 3(0)-5
y = 0-5
y = -5
When x = 0, it leads to y = -5
One ordered pair is (x,y) = (0, -5)
Let's repeat those steps for x = 1
y = 3x-5
y = 3(1)-5
y = 3-5
y = -2
Another ordered pair is (1, -2)
As you can see, we can pick anything we want for x to get some paired y output. There are infinitely many x values to pick from. This means there are infinitely many ordered pairs for (x,y).
When it comes to graphing, you only need two points at minimum to form a straight line.
Someone please help me with this problem.
A survey of a club's members indicates that 40% own a home, 90% own a car, and 95% of the homeowners who subscribe also own a car
What is the probability that a club member owns neither a house nor a car?
The probability that a club member owns neither a house nor a car is 0.08 or 8%.
As per the survey of a club's members-
percentage of members who own a home 40% = 0.4
percentage of members who own a car → 90% = 0.9
Further, 95% of the homeowners also own a car
⇒ percentage of members who own a car as well as a home = 95% of 40%
= 95/100 x 40/100
= 3800/10000
= 0.38
Let P(A) be the probability that a member owns a home and P(B) be the probability that a member owns a car
we have,
P(A) = 0.4
P(B) = 0.9
also P(A∩B) = 0.38
we need to find the probability that a club member owns neither a house nor a car, that is, P(A'∩B')
According to the rules of probability-
P(AUB) = P(A) + P(B) - P(ANB)
⇒ P(AUB) = 0.4 +0.9 -0.38
P(AUB) = 0.92
Thus, P(A'U B') = 1 - 0.92
= 0.08
Thus, the probability that a club member owns neither a house nor a car is 0.08 or 8%.
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NEED HELP!
PLEASE HELP
Answer:
J and I
Step-by-step explanation:
If possible use a graphing calculator this is from Desmos
If you are not allowed to then use the rise over run rule or Rise/run
if the constants or numbers Infront of x match then the lines are parallel for these kinds of lines. The black line was added to show that it is parallel with the same constant
4. The table represents a proportional relationship. Find the constant of proportionality and write an equation to represent the relationship. (Lesson 2-4) a 2 3 10 12 y Equation: y = W|N 2 3 1 10 3 4 Constant of proportionality:
4 and 3.14 are the constant of proportionality .
What does the arithmetic word proportional mean?
In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.There is a correlation between the quantity of fuel we put in our car's tank and the price we will have to pay when we fill it up. In other words, we will pay more money the more gas we put in.2×4 = 8
2×3.14=6.28
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PLS HELP!! ILL GIVE BRAINLYEST!!
The school cafeteria serves portions of fried rice that are 140 grams each.
A. If 64 portions of rice are served, how many grams of rice would that be?
B. Write an expression for the total weight in grams of rice needed for p portions.
C. One day, the total weight of rice served was 11,340 grams. How many portions were served that day?
D. Write an expression for the number of portions served if the total rice weighed t grams
Please answer all questions
A. The grams of rice served for 64 portion is 8960 grams.
B. The expression for the total weight in grams of rice needed for p portions is 140p.
C. The portion when a total weight of 11340 grams was served is 81 portion
D. The expression for the number of portions served if the total rice weighed t grams is t / 140
How to find the expression for the number of grams served?The school cafeteria serves portions of fried rice that are 140 grams each.
A.
64 portions of rice are served. The grams of rice served is as follows:
1 portion = 140 grams
64 portions = ?
cross multiply
grams of rice served = 64 × 140
grams of rice served = 8960 grams
B.
The expression for the total weight in grams of rice needed for p portions is as follows:
total weight = 140p
C.
The portion when a total weight of 11340 grams was served is as follows:
140 grams = 1 portion
11340 grams = ?
portion = 11340 / 140
portion = 81 portion
D.
The expression for the number of portions served if the total rice weighed t grams is as follows:
portion = t / 140
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The puppy shelter where Isaac works is moving to a new building. The rooms in the new building are built to hold 6 puppies each. Isaac needs to figure out how many rooms he'll need to house a total of 78 puppies.
Use an equation to find the number of rooms Isaac needs.
The equation to find the number of rooms Isaac needs is r = 13.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
1 room holds = 6 puppies
So, 1 puppy acquire = 1/6 room
Let r be the rooms need to house a total of 78 puppies.
Therefore, 78 puppy acquire, r = 78*1/6 room
⇒ r = 78/6 room
⇒ r = 13 room
Thus, the equation to find the number of rooms Isaac needs to house a total of 78 puppies is r = 13.
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Shirley, Benny, and Gil have a coupon for $2.00 off a large pizza. They each pay one
third of the total after the discount. If each person pays $6, how much was the total
before the discount?
Answer:
20 dollars
Step-by-step explanation:
Because there is 3 people according to where it said the amount of names there are and they each had to pay 6 dollars. 6 x 3 is 18. That is the price after discount. The coupon is 2 dollars so 18 + 2 is 20 dollars. That is the final price.
The vertex of this is at parabola is at (-1, -3). Which could be its equation?
Answer:
What are the options I can choose from?
Step-by-step explanation:
