Which could be the entire interval over which the
function, f(x), is positive?
O (-∞, 1)
O (-2, 1)
O (-∞, 0)
O (1,4)
Answers
Answer:
(-2, 1)
Step-by-step explanation:
So assuming this table contains all the zeroes of f(x) and all of them having a multiplicity of 0. This quadratic equation can be defined as
[tex]f(x) = a(x+2)(x-1)[/tex]. So if you look at the top where its f(-3) then f(-2) then f(-1) it appears to be increasing and then somewhere in between f(-1) and f(0) it has a turning point in which it starts decreasing. and then after f(1) it no longer outputs positive values and appears to be going towards negative infinity. So the interval in which f(x) is positive seems to be finite and using this table it appears to be at (-2, 1) and make sure to use parenthesis since at f(-2) and f(1) it's not positive, because 0 is not positive, so it's not included in the interval
Related Questions
2. A shop owner raises the price of a $150 pair of shoes by 40%. After a few weeks, because of falling sales, the owner reduces the price of the shoes by 40%. A customer then says that the shoes are back at the original price.
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. What do the shoes actually cost now? show calculation
d. By what percent should the shoes be decreased in order to have the price back at $150? Round to the nearest 10th percentage. (for example if your decimal answer is .058267 your answer would be 5.8267% round to nearest 10th percent answer is 5.8%) show calculation
Answers
The mistaken assumption is that the customer thinks the shoes are back to their original price.
The assumption is wrong because the price of the shoe is now lower than $150.
The cost of the shoe now is $126.
In order to retain the price of $150, the percentage decrease should have been 28.6%.
What is the cost of the shoe now?Price of the shoe after it was increased : 1.4 x 150 = 210
Price of the shoe after it was decreases: (1 - 0.4) x 210
0.6 x 210 = $126
The percentage the price should be decreased for the price to be back to $150 = (150 / 210) - 1 = 28.9%
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Write a compound inequality that represents the given graph
Answers
Answer:
A
Step-by-step explanation:
The graph is composed of two different rays.
Eliminate B and C.Also, when x = -2, there is an open hole.
Eliminate D.This leaves A as the answer.
it is 1.8 km from Rachel's house to the nearest mailbox Use the facts to find how far this is in meters.
Answers
Answer:
1800 m
Step-by-step explanation:
1 km = 1000 m
1.8 km = 1.8 × 1 km = 1.8 × 1000 m = 1800 m
Let
X
be a random variable such that
E
(
X
2
)
=
81
and
V
(
X
)
=
58
. Compute V
(
2
X
+
10
)
E
(
2
X
+
10
)
Answers
What I gather from the question is that [tex]X[/tex] has second moment [tex]E(X^2)=81[/tex] and variance [tex]V(X) = 58[/tex], and you're asked to find the expectation and variance of the random variable [tex]Y=2X+10[/tex].
From the given second moment and variance, we find the expectation of [tex]X[/tex] :
[tex]V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}[/tex]
Expectation is linear, so
[tex]E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}[/tex]
Using the same variance identity, we have
[tex]V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2[/tex]
and
[tex]E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}[/tex]
so that
[tex]V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}[/tex]
Alternatively, we can use the identity
[tex]V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232[/tex]
Identify the missing justifications.
(a) =
(b) =
A 2-column table has 7 rows. The first column is labeled Step with entries 2 x minus 7 = 15, 2 x minus 7 + 7 = 15 + 7, 2 x + 0 = 22, 2 x = 22, (one-half) 2 x = (one half) 22, 1 x = 11, and x = 11. The second column is labeled Justification with entries Given, Addition property of equality, (a), Additive identity, (b), Multiplicative inverse, and Multiplicative identity
Answers
The missing algebra property justification for the equation solution is; Multiplicative Inverse
How to use algebraic properties?
We are given the equation;
2x - 7 = 15
Step 1; Add 7 to both sides to get; 2x - 7 + 7 = 15 + 7
2x = 22
Reason; Addition property of equality
Step 2; Multiply both sides by 1/2(one half) to get;
(1/2) * 2x = (1/2) * 22
x = 11
Reason; Multiplicative Inverse
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How can you determine the measure of an angle if you know the opposite side of the angle and the hypotenuse?
Answers
Answer:
Use sine rule.
Explanation:
[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]
If opposite side of an angle and hypotenuse is given.
Use sine rule: sin(θ) = opposite/hypotenuse
For example:
Given that opposite of the angle is 10 cm and hypotenuse is 20 cm.
To find the angle:
sin(θ) = 10/20
θ = sin⁻¹(10/20)
θ = sin⁻¹(1/2)
θ = 30°
Several ways
You can use sin directly
As
sinØ=Opposite/HypotenuseThen you can find Ø from it
Otherwise
You may find adjacent using Pythagorean theorem
Then you can use cos
cosØ=Adjacent/HypotenuseYou may use tan even
tanØ=Opposite/AdjacentThe current salaries in Sasha’s department are $42,000, $32,000, $33,000, $38,000, and $50,000. Sasha wants to adjust the lowest salary up to $40,000. If Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary, Find the total cost for the increment?
Answers
The total cost for the increment is $13,000.
What is the total cost for the increment?There are 5 employee's in Sasha's department. The total amount of increment is $5000. (5 x $1000).
The lowest salary is 32,000. If it is increased to $40,000. The total cost of the increment is $8000 (40,000 - 32,000)
Total cost of the increment = $8000 + $5000 = $13,000
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What is the value of x if e³x+6 - 87
Answers
QUESTION 4
.
1 POINT
The sum of eight times a number and four is ninety-two. Find the number.
Provide your answer below:
Answers
Answer:
The missing number is 11
Step-by-step explanation:
Step-by-step explanation:
x is the number
8x + 4 = 92 (8 times the number plus 4 is 92).
8x = 88
x = 11
the number is 11.
Calculate the amount of air in a room 6m long, 5m wide and 3mm high.
Answers
Answer:
90.000 m³
Step-by-step explanation:
L = 6 mW = 5 mH = 3 mm = 3.000 mV = L × W × H
V = 6 × 5 × 3.000
V = 30 × 3.000
V = 90.000 m³
Hello !
[tex]6 \times 5 \times 3 = 90 {m}^{3} [/tex]
The amount of air is 90m³.
Have a nice day ;)
PLEASE ANSWER THIS QUESTION! I BEG OF YOU
Two function are represent below.
FUNCTION A FUNCTION B
y=35x. (image below)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer.
EXPLAIN THE ANSWER!
Answers
The difference between the rate of change of B and the rate of change of A is 15.
How to get the difference in the rates of change?
First, we need to get the two rates of change.
We have two linear functions.
A: y = 35*x
For function A the rate of change is the slope, wich is 35.
Function B is graphed.
Remember that if a line passes through two points (x₁, y₁) and (x₂,y₂) then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In the graph, we can see that line B passes through (0, 0) and (1, 50), then the slope is:
[tex]a = \frac{50 - 0}{1 - 0} = 50[/tex]
Then the rate of change of B is 50.
The difference between the rates of change is:
diff = 50 - 35 = 15
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Shelly completed 10 problems. She has 2/7 to complete. How many problems are left?
Answers
The number of problems Shelly has to complete is 25 problems
Fraction:Total problems = xNumber of problems completed = 10Number of problems to complete = 2/7xx = 10 + 2/7x
x - 2/7x = 10
(7x-2x)/7 = 10
5/7x = 10
x = 10 ÷ 5/7
= 10 × 7/5
= 70/5
x = 35 problems
So,
Number of problems to complete = Total problems - completed problem
= 35 - 10
= 25 problems
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Giving brainliest :)
Answers
Answer:
[tex]f^{-1}(x)=x^2+1[/tex]
Step-by-step explanation:
The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y
Original Equation:
[tex]f(x)=\sqrt{x-1}\\[/tex]
write f(x) as y (since that's what it represents)
[tex]y=\sqrt{x-1}[/tex]
Swap x and y
[tex]x=\sqrt{y-1}[/tex]
Square both sides
[tex]x^2=y-1[/tex]
Add 1 to both sides
[tex]x^2+1=y[/tex]
So this gives you the equation:
[tex]f^{-1}(x)=x^2+1[/tex]
Joyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
PLS HELP ASAP! will mark brainliest and 20 points
Answers
Answer:
x + 10
Step-by-step explanation:
You want to know how much money Joyce has if she won a bet with George in which they both started with the same money, both bet 5 cents, and George ended up with x cents.
BetWe assume that both Joyce and George put 5 cents in the pool. After doing that, each had x cents. If Joyce won the 10-cent pool, she now has ...
x + 10 cents
__
Additional comment
If they both bet against a house, or in a situation where a third party was involved, the amount Joyce ends with depends on the odds of the game, or the percentage collected by the house.
Given that the game is not specified, we have made up the rules.
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Write an inequality, in slope-intercept form, for the graph below. If necessary,
use "<=" for < or ">=" for >.
-5
(1,1)
(0, -2)
5
Answers
The inequality of the given graph in Slope Intercept Form is;
y ≥ 3x - 2
How to write an inequality in slope intercept form?From the attached graph, we see that the boundary line passes through the points (0,-2) and (1,1), and as such the equation of the boundary line is gotten from the general formula;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Thus, we have;
(y + 2)/(x - 0) = (1 + 2)/(1 - 0)
(y + 2)/x = 3
y + 2 = 3x
y = 3x - 2
Now, the boundary line is a solid line and the shaded area lies above the boundary line, therefore the sign of inequality must be ≥.
The inequality of the given graph in Slope Intercept Form is;
y ≥ 3x - 2
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Find data on the increase in consumer credit card debt in the U.S.A. Based on your findings, do you think the extent of the consumer debt is (a) a crisis, (b) a significant occurrence but nothing to worry about or (c)a good thing?
Justify your conclusion.
Answers
Increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.
What is Consumer Credit Card Debt ?
It is the debt which has been accumulated due to the consumers buying products and services out of the credit card and not paying them back in the period of 90 days.
In USA , the credit card balance is $841 billion in the first quarter of 2022 , which is $15 billion less form the last year but at a significant peak.
This extent of the consumer debt is a debt crisis.
The debt on the bank increases as the debt on the consumer increases , causing in bank recession and a recession brings harm to the economy , It is a crisis situation and need to be handled before it affects the market.
Therefore increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.
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In a psychology class, 44 students have a mean score of 96.6 on a test. Then 13 more students take the test and their mean score is 66.3.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students
Answers
Answer: 89.7
Step-by-step explanation:
The mean of a data set is the average of all the information given. Therefore, the total combined score is the number of students multiplied by the mean
The total score of the first 44 students: 96.6*44 = 4250.4
The total score of the later 13 students: 66.3*13 = 861.9
(4250.4 + 861.9)/(44 + 13) = 89.7
Hope this helped
a recent study by a researcher found that 82% of teenagers have used cellphones while driving a vehicle.suppose a random sample of 100 teen drivers is taken.calculate the probability that the sample proportion is less than 0.80
Answers
The probability that the sample proportion is less than 0.80 is mathematically given as P(z<-0.52)
What is the probability that the sample proportion is less than 0.80?Generally, the equation for probability is mathematically given as
p=82/100
Therefore
p=0.82
q=1-p
q=1-0.82
q=0.18
[tex]SE=\sqrt{\frac{p(1-p)}{n}}\\\\SE=\sqrt{\frac{0.8(1-0.8)}{100}}\\\\SE=0.03841[/tex]
b)
[tex]P(p < 0.80)=p(\frac{p-0.82}{0.0384} < \frac{0.8-0.82}{0.0384})\\\\P(z < -0.52)[/tex]
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Use the properties of exponents to simplify the expression (27 1/2) 2/3
Answers
Answer:
3
Step-by-step explanation:
using the power we multiply the exponents (27^1/2)^2/3 to get 27^1/3=3
What is the solution to the inequality?
15<4+x
Answers
Answer:
Step-by-step explanation:
Hello!
15 < x + 4
We can subtract 4 from both sides, to cancel it out.
15 - 4 is 11.
11 < x
x = {12,13,14,15,16,..........................................................................Infinity}
Hope I Helped!
solve for X in the figure
Answers
Answer:
35
Step-by-step explanation:
This shape has 6 sides.
Sum of interior angles of a 6 sided shape is 720.
117 + 4x - 5 + 4x - 3 + 118
+ 3x + 6 + 3x - 3 = 720
4x + 4x + 3x + 3x
+ 117 + 118 + 6 - 5 - 3 - 3 = 720
14x + 241 - 11 = 720
14x + 230 = 720
14x = 720 - 230
14x = 490
x = 490/14
x = 35
Please help!!! Rationalize the denominator and simplify the following expression:
Answers
Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
What is the simplified form of this expression?Given that;
[tex]\frac{4+\sqrt{5} }{\sqrt{5} -2}[/tex]
To rationalize the denominator, we multiply the expression by [tex]\frac{\sqrt{5} +2 }{\sqrt{5} +2}[/tex]
Hence
[tex]\frac{4+\sqrt{5} }{\sqrt{5}-2 } *\frac{\sqrt{5} +2 }{\sqrt{5} +2}\\\\\\\frac{(4+\sqrt{5}) }{(\sqrt{5}-2) } \frac{(\sqrt{5} +2) }{(\sqrt{5} +2)}\\\\\\\frac{(4+\sqrt{5})(\sqrt{5}+2) }{\sqrt{5}^2+\sqrt{5}*2-2\sqrt{5} -4 } \\\\\\\frac{(4+\sqrt{5} )(\sqrt{5}+2 )}{1}\\ \\(4+\sqrt{5} )(\sqrt{5}+2 )\\\\4\sqrt{5}+4*2+\sqrt{5}\sqrt{5}+\sqrt{5}*2\\ \\ 4\sqrt{5}+8+5+2\sqrt{5}\\ \\ 6\sqrt{5}+13[/tex]
Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
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-(8/24)^{2} ÷ -(8/24)^{0}
Answers
Answer: 1/9
Step-by-step explanation:
-(8/24)^2 / -(8/24)^0
cancel the negatives and simplify 8/24 to 1/3
(1/3)^2 / (1/3)^0
(1/3)^0 = 1
so,
(1/3)^2 = 1/9
The circumference of a circle is 8 pi
kilometers. What is the diameter?
Answers
Answer:
Using the formulas
C=2πr
d=2r
Solving for d
d=C
π=8
π≈2.54648
d≈2.55
Lee put $5,000 into a stock market index mutual fund that grew at an average of 6.5% per year for 10 years. without any added deposits or withdrawals, about how much is in lee's mutual fund account after only 8 years, if you ignore compounding?
Answers
The amount in lee's mutual fund account after 8 years will be $7600
Given: Principal amount (P) = $5000,
Time (t) = 10 years,
Rate of interest (r) = 6.5% per year
To find: lee's mutual fund account after only 8 years
We know that Simple interest (SI) is given by:
[tex]S.I = \frac{PTR}{100}[/tex].......(1)
So, by using equation (1) money (P') in a mutual fund account after 8 years will be
[tex]P'=P+\frac{PTR}{100}[/tex]
[tex]=5000+\frac{5000*6.5*8}{100}[/tex]
[tex]= 5000+50*6.5*8[/tex]
= 5000+2600
= 7600
Hence, the amount in lee's mutual fund account after 8 years will be $7600
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What are the horizontal shift and vertical shift for y=srx+2-3
Answers
Answer:
vertical shift is 3 units down
horizontal shift is 2 units left
Step-by-step explanation:
y=srx+2-3
vertical shift is 3 units down
horizontal shift is 2 units left
A rectangular sheet of metal has a perimeter of 82 inches. Its area is 348 square inches. What are the dimensions of the sheet?
Answers
The area of a 2D form is the amount of space within its perimeter. The length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the sheet be represented by x and the length be represented by y.
Area = x × y
348 = xy
x = 348/y
Perimeter = 2(x+y)
82 = 2(x+y)
41 = x + y
41 = (348/y) + y
0 = y² - 41y + 348
y = 29, 12
Therefore, the length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
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Use the function below to find F(-4)
F(x) = 2^x
Answers
Answer:
1/16
Step-by-step explanation:
F(-4) = 2^-4
= 1/(2^4) = 1/16
Wrote an expression gor
m < RST
Answers
The expression for the angle m∠RST from the given bisctor is; 6x - 18
How to find the expression for a given angle?From the given image in the attachment we are given that;
SQ bisects ∠TSR
m ∠RSQ = 3x - 9
Now, since SQ is a bisector of ∠TSR, we can say that
m∠RST = 2 * m∠RSQ
Thus angle RST is expressed as;
m∠RST = 2(3x - 9)
m∠RST = 6x - 18
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Find the value of 7.1a when a=1.5.
Answers
Final answer:
The answer is 10.65.
Step-by-step explanation:
Step 1
Substitute a=1,5 into expression
7.1a, a=1.5
7.1 x 1.5
Step 2
Multiply the numbers
7.1 x 1.5 = 10.65
Answer:
10.65
Step-by-step explanation:
Plug a into the expression
[tex]7.1\times1.5=10.65[/tex]
Hope I helped you in some way!