Answers
Using it's concept, the domain and the range of the function are given as follows:
Domain: [tex]x \leq 4[/tex].Range: [tex]y \geq 0[/tex]What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.The function for this problem is:
[tex]y = \sqrt{4 - x}[/tex]
The square root is defined only for non-negative numbers, hence the domain is given as follows:
[tex]4 - x \geq 0 \rightarrow x \leq 4[/tex]
The outputs of the square root function are also non-negative numbers, hence the range is given as follows:
[tex]y \geq 0[/tex].
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Related Questions
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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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]
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/AdjacentWhat is the value of x if e³x+6 - 87
Answers
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
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.
Select the correct answer.
Here's another plant stand. It has 2 rows, each holding 4 plants. Suppose this plant stand is turned upright.
Choose the number sentence that represents the plants on the upright plant stand.
8 × 1 = 8
4 × 2 = 8
2 × 2 = 4
4 × 4 = 16
Answers
The number sentence that gives the best representation of the plants on the upright stand is 8 × 1 = 8.
How to solve for the plant on the upright stand.Given that the plant is said to be upright, then the number of row would be seen as 1.
The rows of the plants are made up of 2 and the plants in them are said to be 4. Hence we would have 4 x 2 = 8
From here we would conclude that 8 × 1 = 8 is the plants on the upright stand.
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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
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.
Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation Vh=500(1.025)^t , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
B) Va=500(1.025)^t+3 and Va=538.45(1.025)^t
C)Va=500(1.025)^t-3 and Va=538.45(1.025)^t
D)Va=500(1.025)^t+3 and Va=464.30(1.025)^t
Answers
The exponential function that represents the value of Andres’s account after t years is:
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
What is the equation for the value of Andres's account?For Henry, it is given by:
[tex]Vh = 500(1.025)^t[/tex]
Andres starts 3 years later than Henry, hence the equation is:
[tex]Va = 500(1.025)^{t - 3}[/tex]
Applying an exponential simplification, we have that:
[tex]Va = 500\frac{1.025^t}{1.025^3} = 464.3(1.025)^t[/tex]
Hence option A is correct.
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The 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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the cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. on a piece of paper graph c(x) =2x + 3.00. then determine which answer matches the graph you drew, including the correct axis
Answers
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete options of the question are mentioned in the below image.
The cost cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. Therefore, the graph of the equation can be drawn as shown below.
Hence, the correct option is D.
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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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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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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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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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-(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
Find the coordinates of the circumcenter of DEF.
11. D (6,0), E (0,6), F (-6,0)
12. D (0,0) E (6,0), F (0,4)
Answers
In order to determine the coordinates of the circumcenter of triangle DEF with the given vertices, let its circumcenter be P(x, y). Hence, PD = PE = PF.
By squaring all sides of triangle DEF, we have:
PD² = PE² = PF²
From PD² = PE², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 6)²
x² - 12x + 36 + y² = x² + y² - 12y + 36
-12x + 12y = 0 ..........equation 1.
From PE² = PF², we have:
(x - 0)² + (y - 6)² = (x - (-6))² + (y - 0)²
x² + y² - 12y + 36 = (x + 6)² + y²
x² + y² - 12y + 36 = x² + 12x + 36 + y²
-12x - 12y = 0 ..........equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
x = 0 and y = 0.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (0, 0).
At D (0,0) E (6,0), F (0,4).From PD² = PE², we have:
(x - 0)² + (y - 0)² = (x - 6)² + (y - 0)²
x² + y² = x² - 12y + 36 + y²
12y = 36
y = 3.
From PE² = PF², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 4)²
x² - 12x + 36 + y² = x² + y² - 8y + 16
-12x - 8y = -20
-12x - 8(3) = -20
-12x - 24 = -20
12x = -4
x = -1/3.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (-1/3, 3).
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The price of an item has been reduced by 85%. The original price was $33.
Answers
Answer:
4.95
Step-by-step explanation:
85% of 33 = 28.5
33 - 28.5 = 4.5
You are 22 years old and are starting a savings plan and will deposit $200 every 2 months until you retire. The account will give you 7% interest. How much do you expect your account to be worth when you retire at 67 years old?
Answers
Answer:
Formulae can be searched for confirmation : compounding interest with regular payments
Step-by-step explanation:
Calculations do it by yourself
Answer:
clchjtdjgdtklgdlnajajhbshsjzsnnjdndmqjsnsn him
Given: -2x^(2)-3x+4=0, use the quadratic formula to solve for the roots
Answers
The roots of the quadratic equations are -4 and -1
How to determine the roots-2x^(2)-3x+4=0
Expand the equation first
[tex]-2(x^2 - 3x + 4) = 0[/tex]
Find two factor that are multiples of -8 and sum up to give -3, the facors are -4 and -1
Replace -3x with 4x and -x
[tex]-2(x^2 -4x + x + 4) = 0[/tex]
Factorize the equation
[tex]-2 (x (x + 4) + 1 (x + 4)[/tex]
We have
2(x + 1) = 0 and 2(x+ 4) = 0
2(x + 1) = 0
2x + 2 = 0
x = -1
2(x+ 4) = 0
2x + 8 = 0
x = -8/2
x = -4
Therefore, the roots of the quadratic equations are -4 and -1
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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 ;)
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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En la feria el juego de gusano da 5 vueltas y equivale a 150 metros, calcula a cuento equivale lo siguiente: 8/4 de vuelta =_____3 4/6 de vuelta =_____1 4/6 de vuelta= _____3/4 de vuelta= ___4/6 de vuelta= ____7/9 de vuelta =___
Answers
las ecuaciones con fracciones dan:
8/4 de vuelta = 60m(3 + 4/6) de vuelta = 110m4/6 de vuelta = 20m3/4 de vuelta = 22.5m7/9 de vuelta= 23.33 m¿Cuanto vale cada una de las expresiones?Sabemos que 5 vueltas es igual a 150 metros, entonces cada vuelta es equivalente a:
v = 150m/5 = 30m
Es decir, cada vuelta equivale a 30 metros.
Ahora simplemente podemos resolver las ecuaciones con fracciones:
8/4 de vuelta = (8/4)*30m = 60m(3 + 4/6) de vuelta = (3 + 4/6)*30m = 110m4/6 de vuelta = (4/6)*30m = 20m3/4 de vuelta = (3/4)*30m = 22.5m7/9 de vuelta = (7/9)*30m = 23.33 mSi quieres aprender más sobre fracciones:
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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.
<95141404393>
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
Simplify the expression: 2 * | 12 - 14 | =
Answers
[tex]2 \times |12-14|=2 \times |-2| =2\times 2=\boxed{4}[/tex]
Do you know the answer to 8+(10-4)-3*2 and how to solve it?
Answers
Answer:
8
Step-by-step explanation:
10 minus 4 goes first because of BODMAS so thats 6
then 3 times 2 because again bodmas to thats 6
so then its 8 + 6 - 6
can be done in any order not affected by bodmas
6-6 cancels out so the answer is 8
comment if you want an in depth explanation on bodmas lol
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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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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