25 PTS
The graph of the piecewise function is shown.
What is the range of f(x)?
{ f(x)| –∞ < f(x) < ∞}
{ f(x)| –∞ < f(x) ≤ 4}
{ f(x)| 4 < f(x) < ∞}
{ f(x)| 0 ≤ f(x) < ∞}
Answers
{ f(x)| –∞ < f(x) ≤ 4}
Explanation:
Range of the function mean the y-values range of the function.The answer is
{ f(x)| –∞ < f(x) ≤ 4} beacuse the other 3 equationsa are incorrect.
The range of the function f(x) is:
{ f(x) | –∞ < f(x) ≤ 4}
Step-by-step explanation:By looking at the graph of the function f(x) we see that in the interval :
(-∞,0]
The function f(x) takes a constant value as: f(x)=4
and after that i.e. for x≥0 , the function f(x) is decreasing continuously.
Hence, we could say that the function f(x) takes all the real values which are less than and equal to 4.
Hence, the range of the function is:
{ f(x)| –∞ < f(x) ≤ 4}
Related Questions
If ƒ(x) = 2x, then ƒ -1(x) =
-2x
½x
x - 2
Answers
recall that to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=2x\implies \stackrel{\textit{switcheroo}}{x=2y}\implies \cfrac{x}{2}=y\implies \cfrac{1}{2}x=\stackrel{f^{-1}(x)}{y}[/tex]
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answers
Answer: 4 and 9
Step-by-step explanation:
9 x 4 = 36
The square root of 9 is 3, so 9 is a perfect square.
The square root of 4 is 2, so 4 is a perfect square.
Answer:
9 x 4 = 36
Step-by-step explanation:
you should be able to mark him brainliest now =) =) =)
A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $15 for 6 apples and 6 oranges. What is the cost for an apple
Answers
Answer:
$1.25
Sorry that i dont have an explanation i just didnt wanna confuse you lol
Rita spends 52% of her pocket money on magazines and 23% on movies. If her pocket money was RS.144 what amount of her pocket money is left
Answers
Answer:
The amount of Rita's pocket money left is Rs. 36.
Step-by-step explanation:
Pocket money that Rita had before = 144
Money spent for magazines = 52% of 144
= [tex]\frac{52}{100} (144)[/tex]
= 0.52(144)
= 74.88
Money spent for movies = 23% of 144
= [tex]\frac{23}{100} (144)[/tex]
= 0.23(144)
= 33.12
Money left with Rita = 144 - (74.88 + 33.12)
= 144 - 108
= 36
Hence, Rita left with Rs. 36.
Aliter:
Total money spent = (52 + 23)% = 75%
So, money left with Rita = 100 - 75 = 25%
25% of 144 = 0.25(144) = 36.
Three times one number plus a second number is 40, and the one number minus the second number is 4. Find the numbers.
Answers
Answer:
The numbers are 11 and 7
Step-by-step explanation:
To find these, use the statements to create equations in standard form.
3x + y = 40
x - y = 4
Now that we have these two, we can add them together and get the y's to cancel out.
3x + y = 40
x - y = 4
-------------------
4x = 44
x = 11
Now that we have the first number as 11, we can solve for y using either equation.
x - y = 4
11 - y = 4
-y = -7
y = 7
A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 3/2 to create a new pentagon?
Answers
Answer:
if that is all it says you can do simple cross multiplication
Step-by-step explanation:
18*3/2=x
x will give you the nre number. If you dont know how to do that math go to desmos and type it in. the answer should be 27 if i did it correctly in my head but please check my work.
A student helping a student
The new pentagon has a perimeter of 27 centimeters.
Explanation:To find the perimeter of a regular pentagon, we multiply the length of one side by the number of sides. In this case, the perimeter is 18 centimeters, so each side of the pentagon is 18/5 = 3.6 centimeters long.
When this pentagon is dilated by a scale factor of 3/2, each side of the new pentagon will be 3/2 x 3.6 = 5.4 centimeters long.
Therefore, the new pentagon has a perimeter of 5.4 x 5 = 27 centimeters.
Learn more about perimeter of polygons here:https://brainly.com/question/15387363
#SPJ3
Find the perimeter of the figure:
15 units
30 units
27 units
29 units
Answers
Answer:
To find the perimeter, just add up the lengths of the each side.
AB = 13 units
BC = 12 units
CA = 5 units
P = 13 + 12 + 5 = 30 units
unction f is an exponential function
X -2 | 0 | 2 | 4| 6
F(x) 1/8 | ½| 2 |8 | 32
By what factor does the output value increase as each
input value increases by 1?
Answers
Answer:
4
Step-by-step explanation:
As each x value increases by 1, the output values increase by a factor of 4. This means that each y value can be multiplied by 4 to get the next y value.
1/2(4)=2
2(4)=8
8(4)=32
4 is the factor.
Is the triangle with side lengths of 18cm, 24cm and 30 cm a right triangle ?
Answers
If a, b and c are the lengths of a right triangle and c is the longest side, then:
[tex]a^2+b^2=c^2[/tex]
We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:
[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]
Answer: It's the right triangle.Please Help ASAP!! 98 Points to Brainliest!!
Answers
Answer:
all the lines are correct but for x<= 2 there need to be a closed circle, and vica versa for all the others.
Step-by-step explanation:
The lines are correct but for x<= 2
Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels, what percent of bagels are plain? How many bagels are plain? Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram. Use a percent to compare the amount of salt in a plain bagel to that in a sesame bagel.
Answers
Answer:
The number of plain bagels are 18 and it is 75% of the total bagels .
The amount of salt in a plain bagel to that in a sesame bagel is 81.5% .
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels .
As one dozens contains 12 items .
Thus
Total number of bagels bought by Jen = 2 × 12
= 24
Let us assume that the x be the scalar multiple of sesame bagels and plain bagels .
Number of sesame bagels = 1x
Number of plain bagels = 3x
Than the equation becomes
x + 3x = 24
4x = 24
[tex]x = \frac{24}{4}[/tex]
x = 6
Thus
Number of plain bagels = 3 × 6
= 18
Part value = 18
Total value = 24
Putting all the values in the formula
[tex]Percentage = \frac{18\times 100}{24}[/tex]
[tex]Percentage = \frac{1800}{24}[/tex]
Percentage = 75 %
Therefore the number of plain bagels are 18 and it is 75% of the total bagels .
As given
Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram.
Part value = 0.53 grams
Total value = 0.65 grams
Putting all the values in the formula
[tex]Percentage = \frac{0.53\times 100}{0.65}[/tex]
[tex]Percentage = \frac{5300}{65}[/tex]
Percentage = 81.5 %
Therefore the amount of salt in a plain bagel to that in a sesame bagel is 81.5% .
What are the factors of m^2-6m+6m-36?
Answers
Cataloged 2/3 of new books in shipment. Is she has cataloged 52 books what is the number of books shipped in total
Answers
Answer:
78 books
Step-by-step explanation:
Use proportion: If 52 is 2/3 of the books then number of books shipped = 52 * the inverse of 2/3 which is 52 * 3/2:-
52 * 3/2
= 156/2
= 78 books
The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be required to cover 150 such boxes.
Answers
Answer:
142.2 meters.
Step-by-step explanation:
We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.
Let us find total surface area of box using surface area formula of cuboid.
[tex]\text{Total surface area of cuboid}=2(lb+bh+hl)[/tex], where,
[tex]l[/tex] = Length of cuboid,
[tex]b[/tex] = Breadth of cuboid,
[tex]w[/tex] = Width of cuboid.
[tex]\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)[/tex]
[tex]\text{Total surface area of box}=2(2520+432+840)[/tex]
[tex]\text{Total surface area of box}=2(3792)[/tex]
[tex]\text{Total surface area of box}=7584[/tex]
Therefore, the total surface area of box will be 7584 square cm.
To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.
[tex]\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}[/tex]
[tex]80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2[/tex]
[tex]\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}[/tex]
[tex]\text{ Length of canvass}=14220\text{ cm}[/tex]
Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]
[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}[/tex]
[tex]\text{ Length of canvass}=142.20\text{ m}[/tex]
Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.
ANSWER THIS PLEASSSSSSSSSS
17. Write a function rule for the following arithmetic sequence and use it to find the 250th term. Show your work.
−3, 1, 5, 9, ….
Function Rule: Determining 250th term:
Answers
First check the difference between terms:
[tex]\{1-(-3),5-1,9-5,\ldots\}=\{4,4,4,\ldots\}[/tex]
So every term differs by 4. The first term in the sequence is [tex]a_1=-3[/tex]. Recursively, the sequence is given by
[tex]\begin{cases}a_1=-3\\a_n=a_{n-1}+4&\text{for }n>1\end{cases}[/tex]
Then
[tex]a_2=a_1+4[/tex]
[tex]a_3=a_2+4=a_1+4(2)[/tex]
[tex]a_4=a_3+4=a_1+4(3)[/tex]
and so on, with the general rule
[tex]a_n=a_1+4(n-1)\implies a_n=4n-7[/tex]
Then the 250th term of the sequence would be
[tex]a_{250}=4(250)-7=993[/tex]
A patient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. The doctor wants to know when 15 milligrams of the drug remains.
Write an equation that models the situation. Explain each aspect of your equation.
Answers
Answer:
16.3 hours.
Step-by-step explanation:
"Decays exponentially at a rate of 11% per hour" translates into
(1 - 0.11)^h, where h is the number of hours during which the drug decays.
The negative sign comes from "decay."
The complete formula applicable here is
d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.
We want to know how many hours it will be until all but 15 mg remain. The appropriate formula for this is
15 mg = (100 mg)()^h. Dividing both sides by 100 mg, we get:
15 mg
------------- = 0.89^h, or 0.15 = 1.11^h
100 mg
Apply properties of logs to solve this. Take the natural log of both sides of the above equation. We get:
ln 0.15 = h(ln 0.89). Dividing both sides by ln 0.89, we get:
h = 16.3
The original 100 mg dosage would decay to 15 mg after 16.3 hours.
Write an expression for the sequence of operations described below. add q and 10, then subtract r from the result Do not simplify any part of the expression.
Answers
Answer:
q + 10 - r
Step-by-step explanation:
add q and 10 = q + 10
then subtract r from the result = q + 10 - r
Answer:
(q + 10) - r
Step-by-step explanation:
The given verbal expression is " add q and 10, then subtract r from the results."
Add q and 10 = q + 10
subtract r from the result = (q + 10) - r
So, the final expression is (q + 10) - r
Sammy buys his clothes at super discounts. On saturday he bought shoes regularly priced at $40 for 25% off, and jacket regularly priced at $100 for 30% off before the sales taxe what was the total price of the items sammy bought .Approximately what percent discount did Sammy get on his total purchases
Answers
Answer:
A. $100
B. 29%
Step-by-step explanation:
A. To find total price of the items Sammy bought we will add the price of shoes and jacket after discount.
Let us find price of shoes after 25% discount.
[tex]\text{Price of shoes after discount}=40-(\frac{25}{100}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-(\frac{1}{4}*40)[/tex]
[tex]\text{Price of shoes after discount}=40-10=30[/tex]
Therefore, price of shoes after discount is $30.
Now let us find price of jacket after 30% discount.
[tex]\text{Price of jacket after discount}=100-(\frac{30}{100}*100)[/tex]
[tex]\text{Price of jacket after discount}=100-30[/tex]
[tex]\text{Price of jacket after discount}=70[/tex]
Therefore, price of jacket after discount is $70.
Now let us add both prices to find the total price of the items.
[tex]\text{Total price of items}=30+70[/tex]
[tex]\text{Total price of items}=100[/tex]
Therefore, the total price of the items bought by Sammy is $100.
B. To find the percent discount which Sammy got on his total purchases, we will use percent change formula.
[tex]\text{Percent change}=\frac{\text{Difference}}{\text{Original value}}\times 100[/tex]
Total price without discount= 100+40=140
[tex]\text{Discount percent}=\frac{140-100}{140}\times 100[/tex]
[tex]\text{Discount percent}=\frac{40}{140}\times 100[/tex]
[tex]\text{Discount percent}=0.2857142857142857\times 100[/tex]
[tex]\text{Discount percent}=28.57142857142857\approx 29[/tex]
Therefore, Sammy got approximately 29% discount on his total purchases.
Answer:
Sammy bought a car and got a discount of 2/5 off the original price of $30,000. How much did Sammy pay for the car after the discount?
Step-by-step explanation:
Mr. Fox's had is students identify the sex of each of their frog's while they performing their dissections. There were a total of 46 groups for which there were 19 females and 27 males identified. He has one more group that needs to complete their dissection, the probability that it will be a male is approximately 59% based on the results of the first 46 groups. This is an example of:
A Experimental Probability
B Can not determine
C Theoretical Probability
D Neither
Answers
Answer:
A Experimental Probability
Step-by-step explanation:
The 59 percent is based on the data from the actual data. The theoretical probability is 50 percent for male and 50% and female.
Which equation shows a line perpendicular to the line
Answers
Answer:
The second answer: y= 3/4x + 2
Step-by-step explanation:
Subtract 4x to the other side
Divide by 3 to get y by itself
Make the coefficient of the x term the negative reciprocal, for that is the perpendicular slope of the line
Gabriela has dinner at a cafe and the cost of her meal was $45.00 she wants to leave a tip of 15% what is her total bill
Answers
45+0.15·45=45+6.75=51.75$
Mr. Grimm is trying to build a playground set in his backyard. Part of the playground set will have a slide. The ladder is 5 feet tall, and the slide is 7 feet long. What is the distance between the ladder and the bottom of the slide?
Answers
Answer:
~5 feet.
Step-by-step explanation:
assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
where a and b are sides of the triangle and c is the hypotenuse.
from my image we can see:
[tex]c = 7 \\ b = 5[/tex]
so plugging these numbers into the Pythagorean theorum gives
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {a}^{2} + {5}^{2} = {7}^{2} \\ {a}^{2} + 25 = 49 \\ {a}^{2} = 49 - 25 \\ {a}^{2} = 24 \\ a= \sqrt{24} \\ a \: = 4.90[/tex]
so the length from the ladder to the end of the slide is 4.90 feet.
Show all work plz and answer it quickly
Answers
Answer:
x + 4 = 7 + 4 = 11 feet
Step-by-step explanation:
Do you ever have a nice "fist", meaning you have very neat handwriting.
You are told that A to MSG = B to MSG
So
Equation
3x - 10 = x + 4
Solution
Subtract x from both sides
3x - x - 10 = x - x + 4 Simplify
2x - 10 = 4 Add 10 to both sides
2x - 10 + 10 = 4 + 10 Simplify
2x = 14 Divide by 2
2x/2 = 14/2
x = 7
x + 4 = 7 + 4 = 11 feet from A to Madison Square Garden
Sammy bought 3 T-shirts for $15.75 each and pairs of jeans for $28.79 each. If the sales tax on his purchases totaled $5.24, how much money did Sammy spend in all?
Answers
Answer:
Sammy, after picking out her clothes, bringing them to the counter and ringing them up. owes in total: $49.78
Step-by-step explanation:
Final answer:
This answer explains how to calculate the total amount of money Sammy spent on T-shirts and jeans including sales tax.
Explanation:
To find out how much Sammy spent in total:
Calculate the total cost of the 3 T-shirts: $15.75 x 3 = $47.25
Calculate the total cost of the pairs of jeans: $28.79 x 2 = $57.58
Add the total costs of the T-shirts and jeans: $47.25 + $57.58 = $104.83
Add the sales tax to get the final amount: $104.83 + $5.24 = $110.07
Therefore, Sammy spent $110.07 in all.
You have performed increasingly well this past year and you are earning a 6% pay increase to your current $62,900 annual salary."
Answers
To calculate a new salary after a pay increase, multiply the current salary by the percentage increase and add it to the original salary. In this case, a 6% increase on a $62,900 salary results in a new annual salary of $66,674.
Explanation:The subject of this question is determining the new salary after a pay increase, which is a common problem in mathematics related to percentages. To calculate the new salary after a 6% pay increase to a current salary of $62,900, you multiply the current salary by the percentage increase in decimal form, which is 0.06.
Step-by-Step Calculation
Determine the increase amount by multiplying the current salary by the percentage increase: $62,900 × 0.06 = $3,774.
Add the increase to the current salary to get the new salary: $62,900 + $3,774 = $66,674.
The new annual salary after a 6% increase will therefore be $66,674.
To generalize, the formula to calculate the percentage change or growth rate is given by:
Percentage change = (Change in quantity / Original Quantity) × 100
For example, a $2 per hour raise on a $10 per hour job represents
Percentage change = ($2 / $10) × 100 = 20%
When the sum of 8 and twice a positive number is subtracted from the square of the? number, 0 results. Find the number.
Answers
Answer:
4
Step-by-step explanation:
The equation is
x^2 - (2x + 8) = 0 where x is the number to be found.
removing the parentheses by distributing the negative:-
x^2 - 2x - 8 = 0
(x - 4)(x +2) = 0
x = 4, -2.
The value of x must be 4 because it is positive.
What is the solution set for the open sentence, using the given replacement set ? 6x?2=10 ; {1, 2, 3, 4} ?
Answers
Answer:
answer is x=2
Step-by-step explanation: 6x2=12-2=10The solution set for the equation 6x - 2 = 10 using the replacement set {1, 2, 3, 4} is {2}, as 2 is the only number in the set that, when substituted into the equation, satisfies it.
The solution set for the open sentence 6x - 2 = 10 using the given replacement set {1, 2, 3, 4} can be found by solving the equation for x and then checking which numbers in the replacement set satisfy the equation.
Add 2 to both sides of the equation: 6x - 2 + 2 = 10 + 2, which simplifies to 6x = 12.Divide both sides by 6: 6x/6 = 12/6, which simplifies to x = 2.Check if x = 2 is within the replacement set: Since 2 is in the set {1, 2, 3, 4}, x = 2 is the solution that belongs to the replacement set.Therefore, the solution set is {2}.
The measurement, y, varies directly with regard to another value, x. If y = 9 and x = 24, find x for y = 25.
Answers
Answer:
x=66.667
Step-by-step explanation:
Basically, if y varies directly with a value x, you get an equation of the form y=kx, where k is a constant. To answer the question, first substitute 9 into y, and 24 into x.
9=24k
k=0.375
k is 0.375, so to get x, substitute 0.375 into k and 25 into y
25=0.375x
x=66.667
And we got it!
Final answer:
To find x when y = 25 in a direct variation where y = 9 when x = 24, first find the constant of proportionality (k = 3/8), then use this constant to solve the equation 25 = (3/8)x which yields x ≈ 66.67.
Explanation:
The student's question concerns direct variation, which is a concept where one variable changes in proportion to another variable. In this particular problem, the measure y varies directly with x. Given that y = 9 when x = 24, we can use this information to establish the constant of proportionality k where y = kx.
First, we solve for k using the initial condition:
9 = k * 24
k = 9/24
k = 3/8
Now that we have the constant of proportionality, we can find x when y = 25 by setting up the equation:
25 = (3/8)x
x = 25 * (8/3)
x = 200/3
x ≈ 66.67
Therefore, when y = 25, the value of x is approximately 66.67.
Enter a rational number that is equivalent to
−20/4
Answers
The rational number equivalent to -20/4 is -5.
Explanation:A rational number equivalent to -20/4 is -5. This can be found by dividing the numerator (which is -20) by the denominator (which is 4). The result of this division is -5. Hence, -5 is the rational number equivalent to -20/4.
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x - 3 and y = x + 39
y = 2x - 3 and x + y = 39
y = 2(x - 3) and x + y = 39
Answers
y = 2x- 3 and x + y = 39
Explanation:
Twice of a number indicates the 2x in the equation. It’s also 2 less than the 2x. That’s where the 2x-3 part comes from. The question indirectly states to find the sum of x and y. That sum should equal 39We can now plug in the information and get the second part of the equation, x+ y = 39
Answer with Step-by-step explanation:
Let x and y be two numbers.
One number is 3 less than twice another.
⇒ y=2x-3
Their sum is 39.
⇒ x+y=39
Hence, system of equations are:
y = 2x - 3 and x + y = 39
Putting y=2x-3 in x+y=39
x+2x-3=39
⇒ 3x-3=39
⇒ x-1=13 (dividing both sides by 3)
⇒ x=14
y=2x-3
⇒ y=2×14-3
⇒ y=28-3
⇒ y=25
Hence, Two numbers are:
14 and 25