Answers
9514 1404 393
Answer:
[tex]f(x)=\left\{\begin{array}{cl}-x^2+11x-28&\text{for $4<x<7$}\\x^2-11x+28&\text{otherwise}\end{array}\right.[/tex]
Step-by-step explanation:
The absolute value function negates its contents when those contents are negative. Here, the quadratic factors as ...
x^2 -11x +28 = (x -4)(x -7)
so will be negative when the factors have different signs. That will be the case for 4 < x < 7.
The piecewise function can be written in 3 parts, one part for x ≤ 4, another part for 4 < x < 7, and the remaining part for 7 ≤ x. The function expressions for x ≤ 4 and 7 ≤ x are identical.
In the answer above, we chose to write it with the part where the quadratic is negated being defined on the appropriate interval, and using "otherwise" for the rest of the function. It is a little unconventional to do it this way, but it is more compact and completely defines the function.
Related Questions
a recipe for 30 cookies calls for 4 tablespoons of sugar. If you make 40 cookies and use 5 tablespoons of sugar, will the cookies taste the same? HELP ASAP WILL MARK BRAINLISET IF CORRECT
Answers
Does 6.3=6.33 plz help
Answers
no
it does not
6.3 is 6.30
6.33 is not equal to 6.30
so the answer is No
PLS HELP ME WITH THIS ALGEBRA!
A salt solution contains 10% salt and weights 80g. How much pure water must be added so that the percentage of salt drops to 4%
Answers
Answer:
120 gStep-by-step explanation:
A salt solution contains 10% salt and weights 80g.
Salt content of the solution is:
80*0.1 = 8 g4% solution has 8 g salt, total solution is:
0.04x = 8x = 8/0.04 = 200 gWater to be added:
200 - 80 = 120 gLin ran 2 3/4 miles in 2/5 of an hour
Noah ran 8 2/3 miles in 4/3 of an hour
Who ran faster?
Answers
Answer:
Lin runs faster
Step-by-step explanation:
Lin: 11/4 ÷ 2/5 = 11/4 · 5/2 = 55/8 or 6.875 mph
Noah: 26/3 ÷ 4/3 = 26/3 · 3/4 = 13/2 or 6.5 mph
Pls help me I’ll brainlest due in 10 minutes
Answers
Answer:
7.65
Step-by-step explanation:
Add 1.8 to 5.85 to find initial height
7.65 just add the 2 I answered first btw! Give brainliest pls since im first.
rob is saving to buy a new mp3 player. for every $15 he earns babysitting, he saves $8. On Saturday, Rob earned $90 babysitting. how much money did he save?
Answers
Answer: 42
Step-by-step explanation: 15 -8=7 90/15=6 6*7=42
PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!
what kind of figurative language is stanza 86?
86. Is heard the tramp of his steed as he rides.
Answers
Two puppies, Ruth and Scoonsie, are playing together. Scoonsie weighs 111111 kilograms, and Ruth is lighter than Scoonsie.
Write an inequality that describes r, Ruth's weight in kilograms.
Answers
Answer:
[tex]r < 11[/tex]
Step-by-step explanation:
Given
Represent Ruth with r and Scoonsie with s
[tex]s = 11kg[/tex]
Required
Represent Ruth's weight as an inequality
From the question, Ruth weighs lesser than Scoonsie. This is represented as:
[tex]Ruth < Scoonsie[/tex]
For proper representation, it is:
[tex]r < s[/tex]
Substitute 11 for s
[tex]r < 11[/tex]
The above inequality represents Ruth's weight
Exercise
Sophia's friend has saved $118 but is not sure how many songs she can afford if she buys the membership and
some songs. Use the expression in part (b) to write an equation that can be used to determine how many
songs Sophia's friend can buy
Answers
Answer:
Step-by-step explanation:
Jacob spent 24% of his allowance last week. What fraction of his allowance did Jacob spend? Write the answer in simplest form.
Answers
6/25
Step-by-step explanation:
24/100
both can be multiplyed or divided by 4 and that is the lowest.
so
24÷4=6
100÷4=25
The formula for the volume of this rectangular prism is:
V = x 3 + 5x 2 - 4x - 20
The length is x+5; the width is x+2; the height is unknown. Find an expression for the height.
Show all steps of your work for full credit.
Answers
Answer:
Step-by-step explanation: Explanation:
If
L
,
H
and
W
represent the length, height and width of the prism, then the volume of the rectangular prism is :
V
=
L
.
H
.
W
............. (1)
Given :
V
=
x
3
+
11
x
2
+
20
x
−
32
;
............... (2)
W
=
(
x
−
1
)
;
H
=
(
x
+
8
)
.
Let
L
=
(
x
+
l
0
)
be the expression for the length, then the RHS of equation (1) becomes
L
.
H
.
W
=
(
x
−
l
0
)
(
x
+
8
)
(
x
−
1
)
,
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
x
3
+
(
7
+
l
0
)
x
2
+
(
7
l
0
−
8
)
x
−
8
l
0
..... (3)
Comparing this to the LHS of equation (1), we get the following set of equations to solve for
l
0
,
7
+
l
0
=
11
;
7
l
0
−
8
=
20
;
8
l
0
=
32
;
l
0
=
4
Therefore
L
=
(
x
+
4
)
Fill in the blank to make the number sentence true. Explain how you know. ?/3 x 11 > 11
Answers
Answer:
6
Step-by-step explanation:
Answer:
6/3 x 11 > 11
Step-by-step explanation:
Steven and Mark each carried 48 ounces of juice for trekking. At the end of their journey, Steven's juice bottle was 3/4 empty and Mark's bottle was 2/3 empty. Which of the following sentences is correct?
A. 28 ounces of juice was remaining at the end of their journey.
B. 4 ounces of juice was left at the end of their journey.
C. Mark drank 36 ounces of juice during the journey.
D. Steven drank 32 ounces of juice during the journey.
Answers
Answer:
A, C and DStep-by-step explanation:
Initial volume of juice = 48 ounces each
Mark
Used: 48*3/4 = 36 ouncesLeft: 48 - 36= 12 ouncesSteven
Used: 48*2/3 = 32 ouncesLeft: 48 - 32 = 16 ouncesTotal remaining juice: 12 + 16 = 28 ounces
Correct choices: A, C and D
A manager has hired a consultant to compare two ways a product is presented to customers. Twelve customers are presented with each product. What would be the roles of descriptive and inferential statistics in the analysis of these data
Answers
Answer:
The role of descriptive statistics in data analysis is to provide descriptions of the population characteristics, using numerical calculations, graphs, and tables. Descriptive statistics describe what is going on in a population or data set.
On the other hand, inferential statistics make predictions and draw inferences about a population using the population sample.
Step-by-step explanation:
The two types of statistics are descriptive statistics and inferential statistics. Descriptive statistics describe sets of data, allowing patterns to emerge from the data. These also enable the presentation of the data in a more meaningful way, allowing for simpler interpretation of the data. Two types of descriptive statistics help in this regard. They are measures of central tendencies and measures of spread. Inferential statistics draws conclusions about the sets of data based on sampling, allowing for the making of generalizations and testing of hypotheses.
PLEASE HELP! i have by the end of the day to turn this in, PLEASE DONT GUESS
Answers
hope it helps
Answer:
45 degrees
Step-by-step explanation:
All 3 angles have to add up to 180, so you have:
[tex]x + 32 + 103 =180[/tex]
[tex]x + 135 = 180[/tex]
subtract 135 from both sides
[tex]x = 45[/tex]
What is the percent of change? Round to the nearest whole percent if necessary. Is the percent of change an increase or decrease? 100 to 150
Answers
Answer:
1)increase
2)50%
Explanation:
Use the formula↓
(y2 - y1) / y1)*100
(150 - 100) / 100) * 100 = 50 %
y1= first value
y2= second value
In a triangle, the sum of the lengths of any two legs must be ______________ the length of the third leg.
Plz help this is due in 40 minutes
Answers
Answer:
Step-by-step explanation:
Sum of two sides must be longer than the third.
The slope of the line below is 1 .write the point slope equation for the line using the coordinates of the labeled point. (5,7)
Answers
Answer:
y - 7 = 1 (x-5)
Step-by-step explanation:
The point slope equation of a line is expressed as;
y - y0 = m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given the following
m = 1
(x0, y0) = (5, 7)
Substitute into the formula
y - 7 = 1 (x - 5)
y - 7 = x -5
y = x - 5 + 7
y = x + 2
Hence the point slope equation of the line is y - 7 = 1 (x-5)
Tara needs an $8,000 personal loan.
Which loan option would require her to pay back the least amount of money?
36-month loan with a 9% annual simple interest rate
42-month loan with a 7% annual simple interest rate
48-month loan with an 8% annual simple interest rate.
54-month loan with a 6% annual simple interest rate
Answers
The least amount is paid back in a 42-month loan with a 7% annual simple interest rate.
What is simple interest?The term simple interest refers to a type of interest that is paid only on the principal and not on the interest. We have to note that the time and the interest rate all contribute to increasing the amount of money to be paid back.
In the first case, the amount to be paid back is;
A = $8,000 + ($8,000 * 9 * 3/100)
= $10160
In the second case;
A = $8,000 + ( $8,000 * 7 * 3.5/100)
A =$ 9960
In the third case;
A = $8,000 + ($8,000 * 8 *4/100)
A = $10560
In the fourth case;
A = $8,000 + ($8,000 * 6 * 4.5/100)
A = $10160
Hence, the least amount is paid back in a 42-month loan with a 7% annual simple interest rate.
Learn more about simple interest: https://brainly.com/question/26437826?
Silvia has a coupon for 25% off an item that regularly costs $8. How much will Silvia pay if she uses the coupon?
Answers
Answer:
0.32
Step-by-step explanation:
just divide
Answer:
$6
Step-by-step explanation:
25%= 1/4
8 divided by 4 =2
$2 is what is taken off
$8-$2 which is $6
Mike Jones bought an older house and wants to put in a new concrete driveway. The driveway will be 30 feet long, 10 feet wide, and 9 inches thick. Concrete (a mixture of sand, gravel, and cement) is measured by the cubic yard. One sack of dry cement mix costs $7.30, and it takes four sacks to mix up 1 cubic yard of concrete. How much will it cost Mike to buy the cement
Answers
Answer:
$26280
Step-by-step explanation:
Cuz i said so
Find the area of these shapes
Answers
Answer:
Step-by-step explanation:
Left figure:
area of rectangle = 4×6 = 24 cm²
area of triangle = ½×(base of triangle)×(height of triangle) = ½×6×4 = 12 cm²
area of shape = 24+12 = 36 cm²
Right figure:
area of rectangle = 6×8 = 48 m²
area of triangle = ½×(base of triangle)×(height of triangle) = ½×8×(8-6) = 8 m²
area of shape = 48+8 = 56 m²
Given the area of a circle to be 10 inches^2 what is the radius and the diameter the circumference
Answers
Answer:
Radius = 1.78 inches
Diameter = 3.56 inches
Circumference = 11.18 inches
Step-by-step explanation:
Area of circle = 10 inches square
[tex]\pi r^2 = 10\\r^2 = \frac{10}{3.14}\\r^2 = 3.18\\\sqrt{r^2}=\sqrt{3.18}\\r=1.78[/tex]
Radius = 1.78 inches
Diameter = 2r = 2(1.78) = 3.56 inches
Circumference = 2πr = 2*3.14*1.78 = 11.18 inches
Which ordered pair is the solution to the system of linear equations y=-7x+2 and y = 9x-14?
(-5,1)
(1.-5)
(5,-1)
O (-1.5)
Answers
Answer:
(1,-5)
Step-by-step explanation:
you see ; equation 1 = equation 2
because it both = y
so,
-7x+2 = 9x-14
2+14 = 9x+7x (change side for easier solutions)
16 = 16x
x = 16÷16
x = 1
you can find x, so from choice it has only choice that x = 1
so you can answer!
hope it helps ☺️
What is the measure of Angle A B C ? 36° 43° 72° 144°
Answers
Step-by-step explanation:
the correct answer is C because the measurementor an angle cannot be under 72 :)
Answer:
36
Step-by-step explanation:
Write the ratio as a fraction in simplest form with whole numbers in the numerator and denominator
64 hr to 72 hr
Answers
Answer:
8/9
Step-by-step explanation:
Find the HCF of 64 , 72
64 = 2 * 2 * 2 * 2 * 2 *2 = 2^6
72 = 2 * 2 * 2 * 3 * 3
HCF = 2*2*2 = 8
64 : 72 = [tex]\frac{64}{72}[/tex]
= 64 ÷ 8
72 ÷ 8
[tex]=\frac{8}{9}[/tex]
1. Louis ran a race in 2.4 minutes. Laura ran the same race in 124 seconds. What is the difference between the two times?
Answers
Louis: 2.4 minutes is 2 minutes and 24 seconds (0.4 minute is 24 seconds)
So, the difference between the times is 20 seconds. Laura was 20 seconds faster.
Answer:
20 sec
Step-by-step explanation:
2.4 in = 144 sec
124
144 - 124 = 20
A team in the Department of Institutional Review at a large university wanted to study the relationship between completing an internship during college and students' future earning potential. From the same graduating class, they selected a random sample of 80 students who completed an internship and 100 students who did not complete an internship and examined their salaries 5 years past graduation. They found that there was a statistically higher mean salary for the internship group than for the non-internship group. Which of the following interpretations do you think is the most appropriate?
A. More students should take internships because having an internship produces a higher salary.
B. There could be a confounding variable, such as student major, that explains the difference in mean salary between the internship and no intership groups.
C. You cannot draw any valid conclusions because the samples are not the same size.
Answers
Answer:
b
Step-by-step explanation:
Help ASAP! 25 points! I will also give brainliest!
Answers
Answer:
756 m²
Step-by-step explanation:
I just know the answer XD
Which of the following lists of ordered pairs is a function?
O A. (2, 4), (0, 2), (2, -4), (5,3)
O B. (1,6), (2,7),(4,9), (0,5)
O c. (0, 2), (2, 3), (0, -2), (4,1)
O D. (1, 2), (1, -2), (3, 2), (3, 4)
Answers
Answer:
b
Step-by-step explanation:
Answer:
The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.
Step-by-step explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
Checking option A:
(2, 4), (0, 2), (2, -4), (5,3)
Here, the input x = 2 is repeated twice.
Thus, option A does not represent the function as the input x = 2 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.
Checking option B:
(1,6), (2,7),(4,9), (0,5)
It is clear that no input value is repeated. In other words, each input or x-value of the X set has a unique y-value or output of the Y set.
Thus, the option B represents the function.
Checking option C:
(0, 2), (2, 3), (0, -2), (4,1)
Here, the input x = 0 is repeated twice.
Thus, option C does not represent the function as the input x = 0 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.
Checking option D:
(1, 2), (1, -2), (3, 2), (3, 4)
Here, the input x = 1 is repeated twice, and also x = 3 is repeated twice,
Thus, option D does not represent the function as we can not have duplicated inputs as there should be only 1 output for each input.
Conclusion:
The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.