Find the range of the function f(x)=x^2- 6x if the domain is (-7,-2, 1)
Answers
The range of the function will be;
⇒ Range = (91, 16, - 5)
What is Domain?The set of all inputs of the function is called Domain of set.
Given that;
The function is,
⇒ f (x) = x² - 6x
And, The domain = (- 7, - 2, 1)
Now,
Since, The function is,
⇒ f (x) = x² - 6x
We know that;
The range of the function gives the value of y.
Here, The domain (x) = (- 7, - 2, 1)
Put x = - 7;
⇒ f (-7 ) = (-7)² - 6 × - 7
= 49 + 42
= 91
Put x = - 2;
⇒ f (- 2) = (-2)² - 6 × - 2
= 4 + 12
= 16
Put x = 1;
⇒ f (1) = (1)² - 6 × 1
= 1 - 6
= - 5
Thus, The range = (91, 16, - 5)
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Related Questions
The sum of the digits of a two-digit number is 8. The difference between the number and the reversed number is 10 more than the reversed number. Find the number.
Answers
Answer:
62
Step-by-step explanation:
Let the two digit number be XY
X+Y = 8
10X+Y - (10Y+X) = 10Y+X+10
10X+Y-10Y-X=10Y+X+10
8X-19Y=10
8(8-Y)-19Y=10
64-8Y-19Y=10
27Y=54
Y=2
The number is therefore 62.
The required two-digit number with sum of digits as 8 is 62.
Let us say the number is xy
What is the place value of x and y in xy?
The place value of digits, x and y in the number xy are 10 and 1 respectively.
So the number xy can be written as 10x+y
When the digits are reversed
The new number or reversed number obtained will be yx
So the new number yx can be written as 10y+x
Since the difference between the original number and the reversed number is 10 more than the reversed number.
So, (10x+y) - (10y+x) = 10 + (10y+x)
8x-19y =10.......(1)
Since the sum of digits is 8
So, x+y = 8......(2)
By solving equations (1) and (2) we get
x=6, y=2
So, the required number is xy i.e. 62.
Therefore, The required two-digit number with sum of digits as 8 is 62.
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A fair coin is tossed three times. What is the probability that two heads will be obtained in succession
Answers
Answer:
3/8
Step-by-step explanation:
what is One-eighth times three-elevenths
Answers
Answer:
3/88
Step-by-step explanation:
1/8 x 3/11 =
1x3/8x11 =
3/88
-Chetan K
whats the answer giving brainliest
Answers
Answer:
A
Step-by-step explanation:
Answer:
c x-110
Step-by-step explanation:
if im wrong im so sorry
After w weeks , a student has saved 100 + 15w dollars. How much money has the student saved after 3 weeks ?
A$105
B$65
C$120
D$145
Answers
Answer:
The student will have $145
Step-by-step explanation:
The student would already have $100 and if you take 15 times the number of weeks, 3 weeks. 15 times 3 is $45. $100 + $45 = $145
Answer:
D. $145
Step-by-step explanation:
In order to find out the answer to the equation 100 + 15w = ? we have to multiply 15 by the 3 weeks the student has saved up 15 dollars to get the total money they have saved by saving 15 dollars per week:
15 * 3 = 45
we then add the 100 dollars that was already saved up to 45
100 + 45 = $145
So after 3 weeks $145 have been saved up
Hope this helps!!!
The agricultural practice of irrigation leaves behind which pollutant in the
soil?
O A. Salt
B. Acidic compounds
C. Nitrogen compounds
D. Pesticides
The answer is Salt !!
Answers
Combining negatively correlated assets having the same expected return results in a portfolio with ____ level of expected return and ____ level of risk. Select one: a. a higher; a lower b. the same; a lower c. the same; a higher d. a lower; a higher
Answers
Combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk.
When assets have a negative correlation, their returns tend to move in opposite directions. By combining these assets in a portfolio, their negative correlation offsets each other's risks to some extent. As a result, the overall risk of the portfolio is reduced.
However, the expected return of the portfolio remains the same as the individual assets, assuming they have the same expected return. This is because the negative correlation does not affect the average return of the assets, only their volatility. The diversification benefits provided by negatively correlated assets help to reduce the overall risk of the portfolio, making it less volatile than the individual assets.
Therefore, combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk. This is a desirable outcome for investors as it allows them to achieve a certain level of return while minimizing the overall risk in their investment portfolio.
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Find are of the figure below composed of a rectangular with a semicircle
Answers
Answer:
Step-by-step explanation:
step-by-step
Please help!!!
The mapping displayed is a function…
TRUE
OR
FALSE
Answers
An adventure company wants to run a zip line from the top of one building that is 130 feet tall to the top of another building that is 30 feet tall. The two buildings are 72 feet apart. Estimate the length (in feet) of the zip line. Round your answer to the nearest tenth.
a
about 123. 2 ft
b
about 172. 0 ft
c
about 100. 0 ft
d
about 69. 4 ft
Answers
If the Zip line is from top of the 130 feet building and to the top of 30 feet building , then the estimated length of Zip Line is (a) about 123.2 ft .
The height of the bigger building is = 130 feet ;
the height of the shorter building is = 30 feet ;
the distance between the two buildings is = 72 feet ,
let the length of the zip line be = x feet ;
the given situation form as right triangle , where the Zip length is represented by the hypotnuse , the base is 72 feet , and the perpendicular side is = 130 - 30 = 100 ft ;
By Pythagoras Theorem ,
we get ;
⇒ \(x^{2} = 100^{2} +72^{2}\) ;
⇒ \(x^{2} = 10000 +5184\) ;
⇒ \(x^{2} = 15184\)
⇒ \(x = \sqrt{15184}\) , the value is approx. 123.2233 .
Therefore , the estimated length of the zip line is 123.2 feet .
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A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried. To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Answers
Select a random sample of 35 unmarried and 15 married subjects
A researcher who wishes to study the effects of a prenatal breastfeeding education program on the length of time African-American inner-city women breastfeed infants learns that 70% of women in the target population are unmarried.
To achieve stratified random sampling in a sample of 50 subjects, the researcher will:
Select a random sample of 35 unmarried and 15 married subjects.
hence, Select a random sample of 35 unmarried and 15 married subjects.
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1/3x² + x+5/3x² = 1/9
HAHAHAHA......
Answers
Answer:
\(\huge \bf༆ Answer ༄\)
Step-by-step explanation:
Let's solve for x ~
\( \sf \dfrac{1}{3} {x}^{2} + x + \dfrac{5}{3} {x}^{2} = \dfrac{1}{9} \)\( \sf \dfrac{(1 + 5)}{3} {x}^{2} + x = \dfrac{1}{9} \)\( \sf \dfrac{6}{3} {x}^{2} + x - \dfrac{1}{9} = 0\)\( \sf2 {x}^{2} + x - \dfrac{1}{9} = 0\)Multiply each term with 9 on both sides of the equation
\( \sf(2 {x}^{2} \times 9) + (x \times9 ) - ( \dfrac{1}{9} \times 9 ) = 0 \times 9\)\( \sf18 {x}^{2} + 9x - 1 = 0\)Now, let's use Quadratic formula to find its roots ~
\( \sf \dfrac{ - {b}^{} \pm \sqrt{b {}^{2} - 4ac} }{2a} \)
where,
b is Coefficient of x = 9 a is Coefficient of x² = 18 c is the constant term = -1Let's find the roots ~
\( \sf \dfrac{ - 9 \pm \sqrt{(9 {}^{2}) - (4 \times 18 \times - 1) } }{2 \times 18} \)\( \sf \dfrac{ - 9 \pm \sqrt{81- ( - 72) } }{36} \)\( \sf \dfrac{ - 9 \pm \sqrt{81 + 72} }{36} \)\( \sf \dfrac{ - 9 \pm \sqrt{153} }{36} \)\( \sf \dfrac{ - 9 \pm 3\sqrt{17} }{36} \)\( \sf \dfrac{3( - 3 \pm \sqrt{17} )}{36}\)\( \sf \dfrac{ - 3 \pm \sqrt{17} }{12} \)Therefore the value if x are ~
\( \sf \dfrac{ - 3 + \sqrt{17} }{12} \: \: and \: \: \sf \dfrac{ - 3 - \sqrt{17} }{12} \)I hope it helps ~
URGENTTT PLEASE!! in middle of test help!
I WILL MARK BRAINIEST! if you answers in under 5mins!
Answers
Answer:
equation: 2(2w + 2) = 60
length = 16
width = 14
Step-by-step explanation:
width = w
length = w + 2
perimeter = 2(w + w + 2) = 60
equation: 2(2w + 2) = 60
4w + 4 = 60
4w = 56
w = 14
width = 14
length = w + 2 = 14 + 2 = 16
length = 16
Find the Length of the missing side of the right Triangle using the Pythagorean Theorem. Round your answers to
the nearest tenth. Please show your work in the "Show your work" text box. Draw a Picture!
The size of a television screen is given by the length of the diagonal of
the screen. What size is a television screen that is 21.6 inches wide and
16.2 inches high?
Show Your Work
O 22.5 in
18.4 in
27 in
O 13.2 in
Answers
Answer:
27 inches
Step-by-step explanation:
We can use The Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
21.6 ^2 + 16.2^2 = c^2
466.56+262.44 = c^2
729 = c^2
Taking the square root of each side
sqrt(729) = sqrt(c^2)
27 = c
The polynomial f(x) has degree 4. Choose each statement that could describe all the zeros of f
One zero with multiplicity 3
One zero with multiplicity 4
One zero with multiplicity 5
One zero with multiplicity 1 and one zero with multiplicity 2
One zero with multiplicity 1 and one zero with multiplicity 3
One zero with multiplicity 2 and two zeros with multiplicity 1
One zero with multiplicity 2 and three zeros with multiplicity 1
Two zeros with multiplicity 2
Two zeros with multiplicity 2 and two zeros with multiplicity 1
Two zeros with multiplicity 2 and three zeros with multiplicity 1
Two zeros with multiplicity 1
Three zeros with multiplicity 1
Four zeros with multiplicity 1
Five zeros with multiplicity 1
Answers
The answer choices which could correctly describes all the zeroes of the polynomial in discuss are;
One zero with multiplicity 4.One zero with multiplicity 1 and one zero with multiplicity 3.One zero with multiplicity 2 and two zeros with multiplicity 1.Two zeros with multiplicity 2Four zeros with multiplicity 1.Which answer choices could correctly describe the zeroes of a polynomial with degree 4?It follows from the task content that the answer choices which could correctly represent the zeroes of the polynomial be determined.
Since the degree of the polynomial is 5, the number of factors (linear) such polynomial s would have must be 4.
On this note, the total factors is determined by the aggregate sum of zeroes and multiplicities.
Ultimately, the possible zeroes for the polynomial are as indicated above.
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four pairs of data yield r = 0.942 and the regression y=3x equation . also, y=12.75 what is the best predicted value of y for ?
Answers
best predicted value of y for x = 4.25 is 12.75 .we can use the regression equation y = 3x to find the predicted value of y for any given value of x.
If we assume that the value of x is not given and we want to find the predicted value of y for the average value of x, then we can use the formula for the mean of x and y values to find the average value of x:
x= (x1 + x2 + x3 + x4) / 4
Similarly, we can find the average value of y:
y= (y1 + y2 + y3 + y4) / 4
We are given that y = 12.75, so we can use the regression equation to solve for x:
y = 3x
x = y / 3
x = 12.75 / 3
x = 4.25
we have the value of x, we can use the regression equation to find the predicted value of y
y = 3x
y = 3(4.25)
y = 12.75
Therefore, best predicted value of y for x = 4.25 is 12.75.
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A student has a container with the volume 1.5 liters. She estimates the volume to be 1.2 liters. By what percent is the student's estimate off? I don't need a step-by-step explanation, I just want the right answer.
Answers
Answer:
20%.
1.2/1.5 = 0.8
0.8*100 = 80%
100%-80% = 20%.
We can verify this:
1.5-20% = 1.2.
Answer: 20%
Step-by-step explanation:
Enter the value of x that makes the given equation true.
3(5 - x) = 7x - 2
Answers
Answer:
exact form: x=17/10
Decimal form: x=1.7
mixed number form: 1 7/10
Answer:
x = 17/10 (as a fraction) or x = 1.7(as a decimal) or x = 1 7/10(as a mixed number)
Step-by-step explanation:
3(5-x) = 7x - 2
3 * 5 - 3* x = 7x - 2 (brackets means multiply)
15 - 3x = 7x - 2 (when over equal sign negative changed to positive)
15 + 2 = 7x + 3x
17/10 = 10x/10 (cross-cancel cuz u tryna isolate the x)
17/10 = x
Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot units and the hypotenuse measures 2x units. (150StartRoot 3 EndRoot – 75π) ft2 (300 – 75π) ft2 (150StartRoot 3 EndRoot – 25π) ft2 (300 – 25π) ft2.
Answers
The area of the shaded region is \(\rm (150\sqrt{3} \ - 75\pi ) \ feet^2\) option first is correct.
It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.
It is required to find the shaded area (missing data is attached shown in the picture).
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a hexagon with a side length of 10 feet.
We know the area of the hexagon is given by:
\(\rm A = \frac{3\sqrt{3} }{2} a^2\) where a is the side length.
\(\rm A = \frac{3\sqrt{3} }{2} 10^2\) ⇒ \(150\sqrt{3}\) \(\rm feet^2\)
We have the shortest length = x feet and from the figure:
2x = 10
x = 5 feet
The radius of the circle r = longer leg
\(\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}\) feet
The area of the circle a = \(\pi r^2\) ⇒ \(\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2\)
The area of the shaded region = A - a
\(\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2\)
Thus, the area of the shaded region is \(\rm (150\sqrt{3} \ - 75\pi ) \ feet^2\)
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Answer:
option A
Step-by-step explanation:
Classify the polynomial as a monomial, binomial, trinomial, or none of these. x2 - 10x + 25
Answers
It is a trinomial because it follows the pattern of x^2 + bx + c. In this case, x^2 - 10x + 25. Also, it only has three numbers and two operation symbols, signifying a trinomial (three = tri).
bob, kris, janelle, and pat are in a study team. bob, kris, and janelle have algebra
files on their desks. bob has two x files, four x-tiles, and seven unit tiles, kris has one ?
lile and five unit files, and janelle has ten x-tiles and three unit files, pat's desk is empty. the
team decides to put all of the files from the three desks onto pat's desk. write an algebraic
expression for the new collection of files on pat's desk
Answers
Pat: 6x files + 14 x-tiles + 1 ?-tile + 15 unit files + 7 unit tiles
Let's represent the number of files on each person's desk as follows:
Bob: 2x files + 4x-tiles + 7 unit tiles
Kris: 1 ?-tile + 5 unit files
Janelle: 10 x-tiles + 3 unit files
To find the algebraic expression for the new collection of files on Pat's desk, we add the files from Bob, Kris, and Janelle and represent it as follows:
Pat: (2x files + 4x-tiles + 7 unit tiles) + (1 ?-tile + 5 unit files) + (10 x-tiles + 3 unit files)
Simplifying the expression, we can combine like terms:
Pat: 2x files + 10 x-tiles + 1 ?-tile + 4x-tiles + 5 unit files + 7 unit tiles + 3 unit files
Combining similar types of files and tiles, the final expression for the new collection of files on Pat's desk is:
Pat: 6x files + 14 x-tiles + 1 ?-tile + 15 unit files + 7 unit tiles
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help!! im stuck on this and i can't remeber how to sove this.... 6/3c = 2/3
Answers
Hello!
Answer:
\(\huge\boxed{c = 3}\)
Given:
\(\frac{6}{3c} = \frac{2}{3}\)
Cross multiply:
\(6 * 3 = 3c * 2\)
Simplify:
\(18 = 6c\)
Divide both sides by 6:
\(c = 18/6 = 3\)
Answer:
c=3
Step-by-step explanation:
6 2
----- = -----
3c 3
Using cross products
6*3 = 2*3c
18 = 6c
Divide each side by 6
18/6 = 6c/6
3 =c
PLEASEEE help with this question
Answers
Answer:
Step-by-step explanation:
Prove The Following
------------------------------
Answers
Answer: WAP if yu dont understand look up videos of WAP
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
m < PCA = m < CAD ( alternate angles)
m < BAD = m <CAD ( given)
Also m < CAB = m < PCA + m < CPA ( exterior angle of a triangle theorem).
Also m < CAB = m< CAD + m < BAD (given)
So m < PCA + m < CPA = m < CAD + m < BAD
But m < PCA = m < CAD
so m < CAD + m < CPA = m < CAD + m BAD
So m < CPA = m < BAD
But m < PCA = m < CAD = m BAD
therefore m < CPA = m < PCA
That makes triangle CAP isosceles
Therefore AP = AC.
area of a isocles triangle whose both sides are 5 cm and one side 4cm
Answers
Answer:
9.17cm (3s.f.)
Step-by-step explanation:
Using Pythagoras Theorem,
5² = 2² + (Height of Triangle)²
Height of Triangle = 4.5826cm (5s.f.)
Area = ½ × 4 × 4.5826
= 9.1652cm (5s.f.)
= 9.17cm (3s.f.)
What is System Effectiveness, if Operational Readiness is 0.89, Design Adequacy is 95%, Availability is 98%, Maintainability is 0.93, and Mission Reliability is 0.99? a. 0.763 b. 0.881 c. 0.837 d. 0.820
Answers
The System Effectiveness is approximately 0.763.
To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.
System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability
Plugging in the given values:
System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99
System Effectiveness ≈ 0.763
Therefore, the System Effectiveness is approximately 0.763.
The correct answer is a. 0.763.
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Help please? 10 points
Answers
Answer:
277 cm^2
Step-by-step explanation:
Two of the triangular faces will have areas of ...
A = 1/2bh = (1/2)(8 cm)(11 cm) = 44 cm^2
and the other two will have areas of ...
A = 1/2bh = (1/2)(9 cm)(13 cm) = 58.5 cm^2
The base will have an area of ...
A = LW = (9 cm)(8 cm) = 72 cm^2
So, the total area will be ...
2(44 cm^2) +2(58.5 cm^2) +72 cm^2 = 277 cm^2
_____
Comment on the problem
You could not actually build this pyramid. The height of the peak above the 8-cm edges must be ...
√(11^2 -(4.5)^2) = 10.04 cm
The height of the peak above the 9-cm edges must be ...
√(13^2 -4^2) = 12.37 cm.
The peak cannot be in two places at once. This geometry is impossible.
Miguel had $500 in his checking account at the beginning of the month. He made a deposit of $134.50 and $55.50. He wrote a check for $64.50 and $55.50. What is his current balance?
Answers
Answer:$570
Step-by-step explanation:
At beginning he had 500
He deposited =134.50+55.50=190.00
Total in account is 190+500=690
He withdrew =64.50+55.50=120.0
Total in account =690-120=$570
You have 4 framed portraits. How many ways can you arrange all 4 of them on the top of your bookshelf?.
Answers
There are 24 ways can you arrange all 4 of them on the top of your bookshelf.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
You have 4 framed portraits.
Hence, Number of ways for arrange all 4 of them on the top of your bookshelf is,.
⇒ 4!
⇒ 4 × 3 × 2 × 1
⇒ 24
Thus, There are 24 ways can you arrange all 4 of them on the top of your bookshelf.
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(-3.2)(-41) = ? Please help
Answers
Answer:
131.2
Step-by-step explanation:
If They are side by side like that, with parentheses, They are Multiplying. Negative Times Negative Would Equal Positive. So then Just multiply 3.2 x 41