Answers
Firslty, we need to find the function, whcih we can do by substituting one into the other:
[tex]f(g(x))=2(g(x))^2-1=2(\sqrt[]{x-2})^2-1=2(x-2)-1=2x-4-1=2x-5[/tex]Now, for the domain we have more complicated approach.
We first have to find the domain for both f(x) and g(x).
The domain of f(x) is all real number, because it is a quadratic polynomial.
The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:
[tex]\begin{gathered} x-2\ge0 \\ x\ge2 \end{gathered}[/tex]Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).
Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).
The domain of g(x), as we saw, is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]So, the correct alternative is:
[tex]\begin{gathered} f(g(x))=2x-5 \\ D\colon\mleft\lbrace x\mright|x\ge2\} \end{gathered}[/tex]Related Questions
Subtract -6x+3om -6x+8.
Answers
The difference of the given expressions is 5.
The given expressions are -6x+3 and -6x+8.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Now, subtract -6x+3 from -6x+8
-6x+8 - (-6x+3)
= -6x+8+6x-3
= 5
Therefore, the difference of the given expressions is 5.
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HELP PLEASE ILL MARK U BRAINLIEAST!!
this is for geometry can someone please help me find the missing angles?
Answers
y=40
Explaination: the 90 degree angles are labeled with the little square and 50 + 40 = 90
Answer:
x = 50° , y = 40°
Step-by-step explanation:
x and 40° form a right angle and sum to 90° , that is
x + 40° = 90° ( subtract 40° from both sides )
x = 50°
x and y form a right angle and sum to 90° , then
x + y = 90°
50° + y = 90° ( subtract 50° from both sides )
y = 40°
a manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of 1.3 inches. if one item is chosen at random, what is the probability that it is less than 16.4 inches long?
Answers
The probability of the random item chosen that it is less than 16.4 inches long is 2.7%
Probability means ?
The likelihood of an event happening is calculated using the probability formula. To review, probability is the probability that an event will occur. What is the likelihood that a specific event will occur when a random experiment is considered? is one of the first queries that pops into our heads. A prediction's chance is expressed as a probability. If we suppose that, for example, x represents the probability that an event will occur, then (1-x) is the probability that the event will not occur.
Variance of sample mean =1.3^2/1= 1.69
S D of sample mean =1.69^(1/2)= 1.3
Z score for length of 16.4 is( 16.4-15.4)/1.3= 0.7692307
The p value for -1.67 in standard normal table is 0.04746
The required probability =0.02764
Only 2.7% of the time will the sample mean be shorter than 16.4 inches.
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algebra 1. g(x)=x^{2}-x, g(3b)
Answers
The output value of g( 3b ) in the function g( x ) = x² - x is 9b² - 3b.
What is the value of g( 3b ) in the function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
g( x ) = x² - xg( 3b ) = ?To determine the output value of g( 3b ), replace all the occurrence of x with 3b in the function and simplify.
g( x ) = x² - x
g( 3b ) = (3b)² - 3b
Apply product rule
g( 3b ) = 3²b² - 3b
Raise 3 to the power of 2
g( 3b ) = 9b² - 3b
Therefore, the output value of g( 3b ) is 9b² - 3b.
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A rectangular park is 40 yards wide. Then a city planner designs a path that is 1 yard wide to run all the way around the park. Now the area of the park plus the path is 4200 yd.² how long is the park not counting the path?
Answers
The park is 98 yards long, not counting the path.
We are having a park that is rectangular in shape.The width of the rectangular park is 40 yards.The city planner designs a path that is 1 yard wide to run all the way around the rectangular park.The area of the rectangular park plus the path is 4200 square yards.Let the length of the rectangular park be "x".The width of the rectangular park, including the path, is 42 yards.The length of the rectangular park, including the path, is "x+2" yards.The area of the rectangular park, including the path, is the product of the length and its breadth.42*(x+2) = 4200x+2 = 100x = 98Thus, the length of the rectangular park is 98 yards.To learn more about area, visit :
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A recipe of chicken marinade says mix 3 parts with oil with 2 parts soy sauce and 1 part orange juice if you need 42 cups of marinade in all how much of each ingredient should you use
Answers
Answer:
21 cups oil
14 cups soy sauce
7 cups orange juice
Step-by-step explanation:
Use 1 cup for 1 part. The original recipe as given with its small amounts would make a total of 3 + 2 + 1 = 6 parts, or 6 cups of sauce.
You want to make 42 cups.
42/6 = 7
The amount you want to make is 7 times the amounts in the ratio.
3 parts oil: 3 × 7 = 21: 21 cups oil
2 parts soy sauce: 2 × 7 = 14: 14 cups soy sauce
1 part orange juice: 1 × 7 = 7: 7 cups orange juice
Check: 21 + 14 + 7 = 42
The amounts above do make 42 cups in total.
Answer:
21 cups oil
14 cups soy sauce
7 cups orange juice
PLS HELP ASAP (100 POINTS) The equation for the line of best fit for change in temperature, y, to amount of snow, s, is given by ŷ = − 2.6s + 1.1. On Friday, the observed amount of snow was 1.3 inches and the temperature change was 1.2 degrees. Find and interpret the residual.
1.08; The line of best fit underpredicts the temperature change.
−1.08; The line of best fit overpredicts the temperature change.
−3.48; The line of best fit overpredicts the temperature change.
3.48; The line of best fit underpredicts the temperature change.
Answers
residual = 3.48
The line of best fit underpredicts the temperature change.
============================================================
Explanation:
If s = 1.3, then ŷ is...
ŷ = -2.6s + 1.1
ŷ = -2.6*1.3 + 1.1
ŷ = -2.28
This is the estimated or predicted y value based on the input s = 1.3
Let's now compute the residual
e = residual error
e = (observed y value) - (predicted y value)
e = y - ŷ
e = 1.2 - (-2.28)
e = 1.2 + 2.28
e = 3.48 is the residual
A positive residual means that the predicted y value, aka ŷ, is an underestimate compared to the true observed value. In other words, the observed y value is higher than the ŷ value. Therefore, the line of best fit under-predicts the temperature change.
a pet store owner believes that dog owners spend more on average than cat owners on their pets. the owner randomly records the sales of 40 customers that said they only owned dogs and 40 customers that said they only owned cats. what is the correct decision and summary based on the excel output below? assume the populations are approximately normally distributed with unequal variances.
Answers
The correct decision and summary based on the excel output below is Standard Error =5.389361. and P-value=0.5364.
Two sample T summary hypothesis test:
[tex]u_{1[/tex] : Mean of Population 1
[tex]u_{2}[/tex] : Mean of Population 2
[tex]u_{1} -u_{2}[/tex] : Difference between two means
[tex]H_{0}[/tex] : [tex]u_{1} -u_{2}[/tex] = 0
[tex]H_{a}[/tex] : [tex]u_{1} -u_{2}[/tex]
0
(without pooled variances)
Hypothesis test results:
Difference = u1-u2
Sample Diff=3.34725
Standard Error =5.389361.
DF=77.988073
T-Stat=0.62108476
P-value=0.5364
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can someone please help solve this math problem with solution? thank u!
Answers
Answer:
the answer is 196
63^2-49^2
(7×9)^2 -(7×7)^2
7^2 (9-7)
7^2 ×2^2
49 × 4
196
Answer:
1568
Step-by-step explanation:
i simplified the expression
if you placed $5 into an account that paid interest at a rate of 5%, and compounded interest yearly, how much would that account be worth in 100 years
Answers
After adding interest the sum would be worth $657.51 .
Interest is the amount paid over and above the original amount to a lender or depositor by a borrower or deposit-taking financial institution at a predetermined rate in the domains of finance and economics (the amount borrowed).
Interest differs from any fees the borrower may be required to pay to the lender or another party.interest also contrasts from a dividend, which is cash distributed to shareholders (owners) by a corporation from its profit or reserve, but not at a predefined rate or proportionally; rather, it is a portion of the reward or interest gained by risk-taking businessmen when revenue is made that surpasses all expenditures.Interest when the principal is $5 , time is 100 years and rate is 5%.
We know that from compound interest:
Amount = principal (1 + rate)ⁿ
Therefore
Amount = 5 (1 +0.05)¹⁰⁰
Amount = $657.5062...
Amount ≈ $657.51
Therefore adding interest the sum would be worth $657.51
Which of the following transformations would make corresponding line segments between a pre-image and image not be parallel?
Answers
The transformation of rotating 90° around a point not on the line segment would make corresponding line segments between a pre-image and image not be parallel.
We have a line segment.(a) Suppose we have another line parallel to the given line segment. If we take the reflection of the line segment over the line, it will result in a parallel line segment only.(b) Suppose we have an arbitrary point which is not on the line segment. We rotate the line segment by an angle of 90° about the point. This will change the direction of the line segment.(c) If we translate the line segment in a direction perpendicular to the line segment, it will just change its position, but it will still remain parallel.(d) Suppose we have an arbitrary point which is not on the line segment. We rotate the line segment by an angle of 180° about the point. This will make the line segment again parallel to what it was before.To learn more about lines, visit :
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What’s 8(2y-6x)=4+2x as a sentence?
Answers
Answer:
8 times 2y minus 6x is equal to 4 plus 2x
If x=3yz^2, what is y in terms of x and z?
Answers
Two or more expressions with an Equal sign is called as Equation. y=x/3z^2 for equation x=3yz^2 in terms of x and z
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x equal to three y z square.
x=3yz²
We need to solve for y.
We need to separate y from other variables.
Divide both sides by 3z²
x/3z²=y
Hence y=x/3z² for equation x=3yz² in terms of x and z
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can someone pls explain to me how to find y intercept
Answers
Answer:
(0, -5)
Explanation:
The function is represented by f(x), and the line graphed would be y= f(x). In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
Since we know that the line is linear, any two points along the line would give us the same slope value. Since y-intercepts occur at x= 0, let the y-intercept be (0, y).
[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope between (-3, 1) and (1, -7)= slope between (-3, 1) and (0, y)
[tex] \frac{1 - ( -7 )}{ - 3 - 1} = \frac{y - 1}{0 - ( - 3)} [/tex]
[tex] \frac{1 + 7}{ - 4} = \frac{y - 1}{0 + 3} [/tex]
[tex] \frac{8}{ - 4} = \frac{y - 1}{3} [/tex]
[tex] - 2 = \frac{y - 1}{3} [/tex]
Multiply both sides by 3:
-2(3)= y- 1
-6= y -1
Add 1 to both sides:
y= -6 +1
y= -5
Thus, the y-intercept is (0, -5).
__________
Based on the image, however, we are to find the equation of the linear function in slope-intercept form.
The first step would be to find the slope between any two points, which would be -2. This is found using the slope formula, and we have calculated it above.
Substitute the value of the slope into y= mx +c:
y= -2x +c
The y-intercept can be found by substituting a pair of coordinates the line passes through.
When x= -3, y= 1,
1= -2(-3) +c
1= 6 +c
c= 1 -6
c= 5
Thus, the equation of the line is y= -2x +5.
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Answer:
y = - 2x - 5
The intercept is 5 because that is where the graph cuts the y axis.
PLEASE MARK AS BRAINLIEST IF YOU FOUND IT HELPFUL BECAUSE IT MAKES ME FEEL GOOD!
Step-by-step explanation:
Linear Standard Formy = mx + c;
The m equals the change in y divided by the change in x. If you choose left to right for y then you must do the same for x as well.
Δy = ( - 7 ) - ( - 15 ); Δx = 1 - 5;
Δy = - 7 + 15;
Δy = 8;
Δx = - 4;
m = 8 / - 4;
m = - 2;
y = - 2x + c;
Point SubstitutionPick a point (x, y) and sub it into the equation. Make sure to use brackets when subbing.
- 7 = - 2( 1 ) + c;
- 7 = - 2 + c;
Add 2 to both sides.
- 7 + 2 = - 2 + 2 + c;
- 5 = c;
c = - 5;
The c is the intercept.
y = - 2x - 5
In 5.2, which digit is in the tenths place?
Answers
Answer:
2
Step-by-step explanation:
The number right after the decimal is the tenths place.
More in-depth example:
1.234
1 is your integer(regular number)
2 is your tenths
3 is hundreths
4 is thousandths
* 100 POINTS *
At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost
$2.35. One day, the receipts for a total of 172 cones and sundaes were
$294.20. How many cones were sold?
You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you
purchase 6 gal of paint and 2 brushes for $113.00. How much does each
gallon of paint and each brush cost?
Two separate questions. 100 points for both answered. Brainliest if both answered.
Answers
Answer:
1.) 88 cones were sold
2.) $17.00 per gal of paint; $5.50 per brush
Step-by-step explanation:
1.) ($1.10(88)= $96.80) + ($2.35(84)= $197.40)= $294.20
2.) I have a really complicated process, and it's really late at night where I am
Answer:
For the first question, 88 cones were sold
For the second question, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (that is, 5 dollars and 50 cents).
Step-by-step explanation:
For the first question,
Let the number of ice cream cones be represented by the letter 'x'
And the number of sundaes be represented by the letter 'y'
[tex](1.10x + 2.35y) = 294.20 \: \: \: equ.2 \\ (x + y) = 172 \: \: \: equ.1[/tex]
Solving it simultaneously, subtract equ. 2 from equ. 1
[tex]0.10x - 1.35y = 122.20[/tex]
Making x the subject,
[tex]x = \frac{122.20 + 1.35y}{0.10} [/tex]
Substitute the value of x above in equ. 1
[tex] \frac{122.20 + 1.35y}{0.10} + y = 172[/tex]
L. C. M = 0.10
Multiply through by the L. C. M
[tex]122.20 + 1.35y + 0.10y = 17.2[/tex]
Collect like terms
122.20 - 17.2 = - 1.35y - 0.10y
105 = - 1.25y
[tex]y = \frac{105}{1.25} = 84[/tex]
Substituting the value of y in equ. 1
[tex]x + 84 = 172 \\ x = 172 - 84 \\ x = 88[/tex]
Therefore, 84 sundaes were sold and 88 ice-cream cones were sold.
For the second question, let paint represent 'p' and brush represent 'b'
[tex]8p + 3b = 152.5 \: \: \: equ2 \\ 6p + 2b = 113 \: \: \: equ1[/tex]
Solving simultaneously,
Subtract equ2 from equ 1
[tex]2p + b = 39.5 \\ b = 39.5 - 2p[/tex]
Substituting the value of b in equ1
[tex]6p + 2(39.5 - 2p) = 113 \\ 6p + 79 - 4p = 113[/tex]
Collect like terms
[tex]2p = 113 - 79 \\ 2p = 34 \\ p = 17[/tex]
Substituting the value of p in equ1
[tex]6(17) + 2b = 113 \\ 102 + 2b = 113[/tex]
Collect like terms
[tex]2b = 113 - 102 \\ 2b = 11 \\ b = 11 \div 2 \\ b = 5.5[/tex]
Therefore, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (i.e 5 dollars, 50 cents)
what is the y- intercept of y=4+x
Answers
Answer: the y-intercept of this equation is (0,4)
Step-by-step explanation:
Allison heads out on a three day sailing trip. On the first day, she sails 45 miles east and 15 miles north. On the second day,
she leaves from the exact location she ended the day before and makes it 35 miles east and 30 miles south. On the third
day, she gains another 15 miles east and 55 miles south. At the end of her final day, how far is she from her initial starting
point? Round your answer to the nearest whole number.
Answers
Answer:
118 miles
Step-by-step explanation:
Explanation in photo attached
Rule 1: Add 3 starting from 0. Rule 2: Add 9 starting from 0. Complete the first 5 terms using the rules. How are the corresponding terms related?
Answers
Given the following question:
Rule one: + 3
Rude two: + 9
3, 6, 9, 12, 15
3 + 3 = 6 + 3 = 9
9 + 3 = 12 + 3 = 15
= 15
9, 18, 27, 36, 45
9 + 9 = 18 + 9 = 27
27 + 9 = 36 + 9 = 45
= 45
We are now given..
3, 6, 9, 12, 15
9, 18, 27, 36, 45
They are related because these terms also have a rule, if you mutlply 3, by 3 we get 9, if we multiply 6 by 3 we get 18. The second sequence is three times the corresponding term in the first sequence or the first option.
Your answer is the first option.
4 times 10 by the power8 subtract 9times 10 by the 7
Answers
Answer:
310000000
That’s the answer
0:3:4=9:y
Find y please
Answers
Based on the ratios given of 0.3 : 4 = 9 : y, the value of y can be found to be 120
How to find the value of y?From the given ratios of 0.3 : 4 = 9 : y, we can infer that these are equivalent ratios.
This means that y is to 9, what 4 is to 0.3.
The value of y can therefore be found by direct proportion:
0.3 : 4
9 : y
Cross multiplying gives:
0.3 y = 36
y = 36 / 0.3
y = 120
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round 64,926 cs im lazy
Answers
Answer:
65
Step-by-step explanation:
took the test and passed. I love helping others and so I hope this helps
trucks in a delivery fleet travel a mean of 110110 miles per day with a standard deviation of 2626 miles per day. the mileage per day is distributed normally. find the probability that a truck drives at least 125125 miles in a day. round your answer to four decimal places.
Answers
The probability that a truck drives at least 125125 miles in a day is 0.6839.
Given
trucks in a delivery fleet travel a mean of 110110 miles per day
standard deviation of 2626 miles per day
To find
find the probability that a truck drives at least 125125 miles in a day
Solution :
μ = 110
σ = 26
P ( 63 < x < 125 )
= P [ ( 63 - 110 ) / 26 < ( x - μ ) / σ < ( 125 - 110 ) / 26 ]
= P ( - 1.81 < z < 0.58 )
= P ( z < 0.58 ) - P ( z < -1.81)
using standard normal table
= 0.7190 - 0.0351
= 0.6839
Probability = 0.6839 .
Hence the probability that a truck drives at least 125125 miles in a day is 0.6839
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what is the constant porpotionality of y=7.29x
Answers
Answer:
7.29
Step-by-step explanation:
the equation of proportionality is
y = kx ← k is the constant of proportionality
y = 7.29x ← is in this form with k = 7.29
Mrs. Hull calculated the measure of central tendencies for the two plants in her science class. The measures are recorded below.Which measure of central tendency would be the best for Mrs. Hull to use if she wanted to argue that there is a difference between the plants?
Answers
The measure of central tendency that would be the best for Mrs. Hull to use if she wanted to argue that there is a difference between the plants is the median.
What is central tendency?The definition of central tendency is the statistical metric that identifies a single value as representative of a whole distribution. It strives to provide a complete explanation of the data. It is the single most representative number from the obtained data.
A measure of central tendency is a single value that seeks to represent a set of data by identifying the data's central position. The mode measurement is the one with the highest frequency.
When plants are placed in a circle, the median is the measurement of the middle plant provided in descending be order of sizes.
When there are a few extreme scores in the data distribution, the median is the recommended measure of the central tendency.
In conclusion, the correct option is the median.
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Part D
At one point on the trip, the miles are recorded as 15,121 when the gas tank is
75% full. Use a ratio equation to determine the miles per gallon the sedan
averages. Round your answer to the nearest whole number.
Answers
The sedan gets 1090 miles per gallon on average, according to the ratio equation.
What exactly is a ratio?A ratio is an ordered pair of numbers a and b, denoted by the a / b, where b is not equal to zero.
What is a ratio example?If there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six.
Given: When the gas tank is 75% full, the mileage is recorded as 15,121.
A sedan tank is typically 18.5 gallons in size. So it holds 13.875 gallons of gas if it is 75% full. If it traveled 15,121 miles, the mileage per gallon is 1090, rounded to the nearest whole number.
The calculation of miles per gallon using the ratio equation:
Let, x = miles per gallon
15121:13.875 is the ratio.
x/1= 15121/13.875
13.875x = 15121
x = 15121/13.875
x = 1089.80, which equates to 1090 miles per gallon
As a result, the ratio equation used to calculate the sedan's miles per gallon averages 1090 miles per gallon.
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0.4υ – (3ω + 9) Write an equivalent expression by distributing the “-“ sign outside the parentheses
Answers
The equivalent expression for the given expression is 0.4υ - 3ω - 9.
The given expression is 0.4υ - (3ω + 9).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The equivalent expression for the given expression can be written as follows:
0.4υ - (3ω + 9)=0.4υ - 3ω - 9
Therefore, the equivalent expression for the given expression is 0.4υ - 3ω - 9.
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g(x) = −5x + 2, find g(–4).
Answers
Answer:
g(x)=22
Step-by-step explanation:
Substitute -4 into the equation.
g(x)= -5x+2
g(-4)= -5(-4)+2
g(-4)= 20+2
g(-4)= 22
Find WI if IE = 3
EW and YG are medians of AXYW
Answers
Based on the median and the centroid theorem, the length of WI is 6 units.
What is the Median of a Triangle?The line that joins the vertex of a triangle to the midpoint of the side it is directly opposite is called the median of a triangle.
According to the centroid theorem, since J is the centroid of triangle XYW, then:
the length of IE is 1/3 of the length of segment EW.
Thus, the equation that relates the length of the segments is;
IE = 1/3(EW)
Given that:
IE = 3 units
Now Substitute the value of IE into the equation:
3 = 1/3(EW)
3(3) = EW
9 = EW
EW = 9 units
Therefore:
The Length of WI = the length of EW - the length of IE
Substitute;
Length of WI = 9 - 3
Length of WI = 6 units.
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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answers
Answer:
Step-by-step explanation:
To find the cost of the apples, simply multiply the cost by how much Derek buys. So: 3.8 * 1.35= 5.13.
So, For Part A the answer is A.
For Part B: We need to find the total cost of both apples and oranges. We already know the total cost of apples is 5.13. We need to find the cost of oranges.
We multiply:
5.2* 1.45= 7.54
Now, add the totals together: 7.54+5.13
The total is 12.67.
If Derek payed with a 20 dollar bill, we would subtract 20 with 12.67.
The answer is 7.33. So the answer is A.