Answer:
7, 23
Step-by-step explanation:
R could lie either to the left of S or to the right of S on the number line
Therefore possible values for R are 15-8 = 7
and 15 + 8 = 23
Given the graph of a function f. Identify the function by name. Then Graph, state the domain and range, use set notation forA) 1/2f(x)B) 2f(x)
From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:
[tex]f(x)\text{ = }x^2[/tex]The graph of (a) 1/2 f(x):
This implies that f(x) is compressed vertically by a factor of 1/2.
Using the points:
(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)
The graph of the function using a graphing calculator is shown below:
The graph of (b) 2 f(x)
This implies that the original function was stretched vertically by a factor of 2
Using the points:
(-4, 32), (-2, 8), (0,0), (2,8), (4,32)
The graph using a graphing calculator is shown below:
The domain:
This is a set of allowable x-values
Using interval notation:
[tex](-\infty,\text{ }\infty)\text{ or All real numbers}[/tex]The range:
This is a set of allowable y-values:
Using interval notation:
[tex]\lbrack0,\text{ }\infty)\text{ }[/tex]Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate?
If Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
Total estimateGiven data or information :
Product = ( – 25. 31 ) (9. 61)
Now let estimate the product by first approximating the product to the nearest tenth.
Approximation :
So,
-25.31 = - 25 ( Approximately )
9.61 =10 ( Approximately )
Hence , her estimate can be calculated as :
Estimate :
Estimate = (-25) (10)
Estimate =-250
Therefore based on the information or data given if Seema tend to make used of compatible numbers to estimate the product of (–25.31)(9.61). her estimate is -$250.
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For
f(x) = (x − 1)3
and
g(x) = 1 − 6x,
find the following.
(a)
(f ∘ g)(x)
(b)
(g ∘ f)(x)
(c)
f(f(x))
(d)
f 2(x) = (f · f)(x)
For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
As given,
Given function :
f(x)=(x − 1)³
g(x)=1-6x
The value of following functions are:
a.(f ∘ g)(x)
=f(g(x))
=f(1-6x)
=(1-6x -1)³
=(-6x)³
=-216x³
b. (g ∘ f)(x)
= g(f(x))
=g(x − 1)³
=1 -6(x − 1)³
=1 -6(x³ -3x² +3x -1)
=-6x³+18x² -18x+7
c. f(f(x))
=f(x-1)³
=((x-1)³ -1)³
=(x³ -3x² +3x -1-1)³
=(x³ -3x² +3x -2)³
d. f²(x)= (f · f)(x)
=f(x) × f(x)
=(x-1)³ × (x -1)³
=(x -1)⁶
Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
The complete question is:
For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.
a. (f ∘ g)(x)
b. (g ∘ f)(x)
c. f(f(x))
d. f²(x)= (f · f)(x)
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$6500 earning 25% compounded
weekly for 1 year. What number goes in
the circle?
$8,125 is the compound interest.
What is compound interest?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year. Compound interest allowed you to earn 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.P = $6500
R = 25%
T = 1
compound Interest A = P( 1 + r/100)ⁿ
= 6500( 1 + 25/100)¹
= 6500( 5/4)
= 6500 * 5/4
= $8,125
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Can I please get help on this math problem always been bad at math.If X=-5 and y=-3 what is the value of x (y-10) i can't provide pictures
Given
[tex]x(y-10)[/tex][tex]\begin{gathered} x(y-10) \\ x=5,y=3 \\ 5(3-10) \\ 5(-7) \\ -35 \end{gathered}[/tex]I need help please with number 5 initially. I have attached a scanned document of my book problems.
Considering the z-test formula, it is found that:
a) Increasing the difference between the sample mean and the original population mean increases the test statistic.
b) Increasing the population standard deviation decreases the test statistic.
c) Increasing the sample size increases the test statistic.
What is the z-test formula?Considering a z-test, the formula for the test statistic is given by the following rule:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In item a, increasing the difference between the sample mean and the original population mean is increasing the numerator [tex]\overline{x} - \mu[/tex], meaning that the test statistic z will be increased.
In item b, increasing the population standard deviation [tex]\sigma[/tex] means that the denominator of the formula will be increasing, hence the test statistic will be decreased.
In item c, increasing the sample size n means that the denominator will be decreased, as the denominator is a fraction which is inverse proportional to the sample size, hence the test statistic z will be increased.
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Given the equation of a line
y = mx + 1, for what values of m will the line be increasing? Enter (<,>,=).
greater than 1. If its less than, it will be decreasing.
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called _______.
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called turning point.
What is a turning point?A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.
A turning point is a location on a graph where the trend shifts from rising to dropping or from decreasing to increasing (falling to rising). To determine the point, identify the leading term of the polynomial function if the function were enlarged. A polynomial of degree n will have at most n1 turning points. Next, determine the polynomial function's degree.
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Given that f(x) = x² - 3 and g(x) = 3x + 5, find (g- f)(9), if it exists.
(3x+5)-([tex]x^{2} - 3[/tex])=9
[tex]x^{2}[/tex]-3x-8=-9
[tex]x^{2}[/tex]-3x=-1
[tex]x^{2}[/tex]-3x+1=0
The graph of an absolute value function has a vertexat(-2.3) and passes through the point (-1,0).Using transformations of the parent function, has thegraph been dilated by a scale factor other than 1?Explain.
Step 1 of the solution:
Let the parent function of the absolute value function is f(x) = |x|
Step 2 of the solution:
This function passes through (0, 0) and slope = 1 or -1.
Step 3 of the solution:
After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)
Step 4, let's find the slope of the absolute value funtion, this way:
[tex]S\text{lope = (3 - 0)/(-2 + 1) = 3/}-1\text{ = -3}[/tex]Step 5: Interpretation
Since slope of the absolute value function is less than the parent function: -3 < -1
Therefore, the parent function will be dilated by a scale factor other than 1.
Find the distance between the two points in simplest radical form (-6,8) and (-1,-4)
Answer:
13
Step-by-step explanation:
d) = √(-1 - -6)2 + (-4 - 8)2
= √(5)2 + (-12)2
= √169
= 13
Answer:
13
Step-by-step explanation:
We use the distance formula to find the distance between two points
d = sqrt ( (x2-x1)^2 + y2-y1) ^2)
Where ( x1,y1) and ( x2,y2) are the two points
d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)
= sqrt ( ( -1+6) ^2 + ( -12) ^2)
= sqrt( 5^2 + 144)
= sqrt ( 25+ 144)
= sqrt ( 169)
= 13
a line intercepts the points (13,-4) and (1, 12) whats the slope
Answer:
m=-4/3
Explanation:
Given the points: (13,-4) and (1, 12)
To determine the slope of the line that joins the point, use the formula below;
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substitute the given points:
[tex]\begin{gathered} m=\frac{12-(-4)}{1-13} \\ =\frac{12+4}{-12} \\ =-\frac{16}{12} \\ =-\frac{4}{3} \end{gathered}[/tex]The slope is -4/3.
If 4 bags of chips cost $3.00, how
much would 5 bags cost?
Answer: 6.67
Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5
Write an equation of the line with a
slope of 0 and y -intercept of 5
y=
Answer:
Step-by-step explanation:
it is y
Answer: Y=0x +5
Step-by-step explanation
its going up by 0 so 0x and you start at 5 so plus 5
An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 10 in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
The length of each side of the octagon would be 8.23 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.
Since a side of the square is 20 inches
Here, y is the two equal sides of the right-angle triangle
So y + x + y = 20
Using Pythagoras's theorem for the right angle triangle
y² + y² = x²
2y² = x²
y² = (x²)/2
y = x /√2
So substitute the value of y = x /√2 in the equation
x /√2 + x + x /√2 = 20
2x /√2 + x = 20
2x /√2 + x√2 /√2 = 20
x[2/√2 + √2 /√2] = 20
x[(2 + √2) /√2] = 20
x(2 + √2) = 20√2
x = 20√2/(2 + √2)
x = 28.2843/3.4142 = 8.2343
Round to the nearest hundredth of an inch
x = 8.23
Therefore, the length of each side of the octagon would be 8.23 inches.
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Send answers for the question please and thanks.
Answer:
7⁻²=[tex]\frac{1}{49}[/tex]
3⁻⁴ [tex]=\frac{1}{81}[/tex]
9⁰=1
11⁻¹=[tex]\frac{1}{11}[/tex]
Evaluate ∫(15x2+x2‾‾√34) dx. Here C is the constant of integration.
We use the following formula for integration:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]We have the following integral:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx[/tex]Separate into two integrals:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=\int15x^2dx+\int\frac{\sqrt[3]{x^2}}{4}dx[/tex]Calculate the first integral. Take the coefficient out of the integral:
[tex]\int15x^2dx=15\int x^2dx[/tex]Apply the integration formula:
[tex]\int15x^2dx=15\frac{x^3}{3}+C=5x^3+C[/tex]Calculate the second integral. Take the coefficient out of the integral:
[tex]\int\frac{\sqrt[3]{x^2}}{4}dx=\frac{1}{4}\int\sqrt[3]{x^2}dx[/tex]Express the radical as a fractional exponent:
[tex]\frac{1}{4}\int\sqrt[3]{x^2}dx=\frac{1}{4}\int x^{2/3}dx[/tex]Apply the integration formula:
[tex]\frac{1}{4}\cdot\frac{x^{5/3}}{5/3}+C=\frac{3}{20}\sqrt[3]{x^5}+C[/tex]The total integral is:
[tex]\int(15x^2+\frac{\sqrt[3]{x^2}}{4})dx=5x^3+\frac{3}{20}\sqrt[3]{x^5}+C[/tex]Decide whether there is enough information to prove mn.
m
O Yes
O No
You
An
If so, state the theorem you can use. If not, answer "cannot" for the blank below.
✓prove mn
Yes, there is enough information to prove m||n.
By using the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem we can prove that line m is parallel to line n.
In the given figure,
Let the given angles formed by transversal r, adjacent to line m be angle 1, and to line n be angle 2.
Now, the vertically opposite angle to angle 1 will be equal to it as they both are congruent.
The vertically opposite angle equal to angle 1 would be corresponding to angle 2 and corresponding angles formed by a transversal are equal and congruent.
Moreover, angle 1 and angle 2 are alternate exterior angles and by Alternate Exterior Angles Theorem, they are congruent.
Hence, it is proved by the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem that line m is parallel to line n (m||n).
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Fill in the table using this function rule.
y = 5x-4
What are the minimum and maximum possible measures of 31 centimeters
The the minimum and maximum possible measures of 31 centimeters is {30.5. 31.5}
How do you find the minimum and maximum measurements?To find it, one need to add the biggest possible inaccuracy to each measurement, then multiply to get the biggest volume you can. Also Subtract the largest potential mistake from each measurement, then multiply, to to know the smallest volume that can be produced.
Note that the smallest value in the data set is the minimum. The highest value in the data collection is called the maximum.
Since only one data set is given, the possible measures can only be around it hence the largest and the smallest value close to it.
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$(x) = x2 – 25 and g(x) = x + 5Step 2 of 4 : Find (J - 8)(x), Simplify your answer,Answer( -8)(x) =
Solve for (f - g)(x)
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=(x^2-25)-(x+5) \\ (f-g)(x)=x^2-25-x-5 \\ \; \\ \text{Therefore,} \\ (f-g)(x)=x^2-x-30 \end{gathered}[/tex]when x is decreasd by 2 and then that number is divided by 2, the result is 2. what is the number
Answer:
lets denote x as 6
so,
(x-2)÷2
(6-2)÷2
4÷2
2(proved)
1 If you are paid $232.95 for 22 hours of work, what amount should you be paid for 33 hours of work at this same rate of pay? 2 You should be paid $ (Round to the nearest cent as needed.) Question 3 of 12 for 33 hours of work.
Answer:
349.42499999998
Step-by-step explanation:
$232.95 divided by 22 hours of work = amount per hour = 10.588636363636
If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents
In a jail cell, there are 5 Democrats and 6 Republicans. Four of these people will be randomly chosen for
early release. What is the probability that a group consisting of 2 Democrats and 2 Republicans will be chosen
for early release?
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be 5/11.
What is probability?It should be noted that probability simply means the likelihood that a particular event will happen.
In this case, there are there are 5 Democrats and 6 Republicans and rour of these people will be randomly chosen for early release.
The probability that a group consisting of 2 Democrats and 2 Republicans will be chosen for early release will be:
Number of Democrats = 5
Number of Republicans = 6
Total number = 5 + 6 = 11
This will be illustrated through the combination formula:
= (5C2 × 6C2) / 11C4
= (10 × 15) / 330
= 150/330
= 5/11
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If N = 15 and P = .50, what is the probability of getting exactly 12 P events? Please go to 4 decimal places.
The probability of getting 12 p events is 0.0139
The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.
The binomial distribution formula is calculated as:
[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]
where:
n is the number of trials (occurrences)
X is the number of successful trials
p is probability of success in a single trial
is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.
So, we have given that N = 15, P = 0.50 , and x = 12
So,
[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]
=0.0139
Therefore, the probability of getting exactly 12 P events is 0.0139
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Some cars depreciate at rates as high as 75% per year for the first two years; this means that after one year the car is only worth 25% of the original cost. Suppose that you purchase a car for $16,500 that has a depreciation rate of 75%, then what will be the value of your car in 2 years? Hint: use f(x) = 16500(0.25)*, where x is the time in years. Round your answer to the nearest = dollar. $1.568 7765 then
Given:
Depreciation rate = 75% per year.
[tex]\begin{gathered} f(x)=a(1-0.75)^x \\ \\ f(x)=a(0.25)^x \end{gathered}[/tex]Let's find the value of the car in 2 years.
Given:
Cost = $16,500
Depreciation rate = 75%
From the equation we have:
Present value, a = 16500
x is the number of years = 2
Thus, we have:
[tex]\begin{gathered} f(2)=16500(0.25)^2 \\ \\ f(x)=16500(0.0625) \\ \\ f(x)=1031.25\approx1031 \end{gathered}[/tex]Therefore, the value of the car in 2 years is $1,031
ANSWER:
$1,031
8x^2+9=313 match to correct answer round to nearest 10th if Necessary
Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to evaluate the quadratic equation?The quadratic equation is given as
8x^2 + 9 = 313
Subtract 9 from both sides of the quadratic equation
So, we have
8x^2 + 9 - 9 = 313 - 9
Evaluate the difference in the above equation
So, we have
8x^2 = 304
Divide both sides of the quadratic equation by 8
So, we have
8x^2/8 = 304/8
Evaluate the quotient in the above equation
So, we have
x^2 = 38
Take the square root of both sides
x = 6.2
Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2
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The polynomial -17x^2 + 165x + 14,481 represents the electricity generated (in gigawatts) by geothermal sources during 2002-2007. The polynomial 879x^2 - 72x + 10,140 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002-2007.
The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is given by adding the two other ones, we will get:
862x^2 + 93x + 24,621
How to find the polynomial for the total electricity?Here we have two polynomials:
Polynomial -17x^2 + 165x + 14,481 represents the electricity generatedby geothermal sources during 2002-2007. Polynomial 879x^2 - 72x + 10,140 represents the electricity generated by wind power during 2002-2007Both of these are in gigawatts, so are in the same units, which means that we can directly add the two polynomials to get a polynomial for the total electricity.
-17x^2 + 165x + 14,481 + 879x^2 - 72x + 10,140
Now we group like terms:
(-17x^2 + 879x^2) + (165x - 72x) + (14,481 + 10,140)
862x^2 + 93x + 24,621
This polynomial represents the total electricity generated during 2002-2007
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Hi can you help me find the correct answer to this problem?
we have the equation
[tex]\begin{gathered} \sqrt{10x-1}=7 \\ \end{gathered}[/tex]Solve for x
Step 1
squared both sides
[tex]\begin{gathered} 10x-1=7^2 \\ 10x-1=49 \\ 10x=49+1 \\ 10x=50 \\ x=\frac{50}{10} \\ \\ x=5 \end{gathered}[/tex]The answer is x=5
If I eat pizza after midnight, then I'll
have a stomach ache.
Choose the equivalent statement.
A. If I don't have a stomach ache, then I didn't eat pizza after
midnight.
B. If I don't eat pizza after midnight, then I won't have a stomach
ache.
C. If I have a stomach ache, then I ate pizza after midnight.
Answer:
B. If I don't eat pizza after midnight, then I won't have a stomach ache.