The graph of f(x) = |x| is transformed to g(x) = [X + 11-7. On which interval is the function decreasing?
Answers
Answer:
The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Step-by-step explanation:
* Lets explain how to solve it
- Decreasing function means a function with a graph that moves
downward as it is followed from left to right.
- For example, any line with a negative slope is decreasing function
- Lets look to the attached graph to understand the meaning of the
decreasing function
∵ f(x) = IxI ⇒ green graph
∵ g(x) = Ix + 1I - 7 ⇒ purple graph
- From the graph f(x) translated 1 unit to the left and 7 units down to
form g(x)
- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}
- The range of f(x) is {y : y ≥ 0}
- The range of g(x) is {y : y ≥ -7}
# For f(x)
- The slope of the green line from (-∞ , 0) is negative
- The slope of the green line from (0 , ∞) is positive
# For g(x)
- The slope of the purple line from (-∞ , -1) is negative
- The slope of the purple line from (-1 , ∞) is positive
∵ The line with negative slope represent decreasing function
∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
The function g(x) = |x+11|-7 is a transformed absolute value function, which is decreasing on the interval (-infinity, -11) due to the horizontal shift to the left by 11 units.
The question is asking about the transformation of the absolute function f(x) = |x| into a new function g(x). The function provided, g(x) = |x+11|-7, is a transformed version of f(x) where the graph has been shifted horizontally and vertically. To determine on which interval g(x) is decreasing, we need to consider the properties of the absolute value function and its transformations.
The graph of the standard absolute value function, f(x) = |x|, is shaped like a 'V', increasing for x > 0 and decreasing for x < 0. When we introduce a horizontal shift to the function (such as adding 11 to x), this shifts the vertex of the 'V' horizontally. For g(x), the graph is shifted to the left by 11 units due to the '+11' inside the absolute value. Therefore, the function will be decreasing on the interval (-infinity, -11) since the function will decrease to the left of the vertex (which is now located at x = -11). The vertical shift (subtracting 7) simply moves the graph down but does not affect the intervals of increasing or decreasing behavior.
Related Questions
If the Zeros of a quadratic equation are seven and -4 what would be the x intercepts
Answers
Answer:
7, -4
Step-by-step explanation:
The zeros are just another name for the x intercepts
7, -4
4. A student is chosen at random from the student body at a given high school. The probability that the
student selects Math as the favorite subject is 1/4. The probability that the student chosen is a junior is
116/459. If the probability that the student selected is a junior or that the student chooses Math as the
favorite subject is 47/108, what is the exact probability that the student selected is a junior whose
favorite subject is Math?
Answers
Answer:
The exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
Step-by-step explanation:
Let the following events represents by the alphabets A and B.
A: Student selects Math as the favorite subject
B: Student chosen is a junior
The probability that the student selects Math as the favorite subject is 1/4.
[tex]P(A)=\frac{1}{4}[/tex]
The probability that the student chosen is a junior is
[tex]P(B)=\frac{116}{459}[/tex]
The probability that the student selected is a junior or that the student chooses Math as the favorite subject is 47/108.
[tex]P(A\cup B)=\frac{47}{108}[/tex]
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]
[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]
The exact probability that the student selected is a junior whose favorite subject is Math is
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]
Therefore the exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
The exact probability that the student selected is a junior whose favourite subject is maths is 124/459
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The probability that the student selects Maths the favourite subject:
P(A) = 1/4
The probability that the student chosen is a junior:
P(B) = 116/459
The probability that the student selected is a junior or that the student chooses maths the favourite subject:
P(A∪B) = 47/108
We know:
P(A∩B) = P(A) + P(B) _P(A∪B)
P(A∩B) = 1/4 + 116/459 - 47/108
P(A∩B) = 31/459
The exact probability that the student selected is a junior whose favourite subject is maths:
P(B|A) = P(A∩B) /P(A)
= (31/459)/(1/4)
= 124/459
Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459
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Find the measure of angle 1
Answers
Answer:
120 degrees
Step-by-step explanation:
You can just eyeball that it is greater than 90 degreees so it must be 120 degrees.
Patrick David's charge account statement shows an unpaid balance of $110. The monthly finance charge is
2% of the unpaid balance. What is the new account balance?
Answers
Answer:
Step-by-step explanation:
You take the upaid balance of $110 and multiply it by 2%
which will give you $2.20. Then you add the two together and you get your answer of $112.20.
$110.00 x 2% = $2.20
$110.00
+2.20
$112.20
The new balance on the charge account after applying a 2% finance charge to the unpaid balance of $110 is $112.20.
Explanation:The student is asking about calculating the new balance on a charge account after a monthly finance charge is applied. To find this, we use the original balance and calculate the finance charge based on the given percentage. Since the unpaid balance is $110 and the monthly finance charge is 2%, we compute the finance charge as $110 × 0.02 = $2.20. Adding this to the unpaid balance gives us the new balance: $110 + $2.20 = $112.20.
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Which of the following statements is true of -4 and 4? Select all that apply.
They are a zero pair
They are opposites
They are the same distance from zero
Answers
They are the same distance from zero
Answer:
2 and 3
Step-by-step explanation:
Find the tenth term of the
geometric sequence, given the
first term and common ratio.
a =4 and r=1/2
Answers
Answer:
[tex]\frac{1}{128}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio, hence
[tex]a_{10}[/tex] = 4 × [tex](\frac{1}{2}) ^{9}[/tex] = 4 × [tex]\frac{1}{512}[/tex] = [tex]\frac{1}{128}[/tex]
Final answer:
The tenth term of the geometric sequence with the first term 4 and the common ratio of 1/2 is calculated using the formula for the nth term. Substituting the given values into the formula and simplifying yields the tenth term as 1/128.
Explanation:
To find the tenth term of a geometric sequence, we use the formula for the nth term in a geometric sequence which is an = a1 x r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
In this case, the first term a1 is given as 4 and the common ratio r is 1/2. To find the tenth term, we substitute n with 10 in the formula:
a10 = 4 x (1/2)(10-1)
This simplifies to:
a10 = 4 x (1/2)9 = 4 x 1/512 = 4/512 = 1/128
Therefore, the tenth term of the geometric sequence is 1/128.
If a = m 2 + 2, what is the value of a when m = -3? -7 -4 8 11
Answers
Given
a = m(2) + 2value of a when m = -3Substitute m with -3
a = -3*2 + 2
a = -6 + 2
a = -4
Answer
The value of a when m = -3 is -4
Answer:
=11
Step-by-step explanation:
The equation given is a=m²+2
To find a when m= -3 , we substitute for m in the equation.
a=(-3)²+2
=9+2
=11
Therefore a=11 when m is -3
Answer these questions please: You don't need to plot the point just answer B & C. Also every single coordinate plane is like a normal coordinate plane except there are only 5 and 10 labeled.
1) Use the coordinate plane below to answer the questions.
a. Plot a point at the origin. Label the point O.
b. Plot another point that is three units to the right and four units down from the
origin.
c. What are the coordinates of this point?
2)Use the coordinate plane below to answer the questions.
a. Plot a point at (5, 2). Label the point P.
b. Plot another point that is four units to the left and two units down from point P.
c. What are the coordinates of this point?
3)Use the coordinate plane below to answer the questions.
a. Plot a point at (-6, -1). Label the point Q.
b. Plot another point that is eight units to the right and five units up from point Q.
c. What are the coordinates of this point?
4)Use the coordinate plane below to answer the questions.
a. Plot a point in Quadrant II. Label the point R. What are the coordinates of point
R?
b. Plot another point that is two units to the right and six units down from point R.
c. What are the coordinates of this point?
5)Use the coordinate plane below to answer the questions.
a. Plot a point in the Quadrant IV. Label the point S. What are the coordinates of
point S?
b. Plot another point that is seven units to the left and four units up from point S.
c. What are the coordinates of this point?
Answers
Step-by-step explanation:
When moving left, subtract from the x-coordinate and when moving right, add in the x-coordinate. When moving down, subtract from the y-coordinate and when moving up, add in the y-coordinate.
1) Given point = (0, 0). 3 units right and 4 units down means (0+3, 0-4) = (3, -4).
2) Given point = (5, 2). 4 units left and 2 units down means (5-4, 2-2) = (1, 0).
3) Given point = (-6, -1). 8 units right and 5 units up means (-6+8, -1+5) = (2, 4).
4) In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. So taking R = (-6,6). 2 units right and 6 units down means (-6+2, 6-6) = (-4, 0).
5) In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. So taking R = (6,-6). 7 units left and 4 units up means (6-7, -6+4) = (-1, -2).
one positive integer is 7 less than another. The product of two integers is 44. what are the integers?
Answers
Answer:
4 and 11
Step-by-step explanation:
Lets call the smallest n
And the other one n+7
Then,
n.(n+7)=44
n²+7n=44
Subtract 44 from both sides.
n²+7n-44=44-44
n²+7n-44=0
Factorize the equation.
n²+11n-4n-44=0
n(n+11)-4(n+11)=0
(n+11)(n-4)=0
n+11=0 , n-4=0
n=-11 , n=4
n=4 is the only positive solution, so the numbers are:
4 and 11....
Answer:
The two integers are: 4 and 11.
Step-by-step explanation:
We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.
Assuming [tex]x[/tex] to be one positive integer and [tex]y[/tex] to be the other, we can write it as:
[tex]x=y-7[/tex] --- (1)
[tex]x.y=44[/tex] --- (2)
Substituting x from (1) in (2):
[tex](y-7).y=44[/tex]
[tex]y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)[/tex]
y = 11
Substituting y = 11 in (1) to find x:
[tex]x=11-7[/tex]
x = 4
when numbers are divided, you (add / subtract) exponents and (multiply / divide) the bases.
(Scientific Notation)
Answers
Answer:
you subtract the exponents and divide the bases
PLEASE HELLPPPPPPPP
Answers
Answer:
6
Step-by-step explanation:
f(0) means let x=0
In the table when x=0 f(0) =6
Solve equation -4a/5-8=2
Answers
-4a /5= 10
Multiply both sides by 5
-4a= 50
A= - 12.5
Answer:
a = 3/2
Step-by-step explanation:
Multiply both sides by -3
Simplify
Divide both sides by -4
Take a look at the photo:
Wuts the slope formula
Answers
Answer:
The Slope Formula ( x1, y1 ) And ( x2, y2 )
Find the distance between the points (-3, 2) and (4, -5)
Answers
Answer:
[tex]\large\boxed{7\sqrt2}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 2) and (4, -5). Substitute:
[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]
here is the histogram of a data distribution. which of the following numbers is closest to the mean of this distribution
Answers
Answer:
Option (D)
Step-by-step explanation:
Mean=[tex]\frac{Sum of observations}{Number of observations}[/tex]
here, observations are
1×1=1
2×2=2
3×3=9
4×1=4
5×1=5
6×2=12
7×3=21
8×1=8
9×1=9
10×0=0
hence, sum of observations =1+4+9+4+5+12+21+8+9+0=73
Number of observations are=1+2+3+1+1+2+3+1+1+0=15
Mean=[tex]\frac{73}{15}[/tex]
Mean=4.8..
nearest to 5 .
Hence, option (D) is correct.
The number that is closest to the mean of the distribution is 5.
What is the mean?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Sum of numbers = (1 x 1) + (2 x 2) + (3 x 3) + (4 x 1) + (5 x 1) + (6 x 2) + (7 x 3) + (8 x 1) + (9 x 1) = 73
Total numbers = 1+2+3+1+1+2+3+1+1+0=15
Mean = 73/15 = 4.8 = 5
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four less than the quotient of a number cubed and seven, increased by three
Answers
Answer:
(a^3/7) - 4 + 3
Step-by-step explanation:
We need to translate the words into equations:
The quotient of a number cubed and seven: (a^3/7)
four less than the quotient of a number cubed and seven: (a^3/7) - 4
four less than the quotient of a number cubed and seven, increased by three:
(a^3/7) - 4 + 3
Help me with this please
Answers
Answer:
see explanation
Step-by-step explanation:
Given
4(px + 1) = 64 ( divide both sides by 4 )
px + 1 = 16 ( subtract 1 from both sides )
px = 15 ( divide both sides by p )
x = [tex]\frac{15}{p}[/tex]
When p = - 5, then
x = [tex]\frac{15}{-5}[/tex] = - 3
Jake has just become the senior marketing rep for a new chain of upscale hotels. His first responsibility is to develop a
plan, commonly referred to as the
Answers
Answer:
placement plan
Step-by-step explanation:
<3
As the senior marketing rep, Jake needs to develop a marketing plan. This plan would outline the business's advertising and marketing efforts for the year, including goals, strategies, tactics, a market analysis, and a budget.
Explanation:Jake, as the senior marketing rep for a new chain of upscale hotels, is tasked with creating a marketing plan. A marketing plan is a comprehensive document or blueprint that outlines a company's advertising and marketing efforts for the coming year.
It would detail the business's marketing goals, the strategies and tactics to achieve those goals, an analysis of the current market situation, and a budget for the marketing activities. For an upscale hotel chain, it might include strategies such as premium pricing, high-quality service, and targeted advertising.
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The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 60 units when its width is 12 units and its length is 18 units?
A)No. If the rectangle has L = 18 and W = 12, P would not equal 60.
B) No. The rectangle cannot have P = 60 and L = 18 because L + W is less than 24.
C) Yes. The rectangle can have P = 60 and L = 18 because 60 = 24 + 18.
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60.
Answers
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]P=2L+2W[/tex].
If the width is [tex]W=12\:units[/tex] and the length is [tex]L=18\:units[/tex], then the perimeter becomes:
[tex]P=2\times 12+2\times 18[/tex].
[tex]\implies P=24+36[/tex].
[tex]\implies P=60[/tex].
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is .
If the width is and the length is , then the perimeter becomes:
.
.
.
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Help me on this math question please
Answers
Answer:
B. 24
Step-by-step explanation:
Subtract numbers from left to right.
[tex]\displaystyle 25.73-2.19=23.54[/tex]
Round to the nearest tenths.
[tex]\displaystyle 23.54=24[/tex]
24 is the correct answer.
Answer:
B. 24
Step-by-step explanation:
Estimation:
25.73 - 2.19 = 24
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions 1/7 and 1/3?
Answers
You have to first change the numbers so that they have common numbers then add
After that, you divide the numerator by the denominator.
Work is attached
P is a prime number and q is a positive integers such that p + q = 1696 IF P and Q are co primes and their Lcm is 21879 Then find p and q
Answers
Answer:
P = 1 3
Q = 1 6 8 3
Step-by-step explanation:
through factorization of 21879
The celsius and Fahrenheit scales are related by the equation C=5/9(f-32). What temperature fahrenheit would give a temperature of 5C?
Answers
Answer:
41F
Step-by-step explanation:
41-32=9
9*5/9=5
Answer:
41 degrees F.
Step-by-step explanation:
C = 5/9(f - 32)
5 = 5/9 (f - 32) Multiply both sides by 9/5:
5 * 9/5 = f - 32
9 = f - 32
f = 9 + 32
= 41.
The constraints of a problem are graphed below. What are
vertices of the feasible region?
Answers
Answer:
(0,0),(0,15),(20,25),(40,0)
Step-by-step explanation:
we know that
The feasible region is a quadrilateral
Let
A,B,C and D the vertices of the feasible region
see the attached figure
Observing the graph we have that
The coordinates of point A are (0,0)
The coordinates of point B are (0,15)
The coordinates of point C are (20,25)
The coordinates of point D are (40,0)
therefore
The answer is
(0,0),(0,15),(20,25),(40,0)
Answer:
A
Step-by-step explanation:
(0,0),(0,15),(20,25),(40,0)
The graph shows the solution to a system of inequalities:
Which of the following inequalities is modeled by the graph?
A.
[tex]4x + 3y \leqslant 12;x \geqslant 0[/tex]
B.
[tex]4x + 3y \geqslant 12;x \geqslant 0[/tex]
C.
[tex]4x - 3y \leqslant 12;x \geqslant 0[/tex]
D.
[tex] - 4x - 3y \leqslant 12;x \geqslant 0[/tex]
Answers
Answer:
Option A. [tex]4x+3y\leq 12[/tex] and [tex]x\geq 0[/tex]
Step-by-step explanation:
we know that
The solution of the first inequality is the shaded area below the solid line [tex]4x+3y=12[/tex]
The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)
therefore
The first inequality is
[tex]4x+3y\leq 12[/tex]
The solution of the second inequality is the shaded area to the right of the solid line x=0
therefore
The second inequality is
[tex]x\geq 0[/tex]
Is the following number rational or irrational? -3+π
Choose 1 answer:
A)Rational
B)Irrational
Answers
Answer:
B, irrational
Step-by-step explanation:
We know that π is irrational, since it can not be written as a division between natural numbers (a sub class of Real numbers called N), it's value is 3,1415(a whole bunch of decimals after this)
If you remove the decimal part of π by subtracting the integer part of it, that is the number 3. the result will still being and irrational number
Since π= 3(the rational part) +0,1415... (the irrational part)
The resut of π-=3= 0,1415...
Answer:
B). Irrational
If you are doing this on khan academy this should work
Step-by-step explanation:
You have$560 in an account which pays 4.8% compounded annually. If you invest your money for 8 years, then how many dollars of interest will you earn by the end of term
Answers
Answer:
$ 254.85
Step-by-step explanation:
Total amount invested = $ 560
Interest rate = r = 4.8% = 0.048
Time in years = t = 8 years
The formula for compound interest is:
[tex]A =P(1+\frac{r}{n})^{nt}[/tex]
Here,
A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:
[tex]A=560(1+\frac{0.048}{1})^{8} = \$ 814.85[/tex]
Thus, the total amount accumulated after 8 years will be $ 814.85
The amount of interest earned will be:
Interest = Amount Accumulated - Principal Amount
Interest = $ 814.85 - $ 560 = $ 254.85
By the end of 8 years, $ 254.85 would be earned in interest.
Simplify y^-3
a.3/y
b.1/y^3
c.-3y
d.-1/y^3
Answers
Answer:
b. [tex]\frac{1}{y^3}[/tex]
Step-by-step explanation:
Here we are given [tex]y^{-3}[/tex] and are asked to simplify it. We are going to apply the law of exponents which says that
[tex]a^{-n}=\frac{1}{a^n}[/tex]
Hence applying this rule in our problem we get, where a=y and n=3
[tex]y^{-3}=\frac{1}{y^3}[/tex]
Hence our C) Option is correct
Which expression is equivalent to sin^2 X-sinX-2/sinX-2
Answers
Detail solution ,
(Sin^2X-sinX-2)/sinX-2
=(Sin^2X-2sinX+sinX-2)/(sinX-2)
={sinX(sinX-2)+1(sinX-2)}/(sinX-2)
=(SinX-2)(sinX+1)/(sinX-2)
Canceling the (sinX-2) from numerator and
denominator,we get
=(sinX+1).,,Ans#
To simplify the expression sin² X - sinX - 2 / sinX - 2, we need to factor the numerator and denominator separately and then cancel out the common factor of sin(X) - 2. The equivalent expression is sin(X) + 1.
Explanation:To simplify the given expression, we can factor the numerator and denominator separately and then cancel out common terms. The numerator can be factored as (sin(X) - 2) (sin(X) + 1), and the denominator can be factored as (sin(X) - 2). By cancelling out the common factor of (sin(X) - 2), we are left with (sin(X) + 1) as the equivalent expression.
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identify the graph and describe the solution set of this system of equalities y>1/3x+5 and y<1/3x-1
Answers
Answer:
The solution to the set of inequalities is on the shaded regions.For example point (10,10)
Step-by-step explanation:
The equations are
[tex]y>\frac{1}{3} x+5\\\\\\\\y<\frac{1}{3} x-1[/tex]
plot the equations on a graph tool as shown below and visualize the solution on the shaded areas.
The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).
How to draw regions covered by inequalities?Suppose there is inequality given as: y ≥ f(x)
The region it covers is the region of value pairs (x,y) for which this inequality holds true.
We've to draw the region covered by it.
For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).
The system of inequalities are;
y > 1/3x + 5
The solution of inequality A is the shaded area below the dashed line
y = 1/3x + 5
The slope of line is m = 1/3
Similarly,
y < 1/3x - 1
The solution to inequality B is the shaded area below the dashed line
y = 1/3x - 1
The slope of line is m = 1/3
Thus, The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).
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