Answer
x = -7/2, 7/2
Step-by-step explanation
Given the equation:
[tex]9-|2x|=2[/tex]Subtracting 9 at both sides of the equation:
[tex]\begin{gathered} 9-9-\lvert2x\rvert=2-9 \\ -\lvert2x\rvert=-7 \end{gathered}[/tex]Dividing by -1 at both sides of the equation:
[tex]\begin{gathered} \frac{-\lvert2x\rvert}{-1}=\frac{-7}{-1} \\ |2x|=7 \end{gathered}[/tex]Now we have two options:
[tex]\begin{gathered} 2x=7 \\ \text{ Or} \\ 2x=-7 \end{gathered}[/tex]Solving the first option:
[tex]\begin{gathered} 2x_1=7 \\ \frac{2x_1}{2}=\frac{7}{2} \\ x_1=\frac{7}{2} \end{gathered}[/tex]Solving the second option:
[tex]\begin{gathered} 2x_2=-7 \\ \frac{2x_2}{2}=\frac{-7}{2} \\ x_2=-\frac{7}{2} \end{gathered}[/tex]I need help with questions 5 and 6 the one with the graph?
From the table it can be seen that when r=3, V(r=3) =113
On the other hand, when r=7, V(r=7)=1436 and when r=2, V(2)=33.5, therefore,
[tex]\begin{gathered} V(7)-V(2)=1436-33.5 \\ =1402.5 \end{gathered}[/tex]Jamila has a weather station in her backyard. She uses a rain gauge to track the total rainfallduring two storms3) next Jamilia a graph the function describing thursdays rainfall is this graph liner or non-liner? how do you know?4) what does the Y intercept of the graph on Mondays storm mean? does the Y intercept of the graph of Thursday storm have the same meaning?
a) It's a linear function because if time increases, precipitation increases. I'll graph it. On the graph we observe that the points form a line.
b) Both intercepts have the same meaning.
It means the amount of water (rain) at time = 0, when it still does not started to rain.
help me please
thank you
Answer:
Domain: A, [tex][1, \infty)[/tex]
Range: A, [tex][-4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Identify the vertex and the axis of symmetry of the parabola. Identify pointscorresponding to P and Q.(1, 1), x = 1P'(2, 2), Q'(-1.5)(1, 1). x = 1P'(0, 2), Q'(2.0)(1, 1), x = 1P(2.2), Q1-1,5)(1, 1), x = 1PO, 2). Q'12,0)
The vertex is the minimum/maximum point of the parabola.
This parabola has a dip, minimum point.
Looking at the coordinates, the vertex is at:
Vertex = (1,1)
The axis of symmetry is always the x-coordinate of the vertex coordinate.
That is x = 1.
So,
Axis of Symmetry:
x = 1
Now,
Since x = 1 (vertical line) is the axis of symmetry, we reflect the points P and Q about this line and find the points P' and Q'.
P' = (2,2)
Q' = (-1,5)
Consider the functions f(x) = (x - 5)^2 + 2 and g(x) = (x + 6)^2 - 4. Which of the following statements is true?
To solve the question, we can plot the two functions on the same graph as shown below
The blue graph is that for the function g(x)
While that of the red graph is that of the function f(x)
We can observe that the graph of g(x) is
[tex]\begin{gathered} 2-(-4)=6 \\ 6\text{units below f(x)} \end{gathered}[/tex]Also,
[tex]g(x)\text{ is 11 units to left of f(x)}[/tex]Thus, we can see that
The graph of g(x) is shifted 6 units below and 11 units to the left of the graph f(x)
Thus, option C is correct
A group of 45 people attended a ball game. There were twice as many children as adults in the group, Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the Group
Answer:
There are 15 adults and 30 children
Step-by-step explanation:
Hey there!
Setting up the system of equations
----------------------------------------------------------------------------------------------------------
Lets first set a variable for the children and adults
Children - x
Adults - y
x + y = 45
x = 2y
----------------------------------------------------------------------------------------------------------
Solving the system of equations
----------------------------------------------------------------------------------------------------------
We can use substitution
(2y) + y = 45
3y = 45
y = 15
This means, there are 15 adults
Now we plug in this information
x = 2y
x = 2(15)
x = 30
This means, there are 30 children
----------------------------------------------------------------------------------------------------------
So, there are 15 adults and 30 children
There are three groups in a community. Their demand curves for public television in hours of programming, T, are given respectively by Wy = 200-T W2 = 240-T W3 = = 320-T Suppose public television is a pure public good that can be produced at a constant marginal cost of $200 per hour. What is the efficient number of hours of public television?
In such a competitive private market, 80 hours of programming would be available.
What is defined as the Marginal Social Benefit?The marginal social benefit is the difference with in benefits of consuming one more unit of a product or service. It is determined by the amount of money individuals are inclined to pay for an extra unit of a good or service. When marginal benefit corresponds marginal cost for all groups, the efficient amount of hours of public television is reached.For the given question;
Marginal social benefit = Addition of all groups with in community.
MSB = W1 + W2 + W3
MSB = ($200 - T) + ($240 - 2T) + ($320 - 2T)
MSB = $200 + $240 + $320 - T - 2T - 2T
MSB = $760 - 5T
Calculate efficient number of hours for the public television:
MSB = MC
$760 - 5T = $200
$760 - $200 = 5T
5T = $560
T = 112 hours for the programming.
b. For $200 per hour,
Demand for group 1:
Private marginal benefit = Private marginal cost
$200 - T = $200
T = 0 hours for the programming.
Demand for group 2:
$240 - 2T = $200
$240 - $200 = 2T
$40 = 2T
T = 20 hours for the programming.
Demand for group 3:
$320 - 2T = $200
$320 - $200 = 2T
$120 = 2T
T = 60 hours for the programming.
Hours of television = group 1 + group 2 + group 3
Hours of television = 0 + 20 + 60
Hours of television = 80 hours
Thus, in such a competitive private market, 80 hours of programming would be available.
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Rachel's garden is square in shape. The area of the garden is36 ft? What is the length of one side of the garden?
1) If Rachel's garden is a square and the area is mentioned, let's use the area of the square.
S= l²
36 =l²
Flipping it:
l²=36
l=√36
l=6
2) So the length of Rachel's garden is 6 feet.
Solve for the missing length using trig. Use the calculator below to help you. Round your answer to the nearest tenth. The reference angle measures 190.
As shown in the figure : we have a right angle triangle
We need to find the value of x
The hypotenuse of the triangle = 29
And x represents the opposite side of the angle 19
So,
[tex]\begin{gathered} \sin 19=\frac{opposite}{hypotenuse} \\ \\ \sin 19=\frac{x}{29} \\ \\ x=29\cdot\sin 19\approx9.44 \end{gathered}[/tex]rounding the answer to the nearest tenth
So,
[tex]x=9.4[/tex]If f(x)=sqrt x-x and g(x)+2^3-sqrt x-x, find f(x)-g(x)
Answer:
A
Step-by-step explanation:
f(x) - g(x)
= [tex]\sqrt{x}[/tex] - x - (2x³ - [tex]\sqrt{x}[/tex] - x) ← distribute parenthesis by - 1
= [tex]\sqrt{x}[/tex] - x - 2x³ + [tex]\sqrt{x}[/tex] + x ← collect like terms
= - 2x³ + 2[tex]\sqrt{x}[/tex]
Mateo says that 6⁸÷3⁴= 64 or 1,296 by applying the Quotient of Powers Law. Is Mateo correct? Explain.
Answer:
6⁸÷3⁴ = 20736
Step-by-step explanation:
[tex]6^8\div3^4[/tex][tex]= (2\times 3)^8\div3^4[/tex][tex]= 2^8 \times 3^8\div3^4[/tex][tex]= 2^8 \times 3^{8-4}[/tex][tex]= 2^8 \times 3^{4}[/tex][tex]= 256 \times 81[/tex][tex]6^8\div3^4= 20,736[/tex]So, 6⁸÷3⁴ is neither equal to 64 nor 1296. It is equal to 20,736.A bag contains 7 red, 4 blue, and 6 yellow marbles. If 3 marbles are selected in succession, what is the probability of selecting blue, then yellow, then blue, if no replacement occurs each time?
The probability of selecting blue, yellow and blue marble without replacement is 3/170
Number of red marbles = 7
Number of blue marbles = 4
Number of yellow marbles = 6
Total number of marbles = 17
Probability of selecting a red marble = 7/17
Probability of selecting a blue marble = 4/17
Probability of selecting a yellow marble = 6/17
Now the probability of selecting the first blue marble = Number of blue marbles/Total number of marbles. = 4/17
Probability of selecting the yellow marbles = Number of yellow marbles/Number of marbles left after the first draw = 6/16
Probability of selecting the third blue marble = Number of blue marbles/Total number of marbles left after the second draw = 3/15
So the probability of blue, yellow and blue marble is:
4/17*6/16*3/15 = 3/170
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solve the system by substitution.-3x—6y=45 -5y=x
The second equation already has the value of x isolated, so in order to solve the system by substitution, we can apply this value of x from the second equation in the first one:
[tex]\begin{gathered} x=-5y \\ \\ -3x-6y=45 \\ -3\cdot(-5y)-6y=45 \\ 15y-6y=45 \\ 9y=45 \\ y=\frac{45}{9}=5 \end{gathered}[/tex]Now that we have the value of y, we can find the value of x:
[tex]x=-5y=-5(5)=-25[/tex]So we have that x = -25 and y = 5.
8x - 7=7x - 2What is the answer?
The given equation is
[tex]8x-7=7x-2[/tex]First, we subtract 7x on each side.
[tex]\begin{gathered} 8x-7x-7=7x-7x-2 \\ x-7=-2 \end{gathered}[/tex]Mark’s model train can go 12 laps around its track in 4 minutes. If it runs at the same speed, how many laps can the train go in 9 minutes?Rate needed (laps/minutes)Unit RateInterpretation of unit rateExplain your thinking/Justifying your reasonSolution
rate = 12 laps/4 min = 3 laps/min
3 laps ------------------ 1 min
x ------------------ 9 min
x = (9 x 3) / 1
x = 27 laps in 9 min
Result 27 laps in 9 min
PLS HELP!!
The equation for the graph is:
y>x-4.
y≤x-4.
y
None of the choices are correct.
The correct option for the equation of line is; y ≥ x - 4.
What is termed as the equation of line?A line's equation can be formed using the slope of a line and a point just on line. The slope of a line is its inclination with respect to the positive x-axis, and it is represented as a numeric integer, small percentage, or the tangent of a angle it makes with respect to the positive x-axis. The term "point" refers to a coordinate system point with the x and y coordinates.For the given question;
Consider two points lying on the line.
(x₁, y₁) = (4, 0)
(x₂, y₂) = (0, -4)
The, the slope of the line is found using;
slope = m = (y₂ -y₁)/(x₂ - x₁)
m = (-4 - 0)/(0 - 4)
m = 1
Now, the standard form of equation of line is;
y - y₁ = m(x - x₁)
Put the values,
y - 0 = 1(x - 4)
y = x - 4
As, the origin of the coordinates axis and the shaded portion lies on the opposite side of the line, thus the inequality used is greater than equal to.
y ≥ x - 4
Thus, equation of line obtained for the given graph is y ≥ x - 4.
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Which set of ordered pairs does not represent a function? o{(-5,-2),(3,-2),(5,-9), (6, -7)} o{(-1, -3),(-4,9), (-7,2), (-3,9)} O {(4,5),(-8,-6), (-7,-1), (6,-1)} o {(-4,-9), (-4,4),(-2,2), (9,5)} Submit Answer
{(-4,-9), (-4,4),(-2,2), (9,5)}
Because the x values of -4 occurs more than once, the set of ordered pairs is not a function.
Devaugn’s age is three times Sydney’s age. The sum of their ages is 52. What is Sydney’s age?Solve by using linear equation.
ANSWER:
13 years old
STEP-BY-STEP EXPLANATION:
Let x be Devaugn's age and y be Sydney's age.
We establish the following linear equation system:
[tex]\begin{gathered} x=3y \\ x+y=52 \end{gathered}[/tex]We solve the first equation in the second equation:
[tex]\begin{gathered} 3y+y=52 \\ 4y=52 \\ y=\frac{52}{4} \\ y=13 \end{gathered}[/tex]Which means Sydney's age is 13 years old.
If T is the midpoint of SU, find TU.
S 9x
T 5x+28 U
The length of each segment ST = 63, TU = 63, SU = 126
What is a midpoint theorem?The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
From the given figure
ST = 9x
TU = 5x+28
According to midpoint theorem,
ST = TU
9x = 5x+28
9x-5x = 28
4x = 28
x = 7
It means,
ST = 9×7 = 63
TU = 5×7+28 = 35+28 = 63
SU = ST+TU
= 63+63
ST = 126
Hence, The length of each segment ST = 63, TU = 63, SU = 126
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The sum of two numbers is 6. If one number is subtracted from the other, the result is 2. Find the numbers.
Tabitha has 6 music files, each with 9 songs in it. She is dividing the songs into 7 groups. If each of group will have the same number of songs, how many songs will be left over?
A.
0
B.
3
C.
5
D.
1
Answer:
5
Step-by-step explanation:
6*9= 54
54/7 = 7 with remain 5
V is the midpoint of UW. If UV = 2x and VW = x + 8,what is UV?
Please explain and show work
Based on the definition of the midpoint of a line segment, the length of UV is determined as: 16 units.
What is the Midpoint Definition of a Segment?The midpoint of a segment is defined as the point on a line segment where the line segment is bisected into two equal smaller segments. The length of the smaller segments formed will be equal to each other.
Given that V is the midpoint of segment UW, it means that V divides segment UW into two equal smaller segments, UV and VW.
UV = 2x
VW = x + 8
Therefore:
UV = VW
Substitute
2x = x + 8
2x - x = x + 8 - x [subtraction property of equality]
x = 8
Find the length of UV:
UV = 2x
Plug in the value of x
UV = 2(8)
UV = 16 units.
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-√3+0= -√3
Commutative property of addition
Additive identity Commutative property of multiplication
Multiplicative identity
The most appropriate choice for properties of addition will be given by-
The correct option will be additive identity
What is addition and its properties?
To find the total of two or more numbers, addition is used
There are some properties of addition
Let a, b and c be three numbers
1) Commutative property
The value of a + b is same as the value of b + a
a + b = b + a
2) Associative property
On adding more than two numbers, changing of bracket is permissible.
(a + b) + c = a + (b + c).
3)Additive identity
There is a number called additive identity. If any number is added to the additive identity, we will get back the same number. Here, 0 is the additive identity
a + 0 = a
4) Additive Inverse
Every number has an additive inverse.
On adding a number with the additive inverse, the result will be additive identity.
-a is the additive inverse of a
a + (-a) = 0
Here,
[tex]-\sqrt{3}+0=-\sqrt{3}[/tex]
0 is the additive identity
So this is the case of additive identity.
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You spend $4 to get into an event and spend $1.25 per soda you buy. In your pocket you have a $20 bill that you can spend at the event
Answer:
what is the question?
Step-by-step explanation:
Please write the question so i can answer it.
An ice cream shop has 12 flavors of ice cream. How many ways can you choose three different flavors for a sundae?
Answer:
chose your top 3 flavors
∠A and ∠B are vertical angles. If m∠A = (7x-6)° and m∠B = (8x-27)°, then find the measure of ∠B
Vertically opposite angles are equal
Therefore,
[tex]\begin{gathered} \angle A=\angle B \\ m\angle A=7x-6 \\ m\angle B=8x-27 \\ 7x-6=8x-27 \\ 7x-8x=-27+6 \\ -x=-21 \\ x=21 \\ \angle B=8(21)-27=168-27=141\text{ degre}e \end{gathered}[/tex]I NEED HELP ASAP PLEASE!
The output value of the function is 8 when the input value is -2
What is input and output value ?
A relation's input value is its first value, and its output value is its second. A particular kind of relation called a function is one in which every input value has only one and only one output value.
The value of an input is the independent value, but the value of an output is dependent on the value of the input.
Only data flows, mining flows, and sub processes can use input variables. The variable value that was modified inside a sub process is output using output variables.
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The Weasley brothers estimate that they will need a thousand galleons just to set up their joke shop, Weasley's Wizarding Wheezes. The first products they are manufacturing are pygmy puffs, and they realize that the cost of making a single box of pygmy puffs is 3 galleons. The brothers would like to estimate the cost, in galleons, of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p. Which of the following equations is the correct equation representing this scenario?
1. ()=3−1000
2. ()=3+1000
3. ()=1000−3
4. ()=1000+3
The most appropriate choice for linear equation will be given by -
Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p
C(p) = 3p + 1000
Second option is correct
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Initial cost of manufacturing Weasley's Wizarding Wheezes by the Weasley brothers = 1000 galleons
Cost of producing one pygmy puff = 3 galleons
Cost of producing p boxes of pygmy puffs = 3p galleons
Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p
C(p) = 3p + 1000
Second option is correct
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Complete Question
The Weasley brothers estimate that they will need a thousand galleons just to set up their joke shop, Weasley's Wizarding Wheezes. The first products they are manufacturing are pygmy puffs, and they realize that the cost of making a single box of pygmy puffs is 3 galleons. The brothers would like to estimate the cost, in galleons, of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p. Which of the following equations is the correct equation representing this scenario?
1) C(p) = 3p - 1000
2) C(p) = 3p + 1000
3) C(p) = 1000p - 3
4) C(p) = 1000p + 3
In a bag of Jolly Ranchers, the ratio of blue to red is 3 to 4. If I have a TOTAL of 56 Jolly Ranchers, how many of them are blue?
Answer: 24
Step-by-step explanation:
Which graph represents the solution set to the system of inequalities? y < -3/4x + 1y > 2/3x - 3
Since both inequalities don't have the equal to symbol (≤) Both lines must be dashed lines.
So, the top right option can't be.
Now we have 3 options:
If we graph the inequality: y < -3/4x + 1
It has a slope of -3/4 and a y-intercept on 1.
The only available option that represents this inequality is the right bottom one.
