The outcome of -2 g(x) + f(x) is 4 x -2 x ² and the domain is [ 0 , 2 ] .
Given,
f (x) = x - 2 and g (x) = x² - 3 x + 2
The question states to find the summation of the function f, that is, f (x) = x - 2, and function g, that is, g (x) = x² - 3 x + 2
Performing the addition operation on these functions is just like simple addition.
This means that when we add the two functions f (x) and g (x), we get
f (x) + g (x) = x - 2 + x² - 3 x + 2
=> f (x) + g (x) = x ² - 2 x
This implies that the summation or addition of the two functions f (x) and g (x) gives x ² - 2 x
needed result = -2 g(x) + f(x) = -2 ( x² - 2 x ) = -2 x ² + 4x = 4 x -2 x ²
To find domain,
y = 4 x -2 x²
=> 4x -2 x² ≥ 0
=> 2 x * ( 2 - x ) ≥ 0
=> 2 x ≥ 0 and 2 - x ≥ 0
=>x ≤ 2 and x ≥ 0
=> the final Domain = [ 0 , 2 ]
Therefore, we get the result of -2 g(x) + f(x) as 4x -2 x ² and the domain as [ 0 , 2 ] .
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Simplify each expression. Rationalize all denominators. 5√2/ √7 -√2
The rationalization of all denominators is 5.74165.
A fraction is represented inside the form of 'x/y', wherein 'x' is the numerator and 'y' is the denominator. The numerator represents the entire variety of parts taken into consideration. whereas, the denominator represents the full quantity of equal components in a fraction. The pinnacle quantity in a fragment is usually taken into consideration as a numerator.
Another phrase for a denominator is the divisor. both of those words check with the range beneath the road in a not unusual fraction. similarly, while you're speakme approximately statistical values, a denominator refers back to the whole number or population from which samples are taken.
In a fallacious fraction, the numerator is extra than or the same as the denominator and the denominator must not be the same as zero. In an incorrect fraction, the numerator is less than the denominator and the numerator is extra than 0. In an unsuitable fraction, the numerator is constantly more than the denominator.
[tex]5\sqrt{2} /\sqrt{7}- \sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{\sqrt{7}-\sqrt{2} }[/tex]
Multiply by the conjugate
[tex]\frac{5(\sqrt{7}+\sqrt{2})\sqrt{2} }{(\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} }[/tex]
Expand [tex](\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} ): 5[/tex]
Factor out the common term 5
[tex]\frac{(5\sqrt{7}+5 \sqrt{2})\sqrt{2} }{5}[/tex]
Cancel the common factor: 5
[tex](\sqrt{7} +\sqrt{2}) \sqrt{2}[/tex]
[tex]= \sqrt{14} +2[/tex]
= Decimal:5.74165
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What are five sets of integers that has a mean of -10.
Can you please explain how to get the answer also. :)
The five sets of integers that has a mean of -10 will be 10, -15, -2, -12, and -11.
How to calculate the value?It should be noted that mean simply means average. Therefore, the numbers that will give a mean of -10 will be:
-10, -15, -2, -12, and -11.
Therefore, the mean will be:
= ( - 10 + -15 + -2 + -12 + -11) / 5
= -50 / 5
= -10
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The sum of three consecutive odd num
What is the smallest of the three numbers?
In eight years, Pete will be twice as old as he
was two years ago. How old is he today?
Answer:
10
Step-by-step explanation:
8 + 2 = 10
Please HELP!
Write an algebraic expression for this word phrase:
Seven less than the product of five and a number.
I know that you have to do (5xn) but how do you do seven less?
Answer:
5n - 7
Step-by-step explanation:
The product of five and a number is 5n
Seven less than the product of five and a number means 5n - 7
can someone please help me(10 points will give brainliest!!!)
well i want to know how to spell the word 90
Answer: Ninty
Step-by-step explanation:
Match the directed line segment with the image of polygon P being transformed polygon Q by translation by the directed line segment
The directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.
How to Interpret Translation of line segments?In this question, the translations are defined by a line segment.
Such that in each translation, we can easily find the segment PQ (the measure and the direction).
And all the points in the Polygon P will be connected by that same segment PQ to the equivalent point in the Polygon Q. (where you only move the segment to the correct location, but the length and direction remains constant)
Thus, to find the line segment for each transformation, you need to correctly measure the length of the segment PQ, and also the direction (that can be defined by an angle).
With the above, we can find the directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.
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Given:
2x + 30 = -4(5x- 2); Prove: x=-1
Answer:
so x=-1
Step-by-step explanation:
substitute "-1" for x
so, 2(-1)+30=28
and, -4(5(-1)-2)>>-4(-5-2)>>20+8
so, 28=28
a group of friends are at a baseball game and are purchasing souvenirs. Lacey purchased 4 t-shirts and 2 baseball caps, spending a total of $162. Her Anna purchased 1 t-shirt and 2 baseball caps, which cost her a total of $93. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?
The price of each souvenirs is 28.33 Dollars.
Let X be the same price of all the t-shirts and all the baseball caps.
Lacey purchased
4 T-shirts and 2 Baseball caps = $162
4X + 2X = $162
6X = $162
Anna purchased
1 T-shirt and 2 Baseball caps = $93
1X + 2X = $93
3X= $93
Now we will add the price of souvenirs purchased by Lacey and Anna to find the price each souvenir.
6X = $162 eq. 1
3X= $93 eq. 2
As we have two equations we will add both equations :
6X + 3X = $162 + $93
Then we will determine the value of X .
9X = $255
X = $255 ÷ 9
X = $28.33
Hence the price of each souvenirs is $28.33 .
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3(4-2(8+5))
Can someone show me what to do first?
Answer:14
Step-by-step explanation:
14
Answer:
18
Step-by-step explanation:
addition is always before subtraction so you add 8 plus 5 is 13 then 4 minus 2 is 2 so add all together and its 18
Lesson 10: Connecting Equations to Graphs
(Part 1)
Cool Down: Kiran at the Carnival
Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25
and a ride costs $1.
1. Write an equation to represent the relationship between the dollar amount Kiran is
spending and the number of games, , and the number of rides, , he could do.
2. Which graph represents the relationship between the quantities in this situation?
Explain how you know.
The equation to represent the relationship between the dollar amount Kiran is spending and the number of games and the number of rides is 0.25x + y = 12
The graph that represents the relationship between the quantities in this situation is graph C.
How to illustrate the information?It should be noted that the equation will be:
25x + 100y = 1200 in cents
or 0.25 x + y = 12 in dollars
where
x= games
y= rides
The graph that will connect the x axis and y axis at the points where x= 48 and y= 12, Only graph C seems to have a line that may end at x=48. Therefore, the correct option is C.
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Solve each equation. If necessary, round to the nearest ten-thousandth. log (5 x-4)=3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 4.8170.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: - log (5x - 4)=3
We are given a logarithmic expression: log (5x - 4)=3
We know that e^(log b) = b
Using exponential on both sides, we have
e^(log (5x - 4)) = e^3
5x - 4 = 20.085
5x = 24.085
x = 4.817
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 4.8170.
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Slope intercept form (-6,19) and (3,-2)
Answer:
-7/3 or -2.3
Step-by-step explanation:
1. y2-y1 divided by x2-x1 which would be y2-y1/x2-x1
2. plug in : -2-19/3-(-6)
4. Solution ( -7.3 or -2.3 )
Answer:
[tex]y = -\dfrac{7}{3}x +5[/tex]
Step-by-step explanation:
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
For the line passing through (-6, 19) and (3, -2) , the slope
[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]
[tex]\\\\m= \dfrac{-21}{9}[/tex]
[tex]m = -\dfrac{7}{3}[/tex]
So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]
To compute y-intercept, b, plug in any of the two points into the above equation and solve for b
Let's choose point (3, -2)
Plugging x = 3 and y = -2 gives
[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]
So equation of line is
[tex]y = -\dfrac{7}{3}x +5[/tex]
Archie and three friends go on holiday together for a week.
The costs of the holiday will be shared equally between the 4 friends.
These are:
1) £1360 for 4 return plane tickets.
2) £850 for the accommodation.
3) £210 for the care hire for a week.
How much does Archie have to pay for his share of the costs?
The amount that Archie has to pay for his share of the costs is £605
What is the amount of total cost for the holiday?
The total costs of the holiday comprise of plane tickets, accommodation as well as the care hire for a week, in essence, the total costs to be shared equally among the four friends is as shown below:
total costs of holiday=£1360+£850+ £210
total costs of holiday=£2420
Archie's share of costs=£2420/4
Archie's share of costs=£605
In other words, the cost of the holiday, in this case, is not just plane ticket, accommodation cost as well as the cost of care hire, without any of the those , the holiday experience is not complete
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. slope
= -3, (0,0)
Write in standard form
Answer:
y= -3x
Step-by-step explanation:
the equation is " y = (slope)x + (y-intercept) " hope this helps !!
Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree cast a show that is x+5 feet long. how tall is the tree? how long is the trees shadow?
The height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
It is given that:
Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree casts a show that is x+5 feet long
By using scale factor:
Let x be the height of the tree
x/6 = = (x + 5)/8
8x = 6(x + 5)
8x = 6x + 30
2x = 30
x = 15 feet
Thus, the height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.
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I need help with number 2
What is the question?
The name of the figure below is ___ ___.
[ Brainliest + easy points ]
Answer: A line or GH
Step-by-step explanation:
Answer: ray
Step-by-step explanation:
Column 1 Sections of a Lab
Report
19. Problem or Question
20. Hypothesis
21. Materials
22. Procedure
23. Observations
24. Analysis
25. Conclusion
Column 2 Information to Use in a Lab Report
a. If you increase the water temperature, then the yeast will
give off more gas.
b. After five minutes, Balloons A and B expanded.
c. Yeast give off more gas at higher temperatures.
d. What factors help yeast to grow?
e. Balloon B became bigger than Balloon A, so that means
that the yeast in Balloon B gave off more gas.
f. Combine the yeast, sugar and water in a bottle. Put a
balloon on the bottle.
g. Yeast, sugar, warm and cool water, containers
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if 2x = 32
find the value of x
Answer:
x = 16
Half of 32 is 16
Therefore, 2 × x(16) = 32
The data in this table represents a linear function.
What is the slope of this line?
Y
-16
-24
-44
X -48
6
8
13
14
The slope of the line whose data represents a linear function is m = -1/4.
What is Slope of a line?Slope of an straight line is denoted by m and is the measure of rate of change of 'y' with respect to 'x'. Mathematically -
m = tan(θ) = Δy/Δx
Given is a table representing a linear function. From the question, we can write -
X → 6 8 13 14
Y → -16 -24 -44 -48
We can find the slope of this line using the formula -
m = Δy/Δx
m = (y₂ - y₁) / (x₂ - x₁)
Take any two coordinates from the table -
(x₁, y₁) → (6, -16)
(x₂, y₂) → (8, -24)
Substitute the values in the formula -
m = (8 - 6)/(-24 + 16)
m = - 2/8
m = -1/4
Therefore, the slope of the line whose data represents a linear function is m = -1/4.
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What do I do for the final mark?!?!!?
, The graphical solution of the simultaneous equation is
x = 3 and y = 3.What are simultaneous equations?Simultaneous equations are pairs of equations that contain two unknowns.
How to solve simultaneous equations?Simultaneous equations are solved by any three (3) of the following methods.
Substiution method, Elimination method and Graphical methodHow to solve the given simultaneous equations by graphical methods?Given the simultaneous equations
x + y = 6 and y = x
We first confirm the solution by using the substitution method.
Substiutitng y = x into the first equation, we have
x + y = 6
x + x = 6
2x = 6
x = 6/2
x = 3
Since y = x. So, y = 3.
So, the solution is x = 3 and y = 3.
So, for a graphical solution, plotting the graph of
y = x and x + y = 6 on the x and y axis, their point of intersection is at the point (3, 3)So, the graphical solution of the simultaneous equation is
x = 3 and y = 3.This is seen in the intersection on the graph attached.
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Please help me with this question
Simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.
Evaluating the expression gives?Given the expression in the question;
( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)
First, perform the operations inside the parenthesis
( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)
( (-9(2)³ )/4 ) + ((1/2)(6)² )/( 4²÷2⁴)
Raise 2 to power 3, 6 to power 2, 4 to power 2 and 2 to power 4
( (-9(8) )/4 ) + ((1/2)36 )/( 16 ÷ 16)
Perform the operations in the parenthesis
-72/4 + 18/1
Divide -74 by 4
-72/4 + 18/1
-18 + 18
Negative 18 and positive 18 cancels out each other.
-18 + 18
0
Therefore, simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.
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One less than four times a number is 11.
(Could you also help me solve the question too?)
Answer:
3
Step-by-step explanation:
Let's put that number as x.
It says that one minus 4 times x is 11.
So the equation is 4x - 1 = 11.
Add one on both sides to get 4x = 12.
Divide by four on both sides to get x = 3.
Since x is what we are looking for, the answer is 3!
(Hope this helps!)
Evaluate each logarithm.
log₂ 16
The answer to the given logarithm expression is log₂ 16 = 4
A power to which a number must be increased in order to achieve another value is referred to as a logarithm. The easiest way to represent enormous numbers is in this way.
The fact that addition and subtraction logarithms can be used to multiply and divide logarithms is supported by a number of significant features of logarithms. The use of logarithmic operations is subject to a set of rules. These guidelines are known as: Division regulations apply to products. Exponential/Power Law Changes to fundamental laws Rule of Base Change Log elaboration
We need to evaluate log₂ 16
Using the property logₐ (mⁿ) = n logₐ m
16 = 2⁴log₃ 125 can be written as
log₂ 16 = 4 log₂ 2
We know that logₐ a = 14 log₂ 2= 4
Hence , we evaluated the logarithm which is log₂ 16 = 4
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determine whether descriptive or inferential statistics were used in the statement. 67% of cell phone users check their phone even though it is not ringing or vibrating. (source: pew research center)
Inferential Statistics
Inferential Statistics is the part of statistical analysis that helps you to determine or predict further steps from the data studied according to Statistical methods. It is helpful in understanding people's perspectives or analyzing data from the samples obtained from it. It can be defined as the analytical tool used to draw conclusions about a population by analyzing random samples.
Descriptive Statistics are used to describe the data and make generalizations about the studies. It is used the define the characteristics of the data obtained.
In the given situation, the statistical analysis is done and it has been inferred from the studies that 67% of people check their cell phone even when it is not ringing or vibrating.
Hence, It is a case of Inferential Statistics.
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Using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 18 cents per minute. If the total cost of the call is $2.75, how long is the phone call?
The total duration of the phone call was 10 minutes.
Given that, by using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 18 cents per minute. If the total cost of the call is $2.75 and we have to calculate the time how long was the phone call.
Let the number of minutes a phone call held be x.
Now, we will be representing the above given information in terms of linear equation and then solve for the value of x which will give us the number of minutes the phone call held.
Total cost = $0.95 + $0.18x
$2.75 = $0.95 + $0.18x
2.75 = 0.95 + 0.18x
2.75 - 0.95 = 0.18x
1.8 = 0.18x
1.8/0.18 = x
10 = x
Therefore, the call will go 10 minutes long.
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Suppose a population of 160 crickets doubles in size every month. The function
f(x) = 160:2* gives the population after x months. How many crickets will there be after 2
years?
O2,684,354,560 crickets
O640 crickets
07,680 crickets
O655,360 crickets
Answer:
1. no
2. 2,684,354,560 crickets
3. $9,200
4. b
5. 7.5
6.b
Anna ordered 200 party favors. she
received only 1/10 of the party favors
she ordered. how many party favors
did anna receive?
Answer: 20
Step-by-step explanation: She received 1/10 of the party favors, and 1/10 of 200 is 20.
Anna ordered 200 party favors, she received only 1/10 of the party favors
she ordered, i.e., Anna received 20 party favors.
Here, given that, Anna ordered 200 party favors. she received only 1/10 of the party favors she ordered.
Now, we have to find out how many party favors Anna received,
we need to calculate 1/10 of the total number of party favors she ordered.
Anna ordered 200 party favors, and she received only 1/10 of that amount.
As, we know that, 'of' indicates 'multiplication'
so, we have to find 1/10 of 200, so that, we multiply 200 by 1/10:
1/10 * 200
= 200/10
= 20
i.e. She received 1/10 of the party favors, and 1/10 of 200 is 20.
So, Anna received 20 party favors.
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