The function g is defined by the following rule.
g(x) = (1/2)x
Find g(x) for each x-value in the table.
-1
0
1
2
3
Answer:
g(-1)=2, g(0)=1, g(1)=1/2, g(2)=1/4, g(3)=1/8
Step-by-step explanation:
How can you transform the equation 8x - 10 + 10 + 4x = -10 + 6x + 6x + 10 into the form of a = a, where a is a number, to show that the equation has an infinite number of solutions? Select all that apply.
A. by adding 12x to both sides of the equation and then simplifying
B. by subtracting 8x to both sides of the equation and then simplifying
C. by subtracting 12x from both sides of the equation then simplifying
D. by subtracting 20 from both sides of the equation then simplifying
E. by dividing 6x from both sides of the equation and then simplifying
Step-by-step explanation:
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Pat and Terry believe the color yellow attracts hummingbirds. They decided to test their hypothesis by doing an experiment in which they set up four hummingbird feeders with the same amount of food and placed them in locations only hummingbirds could reach. One feeder was yellow, one was red, one was blue, and one was clear. Each day for one week, Pat and Terry measured and recorded the amount of food left in each of the feeders. At the end of the experiment the red feeder had the least amount of food left in it. What conclusion should Pat and Terry reach?
Step-by-step explanation:
red feeder is smarter
Where does the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6?
The line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).
As given,
Equation of the line passes through two points (1, 0, 1) and (4, −4, 4) is:
[tex]\frac{x-4}{4-1}=\frac{y+4}{-4-0}=\frac{z-4}{4-1}[/tex]
From the above equation we have
(x-4)/3 =(y+4)/-4
⇒-4x+16= 3y+12
⇒y=(-4x +4)/3 __(1)
And
(x-4)/3=(z-4)/3
⇒z=x __(2)
Substitute the value of y and z in the plane x +y+ z=6 to get point of intersection of line and plane
x+ [(-4x +4)/3] +x=6
⇒3x-4x+4 +3x =18
⇒2x=14
⇒x=7
Substitute value of x in (1) and (2)
y=-8 and z=7
Therefore, the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).
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When Bob runs at 4 miles an hour, it takes him 20 minutes to run the path around the
park. If he ran instead at 5 miles an hour, how long would it take him to run that path
around the park?
Time taken to cover path around the park if he runs at speed 5miles/hour is 15.96min
What is Speed ?
Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance x time.
Given that,
Time taken when Bob runs 4miles/hour = 20min
Time taken when Bob runs 5miles/hour = ?
First we have to find the distance of the path around the circle
Distance = speed x time
= 4 x 20/60
= 4/3 miles
= 1.33 miles
Now to calculate the time when he ran 5 miles/hours:
Time = distance / speed
= 1.33 / 5
= 0.266hours
0r
= 0.266 x 60 min
= 15.96 min
Hence, its will take 15.96min to cover the path around the park
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Manuel's younger brother Ricky loves hot
wheels. Ricky has 28 boxes of toy cars. Each
box holds 16 cars. Ricky gives his brother
Manuel 15 cars. How many cars does Ricky
have now?
Answer:
29
Step-by-step explanation:
Add 28 + 16=44
Subtract 44 - 15=29
Please help na po need na po talaga, please correct answers po brainliest
Directions: Draw a Venn diagram and list the elements of each given set. Input your answer inside each box. Enclose your answer with braces and do not put a space in between characters or numbers. Refer to the sample item below.
Sample Given: A ∩ B
Sample Answer: {2,3}
Let A= {1, 2, 3, 4, 5} B = {2, 3, 5, 7, 11}, C= {3, 5, 7, 9}
1.) A ∪ B ∪ C =
3.) (A – B) ∩ C =
5.) A' ∪ B =
The set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11}, (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.
What is the Venn diagram?It is defined as a diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
The universal set will be:
U = {1, 2, 3, 4, 5, 7, 9, 11}
Let:
A = {1, 2, 3, 4, 5}
B = {2, 3, 5, 7, 11},
C= {3, 5, 7, 9}
1) A ∪ B ∪ C = {1, 2, 3, 4, 5, 7, 9, 11}
3) (A – B) ∩ C = {1, 4} ∩ C= {3, 5, 7, 9}
(A – B) ∩ C = ∅
5) A' ∪ B = {7, 9, 11} ∪ {2, 3, 5, 7, 11}
A' ∪ B = {2, 3, 5, 7, 9, 11}
Thus, the set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11}, (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.
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A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 6 insects will die? Round your answer to four decimal places.
The required probability that exactly 6 insects will die is 60%.
Given that,
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. The probability that exactly 6 insects will die is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Total number of sample spaces = 10
Total number of favorable outcomes = 6
probability can be given as,
= 6 / 10
= 0.6 or 60%
Thus, the required probability that exactly 6 insects will die is 60%.
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1) A gallon jug of milk is 3/4 full. After breakfast the jug is 1/12 full. How much milk did your family have at breakfast?
well, your family really ate "x" for breakfast, was pretty good with cereal and strawberries btw.
let's keep in mind that the LCD of the denominators 4 and 12 is "12", so we'll use that to do away with the denominators.
[tex]\stackrel{\textit{before breakfast}}{\cfrac{3}{4}}~~ - ~~\stackrel{for~breakfast}{x}~~ = ~~\stackrel{leftover}{\cfrac{1}{12}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{3}{4}-x \right)~~ = ~~12\left( \cfrac{1}{12} \right)}\implies 9-12x=1 \\\\\\ 9=12x+1\implies 8=12x\implies \cfrac{8}{12}=x\implies {\Large \begin{array}{llll} \cfrac{2}{3}=x \end{array}}[/tex]
pelase slove these two problem i will give out those crown thingy!
Answer: $2.75
Step-by-step explanation:
2) Judy spent 3*5.25 = 15.75 on popcorn bags, 13.60 on a jumbo bag of chips and 7.90 for a dip. This means that overall she spent $37.25. If she had $40, this means that she have left $40 - $37.25 = $2.75.
1) Your answer is right.
left on together, the cold and hot water faucets of a certain bathtub take 8 minutes to fill the tub. If it takes the hot water faucet 18 minutes to fill the tub by itself how long will it take the cold water faucet to fill the tub on its own
The time taken to fill the bathtub by cold water is 14.4 minutes.
Given,
Time taken to fill a bathtub by both cold and hot water = 8 minutes
Time taken to fill the bathtub by hot water = 18 minutes
Time taken to fill the bathtub by cold water = t minutes
We have to find t.
We can take the full bath tub as 1.
Now,
We can equate the given data:
We get,
(8/18) + (8/t) = 1
Now, solve the equation:
((8 × t) + (8 × 18) ) ÷ (18 × t) = 1
(8t + 144) ÷ 18t = 1
8t + 144 = 18t
18t - 8t = 144
10t = 144
t = 144/10
t = 14.4
That is,
The time taken to fill the bathtub by cold water is 14.4 minutes.
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You and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. Whatinteger represents the total change in the time when you use 5 clues?
Integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
As given in the question,
Number of free clues =3
Total number of clues used to escape from a room = 5clues
Out of these 5 clues, 3 clues are free to use. Hence these 3 clues do not result in any time change.
Hence total time elapsed after usage of 3 clues = 0
Each removes 5 minutes from your remaining time
Integer represents the total change in the time for the usage of 4th and 5th clue = 10 minutes
So overall change in timeline after consuming 5 clues = 10 minutes since each of the 4th and 5th clue results in decrease of 5 minutes each; thus effecting 10 minutes total time change (reduction)
Therefore, integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
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7. AXYZ with X(-2, 2), Y(4,2), and Z(1, -5); rotate 180° clockwise. 73 a. What are the vertices of the image after the transformation? 76 b. Graph the original triangle and its image. у
The given coordinate of the vertices of triangle XYZ is X(-2,2), Y(4,2) and Z(1,-5).
a). When rotates 180 degrees clockwise the new coordinate of the triangle can be determined as,
[tex]\begin{gathered} X^{\prime}(2,-2) \\ Y^{\prime}(-4,-2) \\ Z^{\prime}(-1,5) \end{gathered}[/tex]b). The original and the new coordinates of the triangle can be drawn as,
The original and the new triangles can be drawn as,
hi, please help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2/17, 8/17, and 11/17
7/21, 7/18, 7/14, 7/12, and 7/8
2/12, 2/10, 2/8, 2/6, and 2/4.
Step-by-step explanation:
the order would be 2/17, 8/17, and 11/17 since the bottom number (denominator) stays the same while the numerator (top number) increases.
the order for the 2nd one would be:
7/21, 7/18, 7/14, 7/12, and 7/8. The reason for this is that when the numerator stays the same and the denominator increases, the value of the fraction decreases. For example, 1/2 is greater than 1/4, and 1/4 is more than 1/5 because 5 is greater than 4. This only works when the numerator (top number) stays the same.
The order for the 3rd one would be:
2/12, 2/10, 2/8, 2/6, and 2/4. Again, the numerator stays the same while the denominator changes. As the denominator goes down, the value of the fraction goes up.
Also if possible label your question the correct difficulty this is like middle school not college
The skeletal system is not responsible for which of the following?
Answer now
D. moving red blood cells around the body
3. It takes a Ferris wheel 1.5 minutes to complete one full rotation. If a ride lasts for 6 minutes, how many full rotations does the Ferris wheel make? O O T= 9 rotations T= = 4 rotations O Or = 7.5 rotations T = 4.5 rotations
Answer:
Four.
Step-by-step explanation:
6 divided by 1.5 is 4. We do that because if it takes 1.5 mins to make a full rotation and it takes 6 minutes to do blank rotations, the answer is 4 bc we either ti.es 1.5 by 4 to get 6, or do 6 divided by 1.5 to get 4. Sorry if that was confusing.
What is the answer
Three friends ate at a restaurant. They ordered nachos for $18.85 and jalapeno poppers. Each friend paid $9.98, not including sales tax or tip, which was one third of the total. Determine the cost of the jalapeno poppers.
The cost of the jalapeno poppers is $11.09 .
In the question ,
it is given that
Cost of the nachos = $18.85
amount paid by each friend = $9.98
amount paid by three friends = 9.98*3 = $29.94
let the cost of jalapeno poppers = $x
So according to the question
the total amount paid by three friends = cost of nachos + cost of jalapeno poppers
Substituting the values from above , in the equation we get
29.94 = 18.85 + x
simplifying further , we get
x = 29.94 - 18.85
x = 11.09
Therefore , the cost of the jalapeno poppers is $11.09 .
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please help me graph
Answer:
A
Step-by-step explanation:
See that the slope of the parabola changes at x=4
And left of x=4, the slope is positive, meaning the value is increasing (you can also see it directly from the graph)
Right of x=4, the slope is negative, meaning the value of the graph is decreasing. Thus the answer is A
Write and solve an equation for this problem. First represent the number of each item and the total cost for each item.
Kawan buys some protein bars at $0.80 each and bottled water at $0.90 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $52 in total, how many bottles of water and protein bars does he buy?
Let x = the number of protein bars
When he spends $52 in total, the number of bottles of water and protein bars that he buys will be 40 and 20 respectively.
How to calculate the equation?It should be noted that an equation is used to show the relationship between the variables.
In this case, Kawan buys some protein bars at $0.80 each and bottled water at $0.90 each for a group hike and he buys twice as many bottles of water as protein bars.
Let x = the number of protein bars
Table waters = 2x
Therefore, the equation will be:
0.8x + 0.9(2x) = 52
0.8x + 1.8x = 52
2.6x = 52
Divide
x = 52/2.6
x = 20
The number of proteins bars is 20.
The number of water will be:
= 2x.
= 2 × 20 = 40
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pls help me solve this with steps
The solution of the given inequality for the value of x, x ≥ 1/2.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. Both mathematical phrases, equations, and inequalities are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,<,≥,≤,≠ or indicate that the two expressions in inequality are not always equal.
Given Data
Equation
[tex]\frac{4x -7}{2}[/tex] ≥ 4.5
4x - 7 ≥ 9
4x≥2
x ≥ [tex]\frac{1}{2}[/tex]
For the value of x, x ≥ [tex]\frac{1}{2}[/tex]
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a segment drawn from the center of the circle to which letter creates a terminal side that forms a central angle of 2pi/3 radians?
2pi/3 radians=120 degrees
F is 90 degree.
j is 180 degree
midpoint of F and J is 150 degree.
H is 150 degree
Hence,
G is 120 degree
Find the axis of symmetry using the formula. X = -b/2a
x = 2
Explanation:f(x) = -2x² + 8x - 9
Comparing this function with f(x) = ax² + bx + c
a = -2, b = 8, c = -9
The axis of symmetry is given by the formula:
x = -b/2a
Substitute a = -2 and b = 8 into the formula:
[tex]\begin{gathered} x=\frac{-8}{2(-2)} \\ \\ x=\frac{-8}{-4} \\ \\ x=2 \end{gathered}[/tex]x = 2
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
A graph of a proportional relationship can be used to find any ratio in the proportional relationship when the graph passes through the origin.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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question is in box and you don’t need to show work if you don’t want to
ANSWER:
8 square meters
STEP-BY-STEP EXPLANATION:
To calculate the area of the sector, we must first calculate the area of the entire circle and then by means of a proportion, knowing that the entire area is 360° and the sector is 45°, we could determine the area we need.
Just like this:
[tex]\begin{gathered} A_c=\pi\cdot r^2 \\ \\ \text{ We replacing:} \\ \\ A_c=\pi\cdot8^2=64\pi \\ \\ \text{ Therefore, we calculate the value of the area of the sector as follows:} \\ \\ A_s=64\pi\cdot\frac{45\degree}{360\degree} \\ \\ A_s=8\pi\text{ square meter} \end{gathered}[/tex]The area of the sector is 8 square meters
The table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.
Which continent has a lower elevation than North America?
The continents that have a lower elevation than North America are Africa and Asia.
What is elevation?It should be noted that elevation simply had to do with the height above sea level of a particular thing. Any of numerous huge landmasses is referred to as a continent. Up to seven geographical regions are usually regarded as continents, based on convention rather than precise requirements.
A continent is one of the seven major land divisions on Earth. Asia, Africa, North America, South America, Antarctica, Europe, and Australia are the continents, in order of size.
In this case, the table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.
In the table, Africa has -512 and Asia had -1312. It should be noted that these are lower than in North America.
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Given the equation below, find the x and y−intercepts by completing the table.What is the problem with using these intercepts to graph the equation in #7?The ordered pair (x, y) you found in #7 is called the
In order to find the x-intercept we need to make y=0
[tex]-4x+2(0)=0[/tex]Then we isolate the x
[tex]-4x=0[/tex][tex]x=0[/tex]x y Ordered Pair type of intercept
0 0 (0,0) x-intercept
Now for the y-intercept we need to make x=0
[tex]-4(0)+2y=0[/tex]we isolate the y
[tex]2y=0[/tex][tex]y=0[/tex]0 0 (0,0) y-intercept
ANSWER
0 0 (0,0) x-intercept
Which of the following is equivalent to sin 37°?Group of answer choicescos 37°cos 53°sin 53°sin 63°
Recall that:
[tex]sin\theta=cos(90^{\circ}-\theta).[/tex]Therefore:
[tex]sin37^{\circ}=cos(90^{\circ}-37^{\circ}).[/tex]Simplifying the above result, we get:
[tex]sin37^{\circ}=cos53^{\circ}.[/tex]Answer: [tex]\begin{equation*} cos53^{\circ}. \end{equation*}[/tex]Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} The relation is not a function. The relation is a function
Based on the given ordered pairs, yes, the relation is a function.
What is a function?A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.
Based on the ordered pairs shown above, we can reasonably infer and logically deduce that these ordered pairs represent a function because the elements of the set of "x" are uniquely mapped to the elements of the set of "y" as shown below:
x y__
-2 ↔ 4
-1 ↔ 7
0 ↔ -6
5 ↔ 3
7 ↔ 5
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Rational Numbers - Part 1
Which statements about the opposite of -12 are true?
Select each correct answer.
The opposite of the opposite of -12 is -12.
0-12 and its opposite are on located on the same side of zero on a number line.
The opposite of -12 is -1/2
0-12 and its opposite are located the same distance from zero on a number line
The correct statement for the rational number is the opposite of the opposite of -12 is -12.
What is rational number?
Rational numbers are those numbers which include natural numbers, whole numbers as well as integers. And it is written in the form of a/b where a and b are integers. Sometimes, the values of the denominator is one then the given number is not fraction.
According to the question, rational number are those numbers which takes positive integers, negative integers as well as zero.
Therefore, on a number line, the opposite of (-12) is 12. And again the opposite of 12 is (-12). Therefore the first statement is correct.
Hence, the correct statement for the rational number is the opposite of the opposite of -12 is -12.
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I need help with this question.
Given:
There is a graph given in the question
Required:
We want to find the solution of the given graph
Explanation:
As we can see that, both lines are parallel so there is no chance for intersection
now if there is no intersection point means there is no solution
Final answer:
No solution