List the steps that should be used to solve the equation f(x) = g(x) by graphing when f(x) = (1/2)² - 3 and g(x) = 3x + 5?
* So far I got to f(x) = (1/2)² - 3x - 8 = 0 (what is the next step and does this problem require the use of logarithms?)
Answers
value of x is: [tex]x=\frac{-31}{12}[/tex]
Step-by-step explanation:
We need to solve the equation f(x)=g(x)
where [tex]f(x)=(\frac{1}{2})^2-3[/tex]
and [tex]g(x) = 3x + 5[/tex]
Solving to find f(x)=g(x)
Putting values of f(x) and g(x)
[tex]f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}[/tex]
So, value of x is: [tex]x=\frac{-31}{12}[/tex]
The graph will be a straight line x= -2.58 or x = -31/12
Keywords: Composition of Functions
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Related Questions
The graph of a function, f(x), is plotted on the coordinate plane. Select the function that would move the graph of the function to the right of the coordinate plane.
a.f(x+6)
b.f(x)+4
c.f(x-3)+1
d.f(x)-3
Answers
Correct option:
c.f(x-3)+1
Explanation:From the options we have either vertical or horizontal shift. So, for this type of transformation we have:
For any real positive number [tex]c[/tex], vertical and horizontal shift in the graph [tex]y=f(x)[/tex] are expressed as follows:
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
From these rules, we know that:
[tex]f(x-3)+1[/tex]
would move the graph of the function to the right of the coordinate plane because of [tex]f(x-3)[/tex]. In other words, the transformation is as follows:
[tex]f(x-3)+1[/tex] shifts the graph of [tex]f(x)[/tex] three units to the right and one unit up
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A portion of a daycare has been set aside for toddlers under 2. The dimensions are shown. A scale drawing of the room is 1.5 cm tall. How wide is the scale drawing?
Answers
Answer:
2.4 cm.
Step-by-step explanation:
See the given diagram of two similar triangles one with actual dimensions and the other drawn on paper with a certain scale.
The ratio of corresponding sides of two similar triangles is always the same.
Now, 1.5 cm on the drawing is equivalent to 2.5 m i.e. 250 cm. in actual dimension.
So, 4 m i.e. 400 cm in actual dimension will be equivalent to [tex]\frac{1.5}{250} \times 400 = 2.4[/tex] cm. in the drawing. (Answer)
Six friends went out to dinner. Each person ordered the same meal, which was $15.85. The friends left a combine tip of $14. What was the total of the bill and the tip?
Answers
Answer:
$77.40
Step-by-step explanation:
The scatterplot shows the highway miles per gallon and city miles per gallon for 8 different car models.
Based on the scatterplot, what is the best prediction for city MPG if the highway MPG is 40?
A) 20
B) 35
C) 45
D) 50
Answers
Answer:
The best prediction will be B) 35
Step-by-step explanation:
By looking at the scatterplot ,
we can see that it the City MPG vs Highway MPG approximately falls on a straight line.
we can either find the slope of it ( which might be a little out of syllabus ) or we can extend the line connecting the maximum number of points.
When we do so, We get a line as attached in the diagram.
And we extend it.
From the graph attached we find that the value of City MPG falls somewhere in between the lines of 30 and 35 ( though this is just and approximation).
thus the more appropriate answer would be : 35
It takes b minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 3 same-size bathtubs?
Write your answer as an expression.
Answers
Answer:
3b
Step-by-step explanation:
Since it takes b minutes to fill one bathtub, then it will take 3 times b minutes to fill all three bathtubs.
Answer:
3 times b
Step-by-step explanation:
The sum of two numbers is 89. Three times the smaller
number is 71 more than the larger. Find the numbers.
Answers
Answer:
The numbers are 40 and 49
Step-by-step explanation:
Smaller number = x
Larger number = y
Let's write our system of equations:
x + y = 89
3x = y + 71
***************************
x = 89 - y
Substituting x in the 2nd equation and solving for y:
3 (89 - y) = y + 71
267 - 3y = y + 71
-3y - y = 71 - 267 (Like terms)
-4y = - 196
y = -196/-4
y = 49
Solving for x in the 1st equation:
x + y = 89
x + 49 = 89
x = 89 - 49
x = 40
The numbers are 40 and 49
find the value of x to the nearest tenth
Answers
Answer:
20.8
Step-by-step explanation:
Using Pythagorean theorem, you can find 1/2 of x.
12²= 6² +1/2x²
From this we find 1/2 x is ≈ 10.4
Then x itself would be 2 times that, resulting in 20.8, that is your answer
-2.2-(-4x-2)=-(-x-3.1)
Answers
Answer: x=1.1
Step-by-step explanation:
-2.2 - (-4x - 2) = - (-x - 3.1)
-2.2 + 4x + 2 = x + 3.1
-0.2 + 4x = x + 3.1
+0.2 + 0.2
4x = x + 3.3
-x -x
3x = 3.3
/3 /3
x = 1.1
hope this helps!
Point D (-1,5) is reflected across the x-axis which statements about D are true
Answers
Answer:
When a point is reflected across the x axis, it has the same x axis but the y axis is multiplied by -1. Think about the x axis as a mirror and the point is projected across the x axis.
Hence the x coordinate is -1 and the y coordinate is -5.
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
the x coordinate is -1
The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .
What is the equation of the circle in standard form?
You don't have to give me the answer, but at least please help me understand what it is that I need to be looking for in order to solve this problem (step-by-step if it's possible), I'm stuck.
Answers
Answer:
(x + 2)² + (y + 5)² = 25
Step-by-step explanation:
The circle is tangent to the x-axis at (-2, 0). This means the center of the circle must be directly above or below this point. So the x-coordinate of the center is -2.
Since the center of the circle is on the line y = 3x + 1, we can find the y-coordinate:
y = 3(-2) + 1
y = -5
The center of the circle is (-2, -5). The distance between the center and the point (-2, 0) is 5 units. This is the radius of the circle.
We can now write the equation of the circle:
(x − h)² + (y − k)² = r²
(x + 2)² + (y + 5)² = 25
Graph:
desmos.com/calculator/wzionolfli
Th equation of the circle will be (x + 2)² + (y + 5)² = 25.
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
At, the circle is perpendicular to the x-axis (-2, 0). Therefore, the circle's centre must be located directly above or below this point. Therefore, the centre's x-coordinate is -2.
We can determine the y-coordinate because the circle's centre lies on the line y = 3x + 1:
y = 3(-2) + 1
y = -5
The circle's nucleus is (-2, -5). The centre is located 5 units away from the point (-2, 0). This is the circle's radius.
We can now write the equation of the circle:
(x − h)² + (y − k)² = r²
(x + 2)² + (y + 5)² = 25
Therefore, the equation of the circle will be (x + 2)² + (y + 5)² = 25.
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Every time Liliana bakes a batch of brownies,
she uses 3/4 cup of chocolate. If she has 12/8
cup(s) of chocolate remaining, how many
batches of brownies can Liliana make? Input
your answer as a whole number.
Answers
Answer:
2
Step-by-step explanation:
12/8 is equal to 6/4.
6 divided by 3 is 2.
Answer:
2 batches of brownies
Step-by-step explanation:
3/4 = (3x2)/(4x2) = 6/8
(12/8) / (6/8) =
(12/8) x (8/6) =
12/6 =
2
Which of the following pairs are alternate interior angles?
A.6 and 7
B.2 and 7
C.5 and 2
D.5 and 4
Answers
EFGH is a parallelogram. Find the measure of FG.
Answers
Answer:
FG = 47
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent, thus
EH = FG, that is
5z - 18 = 3z + 8 ( subtract 3z from both sides )
2z - 18 = 8 ( add 18 to both sides )
2z = 26 ( divide both sides by 2 )
z = 13
Hence
FG = 3z + 8 = (3 × 13) + 8 = 39 + 8 = 47
Based on the property of a parallelogram, the measure of FG is: 47.
Opposite Sides of a ParallelogramBased on the properties of a parallelogram, the opposite sides of a parallelogram are equal in length.
Therefore:
EH = FG
Substitute5z - 18 = 3z + 8
Combine like terms5z - 3z = 18 + 8
2z = 26
Divide both sides by 2z = 13
FG = 3z + 8
Plug in the value of zFG = 3(13) + 8
FG = 47
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Four more than twice a number is less than negative twelve. Find all numbers that make this statement true.
Answers
Answer:
x<-8
Step-by-step explanation:
four more than twice a number = 4+2X
is less than negative twelve = <-12
4+2X<-12
(4-4)+2X< -12-4
2x<-16
X<-8
To find the numbers that make the statement true, we need to solve the equation 2x + 4 < -12 for x. Any number less than -8 will make the statement true.
Explanation:To find the numbers that make the statement true, we need to translate the given sentence into a mathematical equation. Let's denote the unknown number as 'x'. The sentence 'Four more than twice a number is less than negative twelve' can be written as 2x + 4 < -12. Now, we can solve this equation for x:
Subtracting 4 from both sides, we get 2x < -16.
Dividing both sides by 2, we have x < -8.
Therefore, any number less than -8 will make the statement true.
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Help me with A and B. And gave me the answer and how you got to the answer.
Answers
Answer:
the answer is 12m + 4
Step-by-step explanation:
you do the distributive property which is 3*2m and then 3*4 and you get 6m+12 and then you do it again which you do 2*3m and then 2*-4 and you get 6m-8 and then you get 6m+12+6m-8 and you just add your like terms to get 12+4
hope this helped
in a group of 84 kids 3/7 brought their lunches of those who bought their lunches 9 got a slice of pizza. what fraction of the students who bought their lunches got a slice of pizza?
Answers
Answer:
3/16
Step-by-step explanation:
4/7 of 84 = 48 kids
9/48 = 3/16
Answer:
9/36=1/4
Step-by-step explanation:
3/7x84=36
Ans: 9/36=1/4
what is 2/9+1/3= i need it for for my homework
Answers
Answer:
5/9
Step-by-step explanation:
Answer:
5/9
Step-by-step explanation:
Now we need to make our denominators match.
9 goes into 3 evenly, so we only need to multiply one term to get a common denominator.
Multiply 1 by 3, and get 3, then we multiply 3 by 3 and get 9.
Since our denominators match, we can add the numerators.
2 + 3 = 5
That gives us the sum, which is
5/9
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! Here's the final answer to 2/9 + 1/3
Alicia already spent $8.25 of her paycheck. If this was 15% of her paycheck, how much was she paid?
Answers
Answer:
She was paid $55.
Step-by-step explanation:
15%=0.15
8.25/0.15=55
Answer:
She was paid $55.
Step-by-step explanation:
15%=0.15
8.25/0.15=55
Solve each system of equations algebraically. y=x+5, y=6
Answers
Answer:
x = 1
Step-by-step explanation:
y = 6
Substitute this into y = x + 5
6 = x + 5
1 = x
Answer:
x=1, y=6. (1, 6).
Step-by-step explanation:
y=x+5
y=6
---------
x+5=6
x=6-5
x=1
A class is going on a trip to a museum. It costs $750 to rent a bus. Each ticket to the museum costs $12 Write an algebraic expression that represents the cost of the trip for people. Then evaluate this expression for 37
people
Answers
The total cost of trip for 37 people will be $1194.
Step-by-step explanation:
Given,
Rent of bus = $750
Cost of one ticket = $12
Let,
x be the number of people.
T be the total cost of the trip for people.
According to given statement;
Total cost = Rent of bus + (Cost of one ticket * number of people)
[tex]T=750+12x[/tex]
For 37 people, x=37
[tex]T=750+12(37)\\T=750+444\\T=\$1194[/tex]
The total cost of trip for 37 people will be $1194.
Keywords: linear expression, addition
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Which of the following digits might composite numbers greater than 10 have in the ones place? Select all that apply.
1
2
3
4
Answers
The digits which a composite number greater than 10 might have include; 1, 2 ,3 and 4.
According to the question;
We are required to determine which of the digits a composite number greater than 10 might have in the ones place.The number 10 has two place values namely;
1 is in the tens place0 is in the ones place.In essence, any composite number greater than 10 can have either of 1, 2, 3 and 4 in the ones place.
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A 12 pound turkey takes about 180 minutes to cook. How many hours would it take to cook a 20 pound turkey?
Answers
These are ratios, which are technically equal to each other. So, you can set up the problem like this:
12/180=20/x
180*20=3600
3600/12=300
So, it would take 300 minutes.
The required time consumed to cook 20 pounds of turkey is 300 minutes.
Given that,
A 12-pound turkey takes about 180 minutes to cook.
To determine how many hours would it take to cook a 20-pound turkey.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
A 12-pound turkey takes about 180 minutes to cook.
rate of cooking = 180 / 12 = 15 minute per pound of turkey
Time consumed to cook 20 pounds of turkey = 20 * 15 = 300 minutes
Thus, the required time consumed to cook 20 pounds of turkey is 300 minutes.
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How do we do y=mxtb?
Answers
Answer:
Step-by-step explanation:
y=mx+b is the formula that we use in Algebra I for determining the slope intercept equation so we can graph the function.
A bag contains 10 red, 9 white, 8 yellow and 2 blue marbles. How many marbles must be taken out from the bag so that there will be 4 marbles of the same colour?
Answers
Answer:25
Step-by-step explanation:
10 plus 9+4+2 will give you 21 and it will have 4 yellow ones left
Which action describes an aspect of technological design?
O building a telescope to look deeper into space
O creating a collection of mosquitoes that cause disease
o observing Doppler radar as a storm approaches
O designing an experiment to measure the heat of a volcano
Answers
Answer: A)
Step-by-step explanation: This is correct because a telescope is a piece of technology use to look further into space
Number 31 please help
Answers
===============================================
Explanation:
Going from design 1 to design 2, we add on 3 triangles. This is because the triangle in design 1 has 3 exterior sides to form its perimeter.
Going from design 2 to design 3, we add on 6 triangles
Going from design 3 to design 4, we add on 9 triangles
------------
Note the pattern of triangles we add on each round: 3, 6, 9
This is the set of multiples of 3. Each number is increased by 3. The next design will have us add 12 triangles to the exterior of design 4. Then the next round has us add on 15 triangles to the outside.
-------------
Going from design 4 to design 5, we add on 12 triangles
Going from design 5 to design 6, we add on 15 triangles
--------------
Check out the attached image below for what designs 5 and 6 will look like. Note the use of color coding to help see how the figures build up from step to step. There are 15 orange triangles along the outside in design 6.
Noah started to solve the equation –4.6p – 6.3p + 3.9 = –9.18 below.
Combine like terms: –10.9p + 3.9 = –9.18
Apply the next steps to solve the equation. What is the solution?
Answers
Answer: p = 1.2
Step-by-step explanation:
Answer: p=1.2
Step-by-step explanation:
If stanley bought a sandwich, that cost $3 with 50% off. what was the original price?
Answers
Answer:
The answer is 6$. Half of 6$ is 3$
Answer:
$6
Step-by-step explanation:
Let the original price be =Y,
50% of the original = Y×50/100 = 0.5Y
∴ 50% off =Y - 0.5Y = 3
0.5Y=3
divide both side by the co-efficient 0f Y i.e 0.5
⇒0.5Y/0.5=3/0.5
⇒Y= $6
Barry's house has 4 windows that he is planning to replace to improve energy efficiency. The width of each window is between 3.3 and 3.7 ft, and the length of each window is between 3.7 and 4.1 ft. Barry estimates the area of all 4 windows to be 62 sq ft. Is this a reasonable estimate?
A.
No, the estimate should be lower.
B.
No, the estimate should be higher.
C.
Yes, the estimate given is reasonable.
Answers
Answer:
B)No, the estimate should be higher
Answer:
no the estimate should be lower
Which of the following statement are false?
A) 5/9 can be shown as equivalent to an improper fraction.
B) 8/2 can be simplified as a whole number.
C) 1 1/3 can be shown as equivalent to an improper fraction.
D) 6/7 can be shown as equivalent to a proper fraction.
Answers
Answer:
A
Step-by-step explanation:
Because 5/9 is an example of a proper fraction. In order to be an improper fraction, the numerator needs to be larger than the denominator. 8/2 can be simplified as 4 and 4 is a whole number. 11/3=3 2/3 is an example of improper fraction. 6/7, again, this is another example of a proper fraction.