The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).
Answers
There are two solutions because the two functions cross each other twice.
The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
We have a graphical representation of two functions f(x) and g(x) and where they intersect.
We have to solve the equation f(x) = g(x)
Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.
In the question given - We have a straight line and a parabola -
Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).
Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
Alternative Method -
The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]
The solution can be calculated by equating both of the above expressions and solving them.
mx + c = [tex]\sqrt{4ax}[/tex]
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Related Questions
An adult ticket for hypnotist's show cost $15. A children's ticket for the hypnotist's show cost $9. The number of adult tickets sold 5 more times the number of children's ticket sold. A total of $1512 is taken in for ticket sales. How many of each type of ticket is sold.
1. 21 adult tickets and 110 children's tickets
2. 110 adult tickets and 22 children's tickets
3. 10 adult tickets and 90 children's tickets
4. 10 adult tickets and 18 children's tickets
Answers
because number 2 and 4 are under $1512 and 3 is over
Answer:
The answer is B, or the second one.
90 Adult tickets and 18 Children's tickets
Step-by-step explanation:
(90 x 15) + (18 x 9)
evaluate - 31 - 8 + 31
Answers
Answer:
-8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
-31 - 8 + 31
Step 2: Evaluate
Subtract: -39 + 31Add: -8Evaluate the expression.
| 31 | + | –5 |
Answers
Answer:
36
Step-by-step explanation:
The answer is the absolute value of 31 + (-5)
So it is 36
what is the y intercept y=-4x-5
Answers
Answer:
The y-intercept y = 4x - 5 is (0,-5).
Step-by-step explanation:
hope this helps
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Kevin Fast pulled a CC- 177 Globemaster airplane 8.8m. he plane weighed 188 tons. How many pounds did the lane weigh?
Answers
Answer:
376000 pounds
Step-by-step explanation:
What's required of this question is to convert the given weight of plane from tons to pounds
Given
[tex]Weight = 188\ tons[/tex]
Required
Get pounds equivalent
From standard unit of measurements
[tex]1\ ton = 2000\ pounds[/tex]
Multiply both sides by 188
[tex]188 * 1\ ton = 188 * 2000\ pounds[/tex]
[tex]188\ tons = 376000\ pounds[/tex]
Hence, the weight of the plane in pounds is 376000
Jennifer’s mom is putting a basketball hoop on the garage. The garage door is 8 feet high. There is 7 feet of wall between the top of the garage door to the garage roof. How far down from the garage roof should the hoop be placed so that it is 10 feet above the ground?
a) 3
b) 5
c) 4
d) 2
Answers
Answer:
B
Step-by-step explanation:
A number with no variable attached is called a what
Answers
Answer:
constants
Step-by-step explanation:
That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value.
The term or number with no variable attached is called a constant as in the polynomial or expression.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
A number consists of the expression with no variable.
As we know, the expression is a combination of numbers, variables, and operators.
If we take an example of the polynomial.
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm p(x) = a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
Here a₀ is a constant because the term a₀ has no variables.
Thus, the term or number with no variable attached is called a constant as in the polynomial or expression and the constant value does not change.
Learn more about the expression here:
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5
2
A line passes through the point (-10, 8) and has a slope of
Answers
Answer:
you need more than one point to find the slope of a line?
Step-by-step explanation:
During a thunderstorm, 4
inches of rain fell in 2 1/2
hours. What was the rate of rainfall in inches per hour?
Answers
Answer: 1.6 in per hour
Answer:
hourly rate.
Step-by-step explanation:
As others have noted, it is a simple mathematical division problem (4/2.5) and the average is 1.6 inches per hour.
However, if this is for sizing civil works such as culverts or plumbing storm water drainage systems to mitigate flooding, the highest rate per hour must be known and usually the highest ten minutes rainfall rate expressed as an hourly rate.
For example, if 4.0 inches fell over that 2.5 hours, nothing says that a rain band did not dump 3 inches in the first hour, (3 inches per hour cumulative) or 0.75 inches in a ten minute period (4.5 inches per hour rate), with the remainder of the storm tapering off to lesser rates. So the average is correct, but the peak hour is much more important for practical purposes.
help asap
As x + 0, y →-00
The y-intercept of the graph is -1.
The graph has no relative minimum value.
the graph has a maximum value at x = 5.
The graph has a relative maximum value at x = -3.
As x + -00, y → -
Answers
Answer:
e
Step-by-step explanation:
Here I will be giving a Brainiest to a good answer :D
Answers
Answer:
A. F
B. D
C. C
D. E
E. G
F. G
G. D
Step-by-step explanation:
Answer: A. 9/4
C. -1.75
D. 1.75
E -2
F-1
-2 1/2
Step-by-step explanation:
Two airplanes leave the same airport heading different directions. After 2 hours, one airplane has traveled 710 miles and the other has traveled 640 miles. Describe the range of distances that represents how far apart the two airplanes can be at this time
Answers
Answer:
Step-by-step explanation:
710 + 640 = 1350m
The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?
Answers
Answer:
25
Step-by-step explanation:
45 times 5 = 225
225 divided by 9 = 25
Answer:
25
Step-by-step explanation:
5:9 and x:45
45*5/9 which is 25
Hope this helps!
Bill and Ted are each saving money for a trip to Europe. Bill started with $75 and saves an additional $15 per week. Ted began with $120 and saves an additional $10 per week. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.
Answers
Answer:
9 weeksStep-by-step explanation:
After x weeks Bill will save money:
75 + 15xAnd Ted will save:
120 + 10xSince they save same amount, we have equation:
75 + 15x = 120 + 10x15x - 10x = 120 - 755x = 45x = 45/5x = 9 weeksWhat is the value of 4.32 times 10?
Answers
Answer:
43.2
Step-by-step explanation:
4.32 x 10 = 43.2
Answer:
easy
4.320
Step-by-step explanation:
Jkgdgdkhhgkdksytsktsykkusutskfkxh
Answers
Answer:
39% , 0.39 , 39/100
Step-by-step explanation:
I thought your randomness of letters was your question lol. Hope this helps though!
I'm not understanding
Answers
Answer:
D. x = 3
Step-by-step explanation:
We would like to find out for what value of x does f(x) = g(x). This is essentially the same as asking us to find the x-value for which f(x) = k, where k is some number, and g(x) = k, as well.
Looking at the two tables provided, we notice that when x = 3, both f(x) and g(x) equal -2. So, the answer is D.
Can some one help me please god bless you
25 points
Answers
Х
Y
K
6
un 00
5
9
??
K= Y/X
Y = K(X). K=. Y=?????
Answers
Answer:
Yep
Step-by-step explanation:
Find the slope, if it exists, of the line containing the pair of points.
(8,-6) and (3,9)
Answers
Answer:
The slope is -3
Step-by-step explanation:
the equation for finding the slope between two different points is:
M= (y2-y1)/(x2-x1)
Or in other words the change in y over the change in x.
M= (9+6)/(3-8) = 15/-5 = -3.
(sidenote: I added 9 and 6 for the change in y because you cannot subtract a negative number. Instead you have to add it.)
Write two numbers that multiply to the value on top and add to the value on bottom.
-14
Х
+
13
Answers
#2: -1
Explanation:
14 * -1 = -14
14 + (-1) = 13
GIVING 20 POINTS! PLEASE HELP!
Answers
Answer:
Option C
Step-by-step explanation:
x + 6) 3x⁴ + 20x³ + 14x² + 17x + 30 (3x³ + 2x²+ 2x + 5
3x⁴ + 18x³
2x³ + 14x²
2x³ + 12x²
2x² + 17x
2x² + 12x
5x + 30
5x + 30
0
Therefore, quotient is (3x³ + 2x²+ 2x + 5).
Option C is the correct option.
answer helppppp plsss i’m on quizzzz
Answers
The polygons are similar. Find the value of the variable. Please HELPPPPPP!!!!
Answers
Answer:
C)
Step-by-step explanation:
Well, we know for the first polygon that the short side of the rectangle is 3 and for the second polygon the short side is 6, this means that for the second polygon, all sides will be double of the other side. 2 times the long side of the first rectangle is 18, this is why x = 18.
Hope this Helps!!! :)
Let me know in the comments if the answer was perfect or if I should change anything!
Answer:
C
Step-by-step explanation:
Because since 3 divided by 9 is 3 u have to double up the amount by 3 and that will be 18
what is the slope of (0,0) , (3,3)
Answers
Answer:
The slope is 1
Step-by-step explanation:
[tex]\frac{3-0}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Two cups of flour make 23 batch of bread. How many cups of flour make 1 batch?
Answers
PLZ HELP ME I BEGG YOU
Answers
I- JUST NEED THE ANSWERS TO THIS QUESTION
Answers
Answer:
Undefined
Step-by-step explanation:
James and Eric each mix 6 pitchers of lemonade. James makes 26 fluid Ounces of lemonade per pitcher, and Eric makes 32 fluid Ounces of lemonade per pitcher. They combine their lemonade and pour all of it into glasses. They fill as many glasses as possible with 8 fluid Ounces each. They pour the remaining lemonade into the last glass.
Answers
The number of fluid ounces of lemonade made by James and Eric is a
multiple of the number pitchers mixed.
Possible responses are as follows;The number of glasses filled = 43 glassesThe volume of lemonade in the last glass = 8 fluid ouncesReasons for arriving at the above responses:Given and derived parameters;The number of pitchers James and Eric mix = 6 pitchers each
Number of fluid ounces of lemonade James makes per pitcher = 26 fluid Ounces
Volume of lemonade Eric makes per pitcher = 32 fluid ounces
Solution:Volume of lemonade James makes = 26 fluid Ounce × 6 = 156 fluid Ounces
Volume of lemonade Eric makes = 32 fluid ounces × 6 = 192 fluid Ounces
Total volume of lemonade made by James and Eric = (156 + 192) fluid Ounces = 344 fluid ounces
Volume of lemonade per glass = 8 Ounces
Number of glasses filled = 344 fluid Ounces ÷ 8 Ounces/glass = 43 glasses
Therefore, given that the number of glasses of 8 ounces of lemonade that can be filled using the 344 fluid ounces is exactly 43 glasses, we have;
The last glass is the 43rd glassVolume of lemonade in the last glass is 8 fluid ouncesLearn more about division in arithmetic here:
https://brainly.com/question/3060423
https://brainly.com/question/10910164
How many terms are in this expression?,,,, -2x + 3y - 4
Answers
Hope that helps!