The table below shows some values of f(x) and g(x) for different values of x.
x f(x) = 9x + 7 g(x) = 5x
-2 -11
-1 -2
0 1
1 5
2
Complete the chart and determine the solution of the equation f(x) = g(x)?
A.) x = -1
B.) x = 0
C.) x = 2
D.) x = 25
Answers
Answer:
x = -1.75 makes f(x) = g(x)
Step-by-step explanation:
See the attached for a table. You will notice that for x=-1.75, the values of f(x) and g(x) are the same. That means x = -1.75 is the solution to f(x)=g(x).
Upon calculating the values for f(x) and g(x), it's determined that f(x) = g(x) when x = -7/4. The options provided do not include this answer, suggesting a possible typo in the question or answer choices.
Completing the Values and Finding the Solution for f(x) = g(x)
To complete the given table, we need to apply the functions f(x) = 9x + 7 and g(x) = 5x to the missing x values. For x = -2, g(x) equals -10 (since 5 * -2 = -10). For x = 0, f(x) is 7 (since 9 * 0 + 7 = 7), and for x = 2, f(x) equals 25 (since 9 * 2 + 7 = 25) and g(x) equals 10 (since 5 * 2 = 10).
To determine the solution for the equation f(x) = g(x), we set the two expressions equal to each other:
9x + 7 = 5x
By subtracting 5x from both sides, we get:
4x + 7 = 0
Now, subtracting 7 from both sides, we find:
4x = -7
Finally, by dividing both sides by 4, we get:
x = -7/4
None of the given options A, B, C, or D match x = -7/4, which might indicate there could be a typo in the question or answer choices.
Related Questions
A regular hexagon is shown.
What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.
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In a 30-60-90 triangle, the sides are is the ratio of:
[tex]x \: \\ x \sqrt{3} \\ and \: 2x[/tex]
where x is opposite the 30° and 2x is opposite the 90°
Since the base is 10 and the hypotenuse is 10, 1/2 that is 5 (the x), and so:
[tex]x \sqrt{3} = 5 \sqrt{3} = 8.66[/tex]
So rounded up, you apothem then is closest to D) 9 in.
The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .
What is the apothem of a regular polygon?The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.
It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.
The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.
Using Pythagoras Theorem
[tex]10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}[/tex]
AB = 8.66
So, rounded up, we get the apothem closest to D that is 9 in.
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Witch of the following is closest to 27.8 X 9.6 is it 280, 2800, 300, or 3000
Answers
Hope this helps and thank you for using Brainly!
John Gray bought a basic car for $32,750.00, with options that cost $375.00. There's a 6% sales tax in his state and a combined $50.00 license and registration fee. What was John's total cost
Answers
6% of that is $1,987.50 (33,125 x 0.06)
$1,987,50 + $33,125 + $50=
$35,162.50
Answer:
The total cost of the car be $35162.5 .
Step-by-step explanation:
As given
John Gray bought a basic car for $32,750.00, with options that cost $375.00.
Cost of the car = Car cost + Option cost
= $32750 + $375
= $33125
As given
There's a 6% sales tax in his state .
6% is written in the decimal form.
[tex]= \frac{6}{100}[/tex]
= 0.06
Sales tax price = 0.06 × 33125
= $ 1987.5
As given
A combined $50.00 license and registration fee.
Than
Total cost of the car = Cost of the car + Sales tax price + license and registration fee.
= $33125 + $ 1987.5 + $ 50
= $35162.5
Therefore the total cost of the car be $35162.5 .
Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars. His monthly salary is modeled by the function f(c) = 250c + 500. If Adam doesn't sell a car, how much money does he earn for the month?
Answers
Answer: 500
Step-by-step explanation:
Since, The monthly salary is modeled by the function,
f(c) = 250 c + 500.
According to the question,
Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars.
In the given function c is a variable.
Thus, c must show the number of cars.
Thus, the base pay must be free from any variable.
In the above expression 500 is free from the variable c therefore, 500 is the base pay of Adam.
⇒ f(c) is the total earning by Adam after selling a car.
If he Does not sell any car then c=0,
f(0) = 250×0+500 = 500
Therefore, if he does not sell any car then his earning is 500.
Twice the smallest of three consecutive odd integers is nine more than the largest. find the integers.
Answers
2x =9+ x+4 Twice the smallest is nine more than the largest
2x - x= 13
x= 13 the first
the second integer 15 the third 17
The required Integers are 13, 15, 17
What are the Integers?
Integers are the collection of whole numbers and negative numbers.
Given that twice the three consecutive odd Integers is nine more than the largest.
Let the numbers be x , x+2 , x+4
According to question
2x = 9+x+4
x = 13
Hence the Integers are 13, 15, 17
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The Garcias have $12,000 in a saving account. The bank pays 3.5% interest on saving accounts, compounded monthly. Find the balance after 3 years?
Answers
A=p (1+r/k)^kt
A the balance?
P present value 12000
R interest rate 0.035
K compounded monthly 12
T time 3years
A=12,000×(1+0.035÷12)^(12×3)
A=13,326.49
Hope it helps!
To find the balance after 3 years in a savings account with $12,000 and a 3.5% interest rate compounded monthly, we can use the formula for compound interest.
Explanation:To find the balance after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amountP is the principal amount (initial balance)r is the annual interest rate (as a decimal)n is the number of times interest is compounded per yeart is the number of yearsPlugging in the given values:
P = $12,000r = 0.035n = 12 (monthly compounding)t = 3 yearsThe formula gives us:
A = $12,000(1 + 0.035/12)^(12*3)
Calculating this expression will give us the balance after 3 years.
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Find the value of the variable.
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And x is 58
Describe how the variability of the x bar distribution changes as the sample size increases
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The standard deviation decreases and the sampling distribution becomes more normal as the sample size increases in x bar distribution.
The variability of the x bar distribution changes as the sample size increases. As the sample size increases, the standard deviation of the sampling distribution of the means will decrease, approaching the standard deviation of X. The sampling distribution of the mean becomes more normal as the sample size grows, showing less variability.
To make punch, Sophia mixes 2 liters of clear soda with 70 centiliters of cranberry juice and 236 milliliters of pineapple juice. How much punch does she have in total?
Answers
0.236 + 0.7= 0.936
Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substitution Property of Equality Subtraction Property of Equality
Answers
Answer:
Option 1 - Division Property of Equality
Step-by-step explanation:
Given : If [tex]4x=20[/tex], then x=5.
To find : Which property justifies this statement?
Solution :
The equation is [tex]4x=20[/tex]
To make variable separate we have to remove 4 which is in multiple of variable x.
So, We divide both side by 4,
Applying division property of equality,
We can divide both sides of an equation by the same number and preserve equality.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Therefore, The property justifies the statement is 'Division Property of Equality'.
So, Option 1 is correct.
Which inequality describes all the solutions to 5(3 - x) < -2x + 6?
A) x < -9
B) x > 3
C) x > 7
Answers
The inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given expression 5(3 - x) < -2x + 6 will be solved as below:-
5(3 - x) < -2x + 6
15 - 5x < -2x + 6
-5x + 2x < -15 + 6
-3x < -9
x > 3
Therefore, the inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
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What is the slope of the line perpendicular to the line represented by the equation 2x+4y=12?
Answers
If sinθ = -1/2 and θ is in Quadrant III, then tanθ = _____.
Answers
Answer: [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Step-by-step explanation: Given that
[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.
We are to find the value of [tex]\tan \theta.[/tex]
We will be using the following trigonometric identities:
[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]
We have
[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]
Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.
Thus,
[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]
Two buses leave towns 1631km apart at the same time and travel toward each other. one bus travels 17 /kmh slower than the other. if they meet in 7 hours, what is the rate of each bus?
Answers
the first bus travels a total of 7x km, the second bus travels 7(x-17)km, together they travel the total distance of 1631 km
7x + 7(x-17) =1631
7x + 7x -119 =1631
14x=1750
x=125
x-17=108
Kim drives 378 miles and uses 18 gallons of gasoline. At that rate, how many miles can she go on 24 gallons of gas?
Answers
That equals 21
Then do 21 * 24
That equals 504
Conclusion: It would take 504 miles to go on for 24 gallons of gas.
Tristan jogs a route that is 7/10 mile. If he wants to jog between 2 and 3 miles, how many times should he plan to run the route? Circle the letter for all that apply.
A. 2 times
B 3 times
C. 4 times
D. 5 times
Answers
Answer:
B 3 times
C. 4 times
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)
Find the difference.
5wx2 − 2wx2
Answers
=3wx2
hope it helps
Marcia can make 5 candles in an hour. Kevin can make only 4 candles in an hour, but he already has 7 completed candles. Explain to Marcia how she can use a system of equations to determine when she will have the same number of candles as Kevin. Use complete sentences.
Answers
k = kevin's total amount of candles
h = amount of hours
so in 1hr she makes 5(1), in 2hrs she makes 5(2) and 3 she makes 5(3), in "h" hours she makes 5h.
kevin makes in 1hr 4(1), in 2hrs 4(2) and 3hrs 4(3), in "h" hours 4h. But kevin already has 7 candles done from the day before, so the 4h is really additional to his 7 candles.
[tex]\bf \begin{cases} m=5h\\\\ k=4h+7 \end{cases}\impliedby \textit{when are they equal?}\qquad \stackrel{m}{5h}~~=~~\stackrel{k}{4h+7}\\\\ -------------------------------\\\\ 5h=4h+7\implies h=7[/tex]
Which of the following equations represents the perpendicular bisector of WX graphed below?
Thank you! :)
Answers
First, we find the midpoint M using the midpoint formula:
[tex]\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).[/tex]
Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.
The slope of WX is [tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5} [/tex].
Thus, the slope n of the perpendicular line is [tex]\displaystyle{ \frac{5}{3} [/tex].
The equation of the line with slope [tex]\displaystyle{ n= \frac{5}{3} [/tex] containing the point M(0, -1) is given by:
[tex]\displaystyle{ y-(-1)=\frac{5}{3}(x-0)[/tex]
[tex]\displaystyle{ y+1= \frac{5}{3}x[/tex]
[tex]\displaystyle{ 3y+3=5x[/tex]
[tex]\displaystyle{ 5x-3y-3=0 [/tex]
Answer: 5x-3y-3=0
HELP!!! I GIVE LOTS OF POINTS!! THE ANSWER IS NOT 3!!!!!!!!
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
Answers
the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6
Write a quadratic function (f) whose zeros are −8 and 2.
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How many students had a shoe size greater than the mean shoe size?
Answers
compute the following: 8C3 5C2
Answers
5C2=5*4/2*1=10
56×10= 560 so the answer is 560
2. For the circle with equation , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius and diameter of the circle?
(c) Graph the circle.
Answers
You have to recognize this circular equation form.
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
------------------------------------------------
What are the coordinates of the center?
Ans: (2,-3)
(B) The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.
(C) Realize that the circle is centered at the origin (no h and v) and place this point there.Calculate the radius by solving for r. Set r-squared = 16. ...Plot the radius points on the coordinate plane. ...Connect the dots to graph the circle using a smooth, round curve.
The sum of two right angles always, sometimes, never results in a straight angle. Justify answer
Answers
I hope that helps u
Adding two right angles, each being 90 degrees, always results in a straight angle, which is 180 degrees, so this is always true.
Explanation:The sum of two right angles always results in a straight angle. This can be justified with a basic understanding of angles in a flat plane. A right angle is 90 degrees and a straight angle is 180 degrees. So, if you add two right angles together (90 + 90), you get 180, which is the measure of a straight angle. Hence, this is always true, regardless of the vectors or other elements you are working with. It's also important to note that in broader geometric terms, this statement is also always true: two angles that add up to form a straight line (180 degrees) are referred to as supplementary angles.
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14(z+3)=14z+21
Please state if it has no solutions, one solution, or infinitely many solutions.
Answers
Brainliest for a math answer
Answers
question 6- is 9
question 7-is 4
question 8-is 21
Question 9-is 2
question 10-not sure sorry :(
Tell me if your right ;)
We know b is 7 and a is 2 so plug it in
7 - 2= 5
5=5
The answer is 5
The second question is b / a = ___
We know b is 18 and a is 2 so plug it in
18/2=9
9=9
The answer is 9
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8
x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
Answers
2(-4) + 0 = -8
-8 + 0 = -8
-8 = -8
x - y = -4 (-4, 0)
-4 - 0 = -4
-4 = -4
the ordered pair (-4, 0) is a solution to the system because it makes both equations true.
The length of each side of a square prism is ten ft
Answers
A variable is: an instruction for the compiler a location in memory where a value can be stored a description of a value (such as a number or character) none of the above.
Answers
Final answer:
A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.
Explanation:
A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.
In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.