[tex]f(x) = 6x+2[/tex]
A.
To evaluate f(8), we substitute x with 8 in our expression.
[tex]f(8) = 6*8 + 2\\f(8) = 48 +2\\f(8) = 50[/tex]
Answer: f(8) = 50
B.
To evaluate f(x+6), we do the same but substitute x with x+6 instead.
[tex]f(x+6) = 6(x+6) + 2[/tex]
Expand the parenthesis by multiplying 6 with x and 6.
[tex]f(x+6) = 6x + 6*6 + 2\\f(x+6) = 6x+36+2\\f(x+6) = 6x+38[/tex]
Answer: f(x+6) = 6x + 38
C.
Again, we're doing the same thing, just substituting x with -x.
[tex]f(-x) = 6 * (-x) + 2\\ f(-x)=-6x+2[/tex]
Answer: f(-x) = -6x+2
Answer:
_____________________________________________
[tex] \longmapsto \: f(x) = 6x + 2[/tex]
_____________________________________________
A. [tex]f(8) = 6(8) + 2 = 48 + 2 = \boxed{ 50}✓[/tex]
_____________________________________________
B. [tex]f(x + 6) = 6(x + 6) + 2 \\ = 6x + 36 + 2 \\ = \boxed{ 6x + 38}✓[/tex]
_____________________________________________
C. [tex]f( - x) = 6( - x) + 2 = \boxed{ - 6x + 2}✓[/tex]
_____________________________________________
7) A real number that is less than zero. These represent opposites.
Answer:
A negative number
Step-by-step explanation:
I know this is right. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left.In the context of negative numbers, a number that is greater than zero is referred to as positive. Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. +3 denotes a positive three.
Order the values from
least to greatest:
1-1, 1-2, -3,-4
Given the function y= 2x if x>0 x−3 if x≤0 . Find its values for x=1; 3; 0; −2. Answer: If x = 1, then y = . If x = 3, then y = . If x = 0, then y = . If x = −2, then y = .
Answer:
Step-by-step explanation:
Given the function y= 2x if x>0 and x−3 if x≤0, to find the value of the function for x = 1, we will substitute x = 1 into the function y = 2x since x>0 at that point.
If x = 1;
y = 2(1)
y = 2
Hence when x = 1, y = 2
If x = 3, we will still use the function y = 2x since 3 is still grater than 0 satisfying the condition x>0.
y = 2(3)
y = 6
Hence when x = 3, y = 6
when x = 0, since x is zero, we will substitute x = 0 into the function x-3 because x≤0 at this point.
If y = x-3
y = 0-3
y = -3
Hence when x = 0, y = -3
when x = -2, we will substitute x = 0 into the function x-3 because -2 is also less than zero
If y = x-3 for x≤0
y = -2-3
y = -5
Hence when x = -2, y = -5
The aspect ratio of a TV screen is the ratio of the width to the height of the image. A regular TV has an aspect ratio of 16: 9. Find the height and width of a 51-inch TV screen to the nearest tenth of an inch. (The measure given is the length of the diagonal across the screen.)
Answer:
Width = 44.45 inches
Height = 25.00 inches
Step-by-step explanation:
(16x)^2 + (9x)^2 = 51^2
256x^2 + 81x^2 = 2601
337x^2 = 2601
x^2 = 7.718
x = 2.778
Width = 44.45 inches
Height = 25.00 inches
I think this is right
The width and height of the given TV screen will be 44.45 inches and 25.00 inches.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
The length of any TV is measured diagonally.
So,
Diagonal = 51 inches
Now the ratio is ;
W/H = 16 / 9
Let's say both are fractions of x
So,
Width = 16x , Height = 9x
By Pythagoras theorem,
(16x)² + (9x)² = 51²
256x² + 81x² = 2601
337x² = 2601
x² = 7.718
x = 2.778
So width = 16(2.778) = 44.45 inches.
And height = 9(2.778) = 25.00 inches
Hence "The width and height of the given TV screen will be 44.45 inches and 25.00 inches".
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Morris borrowed $6 from his mother. so far, he has repaid $4. if debt is represented as a negative number, what number sentence shows the amount of jack's remaining dept.?
if it was negitive I would be -2
Step-by-step explanation:
so 6-4=2 and if you make that negative it would be -2
Answer:
-$6 + $4 = -$2
Step-by-step explanation:
Since Morris borrowed 6 dollars to begin with, the first term in my equation is -6$, representing the debt he has incurred from taking a loan of 6 dollars from his mother. After paying $4 dollars, he would still be in debt of $2 to his mother. Since he is still in debt of 2 dollars, the furthest right term in my aforementioned equation is -$2.
A construction crew is lengthening a road that originally measured 41 miles. The crew is adding one mile to the road each day. The length, L (in miles), after d
days of construction is given by the following.
L = 41+d
What is the length of the road after 28 days?
Answer:
69 miles
Step-by-step explanation:
Put the number in place of the variable representing it and do the arithmetic.
L = 41 +28 = 69
After 28 days, the length of the road is 69 miles.
a roller coaster has four cars each with the same number of seats. these are 21 passengers seated in the roller coaster, but 3 seats are empty. write an equation that can be used to determine the number of seats in each car, s
what would that be as an algebraic expression?
Given:
Number of passengers seated in the roller coaster = 21
Empty seats = 3
Number of cars in roller coaster = 4 (each with the same number of seats)
To find:
An equation that can be used to determine the number of seats in each car.
Solution:
Let s be the number of seats in each car.
Total number of seats in 4 cars = 4s
Using the given information,
Total number of seats = Occupied seated + Empty seats
= 21 + 3
= 24
Now, the required equation is
[tex]4s=24[/tex]
Therefore, the required equation is [tex]4s=24[/tex].
Divide both sides by 4.
[tex]s=\dfrac{24}{4}[/tex]
[tex]s=6[/tex]
Therefore, the number of seats in each car is 6.
how many tens and ones are in the number 15
Shivani started the week with $9,000 in her bank account. Then she spent $5,000 on an antique clock. Which integer represents the final balance of the bank account?
Answer:
4,000 is the integer representing the final balance of the bank account
Step-by-step explanation:
Here, we are told that Shiavni had a total of $9,000 in her bank account at the start of the week of which she spent $5,000 out of it on an antique clock.
Now, we want to know the integer that represents the amount which is the final balance of the bank account.
Mathematically, when we talk of an integer, we are simply referring to a whole number, be it negative or positive.
Thus, the integer is the case is the difference in what she had at the beginning of the week minus the cost of the clock
That would be; $9,000 -$5000 = $4,000
Instrument Panel
Identify instruments and gauges on the instrument panel of your family car or that of a friend and
list below.
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
16
Step-by-step explanation:
I counted each of the cubes and got 64.
Then I divided it by 4 since you need to divide it be 1/4.
once I divided 4 for 64 I got 16.
if i weigh 210 and i need to loose 5 pounds a month in 6 months what is my end weight
w−2+2w=6+5w please helppp
The solution to the equation W - 2 + 2w = 6 + 5w is W = -4.
To solve the equation W - 2 + 2w = 6 + 5w, follow these steps:
Begin by gathering the terms with W on one side and the terms without W on the other side of the equation.
Start by subtracting 2w from both sides:
W - 2 + 2w - 2w = 6 + 5w - 2w
Simplify:
W - 2 = 6 + 3w
Next, move the constant term (6) to the left side by subtracting 6 from both sides:
W - 2 - 6 = 6 + 3w - 6
Simplify:
W - 8 = 3w
Now, let's isolate the variable W by subtracting 3w from both sides:
W - 3w - 8 = 3w - 3w
Simplify:
-2w - 8 = 0
Finally, solve for W by adding 8 to both sides:
-2w - 8 + 8 = 0 + 8
Simplify:
-2w = 8
Divide both sides by -2 to isolate w:
(-2w) / -2 = 8 / -2
Simplify:
w = -4
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Translate each question.
Four times the difference of a number and 7 is 32
The ratio of red cars to blue cars in a parking lot was 5:3 . If there was 40 red cars , how many blue cars were there ?
Faith is driving to a concert and needs to pay for parking. There is an automatic fee of
$7 just to enter the parking lot, and when she leaves the lot, she will have to pay an
additional $2 for every hour she had her car in the lot. How much total money would
Faith have to pay for parking if she left her car in the lot for 3 hours? How much
would Faith have to pay if she left her car in the lot for t hours?
Cost for 3 hours:
Cost for t hours:
Submit Answer
attempt 1 out of 2
N]
Ri
Answer: 13
Step-by-step explanation:
cost for 3 hours: 7+2(3)=13
cost for t hours: 7+2t
Simplify: (3x^2-5x +9)+(7x^2+8x-5
Answer:
=10x2+3x+4
Step-by-step explanation:
I hope this helps you
Answer:
10x^2+3x+4 should be the correct answer
1) g(x) = 2x +3
what is slope
Answer: m=2
Use the slope-intercept form
y=mx+b to find the slope m
Step-by-step explanation:
Use the slope-intercept form
y=mx+b to find the slope m
Factor. x^2-11xy-12y^2
Answer:
(x-12y)(x+y)
Step-by-step explanation:
The number is between 0 and 9. It cannot be evenly divided by 2. It is more than five. What is the number?
Answer:
7
Step-by-step explanation:
I'm really confused about this question,
-(q+7) = -6q + 8
plz help 30 points
3(x+2)=18
please solve for x
In 3(x+2)=18, X=4
Divide both sides by the numeric factor on the left side, then solve.
-5x + 3 = 8x + 9 – 3
[tex]\text {Hi There! The answer to your problem is}[/tex]
[tex]\fbox {x=-3/13}[/tex]
[tex]\text {Your 1st Step will be to Simplify the Equation}[/tex]
[tex]\text {-5x+3=8x+9+-3}[/tex]
[tex]\text {-5x+3=(8x)+(9+-3) (Combine Like Terms)}[/tex]
[tex]\text {-5x+3=8x+6}[/tex]
[tex]\text {The Next Step is to Subtract 8x}[/tex]
[tex]\text {-13x+3-3=6-3}[/tex]
[tex]\text {-13x=3}[/tex]
[tex]\text {The Final Step is to Divide by -13}[/tex]
[tex]\text {-13x/13=3/-13}[/tex]
[tex]\text {x=-3/13}[/tex]
[tex]\text {Best of Luck!}[/tex]
[tex]\text {-LimitedX}[/tex]
The midpoint of AB is M=(-2, 1). One endpoint is A=(-8, 7).
Find the coordinates of the other endpoint, B.
PLEASE HELP ME
Answer:
B(4, -5)
Step-by-step explanation:
A(-8, 7)
M(-2, 1)
B(x, y)
x-coordinate:
(-8 + x)/2 = -2
-8 + x = -4
x = 4
y-coordinate:
(7 + y)/2 = 1
7 + y = 2
y = -5
B(4, -5)
Curtis charges a flat fee of $2.50 for each delivery plus $0.20 per mile for each mile he drives. For one delivery Curtis drive 6 miles
How much does Curtis charge to deliver food ??
what is the length of EG
Answer:
I
Step-by-step explanation:
J
PLEASE I NEED THIS IN AN HOUR OR SO (15 point)
A line goes through the points (4, 6) and (–2, 3). What is the slope of the line perpendicular to that line?
Write the equation of the line through the points (–6, 3) and (9, 8).
Help me plz I don't understand this
Answer:
D. [tex]y = 2x[/tex]
Step-by-step explanation:
A proportional relationship is represented by the formula [tex]y = mx + b[/tex].
m = the slope, which is [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex].
b = the y-intercept, the point where the line crosses the y-axis. We actually don't have to worry about the [tex]+ b[/tex] part of the formula because [tex]b = 0[/tex], so it can be left out.
To find the slope, use [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]. Subtract the smaller y value (2) from the larger y value (6).
(6 - 2 = 4)
Then subtract the smaller x value (1) from the larger x value (3).
(3 - 1 = 2)
So it looks something like this now:
[tex]\frac{6-2}{3-1}[/tex] , which equals [tex]\frac{4}{2}[/tex]
Then you divide the top part of the fraction (4) by the bottom part. (2).
[tex]\frac{4}{2}[/tex] = 2. The slope (m) is 2.
So the final equation is [tex]y=2x[/tex].
Name this angle in three different ways
Angle LMN
Angle NML
Angle M
These are the only ways to name this angle
Answer:
Angle NML, LMN, and the angle created by rays MN and ML intersecting at point M.
Step-by-step explanation:
The first two ways are just the points in order. The third can be written in multiple ways but I believe this one is quite explanatory.
scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing?
Answer:
12.5 cm
Step-by-step explanation:
1,000 meters/ 80m is 12.5