Answers
Problem 1
Answer: Choice A. (0,9)---------------------
Explanation:
The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.
Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...
m = (y2-y1)/(x2-x1)
m = (11-15)/(-4-(-6))
m = (11-15)/(-4+6)
m = -4/2
m = -2
Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)
y = mx+b
b = y-mx
b = 15-(-2)*(-6)
b = 15-12
b = 3
The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.
Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.
The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).
So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).
=========================================================
Problem 2
Answer: Choice Ax is any real number but x cannot equal -2, -1 or 1.---------------------
Explanation:
Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get
g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)
The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.
So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".
Side note: We don't involve the numerator function at all.
=========================================================
Problem 3
Answer: Choice B. 2x+1 and x-3---------------------
Explanation:
The height is x, which we can factor out like this
2x^3-5x^2-3x
2x^2*x - 5x*x - 3*x
x(2x^2-5x-3)
Effectively you would use the distribution rule in reverse.
Now let's factor the remaining expression in the parenthesis.
I'll use the factor by grouping method.
2x^2-5x-3
2x^2-6x+1x-3
(2x^2-6x) + (1x-3)
2x(x-3) + 1(x-3)
(2x+1)(x-3)
Therefore, the full factorization is
x(2x+1)(x-3)
which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.
You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.
Related Questions
how do you convert a whole number to a fraction?
Answers
Answer:
Step-by-step explanation:
Example 1: Changing the whole number 5 into a fraction.
Take the whole number (5), add a line below it (/), then add a 1 to the denominator.
5 = 5/1
Example 2: Changing the whole number 5 into a fraction.
Take the whole number (5), multiply it by 2 add a line below it (/), then add a 2 to the denominator.
5 = (5*2)/2 = 10/2
***This can be reduced to 5/1***
Example 3: Changing the whole number 5 into a fraction.
Take the whole number (5), multiply it by 3 add a line below it (/), then add a 3 to the denominator.
5 = (5*3)/3 = 15/3
***This can also be reduced to 5/1***
If you follow the pattern, you will realize all whole numbers are fractions already.
They are fractions with a denominator of 1. This fraction can be manipulated with all of the same standard rules you would traditionally use with fractions, even when the denominator isn’t shown.
A fraction is simply a way to describe portions of a whole. The denominator simply tells you how many pieces to break the whole into. When the denominator is 1, you are breaking the whole into one piece (or not breaking it apart at all.
I hope this helps.
What is -6(-3+5r)=-5-7r
Answers
Answer:
r = 1
Step-by-step explanation:
Use the distributive property to multiply −6 by −3+5r.
18−30r=−5−7r
Add 7r to both sides.
18−30r+7r=−5
Add −30r and 7r to get −23r.
18−23r=−5
Subtract 18 from both sides.
−23r=−5−18
Subtract 18 from −5 to get −23.
−23r=−23
Divide both sides by −23.
r=−23/−23
Divide −23 by −23 to get 1.
r=1
A small boat leaves a port town and travels due north for 7.4 miles and then turns due east for 3.6 miles
and stops. If the boat's captain then turns back to town. a) how far does the boat travel and b) along
what bearing would the boat have to travel from its stopped position?
Answers
11 miles far does the boat travel
Step-by-step explanation:
hope it helps
The total distance travelled will be 22 miles and the bearing will be 60.89° .
It is given that a boat travels from port town to north for 7.4 miles and then east for 3.6 miles and stops at destination.
We have to find out the total distance travelled and bearing from stopped position.
What are bearings ?
A bearing is the angle in degrees measured clockwise from north i.e., 30° from north.
As per the question ;
Boat travels from port town to north for 7.4 miles and then east for 3.6 miles and it then stops at destination.
So ;
a)
Total distance travelled from port town to destination is ;
= 7.4 miles + 3.6 miles
= 11 miles
And
If boat's captain turns back to town , then total distance will be ;
= 11 + 11
= 22 miles
b)
We know that ;
cos θ = B/H
The bearing would be ;
cos θ = [tex]\frac{3.6}{7.4}[/tex]
cos θ = 0.486
θ = [tex]cos^{-1}[/tex] (0.486)
θ = 60.89°
Thus , the total distance travelled will be 22 miles and the bearing will be 60.89° .
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Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon
About
how many gallons will her car use on the trip?
O 12
O 70
067
034
Answers
The number of gallons of fuel required for 200 miles will be 6.7 gallons. The correct option is C.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that Becky is planning a two 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon.
The total miles covered in two trips will be,
100 + 100 = 200 miles
The amount of fuel will be calculated as:-
Fuel = 200 / 30
Fuel = 6.7 gallons
Therefore, the fuel quantity will be 6.7 gallons.
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Directions: Given the point and slope, write the equation of the line. 3. (1,-7); slope = -1
Answers
Answer:
y=-1x-6
Step-by-step explanation:
One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?
Answers
Answer:
Step-by-step explanation:
J
B = 3J
T = J + 5
J + 3J + J + 5 = 60
5J = 55
J = $11
B = $33
T = $16
The amount earned by Jim, Bill and Tom is equal to [tex]\boldsymbol{\$ 11},\boldsymbol{\$ 33},\boldsymbol{\$ 16}[/tex].
"Important information"Let .
The amount earned by Jim be [tex]\boldsymbol{x}[/tex].
Amount earned by Bill [tex]=\boldsymbol{3x}[/tex]
Amount earned by Tom [tex]=\boldsymbol{x+5}[/tex]
Total amount earned by all [tex]=\boldsymbol{\$ 60}[/tex][tex]x+3x+x+5=60\\5x=55\\x=11[/tex]
So,
Amount earned by Jim [tex]=\boldsymbol{\$ 11}[/tex]
Amount earned by Bill [tex]=3(11)[/tex] [tex]=\boldsymbol{\$ 33}[/tex]
Amount earned by Tom [tex]=11+5[/tex] [tex]=\boldsymbol{\$ 16}[/tex]
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what's a real number?
Answers
Answer:
Real Numbers are numerical values that can represent distance on a line. An example of it being one is 15 and an example of it NOT being one is ∞.
Two mechanics worked on a car. The first mechanic charged $75 per hour, and the second mechanic charged $45 per hour. The mechanics worked for a
combined total of 25 hours, and together they charged a total of $1425. How long did each mechanic work?
Answers
Answer:
First mechanic 10 hours, Second is 15 hours
Step-by-step explanation:
x + y = 25, so y = 25 - x
75x + 45y = 1425
Substitute in the first equation
75x + 45(25 - x) = 1425
75x + 1125 - 45x = 1425
30x = 300
x = 10
Therefore, y = 15
Answer:
they both worked
8 hours
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.
C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.
D.
There is not enough information
Answers
Answer:
Hello again! Fellow Connexus user? Because I just had this on my Honors Algebra 1 test today. Anyways the answer is: A. x + y = 126 and 2.25x + 1.50y = 225.75; 49 Hot Dogs and 77 Sodas.
Step By Step Explanation:
To verify just use the substitution method to solve the equations x+y=126 and 2.25x + 1.50y = 225.75 then you'll get your x (Number of Hotdogs) and y (Number of Sodas)
Hope this helps!
The required equations are use to solve this problem;
[tex]x + y =126[/tex]
[tex]2.25x + 1.50y = 223.75[/tex]
There are x = 49 hot dogs, and y = 77 sodas were sold.
Given that,
Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
You sold a total of 126 hot dogs and sodas combined.
We have to determine,
What equations did you use to solve this.
And How many hot dogs were sold and how many sodas were sold.
According to the question,
Let, The x represent the number of hot dogs,
And y represent the number of sodas.
Then,
You sold a total of 126 hot dogs and sodas combined.
Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.
[tex]x + y =126[/tex]
And Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
Then,
Cost of each hot dogs + cost of each soda = total earning end of the night
[tex]2.25x + 1.50y = 223.75[/tex]
On solving both the equation,
[tex]x + y = 126\\\\x = 126-y[/tex]
Substitute the value of x in the equation 2,
[tex]=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77[/tex]
Then,
Substitute the value of y in the equation 1,
[tex]x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49[/tex]
Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.
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Enter the number that belongs in the green box
Answers
Answer:
9 because there the same length
Answer:
the measure of the seg CD is 9
Step-by-step explanation:
It is 9 because the shape is a parallelogram. One of the properties of a parall is that opposite sides are congruent which makes side BA equals side CD
Solve x2 + 5x – 3 = 0 using the quadratic formula.
Solve (2x – 1)2 = 8 using the quadratic formula.
A) x = –1∕2 + , x = –1∕2 –
B) x = 1∕2 + , x = 1∕2 –
C) x = 1∕2
D) x = –1∕2
Answers
Answer:
d
Step-by-step explanation:
distribute two through the parentheses
=4x-2
move the constant to the right side and change its sign
=4x=8+2
=4x=10
divide both sides by 4
x=5/2
16. Use the vertical line test to determine whether the relation is a function.
Answers
Answer:
neither of them are
Step-by-step explanation:
Which of the following have a sum of 0? (Pick 2) *
1:The football team gained 10 yards on the first play, gained 10 yards on the second play, and lost 10 yards on the third play. What was the overall change in yardage?
2: While playing the integer game, Sam pulled the following cards: 8, 4, 5, -6, -8, -3. What is the sum of Sam's hand?
3: -15 - 8 + 12 + 11
4: 6 + (-5) - 7 + (-4) + (-4)
Answers
Answer:
The answer is number 3.
Step-by-step explanation:
-15 - 8 = -23
12 + 11 = 23
When you subtract -23 from 23 you have a sum of 0
Therefore the answer is 0
someoneplease help me
GIVING BRAINLIST TO FIRST RIGHT ANSWER
A. (4,-2)
B. (0,1)
C. (1,0)
D. (-1,0)
Answers
Answer:
C (1,0)
Step-by-step explanation:
Answer:
C. (1,0)
Step-by-step explanation:
When you go 3 to the left, you end up at (0, -2). When you go up 2, you get (1,0).
log, a Consider the graph of the function f 2- X O -2 2 4 6 8 10 -2 - What are the features of function gif g(t) = -|(r) - 1; oyintercept at (0,-1) X-intercept at (1,0) range of (-1,00) domain of (0, 0) vertical asymptote of g = 0
Answers
Answer:
X-intercept at (1/2 ,0)
domain of (0, infinity)
Vertical asymptote of x = 0
Step-by-step explanation:
Plato I got it right on the test
ASAP ASAP!! HELP!! A supermarket needs to display 64 boxes of detergent.
The boxes need to be stacked with the same number of boxes in each row.
There should be at least 3 rows with at least 4 boxes in each row.
Choose the correct answers from the drop-down boxes to complete all the ways the boxes of detergent can be stacked.
Choose...
rows with 16 boxes in each row;
8 rows with
Choose...
boxes in each row;
16 rows with
Choose...
boxes in each row.
Answers
Answer:
Its the first one
Step-by-step explanation:
4x4=16 8x2=16 so its the first
These three lines should say:
4 rows with 16 boxes in each row
8 rows with 8 boxes in each row
16 rows with 4 boxes in each row
8. There are 18 trumpets in a music room. These trumpets will be placed in 3 equal rows. Which number sentence can be used to find the number of trumpets in each row?
Answers
Answer:
18÷3=6
Step-by-step explanation:
18 trumpets have to be DIVIDED into 3 rows so you would divide 18 by three to get 6 trumpets in each row.
what percent of 75cm is 5cm
Answers
Answer:
6.67%
Step-by-step explanation:
5 / 75 = 0.066667
(0.066667)(100) = 6.67%
6/7 divided by 12/14 please show the work
Answers
Answer:
1
Step-by-step explanation:
When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.
Hope this helps!
Jamal wrote that 9 – 8.4 = 6.
Answers
9−8.4=6
0.6≠6
False
I don't know...
Answer:
0.6 his answer is false.
Step-by-step explanation:
...
HELP ME OUT PLEASE!!!
Determine which graph shows y as a function of x.
Answers
40 in^2 to cm^2
Have to find the cm
Answers
Answer:
101.6cm²
Step-by-step explanation:
1 inch = 2.54cm
that means:
40in² × 2.54 = 101.6cm²
The value of the digit 2 in 425.3 is *
Answers
Answer:
20 which is twenty
Step-by-step explanation:
searched it up on chrome
HELp PLeaSE ‼️‼️URGENT
Find the equation of the line of best fit for the points (-4, 10).(-1, 5), (2, -1) (3, (5, --- 7). O
A. y = -2x + 2
B. y = 2x - 2
C. y = 2x - 0.98
D. y = -2x - 0.98
THANKS ^_^ ! ! !
Answers
A rectangular pool is 6 meters wide and 8 meters long. If you swim diagonally across the pool, how many meters would you be swimming?
Answers
If you swim diagonally across the rectangular pool, the distance you swim is 10 meters.
Given the following data:
Width of rectangle = 6 metersLength of rectangle = 8 metersTo determine the distance you swim in meters, we would apply Pythagorean's theorem since the width is along the x-axis while the length is along the y-axis.
Note: The diagonal side of the rectangular pool represents the hypotenuse.
Mathematically, Pythagorean's theorem is given by the formula:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
Substituting the given parameters into the formula, we have;
[tex]Hypotenuse^2 = 6^2 + 8^2\\\\Hypotenuse^2 = 36+64\\\\Hypotenuse^2 = 100\\\\Hypotenuse = \sqrt{100}[/tex]
Hypotenuse = 10 meters.
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Mary had 60$ and spent 3/4 on a coat. plus she brought a skirt with 1/2 she had left . how much do she have left?
Answers
60 - 45 = $15 left
1/2 of $15 = $7.50 for the skirt
15 - 7.50 = $7.50 left
please someone help me this is the third time i have had to post this question bc of bots
Answers
Answer: It,ll increase
Step-by-step explanation:
Answer:
Add all of the numbers together then multipy them by 25
Step-by-step explanation:
35X25=875
What is the slope of the line that passes through the points (6-8) and (10,-8)?
Answers
Answer:
The slope of the line that passes through the points would be 0
Step-by-step explanation:
Lets use the formula : y2-y1/x2-x1
In this case lets let y2 be -8 and y1 be -8
And lets let x2 be 6 and x1 be 10, that would look like..
-8-(-8)/6-10
which equals...
0/-4 = 0
We know that the slope of the line is 0
You buy 3.9 pounds of trail mix. The mix
costs $2.78 per pound. What is the total
price for the trail mix?
Answers
Answer:
Answer:
28+66+86=180
180=180
Step-by-step explanation:
Since there is a triangle and the 3 measures from the angles we can find the value of x using the hint given that the sum of the interior angles must be 180°
Write the equation
\begin{gathered}x+(2x+10)+(3x+2)=180\\\end{gathered}
x+(2x+10)+(3x+2)=180
Simplify left side of the equation
\begin{gathered}6x+12=180\\\end{gathered}
6x+12=180
Solve equation for x
\begin{gathered}6x=180-12\\6x=168\\x=28\end{gathered}
6x=180−12
6x=168
x=28
Replace x into the 3 angles and find their respectives values
\begin{gathered}A=x\\A=28\\\\B=2x+10\\B=2*28+10\\B=56+10\\B=66\\\\C=3x+2\\C=84+2\\C=86\end{gathered}
A=x
A=28
B=2x+10
B=2∗28+10
B=56+10
B=66
C=3x+2
C=84+2
C=86
Check if the answers are correct
\begin{gathered}28+66+86=180\\180=180\end{gathered}
28+66+86=180
180=180
PLEASE MARK ME AS BRAINLIEST
write me 2 equivalent fractions of 3/4=_=_
Answers
Answer:
6/8 and 12/16
Step-by-step explanation:
Important: 3/4 looks like a fraction, but it is actually an improper fraction.
There is an infinity number of equivalent fractions to 3/4. To find an equivalent fraction to 3/4 , or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By multiplying the original fraction by 2, we get:
3x2/3x2=6/8
List of Equivalent Fractions of 3/4:
3/4, 6/8, 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, 27/36, 30/40, 33/44, 36/48, 39/52, 42/56, 45/60, 48/64, 51/68, 54/72, 57/76, 60/80 ...