Answers
Question 9)
From the line graph, taking two points
(-5, 4) (-6, 7)Finding the slope between (-5, 4) and (-6, 7)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:4\right),\:\left(x_2,\:y_2\right)=\left(-6,\:7\right)[/tex]
[tex]m=\frac{7-4}{-6-\left(-5\right)}[/tex]
[tex]m=-3[/tex]
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (-5, 4) and m = -3 in the slope-intercept of the line
y = mx+b
4 = -3(-5)+b
4 = 15+b
b = 4-15
b = -11
substituting b = -10 and m = -3 in the slope-intercept of the line
y = mx+b
y = -3x+(-11)
y = -3x - 11
Thus, equation is slope-intercept form will be:
y = -3x - 11
Hence, option B is true.
Question 10)
From the line graph, taking two points
(4, 7) (-8, 1)Finding the slope between (4, 7) and (-8, 1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(4,\:7\right),\:\left(x_2,\:y_2\right)=\left(-8,\:1\right)[/tex]
[tex]m=\frac{1-7}{-8-4}[/tex]
[tex]m=\frac{1}{2}[/tex]
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (4, 7) and m = 1/2 in the slope-intercept of the line
y = mx+b
7 = 1/2(4)+b
7 = 2+b
b = 5
substituting b = 5 and m = 1/2 in the slope-intercept of the line
y = mx+b
y = 1/2x + 5
Thus, the equation is slope-intercept form will be:
y = 1/2x + 5
Hence, option C is true.
Related Questions
What is the product of (2x – 1)
(3x + 3)?
Answers
Answer:
6x^2 + 3x - 3
Step-by-step explanation:
Using the FOIL method, we would multiply 2x by 3x, then multiply 2x by 3, then multiply -1 by 3x, then multiply -1 by 3. This would bring the answer to 6x^2 + 6x -3x - 3. Combine the like terms 6x and -3x and you get 6x^2 + 3x - 3
What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?
Answers
Answer:
The equation of line parallel to given line passing through (8,-7) is:
[tex]y = -\frac{5}{4}x+3[/tex]
Step-by-step explanation:
Given line is:
5x+4y=16
first of all, we have to convert the equation of given line in slope-intercept form
[tex]4y = -5x+16[/tex]
Dividing both sides by 4
[tex]\frac{4y}{4} = -\frac{5x}{4} + \frac{16}{4}\\y = -\frac{5}{4}x+4[/tex]
Slope intercept form is:
[tex]y=mx+b[/tex]
The slope of given line is:
[tex]m = -\frac{5}{4}[/tex]
Let m1 be the slope of line parallel to given line
"The slopes of two parallel lines are equal"
[tex]m = m_1\\m_1 = -\frac{5}{4}[/tex]
The equation of line parallel to given line will be:
[tex]y = m_1x+b[/tex]
Putting the value of slope
[tex]y = -\frac{5}{4}x+b[/tex]
Putting the point (8,-7) in the equation
[tex]-7 = -\frac{5}{4}(8)+b\\-7 = -(5)(2) + b\\-7 = -10+b\\b = -7 +10\\b = 3[/tex]
Putting the value of b
[tex]y = -\frac{5}{4}x+3[/tex]
Hence,
The equation of line parallel to given line passing through (8,-7) is:
[tex]y = -\frac{5}{4}x+3[/tex]
Regina's father has 3 1/2 cups of pudding to divide equally among Regina and her 3 friends. How many cups of pudding does each person receive?
Answers
Answer:
The answer is .875 cups of pudding for each person
Step-by-step explanation:
To solve this problem you will have to divide 3 1/2 among 4 people.
3 1/2 divided by 4 is equal to .875
Look at the photo pick A B C D either one explanation not needed thank you! <3
Answers
Answer:
A. 5.444444444444 XD
Step-by-step explanation:
Answer:
I just thought about it in my head but possibly try A
Step-by-step explanation:
...
If Rachel can reach 91 inches high, AC = 2x, and BC= 5x+7, how tall is the object she's
reaching for (AC)?
a) 24 inches
b) 13 inches
c) 67 inches
d) 91 inches
Answers
Answer:
d 91
Step-by-step explanation:
she is reaching it perfectly at this height in the problem, its super easy
find the value of x and the measures of the missing angles
Answers
Answer:
Step-by-step explanation:
m∠X + m∠Y + m∠Z = 180 {angle sum property of triangle}
3x + 5 + 40 +4x - 5 = 180
3x + 4x + 5 + 40 -5 = 180 {Combine like terms}
7x + 40 = 180 { subtract 40 from both sides}
7x = 180 - 40
7x = 140
x = 140/7
x = 20
m∠X = 3x + 5
= 3*20 + 5
= 60 + 5
m∠X = 65
m∠Z = 4x - 5
= 4*20 - 5
= 80 - 5
m∠Z = 75
ach light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and ninety percent of the fluorescent bulbs are switched on. If eighty percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent
Answers
Answer:
10%
Step-by-step explanation:
The computation of the percentage of bulbs that switched on incandescent is as follows;
Let us assume the incandescent be I
And, the fluorescent be F
Now the equation is
0.4I + 0.9F = 0.8 (I+F)
0.41I + 0.9F = 0.8I + 0.8F
So here
0.4I = 0.1F
Now the percentage would be for incandescent in the case of switched on is
= 0.4I ÷ 0.8(I+F) × 100
= 0.1F ÷ 1F
= 10%
How much money will we need to buy enough 12 packs for 168 people to
have 1 can each? Explain how you know.
Pls I need it now
Answers
Answer=12x168=2016
What polynomial should be subtracted from 3x^2+4x-1 to get the difference equal to 1
Answers
=====================================================
Explanation:
Assume the polynomial we want to find is in the form Ax^2+Bx+C
The goal is to find the values of A, B, and C.
We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:
(3x^2+4x-1) - (Ax^2+Bx+C) = 1
3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1
(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1
(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1
From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.
Do the same for the x terms to get 4-B = 0 leading to B = 4
Finally, we have -1-C = 1 lead to C = -2
The polynomial Ax^2+Bx+C becomes 3x^2+4x-2
-------------------
Checking the answer:
(3x^2+4x-1) - (Ax^2+Bx+C)
(3x^2+4x-1) - (3x^2+4x-2)
3x^2+4x-1 - 3x^2-4x+2
(3x^2-3x^2) + (4x-4x) + (-1+2)
0x^2 + 0x + 1
0 + 0 + 1
1
We get a difference of 1, so the answer is confirmed.
Jack is trying to make extra money on his summer vacation from school. He works two different jobs, earning $9 per hour washing cars and $6 per hour walking dogs. How much money would Jack earn in a week in which he worked 5 hours washing cars and 2 hours walking dogs? How much money would Jack earn in a week in which he worked w w hours washing cars and d d hours walking dogs? 5 hours washing cars and 2 hours walking dogs: w w hours washing cars and d d hours walking dogs:
Answers
Answer:
$57
[tex]9w+6d[/tex]
Step-by-step explanation:
Given that:
Earnings per hour for washing cars = $9
Earnings per hour for walking dogs = $6
Number of hours for which car washing is done = [tex]w[/tex]
Number of hours taken for walking dogs = [tex]d[/tex]
Earnings for [tex]w[/tex] hours for washing cars = Per hour earnings multiplied by number of hours = $9[tex]w[/tex]
Earnings for [tex]d[/tex] hours for walking dogs = Per hour earnings multiplied by number of hours = $6[tex]d[/tex]
Total earnings by both = $([tex]9w+6d[/tex])
Now, given that
Number of hours spent washing cars = 5 hours
Number of hours spent walking dogs = 2 hours
Therefore, total earnings by both = 9 [tex]\times[/tex] 5 + 6 [tex]\times[/tex] 2 = $57
Please help fast as you can
Answers
Answer:
The elements of the set C will be:
C = {-2, -1, 0, 1, 2, 3, 4, 5}
In other words,
[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]
The solution number line is also attached below.
Step-by-step explanation:
C = {x ∈ Z | such that -2 ≤ x < 6 }
It is clear that the x ∈ Z, meaning the x belongs to the set of integers Z.
It is given that -2 ≤ x < 6.
so x must be greater than or equal to -2 and less than 6.
Therefore, the elements of the set C will be:
C = {-2, -1, 0, 1, 2, 3, 4, 5}
In other words,
[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]
The solution number line is also attached below.
If x = -2/3 and y = 27, what is the value of xy + 5/3 ?
A) -20/3
B) -13/3
C) 5/6
D) 3
Answers
Answer:
b)[tex]\frac{-13}{3}[/tex]
Step-by-step explanation:
[tex]\frac{xy + 5}{3}\\\\\frac{\frac{-2}{3}27 + 5}{3}\\\\\frac{-18 + 5}{3}\\\\\frac{-18 + 5}{3}\\\\\frac{-13}{3}[/tex]
Answer:
B
Step-by-step explanation:
Evaluate the numerator , that is
xy + 5 = ( - [tex]\frac{2}{3}[/tex] × 27 ) + 5 = - 18 + 5 = - 13 , then
[tex]\frac{-13}{3}[/tex]
= - [tex]\frac{13}{3}[/tex] → B
Write an equation of the line passing through the point (2, 10) that is perpendicular to the line 2x+y=17.
Answers
Answer:
y = 0.5x + 9
Step-by-step explanation:
What we know:
An equation with the point (2,10) passing through it is perpendicular to the equation 2x+y=17.
The root of 2x+y=17 is (8.5, 0).
The two equations intersect at (3.2, 10.6)
Let's check if 3.2 and 10.6 work for 2x+y=17.
2(3.2) + 10.6 = 17
6.4 + 10.6 = 17, which is true.
Let's try y = 0.5x + 9, to see if we get the same output as the earlier equation.
y = 0.5(3.2) + 9
y = 1.6 + 9
y = 10.6, so 3.2 as x does work.
As a result, the perpendicular equation is y = 0.5x + 9.
help meeeeeeennsndnxncnvn
Answers
Answer:
12 oz (1) has the lowest
Step-by-step explanation:
ur wlcmeocxjvieirbvuubvuebwdfjvberlbf
Josh runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answers
Answer:
6 / 55 = x / 44
44*6/55= x
x = 4.8 miles
Step-by-step explanation:
Find the sum. You may find using a number line to be helpful. Victor borrowed $20.50 from his mother to go to the theater. A week later, he paid her $20.50 back. How much does he still owe her?
Answers
Subtract the amount he paid his mother back from the amount he borrowed from her:
20.50 - 20.50 = 0
He does not owe his mother any more.
In order for the parallelogram to be a rectangle x=
Answers
Answer:
x = 2
Step-by-step explanation:
Set the two equations 13x+34 and 10x+10 together to add up to 90 on the right which should look like this 13x + 34 + 10x + 10 = 90. Combine the two x-values to get 23x and the two other numbers to get 44. Your equation should now be 23x + 44 = 90. Subtract 44 on both sides to get this equation 23x = 46. Divide 23 on both sides to get your x value which is 2.
Answer:
X is equal to 2
Step-by-step explanation:
90 = 13x + 34 + 10x + 10
Combine Like Terms:
90 = 23x + 44
Subtraction Property of Equality:
90 - 44 = 23x + 44 - 44 ---> 46 = 23x
Division Property of Equality:
46 ÷ 23 = 23x ÷ 23 ---> 2 = x
Check Your Work:90 = 13x + 34 + 10x + 10
Fill In Variables:
90 = 13(2) + 34 + 10(2) + 10
90= 26 + 34 + 20 + 10
90 = 60 + 30
90 = 90
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle PNO = (x+14)^{\circ}m∠PNO=(x+14) ∘ , \text{m}\angle OPQ = (5x-2)^{\circ}m∠OPQ=(5x−2) ∘ , and \text{m}\angle NOP = (x-1)^{\circ}m∠NOP=(x−1) ∘ . Find \text{m}\angle OPQ.M∠OPQ.
Answers
Answer:
<OPQ = 23 degrees
Step-by-step explanation:
Given
Interior angles m∠PNO=(x+14) and m∠NOP=(x−1)
Exterior angle = m<OPQ = (5x-2)
The sum of interior angles is equal to the exterior angle, that is;
m∠PNO+m∠NOP = m<OPQ
x+14 + x-1 = 5x-2
2x + 13 = 5x-2
Collect like terms;
2x-5x = -2-13
-3x = -15
x = 15/3
x = 5
Get <OPQ
<OPQ = 5x - 2
<OPQ = 5(5)- 2
<OPQ = 25-2
<OPQ = 23 degrees
PLEASE HELP V IMPORTANT
the answers I input were just so I could see other questions.
Answers
Step-by-step explanation:
(T-S)(2000), when T(x) and S(x) are functions, is equivalent to T(2000)-S(2000), which is 17-7=10
We know that T(x) is equal to everything else, and everything else is S(x)+G(x), so T(x)-S(x) = G(x), or dollars spent on general science
Please help me. Solve for x state the properties used. 5(x - 2) - 6 = 24
Answers
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
5(x - 2) - 6 = 24
Step 2: Solve for x
Add 6 to both sides: 5(x - 2) = 30Divide 5 on both sides: x - 2 = 6Add 2 to both sides: x = 8Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 5(8 - 2) - 6 = 24Subtract: 5(6) - 6 = 24Multiply: 30 - 6 = 24Subtract: 24 = 24Here we see that 24 does indeed equal 24.
∴ x = 8 is the solution to the equation.
Guys is this correct? Look at the picture attached
Answers
It would be best to label the points if your turning it in. It can help people easily identify the points you've plotted.
From the looks of it, your equation is good.
The base is good and your math is right, but where did you get your height from?
If you count from point R up to line PQ you get 5 as the height.
I understand miscounting's a thing, no worries.
So if we input the correct height, we get A = 1/2 (3)(5)
1/2 * 15
7.5
The area of the polygon is 7.5 units.
I hope that helps and if you ever need any more help don't be afraid to reach out!
Click and drag like terms onto each other to simplify fully.
-y−y+4x+4x-3−3+2+2+2+2-5x−5x
Answers
(-y −y) + (4x + 4x) + (-3 −3 + 2 + 2 + 2 + 2) + (-5x−5x)
-2y + 8x + 2 - 10x
-2y -2x +2
A recipe uses 4 cups of sugar to make 520 cookies. If there are 1300 cookies, how many cups of
sugar would be needed?
Answers
Answer:
Step-by-step explanation:
if there are cups of sugar for 520 cookies
this means with one cup of sugar we can make 130 cookies
520/4=130
1300/130= 10 cups
for 1300 cookies we need 10 cups of sugar
DWhich measurement is equal to 4 quarts?
D)12 pints
)8 cups
D16 pints
)16 cups
Done
Answers
Answer:
16 cups is equal to 4 quarts
Step-by-step explanation:
Multiply the volume by 4
The required 4 quarts are equal to 16 cups. This means that if you have 4 quarts of liquid, you can pour it into 16 cups and it will completely fill them. Option D is correct.
1 quart is equivalent to 4 cups. This is a standard conversion ratio between quarts and cups. It means that if you have 1 quart of liquid and you want to know how many cups it is, you can simply multiply the number of quarts by 4.
So, to find out how many cups are in 4 quarts, we perform the following calculation:
4 quarts * 4 cups/quart = 16 cups
Learn more about conversion ratios here:
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In ΔQRS, r = 380 cm, s = 390 cm and ∠Q=48°. Find the length of q, to the nearest centimeter.
Answers
Step-by-step explanation:
Using Cosine rule, we have:
q² = r² + s² - 2(r)(s)(cosQ)
= 380² + 390² - 2(380)(390)(cos48°)
= 98169.688cm²
Hence q = 313cm. (nearest centimeter)
The required value of side q is 313 cm for the triangle ΔQRS.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
In triangle QRS side r = 380 cm, side s = 390 cm and angle Q = 48°.
To find the length of the side q,
Use cosine rule,
[tex]cos Q = \frac{(r^2 + s^2 - q^2)}{(2\times r \times s)}[/tex]
Substitute the values here,
[tex]cos 48 = \frac{(380)^2 + (390)^2- q^2}{2\times380 \times390} \\[/tex]
[tex]0.67 = \frac{144400 + 152100 - q^2}{296400}[/tex]
198,588 = 296500 - q²
q² = 97912
q = 312.90
q = 313 cm
The value of side q is 313 cm.
To know more about Triangle on:
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A system of equations is shown on the graph below.how many solutions does this system have
Answers
Answer:
1
Step-by-step explanation:
A solution to a system of equations is the point where the 2 lines meet.
One hour after a hiker left camp, a biker set out to catch up. If the hiker traveled 3 miles per hour and the biker traveled 6 miles per hour faster, how long will it take for the biker to catch up with the hiker?
Answers
Answer:
30 minutes after biker left
Step-by-step explanation:
Given that :
Speed of hiker = 3 mph
Speed of biker = (3 +6) = 9 mph
Present Distance of hiker when the biker set out ;
Present Distance of hiker = speed * time = (3 * 1) = 3 miles
Time taken to catchup equals :
Present distance + (distance when biker set out) = bikers distance
Let time taken = x
(3 + (3 * x)) = (9 *x)
(3 + 3x) = 9x
3 + 3x = 9x
3 = 9x - 3x
3 = 6x
x = 3/6
x = 1/2 hours
x = 30 minutes
30 minutes after biker left
Answer:
0.5 hrs or 30 mins
Step-by-step explanation:
simplify:
4 x - -5х + 3x- x+2х - 7х
Answers
Answer:
6x
Step-by-step explanation:
4 x - -5х + 3x- x+2х - 7х
Combine like terms so, so since all are the same you just do the operation they want u to do..
4x + 5x= 9x
9x + 3x = 12x
12x - x = 11x
11x + 2x= 13x
13x - 7x = 6x
Hint: 2 negatives make a postitive
Hint: in there is just an "x" there is always an invisible one in it... 1x
Hope this helped!
Joe walked 1/3 of the journey to the library to his house to meet his cousin Lucy how far did he travel
Answers
a) 34y=15=
b) -58y=20=
c) -x=23=
d) -51=-y=
Answers
a) 34y=15
=> y= 34-15
=> y = 19
b) -58y=20
=> y= -58-20
=> y = -78
c) -x=23
=> -1x=23
=> x= 23+1
=> x= 24
d) -51= -y
=> -51= -1y
=> y= -51+1
=> y= -50
Hope it helps!