Answer:
Step-by-step explanation: Find the y-intercept. Write the equation in slope-intercept form. Write an equation of the line that passes through each pair of points. 5. (4, −3), (2, 3)
y=6x+6 is the function representing the line that includes the points (2,18) and (5,36).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (2,18) and (5,36).
m=36-18/5-2
=18/3=6
slope of line is 6.
Now we need to find the equation of line passing through (2,18) and (5,36).
We need to find the y intercept.
18=6(2)+c
18=12+c
18-12=c
6=c
So y intercept is 6
The equation of line is y=6x+6
Hence y=6x+6 is the function representing the line that includes the points (2,18) and (5,36).
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Martin has read 40% of a book. He has 48 more pages to finish. How many pages are there in the book?
Answer: There are 80 pages in Martin's book.
48 pages = 60%
divide by six
8 pages = 10%
mulitiply by 10
80 pages = 100%
Hope this helps :)
how to tell if an equation is linear without graphing
Answer:
A linear equation has the greatest x power at 1.
If you see an equation with only x (no x^2 or x^3 or stuff like that), you will know that it is linear.
How do you solve this??? I need it fast please help with steps.
(x+3)(x+1)^2(x−4)>0
Answer:
x < -3 or x > 4
Step-by-step explanation:
The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).
The factors tell you the following about the zeros:
x = -3 . . . sign change from + to -
x = -1 . . . graph touches, but no sign change. - on either side of x=-1
x = 4 . . . sign change from - to +
__
The function will be positive for x < -3 and for x > +4.
_____
Additional comments
The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.
However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.
The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).
3 kg of carrots cost £1.80
2 kg of carrots and 5 kg of potatoes cost a total of £3.45
Work out the total cost of 4kg of carrots and 2 kg of potatoes.
You must show all your working.
Step-by-step explanation:
Price of 3 kg carrots = 1.80
Price of 1 kg carrots = 1.80 ÷ 3 = 0.6
Price of 2 kg carrots = 0.6 x 2 = 1.2
Remaining amount = 3.45 - 1.2 = 2.25
Price of 5 kg potatoes = 2.25
Price of 1kg potatoes = 2.25 ÷ 5 = 0.45
Now
Cost of 4 kg of carrots = 0.6 x 4 = €2.4
Cost of 2 kg of potatoes = 0.45 x 2 = €0.9
The total cost of 4kg of carrots and 2 kg of potatoes is £3.30
What is the total cost?Total cost is the product of the cost of each unit and the number of units purchased.
As it is given that the cost of 3 kg carrot is £1.80, therefore, the cost of 1 kg of carrot can be written as,
[tex]\text{Cost of 1 kg carrot}=\dfrac{\text{Total cost of carrot}}{\text{Total amount of carrot}}[/tex]
[tex]=\dfrac{\£1.80}{3}\\\\= \£0.60[/tex]
Thus, the cost of 1 kg carrot is £0.60.
Now., as it is given that the cost of 2 kg carrot and 5 kg potatoes is £3.45, therefore, the cost of 5 kg potatoes can be written as,
[tex]\text{Total cost}=\text{Cost of 2 kg carrot}+\text{Cost of 5 kg potatoes}[/tex]
[tex]3.45= (0.60 \times 2) + \text{Cost of 5 kg Potatoes}\\\\\text{Cost of 5 kg Potatoes} = 2.25[/tex]
Further, the cost of each kg of potatoes can be written as,
[tex]\text{Cost of 1kg of potatoes}=\dfrac{\text{Cost of 5 kg Potatoes}}{\text{Total amount of potatoes}}[/tex]
[tex]=\dfrac{2.25}{5}\\\\=0.45[/tex]
Thus, the cost of each kg of potatoes is £0.45.
Further, the total cost of 4kg of carrots and 2 kg of potatoes can be written as,
[tex]\text{Total cost }=\text{Cost of 4kg of carrots} +\text{Cost of 2 kg of potatoes} \\\\\text{Total cost }=(4 \times 0.60)+(2\times 0.45)\\\\\text{Total cost }= 2.24+0.90=\£3.3[/tex]
Hence, the total cost of 4kg of carrots and 2 kg of potatoes is £3.30
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Which expression is equivalent to 3/5x +3
2/5x + 1/5x
4/5x - 1/5x + 3
2/5x + 3 3/5x -1
1 + 3/5x + 2
1 +x/5 + 2
1 + 2/5x +3
There are blue, red and white counters in a bag in the ratio 16 3 2 There are 112 more blue counters than white counters. How many white counters are there?
We will have 16 white counters in the bag.
Given that there are blue, red, and white counters in a bag in the ratio 16:3:2, the total number of balls will be:
Total = 16 + 3 + 2Total = 21If there are 112 more blue counters than white counters, then;
number of blues = number of white + 112
16x = 2x + 112
14x = 112
x = 8
Number of white counters = 2x = 2(8) = 16
Therefore we will have 16 white counters in the bag.
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2x + 16 = 22x
Variables on both sides
answer: Subtract sixteen from both sides of the equation
2 +16 -16=22x -16
x = 4/5
Question 10 Multiple Choice Worth 1 points)
(4.04 MC)
Which of the following is a linear function?
A) y=3x^2
B) y=1 /3x
C) y=x^3 +5
D) 2/3x = y-1
Please helppp
Graph the line that passes through the points (-2,-1) and (-4,5) and determine the equation of the line
Answer:
y = -3x-7Step-by-step explanation:
Find the slope:
Going from (-4,5) to (-2,-1):
Rise = (-1 - 5) = -6
Run = (-2-(-4) = 2
Slope = Rise/Run = (-6/2) = -3
y = mx + b
y = -3x + b
Find b by using either given point. I'll use (-2,-1)
y = -3x + b
-1 = -3(-2) + b
b = -7
See attachment.
---
y = -3x-7
Determine the slope of the line that passes through pair of points: (-4, 11) and (1,-9)
Answer:
rise/run= -20/5= -4/1=-4 slope
or you sound use the slope formula (y2-y1)/(x2-x1)
(-9-11)/(1+4)
-20/5
-4
Hope this helps
4)Find the value of x and y
x=48, y=110
Explanation:
55-7=48
55+55=110
I will give brainlyst
Answer:
SSS
Step-by-step explanation:
Answer:
SSS
Step-by-step explanation:
SSS means Side Side Side and there are no angles here
write an equation of the line passing through the point (5,2) that is perpendicular to the line "-x+3y=12"
Answer:
y = -3x + 17
Step-by-step explanation:
first, change the equation into slope-intercept form
add 'x' to each side to get:
3y + x = 12
divide each side by 3 to get:
y = 1/3x + 4
now we need to use a slope that is the opposite reciprocal of 1/3 which would be -3, in conjunction with the point (5,2), by entering these values into the slope-intercept form so we can find the y-intercept ('b') of the new line:
2 = -3(5) + b
2 = -15 + b
17 = b
put slope and y-intercept together to get:
y = -3x + 17
Write the inequality that represents the solution set to the given inequality below.
−8≥x−2≥10
Group of answer choices
4≤x≤−5
−4≤x≤5
4≥x≥−5
−4≥x≥5
Answer:
-6[tex]\geq[/tex]x[tex]\geq[/tex]12
Step-by-step explanation:
I can't match it to one of your solutions but I can explain this:
-8[tex]\geq[/tex]x-2[tex]\geq[/tex]10
We can add 2 to each side to eliminate the -2 in the centre.
-6[tex]\geq[/tex]x[tex]\geq[/tex]12
how do u find the order of operations of 8×3+70÷7-7
What is the zero of the function?
1 cause the zero is where the line crosses at the x axis
A coconut cream pie recipe uses 6 ounces of crearn cheese, 12 ounces of condensed milk, and 10 ounces whipped topping In simplest form, how many ounces of cream cheese are there for every ounce of condensed milk?
Answer:
1 oz of cream cheese to every 2 oz of condensed milk
Step-by-step explanation:
We can completely disregard whipped topping because it does not ask for it.
We have 6 ounces of cream cheese to 12 ounces of condense milk. We can write this as a ration:
6:12
6 oz cream cheese:12 oz condensed milk
The question is basically asking to simplify 6:12
Since the greatest commond factor is 6, we can divide both sides by 6 and get:
1:2
Therefore, there is 1 oz of cream cheese to every 2 oz of condensed milk
Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll? Negative two-thirds Negative one-sixth one-sixth Two-thirds.
We want to get the expected value for the given experiment, we will see that it is equal to -1/6 points, so the correct option is "negative one-sixth"
For an experiment with events {x₁, x₂, ..., xₙ}, each one with probability {p₁, p₂, ..., pₙ}, the expected value is given by:
EV = x₁*p₁ + ... + xₙ*pₙ
Here we have two events:
x₁ = she gets 9 points.x₂ = she loses 2 points.Let's find the probabilities of each one of these.
She gets 9 points if the sum of the two dice is equal to 8 or 12.
Each dice has 6 outcomes.
Then a combination of two dice has a total of 6*6 = 36 outcomes.
The outcomes that add to 8 or 12 are:
dice 1 dice 2 sum
2 6 8
3 5 8
4 4 8
5 6 8
6 2 8
6 6 12
So 6 out of the 36 outcomes, then the probability of this event is:
p₁ = 6/36 = 1/6
And the other event is for all the other outcomes, so the probability is just:
p₂ = 5/6
Then the expected value is:
EV = (+ 9 points)*(1/6) + (-2 points)*(5/6) = -1/6 points.
So the correct option is negative one-sixth.
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Answer:
-1/6
Step-by-step explanation:
If the measure of an inscribed angle is 142 degrees, what is the measure of its intercepted arc? (just write the number, no degrees)
(In , (c) in a group of students of them are Science Society members and the rest are Mathematics Society members of the Science Society 5 members or 16 of them are girls. Find the total number of Mathematics Society members. Dalam satu kumpulan murid, daripada mereka 9 ialah ahli Persatuan Sains dan selebihnya ialah ahli 2. Persatuan Matematik. daripada ahli Persatuan . 5 Sains atau 16 orang daripadanya ialah perempuan. Cari jumlah bilangan ahli Persatuan Matematik [3 marks / 3 markah) Answer / Jawapan:
Answer:
50 studentsStep-by-step explanation:
Given:
4/9 of students are Science Society membersThe rest are Mathematics Society members2/5 of Science Society members are girls = 16 peopleFind the number of Science Society members:
2/5x = 16x = 16*5/2 = 40Find the total number of group members:
4/9x = 40x = 40*9/4 = 90Find the number of Mathematics Society members:
90 - 40 = 50c(1)=−20
c(n)=c(n−1)+10
Find the second term in the sequence.
Answer:
c(2) = -10
Step-by-step explanation:
The first equation says that the first term of the sequence is -20.
The second equation is saying that to find any term of the sequence, add 10 to the previous term.
c(2) = c(2-1) + 10
c(2) = c(1) + 10
c(2) = -20 + 10 = -10
Solve for m. 81m2 = 36
Step-by-step explanation:
81m2 = 36
m2 = 36/81
m2 = 4/9
Square root on both sides
m = 2/3
Answer:
Step-by-step explanation:
i hope this help have a great day!
Given the following triangle, what is the cos A?
[tex]\text{Given that, for angle A}\\\\\text{Adjacent side, AB = 7}\\\\\text{Hypotenuse, AC = 25}[/tex]
[tex]\cos A = \dfrac{AB}{AC} = \dfrac{ 7}{25}[/tex]
Will give brainliest and 100 points if you answer correctly plz help!
Write the sentence below as an equation or inequality.
Craig has six less than half of the amount of dollars Bo has.
Group of answer choices
x
=
y
2
−
6
x
=
6
−
y
2
x
=
2
y
−
6
x
=
6
−
2
y
Flag question: Question 2
Question 21 pts
Write the sentence below as an equation or inequality.
To be flagged in a system you need to either score less than ten points, or greater than one hundred points.
Group of answer choices
10
<
x
<
100
10
≤
x
≤
100
10
≥
x
≥
100
10
>
x
>
100
Flag question: Question 3
Question 31 pts
Simplify:
−
5
x
3
+
6
y
2
+
8
x
3
−
6
y
Group of answer choices
3
x
3
+
6
y
2
−
6
y
−
3
x
3
+
6
y
2
−
6
y
11
x
3
+
6
y
2
−
6
y
−
11
x
3
+
6
y
2
−
6
y
Flag question: Question 4
Question 41 pts
Simplify:
3
x
5
+
4
x
2
−
8
x
5
+
3
x
2
−
8
x
Group of answer choices
5
x
5
+
7
x
2
−
8
x
−
5
x
5
+
7
x
2
−
8
x
5
x
5
−
7
x
2
−
8
x
−
11
x
5
+
7
x
2
−
8
x
Flag question: Question 5
Question 51 pts
Solve:
8
x
+
2
(
3
x
−
5
)
=
18
Group of answer choices
x = -2
x = -1
x = 1
x = 2
Flag question: Question 6
Question 61 pts
Solve:
(
4
x
+
5
)
5
=
9
Group of answer choices
x = -10
x = -5
x = 5
x =10
Flag question: Question 7
Question 71 pts
Write the inequality that represents the solution set to the given inequality below.
−
8
≥
x
−
2
≥
10
Group of answer choices
4
≤
x
≤
−
5
−
4
≤
x
≤
5
4
≥
x
≥
−
5
−
4
≥
x
≥
5
Flag question: Question 8
Question 81 pts
Write the inequality that represents the solution set to the given inequality below.
|
x
−
3
|
<
15
Group of answer choices
12
<
x
<
−
18
−
12
<
x
<
18
12
>
x
>
−
18
−
12
>
x
>
18
Flag question: Question 9
Question 91 pts
Determine if the relation below is a function.
(-3,2) ; (-3,5) ; (-3,-2) ; (-3,8)
Group of answer choices
Yes, this relation is a function.
No, this relation is not a function.
Flag question: Question 10
Question 101 pts
Determine if the relation below is a function.
(-5,1) ; (3,1) ; (5,1) ; (2,1)
Group of answer choices
Yes, this relation is a function.
No. this relation is not a function.
Answer:
Step-by-step explanation:
The answer options are too confusing to decipher. Here are my solutions:
1. Craig(x) has six less than half of the amount of dollars Bo(y) has.
x = (1/2)y - 6
Questions 2 through 8 are either missing the statement or are too difficult to interpret.
9. Not a function since there is more than one solution to x=-3.
10. Yes, the function is y = 1
Answer:
Step-by-step explanation:
this makes no sense but okay
Concern airplane flying at a cruising speed of 1/2 km in 1/24 of a minute.Compute the unit rate of the airplanes cruising speed in kilometers per minute
Answer:
12 km/minute
Step-by-step explanation:
In order to convert to kilometers per minute, we are given 1/2 of a kilometer per 1/24 of a minute. First, we must convert to 1 minute. We can multiply both sides by 24 to get 24/2 = 12 kilometers per minute. Since we now have it in kilometers per minute, we have the answer.
Answer:
12 km per min
Step-by-step explanation:
can someone help me with this
[tex]R.H.S\\\\= (a+b)(a^2-ab +b^2)\\\\=a^3-a^2b +ab^2+ba^2-ab^2+b^3\\\\=a^3+b^3\\\\=L.H.S\\\\\text{Hence, proved.}[/tex]
What divided by 6 equals 0.41?
2.46
I think.
Because if you multiply 6 and 0.41 you get 2.46.
Answer:
2.46
Step-by-step explanation:
x/6=0.41
Multiply 6 on both sides and you get 2.46
Find the solution of the equation. 2(2x + 3) = -4 + 2(2x + 5) x = 0 infinitely many solutions x = -2 no solution
Answer:
Infinitely Many Solutions
Step-by-step explanation:
[tex]2(2x+3)=-4+2(2x+5)\\\\4x+6=-4+4x+10\\\\4x+6=4x+6\\\\Infinitely~Many~Solutions[/tex]
1. Convert 36 inches into feet. A. 3.5 ft B. B. 3 ft C. 2.5 ft D. 2 ft
Write, in slope-intercept-form, the inequality shown in the graph.
Two points which the boundary line intersects are shown.
Answer:
[tex]y \leqslant -x + 1[/tex]
Step-by-step explanation:
First write the equation of the line with either inequality sign, like so:
[tex]y \geqslant -x + 1[/tex]
Then check to see if the equation is true. The easiest way to do this is to plug the coordinates (0,0) into the equation:
[tex]0 \geqslant -0 + 1 \\ 0 \geqslant 1[/tex]
Since 0 > 1 is false, you know that the correct inequality must be:
[tex]y \leqslant -x + 1[/tex]
If you want to check this, plug the coordinates (0,0) into the equation:
[tex]0 \leqslant -0 + 1 \\ 0 \leqslant 1[/tex]
Since 0 < 1 is true, you know this equation is correct.
I hope that helped! If I made a mistake, just let me know.