1. 2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 <== slope intercept form
==================
2. y = -2/3x + 490....slope = -2/3.....y int = (0,490)
to graph, start at (0,490)....since the slope is -2/3, we will go down 2 spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.
===================
3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry
===================
4. graph the function....it will be the same line as the graph I explained before...y = -2/3x + 490
y int = (0,490)
x int = (735,0)
===================
5. original : new :
2x + 3y = 1470 2x + 3y = 1593
3y = -2x + 1470 3y = -2x + 1593
y = -2/3x + 490 y = -2/3x + 531
similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.
differences : These lines will have different x and y intercepts
y = -2/3x + 490 : y int = (0,490), x int = (735,0)
y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)
======================
6. pick 2 points on the line.....(0,300) and (450,0)
find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)
(0,300)....x1 = 0 and y1 = 300
(450,0)...x2 = 450 and y2 = 0
now we sub and find the slope
slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3
now we use y = mx + b
slope(m) = -2/3
use either of ur points...(450,0)...x = 450 and y = 0
now sub and find b, the y int
0 = -2/3(450) + b
0 = - 300 + b
300 = b
so ur equation is : y = -2/3x + 300....or 2x + 3y = 900
2. Find the LCM of 3, 11, and 12.
O 396
0 264
O 132
O 33
Answer:
132
Step-by-step explanation:
3 x 44= 132
11 x 12 = 132
Answer:
C)132
Hope this helps
Explanation) LCM(3, 11, 12) = 132
A function is represented by the table. x y 3 -2 5 -26 7 -50 The rate of change of the function represented in the table is . For the given x- and y-values, the function is .
Answer:
Step-by-step explanation:
Here is your x/y table, a bit more organized:
x | 3 5 7
y | -2 -26 -50
The rate of change is the same thing as the slope. If the slope between coordinates 1 and 2 is the same as the slope between coordinates 2 and 3, we have a linear function in the form y = mx + b, where m is the slope and b is the y-intercept. We will have to solve for b if we want to use this form. Or we could use the point-slope form and not have to solve for b. Let's do that. But first things first. The slope:
Between the first 2 coordinates (3, -2) and (5, -26):
[tex]m=\frac{-26-(-2)}{5-3}=\frac{-24}{2}=-12[/tex]
Between coordinates 2 and 3 which are (5, -26) and (7, -50):
[tex]m=\frac{-50-(-26)}{7-5} =\frac{-24}{2}=-12[/tex]
The slopes are the same, so this in fact a linear function with m = -12. But that's all we have, so let's use the point-slope form of a line to write the equation:
[tex]y-y_1=m(x-x_1)[/tex] where [tex]x_1[/tex] and [tex]y_1[/tex] are coordinates found in the table. Plugging in the first coordinate along with the slope of -12:
[tex]y-(-2)=-12(x-3)[/tex] and
y + 2 = -12x + 36 and
y = -12x + 36 - 2 so the equation for the line in slope-intercept form is
y = -12x + 34
Regardless of which coordinate point you choose as your x1 and y1, I promise you that you will still get the same equation for the line!
Answer:
hi its -12 and decreasing.
Ash and Misty are both travelling by train. Ash's train travels 80 km in 50 minutes. Misty's train travels 160 km. It leaves at 12:35 and arrives at 15.05. Work out the difference, in km/h, between the average speed of their trains.
Answer:
∆v = 32 km/h
the difference, in km/h, between the average speed of their trains is 32 km/h.
Step-by-step explanation:
For Ash's Train;
Distance travelled d1 = 80km
Time taken t1 = 50 minutes = 5/6 hour
Average speed = distance travelled/time taken
v1 = d1/t1
Substituting the values;
v1 = 80/(5/6)
v1 = 96km/h
For Misty's train;
Total distance travelled d2 = 160 km
Time taken t2 = 15:05 - 12:35 = 2 hours 30 minutes
t2 = 2.5 hours
v2 = d2/t2 = 160/2.5
v2 = 64 km/h
the difference, in km/h, between the average speed of their trains is;
∆v = v1 - v2 = 96km/h - 64 km/h = 32 km/h
∆v = 32 km/h
the difference, in km/h, between the average speed of their trains is 32 km/h.
Answer:
32km/h
Step-by-step explanation:
Someone helps…………………
Answer:
The third choice is correct
Step-by-step explanation:
Domain > or equal to -3, and range is less than or equal to -2
What is the numerator of the simplified sum? StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction
Answer:
4x + 6
Step-by-step explanation:
Given
[tex]\frac{x}{x^2+3x+2}[/tex] + [tex]\frac{3}{x+1}[/tex]
Before we can add the fractions we require them to have a common denominator.
Factor the denominator of the first fraction
[tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3}{x+1}[/tex]
Multiply the numerator / denominator of the second fraction by (x + 2)
= [tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3(x+2)}{(x+1)(x+2)}[/tex] ← fractions now have a common denominator
Add the numerators leaving the denominators
= [tex]\frac{x+3(x+2)}{(x+1)(x+2)}[/tex]
= [tex]\frac{x+3x+6}{(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{(x+1)(x+2)}[/tex] ← simplified sum with numerator 4x + 6
The position of a swimmer below sea level is represented by –5 meters. The diver descends an additional 3 meters below sea level. Which expression describes the new position of the diver? Negative 5 + (negative 3) Negative 5 + 3 5 + (negative 3) 5 + 3
Answer:
The answer is -5 + (-3).
Step-by-step explanation:
"The diver descends" is a clue that the position of the diver is even lower than before.
Answer:
A
Step-by-step explanation:
i’ve tried multiple ways to answer this question, and i’m so stuck! :( could anyone help me please!
Answer:
160 ounces
Step-by-step explanation:
32 ounces x 5=160 ounces
Look at the data in the table.
ху
4,9
12,28
7,14
9,20
5,9
12,30
10,22
Find the total thickness of two pieces of wood that a carpenter glued together if one is 5/16 inches and the other is 7/8 inches thick?
A) 1 1/4 inches
B) 1 3/16 inches
C) 1 1/8 inches
D) 1 5/8 inches
Which of the following linear equations passes through points (-1,5) and (1,-5)?
Answer:
y = -5x
Step-by-step explanation:
Line A passes through the points (-8, 5) and (-5, 4). Line B passes through the points (0, 1) and (4, -1). Which of the following describes the relationship between line A an line B?
.
Lines A and B are parallel, because they have the same slope
.
Lines A and B are parallel, because they have opposite reciprocal slopes.
.
Lines A and B are perpendicular, because they have opposite reciprocal slopes.
.
Lines A and B intersect, because their slopes have no relationship.
Answer:
Last option is the correct choice.
Step-by-step explanation:
Slope of line A = [tex]m=\frac{4-5}{-5-\left(-8\right)}=-\frac{1}{3}[/tex]
Slope of line B = [tex]m=\frac{-1-1}{4-0}=-\frac{1}{2}[/tex]
Lines A and B intersect, because their slopes have no relationship.
Best Regards!
Lines A and Line B intersect, because their slopes have no relationship.
What is slope of line?Slope of line is defined as the angle of line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
Given,
Line A passes through the points (-8, 5) and (-5, 4)
Let
x₁ = -8, y₁ = 5
x₂ = -5, y₂ = 4
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in formula
m₁ = (4 - 5)/(-5 - (-8))
m₁ = (4 - 5)/(-5 + 8)
m₁ = -1/3
So, the slope of the line A is -1/3
Line B passes through the points (0, 1) and (4, -1).
m₂ = (-1 - 1)/(4 - 0)
m₂ = (-2)/(4)
m₂ = -1/2
So, the slope of the line B is -1/2
Hence, Lines A and Line B intersect, because their slopes have no relationship.
Learn more about Slope of Line here:
brainly.com/question/14511992
#SPJ2
The table shows the number of pages in the books in Box A and the number of pages in the books in Box B.
Which statement is true about the data?
-The mean of Box A is greater than the mean of Box B.
-The mean of Box B is greater than the mean of Box A.
-The median of Box A is greater than the median of Box B.
-The median of Box B is greater than the median of Box A.
Answer:
D: The median of Box B is greater than the median of Box A.
Step-by-step explanation:
edg2020
The median of Box B is greater than the median of Box A. Then the correct option is D.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
The mean is given as the ratio of the sum of the observation and the number of the observation.
The table shows the number of pages in the books in Box A and the number of pages in the books in Box B.
The mean of Box A will be
⇒ (32 + 32 + 28 + 28 + 28 + 28 + 25 + 25 + 35 + 32) / 10
⇒ 29.3
The mean of Box B will be
⇒ (48 + 20 + 32 + 20 + 32 + 32 + 40 + 20 + 21 + 28) / 10
⇒ 29.3
The median of Box A will be
⇒ 25
The median of Box B will be
⇒ 30
The median of Box B is greater than the median of Box A.
Then the correct option is D.
More about the mean link is given below.https://brainly.com/question/521501
#SPJ2
What are TWO equivalent expressions for 2(3j+ 5 + 6j) Remember I need TWO equivalent expressions.
Answer:
Hope it helps:) 18j+10
Step-by-step explanation:
(2)(3j+5+6j)
(2)(3j)+(2)(5)+(2)(6j)
6j+10+12j
18j+10
What would the busked of x be?
Answer:
x = 9
Step-by-step explanation:
Step 1: Look at graph
You can see that both ∠B's are the same. Therefore, both side lengths AD and CD are the same
Step 2: Set equations equal to each other
3x = 2x + 9
Step 3: Solve
x = 9
And we have our answer!
Answer:
9
Step-by-step explanation:
The table shows the ages of players on a football team.
Age
Frequency
a) Work out the mean age of the team.
Round your answer to 1 decimal place.
19
2.
20
3
21
1
b) A new player joins the team and raises
the mean age to 22.
22
4
23
1
Work out the age of this new player.
Answer: A) 20.9 ; B) 34years
Step-by-step explanation:
Given the following :
AGE (X) - - - - - - - 19 - -20 - - - 21 - - - 22 - - - 23
FREQUENCY (F) - 2 - - 3 - - - - 1 - - - - 4 - - - - 1
A)
MEAN(X) = [AGE(X) × FREQUENCY (F)] ÷ SUM OF FREQUENCY
F*X = [(19 * 2) + (20 * 3) + ( 21 * 1)+(22 * 4)+(23 * 1)]
= 38 + 60 +21 + 88 + 23 = 230
SUM OF FREQUENCY = 2 + 3 + 1 + 4 + 1= 11
MEAN(X) = 230 / 11
X = 20.9
B)
WHEN A NEW PLAYER WAS ADDED :
MEAN (X) = 22
Let age of new player = y
Sum of Ages = 19 + 19 +20 + 20 + 20 + 21 + 22 + 22 + 22 + 22 + 23 + y
Number of players = 11 + 1 = 12
Mean(x) = sum of ages / number of players
New mean (x) = 22
x = (230 + y) / 12
22 = (230 + y) / 12
Cross multiply
264 = 230 + y
y = 264 - 230
y = 34 years
What is the standard form for the quadratic function? g(x)=(x+1)2−2 g(x)=x2−1 g(x)=x2−2x−4 g(x)=x2+2x−1 g(x)=x2−3
Answer:
x^2 + 2x - 1
Step-by-step explanation:
g(x)=(x+1)2−2 would be a quadratic if you'd write it like this: g(x)=(x+1)^2−2.
This expands to g(x) = x^2 + 2x + 1 - 2 = x^2 + 2x - 1
Find the factors of 4x2-16x-9.
Answer:
Step-by-step explanation:
[tex]4x^2-16x-9.\\Writ -16x - as -a -difference\\ 4x^2 +2x-18x -9 \\Factor -out- common- terms\\2x(2x+1)-9(2x+1)\\ Factor -out (2x+1)\\(2x+1)(2x-9)[/tex]
I Hope It Helps :)
Answer:
[tex] \boxed{\sf (2x - 9)(2x + 1)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies 4 {x}^{2} - 16x - 9 \\ \\ \sf Factor \: the \: quadratic \: 4 {x}^{2} - 16 x - 9. \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 4 \: and \: the \: constant \\ \sf term \: is \: - 9. \: The \: product \: of \: 4 \: and \: - 9 \: is \\ \sf - 36. \: The \: factors \: of \: - 36 \: which \: sum \: to \\ \sf - 16 \: are \: 2 \: and \: - 18. \\ \sf So, \\ \sf \implies 4 {x}^{2} - (18 - 2)x - 9 \\ \\ \sf \implies 4 {x}^{2} - 18x + 2x - 9 \\ \\ \sf \implies 2x(2x - 9) + 1(2x - 9) \\ \\ \sf Factor \: 2x - 9 \: from \: 2x(2x - 9) + 1(2x - 9) : \\ \sf \implies (2x - 9)(2x + 1)[/tex]
A circle is shown. 2 tangents intersect at a point outside of the circle to form an angle with a measure of 70 degrees. The tangents intersect the circle at points Q and R. Point S is on arc Q R.
What is the measure of arc QSR?
°
Answer:
250 degrees
Step-by-step explanation:
just did it :)
If the sum of first 9 terms of an A.P is equal to sum of its first 11 terms, then what is the sum of its 20 terms?
Pls Anyone help me!!
Answer:
Put the values into the formula....let me know if you need help....
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
Sum of the first 9 terms = 9/2 (2a + 8d)
Sum of the first 11 terms = 11/2 (2a + 10d)
S9 = S11
9a + 36d = 11a + 55d
2a = -19d
2a + 19d = 0...........(1)
S20 = 20/2 (2a + 19d)
= 20/2 (0) . .. ............from (1)
S20 = 0
20 points!!!! match the justification to each statement in the solution of x + 12.7 =-25.2.
Answer: x + 12.7 = -25.2 ✓given
x + 12.7 -12.7 = -25..2 -12.7 ✓ Subtraction property of equality
x + 0 = -37.9 ✓ Additive inverse and simplification
x = -37.9 ✓ Identity property
Step-by-step explanation: Put the steps in order. Then it makes some sense. Why is the step "legit"?
The probability that Paul wins in a raffle is given by the expression
p.
Write down an expression for the probability that Paul does not win.
Answer:
[tex]1 - p[/tex]
Step-by-step explanation:
Consider the [tex](\Omega, \mathcal{F}, \mathbb{P})[/tex] where [tex]\mathcal{F}[/tex] is sigma algebra and [tex]\mathbb{P}[/tex] is probabilistic measure. Denote [tex]A \subset \Omega[/tex] where Paul wins. By additivity of measure we know that
[tex]\mathbb{P}(A) + \mathbb{P}(\Omega \setminus A) = \mathbb{P}(\Omega) = 1[/tex].
So
[tex]\mathbb{P}(\Omega \setminus A) = 1 - \mathbb{P}(A) = 1 - p[/tex].
But [tex]\Omega \setminus A[/tex] is exactly the set where Paul does not win. Q.E.D.
Please verify this question if it is good.If it is not good then do it for me please anyone!
Answer:
You are correct! good job!
Step-by-step explanation:
Mr. Jamieson plans to put some 3-pound math books in a box that can hold 26 pounds or less. The inequality 3b ≤ 26 describes the situation. Which statement about his solution, b ≤ 823, makes the most sense
Answer:
He's wrong, he should have divided both sides by 3
b≤8.66666
Step-by-step explanation:
Answer:
Mr. Jamieson plans to put some 3-pound math books in a box that can hold 26 pounds or less. The inequality 3b ≤ 26 describes the situation. Which statement about his solution, b ≤ 8 2/3, makes the most sense?
Step-by-step explanation:
Solve: 16x2 − 80 = 0 Round the answer to the nearest hundredth.
Answer:
x = ±2.24
Step-by-step explanation:
16x² - 80 = 0
16x² = 80 (Add 80)
x² = 5 (Divide by 16)
x = ±√5 (Square root both sides)
≈ 2.24, -2.24
Answer:
x = −2.24 and x = 2.24
Step-by-step explanation:
To solve, you can use the quadratic formula.
The guy above is correct.
Hope this helps!
I would greatly appreciate the help of these two questions!!
Please hurry? :')
Answer:
b
Step-by-step explanation:
Δ QRP and Δ XRY are similar, thus ratios of corresponding sides are equal, that is
[tex]\frac{XY}{QP}[/tex] = [tex]\frac{RY}{RP}[/tex] , substitute values
[tex]\frac{XY}{4}[/tex] = [tex]\frac{4}{8}[/tex] ( cross- multiply )
8XY = 16 ( divide both sides by 8 )
XY = 2
Match each whole number with a rational, exponential expression.
Answer:
1. 343^2/3 = 49
2. (2197^1/3)² = 169
3. 729^2/3 = 81
4. (1000²)^1/3 = 100
5. (³√9261)² = 441
6. ³√216² = 36
Hope this helps.
Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice? On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4). On a coordinate plane, a straight line with a positive slope begins at point (negative 2.5, negative 5), crosses the x- and y-axis at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).
Answer: Most Viable: On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).
Also possible, but only if someone scoops exact amounts (maybe pre-packaged for people who don't want to do their own scooping.): On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4).
Step-by-step explanation:
The line beginning at (0,0) ending at (2.5, 5) represents all the prices for any amount that the customer scoops. for example, $5 for 2 1/2 pounds or $1 for 1/2 pound or $2 for 1 pound would all be represented in the graphed line.
The graphs with negative values don't make sense. You can't scoop negative pounds!
Again, good descriptions but difficult to sort out. Are you able to hit [enter] or [return] between options, or attach a screenshot?
HELP PLSSSS,I DON'T GET IT
Answer:
Step-by-step explanation:
I THINK IT C
A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.
Answer:
Slope = [tex]-\frac{3}{4}[/tex]
y-intercept = 2
Equation of the line 't': [tex]y=-\frac{3}{4}x+2[/tex]
Step-by-step explanation:
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since line 't' is passing through two points (0, 2) and (8, -4),
Slope of the line 't' = [tex]\frac{2+4}{0-8}[/tex]
m = [tex]-\frac{6}{8}[/tex]
m = [tex]-\frac{3}{4}[/tex]
Since y-intercept of a line is the value of 'y' for x = 0 [from point (0, 2) lying on this line]
Therefore, Y-intercept of line 't' = 2
Slope intercept of an equation is,
y = mx + b
where m = slope of the line
b = y-intercept
Therefore, equation of the line 't' will be,
[tex]y=-\frac{3}{4}x+2[/tex]
Brian and his son have a total age of 84.Brian is 26 years older than his son .how old is Brian?
Answer:
Brian = 55
Son = 29
Step-by-step explanation:
Let the ages of Brian and his son be
x +26 and x
Given that :
x + x + 26 = 84
2x + 26 = 84
2x = 58
x = 29.
We know that x is the age of Brian's son. so, Brian's age is 29 + 26 = 55
Hope this helps.
Good Luck