Step-by-step explanation:
Given the following systems of linear equations, 2x + y = 5, and 3y = 9 − 6x
Write each equation in slope-intercept form.The slope-intercept form is: y = mx + b, where m = slope, and b = y-intercept.
2x + y = 5Subtract 2x from both sides:
2x - 2x + y = - 2x + 5
y = -2x + 5 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 5.
3y = 9 − 6xDivide both sides by 3 to isolate y:
3y = − 6x + 3
[tex]\frac{3y}{3} = \frac{-6x + 9}{3}[/tex]
y = -2x + 3 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 3.
What do the equations have in common?y = -2x + 5
y = -2x + 3
These equations have the same slope, m = -2.
How are they different?They have different y-intercepts.
y = -2x + 5 ⇒ The y-intercept is (0, 5), where b = 5.
y = -2x + 3 ⇒ The y-intercept is (0, 3), where b = 3.
The equations have the same slope but different y-intercepts, meaning they are parallel lines that run parallel to each other and are spaced vertically apart by a difference of 2 units.
Step 1: Write each equation in slope-intercept form.
Given system of equations:
1. 2x + y = 5
2. 3y = 9 - 6x
Slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's rewrite the equations in slope-intercept form:
1. 2x + y = 5
Subtract 2x from both sides: y = -2x + 5
2. 3y = 9 - 6x
Divide both sides by 3: y = -2x + 3
Step 2: The equations have the same slope (-2) but different y-intercepts 5 and 3.
The common slope (-2) indicates that the lines represented by these equations have the same steepness or inclination.
The difference in y-intercepts means that the lines are parallel and run parallel to each other.
Learn more about Slope here:
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A large box contains 12 medium boxes and 18 small boxes. Each small box contains 25 chocolate bars while there are 20 vanilla bars in each medium box. How many chocolate bars are in a large box?
Answer:
Step-by-step explanation:
The answer is there are 450 chocolate bars in the large box because the small box has 25 chocolate bars and it is 18 small boxes in a large box so you will have the problem of 18 x 25= 450
you will receive cookie and 100 points if you help me
Answer:
-8.45
Step-by-step explanation:
Look at -10 and 0 on the number line. I used a ruler to help me, and found that A and B were about 1 - 1.3 cm apart. I looked at the options and found that -8.45 was the closest.
However, another way you could of worked this out would be to look at your options and eliminate the ones you know don’t work. Then look at your options available and work it out from there.
About how tall would you expect one of these trees to be after 22 years? 22.31ft. 35.2ft. 44.25ft. 46.2ft.
Answer:
The correct answer is C, 44.25. I just took the test....
Step-by-step explanation:
For which function is the ordered pair (2, 12) not a solution?
A) y= 6 x
B) y= x - 10
C) y= 14 - x
D)y= x + 10
Answer:
option b
Step-by-step explanation:
y=12 x=2
12 is not equal to 2-10.
lemme know if you didn't understand
Last year, Derek's mother gave him 53 blue stamps and 36 red stamps to start a stamp collection. Now Derek has 4 times as many stamps in his collection How many stamps does Derek have in his collection? Complete the bar diagram to show your work.
Answer:
At present he has x stamps
Every month he adds 6 numbers, for 8 months
So total added 8x6=48
The total will be x+48 which is expected to be twice of x
x+48=2x
Solving x=48
At present he has 48 stamps
Step-by-step explanation:
Answer:
356
Step-by-step explanation:
53 + 36 = 89
89 x 4 = 356
and where is the bar diagram????
In Diagram 6, JCK is a tangent to the circle ABC
Find the value of x.
A 1149 B 76° C 52° D 26°
Answer:
C
Step-by-step explanation:
if you don't know it choose C
Please help asap! Solve for x and y
Answer:
Step-by-step explanation:
You are working with a square. All 4 sides are equal
2x+ 1 = 4x - 7 Subtract 2x from both sides
1 = 4x - 2x - 7 Combine
1 = 2x - 7 Add 7 to both sides
1 + 7 = 2x Combine
2x = 8 Divide by 2
2x/2 =8/2
x = 4
The diagonals of a square bisect the 90 degree angle.
7y + 3 = 45 Subtract 3 from both sides
7y = 45 - 3 Combine
7y = 42 Divide by 7
y = 42/7
y = 6
What is the value of x?
14(6x−2)=x−2
A)-3
B)2
C)-7
D)-9
14(6x-2)=x-2
84x-28=x-2
84x-x= 28-2
83x = 26
x = 26/83
there are no corect answer below
ok done. Thank to me :>
y = 4x – 1 with inputs x = -3, x = -2, and x = -1
Part 1. If x = -3 the equation would be. Y = -12-1 which would be Y= -13
Part 2. If x = -2 the equation Y = -8-1 which would be Y = -9
Part 3. If x = -1 the equation would be. Y =-4-1 which would be Y = -5
Is it possible for a fifth degree polynomial function with
integer coefficients to have no real zeroes?
HELP!!!!!!!!!!!!!!!!
Answer:
The answere is D
Step-by-step explanation:
i know this because thats how a grid works and its really simple
Please help! I'm confused
The solution to the equation f(x) = g(x) is any x-value that makes the equation true. In terms of using graphs, the solutions are the x-coordinates of any point of intersection.
So if the graphs intersect at (1,5), then the solution is x=1.
This checks, because f(1) = 5 and g(1) = 5, so f(1) = g(1).
Given right triangle ABC, where side "c" is the
hypotenuse, angle B measures 44 degrees, and side
c measures 17 m, find the length of side b.
Round your answer to the nearest hundredth of
meter
Answer:
b = 11.81 m
Step-by-step explanation:
b = c . sinB = 17sin44 = 11.81
Find the value of x in each case.
Answer:
Step-by-step explanation:
To find x
Â= 180⁰-8x (angle on a straight line)
B= 180- 9x (angle on a straight line)
:. G + Â + B = 180⁰ ( sum of angles in a triangle)
5x + 180⁰ - 8x + 180⁰ - 9x = 180⁰
5x -8x - 9x + 180⁰ +180⁰ = 180⁰
-12x + 360⁰ = 180⁰
360⁰ - 180⁰ = 12x
180⁰ = 12x ( divide both sides by 12)
x = 15⁰
There are 30 marbles in a bag. Write an expression for the number of marbles in the bag when 5 marbles are added
Answer:
i will clear you.
Step-by-step explanation:
Given:-
Marbels we have =30
when we add marbels =5
Now,
or,30+5
is a function f(x)= 1/x odd or even?
Answer:
the function is odd.
Step-by-step explanation:
f(x) is even if f(−x)=f(x) . f(x) is odd if f(−x)=−f(x) . Since −1x=−f(x).
Answer:
Odd
Step-by-step explanation:
There are two ways a function can be determined even or odd.
1. Graph
If the line of symmetry is the y=axis, the function is even.
If it can be rotated 180˚ about the origin and lines up with the original equation, it is odd.
If none of the cases above are satisfied, the function is neither.
2. f(-x)
If you substitute -x for x and you get the equation to be the same as before, the function is even.
If you substitute -x for x and you get the previous equation * -1, the function is odd.
If none of the cases above are satisfied, the function is neither.
Let 2m - 1 be a prime number. Prove that m is also a prime number
Answer:
False.
Step-by-step explanation:
This is false.
A Counterexample:
7 is prime.
2(4)-1 is 7.
4 is not prime.
Another Counterexample:
11 is prime.
2(6)-1 is 11.
6 is not prime.
Answer:
If m=2 (which is a prime number), then 4-1=3, 3 is a prime number.
Step-by-step explanation:
link is in the comments!
PLEASE HELP!
Answer:
How can I help you?
1.2) Raflte tickets cost $6 for 5 tickets
How many tickets can you get for $90
Suppose that the radius of a sphere is divided by 9. What happens with the surface area?
Answer:
Rad/9
Step-by-step explanation:
Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation . You may use either an explicit or parametric description of the surface across the slanted face of the tetrahedron x in the first octant ; normal vectors point upward . F= langle0,0,-1 rangle; z = 4-x - y
Step-by-step explanation:
Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or a parametric description of the surface. F =( 0,0,-1) across the slanted face of the tetrahedron Z=4-x-y in the first octant; normal vectors point upward
help me with math and ill mark brainliest
Answer:
I and II
Step-by-step explanation:
All trapezoids have a midsegment. The base angles of isosceles trapezoids are always congruent. Because the top and bottom side are parallel, the same side interior angles are supplementary not complementary.
I need help... pls.
Answer:
Administer 14 ml, 350mg/125mg=2.8×5ml=14ml
For each of the 4 walls of the house, John will need 9 large
planks of wood. If each plank of wood needs 8 pieces of nails
to be secured, how many nails does John need for each wall
of the house?
if b=p+5 and a=p^2+10p+1 find an expression that equals 2b+3a in standard form
Answer:
3p² + 32p + 13
Step-by-step explanation:
Okay, so lets first solve for 2b. 2b = 2(p + 5), which is equal to 2p + 10. Now, let's solve for 3a. 3a = 3(p² + 10p +1), simplifying to 3p² + 30p +3. After adding 2b and 3a, we are able to get 2p + 10 + 3p² + 30p + 3 = 3p² + 32p + 13
Answer:
3p² + 32p + 13
Step-by-step explanation:
3p² + 32p + 13
Find the value of y when x=-4
4. 1/3y=2(x-1/6) 5. -6x-y=17.75
Answer:
1/3y=2(-4-1/6)
The first one answer is y=-25
-6×-4-y=17.75
The second answer is y=6.25
A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is the length of the second rectangle?
Answer:
Step-by-step explanation:
As given, the other rectangle has the same area as this one, but its width is 21 cm. Hence, length is 192 cm.
The ratio of men to women working for a company is 5 to 7. If there are 196 women working for the company, what is the total number of employees?
employees
Answer:
336 employees
Step-by-step explanation:
Hi there!
We're given:
Ratio of men to women ⇒ 5:7
Number of women in the company ⇒ 196
1) Solve for the number of men in the company
Set up a proportion
[tex]\displaystyle \frac{5}{7} = \frac{x}{196}[/tex] where x is the number of men working at the company
Multiply both sides by x
[tex]\displaystyle \frac{5}{7} *196= x\\\\x=140[/tex]
Therefore, there are 140 men working at the company.
Now, we know that there are 140 men and 196 women working at the company. Assuming that they are the only people who work there, the total number of employees is 140 + 196 = 336.
I hope this helps!
Answer:
336 total employees
Step-by-step explanation:
divide women by their respective ratio to get unit multiplier
196÷7=28
add the 2 numbers in the ratio to get both men and women
7+5=12
multiply everyone by unit multiplier
12(28)
336
720 is what percent of $800?
the answer is 90 hope this help.
Chris rented a truck for one day. There was a base fee of $14.99, and there was an additional charge of 75 cents for each mile driven. Chris had to pay
$167.24 when he returned the truck. For how many miles did he drive the truck?
M miles
Answer:
Chris drove the truck 203 miles.
Step-by-step explanation
So, first I subtracted the base free cost of the amount he paid and got $152.25. Then, I divided $152.25/0.75 and got 203. S0, that's how I got the answer. I subtracted the base free because we know he had to pay that initially and then I just divided the rest of the money he had to pay by 0.75 because he was charge 0.75 per mile driven.