Solving steps:-
5x+3y=−4
y−2x=6
-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
Explanation : If you think this answer is good, please give "Brainliest" or rate/heart my answer. Hope this helps you.
Question is in image below
A lamppost is 6 feet high and casts and 8 foot shadow. At the same time of day, a flagpole near the lamppost cast a 20 foot shadow. Using the properties of similar triangles, find the height, H, of the flagpole
Answer:
15 ft.
Step-by-step explanation:
I will assume that either both objects are standing straight. We can use similar triangles.
We can see that the side 8 is similar to the side 20, since they are both shadows. Therefore, we can set up an equation:
[tex]\frac{6}{8} =\frac{x}{20}[/tex]
we can cross multiply and get:
8x=120
solve for x:
x=15
Therefore, the lamppost must be 15 feet tall (unless it fell down but we won't talk about that)
What is the missing constant term in the perfect square that starts with x^2+2x?
Answer:
+ 1
Step-by-step explanation:
Given
x² + 2x
Using the method of completing the square
add ( half the coefficient of the x- term)² to x² + 2x
= x² + 2(1)x + 1²
= x² + 2x + 1
= (x + 1)² ← perfect square
Sammy and her family are on a trip. So far, they have traveled 225 miles and are 25% of the way to their destination. How many total miles will they travel?
y=x-5 find the four points in the inverse
How many meters are equal to 18 kilometers?
Answer:
18000
Step-by-step explanation:
The number of meters in 18 kilometers is 18,000 meters(m)
How to convert meters to kilometers1900 meter(m) = 1 kilometer(km)x meters = 18 kilometers
x meters = 18 kilometers × 1000
x = 18,000 meters
Therefore, 18 kilometers is equivalent to 18,000 meters
learn more about conversion:
https://brainly.com/question/9032119
Find the value of the expression
j − 14
for j = 18.
PLEASE ANSWER ILL GIVE 5 STARS AND A HEART
Answer:
25
Step-by-step explanation:
10 + (b - a) · 5
10 + (7 - 4) · 5
10 + 3 · 5
10 + 15 = 25
Answer:
25
Step-by-step explanation:
If a = 4 and b = 7
First you gotta plug it in, so it'd become 10+(7-4)×5
Next we gotta use PEMDAS. So it would be 7-4 which would be 3, multiply that by 5 which would make 15, then add 10 for 25.
A train has 11 train cars. At least 11 passengers are in each train car. No 3 neighboring train cars have more than 50 passengers altogether. What is the maximum possible number of people on the train?
The maximum possible number of people on the train is 183.
Given that a train has 11 train cars, and at least 11 passengers are in each train car, and no 3 neighboring train cars have more than 50 passengers altogether, to determine what is the maximum possible number of people on the train, the following calculation must be done:
50/3 = 16.66 16 + 17 + 17 = 50 16 + 17 + 17 + 16 + 17 + 17 + 16 + 17 + 17 + 16 + 17 = X 16 x 4 + 17 x 7 = X 64 + 119 = X 183 = X
Therefore, the maximum possible number of people on the train is 183.
Learn more about quantities in https://brainly.com/question/21477139
Answer:
189
Step-by-step explanation:
Set up 11 slots on a piece of paper, to simplify since each car must have 11 cars we will be alternating 28,11,11 in a repeated pattern thus getting us 28,11,11,28,11,11,28,11,11,28,11 when you add them up you get 189
Which number is a factor of 14 but not a multiple of 7??
Answer:
2
Step-by-step explanation:
Write out all the factors for 14
Then write out the multiples of 7
Compare the numbers then find the greatest number in 14's factors that isn't in 7's multiples
Find the slope of the line passing through the points (-7,8) and (-7,-6)
Find the slope of the line passing through the points (-9,-8) and (3,-8)
Answer:
1) undefined
2) 0
Step-by-step explanation:
Slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Problem 1:
(x1, y1) = (-7, 8)
(x2, y2) = (-7, -6)
Plug those 2 points into the slope formula and solve:
[tex]m=\frac{-6-8}{-7--7}\\\\m=\frac{-14}{0}[/tex]
Here, you can't divide by 0, so this slope is undefined. An undefined slope would make a completely vertical line on a graph. In this case, the equation of the line would be just:
[tex]x=-7[/tex]
Problem 2:
(x1, y1) = (-9, -8)
(x2, y2) = (3, -8)
[tex]m=\frac{-8--8}{3--9}\\\\m=\frac{0}{12}\\\\m=0[/tex]
The slope is 0, and that would make a horizontal line on a graph. The equation would be:
[tex]y=-8[/tex]
You don't actually need to fully work out the slope that way. If you ever have 2 points with the same x-coordinate, the slope has to be undefined. If you ever have 2 points with the same y-coordinate, then the slope has to be 0, assuming it's linear of course. You can see that in the points given, the first 2 have the same x and the second 2 have the same y.
Which decimal is less than 0.12 and greater than 0.008?
Answer:
Too many examples.
You can pick a number between 120 and 8, then. take that number and move the decimal point to the left 3 spaces.
Here are some examples between 0.12 and 0.008:
0.10.0650.580.07830.119When a retired police officer passes away, he leaves $325,000 to be divided among his five children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
what is the exact value of tan(-π/3)?
A. -√3
B. -√3/3
C.√3/3
D. √3
[tex]\tan \left(-\dfrac{\pi}3\right)\\\\=-\tan \left(\dfrac{\pi}3\right)\\\\=-\sqrt 3[/tex]
(4x 2 − 2x + 10) + (−2x 2 + 4x − 2)
Answer:
2x²+2x+8
Step-by-step explanation:
4x²-2x+10-2x²+4x-2
=4x²-2x²-2x+4x+10-2
=2x²+2x+8
f(x)=x+1/x-2
find the inverse
What rational number represents a drop of 4 1/4 in?
Enter your answer in the box.
Answer:
The fraction 1/4 is a rational number.
It stands for the ratio between the integers 1 and 4.
Answer:
this is your answer
Step-by-step explanation:
this is your answer
Mr. Bailey announced the grade distribution for
his science fair projects. Of the 36 students in the
class, 12 earned A's, 18 earned B's, and 6 earned
C's. If Mr. Bailey were to randomly select one of
his students to talk about their project, what is the
probability that the student chosen had earned an
A on their science fair project?
Answer:
12/36
Step-by-step explanation:
Cuz 12 earned A's so it's 12/, then there are 36 choices so it would be 12/36.
Fred bought a shirt that
was on sale. The original
price was $15.75, but it was
20% off. How much did
Fred save?
Answer:
Fred save about 3.15$ because is 20% off
nvmnvmnvmvnmvnmvnvnmvv
Answer:
ur right
Step-by-step explanation:
MARKING AS BRAINLIEST!! Starr if given functions are inverse)!
Answer: They are inverses of each other
==========================================================
Explanation:
We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.
[tex]h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\[/tex]
and,
[tex]f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\[/tex]
Both composite functions lead to x each time.
The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.
13. The function y = 40(x - 1) + 70 can be used to determine the cost in dollars
for renting a trampoline park for a birthday party for x hours. What is the rate of
change of the cost in dollars to rent the trampoline park with respect to time?
A
$30 per hour
$40 per hour
B
с
$60 per hour
D
$110 per hour
Step-by-step explanation:
the function actually is
y = 40(x - 1) + 70 = 40x - 40 + 70 = 40x + 30
still, the slope (the factor of x) is 40.
that means y (the cost) increases by 40 for every additional hour (x increases by 1).
so, the rate of change (slope) is 40/1 = $40 per hour.
If the Jones family owned a $300,000 home, a $12,000 car, and had $150,000 in other assets, what would be their net worth? $462,000 $450,000 $312,000 $138,000
Answer:
462,000
Step-by-step explanation:
300,000+150,000+12,000=462,000
Answer:
Step-by-step explanation:
write a polynomial function of least degree with integral coefficients that has the given zeros 0,-2,4
Answer:
[tex]x^3-2x^2-8x[/tex]
Step-by-step explanation:
[tex]x(x+2)(x-4)[/tex]
[tex]x(x^2-2x-8)[/tex]
[tex]x^3-2x^2-8x[/tex]
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 18 feet and a height of 15 feet. Container B has a diameter of 16 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
Answer:
5.2%
Step-by-step explanation:
Volume of cylinder= πr²h
In Container A,
D= 18ft, r=18/2=9ft, h=15ft
volume= 22/7 × 9² × 15
= 26730/7 cubic ft.
In Container B,
D=16ft, r= 16/2=8ft, h=18ft
volume= 22/7 × 8² × 18
= 25344/7 cubic ft.
percent of amount of water left in Container A= percent of container A that is full after pumping
Amount of water left in Container A,
26730/7 - 25344/7 = 1386/7
Therefore, % of container A that is full= 1386/7 ÷ 26730/7 × 100
(1386×7×100)/(7×26730)= 5.185
To the nearest tenth= 5.2%
A dog shelter is giving away 18 different dogs, but you have room for only 4 of them.
How many different dog families could you create?
Answer:
..2
Step-by-step explanation:
The number of different dog families that you can create will be 3060.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
A canine sanctuary is offering 18 unique canines, yet you have space for just 4 of them.
Then the number of different dog families that you can create is given as,
¹⁸C₄ = (18!) / [(18 - 4)! x 4!]
¹⁸C₄ = (18 x 17 x 16 x 15 x 14!) / (14! x 4 x 3 x 2 x 1)
¹⁸C₄ = 6 x 17 x 2 x 15
¹⁸C₄ = 3060
The number of different dog families that you can create will be 3060.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ2
Would 5/5x2 3/4 be less greater or equal to 2 3/4
Answer:
greater
Step-by-step explanation:
if you add them and do the multiplication it is greater
Answer:
It would be equal
Step-by-step explanation:
You first divide 5/5, which is equal to 1, multiply that by 2 to get 2.
After that, there is a 3/4 sitting around so you add 3/4 to 2.
Then you will see that both are equal.
5.3mm, 5.0cm, 4.9cm, 5.32cm Which of these following reading is more precise
Answer:
5.32
Step-by-step explanation:
it had a more exact reading than the others
Find the Simple interest paid for eight years on a $850 loan at 7.5% a year
Answer:
850 divided by 7.5
Step-by-step explanation:
The high temperature was recorded as 25.6°F. The low temperature that same day was recorded as −2.7°F. What was the difference between the high and low temperatures for that day? Enter your answer as a decimal in the box.
28.3
Step-by-step explanation:
the difference is the answer to a subtraction problem so we can plug in our numbers like this
25.6-(-2.7) which equals 28.3
a good thing to remember when subtracting negative numbers is that a positive and negative won't always make a negative like in this example
Answer:
He's right it's 28.3
Step-by-step explanation:
152 feet in 16 seconds
Answer:
I'm not sure what you're asking but that is 9.5 feet per second.
Step-by-step explanation:
152÷16=9.5
Answer:
if you are asking about the unit rate it is 9.5 feet per second
Step-by-step explanation:
You just have to do 152/16
hope this helps