Answers
We are given two equations, one of which has an isolated variable [tex]x[/tex].
That screams to me that substitution would be a prefered strategy here, compared to elimination, although both work.
That means we'll be substituting our value of [tex]x[/tex], which is given as [tex]-y+3[/tex], into the first equation, [tex]15x+31y=-3[/tex].
[tex]15x+31y=-3[/tex]
[tex]x=-y+3[/tex]
[tex]15(-y+3)+31y=-3[/tex]
[tex]-15y+45+31y=-3[/tex]
[tex]16y=-48[/tex]
[tex]y=-3[/tex]
With this value, we can plug it back into either of the two equations to solve for [tex]x[/tex], I'll be substituting it back into the second equation, since it's easier.
[tex]x=-y+3[/tex]
[tex]y=-3[/tex]
[tex]x=-(-3)+3[/tex]
[tex]x=6[/tex]
So our solution is [tex](6,-3)[/tex], and to check we can plug it back into the first equation.
[tex]15x+31y=-3[/tex]
[tex]15(6)+31(-3)=-3[/tex]
[tex]90-93=-3[/tex]
Which is true, so our solution is correct.
Hope this helps!
Answer:
Step-by-step explanation:
[tex]\begin{cases} 15x+31y=-3 \\\\ x=-y+3 \ \ | \times 15\end{cases} \Leftrightarrow \ominus\begin{cases} 15x+31y=-3 \\\\ 15x=-15y+45 \ \ \end{cases} \Leftrightarrow \\\\\\ 15x-15x+31y=-3-(-15y)-45 \\\\ 31y=15y-48 \\\\ 31y-15y=-48 \\\\ 16y=-48 \ \ |\div 16 \\\\ y=-3 \ \ ; \ \ x=-y+3=3+3=6 \\\\[/tex]
[tex]\huge \boldsymbol{\mathfrak {Unswer}}: x=6 \ \ ; \ \ y=-3[/tex]
Related Questions
if you help me you get brainly
Answers
Answer:
3 ( 917 ) = 3 ( 900 ) + 3 ( 10 ) + 3 ( 7 )
5 ( 209 ) = 5 ( 200 ) + 5 ( 0 ) + 5 ( 9 )
6 ( 347 ) = 6 ( 300 ) + 6 ( 40 ) + 6 ( 7 )
9 ( 821 ) = 9 ( 800 ) + 9 ( 20 ) + 9 ( 1 )
11 ( 142 ) = 11 ( 100 ) + 11 ( 40 ) + 11 ( 2 )
Step-by-step explanation:
Answer:
Hint(look at the first number in each part and math it with the first number in each answer.) For example, 3(937), the distributive property for that one would be 3(900) + 3(30) + 3(7). Then for 5(209) it would be 5(200) + 5(0) + 5(9), then for 6(342), it would be 6(300) + 6(40) + 6(2). Then for 9(821), it would be 9(800) + 9(20) + 9(1), and for the last one it would be 11(143), it would be 11(140) + 11(40) + 11(3). You basically distribute each amount into different place values.
Step-by-step explanation:
Hope it helps. Mark brainiest if it does!
Farmer David has 24 chickens. He gives a quarter of the chickens to Sally and a sixth of the chickens to Patience. How many chickens does he have left?
Answers
Answer:
14
Step-by-step explanation:
One fourth is 6 and one with is 4. So 4+6=10.24-10=14.
Answer:
14
Step-by-step explanation:
If you have 24 chickens, a quarter of 24 is 6. Then, a sixth of 24 is 4. 6+4=10. 24-10=14. So, he would have 14 chickens left.
How many times does the line y=-1 touch the graph? (Ensure to draw your line on the graph)
Answers
Answer:
The answer is 2 times
Step-by-step explanation:
Well, the line y equals to negative 1 is a horizontal line that crosses through the y axis.
So, if we were to draw that line in how many times is that line intersecting or coming into contact with our graph well it's happening in these two places right here (shown in attached photo) so that would intersect two times.
Thus, The answer is 2 times
-TheUnknownScientist 72
From the set {17, 22, 27}, use substitution to determine which value of x makes the inequality true.
x - 5 < 7
A. 27
B. 22
C. none of these
D. 17
Answers
Answer:
C
Step-by-step explanation:
Solving the inequality
x - 5 < 7 ( add 5 to both sides )
x < 12
None of the given values in the set are less than 12
Then solution is option C
A faucet can fill a bathtub in 6 minutes. the drain can empty the tub in 10 minutes. If both the faucets and the drain are open at the same time, this situation is represented by this expression, where t is the number of minutes it will take to completely fill the bathtub.
[tex] \frac{t}{6} - \frac{t}{10} [/tex]
which expression can also represent this situation?
Answers
Answer:
4t/15
Step-by-step explanation:
Please trust me
HELP ASAP!!!!
I need help finding slopes (100points and brainlyest if it lets me)
Answers
Answer:
Step-by-step explanation:
to find slope, m is slope
m=(y2-y1)/(x2-x1)
let’s use one of the coordinates here:
(50,150) and (100,150)
m= (150-150)/ (100-50)
this is the slope
if this is incorrect please notify me! Thankyou :3 have a great evening :D
Answer:
The slope is 0 and the equation for this graph would be y=150
Step-by-step explanation:
Darcie wants to crochet a minimum of 333 blankets to donate to a homeless shelter. Darcie crochets at a rate of \dfrac{1}{15}
15
1
start fraction, 1, divided by, 15, end fraction of a blanket per day. She has 606060 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways.
Write an inequality to determine the number of days, sss, Darcie can skip crocheting and still meet her goal.
Graph the solution set to this inequality.
Answers
Answer:
s ≤ 15
Step-by-step explanation:
1/15(60 - s) ≥ 3
4 x 15 - s/15 x 15 ≥ 3 x 15
60 - s - 60 ≥ 45 - 60
-s/-1 ≥ -15/-1
s ≤ 15
Can someone please help me with this :( Thank u :))
Answers
Answer:
It would be 54/100
Step-by-step explanation:
because the 4 in 5.4 is in the hundreds so its 54/100
pls mark as brainliest
please help me in questions 15 and 21 with their inequalities and graph
Answers
Answer:
x >= 7 OR x < -8
n <= -3 AND n > -6
Step-by-step explanation:
15) 7x - 6 >= 43 OR 10x + 4 < -76
7x >= 43 + 6 OR 10x < -76 - 4
7x >= 49 OR 10x < -80
x >= 7 OR x < -8
you can draw based on this
for >= it is full dot for < it is like circle on the graph
you have to draw both x>= 7 , x < -8 on the same line because it is OR
so both ranges of x are possible
21) 3 + 2n <= -3 AND 1 - 3n < 19
2n <= -3 -3 AND -3n < 19 - 1
2n <= -6 AND -3n < 18
n <= -3 AND 3n > -18
n <= -3 AND n > -6
so it lies between -6 and -3
u can refer pictures below
HELPP YALL! ILL MARK BRAINIEST!!! LOOK AT PICTURE!!!
Answers
180-67=113 y=113
Answer:
y=113, z= 36
Step-by-step explanation:
because complementary angle to y is isotope with angle 67 degrees so y=113
z=((180-113)+108):5
100 PTS!!!! The perimeter of a rectangle is 4(4x - 5) inches. the length of the sides of the rectangle are 2 x + 3 inches and 3x + 2 inches. WRITE AND SOLVE an EQUATION to find the length of each side of the rectangle. ( you have to show all work for branliest!!!!! :D)
Answers
Answer:
2 sides are [tex]\frac{33}{13}[/tex] or 2.5
2 sides are [tex]\frac{47}{13}[/tex] or 3.6
Step-by-step explanation:
There must be 2 2x+3s and 2 3x+2s
The perimeter is the sum of the sides (it has 4 sides)
2(2x+3) + 2(3x+2) = 4(4x-5)
distributive property
2*2x + 2*3
4x+6
other one
2*3x + 2*2
6x+4
perimeter
4*4x + 4*-5
16x-20
together...
(4x+6) + (6x+4) = 16x-20
add like terms
10x+10 = 16x-20
add 20 to both sides
10x+30 = 16x
subtract 10x from both sides
30 = 26x
divide by 26 on both sides
[tex]\frac{30}{26} = x[/tex]
simplify
[tex]\frac{15}{13}[/tex]
Substitute the x value
2 of the sides are 2x+3
so
[tex]2(\frac{15}{13} ) + 3[/tex]
[tex]\frac{30}{13} + \frac{3}{1}[/tex]
[tex]\frac{33}{13}[/tex]
or 2.5
other sides
[tex]3(\frac{15}{13} ) + 2[/tex]
[tex]\frac{45}{13} + \frac{2}{1}[/tex]
[tex]\frac{47}{13}[/tex] or 3.6
That's all I can say for now! Hope this helps and a thank won't hurt! :)
Write a point-slope equation and a slope-intercept equation for the line graphed below. (ONLY REAL ANSWERS NO LINKS!!!)
Answers
Answer:
Point-slope equation: -2 - 1 = m(-2 - 2)
Slope-intercept equation: y = 3/4x -1/2
Answer:
Step-by-step explanation:
Apples are on sale at the grocery store at a price of 8 apples for $4.00. Maggie buys 12 apples. If she is charged the sale price for apples, how much will Maggie pay?
Answers
Answer:
$6
Step-by-step explanation:
Answer the original questions. (2 points: 1 point ea a) How long is each individual act? b) How long is each group act
Answers
Answer:
a) Each individual act will last 5 minutes.
b) Each group act will last 10 minutes.
Step-by-step explanation:
I think this is right
-40-2[(-8) / 2] please someone explain this how to do it
Answers
Step-by-step explanation:
just try this in calculator
Will give brainliest!
Answers
Answer:
Step-by-step explanation:
25-10=15kgs
15+5=20minutes
1/2*15=7.5hrs
7:05-2:00=5:05pm
The speed of light is approximately 6.71 x 108 miles per hour. Express this number in standard form.
Answers
10^8=100000000
100000000x6.71=671,000,000
Marla filled up her car's gas tank and then went on a trip. After she drove 329 miles, she filled her tank with 14 gallons of gas. If she drove the same number of miles on each gallon of gas, how many miles per gallon did she drive?
Answers
Answer:
23 1/2 miles per gallon
Step-by-step explanation:
We start with dividing 329 miles with 14 gallons because it asks to find the number of miles on each gallon of gas -
Miles
----------------------------- =
Each gallon of gas
329 ÷ 14 = 23 1/2 miles per gallon
Instructions: Find tire slope between the two points given. Then, use the slope and one of the points to write the equation of the line in
Slope-Intercept forn. State the slope and y-intercept.
(0, -3) and (1, -1)
Equation:
Slope:
y-Intercept:
Answers
Answer:
Equation: y = 2x — 3
Slope: 2
Y-intercept: —3
Step-by-step explanation:
m=∆y/∆x
= —3—(—1)/0—1
= —2/—1
= 2
We Know: y - y0 = m (x—x0)
y — (—3) = 2 (x — 0)
y + 3 = 2x
y = 2x — 3
So
Equation: y = 2x — 3
Slope: 2
Y-intercept: —3
Function g gives the amount of a chemical in a persons body in milligrams t hours since the pain ent took the drug. The equation g(t)=600•(3/5)t.
a. What does the fraction (3/5) mean?
B. What are the domain and range of g?
C. Sketch a graph of g
Answers
The fraction 3/5 means that every hour, the amount of chemical increase by a factor of 3/5.
The domain of the function is (0, ∞) and the range is (600, ∞)
What is an exponential function?
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let g represent the amount of a chemical in a persons body in milligrams t hours since the patient took the drug.
[tex]g(t) = 600(\frac{3}{5} )^t[/tex]
The fraction 3/5 means that every hour, the amount of chemical increase by a factor of 3/5.
The domain of the function is (0, ∞) and the range is (0, 600)
Add the fractions
pls helpppp
Answers
Answer:
C
Step-by-step explanation:
WIll give brainliest
In an appellate court,
judges could reverse a trial verdict
citizens may have a trial by jury
cases are heard for the first time
juries may listen to new evidence
Answers
Through (-3,-5), Perpendicular to y = -x-5 in point slope and slope intercept form
Answers
Step-by-step explanation:
I really hope this helps :)
How to find the Focus directrix and the lanth of the latus rectum of the equation below
Answers
Please help!! Very important
Answers
Answer:
A
Step-by-step explanation:
the decreasing part is where is line goes downward. So it's A
Adam went on a shopping trip to Somerville. He purchased a set of dishes originally priced at
$390 but discounted 60%. If sales tax in Somerville is 8%, what was the total cost?
Submit
Answers
Answer:187.2
Step-by-step explanation:
Actual price $390
After 60% discount price will be 156
And Sales tax is 8% . Then the price of sales tax is $31.2.
156+31.2= $187.2
Answer:
168.48
Step-by-step explanation:
IXL
What is the number that is 25 units away from -12?
Answers
Answer:
13
Step-by-step explanation:
25 - 12 = 13
Solve the math problem
Only solve 3 and 4
Answers
Answer:
nothing is being showed
Step-by-step explanation:
Answer:
Step-by-step explanation:
3) Cost of o balloons = 0
4) It represents a proportional relation ship.
Reason
[tex]\dfrac{25.50}{3}=\dfrac{42.50}{5}=\dfrac{59.50}{7}=\dfrac{76.50}{9}=8.5[/tex]
if 2/5 of pizza costs $1.00 how much will the whole pizza cost
Answers
Answer:
2/5
Step-by-step explanation:
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
Answers
Answer:
7x + 2y = 1
Step-by-step explanation:
1. Find the slope of the line.
(y2-y1)/(x2-x1) ----> (11 - (-3))/((-3) -1) ----> (11+3)/ (-3 -1) ----> 14/-4
*lets simplify into (7/-2)*
2. Write into slope intercept form.
y=mx+b (m is the slope) (b is the y intercept)
y = (7/-2)x + b
We now need to find the value of b, this can be done by plugging in values of x and y, and using algebra to solve.
11 = (7/-2)(-3) + b
11 = 10.5 + b
b = 0.5 or 1/2
slope intercept form y = (7/-2)x + 1/2
Now we convert to standard form: ax+by=c
*In this form we our a term cannot be a fraction nor can it be negative*
1. Get x and y on the same side, and since our x term is negative right now, we can make it positive by adding it on both sides.
(7/2)x + y = 1/2
2. We now want to get rid of the fraction in term a, so we multiply the entire function by two, so the denominator cancels out.
2(7/2)x + 2y = 2(1/2)
Simplify and you get
7x + 2y = 1
Answer:
Step-by-step explanation:
Answer:
The Width of the garden will be 9 feet.
Step-by-step explanation:
Given:
Manny has wood =48 feet
Length of the garden = 15 feet
The equation which can be used .
We need to find the width of the garden.
Solution :
Now Length of the garden is given we will substitute in the given equation to find the width.
Now Using Subtraction property we will subtract both side by 30 we get;
Now Using Division Property we will divide both side by 2 we get;
Hence the Width of the garden will be 9 feet.
