(x, y) = (0, -7) and ((28/5 , 21/5)) , as found by solving the system of linear equations.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Given: 2x - y = 7x² + y² = 49
to find: Values of x and y.
Finding:
Solving the system of two linear equations, by deriving the value of one variable from an equation and substituting it in the other equation and solving for the two variables.
eqn1 2x - y = 7
y = 2x - 7
eqn2 x² + y² = 49O
substituting the value of y from eqn1,
we get: x² + (2x - 7)² = 49
x² + 4x² + 49 - 28x = 49
5x² -28x = 0
x ( 5x - 28) = 0
x = 0, x = 28/5
For x = 0, y = -7 (in eqn1)=>
(x, y) = (0, 7)
For x = 28/5
y = 2(28/5) - 7
= (56 - 35) / 5
= 21 / 5
(x,y) = (28/5 , 21/5)
Hence, (x, y) = (0, -7) and (28/5 , 21/5), as found by solving the system of linear equations.
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During an online sale, you buy three sweatshirts and two pairs of sweatpants for $85.50. Later you buy three more sweatshirts and four more pairs of sweatpants for $123. (You can never have too many sweats during a pandemic). What is the sale price of each sweatshirt and each pair of sweatpants?
Answer:
Step-by-step explanation:
let
x = price of a sweatshirt
y = trice of sweatpants
three sweatshirts and two pairs of sweatpants for $85.50
3x + 2y = 85.50
three more sweatshirts and four more pairs of sweatpants for $123
3x + 4y = 123
by solving the system of equations
3x + 2y = 85.50
3x + 4y = 123
we find
x = $16
y = $18.75
HELP 17 POINTS Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What value of p makes the equation true?
Answer:
0.125
Step-by-step explanation:
First, remove the 1/8 by subtracting 1/8 on both sides
-3p = -3/8
Then, isolate the variable by diving each side by -3
p = 0.125
Answer:
0.125
Step-by-step explanation:
did the test and got it right!!
The least common multiple of two numbers is 24. Which could be the two numbers? O 6 and 8 O4 and 6 O 8 and 16 O 4 and 12
Answer: 6 and 8
Step-by-step explanation: because if you multiply and find multiples than its 24
Answer:
THE ANSWER IS B
Step-by-step explanation:
i got 100 :)
the unit digit in the square of 18 is 21 how many natural numbers lie between 12 square and 13 square
Answer:25
Step-by-step explanation:
4x−2y=14 y=12x−1 solve by substitution
Answer:
x= -3/5
Step-by-step explanation:
4x-2y=14
y=12x-1
4x-2(12x-1)=14
4x-24x+2=14
4x-24x=12
-20x=12
×= -12/20
x= -3/5
MORE Math!! please helpppppppppp
Answer:
I need a picture or sum so I can help-
Step-by-step explanation:
Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If AD=3AD=3 and AC=12,AC=12, what is the length of \overline{AB}? AB ? (Note: the figure is not drawn to scale.)
Answer:
The answer is "6"
Step-by-step explanation:
[tex]\to x^2 = 3 \times 12 \\\\\to \sqrt{6^2 +3^2} = \sqrt{45} =\sqrt{9} \sqrt{5} = 3\sqrt{5} \\\\\to x= 6[/tex]
The value of [tex]\overline{AB} =6[/tex]
solve the following
U A room id 48 m long, 3:6 M cared and om hight.
And the cast of dayng tiles on the floor
its 4 walls at the crate of Ro loome
anol
Answer:
is there a picture
Step-by-step explanation:
PLEASE HELP!!
Solve each inequality and graph its solution.
Answer:
the answer is b
A 15% tip on a $14.95 lunch bill is about
I need the answer FASTTTTTT
Answer:
x=7
Step-by-step explanation:
The two triangles are congruent so the equation is
9x-15=7x-1
9x-7x=15-1
2x=14
x=7
Answer:
x=7
Step-by-step explanation:
9x-15=7x-1
which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y?
6y + 4 I guess is the answer for the question
Which expression is equivalent to 24 b minus 34 a b?
Answer:
10 b or who ever is on bottom or top is right
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Trust moi
7(2x-5)=21
What is x?
Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
7(2x - 5) = 21
Step 2: Solve for x
Distribute 7: 2x - 5 = 3Isolate x term: 2x = 8Isolate x: x = 4Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 7(2(4) - 5) = 21Multiply: 7(8 - 5) = 21Subtract: 7(3) = 21Multiply: 21 = 21Here we see that 21 does indeed equal 21.
∴ x = 4 is the solution to the equation.
Solve the system of equations.
7x−3y=20
y=5x−4
x=
y=
Answer:
Step-by-step explanation:
substitute the value of y in the first equation.
7x-3(5x-4)=20
7x-15x+12=20
-8x=20-12
x=8/-8
x= -1
then you substitute the value of x on the y equation to find y
y=5×-1 -4
y= -5-4
y= -9
Answer:
x = -1, and y = -9
Step-by-step explanation:
This is done by solving one of the two equations for x or y, then substituting it in place of that variable in the other equation.
Since y is already clearly defined in the second equation let's go with that:
[tex]Given\ 7x - 3y = 20,\ and\ y = 5x - 4[/tex]
[tex]7x - 3(5x - 4) = 20[/tex]
[tex]7x - 15x + 12 = 20[/tex]
[tex]7x - 15x = 20 - 12[/tex]
[tex]-8x = 8[/tex]
[tex]x = -1[/tex]
Now we can replace x in the equation for y with -1:
[tex]y = 5(-1) - 4[/tex]
[tex]y = -5 - 4[/tex]
[tex]y = -9[/tex]
To make sure our answers are correct, let's substitute them into the original equations:
[tex](-9) = 5(-1) - 4\\-9 = -5 - 4\\-9 = -9[/tex]
Good, let's test the other equation
[tex]7(-1) - 3(-9) = 20\\-7 - (-27) = 20\\-7 + 27 = 20\\20 = 20[/tex]
So we know that our answer is correct.
10÷(2x) when x= -5/4
Answer:
-4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
10 ÷ (2x)
x = -5/4
Step 2: Evaluate
Substitute in x: 10 ÷ (2(-5/4))Multiply: 10 ÷ -5/2Divide: -4Answer: -4
Step-by-step explanation:
2(-5/4) = -5/2
10/ -5/2 = -4
Hope this helps :)
The weight in pounds of seven packages are 25, 10, 20, 4, 6, 3, and 9. The weight of an eighth package is added to the list. The mean weight of the eight packages is 12 pounds. What is the weight in pounds of the eight package?
Answer:
7 because to get the mean it has to be in the middle which comes down to the Number 9 package so that means the the 8th package has to be 7 pounds
Step-by-step explanation:
Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answer:
C. -4a + 22b
Step-by-step explanation:
b 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22
Answer:
Step-by-step explanation:
Solving like terms
-4a + 22b
Option C is the correct answer
Reena bought a jacket for £45 . six months later ,she sold it for £34.65.What was her percentage loss?
When Reena bought a jacket for $45 and after six months later she sold it for $34.65, then the percentage loss is 25%
Given,
Reena bought a jacket for = $45
Selling price of jacket = $34.65
Here, selling price is lower than cost price, so we can consider it as loss
We know,
Loss percentage = (Loss / Initial cost)×100
Loss = Initial cost - Selling price
Loss = 45 -34.65= $10.35
Loss percentage =[tex](\frac{10.35}{45}) 100[/tex]
=0.25×100
=25%
Hence, when Reena bought a jacket for $45 and after six months later she sold it for $34.65, then the percentage loss is 25%
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What is the scale factor of ARST to A UVW?
NEED HELP!
Answer:
B:1
Step-by-step explanation:
the values are the same, so we know the scale is 1:1
hope this helps
Answer:
b)1
Step-by-step explanation:
what is 50% of 180 ?
Answer:
90
Step-by-step explanation:
Answer:
The answer is 90.
Step-by-step explanation:
I hope this helps and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
I need some answers be quick pls. If you get it right I will give you brainliest
Step-by-step explanation:
multiple the power and real number
Answers;
a) Multiply 2 by 3: 6ab.
b) Multiply [tex]c^{5}[/tex] by c by adding the exponents: c^6 or [tex]c^{6}[/tex].
c) Simplify the expression. 10y^7 or [tex]10y^{7}[/tex].
d) Simplify the expression. 12g^4h^5 or [tex]12g^{4}h^{5}[/tex].
PLEASE I NEED HELP W THIS ASAP THANK YOU GUYS PLEASE
Find the product. Write your answer in standard form.
3) (4x+3)(x2 - 4x + 3)
a. 4r + 13.r? + 9
b. 9 - 13.r+ 4r
c. 13 + 9x2 + 4
d. 4r - 13.rº + 9
Answer:
a. 4x³+13x²+9
Step-by-step explanation:
1. Distribute 4x to every term in the second set of parenthesis to get:
4x³-16x²+12x
2. Distribute 3 to every term in the second set of parenthesis to get:
3x²-12x+9
3. Add/subtract terms with the same variables/degrees:
4x³-16x²+12x+3x²-12x+9
4. The simplified answer is:
4x³+13x²+9
Answer:
4x³ - 13x² + 9
Step-by-step explanation:
(4x + 3)(x² - 4x + 3) =
(4x)(x²) + (4x)( - 4x) + (4x)(3) + 3(x²) + 3( - 4x) + 3(3) =
4x³ - 16x² + 12x + 3x² - 12x + 9 =
= 4x³ - 13x² + 9
Question 24 (1 point)
Which of the following is NOT a Congruence Postulate/Theorem
SSS
4
АА
SAS
ASA
I need help asap. Please help me
1 5/8 ,1 1/2 ,1 3/4 , 7/16 Which shows the numbers/fractions in order from smallest to largest?
Answer:
7/16,15/8,13/4,11/2
Step-by-step explanation:
i am not sure but thinking its the wright answer hope it will help you.
Answer:
7/16, 1 1/2, 1 5/8, 1 3/5
Step-by-step explanation:
a simple way to find the smallest to largest is by converting those fractions to decimal. I'll prefer to use a calculator. Then after getting their decimals use the number line system and know which is the highest and lowest from them.
helppp finals are tomorrow
Answer:
Step-by-step explanation:
y = -5x
When x = -2 ; y = -5* (-2) = 10 ; (-2 , 10)
When x = -1 ; y = -5 *(-1) = 5 ; (-1 , 5)
When x = 0 , y = 0 ; (0 , 0)
When x = 1 ; y = -5 *1 = -5 ; (1 , -5)
When x = 2 ; y = -5 *2 = -10 ; (2 , -10)
Mark these points (-2 , 10) , (-1 , 5) , (0 , 0) , (1 , -5) , (2 , -10) and join them.
Please help
I’m stuck on this problem.....
Harry received a package for his birthday. The package
weighed 357,000 centigrams. Select the conversions that
are equivalent to 357,000 centigrams. Mark all that apply.
3,570,000 decigrams
3,570 grams
3.57 kilograms
357 decigrams
Answer:
3.57 kilo
Step-by-step explanation:
factors of tens due to metric system
Answer:
3,570 grams
3.57 kilograms
Step-by-step explanation:
1 centigram is 0.1 decigrams357,000centigram=35,700 decigrams
1 centigram is 0.01 grams357,000 centigram=3570 grams
1 centigram=1e-5 kilograms357,000 centigrams=3.57 kilograms
the opposite of -2.25
Answer:
2.25
Step-by-step explanation:
That's the opposite.
Answer:
Step-by-step explanation:
2.25
Does someone know how to solve this problem?
Answer:
Acute scalene triangle.
Step-by-step explanation:
Acute scalene triangle.
Sides: a = 4 b = 7 c = 8
Area: T = 13.998
Perimeter: p = 19
Semiperimeter: s = 9.5
Angle ∠ A = α = 29.995° = 29°59'41″ = 0.524 rad
Angle ∠ B = β = 61.028° = 61°1'42″ = 1.065 rad
Angle ∠ C = γ = 88.977° = 88°58'37″ = 1.553 rad
Height: ha = 6.999
Height: hb = 3.999
Height: hc = 3.499
Median: ma = 7.246
Median: mb = 5.268
Median: mc = 4.062
Inradius: r = 1.473
Circumradius: R = 4.001
Vertex coordinates: A[8; 0] B[0; 0] C[1.938; 3.499]
Centroid: CG[3.313; 1.166]
Coordinates of the circumscribed circle: U[4; 0.071]
Coordinates of the inscribed circle: I[2.5; 1.473]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 150.005° = 150°19″ = 0.524 rad
∠ B' = β' = 118.972° = 118°58'18″ = 1.065 rad
∠ C' = γ' = 91.023° = 91°1'23″ = 1.553 rad