The resulting equation after substitution in system of equations :2y = 6x , x² + y = 28 will be option B : x^2 + 3x = 28
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given system of equation are :
2y = 6x.....(1)
[x² + y = 28.........(2)
also, Lisa isolated the variable y in the first equation and then substituted it into the second equation that is :
she substitute y = 3x in second equation :
x^2 + y =28
x^2 + 3x = 28
Therefore, the resulting equation after substitution will be option B : x^2 + 3x = 28
Read more about system of equations at :
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Find the missing interest rate.
I = $63
P = $420
r = %
t = 3 years
Answer: r=5%
Step-by-step explanation:
I=Prt
I/P=Prt/P
I/P=rt
I/(P*t)=rt/t
r=I/Pt
r=63/(420*3)
r=21*3/(420*3)
r=21/420
r=1/20
r=0.05
r=0.05 * 100%
r=5%
need this real fast please
Answer:
slope = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 0) ← 2 points on the line
m = [tex]\frac{0-2}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex] = - [tex]\frac{2}{3}[/tex]
Answer:
-2/3
Step-by-step explanation:
The equation for slope is y2-y1 over x2-x1.
Or you can easily do rise over run.
Lets use the point (0,3.) So, we want to calculate slope, but the only other direct point is (0,2) so lets also use that.
If we start at the point (0,2) and go down 2 units, we just have to go over 3 units to get to (0,3) so thats convienient.
The rise is the -2 units, since you go down 2 units to get to the second point. You also have to run 3 units over to get to the second point.
The run is 3, and the rise is -2.
Rise over run
-2 (rise) over 3 (run)
-2/3
-2/3 is the slope.
Hope this helps!
SOMEONE HELP ME PLEASE ILL GIVE BRAINLY
Answer:
Step-by-step explanation:
In order to determine the information you're being asked for, you need to complete the square on that quadratic. The first step is to move the constant over to the other side of the equals sign:
[tex]x^2-2x=3[/tex]
Here would be the step where, if the leading coefficient isn't a 1, you'd factor it out. But ours is a 1, so we're good there. Now take half the linear term (the term with the single x on it), square it, and add it to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is +1. We add +1 to both sides giving us this:
[tex]x^2-2x+1=3+1[/tex]
Now we'll clean it up a bit. The right side becomes a 4, and the left side is written as its perfect square binomial, which is the whole reason we did this. That binomial is
[tex](x-1)^2=4[/tex] (set equal to the 4 here). Now we'll move the 4 back over and set the whole thing back equal to y:
[tex]y=(x-1)^2-4[/tex]
From this it's apparent what the vertex is: (1, -4),
the axis of symmetry is x = 1, and
the y-intercept is found by setting the x's equal to 0 in the original equation and solving for y. So the y-intercept is (0, -3).
Your choice for the correct answer is the very last one there.
Find the unknown length. Round to the nearest tenth if necessary.
Answer:
55 i believe
28 + 27 = 55
Answer:
a = 7.4
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem:
c^2 = a^2 + b^2
28^2 = a^2 + 27^2
784 = a^2 + 729
55 = a^2
a = 7.4
Help pleasee due soon!! WIll give Brainliest
Answer:
9.7
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf x \approx 9.7}}[/tex]
Step-by-step explanation:
This is a right triangle, which we know because of the square in the corner of the triangle. We can use the right triangle trigonometric ratios.
[tex]sin( \theta) =opposite/hypotenuse[/tex] and [tex]cos (\theta) = adjacent /hypotenuse[/tex] and [tex]tan (\theta)=opposite/adjacent[/tex]
First, identify each side of the triangle as adjacent, opposite, or hypotenuse, relative to the 68 degree angle.
The x is next to, or adjacent, to the angle. The 24 is opposite. We are not given the hypotenuse.
[tex]adjacent= x \\opposite= 24 \\hypotenuse= unknown[/tex]
Since we have the adjacent and opposite, we must use tangent.
[tex]tan (\theta)=\frac{opposite}{adjacent}[/tex]
Substitute the values in. The theta (θ) is the angle.
[tex]tan (68)=\frac{24} {x}[/tex]
Solve for x. One way is by cross multiplying.
[tex]\frac{tan(68)}{1}=\frac{24}{x}[/tex]
Multiply the 1st numerator by the 2nd denominator. Then, multiply the 1st denominator by the 2nd numerator.
[tex]tan (68)*x=1*24[/tex]
[tex]tan(68)*x=24[/tex]
Evaluate tan(68) using a calculator.
[tex]2.47508685*x=24[/tex]
Divide both sides of the equation by 2.47508685. This will isolate the variable x. ( We divide because multiplication is occurring between 2.47508685 and x, and division is the inverse of multiplication).
[tex]\frac{2.47508685*x}{2.47508685}=\frac{24}{2.47508685}[/tex]
[tex]x=\frac{24}{2.47508685}[/tex]
[tex]x=9.69662943[/tex]
Round to the nearest tenth. The 9 in the hundredth place tells us to round up. The 6 becomes a 7.
[tex]x \approx 9.7[/tex]
In this right triangle, x is equal to about 9.7
Help me with number 11 please
umm I don't remember I would say if I remembered
simply 8/-4 dived by -3/9
Answer:
-6
Step-by-step explanation:
find the missing value to complete the square.
x^2 +8x+ ___
Answer:
the answer is x^2+8x+ c
Step-by-step explanation:
If x 2 + b x + c is a perfect square, then there is always the same relation ship between b and c "Find half of b and square it" , so c = ( b /2 ) ^2
x^ 2 + 8 x + ( 8/ 2 )^2 =
x^ 2 + 8 x + 4^ 2 =
x^ 2 + 8 x + 16 =
( x + 4 ) ^2
I hope that helps you
Find the length of the hypotenuse of a right triangle with legs of 8 and 6.
m/4 - 3 = 5 HELPPPPPPPPP PLZZZXZZZZZZZZZZZZZZZZZZ
for g(x)=1/2x-11, find x when g(x)=-5
Answer:
x = 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = 1/2x - 11
g(x) = -5
Step 2: Solve for x
Substitute: -5 = 1/2x - 11Isolate x term: 6 = 1/2xIsolate x: 12 = xRewrite: x = 12Please help math 50 points please dont lie
Answer:
8,250
Step-by-step explanation:
10 to the power of 2 is 100, move the decimal 2 spaces to the right.
Answer:
Hi, i think the answer would be the third option, 8,250.
Step-by-step explanation:
You do the exponents first in this equation according to the acronym PEMDAS. 10 to the second power is 100, so now you have
82.5 × 100
This would be equal to moving the decimal point two spaces to the right, giving us 8,250 as the answer
Which fraction is BETWEEN 211 and 311?
Responses
Answer:
3/12 or 1/4
Step-by-step explanation:
To do this you can just increase the denominator by 1, at least for this question
3/11 is around 0.27, while 3/12 is 0.25. 2/11 is 0.19, which is smaller than 0.25, so
3/12 is a justificable answer.
1. 6(4x+1)=78
2. 2(x+10)=60
Solve for x
Answer:
1. x= -3
2. x= 20
Step-by-step explanation:
sorry if this is wrong,
I need the answer to this ASAP!!!! 30 points!!!
Answer:
6(1/4) or (25/4) pounds
Step-by-step explanation:
1 1(1/4) 1(1/2) 1(3/4) 2
<-----|---------|---------|------------|-----------|---->
X X X X X
X X X
X
X
X
1(1/4) or (5/4)
(5/4) x 5 = 6(1/4) or 25/4 pounds
I hope this helps!
9) f(x) = 3-4x – 12
x2 + 3x + 2
y-int:
HA:
Hole:
VA:
x-int:
Answer:
x=3,2i,-2i
Step-by-step explanation:
A triangle has side lengths 4y, 5y and 9y. The longest side of the triangle is 5y. What value of y proves that this triangle is a right triangle?
Answer:
9y i can be rong
Step-by-step explanation:
. A electric jug was sold allowing 20% discount
with Profit of Rs.120. If the jug was sold
allowing 30% discount, there would have
been loss of Rs. 270. Find the MP of the jug.
solu
9514 1404 393
Answer:
marked price = Rs. 3900
Step-by-step explanation:
The difference between the discounts is 30% -20% = 10% of the marked price. The difference in Rs is 120 -(-270) = 390. If Rs. 390 is 10% of the marked price, then the marked price is (Rs. 390)/(0.10) = Rs. 3900.
The marked price is Rs. 3900.
_____
Check
A 20% discount from 3900 is a price of 3120. If the profit is 120, the cost price is 3000. A 30% discount from 3900 is 2730. This is 270 below the 3000 cost price, so our answer is consistent with problem requirements.
Solve 6 + 1/4a = 3 for a.
Answer:
a= -12
Step-by-step explanation:
Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beach balls $4 each. She bought 10 items in total and it cost $34. How many beachballs did she got?
Answer:
6
Step-by-step explanation:
answer correctly pls and i will give BL
Answer:
I would say 4 more miles than you each week
Step-by-step explanation:
-4+5x-7=10+3x-2x. Solve for x
Answer:
-4 + 5x - 7 = 10 + 3x - 2x
5x - 3x + 2x = 10 + 4 + 7
4x = 21
x = 21/4
x = 5 1/4 or 5.25
Answer: 5=x
Step-by-step explanation:
-4+5x-7=10+3x-2x
Combine like terms:
-10+5x=10+x
Subtract 10 on both sides:
-10-10+5x=10-10+x
-20+5x=x
Subtract 5x on both sides:
-20+5x-5x=x-5x
-20=-4x
Divide -4 on both sides:
-20/-4=-4x/-4
5=x
43. (09.01)
Let A = {15, 25, 35, 45, 55, 65} and B = {25, 45, 65}. What is ANB? (1 point)
O {15, 25, 35, 45, 55, 65}
O {15, 35, 55}
{25, 45, 65}
{15, 25, 35, 45}
Answer:
That is;
{25,45,65}
Step-by-step explanation:
Here, we want to find the set of A n B
That is the set that contains values that are present in both sets A and B
Mathematically, that will be;
{25,45,65}
Helpppppppppppppppppppppppp
Answer:
2^17
Step-by-step explanation:
the indices are added when the integers are multiplied. the integer, however, does not need to be changed since it is already the same.
which is an equation for the line passing through the points (-3,3) and (6,9)
Answer:
y=2/3x +5
hope this helps
Answer:
[tex] \red{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Explanation
[tex] slope \:of \:the\: required\:\: line \implies\\\frac{9-6}{6-(-3)}=\frac{6}{9} [/tex]
[tex] equation \:of \:the\: required\:\: line\implies\:\\y - 3 = \frac{6}{9} (x + 3)[/tex]
[tex] \implies \: 9y - 27 = 6x + 18[/tex]
[tex] \implies \: 6x - 9y + 45=0[/tex]
[tex] \implies\:2x-3y+15=0[/tex]
Hence the equation of the line is
[tex] \green{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Write an expression that represents the height of a tree that begins at 2 feet and increases by 4 feet per year. Let y represent the number of years. PLEASE HELP ME
Answer:
2+4y
Step-by-step explanation:
The graph shows the number of bacteria presented in an experiment
What is the rate of change for the number of bacteria from t=2 to t= 4
Answer:
fdsvStep-by-step explanation:
Henry wanted to collect 65 pounds of cans in 7 days. How much should he collect each day to reach his goal? Which two whole numbers does your answer lie between?
Does (2,2) make the inequality 5x+4y>20 true?
Answer:
No
Step-by-step explanation:
substitute the coordinates of the point into the left side of the inequality and check the value obtained against the right side.
5(2) + 4(2) = 10 + 8 = 18 < 20
then (2, 2 ) does not make the inequality true
Asap answer plssss!, John can do a piece of work in 6 days. When he and Marsha work together, it takes only 4 days. How long will it take Marsha to do the work if she works alone? asap answer plssssss
Answer:
12 days
Step-by-step explanation:
Let the amount of work be x.
John:
6 days = x
1 day = [tex]\frac{1}{6}[/tex]x
Together:
4 days = x
1 day = [tex]\frac{1}{4}[/tex]x
Marsha:
1 day = [tex]\frac{1}{4}[/tex]x - [tex]\frac{1}{6}[/tex]x
= [tex]\frac{6}{24}[/tex]x - [tex]\frac{4}{24}[/tex]x
= [tex]\frac{2}{24}[/tex]x
= [tex]\frac{1}{12}[/tex]x
Marsha can do [tex]\frac{1}{12}[/tex] of the work in 1 day.
No. of days taken (Marsha) = x ÷ [tex]\frac{1}{12}[/tex]x
= 12