To determine the constant that makes the expression (x² + kx) a perfect square,
Take the coefficient of the second term which is k and ÷2
In this case, it is (7/2)²
At the end it looks like
x² + 7x + (7/2)² = 27 + 49/4
(x + 7/2)² = 157/4
The number is added is 7/2² or 49/4.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x² + 7x – 27 = 0.
Now, we have to half the coefficient of x and then add and subtract the square of half the coefficient of x
So, x² + 7x – 27 +7/2² - 7/2² = 0.
( x+ 7/2)² – 27- 49/4 = 0.
( x+ 7/2)² = 157/4
Hence, the number is added is 7/2² or 49/4.
Learn more about equation here:
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You're given a side length of 8 centimeters. How many equilateral triangles can you construct using this information
Answer:
1 equilateral triangle
Step-by-step explanation:
Given
Shape: Equilateral Triangle
Side length = 8cm
Required
Determine the number of triangles
From the question, we understand that the triangle is equilateral and the length of a side is 8cm.
This implies that the length of other sides will also be 8cm.
So, only one triangle can be constructed and their side lengths is 8cm.
Construct quadrilateral with the measurements given below:
Quadrilateral ABCD with AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm
and AC = 7 cm
Answer:
Cevap A şkkı
İyi dersler
cuanto es 1/6 - 1/8 =
Answer:
1/24 ≈0.042
Step-by-step explanation:
How many gallons of a 20% antifreeze solution and a 15% antifreeze solution must be mixed to obtain 30 gal of a 18% antifreeze solution? Round to the nearest gallon
Answer:
20% antifreeze solution = 18 gal
15% antifreeze solution = 12 gal
Step-by-step explanation:
Let
20% antifreeze solution = x
15% antifreeze solution = y
x + y = 30
0.20x + 0.15y = 30 * 0.18
0.20x + 0.15y = 5.4
x + y = 30 (1)
0.20x + 0.15y = 5.4 (2)
From (1)
x = 30 - y
Substitute x = 30 - y into (2)
0.20x + 0.15y = 5.4 (2)
0.20(30 - y) + 0.15y = 5.4
6 - 0.20y + 0.15y = 5.4
- 0.20y + 0.15y = 5.4 - 6
-0.05y = -0.6
y = -0.6/-0.05
y = 12 gal
Substitute y = 12 into (1)
x + y = 30 (1)
x + 12 = 30
x = 30 - 12
x = 18 gal
20% antifreeze solution = 18 gal
15% antifreeze solution = 12 gal
Drew orders a video game online for $50.00. He has a 30% discount
code, and the sales tax is 6%. What is the total cost of his order?
50(30%) = 15
50 - 15 = 35
35 (6%) = 2.1
35 + 2.1 = $37.10
the total cost of his order is $37.10 !!
in a survey of 1500 people who owned a certain type of car, 1050 said they would buy that type of car again. what percent of the people surveyed were satisfied with the car?
Answer:
70%
Step-by-step explanation:
Since 1050 were satisfied.....1050/1500=.7 tun into percent u get 70%
Which graph represents the function f(x)=x2−49/x+7
IS MY ANSWER CORRECT????
Answer: yes you are correct
Step-by-step explanation: just took the test
Answer:
Indeed you are(For anyone else, make sure to see that your bottom point is not filled in. The Top point is black and filled and the bottom is not)
Step-by-step explanation:
help help help MARK BRAINLEST
Answer:
x=18
Step-by-step explanation:
S=(n-2)180
S=(5-2)180
S=3x180
S=540
540=(9x-6)+(3x+23)+95+((7x-4)+90
540=19x+198
540-198=19x
342=19x
342/19=x
x=18
If ADEF = AJKL, DE = 18, EF = 23, DF = 9x - 23, JL = 7x-11, and JK = 3y - 21, find the
values of x and y.
Answer:
x = 6
y = 13
Step-by-step explanation:
since DE and JK are congruent, they are both 18
to find 'y':
3y - 21 = 18
3y = 39
y = 13
DF and JL are diagonals that are congruent so:
9x - 23 = 7x - 11
2x = 12
x = 6
A school custodian discovered a leak in a water pipe. The custodian found that 2,432 fluid ounces of water had leaked out. How many gallons of water is this? Use the conversion factor 1 gallon 128 fluid ounces.
Answer: 19 gallons
Step-by-step explanation:
Conversion factor is 1 gallon is to 128 fluid ounces.
If 2,432 fluid ounces leaked out, to find out the amount of gallons this was, you need to divide the fluid ounces by the number of fluid ounces in a gallon. This is what is done when moving from a smaller unit to a larger one.
= 2,432 / 128
= 19 gallons
Pls help
Given the equations, identify which way the parabola opens by matching an equation on the left with a term on the
right.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
When the parabola has a y^2 term it opens horizontally. (Positive and negative values of y give the same value of x.)
When the parabola has an x^2 term it opens vertically. (Positive and negative values of x give the same value of y.)
The sign is negative when the opening is down or to the left.
__
The opening directions are shown in the attachment.
Answer:
look below
Step-by-step explanation:
i did it
Find the slope of the line through the given points (4,-2),(-1,8)
Answer:
[tex]\displaystyle m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (4, -2)
Point (-1, 8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{8+2}{-1-4}[/tex][Fraction] Add/Subtract: [tex]\displaystyle m=\frac{10}{-5}[/tex][Fraction] Divide: [tex]\displaystyle m=-2[/tex]3/4x+3-6/2x-1 algebric fractions
Answer:
-9x-8/4
Step-by-step explanation:
Find all x-values for which f ( x ) = 2 for the function below.
{ ( - 3, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) }
how would i solve this please help
Answer:
x = -3Step-by-step explanation:
First let us get the equation of the coordinates
y-y0 = m(x-x0)
Using the coordinates ( - 3, 2 ), ( - 1, 0 )
m = 0-2/-1-(-3)
m = -2/2
m = -1
Substitute m = -1 and (-1, 0) into the formula
y - 0 = -1(x+1)
y = -x-1
f(x) = -x-1
Since f(x) = 2
2 = -x-1
-x = 2+1
-x = 3
x = -3
Hence the value of x is -3
can u guys plzzzzzzzzzzzz help
Answer: p =2
Step-by-step explanation: Look at how many people I helped, trust me
Amy and Darren each solved the following system of equations using a different method
y=0.5x + 1
4x -2y=4
Is either of them correct? Explain your reasoning and give the correct solution to the system.
Answer:
what is
Step-by-step explanation:
the the 3 4 4
can someone help me pleaseee :)
u have to make the questions become y = mx + b
Answer:
3. 8y= -7x -12
4. -3y= 4x -12
5. 7y= -2x +4
Do you want me to do the rest?
did you got it??
The rest are:
6. -3y =6x +12
7. -10y= 5x+20
8. 4y=2x +12
how do i change y+2=2/7(x-1) from point-slope form to standard
standard form is y=mx+b
to get there lets simplify the equation
y+2=(2/7)(x-1) original in point slope form
y+2=(2/7)x-2/7 distribute 2/7
y=(2/7)x-16/7 subtract 2 from both sides, 2=14/7
answer: [tex]y=\frac{2}{7}-16/7[/tex]
Will give brainliest please answer please
Answer:
E,F,B
Step-by-step explanation:
Answer:
A,C,E
Step-by-step explanation:
12/21= .571428571
4/7, 16/28 and 8/14 all result in this decimal
Answer the photo below thanks
Answer:
6x60=360
Step-by-step explanation:
60
AI need help with this math homework ASAP I need the independent variable the dependent and the equation
Answer:
b is the independent variable
c is the dependent variable
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Greg’s family went to the movie theater and bought tickets and popcorn. They spent $35 altogether with $9.50 spent on popcorn. Write an equation that can be used to find out how much money x they spent on tickets.
Enrique deposited $4,700 into an account. He made no additional withdrawals or deposits. Enrique earned 1.65% annual simple interest on the money in the account.
What was the balance in his account at the end of 4.5 years?
Enter the amount in the account in the box.
Answer:
$5,048.98
Step-by-step explanation:
took the test
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain
The properties of a parallelogram:
1. opposite sides are parallel
2. opposite sides are equal in length
3. opposite angles are equal
4. diagonals bisect each other
if XN=NZ and NY=NW, then
XY=WZ and XW=YZ because the corresponding angles are equal = corresponding sides are equal
The opposite sides are parallel as well because the diagonals are equal (the vertical opposite angles are equal)
This was a word pasta but hope this helps
The opposite sides are parallel because the diagonals are equal.
Properties of parallelogramFrom the given parallelogram, you can see that the diagonals bisect each other.
Also if XN=NZ and NY=NW, then XY=WZ and XW=YZ show that the corresponding angles are equal
Also from the diagram, the opposite sides are parallel because the diagonals are equal (the vertical opposite angles are equal).
Learn more on properties of parallelogram here: https://brainly.com/question/3100335
Help me! Another question on khan.
Answer:
what are you trying to find the slope?
Step-by-step explanation:
Answer:
calculando la circunferencia
What is the equation of this trend line? Enter answers by filling in the box
Answer:
N= 110 M+ 55?
I'm just trying my best to help you
16 üssü 5 sayısının 1 ➗ 8 i kaçtır?
Answer:
The answer is 131072
Step-by-step explanation:
[tex] \frac{1}{8} \times {16}^{5} = 131072[/tex]
Vinay bought a flat for ₹ 4,50,000. He spent ₹ 10,000 on its paintings and repair. Then he sold it for ₹ 4,25,500. Find his gain or loss and also its percent.
Step-by-step explanation:
hence you got the answer
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comment down
If there is any kind of suspicious mistake
then sorry
1.45x + 1.25y =70.85
x + y = 53
Answer:
Your answer is
y= 30
x= 23
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
Find the bank discount and proceeds using ordinary interest for a loan to michelle anders for 7,200 at 8.25% annual simple interest from august 8 to november 8
Answer:
$145.5
Step-by-step explanation:
Period, t = August 8.to November 8 = 3 months
Simple interest formula :
A = P(1 + rt)
A = final amount =. 7200
7200 = P(1 + (0.0825 * 3/12))
7200 = P(1 + 0.020625)
7200 = P(1.020625)
7200 = 1.020625P
P = 7200 / 1.020625
P = 7054.5009
Bank discount :
A - P
7200 - 7054.5009
= $145.4991
= $145.5