ANSWER: The third statement appears to be incorrect.
If using the method of completing the square to solve the quadratic equation
x²-10x – 15 = 0, which number would have to be added to "complete the
square"?
Answer:
For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.
Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:
(x + y)2 = x2 + 2xy + y2 (Square of a sum)
(x − y)2 = x2 − 2xy + y2 (Square of a difference)
To find the roots of a quadratic equation in the form:
\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side.
(v) Equate and solve.
Example 1
Find the roots of x2 + 10x − 4 = 0 using completing the square method.
Answer
Example 2
Solve 4x2 + x = 3 by completing the square.
Answer
Exercises
Solve the following quadratic equations by completing the square
Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s
2
+5s=3Answer
Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x
2
=3−4xAnswer
Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v
2
−6v−2=0Answer
Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0Answer
1. Solving Quadratic Equations by Factoring
3. The Quadratic Formula
The raito of chocolate covered carmels to choclate corvered cherries in my vault is 5 to 2 if i have 84 choclate covereds cherries how many choclate covered caramels do i have
Answer: 1 have 210 chocolate covered caramels
Step-by-step explanation:
step 1
The ratio of chocolate covered caramels to chocolate covered cherries in my vault is 5 to 2 which can also be written as 5:2
But the number of chocolate covered cherries =84
Total ratio is given as 5+2 = 7
Step 2
such that the total number of chocolate i had would be gotten from
Ratio of chocolate covered cherries/ total ratio x Total chocolates = Number of chocolate covered cherries. Let X = Total number of chocolates
2/7 x X = 84
x= 84 x 7 / 2 =294
Therefore The number of chocolate covered caramels= ratio of chocolate covered caramels/ total ratio x Total chocolates =
5/7 X 294= 210
help please!! I need an explanation
Step-by-step explanation:
A triangle's angles add up to be 180 degrees, so you can create an equation to be 180= 130+5x. (the 5x is 2x + 3x)
subtract 130 from both sides and get 50=5x, divide both sides by 5, x is equal to 10.
I'm not sure which angle is angle a, but if you substitute x with 10, you can find the measure of the angle, so if it's 2x, 2(10)=20 and if 3x, 3(10)=30
HELP ASAP
Free response
Question:
Sheri is making a cylindrical-shaped cake for her son's birthday. The cake will be 4 inches tall and 12 inches in diameter.
What will be the volume of the cake? Use 3.14 for pi. Round to the nearest whole number.
Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 2626 thousand dollars and 2 22 thousand dollars, respectively. Suppose we select one of these cars at random. Let X = X=X, equals the sale price (in thousands of dollars) for the selected car.
Complete question :
Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X represent the sale price (in thousands of dollars) for the selected car.1. Find P(26< X<30) You may round your answer to two decimal places
Answer:
0.48
Step-by-step explanation:
Mean, m = 26000 ; Standard deviation, s = 2000
P(x < x)
Zscore = (x - m) / s
P(26< X<30) ;
P[(26 - 26 / 2) < (30 - 26) / 2)]
P[(0 < Z < 2)]
P(Z < 2) - P(Z <0)
Using a z table of z calculator, we can obtain the probabilties of the Z value :
0.97725 - 0.5
= 0.47725
= 0.48 ( 2 decimal places)
(1,5) with a slope of -2
Answer:
y = -2x + 7 is the equation if that's what you are asking for.
answer:
Linear equation :
y= -2x +7
Step-by-step explanation:
Donna packs 14 pounds of nuts in bags . Each bag has 1/4 pound of nuts Which equation shows the number of bags Donna packed with all the nuts
Answer:
Step-by-step explanation:
Where are the equations to choose from?
14 pounds × (1 bag)/(¼ pound) = 56 bags
If the measure of angle 1 is 110° and the measure of angle 3 is (2x+10)", what is the value of x?
w
1
4
2.
3
50
55
60
Save and Fxit
S
Answer:
X is equal to 50..
Step-by-step explanation:
as angle 1 and 3 are equal
2*50+10
100+10
is 110
so X is 50
Marcus borrowed 9000 from his bank to buy a car. The bank charged him a simple interest rate of 1.25%. By the time he paid back the money he had pad a total of 9281.25. How long did it take Marcus to pay back the money?
Answer:
2.5 years
Step-by-step explanation:
Given data
P=9000
r= 1.25%
A= 9281.25
The simple interest expression is given as
A=P(1+rt)
substitute
9281.25= 9000(1+0.0125*t)
9281.25=9000+112.5t
collect like terms
9281.25-9000=112.5t
281.25= 112.5t
t= 281.25/112.5
t= 2.5
Hence the time is 2.5 years
What is six and eighty-seven thousandths
Answer:
6.087
Step-by-step explanation:
0.000
^ones
^tenths
^hundredths
^thousandths
Answer:
depends how u want ur answer... :|
6.087
6 and 870
Hope that helps! :)
Step-by-step explanation:
if f(x)=325(.96)^x find f(6)
9514 1404 393
Answer:
about 254.40
Step-by-step explanation:
Put the value where x is and do the arithmetic. (Any scientific or graphing calculator can do this for you.)
f(6) = 325(0.96^6) ≈ 254.40
Solve for all values of x by factoring.
x2+ 13x + 43 = 1
Answer:
Move 1 to the left side of the equation by subtracting it from both sides. Subtract 1 from 43.
There are 80 dogs and cats in the animal shelter. The ratio of dogs to cat 5/11 how many of animals are dogs
Answer:
Step-by-step explanation:
80/16x5=25
Help please!!!!!!!!!!!!!!!!!! marking brainliest for correct answer!!!!!!!!!!!
Step-by-step explanation:
angle 2 = 49
angle 1 = 131
angle 3 = 112
plz mark my answer as brainlist.hope this will be helpful to you ☺️.
Mr and Mrs. Peters give their 8 year old son an allowance of $5 per week. to keep the same ratio of age to allowance, what allowence should they give their 12 year old daughter?
Answer:
9
Step-by-step explanation:
8-5=3 12-3=9 you subtract 5 and 8 and you get 3 and then you subtract 12 and 3 and you get 9 your answer is 9
Answer: $7.50
Step-by-step explanation: cause it is
write a polynomial in standard form that represents the area of the shaded region
Answer:
x^2-3x+36
Step-by-step explanation:
No question, just whoever needs free answers.
Answer this and get free answers for a bit.
Now what's 2+2?
Answer:
4 lol
Step-by-step explanation:
Answer:
Step-by-step explanation:
The following are Noah's scores on his first ten exams: 89, 90, 79, 92, 80, 94, 86, 91, 82, 89. Calculate the sum of Noah's points
(Only enter the numeric answer - NO WORDS!)
I
Answer:
872
Step-by-step explanation:
89+90+79+92+80+94+86+91+82+89
In the figure, shown, AD, CE, and FB intersect at point F. Find the value of x.
Answer:
8
Step-by-step explanation:
∡AB + ∡BC + ∡CD = 180°
∡CD = ∡AE
∡AB + ∡BC + ∡AE = 180°
(8x + 6)° + (6x + 2)° + (7x + 4)° = 180°
8x + 6 + 6x + 2 + 7x + 4 = 180
21x + 12 = 180
21x = 180 - 12
21x = 168
x = 8
helpppppppppp this is due in 5 minutes!!
Answer:
5
4
1
2
8
,.,.,.,.,.,.,.,
What's ƒ(g(x)) if ƒ(x) = 3x + 7 and g(x) =6x – 5?
Answer:
ƒ(g(x)) = 18x - 8
Step-by-step explanation:
We're looking for the composition of f and g, in which function g is the input to function f. Literally replace "x: in f(x) with g(x) = 6x - 5:
ƒ(g(x)) = 3(6x - 5) + 7, or, after simplification,
ƒ(g(x)) = 18x - 15 + 7, or 18x - 8
The function y=-16x^2+16x+32 represents the height in feet of a firework x seconds after it is launched
Answer:
36feet
Step-by-step explanation:
Since we are not asked what to find, we can as well find the maximum height reached by the rocket
At max height, velocity is zero
V = dy/dx = 0
dy/dx = -32x + 16
0 = -32x+16
32x = 16
x = 16/32
x = 0.5s
Get the maximum height
y = -16(0.5)^2+16(0.5) + 32
y = -4+8+32
y = 36feet
Hence the max height reached by the rocket is 36feet
Can someone please help me with this?!!
I believe that you would need to sell 65 shirts
A man walks 5m due south and then 12m due East. Find his distance from the starting point.
Answer: 13 m
Step-by-step explanation:
distance from starting point = root{(5)^2 + (12)^2 }
=root{ 25 + 144}
= 13
Answer:
13 mStep-by-step explanation:
Between south direction and east direction we have right angle, so we can use Pythagorean theorem:
a² + b² = c²
a = 5 m
b = 12 m
c = the distance
[tex]5^2+12^2=c^2\\\\c^2=25+144\\\\c^2=169\\\\c=\sqrt{169}=13\,m[/tex]
What percent is 50% of 50% of x? Please help.
25% is 50% of 50.
Explaination is on the picture.
50% of 100 is 50.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Let x be a number such that
50% of x is 50
This forms an equation in one variable which can be solved by transposition.
[tex]50/100\times x = 50[/tex]
x/2=50
On multiplying 2 both sides,
[tex]X/2\times 2 =50\times 2[/tex]
X=100
Thus, 50% of 100 is 50.
Learn more about percentage, here:
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Correct question:
50% of what is 50.
Can someone help out I’m confused.
Answer:
y=-2/5x-3
Step-by-step explanation:
the slope is m and the y intercept is b
30 POINTS!!!!! What is the domain for each function below?
Picture included below!
-For the 1st equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and then 3, -3, and 0.
-For the 2nd equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and 0 and 3.
The domain is the set of input values for which the function is real and defined.
Find non negative values for the radicals.
For y = sqrt(3-x) if x is greater than the 3 the value under the square root would be negative which would result in a non real number.
The answer needs to be x <= 3 ( less than or equal to)
For y = sqrt(3x), if x is less than 0, the number under the sqrt root would be negative resulting in a non real number.
The answer is x >= 0 ( greater than or equal to)
The 75 students in the high school band are going on a trip. The total cost of the trip is $1,410. Each student will pay the same amount. How much will each student have to pay?
Find the volume of a cylinder below . The formula for the volume of a cylinder is . The radius of the circle is represented by r and h stands for the height of the cylinder. use 3.14 for pu and round your answers to the nearest tenth
Answer:
The volume of the cylinder V = 942 cm³
Step-by-step explanation:
Step(i):-
Given that the graph
The height of the cylinder (h) = 12cm
The diameter of the cylinder d = 10cm
The radius of the cylinder
d = 2r
r = [tex]\frac{10}{2}[/tex]
r = 5 cm
Step(ii):-
The Volume of the cylinder
V = π r² h
V = π (5)²(12)
V = 300π cubic centimeter
V = 300 × 3.14
V = 942 cm³
Final answer:-
Volume of the cylinder V = 942 cm³
A drug company testing a pain medication wants to know the impact of different dosages on patients' pain
levels. They recruited volunteers experiencing pain to try one of 6 different dosages and then rate their pain
levels on a scale of 1 to 10. Here are the results:
Answer:
A
Step-by-step explanation:
I took the same khan Academy Quiz
The graph which best represents graph A thus option (A) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
As per the given data and graphs.
A good scatter plot will be having a reasonable scale on the x and y-axis.
In the graph, The average pain level is in the range of 2 intervals and dosage in 50 intervals as the data also have close to this range.
Thus, graph A represents the best scatter plot.
Hence "The graph which best represents graph A".
To learn more about graphs,
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The missing graphs are attached below,