The value of x from the quadratic equation is x = { 2 , -12 }
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 10x = 24 be equation (1)
Adding 5² on both sides of the equation , we get
x² + 10x + 25 = 24 + 25
( x + 5 )² = 49
Taking square roots on both sides , we get
x + 5 = ±7
Subtracting 5 on both sides , we get
x = 2
And , x = -12
Hence , the quadratic equation is solved and value of x is x = -12 or x = 2
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Fill in the missing values in the table. Then determine the constant of proportionality.
blank 1) 2 1/3 yards
feet
blank 2)
yards: 3 feet
blank 3) 2 yards :
feet
blank 4)
yards: 4.5 feet
The constant of proportionality is
Answer:
Blank 1) 2 1/3 yards : 7 Feet
Blank 2) 1 yards : 3 Feet
Blank 3) 2 yards : 6 Feet
Blank 4) 1.5 yards : 4.5 Feet
Therefore, the constant of proportionality is: k = 3
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
Here, k is the constant of proportionality.
From the table, taking the first two points to determine the constant of proportionality.
Yards Feet
1/2 1.5
1/3 1
Using the equation
substituting y = 1.5 and x = 1/2
y = kx
k = y/x
k = (1.5) / (1/2)
k = 1.5 / 0.5
k = 3
also substituting y = 1 and x = 1/3
k = y/x
k = 1 / (1/3)
k = 3
As the constant of proportionality is the same.
Therefore, the constant of proportionality = k = 3Determining Blank 1
Yards = x = 2 1/3 = 7/3
y = blank 1 = Feet ?
k = 3
Using the equation
y = kx
blank 1 = Feet = y = 3 (7/3)
blank 1 = Feet = y = 7
Therefore, Blank 1 = y = Feet = 7In other words,
When Yards = 2 1/3, then Feet = 7
Determining Blank 2
Feet = y = 3
Blank 2 = x = yards ?
k = 3
Using the equation
y = kx
Blank 2 = x = yards = y/k
Blank 2 = x = yards = 3/3
Blank 2 = x = yards = 1
Therefore, Blank 2 = yards = x = 1In other words,
When Yards = 1, then Feet = 3
Determining Blank 3
yards = x = 2
Blank 3 = y = Feet ?
k = 3
Using the equation
y = kx
y = Blank 3 = Feet = 3(2)
y = Blank 3 = Feet = 6
Therefore, Blank 3 = Feet = y = 6In other words,
When Yards = 2, then Feet = 6
Determining Blank 4
Feet = y = 4.5
Blank 4 = x = Yards ?
k = 3
Using the equation
y = kx
x = Blank 4 = y/k
x = Blank 4 = 4.5/3
x = Blank 4 = 1.5
Therefore, Blank 4 = x = Yards= 1.5In other words,
When Yards = 1.5, then Feet = 4.5
Summary:
Blank 1) 2 1/3 yards : 7 Feet
Blank 2) 1 yards : 3 Feet
Blank 3) 2 yards : 6 Feet
Blank 4) 1.5 yards : 4.5 Feet
Therefore, the constant of proportionality is: k = 3
this is a trigonometry question .
Answer:
AB ≈ 5.6 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{12}[/tex] ( multiply both sides by 12 )
12 × cos62° = AB , thus
AB ≈ 5.6 cm ( to 1 dec. place )
Simplify the expression (2a^1/3•3b1/2) (a^1/3•3b^3/4)
Answer: [tex]\frac{1}{4}[/tex][tex]a^{2}[/tex][tex]b^{4}[/tex]
GARDENING Jane needs to buy mulch
for the garden with the dimensions
shown in the figure. For how much area
does Jane need to buy mulch? Round to
the nearest tenth.
15.5 yd
Answer:
I suggest you use Socratic, it solves questions like this.
Step-by-step explanation:
Can anyone help I’m struggling with this
Answer:
Maybe if you could be a bit clear with what you need help with? are you struggling with plotting the points? are stuck on the equation that was given? and do you understand slope intercept form?
I can help you with the equation since that's not the full equation:
-2y = -x + 10
so you divide the -2 and then also divide it on the other side
-2y = -x + 10
-2 -2
cross out the -2's on the left side but do not cross out the y since you will need that. Then divide the numbers so:
-1 % -2 is 0.5 but we don't use decimals in our equation so just put
-1/-2x
then do 10 % -2 and you should get -5
so put the equation together:
y = -1/-2x - 5
(Is that all or do you need help with anything else?)
49/8 as a mixed number
ummm [tex]6\frac{1}{8}[/tex] aha-
Is it impossible to answer those without that imagine on the left but can someone try I’ll mark brainliest
13
Find the area and circumference.
(a)
18 in
AREA
Round to the nearest hundredths.
A) 4071.50 in?
B 1017.88 in2
C 113.09 in
D 226.19 in
Answer:
The area of the circle is":
A = 1017.36 in²
The circumference of the circle is:
C = 113.09 in
Step-by-step explanation:
Given
r = 18 in
We need to determine the area and circumference of the circle
Using the formula to determine the area
A = πr²
= 3.14 × (18)²
= 3.14 × 324
= 1017.36 in² (Rounded to the nearest 0.01 or the Hundredths Place)
Thus, the area of the circle is":
A = 1017.36 in²
Using the formula to determine the circumference.
C=2πr
= 2 × 3.14 × 18
= 113.09 in
Thus, the circumference of the circle is:
C = 113.09 in
999998376474 x 9999991737
Answer:
9.99997550221
Step-by-step explanation:
Simplify 3(2y -1) + 2y
Answer: 8y -3
Step-by-step explanation:
3(2y -1) + 2y
6y -3 + 2y
8y -3
Answer:
8 y - 3
Step-by-step explanation - I got it from google so its right 100%
What's the nicest thing someone has said or done for you? Feel free to comment or leave an answer :)
Answer: I actually got a good one
My best friend told me that I was the best person ever and that she hoped nothing would ever separate us. She always is there when I need her, and she supported me when I came out! She is the greatest Friend I could ever ask for!
"I was walking home one day last winter, it was super cold out and some lady I've never seen before stopped to pick me up. She was really nice and drove way out of her way to drop me off at my house. She gave me a winter hat and a piece of chicken (she was on her way home from KFC) I said 'thank you' and she told me to pay it forward." I never got her name though :(
I took an Uber that had a bill of $15.20. I left a 15% tip. How much was the Uber including the tip?
Answer:
$17.48
Step-by-step explanation:
^^^^^^^^^^^^^
pls help. i need to turn this in before midnight
WILL GIVE BRAINLIEST
Given the system of equations presented here:
4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?
Multiply the first equation by −4 to get −16x − 4y = −16.
Multiply the second equation by −4 to get −8x − 24y = −96.
Multiply the first equation by −2 to get −8x − 2y = −8.
Multiply the second equation by −2 to get −4x − 12y = −48.
Answer:
Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Given:
4x + y = 4 (1)
2x + 6y = 24 (2)
Multiply the second equation by −2 to get −4x − 12y = −48.
4x + y = 4 (1)
−4x − 12y = −48 (3)
Variable x can be eliminated by adding the equations
4x + (-4x) + y + (-12y) = 4 + (-48)
4x - 4x + y - 12y = 4 - 48
0 - 11y = -44
-11y = -44
Divide both sides by -11
y = -44/-11
= 4
y = 4
Answer: Multiply the second equation by −2 to get −4x − 12y = −48.
Step-by-step explanation:
Mai skated x miles, and Clare skated 35 3 5 farther than that. Write an equation to represent the relationship between the distance Mai skated (x) and the distance Clare skated (y). BoldItalicUnderline
Answer:
[tex]y = \frac{3}{5} + x[/tex]
Step-by-step explanation:
Given
Represent Mai's distance as x and Clare's distance as y
[tex]Mai = x\ miles[/tex]
[tex]C = \frac{3}{5}[/tex] farther than Mai
Required
Determine the relationship between both
[tex]C = \frac{3}{5}[/tex] farther than Mai
Substitute x for Mai
[tex]C = \frac{3}{5}[/tex] farther than x
Express as a mathematical expression:
[tex]C = \frac{3}{5} + x[/tex]
Recall that Clare's distance is represented by y.
So, we have:
[tex]y = \frac{3}{5} + x[/tex]
Hence, the relationship is: [tex]y = \frac{3}{5} + x[/tex]
Answer: Mai skated x miles, and Clare skated 3/5 farther than that. Write an equation to represent the relationship between the distance Mai skated (x) and the distance Clare skated (y).
Step-by-step explanation:
An artist uses a 3-foot piece of wood to carve statues she uses 1/6 foot pieces of wood for each statue how many statues can be made from all the wood
Answer:
18
Step-by-step explanation:
Dimension of piece of wood = 3 ft
Dimension of piece of wood used for one statue = [tex]\frac{1}{6}[/tex] ft
To find:
Number of statues that can be made from all the wood ?
Solution:
To find the total number of statues that can be carved from the given piece of wood, we need to divide the dimensions of given piece of wood with the piece required to carve one statue.
Formula:
[tex]\dfrac{a}{\frac{b}{c}} = \dfrac{a\times c}{b}[/tex]
Number of statues that can be made:
[tex]\dfrac{3}{\frac{1}{6}}\\\Rightarrow \dfrac{3\times 6}{1}\\\Rightarrow \bold{18}[/tex]
Therefore, 18 number of statues can be made.
4) Kai has 20 songs on his playlist, and is
adding 2 songs per minute. Write an equation
that represents this situation, where y is the
number of songs on Kai's playlist after x
minutes.
Answer: 20+2x=y
Step-by-step explanation:
Before a renovation a movie theater had 117 seats after the renovation theater had 173 what is the approximate percentage increase of the number of seats in the theater if necessary round to the nearest 10th in percentage
Answer:
47.86%
Step-by-step explanation:
Total number of seats in a movie theater Before a renovation = 117
Total number of seats in a movie theater after a renovation = 173
We need to find the percentage increase of the number of seats. It can be calcualted as :
[tex]\%=\dfrac{\text{|final number-initial number|}}{\text{initial number}}\times 100\\\\=\dfrac{173-117}{117}\times 100\\\\=47.86\%[/tex]
So, the increase in percentage is 47.86%.
Hurry please!
How do you put 14 1/2 into a calculator without the '/' ?
Answer:
well you do 1 divided by 2 which is 0.5
Step-by-step explanation:
PLEASEE HELPP ME DO THISS
Click on the photo to view full solution
What is the slope of the line?
Answer:
The slope of the line is y=1x+1.5
Step-by-step explanation:
so the slope is 1/1 which is 1 only
Answer:
4/5
I hope this helps dkdmdmjsdk
solve the inequality
h-(-2)≥10
Let's solve your inequality step-by-step.
h−(−2)≥10
Step 1: Simplify both sides of the inequality.
h+2≥10
Step 2: Subtract 2 from both sides.
h+2−2≥10−2
h≥8
Answer:
h≥8
(Pls mark brainliest)
The solution to the inequality h -(-2) ≥ 10 is h ≥ 8
The given inequality is:
h -(-2) ≥ 10
Simplify the left hand side
h + 2 ≥ 10
Subtract 2 from both sides of the inequality
h + 2 - 2 ≥ 10 - 2
h ≥ 8
The solution to the inequality h -(-2) ≥ 10 is h ≥ 8
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If kate has 179 apples and Chloe steals 69 how many does kate have left
Answer:
110
Step-by-step explanation:
Answer: and 10. 110. Plus chloe savage
Step-by-step explanation:
Is point 25,20 on the line
Answer:
What Line? it doesnt touch the x or y axis.
Step-by-step explanation:
Solve the system of equations 2x + 2y = 6 and 2y - x = 12 using any method.
Answer:
Step-by-step explanation:
2x + 2y = 6
-2x + 4y = 24
6y = 30
y = 5
10 - x = 12
-x = 2
x = -2
(-2, 5)
The student council is selling Fall festival t-shirts. Long sleeve shirt sell for $12 and short sleeve shirts are $2 less. They sell 606 shirts for a total of $6,778. How many long sleeve shirts were sold?
Answer:
359 long sleeve shirts were soldStep-by-step explanation:
Step one:
given data
let long sleeve shirts be x
and short sleeve shirts be y
Long sleeve shirt sell for $12
short sleeve shirts are $2 less= 12-2= $10
They sell 606 shirts
x+y=606--------1
total cost of the shirts =$6,778.
12x+10y=6778-------------2
therefore the systems of equation for the situation si
x+y=606--------1
12x+10y=6778-------------2
from eqn 1, x=606-y
put x=606-y in eqn 2. we have
12(606-y)+10y=6778
7272-12y+10y=6778
solve for y
-2y=6778-7272
-2y=-494
2y=494
divide both sides by 2
y=4944/2
y=247
put y= 247 in eqn 1
x+247=606
x=606-247
x=359
Hence, 359 long sleeve shirts were sold?
Identify the slope and y-intercept: y = ¼x - ⅓
if you could please help me right not I would really appreciate it.
Answer:
Slope: ¼, y-intercept: -⅓
Step-by-step explanation:
We know that slope-intercept is y=mx+b. We also know that m is the slope, b is the y intercept, y is y, and x is x. As we can see, the equation is y = ¼x - ⅓. Since it is minus ⅓, not plus ⅓, that means the y-intercept is negative. Now we know that the y-intercept is -⅓. Now, let's identify the slope. The slope is ¼, because it is the number next to x (y=mx+b). Now that we know this, we have our answer! The slope is ¼, and the y-intercept is -⅓! I hope this helps!
A toy company decreased the size of its dominoes container by 25%. If the old containers held 136 dominoes, how many dominoes do the new container hold?
Answer: 102
Step-by-step explanation:
Answer:
The new container holds 102 dominoes.
Step-by-step explanation:
136 x 25% =34
136-34 = 102
An expression is shown below: square root of 18 plus square root of 2 Which statement is true about the expression? URGENT
it is rational and equal to 3
it is rational and equal to 4
It is irrational and equal to 3 multiplied by the square root of 2 .
It is irrational and equal to 4 multiplied by the square root of 2 .
Answer:
It is irrational and equal to 4 multiplied by the square root of 2.
Therefore, option d is true.
Step-by-step explanation:
As the expression is
'square root of 18 plus square root of 2'.
i.e. [tex]\sqrt{18}+\sqrt{2}[/tex]
Lets solve the expression
[tex]\sqrt{18}+\sqrt{2}[/tex]
[tex]=3\sqrt{2}+\sqrt{2}[/tex] ∵ [tex]\sqrt{18}=3\sqrt{2}[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:3\sqrt{2}+\sqrt{2}=4\sqrt{2}[/tex]
[tex]=4\sqrt{2}[/tex]
or
[tex]=5.65685\dots[/tex] (in decimal place)
5.65685 indicates that it is irrational and can not be written in the form p/qThus, it is irrational and equal to 4 multiplied by the square root of 2.
Therefore, option d is true.
Answer:
I think it is D
Step-by-step explanation:
Convert 11/3 into a mixed number.
3 2/3
4 1/3
3 1/6
Answer:
3 2/3
Step-by-step explanation: