Answers
Answer:
x = √6 - 2 , -√6-2
Step-by-step explanation:
We have ,
=> y = x² + 4x - 2
Let y = 0=> x² + 4x - 2 = 0
=> x² + 2(2)(x) - 2 = 0
=> x² + 2(2)(x) +2² - 2² -2 = 0
=> x² + 2(2)(x) + 2² -4-2 = 0
=> ( x + 2 )² -6 = 0
=> ( x +2)² = 6
=> ( x + 2) = √6
=> x + 2 = ±√6
=> x = √6 - 2 , -√6-2
The solution for x in terms of y is x = √y - 2 + √6.
To solve the quadratic equation y = x² + 4x - 2 by completing the square, we need to follow a few steps:
Step 1: Move the constant term to the right side of the equation:
y + 2 = x² + 4x
Step 2: Take half of the coefficient of x and square it. Add the resulting value to both sides of the equation to create a perfect square trinomial on the left side:
y + 2 + (4/2)² = x² + 4x + (4/2)²
y + 2 + 4 = x² + 4x + 4
y + 6 = (x + 2)²
Step 3: Rewrite the equation in vertex form:
(y + 6) = (x + 2)²
The equation is now in the form y = (x - h)² + k, where (h, k) represents the vertex of the parabola.
Therefore, the vertex is (-2, -6), and the equation represents a parabola that opens upward.
To solve the equation (y + 6) = (x + 2)² for x, we need to isolate x. Here's how:
Start with the equation: (y + 6) = (x + 2)²
Subtract 6 from both sides of the equation: (y + 6) - 6 = (x + 2)² - 6
Simplify: y = (x + 2)² - 6
Take the square root of both sides of the equation: √y = √[(x + 2)² - 6]
Simplify: √y = x + 2 - √6
Subtract 2 from both sides of the equation: √y - 2 = x - √6
Rearrange the equation to solve for x: x = √y - 2 + √6
To learn more about the quadratic equation;
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Related Questions
Please, i need help with letter B
Answers
Answer:
58
Step-by-step explanation:
6*8+2*2+3*2=58
Find the measure of the exterior angle. *
Answers
Step-by-step explanation:
✧ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }: [/tex]
Set up an equation and solve for x :⋆ [tex] \large{ \bf{(4x + 9) \degree = 2x \degree + (3x - 12) \degree}} [/tex] [ Exterior angle is always equal to the sum of two non - adjacent interior angles ]
~Remove the unnecessary brackets
⟶ [tex] \large{ \bf{4x \degree + 9 \degree = 2x \degree + 3x \degree - 12 \degree}}[/tex]
~Add the like terms : 2x ° & 3x°
⟶ [tex] \large{ \bf{4x \degree + 9 \degree = 5x \degree - 12 \degree}}[/tex]
~Move 4x to right hand side and change it's sign
~Similarly move 12 to left hand side and change it's sign
⟶ [tex] \large{ \bf{9 \degree + 12 \degree = 5x \degree - 4x \degree}}[/tex]
⟶ [tex] \large{ \bf{21 \degree = x \degree}}[/tex]
⟶ [tex]{ \large{ \bf{x = 21 \degree}}}[/tex]
Now , Substituting the value of x in (4x+9)° [ Exterior angle ]⤿ [tex] \large{ \bf{4 \times 21 \degree + 9 \degree}} = \boxed{93 \degree}[/tex]
☥ [tex] \boxed{ \boxed{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline { \tt{93\degree}}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
❅ Let me know if you have any questions regarding my answer! ❅
☞ [tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎
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Answer:
exterior angle=4x+9=4×21+9=93
Step-by-step explanation:
2x+3x-12=4x+9 exterior angle is equal to the sum of two opposite interior angle of the triangle
5x-4x=12+9
x=21
The figure shows two intersecting lines and measures of the resulting angles.
ول
(3x - 8)°
(2x +12)°
What are the values of x and y?
Answers
Answer:
hiiiiiiiii
burrgerry.com
A cylinder has a radius of 10 inches and a height of 6 inches. About what is its volume in cubic inches? Use 3.14 for π.
Answers
188.4 inches square.............
Answer:
1884
Step-by-step explanation:
The restaurant’s location has the same x-coordinate as City Hall but the opposite Y-coordinate. In which quadrant is the restaurant located?
Answers
Answer:
Quadrant lll
Step-by-step explanation:
The coordinates of the restaurant are (-1, -0.5)
Both coordinates negative means quadrant lll
I HELP NEED ASAP PLZ HELP ME
Answers
Last Friday, Kira and Marcy got dinner at Seaside Sushi restaurant. Kira ordered 2 pieces of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Did Kira and Marcy order the same ratio of tuna pieces to crab pieces?
yes or no
Answers
Answer:
No they did not they ate more crab then tuna
Step-by-step explanation:
Need help! Not good at solving math
Answers
Answer:
90-49=41
Answer:
41
Step-by-step explanation:
Erase the line in the middle and it's a right angle, which is 90 degrees, therefore if you subtract 49 from 90 you get 41, the missing angle.
if 100 ml of rat poison is mixed with 2,5l of water then what would be the simplified poison water ratio be
Answers
Answer:
1: 25
Step-by-step explanation:
100 : 25L
25L equal 2500 mL
100:2500 ( divide by 100)
1:25
Please help!!!!! I’ll mark you as brainliest!!!!
Answers
Answer:
B
Step-by-step explanation:
To solve this problem you need to add up all the expenses after this you divide by 12 to figure out how much they will all cost per month
HEEEEELP! pls................
Answers
A shipping container will be used to transport several 140-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 26000
kilograms. Other shipments weighing 13200 kilograms have already been loaded into
the container. Which inequality can be used to determine c, the greatest number of
140-kilogram crates that can be loaded onto the shipping container?
Answers
Answer:
91.42 crates
Step-by-step explanation:
Let
Greatest Number of 140kg crates = x
weight of crate = 140-kilogram
Weight of other shipment = 13200 kilograms
greatest weight of container = 26000 kilograms
Weight of other shipment + (weight of crate * number of crates) ≤ greatest weight of container
13,200 + 140x ≤ 26,000
140x ≤ 26,000 - 13,200
140x ≤ 12,800
x ≤ 12,800/140
x ≤ 91.42 kilograms
Greatest Number of 140kg crates = 91.42 crates
A line graph titled Text messages sent has time of day on the x-axis and number of text on the y-axis. Girls sent 10 in the morning, 25 in the afternoon, 40 in the evening, and 5 at night. Boys sent 5 in the morning, 15 in the afternoon, 20 in the evening, and 15 at night.
The graph shows the number of text messages sent by the boys and girls in one day. Complete the statements.
Boys sent more text messages than girls during the
.
In the morning, girls sent about
more text messages than boys.
Both boys and girls sent the most text messages in the
.
During the afternoon, the students sent a total of approximately
text messages.
Answers
Answer:
Boys sent more text messages than girls during the
✔ night
.
In the morning, girls sent about
✔ 5
more text messages than boys.
Both boys and girls sent the most text messages in the
✔ evening
.
During the afternoon, the students sent a total of approximately
✔ 40
text messages.
Step-by-step explanation:
Answer:
Boys sent more text messages than girls during the
✔ night
.
In the morning, girls sent about
✔ 5
more text messages than boys.
Both boys and girls sent the most text messages in the
✔ evening
.
During the afternoon, the students sent a total of approximately
✔ 40
text messages.
Step-by-step explanation:
if f(x) = 2x -3 what is the value of f(x) when x is -5?
Answers
Answer:
-13
Step-by-step explanation:
To find the value of f(x) when x is -5, substitute -5 for the x in the equation. Then, simplify:
[tex]f(x) = 2x-3\\\\f(-5) = 2(-5)-3\\f(-5) = -10-3\\f(-5) = -13[/tex]
So, when x is -5, the value of f(x) will be -13.
PLEASE HELP ME
Will give brainiest
The graph shows the amount
of money you are saving for
a computer.
What is the slope?
Interpret the slope of the line in the context of the problem.
Answers
Answer:
i think its 2/1
Step-by-step explanation:
take those 2 points and do y2-y1
-----------
x2-x1
12. Which of the following is another way to
classify a scalene triangle with one angle
greater than 90°?
A- acute
B - obtuse
C - right
D equilateral
Answers
Answer:
The correct answer would be obtuse
Step-by-step explanation:
An obtuse angle is an angle that has a measure of more than 90°
So if a triangle has an angle greater than 90° it would be classified as an obtuse triangle
Which of the following is the best example of a statistical question?
Group of answer choices
What was the best-selling single in 2018?
What are students’ favorite types of music?
What artist won a Grammy in 2012?
Where is the Rock-and-Roll Hall of Fame located?
Answers
2(x - 1) 3(x - 2)
3
4
1
I did not understand
Answers
Answer:
3(x-2)
4(x-5)
5(x-6)
1(x-2)
Sally deposited $25000 into Bank A for 2 years at5% per annum. After the 2 years ,she withdrew her all her money from that bank and deposited all into Bank B for 3 years at 7%per annum. How much money did she have in Bank B after the 3 years ?
Answers
Answer:
$525
Step-by-step explanation:
25000×5%×2years/100=$2500
2) 2500×7%×3years/100=$525
A triangle has an area of 46 square inches. If the height of the triangle is 10, what is the length of the base?
Answers
if the height is 10...
9.2 should be the base
9.2 x 10 = 92
92 divide by 2 is 46
If the circumference of a circle is
21.98 feet, what is the diameter of
the circle?
Use 3.14 for pi
Answers
Answer:
diameter = 7 feet
Step-by-step explanation:
Circumference of the circle = pi x d
21.98 = 3.14 x d
d = 21.98/3.14
d = 7 feet
Victoria earns $255 by working 20 hours each week
babysitting. Victoria earns $2.90 more per hour than
her friend, Tanaja. How much does Tanaja make in 10
hours?
Answers
Explanation :
255/20 = 12.75
12.75 - 2.90 = 9.85
9.85 x 10 = 98.50
PLSS HELP IVE BEEN ASKING FOR SO LONG :(
Answers
Answer: 7
Step-by-step explanation:
\frac{-14}{-2}
Both 14 and 2 are divisible by 2, so we can divide both of these numbers by 2.
\frac{-7}{-1}
Both numbers are negative, so we can divide both of these numbers by -1.
\frac{7}{1}
This gives us 7.
Answer:
Step-by-step explanation:
=14 / -2 = 7
-14 / -2 = 14/2 = 7
Kaia's window is in the shape of a trapezoid. Three of the angles are 80°, 100°, and 109°. What is the measure of the fourth angle?
Answers
Answer:
71°
Step-by-step explanation:
Kaia's window is in the shape of a trapezoid. Three of the angles are 80°, 100°, and 109°. What is the measure of the fourth angle?
The sum of angles in a trapezoid is equal to = 360°
We are given 3 angles in the trapezoid as: 80°, 100°, and 109°.
The measure of the fourth angle is calculated as:
360° = 80°+ 100° +109° + fourth angle
360° - (80°+ 100° +109°)
360° - 289°
= 71°
The measure of the fourth angle is 71°
What is 15 percent of 30?
Answers
Answer:
4.5
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
3/20 * 30 = 90/20 = 4.5
You have 10 gallons of lemonade to sell. (1 gal $\approx$ 3785 cm3) a. Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy? b. How many cups will be left over if you sell 80% of the lemonade?
Answers
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Calculating the volume of cone cup:
[tex]= \frac{1}{3}\pi r^2 h \\\\ = \frac{1}{3}\times 3.14 \times 4^2 \times 11 \\\\ = \frac{1}{3}\times 3.14 \times 16 \times 11 \\\\ = \frac{1}{3}\times 3.14 \times 176 \\\\ = 3.14 \times 58.66 \cong 184.31 cm^3[/tex]
[tex]\to 10 \ gal \times 3,785\ \frac{cm^3}{gal} = 37,850\ cm^3\\\\\to 37,850 cm^3 \times \frac{(1 \ cone)}{(184.31 \ cm^3)} \times 205.4 \ cones[/tex]
When buying 5 packages (250 cones):
[tex]\to 8 \ gal \times 3,785 \ \frac{cm^3}{gal} = 30,280\ cm^3 \\\\\to 30,280 \ cm^3 \times \frac{(1\ cone)}{(184.31 \ cm^3)} \cong \ 165 \ cones[/tex]
Calculating the left over cones values:
[tex]\to 250 - 165 = 85[/tex]
Answer:
A.206 cups
B.5 packages
C.85
Step-by-step explanation:
Clarifiction answer
Also the reason why mine's was 206 because it had no option for 205 but 206 so it saids 206 is the right answer so if you say i'm wrong,it's the online homework's fault and not mines.
ps:You couldn't write the answer,you can only select the answer.
At the local store, the cost of 1 pair of jeans is $24 and the cost of 3 pairs is $24 × 3 = $72. At the online store, the cost of 2 pairs of jeans is ($22 × 2) + $6 = $50 and the cost of 3 pairs is ($22 × 3) + $6 = $72.
Answers
Complete question :
Complete the tables to relate the numbers of pairs of jeans to the cost of the jeans at each store. Assume that Tim is placing a single order, and
ignore any taxes.
Answer:
$24, $72
$50
Step-by-step explanation:
From the table :
At local store :
2 pair of jeans cost $48
Cost of a pair :
Cost of 2 pairs / number of pairs
$48 / 2 = $24
Cost of 3 pairs :
Cost per pair * number of pairs :
$24 * 3 = $72
At online store :
Cost of Jean include a fixed fee of $6
Cost of one pair of Jean = $28
Actual cost of Jean :
$28 - $6 = $22
Hence, cost of 2 pair of jeans:
($22*2) + $6
$44 + $6 = $50
A ball shaped like a sphere has a radius of 2.7 centimeters. Which measurement is closest to
the volume of the ball in cubic centimeters?
A 46.38 cm
B 33.93 cm
C 122.15 cm
D 82.45 cm
Answers
Answer:
D) 82.45 cm
Step-by-step explanation:
yall i need an answer within a half hour im stuck
about how many more mile per gallon can you get when you purchase a hybrid car than a nonhybrid car?
Answers
Answer:
26 more mile per gallon
Answer:
26 is the answer
mark me brainliest
Solve for x. Your answer must be simplified. x-24>_9
Answers
Answer:
x[tex]\geq[/tex]33
Step-by-step explanation:
x-24[tex]\geq[/tex]9
x[tex]\geq[/tex]33