Answer:
i think it is the third one but dont know just an educational geuss
Step-by-step explanation:
The given steps from the derivation of the quadratic formula are:
Step 3: [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.
What is the quadratic formula?The quadratic formula is as follows:
x = [-b ± (√b²+4ac)]/2a
This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].
What are the steps to derive the quadratic formula?The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]
Step 1: [tex]ax^2+bx=-c[/tex]
Step 2: Taking 'a' as common
[tex]a(x^2+\frac{b}{a}x)=-c[/tex]
Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides
[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]
⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: Factoring the polynomial
[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: Converting to a common denominator
[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)
⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]
⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]
⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides
⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
⇒ x = [-b ± (√b²+4ac)]/2a
Thus, step 4b best explains or justifies the property "Converting to a common denominator".
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A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches. What is the length of the base of the triangle? A. 17.5 in. B. 35 in. C. 42.7 in. D. 56 in. Please include all work.
Answer:
A. 17.5 in.
Step-by-step explanation:
The formula for the area of a triangle is 1/2 * (b * h), where h represents the height and b represents the base. We can solve from reverse using area/height = base*2
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
Answer:
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
hope I helped you
PLEASE HELP ME!!!!!!!!!!!!
Answer:
1. 4, 4, 6, 8
2. 5, 11, 3, 1
3. 11, 27, 111
4. [tex]16\sqrt{14}-31[/tex]
5. [tex]20\sqrt{2}-56[/tex]
Step-by-step explanation:
For the tables remember that after you solve any negative number will turn positive
For 4-5 just plug in what is in the parenthesis into x and solve
TELL ME THE FORMULA FOR VOLUME AND SURFACE AREA OF PRISMS
Answer:
surfacevolume = 1/2 (bh) l
surfacearea = bh + pl
The parallelogram shown below has an area of 120 units^2 . Find the missing height.
Answer:
Step-by-step explanation:
133
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
Answer:
x=127°
Step-by-step explanation:First you have to solve for n and to do so you have to add the interior angles together and equal them to the remote exterior angle.
n+7+6n+22=197-5n
12n+29=197
12n=168
n-14
once you get n you have to plug it into 197-5n
197-5(14)
197-70
127
The required value of exterior angle m∠x is 127.
From figure x is remote exterior angle m∠x=(197−5n)°. and y and z are interior angles m∠y=(6n+22)° and m∠z=(n+7)° respectively. value of x to be determine.
Angle made at outer side of the corner is called exterior angles.
Here, by properties, sum of the interior angle = remoter exterior angle
So,
m∠x = m∠y + m∠z
197−5n = 6n+22+n+7
168 = 12n
n = 14
put n in m∠x
m∠x=(197−5n)°
m∠x=(197−5*14)°
m∠x=(197−70)°
m∠x=127°
Thus, the required value of exterior angle m∠x is 127.
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Given quad overline{PQ}\perp\overline PQ ⊥ PS start overline, P, Q, end overline, \perp, start overline, P, S, end overline \qquad m \angle QPR = 7x - 9^\circm∠QPR=7x−9 ∘ m, angle, Q, P, R, equals, 7, x, minus, 9, degrees \qquad m \angle RPS = 4x + 22^\circm∠RPS=4x+22 ∘ m, angle, R, P, S, equals, 4, x, plus, 22, degrees Find m\angle QPRm∠QPRm, angle, Q, P, R: Solve for PQR and x. PLZ HELP
Answer: Khan Academy 2020! The answer is 40!
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Find RS. A. 5 B. 10 C. 9 D. 12
Answer:
x=9
Step-by-step explanation:
PQ + QR + RS = PS
2x-6 + 1 + x-4 = 18
Combine like terms
3x -9 = 18
Add 9 to each side
3x-9+9= 18-9
3x = 27
Divide by 3
3x/3 = 27/3
x = 9
Answer:
RS=5
Step-by-step explanation:
solve for x:
2x-6+1+x-4 = 18
combine like terms
3x-9=18
subtract both sides to make x isolated
3x=27
divide by 3 to get x
x=9
RS=x-4
RS=9-4
RS=5
What is the value of the expression in the image? A. 216 B. 224 C. 666 D. 678
Answer:
C. 666
Step-by-step explanation:
USING PEMDAS we can solve this problem.
[tex]675-(15-12)^3 / 3\\15-12=3\\675-(3)^3/3\\675-27/3\\675-9=666[/tex]
Answer:
666
Step-by-step explanation:
Following Order of Operations rules (PEMDAS), we must do first any operations that appear inside parentheses. Here (15 - 12) = (3).
Next we must perform any exponentiation. Here we have 3^3 = 27.
Then we have 675 - 27 / 3, or 666 (Answer C)
What is 3 divided by 2,127
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Hi my lil bunny!
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[tex]3\ \div \ 2127[/tex]
[tex]= \frac{1}{709}[/tex] (Decimal: 0.00141)
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If this helped you, could you maybe give brainliest..?
❀*May*❀
Simplify
-
12 – 81 – 9
5.12
- 451
Answer:
-615.12
Step-by-step explanation:
hope this helps
plz mark as brainliest!!
Plzz help I’ll mark brainliest
Answer:
c
Step-by-step explanation:
the correct answer is c
plz mark me brainliest
What is the length of AC
Answer:
|AC| = 144
Step-by-step explanation:
The larger triangle (on the left) and the smaller one (on the right) are similar.
Therefore the following equation of ratios is correct:
x 7
---------- = ---------
156 - x 84
Then 84x = 7(156) - 7x, or
91x = 1092, or x = 12
Then the length of AC is 156 - x, or 144
i’ll mark you brainliest, please show work!! i’ll also give more points
Answer:
414
Step-by-step explanation
80+10hrs=230
23bacteria:1hr
414bacteria:18hrs
Math Question (10 Points):
Answer:
A
Step-by-step explanation:
Becuase It expands the (2+4)8=2*8+8*4=6*8=48
WILL GIVE BRAINLY PLEASE HELP!!!!A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
x2 – 99 = 0
x2 – 99x = 0
x2 + 5x + 104 = 0
x2 + 5x – 104 = 0
Answer: x2 + 5x – 104 = 0
Step-by-step explanation:
Distribute the x into the x + 5 to make it x2 + 5xSubtract 104 from the other side to set the equation equal to zeroFinal answer is x2 + 5x – 104 = 0How is 30% equivalent to 1.3?
Answer:
30% = 30/100 = 0.3
1.3 would be 130%
I hope this helps you!
30% is equivalent to 0.30 or 3/10, but not 1.3.
There seems to be an error in the statement that 30% is equivalent to 1.3. That is not correct.
To clarify, 30% is equivalent to the decimal value 0.30 or the fraction 3/10.
To convert a percentage to a decimal, we divide the percentage value by 100. In this case, 30 divided by 100 equals 0.30.
If you were looking for a value that represents a 30% increase or an amount including a 30% addition, you would multiply the original value by 1.3, not 30%. For example, if you have a value of $100 and want to increase it by 30%, you would multiply $100 by 1.3, resulting in $130.
So, 30% is equivalent to 0.30 or 3/10, but not 1.3.
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A shipping container in the shape of a rectangular prism is 60 feet long, 45 1/2 feet wide, and 14 feet tall. What is the volume of the shipping container? A. 2,400 ft.^3 B. 2,730 ft.^3 C. 38.220 ft.^3 D. 76,440 ft.^3 Please include work!!
Which of the following are exterior angles? Check all that apply.
6
52
3
O A. 21
O B. 25
O c. 24
O D. 23
E. 22
O F. 26
Using it's concept, it is found that the exterior angles of the triangle are given as follows:
B. <5
C. <4
What are the exterior angles of a triangle?The exterior angles of a triangle are the angles that are outside the triangle.
In this problem, the angles are 4 and 5, which means that options B and C are correct.
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If you have a problem that has multiple variables, you can solve it using a
system of equations. Think of a real-world example where you would need
to solve using a system of equations. Write two or three sentences
describing your example. Include the equations in your description, but do
not solve the system. That will be left to your classmates. helppppp
Step-by-step explanation:
two times of a number added to 18 gives 70
what is value of X.
2x + 18 = 70
2x = 52
X = 26 is answer
can u talk to me in comment section
The system of equations representing the described condition will be [tex]x+y=15\;and \;2x+4y=40[/tex].
A variety of problems can be solved using the system of equations.
Consider a simple problem of purchasing notebooks and pens from the market.
You bought some pens at $2 per pen and some notebooks at $4 per notebook from the market. At the end of shopping, you have spent $40 and you got 15 objects in your bag.
Write the given situation in the form of equations.
Let x be the number of pens bought and y be the number of notebooks bought.
So, the equations can be made as,
[tex]x+y=15\\2x+4y=40[/tex]
Therefore, the system of equations representing the described condition will be [tex]x+y=15\;and \;2x+4y=40[/tex].
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PLS PLEASE HELP!!!!!!
Evaluate 18 + 4 ÷ 2 − 8. (5 points) 2 8 12 3
18 + 4 ÷ 2 − 8
Following PEDMAS, divide first:
18 + 2 -8
Now add and subtract to get the final answer:
18+2 = 20
20-8 = 12
The answer is 12
Answer:
12
Step-by-step explanation:
Please help me with this geometry question:((
Answer:
x = 13
Arc RQ = 180°
Step-by-step explanation:
PEQ is an inscribed angle and the measure of an inscribed angle in a circle is equal to half of the arc it sees.
The perimeter of a circle is always 360° therefore
2 × (5x + 15) + 9x + 17 + 6x - 12 = 25x + 35 = 360°
25x = 360 - 35
25x = 325
x = 13
Since arc RQ is equal to 10x + 30 we replace x with the value we just got
10×13 + 30 = 160°
Help me ASAP for this picture
The graph of f(x) = xx is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
Answer:C and F are correct
Step-by-step explanation:
got it right on edge
22% of $900 = twenty two percent of $900 =
━━━━━━━☆☆━━━━━━━
▹ Answer
$198
▹ Step-by-Step Explanation
[tex]\frac{22}{100} * 900\\\\\frac{22}{1} * 9 = \frac{198}{1} \\\\= 198[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
198
Step-by-step explanation:
22% of 900
22% * 900
Change to decimal form
.22 * 900
198
A power line stretches down a 400-foot country road. A pole is to be put at each end of the road, and 1 in the midpoint of the wire. How far apart is the center pole from the left-most pole?
Answer:
200 ft
Step-by-step explanation:
Since the road is 400 ft, the midpoint of the road is 200 ft from each end of the road.
Please someone help me
Answer:
r = 0.046212737
Step-by-step explanation:
A = 14,400 (what your investment originally is)
P = 7,200 (what you want your investment to be)
n = 365 (interest is compounded daily)
t = 15 (15 years)
Plug all of these numbers into the equation, then solve for r
14,400 = 7,200(1 + r/365)^365 · 15
Divide 7,200 on both sides --> 2 = (1 + r/365)^365 · 15
365 · 15 = 5475 --> 2 = (1 + r/365)^5475
5475√(2) = 1 + r/365 (root 5475 both sides to cancel out the exponent)
(5475√(2)) - 1 = r/365 (subtract one from both sides)
((5475√(2)) - 1) · 365 = r (multiply both sides by 365 to isolate r)
Type the left side into the calculator to get r --> 0.046212737.
Hope this helps!
Find the total cost, to the nearest cent, for a sweater that costs $22.95 with an additional 5.5% sales tax. Show your work.
Answer:
22.95×1.055≈$24.21
Find the measure of a A. 44 B. 88 C. 46 D. 90
====================================================
Explanation:
Since we have a circle, the segments extending from the center outward to the edge of the circle are radius segments. Any two radii of the same circle are the same length. The triangle on the left with the 92 degree angle is isosceles. Any isosceles triangle has exactly two side lengths that are the same, which leads to the base angles being the same as well.
For the triangle on the left with angles a,b,92, the base angles are 'a' and 'b'. So a = b.
For any triangle, the angles add to 180
a+b+92 = 180
a+a+92 = 180 ... Replace b with 'a'
2a+92 = 180
2a = 180-92
2a = 88
a = 88/2
a = 44
angle b is also 44 as well
a+b+92 = 44+44+92 = 180
Find the distance between the points P and Q shown. Question 6 options: A. 73−−√ B. 13−−√ C. 5–√ D. 65−−√
Answer:
[tex]d=\sqrt{73}[/tex]
Step-by-step explanation:
[tex]Q(5, -1)[/tex]
[tex]P(-3, 2)[/tex]
Using the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_2+y_1)^2}[/tex]
[tex]d=\sqrt{(-3-5)^2+(2-(-1))^2}[/tex]
[tex]d=\sqrt{(-8)^2+(3)^2}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{64+9}[/tex]
[tex]d=\sqrt{73}[/tex]
[tex]d\approx 8.5[/tex]
if alan had bought a figure at a discount of 5%, he would pay $20 less. How much would he pay if he had bought it at a discount of 20%
Answer:
80
Step-by-step explanation:
5%-->20% is increased by x4, therefore you multiply 20 by 4 which is 80 or you can set an proportion
5/20=20/x5x=400x=80