What equation results from completing the square and then factoring?
x^2 - 10x = 46
Answers
Answer:
x^2 - 10x = 46
Step-by-step explanation:
\(\bold{Hello!}\\\bold{Your~Answer~Is~Below!}\)
______________________________
\(\bold{Solution~Steps:}\)
\(1.)~Quadratic~equations~such~as~this~one~can~be~solved~by~completing\\~the~square.~In~order~to~complete~the~square,~the~equation~must~first~be~in~the~form:\)
\(\bold{x^2~\frac{+}}~bx=c}\)\(\bold{x^2-10x=46}\)\(2.)~Divide-10~by~2:\)
\(\bold{-10}\) ÷ \(\bold{2=-5}\)\(3.)~Add~the~square~of -5~to~both~sides~of~the~equation:\)
\(\bold{-5^2=25}\)\(\bold{46+25=71}\)\(\bold{This~step~makes~the~left~hand~side~of~the~equation~a~perfect~square.}\)\(4.)~Factor~x^2-10x+25:\)
\(\bold{In~general,~when~x^2+bx+c~is~a~perfect~square,~it~can~be~factored~as~(x+\frac{b}{2}^2).}\)\(\bold{(x-5)^2=71}\)\(5.)~Take~the~square~root~of~both~sides:\)
\(\bold{\sqrt{(x-5)^2}=\sqrt{71}}\)\(\bold{x-5=\sqrt{71}}\)\(\bold{x+5=\sqrt{71}}\)
______________________________
\(\bold{Answer:}\)
\(\bold{\frac{+}~\sqrt{71}}\)\(\bold{x=5+\sqrt{71}}\)\(\bold{x=5-\sqrt{71}}\)______________________________
\(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}\)
Related Questions
please hurry
making it 18 points !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?
The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
The vertical asymptote x = 0 represents that the cost per person approaches $0 as the number of people increases.
The vertical asymptote x = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
Answers
B.) The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.
Good luck with the test! :)
The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
What are asymptotes?"An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity."
"The curves visit these asymptotes but never overtake them. The method opted to find the horizontal asymptote changes involves comparing the degrees of the polynomials in the numerator and denominator of the function. If both the polynomials have the same degree, divide the coefficients of the largest degree terms."
From the equation, y = 11.95x + 25
And from the given graph it is clear that the horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.
Hence, A is the correct option.
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Find the equation of the line, given the following information:
Passes through (1,4) and is parallel to y = 5x + 2.
Answers
Answer:
Step-by-step explanation:
y - 4 = 5(x - 1)
y - 4 = 5x - 5
y = 5x - 1
Can someone explain their answer?
Answers
13,6,-1,-8,-15,-22,-29,-36
Answer: -36
Step-by-step explanation:
13, 6, -1
to get from 13 to 6 and 6 to -1, you would subtract by 7 so keep subtracting by 7 until you get 8 different terms
13, 6, -1, -8, -15, -22, -29, -36
the eighth term would be -36
i hope that makes sense
BRAINLIEST FOR CORRECT ANSWER.
How are reciprocals used in division with rational numbers?
Answers
Answer:
for KCF (or KFC) its keep (so it stays teh same), flip (as in the reciprocal) and change (the sign)
Step-by-step explanation:
Please hurry I will mark you brainliest
View the following image and create a story that MATCHES the graph. Create your own scales and values to incorporate in the story.
Answers
Step-by-step explanation:
A body at rest accelerates to 2.5 meters in 1 second, it then maintains a constant speed for 2 seconds and accelerate 2.5 meters in 2 seconds. It then maintains a constant speed for 2 seconds and finally decelerates for the next eight seconds.
scale = 1cm : 1 unit.
distance axis : 1 to 7.5 meters
Time axis : 1 to 15 seconds
for A boy walk at 8km/h quarter of an hour and he travelled the rest by bus at 28km/h for 12h. What was the total direction travelled
Answers
The boy traveled a total distance of 338 kilometers.
To solve this problem
We can start by calculating the boy's walking distance.
Distance = speed x time.
The boy walked for 0.25 hours, or one-quarter of an hour. The distance covered on foot is calculated as follows:
Distance = 8 km/h x 0.25 h = 2 km
Next, we can determine how far a bus travels. The boy covered the following distance in 12 hours by bus at a speed of 28 km/h:
Distance = Speed x Time
Distance = 28 km/h x 12 hours = 336 km.
The sum of the distances walked and traveled by bus represents the total distance traveled:
Total distance = 2 km + 336 km = 338 km
Therefore, the boy traveled a total distance of 338 kilometers.
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Hi can someone assist me with this question and help me solve it?
Answers
Answer:
40°
Step-by-step explanation:
Given l \\ m,
m∠13 = m∠7 (alternate interior angles)
m∠13+m∠15 = 180° (Sum of angles in a straight line)
\(6x+4+(14x-4)=180\\6x+4+14x-4=180\\20x=180\\x=\frac{180}{20} \\=9\\\\\)
Substitute x to find m∠13
m∠13= 6x+4 = 6(9)+4 = 36 + 4 = 40°
How many kilograms of coffee worth $9.40/kg must be mixed with coffee
worth $11/kg to give 12 kg of coffee worth $9.50/kg?
Answers
Answer:
11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.
Step-by-step explanation:
Let x be the amount of coffee worth $9.40/kg that needs to be mixed with coffee worth $11/kg to get 12 kg of coffee worth $9.50/kg.
We can start by setting up a system of linear equations based on the information given:
Equation 1: x + y = 12 (the total amount of coffee is 12 kg)
Equation 2: (9.4x + 11y)/12 = 9.5 (the average price of the mixed coffee is $9.50/kg)
Simplifying equation 2, we get:
9.4x + 11y = 114
We can now use substitution to solve for x. Solving equation 1 for y, we get:
y = 12 - x
Substituting this into equation 2, we get:
9.4x + 11(12 - x) = 114
Simplifying and solving for x, we get:
9.4x + 132 - 11x = 114
-1.6*x = -18
x = 11.25
Therefore, 11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.
A cylinder with a top and bottom has radius 3x-1 and height 3x+1. Write a simplified expression for its volume.
Answers
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
In this case, the radius of the cylinder is 3x - 1 and the height is 3x + 1. We can substitute these values into the formula to find the volume:
V = π(3x - 1)^2(3x + 1)
Expanding the square of (3x - 1), we get:
V = π(9x^2 - 6x + 1)(3x + 1)
Multiplying the terms using the distributive property, we have:
V = π(27x^3 + 3x^2 - 18x^2 - 2x + 9x + 1)
Simplifying the expression, we combine like terms:
V = π(27x^3 - 15x^2 + 7x + 1)
Therefore, the simplified expression for the volume of the cylinder is V = 27πx^3 - 15πx^2 + 7πx + π.
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What is the equation of the hyperbola?
x2
482
= 1
142
72
142
= 1
482
x2
502
7
482
= 1
x2
482
F
= 1
502
Answers
- 3/8 + 1/6
i kinda just didn't pay attention in class, i just need an explaination of how to solve it and im good to go
Answers
Answer:
\({ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} \)
Marissa wanted a laptop. Best Buy was selling it for $329.00. She had a coupon for 15% off. The sales tax was 8.5%. How much did Marissa end up spending?
Answers
Answer:
you need to divied 15 them subtrac 8.5
Step-by-step explanation:
99g in the ratio 5:2:4
Answers
Answer:
45:18:36
Step-by-step explanation:
\(99 = 5x +2x+4x\\99=11x\\x=9\\\)
substitute x back into 5x:2x:4x
Therefore, 99 in the ratio of 5:2:4...
45:18:36
1,436,492÷2 with steps please
Answers
The expression 1,436,492÷2 has a value of 718246 when evaluated because we divided the numbers
Evaluating the expression 1,436,492÷2From the question, we have the following parameters that can be used in our computation:
1,436,492÷2
The above statement is a quotient expression that divide the values of 1,436,492 and 2
Also, there is no need to check if there are like terms in the expression or not
This is because we are dividing the factors
So, we have
1,436,492÷2 = 718246
This means that the value of the expression is 718246
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(02.07)
Solve for x.
-ax + 3b > 5
Answers
Answer:
X<-3b+5/-a
Step-by-step explanation:
Isolate x, move 3b to the other side, switching its sign to negative.
S1: -ax>5-3b
Next, divide both sides by -a, fully isolating x.
S2: x> 5-3b/-a
Since we divided both sides by -a, we switch the inequality sign per rule.
S3: x<5-3b/-a
find the exact value of sin(cos^-1(2 5))
Answers
The exact value of sin(cos^-1(2/5)) is √21 / 5.
We know that cos(cos^-1(x)) = x for all x in [-1, 1]. Hence,
cos(cos^-1(2/5)) = 2/5
Now we need to find sin(cos^-1(2/5)).
We can use the identity sin^2(x) + cos^2(x) = 1 and substitute cos(x) = 2/5 to get:
sin^2(cos^-1(2/5)) + cos^2(cos^-1(2/5)) = 1
sin^2(cos^-1(2/5)) + (2/5)^2 = 1
sin^2(cos^-1(2/5)) = 21/25
Taking the positive square root (since sine is positive in the first and second quadrants), we get:
sin(cos^-1(2/5)) = √(21/25)
= √21 / 5
Therefore, the exact value of sin(cos^-1(2/5)) is √21 / 5.
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Which expression is equivalent to (x^6y^8)^3/x^2y^2
Answers
Answer:
x^7y^9
Step-by-step explanation:
Remembering the laws of indices and applying BODMAS
(x^6y^8)^3/x^2y^2
(x^6 * y^8)^3/x^2 * y^2
opening bracket
we get;
x^6+3 * y^8+3/x^2 * y^2
x^9 * y^11/x^2 * y^2
Applying law of indices at which when the values are the same during division we pick one coefficient and minus the power
therefore;
x^9-2 * y^11-2
x^7 * y^9
=x^7y^9
Find a quadratic equation which has solutions 2 = 2+6√7 and 2 = 2-6√7. Write the quadratic form in the simplest standard
form ²+bx+c. ASAP IT EXAM
Answers
The quadratic equation in the simplest Standard form, ²+bx+c, with solutions 2 = 2 + 6√7 and 2 = 2 - 6√7, is x² - 4x - 248.
A quadratic equation with the given solutions, we can start by using the fact that if a quadratic equation has solutions x = p and x = q, then it can be written in the factored form as (x - p)(x - q) = 0.
the solutions are 2 + 6√7 and 2 - 6√7. Therefore, the factored form of the quadratic equation is:
(x - (2 + 6√7))(x - (2 - 6√7)) = 0
To simplify this, we can expand the equation:
(x - 2 - 6√7)(x - 2 + 6√7) = 0
Now, let's apply the difference of squares formula:
(x - 2)² - (6√7)² = 0
Simplifying further:
(x - 2)² - 36 * 7 = 0
(x - 2)² - 252 = 0
Finally, we can rewrite the equation in the standard quadratic form, ax² + bx + c:
x² - 4x + 4 - 252 = 0
x² - 4x - 248 = 0
Therefore, the quadratic equation in the simplest standard form, ²+bx+c, with solutions 2 = 2 + 6√7 and 2 = 2 - 6√7, is x² - 4x - 248.
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Write an equation for the transformed logarithm shown below, that passes through (3,0) and (0,2) f(x)= Question Help: −b Video
Answers
The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.
To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:
0 = -b * log(base a)(3 - h) + k
Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:
2 = -b * log(base a)(0 - h) + k
Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.
In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.
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160 fl oz = __ qt? round to the nearest 100th help
Answers
Answer:
5 Quarts
Step-by-step explanation:
Someone help please
Answers
Answer:
12/35
Step-by-step explanation:
(6/7)*(2/5)=(12/35)
Answer:
12/35 don't know if you haft to simplify tho
Step-by-step explanation:
6/7×2/5=12/25
Which ratios form a proportion?
Answers
Which best describes the inventor of a triangle?
Answers
Answer:
I think C
Step-by-step explanation:
Find b given that A (-6, 2), B (b, 0), and C (3,-4) are collinear.
Answers
Answer:
b = -3.
Step-by-step explanation:
If the 3 points are collinear then:
Slope of AB = Slope of BC and so
(0-2)/(b + 6) = (-4-0)/( 3 - b)
-4(b + 6) = -2(3 - b)
-4b - 24 = -6 + 2b
-24 + 6 = 2b + 4b
6b = -18
b = -3.
Bruce paid $975 for 12 months of cable. If the monthly cost is $68, write an equation to represent the total cost. what is the total cost of purchasing cable for 15 months?
Answers
Answer:
Step-by-step explanation:
$68
--------------- * 15 months = $85
12 months
15 months will cost $85. Total cost (m) = ($5.67/mo)*m, where m represents the number of months of service purchased.
What is the product of the difference between 12 and 3 and the quotient of 12 and 3
Answers
Answer: 12 divided by 3 equals 4
Step-by-step explanation: this should answer your question if not, then please feel free to message me.
According to the given information, the difference between 12 and 3 is 9 and the quotient of 12 and 3 is 4. Hence, the Product of the difference and the quotient is 36.
Use the concept of multiplication defined as:
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
To find the product and quotient you mentioned,
Break it down step by step.
First, let's find the difference between 12 and 3.
The difference is the result of subtracting one number from another. So,
12 - 3 = 9.
Next, let's find the quotient of 12 and 3.
The quotient is the result of dividing one number by another. So,
12 ÷ 3 = 4.
Finally, to get the product of the difference and the quotient,
We multiply them together.
In this case,
9x4 = 36.
Hence, the product of the difference between 12 and 3 and the quotient of 12 and 3 is 36.
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From the top of a lighthouse 210 feet high, the angle of depression of a boat is 7°. Find the distance from the boat to the foot of the lighthouse. The lighthouse was built atsea level. round measure of distance to the nearest hundredth.
Answers
Apply the trigonometric function:
Tan a = opposite side / adjacent side
Where:
a = angle = 7°
opposite side = 210
adjacent side = x
Replacing:
Tan 7 = 210/x
x =210/tan 7
x= 1,710.31 feet
The distance from the boat to the foot of the lighthouse is 1,710.31 feet
What is the equation of the parent graph shown?
Answers
Answer: b
The answer for this question is b
write a linear function f with the values f ( - 2 ) = 3 and f ( 5 ) = 7
Answers
You write f (-2) = 3 as (-2, 3) and f (5) = 7 as (5, 7).
The answer for the graph is \(\mathbf{\frac{4}{3}}\textbf{\textit{x}}\mathbf{+\frac{1}{3}}\).
PLEASE HELP! WILL MARK BRAINLIEST
The perimeter of the rectangle is 108 units. Find the dimensions of the rectangle.
Base: 5(x+3)
Height: 2(x+9)
The value of x =
The length of the rectangle is ___ units and the Width is ____ units.
PLEASE HELP THANK YOU!!
Answers
The value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.
How to determine the dimensions?The given parameters are:
Base = 5(x+3)
Height = 2(x+9)
Perimeter = 108
The perimeter of a rectangle is
P = 2 *(Base + Height)
So, we have:
2 *(5(x + 3) + 2(x + 9)) = 108
Divide both sides by 2
5(x + 3) + 2(x + 9) = 54
Open the brackets
5x + 15 + 2x + 18 = 54
Evaluate the like terms
7x = 21
Divide by 7
x = 3
Substitute x = 3 in Base = 5(x+3) and Height = 2(x+9)
Base = 5(3+3) = 30
Height = 2(3+9) = 24
Hence, the value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.
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