Factorize;Answer the tick one i will mark you as brainlist please quickly step by step explanation also please show it clearly i will mark you as brainlist
Answers
Answer:
Solved only ticked ones
4a² + 49b² = (2a + 7b)² - 28ab = 11² - 28*2 = 654x² + 9y² = (2x + 3y)² - 12xy = 12² - 12*6 = 724x² + 9y² = (2x - 3y)² + 12xy = 2² + 12*8 = 10016x² + 25y² = (4x - 5y)² + 40xy = 6² + 40*8 = 356Answer:
use the formula:
[tex]a {}^{2} + {b}^{2} = (a + b) {}^{2} - 2ab[/tex]
1) 4a² + 49b²
= 2²a² + 7²b²
= (2a)² + (7b)²
based on the formula above, a = 2a and b = 7b
= ( 2a + 7b )² - 2(2a)(7b)
substitute 2a+7b = 11 into the equation
= 11² - 2( 14ab )
= 121 - 28ab
substitute ab = 2 into the equation
= 121 - 28(2)
= 121 - 56
= 65
2) 4x² + 9y²
= 2²x² + 3²y²
= (2x)² + (3y)²
based on the formula, a = 2x and b = 3y
= ( 2x + 3y )² - 2(2x)(3y)
substitute 2x+3y = 12 into the equation
= 12² - 2(2x)(3y)
= 144 -2(6xy)
= 144 - 12xy
substitute xy = 6 into the equation
= 144 - 12(6)
= 144 - 72
= 72
3) 4x² + 9y²
= 2²x² + 3²y²
= (2x)² + (3y)²
= (2x)² - (-3y)²
based on the formula, a=2x and b=-3y
= ( 2x-3y )²- 2(2x)(-3y)
substitute 2x-3y = 2 into the equation
= (2)² - 2(2x)(-3y)
= 4 - 2( -6xy )
= 4 + 12xy
substitute xy = 8 into the equation
= 4 + 12(8)
= 4 + 96
= 100
4) 16x² + 25y²
= 4²x² + 5²y²
= (4x)² + (5y)²
= (4x)² - (-5y)²
based on the formula, a = 4x and b = -5y
= (4x-5y)² - 2(4x)(-5y)
substitute 4x-5y = 6
= (6)² -2(4x)(-5y)
= 36 -2(-20xy)
= 36 + 40xy
substitute xy = 8 into the equation
= 36 + 40(8)
= 36 + 320
= 356
Related Questions
Simplify 81 to the negative 3 fourths power. (1 point)
Question 8 options:
1)
−27
2)
negative 1 over 27
3)
27
4)
1 over 27
Answers
Answer:
negative 1 over 27
Step-by-step explanation:
81 * negative 1 over 27 = -3
Answer:
[tex] \dfrac{1}{27} [/tex]
Step-by-step explanation:
[tex] 81^{-\frac{3}{4}} = [/tex]
[tex] = \dfrac{1}{81^{\frac{3}{4}}} [/tex]
[tex] = \dfrac{1}{(\sqrt[4]{81})^3} [/tex]
[tex] = \dfrac{1}{(3)^3} [/tex]
[tex] = \dfrac{1}{27} [/tex]
Not sure what this is but last choice is 60 miles FIRST ANSWER GETS BRAINLIEST HEHEHE
Answers
Answer: b
Step-by-step explanation:
Hope this helps!!
What is the equation, in point intercept form, for a line that goes through (2, -6) and has a slope of -3/4
The answers are in the photo.
Oh and ignore the highlighted answer I mistakenly hit it.
I will give Brainlyist!!!
Answers
Answer:
y+6=-3/4(x-2)
Step-by-step explanation:
"Seventeen more than the product of a number and -3 is less than -29" translate this inequality
Answers
Answer: -3x + 17 < 29
product means multiply, so we multiply -3 and x as seen in the answer.
the less than sign is <. to remember it: less than starts with L and the sign < looks like an L
Carol observes that all of the juniors are taking physics this year. She concludes that when she is a junior, she will take physics for her science class. What kind of reasoning is Carol using to from her conjecture?
A.) Deductive Reasoning
B.) Inductive Reasoning
Answers
Answer:
The answer is B.) Inductive Reasoning
Step-by-step explanation:
Deductive reasoning requires one to start with a few general ideas, called premises, and apply them to a specific situation. Recognized rules, laws, theories, and other widely accepted truths are used to prove that a conclusion is right.
Answer:
Inductive Reasoning
Step-by-step explanation:
Carol’s conjecture is based on her observations.
The cost of an limited edition figurine starts at $255 and it increases in value by 8% each year. What is the growth or decay rate as a decimal? What is the initial value? Write an exponential model that represents the cost f (t) of the figurine t years after it's bought. After 6 years the figurine's value is ?
Answers
Answer:
Growth rate = 8% = 0.08
Initial value (Po) = $255
F(t) = Po* e^rt
F(t) = $412.09897
Step-by-step explanation:
Given that:
Initial cost = $255
Rate of increase per year (r) = 8% = 0.08
Growth rate :
Final amount = Initial amount * (1 + rate)^time
Growth rate = 8% = 0.08
Initial value (Po) = $255
Exponential model for the cost :
F(t) = Initial value * e^(rate * time)
F(t) = Po* e^rt
Value after 6 years :
F(t) = Po* e^rt
t = 6
F(t) = 255 * e^(0.08*6)
F(t) = 255 * 1.6160744
F(t) = $412.09897
what is the answer to this one need asap
Answers
The correct answer is 18.
Hope this helps!!
Brainliest?
1. Natasha worked at a diner for $10per hour last week and already had $42 in her bank account? She paid $206 for a prom dress. The equations 206 = 42 + 10h represents this problem. How many hour did she work to pay for the prom dress?
2. Translate the following sentence into a mathematics equation. The sum of 10 and five time a number is the same as the difference of the number and 6
Answers
Answer:she worked 17 hours
Step-by-step explanation: 10×17=170+42=212
Answer:
She worked 16.4 hours
Step-by-step explanation:
The product of a number and -7 is greater than 42
Answers
divide by -7
x < -6
Answer:
-7*x>42
Step-by-step explanation:
-7 times any negative number greater than 6 is equal to more than 42
pls help ill give brainly
A soup can is 2 in. tall and has a diameter of 8 in.
What is the amount of metal used to make the can?
16π in²
24π in²
48π in²
160π in²
Answers
Answer:
the answer is 48π in²
explanation:
i took the quiz
If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?
Answers
Answer:
D: AT = OG
Step-by-step explanation:
I just took this quiz so that's how I know
Kevin gathered data from his classmates about the number of books they consulted and the total time they spent on a research paper. The scatter plot shows the data he gathered and the line of best fit.
The equation of the line of best fit is y = 70.28x + 425.77.
Based on the line of best fit, approximately how many minutes would a student who consults 3 books spend on a research paper?
211
372
496
637
Answers
The student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have:
Kevin gathered data from his classmates about the number of books they consulted and the total time they spent on a research paper.
The line of best fit is:
y = 70.28x + 425.77
Plug x = 3 in the line of best fit:
y = 70.28(3) + 425.77
y = 21.084 + 425.77
y = 636.61 minutes ≈ 637 minutes
Thus, the student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
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In 2007, Linda purchased a house for $120,000. In 2017, the house was worth $245,000. Find the average annual rate of change in dollars per year in the value of the house
Answers
Answer:
$12,500
Step-by-step explanation:
Given that, Linda purchased a house for $120,000 in 2007 and the value of the house was $245,000 in 2017.
Total change in the value of house= $245,000- $120,000=$125,000.
Total time (in years) between 2007 and 2017 = 2017-2007=10 years.
The value of the house changes by $125,000 in the time interval of 10 years.
So, the average annual rate of change in the value of the house = $125,000/10=$12500 per year.
Hence, the average annual rate of change in the value of the house is $12,500.
here's the question for is you can't see.
what is the vertex of the equation below?
y=2(x-3)>2+4
1. (2,4)
2. (-3,4)
3. (-2,4)
4. (3,4)
Answers
From [tex]y=a(x-h)^2+k[/tex]
The vertex is at (h, k)
Therefore, from [tex]y=2(x-3)^2+4[/tex]
The vertex is at (3,4).
Thus, the answer is 4. (3,4)
Help pls I am in 4th and my sister is at school help
Answers
Answer:
0.125
Step-by-step explanation:
Answer
0.125
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An ordinary coin is thrown 50 times.
Barry says "I am going to get heads 25 times and tails 25 times."
Explain why he could be wrong.
Answers
He could get 25 heads out of the 50 times but the percentage of happening that is very narrow.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
given, An ordinary coin is thrown 50 times. Barry says "I am going to get heads 25 times and tails 25 times."
To better understand Why he could be wrong we need to Understand the difference between Theoretical probability and Actual probability:
The theoretical probability of an occurrence indicates its propensity to occur. The theoretical probability of receiving heads is 1/2 since we know that flipping a coin has an equal chance of landing heads or tails. The frequency of an event actually occurring in an experiment is referred to as its experimental probability.
Because theoretical probability is based on models rather than reality, it isn't very helpful for determining probability in the actual world. Subjective probability is dependent on an individual's own assumptions and biases. It's the likelihood that an individual will encounter the result they are anticipating based on their prior experiences.
Learn more about probability here:
https://brainly.com/question/30034780
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Write the slope-intercept form of the equation that is described below.
Through (-3, 3) and perpendicular to y = 1/3x + 5
What is the equation:
Answers
Answer:
3=-3*-3+b
3=9+b
-9 on both sides
-6=b
y=-3x-6
*-3 because the opposite of 1/3 is -3*
a car rental company charges an initial fee plus a fee per kilometer driven. if a car drives 105 kilometers and pays 183 dollars what is the company's initial fee
Answers
Answer:
a
mark
me
brainlist
omg
Step-by-step explanation:
If rong let
p
l
e
a
s
.
me know
the answer is 100 dolers$
find the least number that must be added to 1400 so as to get a perfect squre. full explanation
Answers
Answer:
so what is the next perfect square after 1400? That's what they are asking.. so I used my calculator to find it..
Step-by-step explanation:
the square root of 1400= 37.41..... but since we want a perfect square.. take 38 squared.. which is 1444 so now we know.. to add 44 to 1400 .... that's your answer 44
A 20-oz bottle of soda costs $2.98.What is the cost per ounce?
Answers
Answer:
$0.15
Step-by-step explanation:
Answer:
0.149
Step-by-step explanation:
2.98 divided by 20 = 0.149
Answer - 0.149
PLEASE HELP :)))
Suppose 3 rooms cost $596 and 5 rooms cost $860. What is the total cost for the number of rooms
Answers
Answer: 596 + 860 = 1456
There are three times as many girls as boys in a school .Find an expression in term of x for the total number of student in school ,where x represent the number of boys in the school
Answers
Answer:
Total number of students = 4x
Step-by-step explanation:
Let the number of boys be x
Since, no of girls = 3 times the no of boys
So, number of girls = 3x
Total number of students = no of boys + no of girls
Total number of students = x + 3x
Total number of students = 4x
Answer:
The total number of students is 4x
Step-by-step explanation:
Hope this helped have an amazing day!
Which is an integer
Answers
Answer:
6.2 is an integer
Step-by-step explanation:
Answer
6.2
Step-by-step explanation:
Why are inverse operations and
properties of equality important when solving
equations? Explain.
Answers
Answer:
An inverse operation is two operations that undo each other e.g. addition and subtraction or multiplication and division. You can perform the same inverse operation on each side of an equivalent equation without changing the equality. This gives us a couple of properties that hold true for all equations.
Solve. x =
A
41°
B.
C
Plz help me fast
Answers
Answer:x= 49°
Step-by-step explanation:
HELP WILL MARK BRAINLIESTTT!!!!
Answers
Answer:
Real= 3 . Imaginary = 3.6
Step-by-step explanation:
mark me brainliest plz
Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).
A) y =
1
3
x + 1
B) y = –
1
3
x + 1
C) y = 3x – 5
D) y = –3x – 5
Answers
Answer:
A. y=1/3x+1
Step-by-step explanation:
When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:
3=1/3*6+b
3=2+b
1=b
now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1
What is the solution to the equation x/2 - 4 = 6?
x = 5
x = 20
x = 1
x = 10
Answers
Answer:
x=5
hope it helps.....
Answer:
I got the answer from the Tutor.
3. A certain 50 cm spring will stretch (in
cm) the weight (in kg) attached to
it. How long will the spring be if a 35
kg weight is attached to it?
Answers
Complete Question
A certain 50 cm spring will stretch (in cm) one fifth the weight (in kg) attached to it. How long will the spring be if a 35 kg weight is attached to it
Answer:
The value is [tex]L_w = 57 \ cm[/tex]
Step-by-step explanation:
The length of the spring is [tex]L = 50 \ cm = 0.5 \ m[/tex]
The mass attached to it is [tex]w = 35 \ kg[/tex]
Generally given from that the spring will stretch one fifth of the weight (in kg)attached to it , it then means that the new length of the spring whenever a weight is attached to it is mathematically represented as
[tex]L_w = L + \frac{W}{5}[/tex]
=> [tex]L_w = 50 + \frac{35}{5}[/tex]
=> [tex]L_w = 57 \ cm[/tex]
Katrina wants to build a fence around her Square Garden the garden has an area of 121 square feet How much Fencing will Katrina Need?
A. 13 Feet
B. 26 Feet
C. 39 Feet
D. 44 Feet
Answers
Answer:
The perimeter of the fencing is 44 feet (Option D)
Step-by-step explanation:
Area and Perimeter
A square shape of side length (a) has an area given by:
[tex]A = a^2[/tex]
And its perimeter is calculated as:
P = 4a
The area of Katrina's square garden is given as A=121 square feet. We need to calculate the side length by solving for a:
[tex]a=\sqrt{121}[/tex]
a = 11 feet
Once we know the value of a, then we calculate the perimeter:
P = 4*11 = 44
The perimeter of the fencing is 44 feet (Option D)