Answer:
Factor 3 out of the variable terms
Answer:
Factor 3 out of the variable terms.
Step-by-step explanation:
To complete the square the coefficient on the x^2 term must be 1
Therefor
Factor 3 out of the variable terms.
Which statement can you use to conclude that a relationship must be non-proportional?
The graph of the relationship is linear.
The graph of the relationship is linear.
The equation of the relationship is in the form y = kx
The equation of the relationship is in the form, y = kx
The relationship has a constant rate of change.
The relationship has a constant rate of change.
The y-intercept of the graph of the relationship is ( 0, 1).
9514 1404 393
Answer:
(d) The y-intercept of the graph of the relationship is ( 0, 1).
Step-by-step explanation:
The y-intercept of a proportional relation is always zero. If it is 1, the relationship must be non-proportional.
if a system of linear equations has infinitely many solutions
Use the information given to enter an equation in standard form.
(−1, 1) and (0, 2) .
First find the slope:
m = ( 2 - 1 ) / ( 0 - (-1) ) = 1 / 1 = 1
Set up slope-intercept form:
y = 1·x +2
Now move x and y to the left and leave 2 on the right:
-x + y = 2
This is also equivalent to x - y = -2, so that just depends if you want your x coefficient to be positive or negative.
Answer:
Standard form: x - y = -2
Step-by-step explanation:
The standard form of linear equations is Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.
Given the two points, we must first solve for the value of the slope.
Let (x₁, y₁) = (-1, 1)
(x₂, y₂) = (0, 2)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 - 1)/[0 - (-1)]
m = 1/(0 + 1) = 1
Therefore, the value of the slope, m = 1.
Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. The y-intercept is also the value of y when x = 0. One of the given points happens to be the y-intercept, (0, 2). Its y-coordinate is the value of b in the slope-intercept form, y = mx + b. Substitute the slope and the y-intercept into the equation:
y = mx + b
y = x + 2
Next, we need to rewrite the slope-intercept form into its standard form, Ax + By = C:
y = x + 2
Subtract x from both sides:
- x + y = x - x + 2
-x + y = 2
Multiply both sides of the equation by -1, so that the coefficient of x becomes a positive integer:
(-1) (-x + y) = 2(-1)
x - y = -2 ⇒ This is the standard form where A = 1, B = -1, and C = -2
A bike that weighs 22 pounds and 3 ounces weighs a total of ____ounces.
Answer:
355 ounces
Step-by-step explanation:
Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:
[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]
"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.
[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]
[tex]\frac{352oz}{1} + 3 = x[/tex]
[tex]352+3 = x[/tex]
[tex]x=355[/tex]
So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)
Which number represents a square root of 3 [cos(pi/2) + i sin (pi/2)]?
===========================================================
Explanation:
We use De Moivre's Theorem. It says that if you started with
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
then raising both sides to the nth power leads to
[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]
The term out front r is raised to the nth power. We also have copies of n inside the trig functions.
The square root operation undoes the squaring operation, so we'll be dealing with n = 2.
If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.
[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]
Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.
The complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number in the trigonometric form:
Z = √(3[cosπ/2 + i sinπ/2])
It is required to find the square root of the complex number.
To find the square root of the complex number we can use the De Moivre's theorem:
If
Z = r[cosθ + i sinθ]
Zⁿ = rⁿ[cosnθ + i sinnθ]
Using the above theorem:
Z = √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]
Z = √3[cosπ/4 + i sinπ/4]
Thus, the complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
Learn more about the complex number here:
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Edwin and Franklin share money in the ratio 3:7 Franklin received $20 more than Edwin. Find the amount shared and what each of them received.
Step-by-step explanation:
We have,
Edwin and Franklin share money in the ratio 3:7.Franklin received $20 more than Edwin.We've to find the amount shared and what each of them received.
★ Amount Shared = Amount received by Edwin + Amount received by Franklin ★
As, Edwin and Franklin share money in the ratio 3:7. So, let's say that,
Amount received by Edwin = $ 3xAmount received by Franklin = $ 7xAlso, Franklin received $20 more than Edwin. So,
→ Amount received by Franklin = 20 + Amount received by Edwin
→ 7x = 20 + 3x
Solving the equation further.
→ 7x - 3x = 20
→ 4x = 20
→ x = 20/4
→ x = 5
Hence,
→ Amount received by Edwin = $ 3x
→ Amount received by Edwin = $ 3(5)
→ Amount received by Edwin = $ 15 [Ans]
And,
→ Amount received by Franklin = $ 7x
→ Amount received by Franklin = $ 7(5)
→ Amount received by Franklin = $ 35 [Ans]
Lastly,
→ Total amount shared = 3x + 7x
→ Total amount shared = $35 + $15
→ Total amount shared = $50 [Ans]
Hence, solved!the diagonal of a cube is root 12. What is the edge?
Step-by-step explanation:
Given length of diagonal of a cube = √12 cm Recall that length of diagonal of a cube = √3 × Length of edge of the cube ⇒ √12 = √3 × Length of edge of the cube ∴ Length of edge of the cube = √12 / √3 = 2√3 / √3 = 2 Thus the edge of the given cube is 2 cm
Leah bought 3/4 pound of trail mix to make snack bags. She put 1/8 pound of trail mix into each snack bag. Which expression can be used to find how many snack bags Leah made? (Show work and simplify pls)
Answer:
3/4 ÷ 1/8 = 6
Step-by-step explanation:
first you would have to figure out how to make them even factors.
6/8 ÷ 1/8
Then you would divide, and get 6.
Identify if the table below shows a proportional relationship.
x
y
1
5
02
2
.
7
5
13
Proportional
Not Proportional
Answer:
i know answer i heard some were i think
7 less than 6 times a number is equal to 9 more than 4 times a number. What is the number?
Answer:
Write an equation the represents the words.
6x - 7 = 4x + 9
To solve for x (the number), isolate it from the other variables.
Subtract 9 from both sides.
6x - 7 - 9 = 4x
Combine like terms.
6x - 16 = 4x
Subtract 6x from both sides.
-16 = 4x - 6x
Combine like terms.
-16 = -2x
Divide both sides by -2.
-16/-2 = x
x = 8
The number is 8.
Hope this helps! :)
Answer:
The number is 8.
Step-by-step explanation:
Hello there!
We're given an unknown number, let's call this number n
We know that 7 less than 6 times n is equal to 9 more than 4 times n
Let's break that statement down, starting with "7 less than 6 times n"
6 times n should be 6n, since 6 * n = 6n
"7 less" means subtraction.
So "7 less than 6n" should be 6n-7
Now with "9 more than 4 times n"
4 times n should be 4n, as 4 * n = 4n
"9 more" means addition
So "9 more than 4n" should be 4n+9
The statement says that 6n-7 is equal to 4n + 9, and so when we write it as an equation:
6n - 7 = 4n + 9
Now we can solve the equation
Subtract 4n from both sides
2n - 7 = 9
Add 7 to both sides
2n = 16
Divide both sides by n
n=8
The number is 8
PS. we can substitute 8 back into the equation as n to see if it works:
6(8)-7=4(8)+9
Multiply
48-7=32+9
41= 32 + 9
41=41
It works :))
Hope this helps!
Patricia has $12 to spend at an arcade. The arcade charges $6 admission and $3 per hour to play as many games as she wants. Which inequality can be used to find any possible number of hours, X, Patricia can play games without spending more than $12
A) 6+3x < 12
B) 6-3x < 12
C)12<6+3x
D) 12 < 6-3x
***All of them have a line underneath the <****
Answer:
Step-by-step explanation
c
Under his cell phone plan, Josiah pays a flat cost of $37 per month and $3 per gigabyte. He wants to keep his bill at $43.60 per month. Write and solve an equation which can be used to determine xx, the number of gigabytes of data Josiah can use while staying within his budget.
The number of gigabytes of data Josiah can use while staying within his budget is 2.2 gigabytes.
Flat costs and Variable costThe total amount of money that can be spent on the cell phone plan is the sum of the flat cost and the variable cost.
Total cost = flat cost + variable cost
Determination of the equation required to solve for the gigabytes neededThe flat cost is the cost that remains constant each month. The variable cost is the cost that increases by gigabyte used.
$43.60 = $37 + $3x
The gigabytes neededIn order to determine the value of x, combine similar terms together
$43.60 - $37 = $3x
6.6 = $3x
Divide both sides by 3
6.6/3 = x
x = 2.2 gigabytes
To learn more about flat costs, please check: https://brainly.com/question/25879561
nico wanted to determine the number of students in his school who buy school lunch. he walked around the cafeteria one lunch period looking to see whether every fifth person in the cafeteria purchased lunch or brought their own. which method did he use to collect his data? survey simulation experiment observational study
Answer:
Observation
Step-by-step explanation:
He walked around seeing if every fifth person bought lunch
Survey - Requires asking questions
Simulation - Needs prior data to make an estimation
Experiment - Testing something
Observation - Just observing and watching
Study - Looking up data
The method he used to collect his data is observational method.
When do we perform observational study, sample survey, controlled experiment, or random experiment?Observational study is usually chosen when the researches the system is likely to produce different result if interfered.
Sample survey is done if the population is too big to analyze or destructible as the analysis occurs.
Controlled experiment is done manually, specifically to deduce conclusions. Its steps are fixed.
Random experiment is done specifically to deduce conclusions, but it is done in a random manner.
We are given that;
He saw every fifth person in cafeteria
Now,
An observational study is a method of collecting data by observing and recording the behavior or characteristics of individuals or groups without interfering or manipulating any variables. Nico did not ask any questions or change any conditions, he just observed whether every fifth person in the cafeteria bought lunch or brought their own.
Therefore, by sampling the answer will be observational method.
Learn more about sampling here:
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Someone help me pls!
You can buy 3 apples at Quick Mart for $1.17. You can buy five of the same apples at Shop & Save for $2.40
How much will you save per apple if you buy them at the cheaper store?
Answer:
$0.09 or 9 cents
Step-by-step explanation:
1.17/3=0.39
2.4/5=0.48
0.48-0.39=0.09
Answer:
Well you can divide them by each
1.17/3 which is 0.39 (quick mart)
2.4/5 Which is 0.48 (stop and save)
39 cent is what you pay at the cheaper store
9 cents is what you would save
-also you go to bay academy?
I haven’t seen Jupiter ed in so long hahah
Factorise this expression as fully as possible 12x - 9x?
Answer:
4x
Step-by-step explanation:
12x-9x
=4x
I hope my answer is correct
and if u like mark me as brainliest answer.
Answer:
12x - 9x
= 3x ( 4- 3)
= 3x ( 1)
= 3x
∆ABC has the vertices A(0,0) B(3,3) C(-3,3). Classify the triangle by its sides. Then determine whether it is a right triangle.
Your friend solved the equation 4x+12x−6=4(4x+7) and got x=34. What error did your friend make? What is the correct solution?
Answer:
=34
Step-by-step explanation:
4x+12x-6=4(4x+7) ur question
using BODMAS
4x+12x-6=16x+28
16x-6=16x+28
16x-16x=28+6
0=34
but make sure your question is right, can you go through it again
I borrow $5 from Luis and $ 8 from Stephanie.
How do I show my debt with integers.
Answer:
-5 + -8 = -13
Step-by-step explanation:
-5 + -8 = -13
in total you owe $13 but seperat it’s $5 and $8.
also you show a debt with Integers by using negative numbers.
The length of a planet's orbit around a star is approximately 22,200,000 km. It takes the planet about 1230 Earth days to complete a full orbit. What is the planet's average speed in kmh-1 to 3sf?
Answer:
Approximately [tex]12.9\; \rm km \cdot h^{-1}[/tex], assuming that this orbit is circular.
Step-by-step explanation:
The question is asking for a tangential velocity with the unit [tex]\rm km \cdot h^{-1}[/tex]. The unit of the given distance is already in [tex]\rm km[/tex] as required. Convert the unit of the orbital period to hours:
[tex]\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}[/tex].
Calculate the angular velocity [tex]\omega[/tex] of this planet from its orbital period:
[tex]\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}[/tex].
Given the radius [tex]r[/tex] of the orbit of this planet, the tangential velocity [tex]v_{\perp}[/tex] of this planet would be:
[tex]\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}[/tex].
If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: [tex]4.73\times 10^{3}\; \rm km \cdot h^{-1}[/tex].
Please answer my question
Answer:
180 667 777 98827
Step-by-step
the graaph has three differnt lines that connet
Q1
Put these decimals in order, least to greatest:
?
0.11 0.3 0.12 0.2
Answer:
0.11<0.12<0.2<0.3
Step-by-step explanation:
Answer:
0.11, 0.12, 0.2, 0.3
Step-by-step explanation:
pls brainliesttt
evaluate -4(5-(36÷4))
Answer:
16
Step-by-step explanation:
- 4 ( 5 - ( 36 ÷ 4 ) )
= - 4 ( 5 - 9 )
= - 4 ( - 4 )
= - 4 * - 4
= 16
easy one - giving brainly if correct - show work.
my teacher said this was wrong so what's the correct answer? answer both!
Answer:
a = 9.6 b = 11.2
Step-by-step explanation:
10 percent of 8 is .8
8 + (8 x .1) = 8.8
8.8 + .8 = 9.6
She will be paid 9.6 dollars after 1 full year of working, because working for one year is 12 months, and thats 10 percent of 8 twice. You can also put that as 20 percent of 8, aka 1.6
When you do 8+1.6 it equals 9.6
For the second part, that is 24 months, so 10 percent of 8 4 times. .8+.8+.8+.8 = 3.2
8+3.2 = 11.2
She will be paid 11.2 dollars after 2 full years of working.
Your answer isnt wrong, I dont know why your teacher is saying it is.
What is the measure of < A B C ?
143.25 °
is the correct answer.
please mark my answer as brainest and follow me to get the answer faster.
plss help ill give brainlest
what divided by 13 is 4
Answer:
52Step-by-step explanation:
what divided by 13 is 4
4 * 13 = 52
----------------------------
check
52 : 13 = 4
the answer is good
Answer:
52
Step-by-step explanation:
Help help help help
Answer: main
Step-by-step explanation:
Answer:
yeah it's main it cuts up through oak and elm
HELP IM LATE LOL In an aquarium, ⅖ of the fish are surgeonfish. Of these, ¾ are yellow tangs. What portion of all fish in the aquarium are yellow tangs?
Answer:
1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.
Step-by-step explanation:
2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.
To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.
8/20 + 15/20 = 23/20 or 1 3/20
Find the missing exponent
Answer:
-6
Step-by-step explanation:
Because 2×(-6) is - 12
Answer:
-24
Step-by-step explanation:
5. Which pair of trig functions are equivalent?
(20 Points)
sin 23. sin 67
cos 41. sin 41
cos 58, sin 122
cos 76, sin 14
WILL MAKE BRAINLIEST IF CORRECT <3
Answer: cos(76°) ---> sin(14°)