Answer:
ab+bc+ca=0
Step-by-step explanation:
We are given:
[tex]x^a=y^b=z^c[/tex]
xyz=1
Separating equations:
[tex]x^a=z^c[/tex]
[tex]y^b=z^c[/tex]
Solving the first equation for x:
[tex]\displaystyle x=z^\frac{c}{a}[/tex]
Solving the second equation for y:
[tex]\displaystyle y=z^\frac{c}{b}[/tex]
Substituting in
xyz=1:
[tex]\displaystyle z^\frac{c}{a}z^\frac{c}{b}z=1[/tex]
Adding the exponents:
[tex]\displaystyle z^{\frac{c}{a}+\frac{c}{b}+1}=1[/tex]
Since [tex]1=z^0[/tex]:
[tex]\displaystyle z^{\frac{c}{a}+\frac{c}{b}+1}=z^0[/tex]
The base is z on both sides so we get rid of them:
[tex]\displaystyle \frac{c}{a}+\frac{c}{b}+1=0[/tex]
Multiplying by ab:
bc+ac+ab=0
Reordering:
ab+bc+ca=0
Given parallelogram SNOW, diagonals SO and NW intersect at D.
If SD = 9x+5 and OD = 13X - 3, find the length of SO
Answer:
The length of SO is 46 units
Step-by-step explanation:
In a parallelogram, diagonals bisect each other, which means meet each other in their mid-point
∵ SNOW is a parallelogram
∵ SO and NW are diagonals
∵ SO ∩ NW at point D
→ That means D is the mid-point of SO and NW
∴ D is the mid-point of SO and NW
∵ D is the mid-point of SO
→ That means D divide SO into two equal parts SD and DO
∴ SD = DO
∵ SD = 9x + 5
∵ DO = 13x - 3
→ Equate them
∴ 13x - 3 = 9x + 5
→ Subtract 9x from both sides
∵ 13x - 9x - 3 = 9x - 9x + 5
∴ 4x - 3 = 5
→ Add 3 to both sides
∵ 4x - 3 + 3 = 5 + 3
∴ 4x = 8
→ Divide both sides by 4
∴ x = 2
→ To find the length of SO substitute the value os x in SD and DO
∵ SO = SD + DO
∵ SD = 9(2) + 5 = 18 + 5 = 23
∵ DO = 13(2) - 3 = 26 - 3 = 23
∴ SO = 23 + 23 = 46
∴ The length of SO is 46 units
When adding rational numbers with the same sign, you must
Answer:
put one number in front of the other
Simplify the fraction 44/77 as much as possible.
Answer:
4/7
Step-by-step explanation:
Find the arithmetic means between 42 and 86
Answer:
The arithmetic between 42 and 86 is 44
Step-by-step explanation:
When a rubber ball is dropped on a particular surface , It bounces back to 8/10 of drop height. The ball's height after bounce x is * (8/10) ^ x times its drop height . What fraction of its drop height will the ball bounce up to after its fourth bounce ? Show your work
Answer:
The fraction of its drop height after the fourth bounce is
[tex]\displaystyle \frac{16}{625}[/tex]
Step-by-step explanation:
Let's suppose the rubber ball is dropped from a height H0. Every time the ball bounces back it reaches 8/10 of the initial drop height.
The ball's height H(x) after bounce number x is:
[tex]\displaystyle H(x)=H_o\left(\frac{8}{20}\right)^x[/tex]
Simplifying:
[tex]\displaystyle H(x)=H_o\left(\frac{2}{5}\right)^x[/tex]
After the fourth bounce, the height is:
[tex]\displaystyle H(4)=H_o\left(\frac{2}{5}\right)^4[/tex]
[tex]\displaystyle H(4)=H_o\frac{2^4}{5^4}[/tex]
[tex]\displaystyle H(4)=H_o\frac{16}{625}[/tex]
The fraction of its drop height after the fourth bounce is
[tex]\mathbf{\displaystyle \frac{16}{625}}[/tex]
After completing the fraction division 5 divided by five-thirds, Miko used the multiplication shown to check her work. 3 times five-thirds = StartFraction 3 Over 1 EndFraction times five-thirds = StartFraction 15 Over 3 EndFraction or 5 Which is the most accurate description of Miko's work? Miko found the correct quotient and checked her work using multiplication correctly. Miko found the correct quotient but checked her work using multiplication incorrectly. Miko found an incorrect quotient but checked her work using multiplication correctly. Miko found an incorrect quotient and checked her work using multiplication incorrectly.
Answer:
Miko found an incorrect quotient and checked her work using multiplication incorrectly.
Step-by-step explanation:
The given expression is
[tex]\dfrac{5}{\dfrac{5}{3}}[/tex]
Applying the reciprocal rule we get
[tex]5\times \dfrac{3}{5}=5[/tex]
What Miko did was
[tex]3\times \dfrac{5}{3}=\dfrac{3}{1}\times\dfrac{5}{3}=\dfrac{15}{3}\ \text{or}\ 5[/tex]
So, Miko took the wrong values of the quotients and applied multiplication incorrectly.
Hence, Miko found an incorrect quotient and checked her work using multiplication incorrectly.
State two equivalent ratios of 18:36
3 drinks and 2 pretzels costs $16, but 5 drinks and 5 pretzels costs $31.25. What is the price
of one pretzel and one drink?
Answer:
7.125
and 5.1
Step-by-step explanation:
Lucas is walking around the edge of the playground shown. How far will lukas have to walk when he finishes one loop around the playground? Round to the nearest unit, if necessary.
Answer:
See Explanation
Step-by-step explanation:
Required
Determine how far he walked in one loop
This question is incomplete, as the playground diagram and dimensions are missing. However, I'll answer on a general terms.
What this question requires is to calculate the perimeter of the playground.
Assume that the playground is rectangular and the dimensions are: 2 meters by 3 meters.
The distance walked will be calculated using the following perimeter formula.
[tex]Distance = 2(2m + 3m)[/tex]
[tex]Distance = 2(5m)[/tex]
[tex]Distance = 10m[/tex]
If it is a square with 5m as the length of one of its side, the distance would be:
[tex]Distance = 4 * 5m[/tex]
[tex]Distance = 20m[/tex]
So basically, all you need to do is calculate the perimeter of the playground.
Adam is a field goal kicker. If he made 30 field goals out of his last 32 attempts, what percent of the attempts did he make?
Jahmya wants to leave $1.75 as a tip for her server. She has a $20 bill. How much change should she receive after paying for her food AND leaving a tip? (The amount of money for her food is $8.87)
Answer:
$9.38
Step-by-step explanation:
( $1.75 + $8.87 ) = 10.62 (10.62 - $20 ) = $9.38
brainliest please
Tyra's family is spending the afternoon in Millersville. They plan to see a movie and then explore the town. The movie will cost the family $36, and parking costs $4 per hour.
Which cost will change depending on how long they are there?
A. $36
B. $4
Bernite is selling candy bars for a school fundraiser. The school paid $20.00 for a box of 15 king-size candy bars and Bernite sells them for $2.00 each. What is the relationship between the amount of candy sold and the amount of money earned?
The relationship is linear.
The relationship is non-linear.
The relationship is proportional.
The relationship is non-proportional.
The relationship always results in a positive profit.
The relationship always results in a negative profit.
Answer:
linear and positive profit
Step-by-step explanation:
witch of the following best forms the figure shown. iready
Fred weighs 40 pounds less than twice Barney. Their combined weight is 320 pounds. Let F = Fred's weight in pounds and B = Barney's weight in pounds. Write a system to represent the situation. DO NOT SOLVE.
Answer:
Step-by-step explanation:
Using the information provided we can create two different equations for this system. The first of which would be Fred's overall weight, while the second equation would be Fred's and Barney's combined weight. These equations would be the following...
F = 2B - 40
320 = F + B
As requested I will not solve the system of equations and leave them as they are.
Four equations are graphed on the coordinate grid:
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 8, 5 and 4, negative 7. Line B passes through the ordered pairs negative 3, 8 and 2, negative 7. Line C passes through the ordered pairs 0, 9 and negative 7, negative 5. Line D passes through the ordered pairs 1, 4 and negative 4, negative 1 and is extrapolated further in the quadrant.
Which set of equations has (−3, 0) as its solution?
A and B
B and D
B and C
A and D
Answer:
b and d i think.
Step-by-step explanation:
B passes through the ordered pairs negative 3, 8 and 2, negative 7.
D passes through the ordered pairs 1, 4 and negative 4, negative 1 and is extrapolated further in the quadrant.
Answer:
b and d
Step-by-step explanation:
Let u = ⟨9, –2⟩, v = ⟨–4, 3⟩, and w = ⟨5, 1⟩. Kelcy incorrectly determined 3u – 5(v + w) to be ⟨32, –26⟩. Review her steps as shown.
3u – 5(v + w)
3⟨9, –2⟩ – 5[⟨–4, 3⟩ + ⟨5, 1⟩]
⟨27, –6⟩ – 5[⟨–1, 4⟩]
⟨27, –6⟩ + ⟨5, –20⟩
⟨32, –26⟩
What mistake did Kelcy make?
Answer:
She added incorrectly
Step-by-step explanation:
Answer should be (22, -26) but Kelcy got wrong because she has taken -1 in third step instead of taking 1 because -4 +5 is 1.
What are Vectors?A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.
Let u = ⟨9, –2⟩, v = ⟨–4, 3⟩, and w = ⟨5, 1⟩
3u – 5(v + w)
3(9, -2)-5(⟨–4, 3⟩+⟨5, 1⟩)
Multiply 3 to (9, -2) and add v and w
(27,-6)-5(1,4)
(27, -6)-(5, 20)
Subtract the vectors
(27-5, -6-20)
(22, -26)
The answer should be (22, -26) but Kelcy got wrong because she has taken -1 in third step instead f taking 1 because -4 +5 is 1.
Hence, answer should be (22, -26) but Kelcy got wrong because she has taken -1 in third step instead f taking 1 because -4 +5 is 1.
To learn more on Vectors click:
https://brainly.com/question/29740341
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Janna and Travon are creating posters for the school play. Together they will have f(t) posters after creating posters for t hours. f(t) = 5t + 3 The function f represents the fact that every hour —
Answer:
8posters are created
Step-by-step explanation:
Given the function that represents the total number of posters expressed as
f(t)= 5t+3
The total posters every hour occur at t = 1hr
Substitute into the equation
f(1) = 5(1)+3
f(1) = 5+3
f(1) = 8
Hence the function f represents the fact that every hour, 8posters are being created
I picked the blue one, was I correct?
Answer:
Yea i think it is the first one
Step-by-step explanation:
The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X . What are the mean and standard deviation of W ?
Answer:
The mean and standard devaition of W are 6 and 31 respectively.
Step-by-step explanation:
Given that:
W = 7 + 2X
Variance (W) = Variance(7 + 2X)
For a term constant term, the variance is zero.
So;
[tex]W = Var (2X)[/tex]
W = 4 × Var(X)
W = 4 × (SD (X))²
W = 4 × (3)²
W = 4 × 9
W = 36
Thus, Variance (W) = 36
The standard deviation of W = [tex]\sqrt{variance}[/tex]
W = [tex]\sqrt{36}[/tex]
W = 6
Also;
E(W) = E(7 +2 X)
E(W) = 7 + 2 × E(X)
where;
mean X = 12
E(W) = 7 + 2(12)
E(W) = 31
Thus, the mean and standard devaition of W are 6 and 31 respectively.
The mean and the standard deviation of W are 31 and 6 respectively.
The given parameters are:
[tex]\mathbf{\bar x_x = 12}[/tex]
[tex]\mathbf{\sigma_x = 3}[/tex]
The definition of W is given as:
[tex]\mathbf{W = 7 + 2X}[/tex]
This means that:
[tex]\mathbf{Var(W) = Var(7) + Var(2X)}[/tex]
So, we have:
[tex]\mathbf{Var(W) = 0 + Var(2X)}[/tex] --- the variance of a constant term is 0
[tex]\mathbf{Var(W) = Var(2X)}[/tex]
This gives
[tex]\mathbf{Var(W) = 2^2 \times Var(X)}[/tex]
We have:
[tex]\mathbf{Var(X) = \sigma^2_x}[/tex]
So, the equation becomes
[tex]\mathbf{Var(W) = 2^2 \times \sigma^2_x}[/tex]
[tex]\mathbf{Var(W) = 2^2 \times 3^2}[/tex]
[tex]\mathbf{Var(W) = 36}[/tex]
The standard deviation is then calculated as:
[tex]\mathbf{\sigma_W = \sqrt{Var(W)}}[/tex]
[tex]\mathbf{\sigma_W = \sqrt{36}}[/tex]
[tex]\mathbf{\sigma_W = 6}[/tex]
The mean is then calculated as:
[tex]\mathbf{E(W) = E(7 + 2X)}[/tex]
This gives
[tex]\mathbf{E(W) = 7 + 2E(X)}[/tex]
So, we have:
[tex]\mathbf{E(W) = 7 + 2 \times 12}[/tex]
[tex]\mathbf{E(W) = 31}[/tex]
Hence, the mean and the standard deviation of W are 31 and 6 respectively.
Read more about mean and standard deviation at:
https://brainly.com/question/10729938
PLEASE HELP ME ON MY RECENT QUESTION WILL GIVE BRAINLIEST ON IT
IF YOUR NOT GOOD AT MATH THEN YOU MIGHT NOT BE ABLE TO ANSWER
Answer:
ok i will look at it :)
Step-by-step explanation:
Answer:
Ok, I will try!!! :D
What is your recent question, btw....you most recent is ELA
During a sale, a store offered a 40% discount on a particular camera that was originally priced at $450. After the sale, the discounted price of the camera was increased by 40%. What was the price of the camera after this increase?
Answer:
378
Step-by-step explanation:
Remark
This is a question that all investors in stocks should be aware off. It does not come back to 450 dollars.
Step One
Find out the price of the discounted camera.
40% reduction price = 450 - (40/100)*450
40% reduction price = 450 - 180 = 270
Step Two
Now add 40% onto the new price.
New price = Reduced price + 40% of reduced price
New Price = 270 + 40%* 270
New Price = 270 + 108
New Price = 378
Remark
The reason stock investors should be aware of this is that if you take a 40% loss on a stock it takes more than a 40% gain to make the price of your stock loss back.
A pair of angles is supplementary if the sum of their measures is 180 degrees. A pair of angels is complementary if the sum of their measures 90 degrees. the supplement of a given angel is 10 degrees more than twice its complement. Let 90-x equal the degree measure of its complement and 180-x equal the degree measure of its supplement. Write and solve an equation to find the measure of the given angel.
Answer:
The measure of the complement =
= 80°
The measure of the supplement=
= 170°
Step-by-step explanation:
Let
90-x equal the degree measure of its complement
180-x equal the degree measure of its supplement.
We are told in the question that: the supplement of a given angle is 10 degrees more than twice its complement.
Hence, the Equation is;
(180 - x) = 10° + 2(90 - x)
180 - x = 10 + 180 - 2x
Collect like terms
-x + 2x = 10 + 180 - 180
x = 10°
Hence,
The measure of the complement =
90 - x
= 90 - 10
= 80°
The measure of the supplement=
180 - x
= 180 - 10
= 170°
PLZ HELP I DONT UNDERSTAND
Answer:
62
Step-by-step explanation:
Turn the percentage into a decimal.
50% = 0.5
Divide.
31 / 0.5 = 62
Best of Luck!
Answer:
62
Step-by-step explanation:
50% is technically 1/2 right?
So, if 31 is half of this mysterious number then we just need to times 31 by 2.
Therefore, 31 * 2 = 62.
We can check this by multiplying 62 by .50 (remember that when using percents in an operation we move the decimal over twice)
62 * .50 = 31
I hope this helps!!
If you have any question just ask!
- Kay :)
Best answer gets brainliest hurry ASAP
A function is defined as y = 2x + 4 with the domain of all real numbers greater than or equal to 4. What is the range of the function?
Answer: y => 12
y is greater than or equal to 12
Step-by-step explanation:
So they give you the function of y = 2x + 4 and the domain of all real numbers is greater than or equal to 4.
In simple term, the domain is x => 4, x is greater than or equal to 4.
Using that we can substitute the x in the function by 4.
y = 2(4) + 4
y = 8 + 4
Which gave us the answer of 12.
Since the domain can be anything greater than 4 or 4. We can expect the
same for the range.
Then the range will be 12 or greater than 12. For example, 13, 14, 15, 16...
Ex. y = 2(5) + 4
y = 10 + 4
y = 14
Ex. y = 2(4.5) + 4
y = 9 + 4
y = 13
Answer the question ..plzzz.......
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Step-by-step explanation:
please talk to me I'm missing u so much
Please helpppp !!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer:
7
Step-by-step explanation:
[tex] \frac{6}{24} = \frac{x}{28} \\ \\ x = \frac{ \cancel6 \times \: 28}{ \cancel{24} \: \: \:\red{\bold {4}} } \\ \\ x = \frac{28}{4} \\ \\ x = 7[/tex]
I NEED HELP ASAP!!!
I will mark the correct answer the brainliest!!!
Part A: Linear Equation (=)
1. Name all the equations of the lines found on the coordinate plane.
Line A:
Line B:
Line C:
Line D:
Line E:
Line F:
Line G:
2. Draw the lines described below and answer the questions that follow.
H. Passes through the point (5, -11) and is perpendicular to the y-axis. What is the equation of the line?
I. Passes through the point (-1, -13) and the slope is zero. What is the equation of the line?
J. Passes through the point (0, -15) and is parallel to the x-axis. What is the equation of the line?
Part B: Linear Inequalities (<, <=, >, >=)
Colors must be outside the start.
1. Color the shaded region for the following inequalities:
Orange: y >= 2x + 9
Red: y >= x
Green: y >= -11
Blue: y >= -13
Green: y <= -13
2. Answer the questions below:
A. Write an inequality for line B if it is a dashed line and shaded below. Answer:
B. Write an inequality for line E if it is a solid line and shaded below. Answer:
C. Where will the shade be if the inequality is y >= 6? Answer:
D. What will be the line for y < 6? Answer:
Need help can some help me explain what the measure of angle A is
Answer:
106
Step-by-step explanation:
side a and c have to equal 180