Answer:
x = ± [tex]\sqrt{\frac{a^2b^2-a^2y^2}{b^2} }[/tex]
Step-by-step explanation:
Given
[tex]\frac{x^2}{a^2}[/tex] + [tex]\frac{y^2}{b^2}[/tex] = 1
Multiply through by a²b² to clear the fractions
b²x² + a²y² = a²b² ( subtract a²y² from both sides )
b²x² = a²b² - a²y² ( divide both sides by b² )
x² = [tex]\frac{a^2b^2-a^2y^2}{b^2}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{a^2b^2-a^2y^2}{b^2} }[/tex]
In formula x²/a²+y²/b²=1
Value of x as subject, x = ± [a√(b² - y²)]/b
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Given equation,
x²/a² + y²/b² = 1
moving y²/b² to right side
x²/a² = 1 - y²/b²
multiplying a² on both sides
a². x²/a² = a². 1 - a². y²/b²
Simplifying
x² = a² - a²y²/b²
x = ± √(a² - a²y²/b²)
x = ± a√(1 - y²/b²)
x = ± [a√(b² - y²)]/b
Hence, value of x = ±[a√(b² - y²)]/b in formula x²/a² + y²/b² = 1
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How many modes, if any, does the group of data have?
Kate, Tim, John, John, Angela, Tim, Sue 1 mode 2 modes no mode 3 modes
The number of modes in the dataset is 1. The dataset is unimodal. The correct option is therefore;
1 mode
What is a unimodal data?A unimodal data is a set of data that has only one mode. The mode is a measure of central tendency.
The data in the question can be presented as follows;
Kate, Tim, John, John, Angelam, Tim, Sue
The frequency of each of the data is therefore;
Kate; 1, Tim; 1, John; 2, Angela; 1, Tim; 1, Sue; 1
The mode of a dataset, is the value that has the highest frequency, or that appears the most in the dataset.
The data that has the highest frequency is John, the mode of the dataset is therefore, John, which has a frequency of 1
The dataset, therefore, has only 1 mode.Learn more on the measures of central tendency, mode median, and mean, of a dataset here: https://brainly.com/question/24994390
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what is -2(15 ÷ 5) + 7(-2)
Answer:
-20
Step-by-step explanation:
What is 4.9 x 10 -3 in standard form?
Answer:
0.0049
Step-by-step explanation:
if two thirds of a number is 56, what is three-quarters of that number?
Answer:
84
Step-by-step explanation:
56/2 = 28
28 x 3 = 84
To check work: 84/3 =28
solve the question.
Answer: 1
[tex](\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1[/tex]
Step-by-step explanation:
Which two integers is –85 between?
Answer:
-84 and -86
Step-by-step explanation:
HELP PLEASE GET BRAINLIST!!
solve for x,
90 - 3/2x ≤ 30
Answer: x>- -40
Step-by-step explanation:
(-4/3)x -6 =26
solve for x
Answer:x =24
Step-by-step explanation: If we reverse that we will get x= 32x3/4 which is 24
Answer:
x = -24
Step-by-step explanation:
(-4/3)x -6 =26
Add 6 to both sides:
(-4/3)x = 32
(-4/3) = -1.33333333
divide both sides by -1.33333333
x = -24
Substitute:
(-4/3)(-24) -6 =26
32 - 6 = 26
26 = 26
x = -24
A store sells toys in bulk. It sells wooden blocks for $5 a pound and plastic bricks for $10
a pound. How many pounds of wooden blocks and plastic bricks should be used to make a
A 10-pound mixture that would sell for $80?
Answer:
six plastic bricks and four wooden blocks
Step-by-step explanation:
plastic bricks=10
wooden blocks:5
lets make plastic x and wooden y
if we made an eight pound mixture of only plastic bricks, that would get us to 80, but would not be enough weight. if we substitute one x pound for two y, we would have 9 pounds and $80. if we substitute this again, we have ten pounds and $80. we added four wooden blocks, and we took two away from the 8 plastic we had, so that is 6 plastic. so we have 6x and 4y, using the variables I assigned for the blocks above.
When Kim works 40 hours in a week, she earns $560. If she works only 35 hours, how much should she expect to earn?
Answer:
$490
Step-by-step explanation:
$560 divided by 40 is $14 an hour and 14 times 35 is 490, so $490.
Answer:
£490
Step-by-step explanation:
So you do 560 divided by 40, which is 14 then you × 35 by 40 =£490.
Which relation is a function?
Answer:
Bottom right
Step-by-step explanation:
Each domain value can only have 1 range value.
River needs to buy a shade for a window in his house. He measured the width of the window as 27 inches. The actual measurement is 24 inches. What is rivers percent error?
Answer:
12.5%
Step-by-step explanation:
Actual measurement of the window = 24 inches
Measured measurement of the window = 27 inches
We need to find the Rivers percent error. It can be calculated as follows :
% = (|actual value-measured value|)/actual value × 100
[tex]\%=\dfrac{27-24}{24}\times 100\\\\\%=12.5\%[/tex]
So, River's percent error is 12.5%.
1/4(z +3z)+ 7=−z + 1 please help with this ive been stuck
Answer:
z = -3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
z+7=−z+1
Step 2: Add z to both sides.
z+7+z=−z+1+z
2z+7=1
Step 3: Subtract 7 from both sides.
2z+7−7=1−7
2z=−6
Step 4: Divide both sides by 2.
2z = −6
2 2
z=−3
Answer:
Why you delete my answer
Step-by-step explanation:
PLEASE HELP WITH ANY OF THE QUESTIONS IN THE PICTURE I WILL GIVE 50 POINTS AND BRAINLEIST
Answer:
RU=4.44500 cementers
Step-by-step explanation:
I learned from my bigger sister
What is the answer to 3z−6/7−2z = 1.2/3.2 ? Please help
Answer:
= 1.23214285
Step-by-step explanation:
Im so confused pls help
Step-by-step explanation:
[tex] f(x) \: = \: \frac{4}{5} - \frac{5}{x + 1} [/tex]
[tex]f(x) \: \: = \: \: \frac{(4)(x + 1) - 5(5)}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x + 4 - 25}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x - 21}{5x + 5} [/tex]
f(x) = g(x)
[tex] \frac{4x - 21}{5x + 5} = \frac{2}{5x + 5} [/tex]
4x - 21 = 2
x = (21 + 2)/4
x = 5.75
Sry I don’t get this math-_- but plz help
Answer:
128+32=160
Step-by-step explanation:
Since a rectangle is 8 x 4=32, and there are 4 rectangles, the surface area of the four rectangles is 32 x 4=128
There are also two squares whose area is 4 x 4=16
16 x 2=32
Hope I helped!
Which best describes independent events?
The results of all events have different individual probabilities.
The results of any previous events affects the probability of future events.
The results of all events have the same individual probability.
The results of all previous events do not affect the probability of future events.
The statement (D) The results of all previous events do not affect the probability of future events best describes independent events option (D) is correct.
What is independent events?An independent event is one that is unaffected by other events. The occurrence of one event has no bearing on the other.
We have a statement:
Which best describes independent events?
As we know from the definition of independent events, the events that is unaffected by other events.
Also, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Thus, the statement (D) The results of all previous events do not affect the probability of future events best describes independent events option (D) is correct.
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I’m not sure how to do this, someone please help.
Answer:
A
Step-by-step explanation:
Answer: It is E (3, -7)
A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings. If Elena’s ice cream cost $1.50 more than Jada’s ice cream, how much more did Elena’s toppings weigh?
Answer:
3 ounces more
Step-by-step explanation:
50*3 =1.50
3.00+1.50= 4.50
find the x and y intercept
y=5x-13
Answer:
X int = 13/5 Y int= -13
Step-by-step explanation:
4. On the day Alex was born, his father invested $5000 in an account with a 1.2% annual growth rate.
Answer the questions below.
(a) Write a function, A(t), that represents the value
of this investment t years after Alex's birth.
(b) Use your equation to determine how much the
investment will be worth when Alexander turns
21
Answer and Step-by-step explanation:
A) A(t) = 5000(1 + 0.012)t
B) A(t) = 106260
A) 5000 is the initial amount, 1 + 0.012 is the interest rate, and t represents the years.
B) When we plug 21 into the equation, we get 106260.
I hope this helps!
Model 3+ (-4) on the number line
Answer:
-1
Step-by-step explanation:
If u add 3 whole numbers to a negative number 4 then it'll equal -1. Think of it like 4-3 but add the negative sign at the begining
Answer:
-1
Step-by-step explanation:
Simplify: 3 - 43 - 4 = -1Mark -1 on the number lineI hope this helps!
Which of the ratios below is equivalent to 1:8? Select all that apply.
A) 16:2
B) 3:24
C) 4:12
D) 5:40
E) 7:56
Answer:
B. 3:24, D. 5:40 E.7:56
Step-by-step explanation:
3:24 = 1:8 (Dividing by 3)
5:40 = 1:8 (Dividing by 5)
7:56 = 1:8 (Dividing by 7)
The ratios that are equivalent to 1:8 are:
3:24, 5:40, and 7:56.
Options B, D, and E are the correct answer.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
A)
16:2
= 16/2
= 8/1
= 8:1
B)
3:24
= 3/24
= 1/8
= 1:8
C)
4:12
= 4/12
= 1/3
= 1:3
D)
5:40
= 5/40
= 1/8
= 1:8
E)
7:56
= 7/56
= 1/8
= 1:8
Thus,
3:24, 5:40, and 7:56 are equivalent to 1:8.
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Determine if the equations are parallel, perpendicular or neither. -9y=-3x+18 and 2x-6y=30
Answer:
The answer is They are parallel
Step-by-step explanation:
They have the same slope but different y-intercepts
y = 1/3x - 2
y = 1/3x - 30
pls mark me as brainliest
Answer: Parallel
Step-by-step explanation: They never cross therefore making the two equatons parallel lines
Find x (Type the number answer)
Answer:
18.41
Step-by-step explanation:
[tex]x^{2} = 12^{2} + 8^{2} - 2(12)(8)(cos 133)\\\\x= \sqrt{338.94} = 18.41[/tex]
Which of the below images is a translation of ........
Answer:
B
Step-by-step explanation:
Cause it's the opposite of the original
Answer:
a
Step-by-step explanation:
Suzy ordered some games online for $19 each. She paid a total of $8 for shipping. The total cost of the purchase was $122. How many games did she buy? 7) Using the word problem above, write an equation to find the number of games Suzy bought. (Hint: Don't do any of the steps to solve it, just write the equation) Your answer
Answer:
6
Step-by-step explanation:
122-8 shipping =114 /19=6
1
2 3
4
5
6
7
8
7
During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them.
How many successful free throws did she make?
The answer
Answer:
10Step-by-step explanation:
Total attempts = 40Successful attempts = 25%Number of successful free throws:
25% of 40 =0.25*40 = 10A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00for 20 hours of work. Find the amount of pay for 31 hours of work. ONLY NUMERICAL VALUE
Answer:
$190.65 for 31 hours
Step-by-step explanation:
P= ha
123=20a
123/20=a
6.15=a
P=6.15h
P= 6.15(31)
p=190.65