Isolating a variable involves changing the subject of the equation.
The result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
The equation is given as:
[tex]\mathbf{9x^2 + 7y^2 = 42}[/tex]
Subtract 9x^2 from both sides
[tex]\mathbf{7y^2 = 42 - 9x^2}[/tex]
Divide through by 7
[tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
Hence, the result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
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What is the midpoint of (-3,-7) and (9,8)
Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. Use 3.14 for pi.
a) 89 miles per hour
b) 117 miles per hour
c) 149 miles per hour
d) 129 miles per hour
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commision on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $388. If she sells $1,000, she is paid $520. Find Alysse's salary when she sells $3,300 worth of merchandise.
Answer:
Step-by-step explanation:
In order to solve this we just have to create a system of equations, because we have to unknown values, for the base salary we are going to use X and for the comission we will use Y, now we know that when she sold $400 in merchandise she earned $388 and and when she sold $100 se got paid $520 both equations would look like this:
[tex]x+400y=388\\x+1000y=520][/tex]
Now we can solve them by elimination, multiplying one function by -1.
[tex](-1)(x+400y=388)= -x-400y=-388\\x+1000y=388\\1000y-400y=132\\600y=388\\y=\frac{132}{600} \\y=0.22=22%[/tex]
Now we know that the percentage that she earns is 22% of the merchandise she sells.
Now to know how much does she makes on her base pay we just put the value into one of the functions:
[tex]x+1000y=520\\x+1000(.22)=520\\x+220=520\\x=300[/tex]
So her base pay is $300.
To calculate how much she will earn when she sells $3,300 in merchandise we just put that value into the formula:
[tex]x+3300y=\\300+3300(.22)\\300+726=1026[/tex]
So when she sells 3300 she will make 1026 total.
There is a 6 digit number consisting of the digits: 1, 1, 2, 2, 3 and 3. the 1's are one digit apart, the 2's are two digits apart and the 3's are three digits apart. what is the number?
Write a congruency statement for the pair of triangles.
Answer:
ΔABP is congruent to ΔBAQ
ΔABP ≡ ΔBAQ
Explanation:
We are given two triangles; ΔABP and ΔABQ
In these two triangles, we have:
AB as a common side
∠ABP = ∠BAQ
AQ = BP
We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:
"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"
Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.
Based on the above, the congruency statement would be:
ΔABP is congruent to ΔBAQ
Hope this helps :)
A bag contains 25 marbles: 10 black, 13 red, and 2 blue. a marble is drawn from the bag at random. what is the probability of getting a red or a blue marble? 3/5 2/3 1/2 1/6
Final answer:
The probability of drawing a red or blue marble from a bag containing 25 marbles (10 black, 13 red, 2 blue) is 3/5. This is calculated by dividing the total number of red and blue marbles (15) by the total number of marbles (25).
Explanation:
The question involves calculating the probability of drawing a red or a blue marble from a bag containing 25 marbles: 10 black, 13 red, and 2 blue. To find the probability of an event happening, we divide the number of ways that event can happen by the total number of outcomes. Here, the total number of marbles is 25.
The total ways to get a red or a blue marble is the sum of red and blue marbles, which is 13 (red) + 2 (blue) = 15. Therefore, the probability of drawing a red or blue marble is 15/25. Simplifying that fraction gives us 3/5.
The correct answer is 3/5. This calculation shows how to approach problems involving the probability of one event or another happening, especially when dealing with specific quantities.
What is the range of the function g(x) = |x – 12| – 2?
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
If x varies inversely with y and x = 2 when y = 48, find x when y = 24.
X=k/y
X=2, y=48
2=k/48
K=2*48 = 96
X= 96/24
X=4
The record ski jump for women is 110 meters. What is this length in feet?
Answer:
The record ski jump for women is 360.89 feet.
Step-by-step explanation:
The record ski jump for women is 110 meters.
Record ski jump = 110 m
We need to find what is this length in feet.
We have the conversion 1 m = 3.28084 ft
Using the above conversion
We will get
1 m = 3.28084 ft
110 m = 110 x 3.28084 = 360.89 ft
The record ski jump for women is 360.89 feet.
Find y' if x = tan(y)
The excel function ________ would be used to find the lowest score on a series of student test scores. min median sum dmin
The Excel function you should use to find the lowest score in a series of test scores is the MIN function. It determines the smallest number in a set of values.
Explanation:The Excel function that should be used to find the lowest score on a series of student test scores is the MIN function. This function allows you to determine the smallest number in a set of values. For instance, if you have the scores in cells A1 to A10, you would write the formula as =MIN(A1:A10).
It's important to note that the other options provided, such as median, sum, and dmin, would not accurately find the lowest score. The median would find the middle score, sum would add all the scores together, and dmin is a database function that extracts the smallest number from a selected database column based on the specified conditions.
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In some countries congress, the number of representatives is 80 less than 5 times the number of senators. there are a total of 520 members. find the number of senators and the number representatives
Algebra 2
In a sample of 200 households, the mean number of hours spent on social networking sites during the month of January was 55 hours. In a much larger study, the standard deviation was determined to be 7 hours. Assume the population standard deviation is the same. What is the 99% confidence interval for the mean hours devoted to social networking in January?
A) The 99% confidence interval ranges from 53.73 to 56.27 hours.
B) The 99% confidence interval ranges from 7 to 55 hours.
C) The 99% confidence interval ranges from 54.51 to 55.49 hours.
D) The 99% confidence interval ranges from 55 to 60 hours.
Can i get an explanation?
All i know is that this question has something to do with the Margin of error.
The Margin of error has two different formulas
Please help :)
Answer:
Step-by-step explanation:
n=sample size =200
Mean = x bar = 55 hours
Std deviation (Population) = 7 hours
For 99% confidence level
Z critical value = 2.58
Margin of error = ±2.58(std error)
Std error = [tex]\frac{7}{\sqrt{n} } =0.495[/tex]
Hence margin of error = ±0.495(258)=1.28
Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)
~(53.73, 56.27)
Hence option A
Help a sphere has a radius of 8ft if the radius is doubled what is the effect on volume
find the common ratio of the following geometric sequence: 3.512,12.292,43.022,150.577,527.020
A) 2.5
B) 3.5
C) 8.78
D) 0.29
Solve 2(x-1) = 3x+4
AP calculus HW Need help on #61
Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°.
The measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
What are complementary angles?Complementary angles are a pair of angles whose sum is always equal to 90°.
If A and B are complementary angles, then A + B = 90°.
How to solve the given question?In the question, we are asked to find the measure of each angle, given that the angles (5x)° and (4x - 18)° are complementary angles.
As we know that these angles are complementary, we can write the equation to solve for x as,
5x + (4x - 18) = 90
or, 5x + 4x - 18 = 90
or, 9x = 90 + 18 = 108
or, x = 108/9 = 12.
Therefore, the value of these angles are:
(5x)° = (5*12)° = 60°.(4x - 18)° = (4*12 - 18)° = (48 - 18)° = 30°.Therefore, the measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
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The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?
find the value of x.
The art club spent $45 on supplies for Valentines to sell during lunches. they made 60 valentines. what's selling price for a valentine would result in a profit of zero if all valentines are sold?
Answer:
0.75
Step-by-step explanation:
What is the probability that the student will have score between 71 and 80
bag has 2 green marbles, 3 red marbles, and 3 yellow marbles. What is the probability that you pick a red marble, do not replace it, and pick yellow marble?
To isolate the variable in the equation -3x - 9 = -27, the first step is to add 9 to both sides. This gives you -3x = -18. What is the next step to isolate the variable?
A.+ 18 B.18 C. -3 D.+ 3x
Next step to isolate the variable is to divide by -3 .
Given,
-3x-9=-27
Firstly,
Add 9 to both side of the equation,
-3x-9+9=-27+9
-3x=-18
Now,
Divide -3 to each side
-3x/-3=-18/-3
x=6
Now,
Check:
-3x-9=-27
Substitute x with 6
-3(6)-9=-27
-18-9=-2
Thus, the next step to isolate the variable is to divide -3 to both side of equation.
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find the center of the circle that can be circumscribed about triangle EFG, E(6,4) F(6,2) and G(10,2)
Final answer:
The center of the circumscribed circle about triangle EFG with given vertices is found by calculating the perpendicular bisectors of the triangle's sides and locating their intersection point, which is the center (8,3).
Explanation:
To find the center of the circumscribed circle about triangle EFG with vertices E(6,4), F(6,2), and G(10,2), we need to determine the perpendicular bisectors of at least two sides of the triangle and then find their intersection point, which will be the center of the circumscribed circle.
First, find the midpoint of side EF, which has the same x-coordinate (since E and F have the same x-coordinate), so the midpoint is (6,3).Next, we need the equation of the perpendicular bisector of EF. Since EF is vertical, its perpendicular bisector is a horizontal line that passes through the midpoint, hence the equation is y = 3.Then, find the midpoint of side FG. As the endpoints have the same y-coordinate, the midpoint will have that y-coordinate (2) and the x-coordinate will be the average of the x-coordinates of F and G, which is (6+10)/2 = 8. So, the midpoint of FG is (8,2).The slope of side FG is 0 (since it's horizontal), so the slope of its perpendicular bisector is undefined, meaning it's a vertical line. Consequently, the equation of this perpendicular bisector is x = 8.Last, by solving the system of equations formed by the two perpendicular bisectors x = 8 and y = 3, we find the intersection point, which is the center of the circumscribed circle: (8,3).Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
The polar coordinate of any point can be written as:
(r, θ) = (r, θ + 2nπ) --> when positive
(r, θ) = [ - r, θ + (2n + 1)π ] --> when negative
where n is any integer.
The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).
When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)
where n is any integer.
When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.
Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].
The polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
The coordinates of point p are given as:
p = (5, [tex]\pi[/tex]/3)
A point represented as (r, θ) has the following polar coordinates
(r, θ + 2n[tex]\pi[/tex]) for positive r, and (- r, θ + [2n + 1][tex]\pi[/tex]) for negative r
By comparing (r, θ) and (5, [tex]\pi[/tex]/3), we have:
r = 5
[tex]\theta = \pi/3[/tex]
So, we have:
(r,[tex]\theta[/tex]) = (r, [tex]\theta[/tex] + 2n[tex]\pi[/tex])
The equation becomes
(5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Also, we have:
(-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Hence, the polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
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what is the solution to this linear equation? 2/3x-1/2=1/3+5/6x
(05.06)Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week. Finally, she spent $15 on new sunglasses.
Which part of the scenario is best represented by a linear increasing interval?
Bentley has $40 in her piggy bank.
Bentley spent $10 on new flip flops.
Bentley got $20 for her allowance.
Bentley spent $15 on sunglasses.
linear increase would be something added to an equation.
she started with 40,
she spent 10 on flip flops and also spent 15 of sunglasses those are decreases
she added 20 for allowance which is an increase and we can assume she gets the same amount of allowance every week
so that would be the linear increase
Bentley had $40 in birthday money in her piggy bank. Bentley got $20 for her allowance which is represented by a linear increasing interval.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bentley had $40 in birthday money in her piggy bank.
She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week.
Finally, she spent $15 on new sunglasses.
linear increase would be something added to an equation.
she started with $40 in her piggy bank.
She spent 10 on flip-flops and also spent 15 on sunglasses. This show decreases.
she added 20 for the allowance which is an increase and we can assume she gets the same amount of allowance every week.
So, that would be the linear increase.
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Larry's dining room table measures five feet in diameter. what scale diameter will he use if the scale he is using is 1 inch = 2 feet?
Answer: 2.5 inches.
Step-by-step explanation:
The given statement : Larry's dining room table measures five feet in diameter.
i.e. We are given that the diameter of Larry's dining room table = 5 feet
The scale used by him 1 inch =2 feet
i.e. [tex]\text{1 feet =}\dfrac{1}{2}\text{ inch}[/tex]
Now, [tex]\text{5 feet =}5\times\dfrac{1}{2}\text{ inches}=2.5\text{ inches}[/tex]
Therefore, the scale diameter he will use = 2.5 inches.
PLEASE HELP!!!!!! picture inserted