Answers
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.
Step One
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12) Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2
4/x^2 + 2/y^2 = 24
Step Two
Add the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24
5 / x^2 = 1 + 24
5/x ^2 = 25 Divide both sides by 5
1/x^2 = 5 Reciprocate the x^2 and the 5 (That means turn them upside down.
x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5) Rationalize the denominator.
[tex]{x = } \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }\\ \\{x = } \frac{ \sqrt{5} }{5} [/tex]
Step 3
Place this answer in for x^2 to get y^2. and then y
1/(1/5) - 2/y^2 = 1
Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5
Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
- 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2 Now reciprocate both sides.
y^2 = 1/2 Take the square root.
y = +/- 1/sqrt(2) And rationalize the denominator
y = +/- sqrt(2) / 2 Done the same way as for the x.
There's only 1 there. I'll let you find it.
Related Questions
How many terms are in the arithmetic sequence 6, 2, −2, …, −102?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Answers
6, 2, −2, …, −102
will evaluated as follows:
the explicit formula is:
an=a1+d(n-1)
a1=first term
d=common difference
n=number of terms
thus from the question:
a1=6
d=2-6=-4
an=-102
plugging the values in the expression we get:
-102=6-4(n-1)
solving for n we shall have:
-102-6=-4(n-1)
-108=-4(n-1)
27=n-1
thus
n=27+1
n=28
Answer: 28 terms
Final answer:
Calculate the number of terms in the arithmetic sequence 6, 2, -2, ..., -102 using the provided formula to find it is 28.
Explanation:
In mathematics, an Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, denoted by d.
Arithmetic sequence: 6, 2, -2, ..., -102
Formula: an = a1 + d(n - 1)
Identify a1 = 6 and an = -102Calculate d = an - a1 = -102 - 6 = -108Substitute the values into the formula and solve for n to find the number of termsTherefore, the number of terms in the arithmetic sequence is 28.
$2,400 principal earning 2%, compounded annually, after 7 years
Answers
so i think the answer is 14 lol i could be wrong i did this so long ago...
Answer:
The answer is 2,765.85 dollars. Thanks.
Step-by-step explanation:
Which equation in point-slope form contains the points (6, 2) and (2, 4)? A -4=-1/2(x-6) B y – 4 = –2(x – 2) C y-2=-1/2(x-6)
Answers
The equation for point-slope form is
y - b = m(x - a)
m is the slope
(a, b) is a point the line passes through
We are looking for a equation that follows this
The answer is C because a point the line goes through is (6, 2)
The answer is C
Hope this helps!
A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Milk? There are 128128128 ounces in 111 gallon.
Answers
A gallon of Moo Milk costs $5.12 What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gallon.
Solution:
Cost of 1 gallon of Moo Milk = $ 5.12
1 gallon = 128 ounces, so we can write:
Cost of 128 ounces of Moo Milk = $ 5.12
Cost of 1 ounce of Moo Milk = $ 5.12/128 = $ 0.04
Cost of 8 ounces of Moo Milk = $ 0.04 x 8 = $ 0.32
Thus, 8 ounces of Moo Milk will cost $ 0.32
Answer:
0.32
Step-by-step explanation:
The ration of gallons to cost is 1:$5.12
We want to know the ratio of ounce to cost.
We need to convert gallons to ounces.
There are 128 ounces in 1 gallon.
So, if one Moo Milk costs $5.12, then 128 ounces also cost $5.12
The ratio of ounces to cost is 128:$5.12
Now, we can find an equivalent ratio to find the cost for 1 ounce.
Then we can multiply by 8 to find the cost of 8 ounces
Ounces ---------> Cost
128 ------------> 5.12 (Both divided by 128)
1 -------------> 0.04 (Both times 8)
8 ------------> 0.32
An 8 ounce of Moo Milk costs $0.32
Assuming a truck container holds 24 cases, how many cases would 6 truck containers hold?
Answers
6 truck will hold 144 containers in total
A car wash machine cleaned 20 cars in 50 minuets at this rate how many minutes will it take the machine to clean 1 car
Answers
x: time in minutes
y: number of clean cars
We then have the following equation:
y = (20/50) x
For 1 car we have:
1 = (20/50) x
Clearing x:
x = 50/20
x = 2.5 minutes
Answer:
It will take the machine to clean 1 car about:
x = 2.5 minutes
The machine will take 2.5 minutes to clean 1 car.
Explanation:To find the number of minutes it will take the machine to clean 1 car, we can use the concept of ratios. If the machine cleaned 20 cars in 50 minutes, we can set up a ratio:
20 cars / 50 minutes = 1 car / x minutes
Using cross-multiplication, we can solve for x:
20x = 50
x = 50 / 20 = 2.5 minutes
Therefore, it will take the machine 2.5 minutes to clean 1 car.
A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then, find the probability.
P(a red card or a queen)
a.
inclusive, 15/26
c.
inclusive, 7/13
b.
mutually exclusive, 15/26
d.
mutually exclusive, 7/13
Answers
The two events are inclusive because they can both happen at the same time.
This means we find the probability using
P(A or B) = P(A) + P(B) - P(A and B)
P(r or Q) = P(r) + P(Q) - P(r and Q)
There are 26 red cards out of 52 cards.
There are 4 queens out of 52 cards.
There are 2 red queens out of 52.
26/52+4/52-2/52 = 28/52 = 7/13
The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.
Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52
= 28/52
=7/13
Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
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the supplement of angle t is 4 times the measure of angle t
Answers
one angle = t
the other angle = 4 x t or 4t
so we now have t + 4t = 180
4 + 4t = 5t
so we have 5t = 180
divide both sides by 5:
t = 180 /5
t = 36
so angle t = 36 degrees
the other angle = 4 x 36 = 144 degrees
A square can be changed into a rectangle by increasing the length of the square by 5 units and increasing the width by 3 units. which expression represents the area of the rectangle in square units?
Answers
The area of the rectangle that was transformed from a square by increasing the length by 5 units and the width by 3 units is given by the expression (a + 5)(a + 3), or when expanded a² + 8a + 15.
Explanation:Given that the original shape was a square, the length and width of the square are the same. Let's denote this common length as 'a'. When transformed into a rectangle, the length was increased by 5 units and the width increased by 3 units. Therefore, the new length and width of the rectangle are 'a + 5' and 'a + 3' respectively.
The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the rectangle in square units is represented by the expression (a + 5)(a + 3), which when expanded gives a² + 8a + 15.
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The area of a new rectangle formed from a square by increasing the length by 5 units and the width by 3 units is represented by the mathematical expression (side+5) * (side+3) in square units. This equation stems from the basic geometric formula of calculating the area by multiplying the length by the width.
Explanation:The area of a shape, such as a square or rectangle, is calculated by multiplying its length by its width. In the case of a square, where all sides are equal, the formula for area can be represented as side² or side * side. If we know the side of the square, and it is increased in length by 5 units and width by 3 units, we are essentially creating a rectangle now. The formula for the rectangle area changes to (side+5) * (side+3). So, if you have a square and you increase the length by 5 units and the width by 3 units, the expression that represents the area of the new rectangle in square units would be (side+5) * (side+3). For example, if side of the square was 5 units originally, upon modification, length of rectangle will be [tex]5+5 = 10[/tex] and width will be [tex]5+3 = 8[/tex]. So, area of rectangle becomes [tex]10*8 = 80[/tex] square units.
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Factor the trinomial below.
6x2 – 9x – 6
A. 3(2x + 1)(x – 6)
B. 3(2x + 2)(x – 1)
C. 3(2x + 1)(x – 2)
D. 3(2x + 6)(x – 1)
Answers
6x2 - 9x - 6
Rewriting we have:
3 (2x2 - 3x - 2)
Factoring we have:
3 (2x + 1) (x-2)
Answer:
The factored expression for this case is given by:
C. 3 (2x + 1) (x - 2)
Answer:
C. 3(2x+1)(x-2)
Step-by-step explanation:
To factor the trinomial 6x² - 9x -6, we will follow the steps below;
First, 3 is common among the three numbers, so we will start by factoring out 3, so that the expression becomes;
3(2x² - 3x - 2)
We will now proceed to factorize; 2x² - 3x - 2
Find two numbers such that its product gives -4 and its sum gives -3.
Such number is -4 and 1
-4 × 1 = -4
-4 + 1 = -3
We will replace -3x by -4x + x in the above expression
2x² - 4x + x - 2
(2x² - 4x) (+x - 2)
In the first parenthesis, 2x is common, so we will factor out 2x while in the second parenthesis 1 is common, so we will factor out 1. Hence;
2x(x - 2) + 1(x-2)
(2x+1)(x-2)
3(2x² - 3x - 2) = 3(2x+1)(x-2)
6x² – 9x – 6 = 3(2x+1)(x-2)
Therefore the factorized form of 6x² – 9x – 6 is 3(2x+1)(x-2)
what equations is equivalent to y = log x
Answers
"log" standing alone actually means "logarithm to the base 10."
Thus, y = log x <=> y = log x
10
y
Stated another way (inverse functions), x = 10
In which type of quadrilateral are consecutive sides congruent?
Select the best answer from the choices provided.
trapezoid
parallelogram
square
rectangle
Answers
Final answer:
A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.
Explanation:
The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.
The circumference of a roll of party streamers is 9 inches. The circumference decreases by 2 inches after you use the streamers to decorate for a graduation party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.
Answers
C = 9 - 2
C = 7 inches
By definition, the circumference is:
C = 2 * pi * r
Where,
r: radio
Substituting values:
7 = 2 * pi * r
Clearing the radio:
r = 7 / (2 * pi)
Then, the diameter is:
d = 2 * r
Substituting:
d = 2 * (7 / (2 * pi))
d = 2.228169203
Round to the hundredth:
d = 2.23 inches
Answer:
The diameter of the roll after the decrease is:
d = 2.23 inches
The diameter of the roll of streamers after the circumference decreases to 7 inches is approximately 2.23 inches.
To find the diameter after the circumference decreases, we can use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter.
Initial circumference, C₁ = 9 inches.After using some streamers, the new circumference, C₂ = 9 inches - 2 inches = 7 inches.Using the formula C₂ = πd₂, we solve for d₂:d₂ = C₂ / π
d₂ = 7 / ππ (pi) approximately equals 3.14159.
So, d₂ = 7 / 3.14159 ≈ 2.23 inches.
Therefore, the diameter after the decrease is approximately 2.23 inches.
PLease dont answer if you dont know...
Use the Law of Sines to find side "b" of the triangle.
Answers
side a / sin (angle A) = side b / sin(Angle B)
Side a is opposite angle A, so from the picture we know side a = 50, angle A is 58 degrees and angle B is 48 degrees.
replace those values in the formula we get:
50 / sin(58) = b/ sin(48)
so now we can cross multiply the 2 fractions to get:
50 * sin(48) = b*sin(58)
to get b by itself, divide both sides by sin(58) to get:
b = (50*sin(48)) / sin(58)
b = 43.82
You may need to round the answer as needed.
There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. find p(green, then yellow).
a. start fraction 40 over 900 end fraction
b. the term shows 5 over 30.
c. the term shows 8 over 30.
d. start fraction 40 over 870 end fraction
Answers
Green: 5/30
Yellow: 8/29 (you subtract one from the denominator because you already picked a green the first time)
5/30 x 8/29 = 40/870
The correct option is d. [tex]\( \frac{40}{870} \)[/tex]
To find the probability of selecting a green gum ball followed by a yellow gum ball, we first calculate the total number of gum balls and then determine the number of ways to select a green gum ball followed by a yellow gum ball.
[tex]\text{Total number of gum balls} = 9 (red) + 5 (green) + 8 (yellow) + 8 (blue) = 30[/tex]
Number of ways to select a green gum ball followed by a yellow gum ball:
There are [tex]5[/tex] green gum balls and [tex]8[/tex] yellow gum balls.
Therefore, the number of ways to select a green gum ball followed by a yellow gum ball is [tex]\(5 \times 8 = 40\)[/tex]
The probability of selecting a green gum ball followed by a yellow gum ball is the number of ways to select them divided by the total number of gum balls:
[tex]\[ P(\text{green, then yellow}) = \frac{40}{30 \times 29} \][/tex]
[tex]\[ P(\text{green, then yellow}) = \frac{40}{870} \][/tex]
12 POINTS
Simplify i38.
i
−1
−i
1
Answers
Note that i^38 = i^32 * I^4 * I^2.
Note that i^0, i^4, i^8, etc., all equal 1. Therefore,
i^38 = (1)(1)i^2 = 1*(-1) = -1 (answer)
Answer:
-1
Step-by-step explanation:
I got this correct on my quiz
i^38 = -1
During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. if the first caller has a chance to win $100, which equation finds the amount the 10th caller receives, if the 10th is the first to answer the question correctly?
Answers
1. You have that $50 is added to the prize money each time a caller answers the contest question incorrectly and the first caller has a chance to win $100.
2. Therefore, the amount the 10th caller receives, if the this caller answers the question correctly, is:
x: the amount the 10th caller receives.
y: the number of caller
x=100+50(y-1)
As y=10 (the 10th caller), you have:
x=100+50(10-1)
x=100+50(9)
x=100+450
x=$550
Answer:
a is correct on edege
Step-by-step explanation:
Harry needs to paint a cereal box for a school project. What measure should he use to find the total amount of paint he needs to cover the cereal box with paint? area lateral area surface area volume.
1. area
2. lateral area
3. surface area
4. volume
Answers
Therefore, he must paint:
Base and roof.
Left and right side.
Front and back side.
The measure you need to know therefore is:
Surface area of the box.
Answer:
He should use to find the total amount of paint I need to cover the cereal box with paint:
3. surface area
Answer: C
Step-by-step explanation:
Can someone answer this question for me as well.
The equation tan-1 (9.4/8.2) = x can be used to find the measure of angle LKJ. What is the measure of angler LKJ? Round to the nearest whole degree.
*KL = 7.7 cm, LJ = 8.9 cm*
Answers
tan(x) = 9.4/8.2
x = (tan^-1)(9.4/8.2)
Simplifying gives:
x = (tan^-1)(1.146)
x = 48.9 degrees.
This is approximately equal to 49 degrees.
What is the area of a square
Answers
For example, if a square's length is 4cm, then you can assume the width is going to be 4cm. Finding area, you multiply 4 and 4 to get 16, and the unit of measurement (cm) and square it (^2). Thus meaning this answer would be 16cm^2.
I hope this helps!
The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. What are the coordinates of the point P on the line segment such that P is the length of the line segment from G?
Answers
The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. Hence the required coordinate point is (9/4, 11/4).
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment [tex]\overline{AB}[/tex] such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is[tex](x_1, y_1)[/tex]
and the coordinate of B is [tex](x_2, y_2)[/tex]
The coordinate point between two points P and G divided between ratios a and b is expressed as;
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
Given the coordinate points F(3, 5) and G(0, –4) divided within the ratio 1:3
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{1(0) + 3(3)}{1+3} , \dfrac{1(-4)+ 3(5)}{1+3} \right)\\\\(x,y) = \left( \dfrac{9}{4} , \dfrac{11}{4} \right)[/tex]
Hence the required coordinate point is (9/4, 11/4).
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Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs are: utilities = $100, salary = $2,000, advertising = $0, insurance = $0, interest = $0, rent (cart) = $600, depreciation = $0. what are carla's fixed costs?
Answers
Cost=(cost of beverages)+(salaries)+(utilities)+(rent)
cost=800+2000+100+600
cost=$3500
Thus the total fixed cost was $3500
It is 3500
Carla sells hot coffee, cider and tea from a sidewalk cart near wall street in new york city. last month she sold $4,500 worth of product to 1,000 customers. she spent $800 on buying her beverages in bulk. her monthly costs
What is the trigonometric ratio for cos D?
Answers
The definition of the cosine:
[tex] \cos( \alpha ) = \frac{adjecent}{hypotenuse} [/tex]
When we fill in this formula with the data from the picture, we get the following:
[tex] \cos(d) = \frac{21}{75} = \frac{7}{25} [/tex]
Therefore, the answer is 7 / 25
A hyperbola centered at the origin has a vertex at (9, 0) and a focus at (−15, 0).
Which are the equations of the asymptotes?
Answers
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Asymptotes:
[tex]y = \pm \frac{b}{a} x[/tex]
'a' is distance vertex is from center --> a = 9
'c' is distance focus is from center --> c = 15
[tex]a^2 + b^2 = c^2 \\ \\ b^2 = 15^2 - 9^2 = 144 \\ \\ b = 12[/tex]
Asymptotes are:
[tex]y = \pm \frac{12}{9} x = \pm \frac{4}{3} x[/tex]
Answer:
C
Step-by-step explanation:
What does a residual value of 1.3 mean when referring to the line of best fit of data set?
-a data point is 1.3 units above the line of best fit
-a data point is 1.3 units below the line of best fit
-the line of best fit has a slope of -1.3
-the line of best fit has a slope of 1.3
Answers
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
To find a residual value of 1.3 mean when referring to the line of best fit of data set.
Since, A residual is defined as the difference between the observed value of a dependent variable and the predicted value of that variable using the regression equation.
Hence, In this case, the residual value of 1.3 indicates that the observed value of the dependent variable is 1.3 units above the predicted value, or the line of best fit.
Thus,
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
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Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
Answers
N = 7LH
Clearing H we have:
H = N / (7L)
Substituting the values we have:
H = 2310 / (7 (30))
Rewriting we have:
H = 2310/210
H = 11 feet
Answer:
the height of a wall that is 30 feet long and that requires 2,310 bricks to build is:
c. 11 ft
Explain why the graph shown may be misleading.
Answers
there are 30 mid-size, 3 of 10 each.
and there are 20 trucks,
however, in the graph, they all seem to have the same start point and end point, and the mid-size are elongated more than the compacts, and the trucks are much larger than the others above it, almost suggesting the amounts for all are equal somehow for that period.
the amounts must correlate horizontally as they're laid, thus the compacts should be longer than the rest, the mid-size behind it and the trucks half-way of the compacts.
please verify my probability answer!!!
Answers
The probability that the second student likes to play baseball:[tex]P(B)=\dfrac{15}{24}=\dfrac{5}{8}[/tex]
Together:
[tex]P(A)\cdot P(B)=\dfrac{2}{5}\cdot\dfrac{5}{8}=\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
Hope this helped :)
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/y = dx/(x^2)
int[dy/y] = int[dx/(x^2)] ... apply integral to both sides
ln(|y|) = (-1/x) + C
|y| = e^{(-1/x) + C}
|y| = e^C*e^(-1/x)
|y| = C*e^(-1/x)
y = C*e^(-1/x)
So you have the correct answer. Nice job.
------------------------------------------------
Check:
y = C*e^(-1/x)
dy/dx = d/dx[C*e^(-1/x)]
dy/dx = d/dx[-1/x]*C*e^(-1/x)
dy/dx = (1/(x^2))*C*e^(-1/x)
is the expression for the left hand side (LHS)
y/(x^2) = [C*e^(-1/x)]/(x^2)
y/(x^2) = (1/(x^2))*C*e^(-1/x)
is the expression for the right hand side (RHS)
Since LHS = RHS, this confirms the solution for dy/dx = y/(x^2)
Calculate the length b to two decimal places A) 890.68 B) 36.99 C) 36 D) 29.84
Answers
we know that
the law of cosines established that
b² = a² + c² − 2ac cos(B)
in this problem
a=22 units
c=14 units
B=110°
b² = 22² + 14² − 2*22*14*cos(110°)----> b²=890.68------> b=29.84 units
the answer is the option
D) 29.84