Answer:
xy = 1
Step-by-step explanation:
Given
[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0[/tex]
Simplify the first expression:
[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}][/tex]
Help?
Would the answer for this be (-9,3) or (3,9) or (9,-3) or (-9,-3)???
Answer:
(-9, 3)
Step-by-step explanation:
To rotate a point 270°:
R₂₇₀ (x, y) = (y, -x)
So the answer would be (-9, 3).
Graph the solution of the inequality on a number line 2(x-3)-5x
Answer:
Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.
Step-by-step explanation:
The inequality is given as follows:
[tex]2\left(x-3\right)-5x<x-2[/tex]
Let's solve your inequality step-by-step
[tex]2\left(x-3\right)-5x<x-2[/tex]
[tex]2x-6\right)-5x<x-2[/tex]
[tex]-3x-6<x-2[/tex]
[tex]-6+2<x+3x[/tex]
[tex]-4<4x[/tex]
Divide both sides by -4.
[tex]x>-1[/tex]
Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.
Keywords: inequality, graph solution
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Susie works out in the gym three times a week. Her heartbeat
increased to 94 beats per minute during one workout. If she
maintained this rate for 25 minutes, how many times did her heart
beat during the 25-minute workout?
Answer:
Step-by-step explanation:
94 beats per minute during one workout.
If the rate was maintained for 25 minutes, the heart beats = 94×25
= 2350 beats
What are like terms for 28?
Answer:
all the constants
Step-by-step explanation:
HELP FAST PLS
What is the difference between the Pythagorean Theorem and its converse?
A. The Pythagorean Theorem states that the sum of the squares of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that the sum of the squares of the two shortest sides of a triangle that is not a right triangle does not equal the square of the longest side.
B. The Pythagorean Theorem states that the sum of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that the sum of the two shortest sides of a triangle that is not a right triangle does not equal the square of the longest side.
C. The Pythagorean Theorem states that the sum of the squares of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that if the sum of the squares of the two shortest sides of a triangle equals the square of the longest side, then the triangle is a right triangle.
D. The Pythagorean Theorem states that the sum of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that if the sum of the two shortest sides of a triangle equals the square of the longest side, then the triangle is a right triangle.
Answer:
The converse of the Pythagorean theorem states that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Answer:
its C basically
Step-by-step explanation:
Solve this system of linear equations. Separate
the x- and y-values with a comma.
- 14x = -1 - 9y
17x = 7 +9y
NEED HELP ASAP!!
Step-by-step explanation:
making x subject in eq 1
x= (-1-9y)/-14
substituting the value of x in eq 2
17(-1-9y/-14)=7+9y
(-17-153y)/-14=7+9y
-17-153y=-98-126y
-17+98=153y-126y
81=27y
y=3
substituting this value of y in eq 1
-14x=-1-9(3)
-14x=-28
x=2
(x,y) = (2,3)
a=2/3b,b=15,c=?
please help dear lord
Answer:
10.
Divide b into thirds, and then add together 2 of those thirds.
15/3 = 5
5x2 is 10.
Sorry if that doesn't make sense but it's how I do it in my head lol.
Brent has a shopping bag with 8 similar size containers of yogurt: 2 strawberry, 3 cherry, and 3 raspberry. If he randomly takes 2 yogurt containers from the bag
without replacement, what is the probability that neither will be strawberry yogurt?
Answer:[tex]\frac{15}{28}[/tex]
Step-by-step explanation:
Number of strawberry = 2
Number of cherry = 3
Number of = 3
Total number = 8
Brent randomly takes 2 yogurt containers from the bag
without replacement ,we are to find the probability that hat neither will be strawberry yogurt.
Let r represent raspberry and c represents Cherry ,then Bent selection could be :
{ rr , cc , rc , cr}
Calculating this , we have
([tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{3}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{3}{7}[/tex] )
= [tex]\frac{30}{56}[/tex]
= 15/28
Therefore , the probability that neither will be strawberry yogurt= 15/28
A square playground is surrounded by a sidewalk on all sides. The sidewalk is 2n+3 yards along each side. The sidewalk is 0.5 yard wide. What is the perimeter of the playground? Write two equivalent expressions for the perimeter of the playground.
Final answer:
The perimeter of the square playground can be found by adding the lengths of all four sides. Two equivalent expressions for the perimeter are 8n + 8 and 4(2n + 2).
Explanation:
To find the perimeter of the playground, we need to add up the lengths of all four sides. Since the playground is a square, all four sides are equal in length.
The length of each side of the playground can be found by subtracting twice the width of the sidewalk from the overall length of the sidewalk. This is because the sidewalk wraps around the playground on all sides.
So, the length of each side of the playground is (2n+3) - 2(0.5) = 2n + 2.
The perimeter of the playground is then 4 times the length of each side, which is 4(2n + 2) = 8n + 8 yards.
Two equivalent expressions for the perimeter of the playground are 8n + 8 and 4(2n + 2).
URGANT NEEDED RIGHT NOW MUCH APPRECIATED:
A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.
It is spun twice.
What is the probability of getting blue both times?
Answer:
Probability of getting blue both times = [tex]\frac{16}{81}[/tex]
Step-by-step explanation:
A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.
It is spun twice.
We have to find the probability of getting blue both times?.
For both times , the probability of getting blue is the same.
Probability = [tex]\frac{number of favorable cases}{total number of cases}[/tex]
The number of favorable cases for blue = 4
Total number of cases = 9
Hence the probability = [tex]\frac{4}{9}[/tex]
We have to get it two times so final probability = [tex]\frac{4}{9}\times \frac{4}{9} = \frac{16}{81}[/tex]
What is the remainder of 28,254 divided by 52?
Answer:
18
Step-by-step explanation:
Finding the remainder of 28254 divided by 52.
Steps1. Use calculator to divide 28254 by 52:
28254/52= 543.346...2. Take whole part of the quotient and multiply by divisor:
543*52= 282363. Subtract this number from the initial dividend:
28254 - 28236 = 18This is the remainder: 18
Final answer:
The remainder when 28,254 is divided by 52 is 9. This is found by dividing the number step by step until no more digits can be brought down, leaving the remainder.
Explanation:
The student is asking for the remainder when 28,254 is divided by 52. To solve this, we perform the division process until we reach a point where we cannot divide any further without going into decimals. The number that is left over at this point is the remainder. Below is a step-by-step explanation of the process.
Begin dividing 28,254 by 52.52 goes into 282 five times (since 52 x 5 = 260), with a remainder of 22.Bring down the next digit, 4, to make 224.52 goes into 224 four times (since 52 x 4 = 208), with a remainder of 16.Bring down the final digit, 5, to make 165.52 goes into 165 three times (since 52 x 3 = 156), with a remainder of 9.Since there are no more digits to bring down, we have our final remainder.The remainder when 28,254 is divided by 52 is 9.
Find the value of x that makes A || B.
Answer:
x = 90.
Step-by-step explanation:
< 1 and < 4 are corresponding angles and are congruent if line a is parallel to line b. So:
3x - 160 = x + 20
2x = 180
x = 90.
Find domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36
Answer:
[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]
Step-by-step explanation:
Domain of Functions
Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.
The question provides us with the following functions
[tex]\displaystyle f(x)=x^2-3x-18[/tex]
[tex]\displaystyle g(x)=x^2-36[/tex]
[tex]\displaystyle h(x)=\frac{x^2-3x-18}{x^2-36}[/tex]
We called h(x) to the newly created function f/g(x)
To investigate the possible points of nonexistence for h, we factor h(x)
[tex]\displaystyle h(x)=\frac{(x-6)(x+3)}{(x-6)(x+6)}[/tex]
We can clearly see the denominator has two zeros at
[tex]\displaystyle x=6,\ x=-6[/tex]
A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.
So, the domain of h is
[tex]\displaystyle (-\infty,\ -6 )\bigcup (-6,\ 6)\bigcup (6,+\infty )[/tex]
Or equivalently
[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]
The domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, is all real numbers except x = 6 and x = -6. This is because we can't have g(x) equals to zero in (f/g)(x). Hence the domain is (-∞, -6) U (-6, 6) U (6, ∞).
Explanation:In Mathematics, when dealing with the domain of the function (f/g)(x) it is important to understand that the domain is the set of all possible x values that we can input into the function. For the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, the denominator g(x) cannot be zero as this would mean dividing by zero, which is undefined in Mathematics. So we need to find the values of x for which g(x) ≠ 0. To do this, we set g(x) equal to zero and solve for x. So, x^2-36=0. Simplifying this, we get (x+6)(x-6) = 0. Hence the roots of the equation are x = 6, x = -6.
These are the values for which g(x) will become zero. Since we can't have g(x)=0 in (f/g)(x), the domain of the function (f/g)(x) is all real numbers except x = 6, x = -6. So, the domain of (f/g)(x) is (-∞, -6) U (-6, 6) U (6, ∞).
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help asap will give BRAINLIEST
a. < 2 and < 8
b. < 3 and < 7
c. < 2 and < 4
d. < 1 and < 8
The answer: d. < 1 and < 8
if 10 custom engraved pens cost $100, how much will 8 of the same pens cost?
Answer:
They will cost $80.
Step-by-step explanation:
First, find the out how much 1 pen cost(unit rate).
To do that, divide 100 by 10.
100÷10= 10
So, each pen cost $10.
Now, multiply the cost of 1 pen times 8.
10×8= 80
This concludes that 8 of the same pens cost $80.
What is the distributive property of 8(y-7)=-16
Step-by-step explanation:
[tex]\text{The distributive property:}\\\\a(b-c)=ab-ac\\\\8(y-7)=(8)(y)-(8)(7)=8y-56\\\\\text{If you want whole solution:}\\\\8(y-7)=-16\\8y-56=-16\qquad\text{add 56 to both sides}\\8y-56+56=-16+56\\8y=40\qquad\text{divide both sides by 8}\\\dfrac{8y}{8}=\dfrac{40}{8}\\\boxed{y=5}[/tex]
Answer:
y=5
Step-by-step explanation:
8(y-7)= -16
(8)y-(8)7= -16
8y-56= -16
-16+56= 40
40/8= 5
y=5
(when you get y by itself)
hoped this helped a little bit.
PLEASE HELP ME ASAP NEED THIS FOREAL!! picture shown below
Denzel is coming web sites for downloading music. One charges a 50 membershy lee plus
160.50 per song. Another Charges & 1.00 per song but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both web site
Question is not proper, Proper question is given below.
Denzel is comparing websites for downloading music. One charges a $5 membership fee plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both websites.
Answer:
Denzel would have to buy 10 songs to spend the same amount at both websites.
Step-by-step explanation:
Let the number of songs be 'x'.
Given:
One charges a $5 membership fee plus $0.50 per song.
So the total cost at one site will be membership cost plus charges per song multiplied by number of songs.
framing in equation form we get;
Total Cost at one site = [tex]5+0.5x[/tex]
Another website charges $1.00 per song, but has no membership fee.
So the total cost at Another site will be charges per song multiplied by number of songs.
framing in equation form we get;
Total Cost at Another site = [tex]1\times x=1x[/tex]
To find the number of songs that results in same cost we should equate the two expression and solve.
[tex]5+0.5x=x[/tex]
Combining like terms we get;
[tex]5 = x-0.5x\\\\5=0.5x[/tex]
Now Dividing both side by 0.5 we get;
[tex]\frac{0.5x}{0.5} = \frac{5}{0.5} \\\\x=10\ songs[/tex]
Hence Denzel would have to buy 10 songs to spend the same amount at both websites.
Given the following points, write the equation of the line that goes through them. ( -12,56), (0,8), and (8,-24).
Answer:
[tex]y=-4x+8[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the data
(0,8), and (8,-24).
substitute
[tex]m=\frac{-24-8}{8-0}[/tex]
[tex]m=\frac{-32}{8}[/tex]
[tex]m=-4[/tex]
step 2
Find the equation of he line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-4[/tex]
[tex]b=8[/tex] ----> the y-intercept is given
substitute
[tex]y=-4x+8[/tex]
Please help me ASAP I really need help 15 points
Answer:
45,2316
Step-by-step explanation:
You have to move the numbers to their new respective places as told by the description of the new place
In the diagram m ∠ 3 = x + 30 and m ∠ 4 = 2x - 80. What is the measure of angle 3?
50
80
110
140
Answer:
140 degrees
Step-by-step explanation:
Due to ∠3 and ∠4 being vertical angles (they are across from one another) their measures are the same, therefore:
⇒ m∠3=m∠4
and since their measures are given in terms of x to find x just substitute:
⇒ x+30=2x-80 ⇒ x=110
We substitute x in m∠3=x+30 and find that m∠3=140 degrees
Answer:
The answer is 140 i just did the lesson
Step-by-step explanation:
Determine the intercepts of the line.
-5x+9y=-18−5x+9y=−18
x-intercept: (__), (__)
y-intercept: (__), (__)
Answer:
x-intercept: (18/5,0)
y-intercept: (0,-2)
Step-by-step explanation:
btw .. you put the equation twice it's supposed to be " -5x+9y=-18 "
Why is 3 x 1/10 less than 3 x 10
3 x 1/10 is 0.3 because it represents one tenth of 3, while 3 x 10 is 30 as it increases the value of 3 tenfold. Powers of ten and negative exponents demonstrate that each step in exponent changes the scale of the number by a factor of ten.
The reason why 3 x 1/10 is less than 3 x 10 is due to the values being multiplied by 3. When multiplying 3 by 1/10, you are essentially taking one tenth of 3, which gives you 0.3. However, when multiplying 3 by 10, you are increasing 3 tenfold, which results in 30.
To understand the scale, considering that each positive power of 10 is ten times bigger than the previous one, for instance from 3.2 to 3.2 x 10, and each negative power is ten times smaller, like from 3.2 to 3.2 x 1/10 . Powers of ten and their associated exponents allow us to easily compare and calculate with vastly different magnitudes, and this concept underlies the multiplication comparisons posed in the initial question.
A sequence of transformations which moves ΔRST onto ΔXYZ shows that ΔRST ≅ ΔXYZ. Which part of the triangles are congruent by CPCTC?
Answer:
Here's what I get
Step-by-step explanation:
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
If ΔRST ≅ ΔXYZ then
∠R = ∠X
∠S = ∠Y
∠T = ∠Z
RS = XY
ST = YZ
RT = XZ
To prove ΔRST ≅ ΔXYZ, perform a sequence of transformations and apply CPCTC to identify congruent parts.
Explanation:To prove that ΔRST ≅ ΔXYZ, we need to perform a sequence of transformations that move ΔRST onto ΔXYZ. Once the triangles are superimposed, we can use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to identify congruent parts.
CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent. In this case, the parts of ΔRST that are congruent to the corresponding parts of ΔXYZ are:
Side RS is congruent to side XYSide ST is congruent to side XZAngle R is congruent to angle XLearn more about Congruent Triangles here:https://brainly.com/question/31700817
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Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
9 feet
18 feet
30 feet
33 feet
Answer:
The Width of the garden will be 9 feet.
Step-by-step explanation:
Given:
Manny has wood =48 feet
Length of the garden = 15 feet
The equation which can be used [tex](2l+2w) = 48[/tex].
We need to find the width of the garden.
Solution :
Now Length of the garden is given we will substitute in the given equation to find the width.
[tex]2l+2w=48\\\\2\times15+2w=48\\\\30+2w=48[/tex]
Now Using Subtraction property we will subtract both side by 30 we get;
[tex]30+2w-30=48-30\\\\2w =18[/tex]
Now Using Division Property we will divide both side by 2 we get;
[tex]\frac{2w}{2}=\frac{18}{2}\\\\w= 9\ ft[/tex]
Hence the Width of the garden will be 9 feet.
Answer:
its A 9 ft
Step-by-step explanation:
i know things...
Bank Card is charging 1.7% monthly interest on credit card charges. If you charged a $175 pair of running shoes on the card and did not pay it off this month, what would be the interest for the shoe charge?
$298
$5.96
$2.98
$23.84
5n+-3n=-18 solve for n
Answer:
[tex] \: \: \: \: \: \: \: \: 5n + ( - 3n) = - 18 \\ = > 5n - 3n = - 18 \\ = > 2n = - 18 \\ = > n = \frac{ - 18}{2} \\ = > n = - 9[/tex]
If you know a root of a function is -2 + the square root of 3i then _____. 2 + the square root of 3i is a possible root. 2 + the square root of 3i is a known root. -2 - the square root of 3i is a possible root. -2 - the square root of 3i is a known root. Just finished the assignment got it wrong but the correct answer is -2 - the square root of 3i is a known root
Answer:
-2 - the square root of 3i is a known root
Step-by-step explanation:
we know that
The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial
we have that
The root of a function is [tex]-2+\sqrt{3}i[/tex]
so
Applying the conjugate root theorem
[tex]-2-\sqrt{3}i[/tex] ---> is also a root of the function
therefore
-2 - the square root of 3i is a known root
Answer:
-2 - Squared 3i is a known root
Step-by-step explanation:
the label on a 1 and 1/2 pound bag of wildflower seeds states thatbit will cover an area of 375 Square feet.Bags are sold by the pound and cost $2.50 per bag.If silas wants to cover 1,000 square feet ,how much does he need to spend on tthe wildflower seeds?
Answer:
I think its like $6.67
Step-by-step explanation:
divide 1000 by 375 then multiply the answer to that by 2.50 u should get 6.666666666666667 round it to 6.67
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds?
121.862 years
12.1862 years
10.155 years
1.0155 years
It takes 10.155 years until you have $3,000 ⇒ 3rd
Step-by-step explanation:
The formula for compound interest, including principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
A is the future value of the investment/loan, including interestP is the principal investment amount r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed for∵ You decide to put $2,000 in a savings account
∴ P = 2000
∵ You want to save for $3,000
∴ A = 3000
∵ The account has an interest rate of 4% per year and is
compounded monthly
∴ r = 4% = 4 ÷ 100 = 0.04
∴ n = 12 ⇒ compounded monthly
- Substitute all of these values in the formula above to find t
∵ [tex]3000=2000(1+\frac{0.04}{12})^{12t}[/tex]
- Divide both sides by 2000
∴ [tex]1.5=(1+\frac{1}{300})^{12t}[/tex]
∴ [tex]1.5=(1\frac{1}{300})^{12t}[/tex]
- Change the mixed number to an improper fraction
∴ [tex](1.5)=(\frac{301}{300})^{12t}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(1.5)=log(\frac{301}{300})^{12t}[/tex]
- Remember [tex]log(a)^{n}=nlog(a)[/tex]
∴ [tex]log(1.5)=(12t)log(\frac{301}{300})[/tex]
- Divide both sides by [tex]log(\frac{301}{300})[/tex]
∴ 121.84 = 12 t
- Divide both sides by 12
∴ 10.155 = t
It takes 10.155 years until you have $3,000
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