First find x and y.
Solve system of equations by elimination.
3x-y=3
+(-x+y=3)
---------------
2x=6
x=3
Now plug in x into one of the equations to find y.
-3+y=3
y=6
xy=3x6=18
Final answer:
The product of xy, given the system of equations 3x - y = 3 and -x + y = 3, is 18. This is found by first solving for x and y using the elimination method and then multiplying the obtained values.
Explanation:
To find the product of xy, we need to solve the system of equations given by 3x - y = 3 and -x + y = 3. Here we'll use the elimination method. Adding both equations together, we eliminate y:
3x - y + (-x + y) = 3 + 3
Which simplifies to:
2x = 6
Dividing both sides by 2, we get:
x = 3
To find y, we substitute x back into one of the original equations, for example, the second equation -x + y = 3:
-(3) + y = 3
-3 + y = 3
Adding 3 to both sides gives us:
y = 6
Now we can find the product of xy:
xy = 3 * 6
xy = 18
Therefore, the product of xy is 18.
GIVING BRAINLEST!!!Joe and Tim observed two points, P and Q, on a number line. A number line is shown from negative 1 to positive 1 with increments of 1 over 8. The numbers negative 1, negative 6 over 8, negative 4 over 8, negative 2 over 8, 0, 2 over 8, 4 over 8, 6 over 8 are labeled on the number line. A point P is shown to the third place on the left of 0, and a point Q is shown to the third place on the right of 0. Joe said that the absolute values of the numbers represented by the two points are different. Tim said that the absolute values of the numbers represented by the two points are the same. Which of the following explains who is correct?
Answer:
Step-by-step explanation:
P is 5 ticks to the left of 0, so it would be -5/8
Q is 5 ticks to the right of 0, so it would be at 5/8
an absolute value turns a negative number into a positive number
so absolute value of P located at -5/8 = 5/8
this is the location of point Q
Joe said that the absolute values of the numbers represented by the two points are the same.
Answer:
Tim, because each point is fraction 3 over 8 units away from 0.
Step-by-step explanation:
That is how absolute value works.
what is the inverse of f(x)=2x^3
Answer:
f^-1 (x)=(x/2)^(1/3)
Step-by-step explanation:
y=2x^3
x=2y^3
2y^3=x
y^3=x/2
y=(x/2)^(1/3)
Which of the following could be the first step in solving this problem? 9(12-3)+4
The first step in solving the expression 9(12-3)+4 is to perform the operation within the parentheses, subtracting 3 from 12. This operation adheres to the Order of Operations (PEMDAS) and simplifies the expression for further steps.
Explanation:The first step in solving the problem 9(12-3)+4 involves using the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, according to PEMDAS, we start with the operation within the parentheses. So, we subtract 3 from 12, resulting in 9 times 9, plus 4. The operation within the parentheses simplifies the problem and sets the stage for the subsequent multiplication and addition.
After simplifying the operation within the parentheses, we multiply the result by 9 and then add 4 to get the final answer. This step-by-step approach helps in solving the problem accurately.
Step One: Identify the unknown in the problem. In this case, the unknown is the result of the expression 9(12-3)+4.
Step Two: The first step in solving this problem is to simplify the expression inside the parentheses using the order of operations (PEMDAS/BODMAS).
Step Three: Perform the operations within the parentheses first, then multiply the result by 9 and finally add 4. This will give you the solution to the given expression.
last year, Mr. Petersen's rectangular garden had a width of 5 meters and an area of 20 square meters.
This year, he wants to make the garden three times as long and two times as wide.
a
Solve for the length of last year's garden using the area formula. Then, draw and label the
measurements of this year's garden
Last Year
This Year
20
square
meters
Answer:
Last year: length of 4 meters
This year: width of 10 meters and a length of 12 meters
Step-by-step explanation:
Use the expression to complete the table.
**Look above for the picture.
Answers:
110
95
80
65
75
Yay
solve the systems of equations by subsiturion
y=x+15
y=2x
next question
y=x+12
4x+2y=27
Answer:
1) x = 15, y = 30 is the solution of the given system of equation.
2) x = 0.5 , y = 12.5 is the solution of the given system of equation.
Step-by-step explanation:
First QUESTION:
Here the given set if equation are:
y = x + 15
y = 2 x
Substituting the value of y = 2 x in the first equation, we get:
y = x + 15 ⇒ 2 x = x + 15
or, 2 x - x = 15
⇒ x = 15
⇒ y = 2 x = 2 ( 15) = 30, or y = 30
Hence, x = 15, y = 30 is the SOLUTION of the given system of equation.
Second QUESTION:
Here the given set if equation are:
y = x +12
4 x + 2 y = 27
Substituting the value of y = x + 12 in the second equation, we get:
4 x + 2 y = 27 ⇒ 4 x + 2 (x + 12) = 27
or, 4 x + 2(x) + 2 (12) = 27
⇒ 6 x = 27 - 24 = 3
⇒ x = 3 /6 = 0.5
Now, y = x + 12 = 0.5 + 12 = 12.5 or y = 12.5
Hence, x = 0.5 , y = 12.5 is the SOLUTION of the given system of equation.
(PLEASE HELP) Which rules represent a transformation that maps one shape onto another to establish their congruence? Select all of the possible answers.
A) A dilation by scale factor of 3 about the origin.
B) A translation to the right 2 and down 6.
C) A reflection across the line y=2.
D) A counter-closckwise rotation of 90 degrees about the origin.
E) A horizontal stretch by a factor of 2 about the origin.
The possible transformations that establish congruence between shapes are dilation, translation, and reflection.
Explanation:The possible rules that represent a transformation mapping one shape onto another to establish congruence are:
A) A dilation by a scale factor of 3 about the origin.B) A translation to the right 2 and down 6.C) A reflection across the line y=2.A dilation by a scale factor of 3 about the origin stretches or shrinks the shape uniformly in all directions. A translation moves the shape without changing its size or shape. A reflection across a line is a flip of the shape over that line. These transformations can establish congruence between shapes.
Transformations that establish congruence between shapes by preserving size, shape, and orientation ensure that the transformed shape aligns with the original shape. The correct answer is option
B) A translation to the right 2 and down 6.
C) A reflection across the line y=2.
D) A counter-closckwise rotation of 90 degrees about the origin.
The rules that represent transformations mapping one shape onto another to establish congruence are:
B) A translation to the right 2 and down 6, which preserves both size and shape, simply moving the shape to a different location without changing its orientation or proportions.
C) A reflection across the line y=2, which reflects the shape across a line, maintaining its size and shape but reversing its orientation.
D) A counter-clockwise rotation of 90 degrees about the origin, which rotates the shape by a right angle, preserving its size and shape while changing its orientation.
These transformations preserve congruence by maintaining the size, shape, and orientation of the original shape.
Options B, C, and D represent transformations that map one shape onto another to establish their congruence, preserving size, shape, and orientation.
Plato Question!!!!
Type the correct answer in each box.
What is a polar form of (-1, √3 ) is ( _ , _ ) ?
Answer:
(2, 120° )
Step-by-step explanation:
To convert from rectangular to polar form, that is
(x, y) → (r, Θ ), use
r = [tex]\sqrt{x^2+y^2}[/tex]
Θ = [tex]tan^{-1}[/tex]( [tex]\frac{y}{x}[/tex])
here (x, y ) = (- 1, [tex]\sqrt{3}[/tex])
r = [tex]\sqrt{(-1)^2+(\sqrt{3} }[/tex] )^2
= [tex]\sqrt{1+3}[/tex] = [tex]\sqrt{4}[/tex] = 2
Θ = [tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]) = 60° ← related acute angle
Note (- 1, [tex]\sqrt{3}[/tex]) is in the second quadrant so Θ must be in the second quadrant.
Θ = 180° - 60° = 120°
(- 1, [tex]\sqrt{3}[/tex]) → (2, 120°)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The polar form of a Cartesian coordinates is given by (r, @) where r = √x^2 + y^2
@ = tan^-1 y/x
r = √-1^2 + √3^2
r = √4
r= 2
@ = tan ^-1 √3/-1 -tan √3/1 = -60°
@ = 180-60 = 120°
Hello, i need help!
5/2 multiplied by what equals 1?
equation: 5/2×?=1
Answer:
[tex]\large\boxed{\dfrac{2}{5}}[/tex]
Step-by-step explanation:
[tex]\text{The product of the number and its reciprocal gives us 1.}\\\text{Reciprocal of }\ \dfrac{5}{2}\ \text{is equal}\ \dfrac{2}{5}.\\\\\dfrac{5}{2}\times\dfrac{2}{5}=\dfrac{5\!\!\!\!\diagup}{2\!\!\!\!\diagup}\times\dfrac{2\!\!\!\!\diagup}{5\!\!\!\!\diagup}=\dfrac{1}{1}\times\dfrac{1}{1}=1\times1=1[/tex]
Students were surveyed about their wither break plans.Of the people that stated they were going skiing, 25% did not actually go.How many students actually went skiing?
Answer:
The total number of students actually went for skiing is 0.75 times the total students .
Step-by-step explanation:
Given as :
Some Students were surveyed about their wither break plans.
The percentage of students who actually did not go for skiing = 25 %
So , The percentage of students who actually go for skiing = 100 % of students - 25 %
I.e The percentage of students who actually go for skiing = 75 %
Let The total number of students = x
So, out of x students , The The percentage of students who actually go for skiing = 75 % of the total students
I.e The The percentage of students who actually go for skiing = 75 % of x
Or, The The percentage of students who actually go for skiing = 0.75 × x
So, The number of students for skiing = 0.75 x
Hence The total number of students actually went for skiing is 0.75 times the total students . Answer
Line has the equation y=2x+2. Write the equation of the image of after a dilation with a scale factor of 4, centered at the origin.
Write your answer in slope-intercept form.
Final Answer:
The equation of the image after a dilation with a scale factor of 4, centered at the origin, is y = 8x + 8.
Explanation:
When a function undergoes dilation centered at the origin, each coordinate (x, y) is transformed to (kx, ky), where k is the scale factor. In this case, the original equation y = 2x + 2 is dilated by a factor of 4. Therefore, the new equation becomes y' = 4(2x + 2), which simplifies to y' = 8x + 8. The scale factor of 4 multiplies both the coefficient of x and the y-intercept, resulting in a steeper slope and a vertical shift.
In the original equation, the coefficient of x was 2, indicating a slope of 2. After the dilation, the coefficient becomes 8, indicating a steeper slope of 8. Additionally, the y-intercept of 2 is multiplied by 4, yielding a new y-intercept of 8. This transformation preserves the line's direction while magnifying its steepness and shifting it vertically. The equation y' = 8x + 8 represents the dilated image of the original line.
To summarize, the process involves multiplying both the coefficient of x and the y-intercept by the scale factor. This scaling maintains the line's direction while adjusting its steepness and vertical position. The resulting equation, y' = 8x + 8, accurately describes the image of the original line after dilation by a factor of 4 centered at the origin.
If I have a shirt that's 15 dollars how do I take 20% off the price
Well, first find out what 20% of $15 is.
20% x $15 = $3
Take that from the original price.
$15-$3=$12
24.5 written in scientific notation
Answer:24.5
=
2.45
×
10
=
2.45
×
10
1
⇒
24.5
×
10
−
5
=
2.45
×
10
1
×
10
−
5
=
2.45
×
10
−
4
Step-by-step explanation:
Answer:
[tex]2.45*10^1[/tex]
Step-by-step explanation:
You move the decimal point of a number until the new form is a number from 1 up to 10 (N), and then record the exponent (a) as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.
If Logx (1 / 8) = - 3 / 2, then x is equal to
Answer:
Let's solve!
Step-by-step explanation:
[tex]logx^{\frac{1}{8} } = -\frac{3}{2}[/tex]
[tex]then[/tex]
[tex]10^{-\frac{3}{2}} = x^{\frac{1}{8} }[/tex]
[tex](10^{-\frac{3}{2} })^{8} = (x^{\frac{1}{8} })^{8}[/tex]
[tex]x = 10^{3*4} = 10^{-12}[/tex]
[tex]x= 10^{-12}[/tex]
If the equation looks like this, then it has the solution
[tex]x= 10^{-12}[/tex]
Another answer is
√x = 2 or x = 4
I hope this helps!
For more help:
https://brainly.com/question/9719370
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https://brainly.com/question/3505855
Tristan took a math quiz last week. He got 26 out of 52 problems correct. What percentage did Tristan get correct? Write your answer using a percent sign (%).
Answer:
50%
Step-by-step explanation:
To find the percentage of his correct answers, divide the amount of correct answers he got by the total number of problems.
26 out of 52 is another way to say
26/52
= 26 ÷ 52
= 0.50
0.5 is the decimal form of the answers Tristan got correct.
To convert it to a percentage, more the decimal two places to the right.
0.50 => 50%
Tristan got 50% of the problems correct.
The quadrilateral shown is a rhombus. If AB = 17 and AE = 8, what is the measure of BE
Answer:
[tex]BE=15\ units[/tex]
Step-by-step explanation:
we know that
In a rhombus the diagonals are perpendicular
so
The triangle ABE is a right triangle
see the attached figure to better understand the problem
Applying the Pythagoras Theorem to the right triangle ABE
[tex]AB^2=AE^2+BE^2[/tex]
where
AB is the hypotenuse of the right triangle (greater side)
AE and BE are the legs of the right triangle
we have
[tex]AB=17\ units\\AE=8\ units[/tex]
substitute
[tex]17^2=8^2+BE^2[/tex]
solve for BE
[tex]289=64+BE^2[/tex]
[tex]BE^2=289-64[/tex]
[tex]BE^2=225[/tex]
[tex]BE=15\ units[/tex]
Answer:
C) 16
Step-by-step explanation:
is (1 2) a solution of 6x-y>3
Answer:This can be checked by the following steps;
Step-by-step explanation:
The pair (1,2) is a solution to the inequality 6x - y > 3 because when these values are substituted into the inequality, the result is 4 > 3, which is a true statement.
Explanation:The question is asking if the pair of numbers (1,2) is a solution to the inequality 6x - y > 3. We can evaluate this by substituting the pair of values (1, 2) into the inequality in place of x and y. This gives us 6*1 - 2 > 3, or 6 - 2 > 3, which simplifies to 4 > 3. Since 4 is indeed greater than 3, we can conclude that the pair (1,2) is a solution to the inequality 6x - y > 3.
Learn more about Inequality Solutions here:https://brainly.com/question/22010462
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urgent, please help, I really appreciate (100 points)
Which sequence isn't a geometric
progression?
Answer:
3, 6, 9, 12 is not geometric
Step-by-step explanation:
A geometric progression has a common ratio r between consecutive terms.
3, 6, 9 , 12
has a common difference of 3 between terms and is arithmetic
1, 5, 25, 125
r = 5 ÷ 1 = 25 ÷ 5 = 125 ÷ 25 = 5 ← geometric
4, 8, 16, 32
r = 8 ÷ 4 = 16 ÷ 8 = 32 ÷ 16 = 2 ← geometric
2, 6, 18, 54
r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 ← geometric
Answer:
3, 6, 9, 12 would not be a geometric sequence.
Step-by-step explanation:
The reason for this is because, geometric sequence is multiplication or division while arithmetic is addition and subtraction.
1, 5, 25, 125 is multiplication. x5
4, 8, 16, 32 is multiplication as well. x2
2, 6, 18, 54 is multiplication as well. x3
While 3, 6, 9, 12 would be +3.
Therefore, 3,6, 9, 12 would not be a geometric sequence.
So how am I supposed to get my.anwsers
You can look them up on here or other apps/websites.
Which of the following equations is equivalent to y + 3 = -4(x - 2)?
Answer:
D. y= -4x +5
Step-by-step explanation:
The equation [tex]y+3=-4(x-2)[/tex] can be transformed by doing some algebra.If we solve the second term of the equation -4(x-2)= 8 - 4x, then we have [tex]y+3=8-4x[/tex] (this is done by distributing the multiplication into the two terms: remember that the product of -4x(-2)=+8 because the product of two negative numbers is a possitive number).Then, by subtracting both sides 3, we have [tex]y=5-4x[/tex]. Rearranging terms in the right side, we have [tex]y=-4x+5[/tex], which is option D.To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form.
Explanation:To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form. Here are the steps:
Distribute -4 to (x - 2): y + 3 = -4x + 8Move y to the right side: -4x + y + 3 = 8Combine like terms: -4x + y = 5Therefore, the equation that is equivalent to y + 3 = -4(x - 2) is -4x + y = 5.
Mathematical
PRACTICE 5 Use Math Tools Sarah buys a pen that costs
$0.75. How much will 2 pens cost?
Answer: 1.5
Step-by-step explanation:
0.72 • 2 = 1.5
Answer:1.50
Step-by-step explanation: 75•2 = 1.50
zen the
20,1.
A water tank is being filled by pumps at a constant rate. The volume of water in the tank V, in gallons, is
given by the equation:
v(t) = 65t + 280, where t is the time, in minutes, the pump has been on
(a) At what rate, in gallons per minute, is the (b) How many gallons of water were in the tank
water being pumped into the tank?
when the pumps were turned on?
Ult=65 1280
v101=6510) +250=280
rate is 65
wakers of gallon
tank had 280 gallons.
(c) What is the volume in the tank after two hours (d) The pumps will turn off when the volume in
of the pumps running?
the tank hits 10,000 gallons. To the nearest
minute, after how long does this happen?
edict
Answer:
(a) 65 gallons per minute
(b) 280 gallons
(c) 8080 gallons
(d) 150 minutes.
Step-by-step explanation:
Water is filled up by pumps into a tank at a constant rate.
The volume of water in the tank V, in gallons, is given by the equation
V(t) = 65t + 280 ......... (1), where t is the time, in minutes.
(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)
(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)
(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)
(d) The tank has a capacity of 10000 gallons of water.
So, if the tank starts to overflow after t minutes, then
10000 = 65t + 280
⇒ 65t = 9720
⇒ t = 149.53 minutes ≈ 150 minutes (Answer)
Final answer:
The rate at which water is being pumped into the tank is 65 gallons per minute, the tank initially had 280 gallons of water, after two hours the volume will be 8,080 gallons, and the pumps will turn off after approximately 150 minutes when the volume reaches 10,000 gallons.
Explanation:
The water tank problem can be analyzed step by step based on the given linear equation v(t) = 65t + 280, which describes the volume V of water in gallons as a function of time t in minutes.
(a) Rate of Water Being Pumped
The coefficient of t in the equation represents the rate at which water is being pumped into the tank. Therefore, the water is being pumped at a constant rate of 65 gallons per minute.
(b) Initial Volume of Water
The constant term in the equation, 280, represents the volume of water that was in the tank when the pumps were turned on. This means the tank initially had 280 gallons of water.
(c) Volume After Two Hours
To convert two hours to minutes, we multiply by 60 minutes per hour, giving us 120 minutes. Plugging this value into the equation gives us v(120) = 65(120) + 280 = 7,800 + 280 = 8,080 gallons. So, after two hours, the volume of water in the tank would be 8,080 gallons.
(d) Time to Reach 10,000 Gallons
To find the time when the volume reaches 10,000 gallons, we set the equation equal to 10,000 and solve for t: 10,000 = 65t + 280. Subtracting 280 from both sides gives us 9,720 = 65t, and dividing both sides by 65 gives us t ≈ 149.54 minutes. To the nearest minute, the pumps will turn off after approximately 150 minutes.
3(x-4)=12 solve for x
Step-by-step explanation:
Step 1: Distribute the 3 to (x-4)
⇒ 3(x)-3(4) = 12
Step 2: Calculate the left side!!
⇒ 3x-12= 12
Step 3: Add 12 to both sides!
⇒ 3x= 24
Step 4: Divide 3 by both sides!
⇒ 3x/3= 24/3
Step 5: YOUR ANSWER!!
⇒ 8
ANSWER: 8
What is the simplified form of the fraction below 6/24
1/4 is the simplified fraction for 6/24.
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
you can divide the numerator and denominator of [tex]\frac{6}{24}[/tex] by 6, resulting in [tex]\frac{1}{4}[/tex]
Kayla receives a bill for $754 for a new sofa. The bill includes a 6.2% tax on the sofa selling price and a $26 delivery fee. To the nearest cent, what was the selling price of the sofa?
Answer:
685.50
Step-by-step explanation:
754 - 26 = 728
728 / 1.062 = 685. 50
Answer: $685.50
Step-by-step explanation:
1.062x+26=754
1.062x=728
x=685.499
to nearest cent $685.50
if an airplane consumes 30.25 gallons of fuel in 2.8 hours of flying how many gallons will it consume and 4.3 hours of flying?
Answer:
46.46 gallons
Step-by-step explanation:
we know that
An airplane consumes 30.25 gallons of fuel in 2.8 hours of flying
so
using proportion
Find out how many gallons will it consume in 4.3 hours of flying
[tex]\frac{30.25}{2.8}\ \frac{gal}{h}=\frac{x}{4.3}\ \frac{gal}{h}\\\\x=30.25*(4.3)/2.8\\\\x= 46.46\ gal[/tex]
WRITE THE TERM,FILL IN THE BLANK
When we rewrite an expression so that it has no grouping symbols and all of the like terms have been combined, we ___ it.
Example: The process of turning (5x - 6) + 10x into 15x - 6.
The answer you’re looking for is: simplify.
When you rewrite an expression, we are simplifying it. We first use the distributive property through any groupings symbols, then evaluate terms we exponent that are given. Lastly, we combine any like terms, weather they are constants or variables.
Hope this helps! :)
Answer:
It is simplify. It is what you do when like terms are combined in order to get your answer.
Hope this helps!
A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or f(x)=x+60/x+300. Which statement describes the meaning of the horizontal asymptote?
A The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
B The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
C As more pure acid is added, the concentration of acid approaches 0.
D As more pure acid is added, the concentration of acid approaches 1.
Final answer:
The horizontal asymptote indicates that as more pure acid is added, the concentration approaches 1, meaning the acid concentration trends towards 100% purity but never fully reaches it. (Option D)
Explanation:
The horizontal asymptote of the function f(x) = x + 60 / (x + 300) describes the behavior of the acid concentration as the volume of pure acid x becomes very large. When an increasingly larger volume of pure acid is added, the concentration of the acid in the new substance approaches a certain value. This implies that, no matter how much more acid is added past a certain point, the concentration doesn't change significantly.
The correct statement regarding the horizontal asymptote is: D. As more pure acid is added, the concentration of acid approaches 1. This means that the concentration of the acid will get closer and closer to 100%, or pure acid, but it will never actually reach that concentration because you are always adding the acid to some amount of solution.
2 coins and 1 6 sided number cube. What is the probability of getting two heads and a 4?
Answer:
1/24 ≈ 4.2%
Step-by-step explanation:
P(head) = 1/2
P(4) = 1/6
P(2 heads and 4) = (1/2)² (1/6) = 1/24 ≈ 4.2%.
please help asap im stuck
Answer: 65%
Step-by-step explanation:
2258 glove-784 remaining = 1474 gloves used
now create part to whole relationship
1474 gloves used/2258 total gloves = 0.65 approx or 65%