Answer:
Option 4
Step-by-step explanation:
Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:
(2x + 3y = 5 ) * 2 =
4x + 6y = 10
Now, subtract the second equation from the first one:
(4x - y = -11) - (4x + 6y = 10)
4x - 4x = 0
-y - 6y = -7y
-11 - 10 = -21
-7y = -21
Divide both sides by -7:
y = 3
Plug 3 into the first equation as y:
4x - 3 = -11
4x = -11 + 3
4x = -8
x = -2
So x = -2 and y = 3. We need to find one of the options that equals this.
-4x - 9y = -21
-10y = -30
40x - 90y = -210
-90y = -270
40x - 0 = 40x
-90y - - 90y = -90 + 90 = 0y
-210 - -270 = -210 + 270 = 60
40x = 60
x = 1.5
We already know this isn't equivalent because the x value is not the x value of the given equation.
4x + 3y = 5
2y = -6
_______
8x + 6y = 10
6y = -18
8x - 0 = 8x
6y - 6y = 0
10 - -18 = 10 + 18 = 28
8x = 28
x = 3.5
So we know this isn't equivalent because again, the x value isn't the same as the given equation.
7x - 3y = -11
9x = -6
-----------
63x - 27y = -99
63x = -42
----------------
63x - 63x = 0
-27y - 0 = -27y
-99 - - 42 = -99 + 42 = -57
-27y = -57
-9y = -19
9y = 19
y = 19/9
So we know this one isn't equivalent as the y value isn't the same as the given equation.
12x - 3y = -33
14x = -28
x = -28/14 = -2
12(-2) - 3y = -33
-24 - 3y = -33
-3y = -33 + 24
-3y = -9
y = 9/3
y = 3
So x = -2 and y = -3 which is the same as the first equation.
Final answer:
Option 4 is the correct equivalent system for the given linear equations because you can derive the system in Option 4 by multiplying the original system's equations by constants and rearranging them.
Explanation:
We are given the system of linear equations:
4x − y = −112x + 3y = 5To find an equivalent system, each equation from the new system should be derivable from the original system. A common method is to multiply one or both of the original equations by a constant to see if it matches one of the offered options.
Option 4 is the correct choice. Multiplying the first original equation by 3, we get:
(4x − y) ⋅ 3 = −11 ⋅ 312x − 3y = −33And multiplying the second original equation by 7 and rearranging yields:
(2x + 3y) ⋅ 7 = 5 ⋅ 714x + 21y = 3514x = 35 − 21yBut since y = 0 (from 2y = −6, which implies y = −3),14x = 35 − 21(−3)14x = −28The other options cannot be derived from the original system through multiplication or other allowed operations, hence they are not equivalent.
Lia finds a second dress that was originally $72.00 and now was marked 15% off. How much did she pay for the second dress?
Answer:
The answer is $61.20
Step-by-step explanation:
First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.
what is the solution to the system of equations y=x+3, y=3x+1
Substitution method
y = x + 3 (*)
y = 3x + 1 (**)
Substitute (*) to (**):
3x + 1 = x + 3 subtract 1 from both sides
3x = x + 2 subtract x from both sides
2x = 2 divide both sides by 2
x = 1Put the value of x to (*):
y = 1 + 3
y = 4Answer: x = 1 and y = 4 → (1, 4).fill in the missing reasons for the proof below.
Please answer number 3.
I can't exactly SHOW you where to put the numbers, but I can teach you the process of how you'd do it.
First off, label your number line from 0-15, as it is the simplest. (You'd be counting by 1 per each line). Then, follow this process:
1) Look at the first digit of your value. Place your number according to your first digit. (So, you'd put 0.365 at the 0 line and 3.521 at the 3 line)
2) Look at the second digit of your value. Imagine that between the two main lines (0-1 and 3-4) that there is 10 smaller lines. Then, you can place your number according to your second digit. (So, you'd put 0.365 at the 0.3 line and 3.521 at the 3.5 line).
3) Look at the third digit of your value. Imagine that between the two smaller lines (0.3-0.4 and 3.5-3.6) that there is 10 smaller lines. Then, you can place your number according to your third digit. (So, you'd put 0.365 at the 0.36 line and 3.521 at the 3.52 line).
4) Look at the fourth digit of your value. Imagine that between the two even smaller lines (0.36-0.37 and 3.52-3.53) that there is 10 smaller lines. Then, you can place your number according to your fourth digit. (So you'd place 0.365 at the 0.365 line and 3.521 at the 3.521 line)
Mrs.Maxwell is buying pencils for her students. She has 3 classes of 28 students each. For Valentine’s Day, she wants to give each of her students 4 pencils. She can purchase packs of 18 pencils for $2.52. How many packs of pencils will Mrs. Maxwell need to purchase? Justify your answer.
Answer:
the answer might be 336 sorry if i am not right
Step-by-step explanation:
Answer:
I think the answer is approximately 5 packs of pencils.Hooe this helps :)
Step-by-step explanation: what I did was I multiplied 3 and 28 then divide that number by 12 and rounded my answer up.
You've baked 26 cookies, which is two-thirds of all the cookies you planned to bake. How many cookies did you plan to make?
Equation:
Solution:
Answer,
(26/2) * 3
= 39
Explanation,
26 cookies is only 2/3 of 3/3. So, we divide 26 by 2 to see how many cookies are in 1/3. We then can find out that when you make 1/3 of the cookies there are 13. Since that is only 1/3 and we want to find out 3/3. We multiply 13 by 3 and get 39 which is all the cookies she planned to make.
Hope this helps :-)
Change each improper fraction into an equal mixed number.
a. 15⁄4
b. 41⁄9
c. 67⁄8
d. 135⁄11
e. 107⁄20
f. 493⁄174
Answer:
A. 3 3/4
B. 4 5/9
C. 8 3/8
D. 12 3/11
E. 5 7/20
F. 2 145/174
Hope That Helps!
Anu bought an air cooler as shown below. Its water tank is in the shape of a cuboid and can take 40 litres of water. Its dimensions are 50cmx 20cm. What will be the length of the water tank?
Answer:
40 cm
Step-by-step explanation:
Using the conversion
1 litre = 1000 cm³, then
40 litres = 40 × 1000 = 40000 cm³
The volume ( V) of a cuboid is
V = lbh ( divide both sides by bh )
l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm
Length of water tank is 40 cm
Given that;
Capacity of tank = 40 liters
Dimensions of tank = 50cm × 20cm
Find:
Length of water tank
Computation:
Capacity of tank = 40 liters
Capacity of tank = 40 × 1000
Capacity of tank = 40,000 cm³
Length of water tank = 40,000 / [50cm × 20cm]
Length of water tank = 40,000 / 1,000
Length of water tank = 40 cm
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Which characteristics describe the scatterplot? Check all that apply.
1.Negative Correlation
2.Positive Correlation
3.Strong Correlation
4.Weak Correlation
5.Linear
6.Nonlinear
A. Negative Association
C. Strong Association
E. Linear
Answer:
1. Negative Correlation
3. Strong Correlation
5. Linear
Step-by-step explanation:
We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.
Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.
We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.
We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.
If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.
what is the value of B
Answer:
B = 2
Step-by-step explanation:
using the rule of exponents
• [tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
consider [tex]83^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{83^{2} }[/tex]
⇒ B = 2
Mother has purchased 75 yards of green fabric and 125 yards of white fabric to make green and white curtains. What is the largest number of curtains she can make if she wants all the curtains to be exactly the same length, and to have no fabric left over? How many yards of each kind of fabric would be used for each curtain?
The mother can make 3 green curtains and 5 white curtains, using the greatest common divisor of 75 and 125 yards which is 25. Each curtain would thus be 25 yards.
Explanation:This question can be solved using the concept of Greatest Common Divisor (GCD), which finds the largest possible length that can divide two given lengths without leaving any remainder. In this case, the lengths are 75 yards and 125 yards, which are the quantities of green and white fabric respectively. The GCD of 75 and 125 is 25.
Therefore, the largest number of curtains that can be made is based on this length, which means the mother can make 75/25=3 green curtains and 125/25=5 white curtains. Each curtain would be 25 yards.
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Simplify completely 12x+36/x^2-4x-21 and find the restrictions on the variable
Answer:
[tex]\dfrac{12}{x-7},[/tex]
[tex]x\neq 7,\ x\neq -3.[/tex]
Step-by-step explanation:
Consider the expression
[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]
1. The numerator can be factored as
[tex]12x+36=12(x+3).[/tex]
2. The denominator [tex]x^2-4x-21[/tex] has the discriminant
[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]
Then
[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]
Then
[tex]x^2-4x-21=(x-7)(x+3).[/tex]
Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]
3. Simplify the fraction:
[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]
Triangle ABC is reflected over the y-axis. The coordinates of Point A are (–3, –1). What are the coordinates of Point A', the reflected image, using an algebraic representation?
Answer:
A'(3, - 1)
Step-by-step explanation:
Under a reflection in the y-axis
a point (x, y) → (- x, y), hence
A (- 3, - 1) → A'(3, - 1)
The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The coordinate of a Triangle A as (-3,-1)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Thus The vertex of the triangle (-3,-1) it changes to (3,-1)
The algebraic representation for the transformation is given by '
(x,y)⇒(-1×x,1×y)
⇒(-x, y)
Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
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You want to use square tiles to cover the top of a stepping stone you're making. The top is 24 inches by 20 inches. What is the side measure of the largest-sized square tile you can use to cover the stepping stone without any overlap or cutting?
The side measure of the largest-sized square tile will be 4 in.
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given that, The top of a stepping stone is 24 inches by 20 inches.
GCF of 24 and 20 = 4
Hence, The side measure of the largest-sized square tile will be 4 in.
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find f(x).g(x) if f(x) = 3x+11 and g(x)= -2x+7
Answer:
f(x)·g(x) = -6x² -x +77
Step-by-step explanation:
Given:
f(x) = 3x + 11
g(x) = -2x+7
f(x) * g(x) = (3x+11)*(-2x+7)
= -6x²+21x-22x+77
= -6x² -x +77
Please help me with this and dont get any wrong!!!!!
1. The answer is A.
Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.
2. The answer is A.
On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.
3. The answer is C.
If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.
what is i + 6i? You have to simplify
[tex]i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}[/tex]
Hello! I kinda need a little help with this...
Lines m contains (6,8) and (-1,2). Lines n contains (-1,5) and (5,y). What is the value of y if line m is perpendicular to line n?
Can someone please help? The Maths is not something I'm too good at. :D
I honestly don't know or I would have replied. Sorry :(
Answer: y = -2
========================================
Explanation:
Find the slope of line m using the slope formula
slopeM = (y2-y1)/(x2-x1)
slopeM = (2-8)/(-1-6)
slopeM = -6/(-7)
slopeM = 6/7
The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes
We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.
slopeN = (y2-y1)/(x2-x1)
slopeN = (y-5)/(5-(-1))
slopeN = (y-5)/(6)
-7/6 = (y-5)/6
-7*6 = 6(y-5)
-42 = 6y-30
6y-30 = -42
6y = -42+30
6y = -12
y = -2
So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...
slopeN = (y2-y1)/(x2-x1)
slopeN = (-2-5)/(5-(-1))
slopeN = (-2-5)/(5+1)
slopeN = -7/6
which is the proper slope value we want.
The two rectangles shown have equal areas. Find the value of x
Answer:
x=18
Step-by-step explanation:
We need to find the areas of the rectangles
1st rectangle
A= l*w
A = (2x+4)*9
= 18x+36
2nd rectangle
A = l*w
= 15*(3x-30)
= 45x-450
Since the area of the rectangles are equal, we set these two equations equal
18x+36 = 45x-450
Subtract 18x from each side
18x-18x+36 = 45x-18x-450
36 = 27x-450
Add 450 to each side
36+450 =27x
486 = 27x
Divide by 27 on each side
486/27 = 27x/27
18=x
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Find the measures of all angles formed by line a parallel to line b with transversal m, if one angle is 25° bigger than another
Answer:
Measures of all angles is either 77.5° or 102.5°
Step-by-step explanation:
See the attached figure.
As shown:
line a parallel to line b with transversal m
So, all the angles are either congruent or supplementary.
Let the supplementary angles x and y and y > x
x + y = 180° ⇒ (1)
one angle is 25° bigger than another
y - x = 25° ⇒ (2)
solving (1) and (2)
∴ x = 77.5° and y = 102.5°
find the slope of the line through each pair of points.
what is seven decreased by 3 times some number
the answer to the question is 7-3x.
Answer:
7 - 3x
Step-by-step explanation:
let "some number" = x
"3 times x" = 3(x)
"seven decreased by" 7 -
Put together the phrases.
"seven decreased by 3 times x" is 7 - 3x
7 - 3x is your answer
~
A marketing company surveys 100 males and 100 females between the ages of 55 and 70 to determine how many times they text each day. The mean for males is 6 with a range of 4. The mean for the females is 8 with a range of 4. According to the statistics, which statement is TRUE?
A)
On average, females text more than males.
B)
On average, females text less than males.
C)
On average, females and males text about the same .
D)
On average, both males and females text 4 times each day.
Answer: I believe that A is the correct answer.
Answer:
It's A
Step-by-step explanation:
I just did this question
4m of timber costs £33.60 what is the cost of 9m?
Answer:
£ 75.60
Step-by-step explanation:
4 m ↔ £ 33.60
1 m ↔ £ 8.40
9 m ↔ £ 75.60
The cost of one meter of timber is £8.40, calculated by dividing £33.60 by 4. To find the cost of 9 meters, multiply £8.40 by 9, resulting in a total cost of £75.60.
To determine the cost of 9 meters of timber when we know that 4 meters cost £33.60, we can use a unit rate approach. First, we need to calculate the cost of one meter of timber by dividing the total cost by the number of meters. Then, we multiply the cost per meter by 9 to find the cost of 9 meters of timber.
Find the cost per meter: £33.60 / 4 meters = £8.40 per meter.Calculate the cost for 9 meters: £8.40 per meter * 9 meters = £75.60.Therefore, the cost of 9 meters of timber would be £75.60.
If the current exchange rate is 1.35261 US dollars for each Euro, how many dollars would be exchanged for 285 Euro?
Answer:
$385.49
Step-by-step explanation:
285x1.35261=385.49385
round to the nearest cent and you get $385.49
To exchange 285 Euros for US dollars at an exchange rate of 1.35261, you would receive 385.80785 US dollars.
Current exchange rate = 1.35261 US dollars
To calculate how many dollars would be exchanged for 285 Euros at an exchange rate of 1.35261 US dollars per Euro:
Set up a simple multiplication problem: 285 Euros multiplied by 1.35261 US dollars per Euro.
Multiply the two numbers to get the total amount in US dollars.
So, 285 Euros x 1.35261 = 385.80785 US dollars would be exchanged for 285 Euros.
A quadratic equation is shown below:
9x^2 - 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work
Part B: Solve 4x^2 + 8x - 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you choose the method used.
the solutions to a general quadratic equation is
X=-b±√b²-4ac/2a ,, When ax²+bx+c=0
the discriminant is the expression under the radical b²−4ac
Part A:
discriminant is (-16)² - 4(9)(60) = -1904
there are two complex solutions
Part B:
4x² + 8x − 5 = 0
4x² + 10x -2x - 5=0
2x ( 2x + 5) - 1(2 x + 5) =0
(2x + 5)(2x-1) = 0
/ \
/ \
2x+5 = 0 2x-1 =0
x = -5/2 x = 1/2
what would the identity be?
[tex] \frac{2}{3} ( \frac{3}{2} ) = 1[/tex]
Answer:
Since both sides equal, there are infinitely many solutions
Step-by-step explanation:
Simplify brackets
2/3×3/1=1
Use this rule: a/b×c/d=ac/bd
Simplify 2×3 to 6
6/3×2=1
Simplify 3×2 to 6
6/6=1
cancel 6
1=1
Since both sides equal, there are infinitely many solutions
The exression below represents Julia's annual salary after t years.
25,000(1.04)t
Interpret the meaning of the expression.
Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.
Answer:
b.
Step-by-step explanation:
Interpret the meaning of the expression.
A.
Julia's initial salary is $4,000, and the growth rate is 25% per year.
B.
Julia's initial salary is $25,000, and the growth rate is 4% per year.
C.
Julia's initial salary is $4,000, and the growth rate is 2.5% per year.
D.
Julia's initial salary is $25,000, and the growth rate is 40% per year.
In Phoenix, Arizona, the average n umber of sunny days is 211 per year. About what percent of the year is Phoenix sunny?
Answer:
21100%
Step-by-step explanation:
Move the decimal point two places to the right.
A=1+Prt solve for p
[tex]A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}[/tex]