Answer:
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.
Step-by-step explanation:
Given
x + y : x - y = 3 : 2
As
[tex]x + y = 3[/tex]
[tex]x - y = 2[/tex]
Solving to find x and y
[tex]\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}[/tex]
[tex]x-y=2[/tex]
[tex]-[/tex]
[tex]\underline{x+y=3}[/tex]
[tex]-2y=-1[/tex]
[tex]\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}[/tex]
solve for y
[tex]-2y=-1[/tex]
Divide both sides by 2
[tex]\frac{-2y}{-2}=\frac{-1}{-2}[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=\frac{1}{2}[/tex]
[tex]x+\frac{1}{2}=3[/tex]
[tex]x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}[/tex]
[tex]x=\frac{5}{2}[/tex]
so
[tex]x=\frac{5}{2},\:y=\frac{1}{2}[/tex]
Thus,
x + y : x - y = (5/2+1/2) : (5/2-1/2)
x + y : x - y = 3 : 2
Therefore, x + y : x - y= 3 : 2 is proved.
can y^4 / x^3 be simplify
Answer:
Nope! Thats as simplified as it gets!
Answer:seems like it cant
Step-by-step explanation:
If the scale factor is 4, what do you do with that scale factor to find the new perimeter and new area of the dilated figure?
Answer:
4/4=1
Step-by-step explanation:
hi, can someone help me on a p e x? learning
Sure whats the problem?
The value of the expression 5³ is 125.
We have,
The concept used in calculating the value of 5 raised to the power of 3 is exponentiation.
In mathematics, exponentiation is an operation that involves raising a base number to a certain power.
The base number (in this case, 5) is multiplied by itself repeatedly, where the number of times it is multiplied is determined by the exponent (in this case, 3).
When we raise 5 to the power of 3, we can interpret it as multiplying 5 by itself three times:
5³ = 5 x 5 x 5 = 125
So, the concept of exponentiation allows us to quickly calculate the result of multiplying a number by itself multiple times, where the exponent indicates the number of repetitions.
Thus,
The value of the expression 5³ is 125.
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The complete question:
What is the value of 5 raised to the power of 3?
Graph each pair of linear equation in one coordinate plane.
Graph po pls
The pair of linear equations graphed using a graphing software. The graphs are attached below :
Graph 1 :
x = 2x + 2 - - - - (1)
2y = 4x + 4 ;
Divide both sides by 2
y = 2x + 2 - - - - - (2)
Hence, the graph would be follow the same trends as the functions are the same.
Graph 2 :
y = x - 5 - - - - - - (1)
y = - x + 3 - - - - - (2)
The pair of lines intersect each other as seen on the graph.
Graph 3 :
y = 2x - 3 - - - - (1)
y = 2x + 4 - - - - (2)
Both Lines are parallel to one another.
The attached graphs are in the attachment below.
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Nila bought a "buy-one-take-one" bag. She paid Php 1, 256. How much did each bag cost
Answer: Php 628
Step-by-step explanation:
Nina got two bags but paid for the price of one according to the sale.
The cost of each bag will therefore be the total price divided by 2 which is;
= 1,256/2
= Php 628
georgia made 48 cupcakes for her sister's birthday party. 1/4 of them are chocolate 1/6 of them are strawberry 5/12 of them are vanilla. how many cupcakes are lemon
Answer:
8
Step-by-step explanation:
I changed all of the denominators to 12. Added it all up and got 10. Multiplied it by 4 and got 40. There is 8 remaining, I hope this helps.
Find all real square roots of 121
If there is more then one answer Separate then with commas if there are none, click on “None”
Answer:
11,-11
Step-by-step explanation:
This is correct.
hope this helps ;D
Answer:
All real square roots of 121 is +11 and -11.
When you square root something, you take the positive and negative of the number, so the square root of 121 would be 11 and -11.
When you do 11 times 11, you get 121 and when you do -11 times -11, you get 121 as well, this is why we do the negative as well.
#teamtrees #WAP (Water And Plant)
Britney already owns 65 necklaces, and additional necklaces are priced at 2 for a dollar. How much money does Britney need to spend on new necklaces in order to own a total of 133 necklaces? Write and solve an equation to find the answer
Answer:
I think the answer is 136
Answer:
Step-by-step explanation:
First, we subtract 133-65 to find out how many new necklaces she need to buy
The answer is 68
Now, two necklaces costs $1, meaning one necklace costs ¢50, or $0.50.
So, we just multiply the number of necklaces (68) by the cost per necklace (0.5)
68×0.5=34
she will need to spend $34 to have a total of 133 necklaces
Chris paid $9.18 for a necklace. This amount includes a sales tax of 8%. What was the
cost of the necklace before tax?
Answer:
8.5
Step-by-step explanation:
What is the value of when x=15
Answer:
Value of what?
Step-by-step explanation:
Put your question DB and I'll answer!
Answer:
x = 15
Step-by-step explanation:
x = 15 means that if you have 1 + x and plug in the 15 for x, 1 + 15 you will get 16.
Note: I'm not quite sure what the question is on this one, but I hope I could help.
Is the line that passes through (8,-4) and (3,6) perpendicular To y=1/2x-4?
Show your work if you can
Thank you!
9514 1404 393
Answer:
yes, the lines are perpendicular
Step-by-step explanation:
A graph of the line through the points (8, -4) and (3, 6) shows it has a slope of -2. That is the opposite reciprocal of the slope of 1/2 that the given line has.
When two lines have opposite reciprocal slopes, they are perpendicular.
The lines are perpendicular.
__
If you like you can compute the slope using the slope equation:
m = (y2 -y1)/(x2 -x1)
m = (6 -(-4))/(3 -8) = 10/-5 = -2
10 points
slope of (-2,-4) and (6,7)
(explain)
Answer:
11/-8
Step-by-step explanation:
-2-6=-8
-4-7=11
then flip
A train freight car weighs 25 tons when empty. A conveyor belt pours coal into the car at a constant rate of 1/3 ton per minute until it is full.
The dump truck (Refer to problem 8) weighs 55 tons when filled. At the same time the freight car is being filled, an identical freight car filled
to capacity is being emptied at a rate of 1/6 ton per minute.
How long, in minutes, until the freight cars are the same weight?
The tucks will weigh the same in
minutes.
How much coal will be in each truck when they weigh the same?
There will be
tons of coal in each truck.
Step-by-step explanation:
Step one:
mass of Freight car=25tons
the rate of filling is 1/3 ton per minute
let the time taken to fill the freight car be x
and the total mass after x minute be y
Hence the mass as a function of time is expressed as
y=25+1/3x----------1
mas of dump truck=55tons
rate of being emptied= 1/6 tons per minute
let the time taken to empty the dump truck be x
and the total mass after x minute be y
Hence the mass as a function of time is expressed as
y=55-1/6x----------2
Step two:
equating equations 1 and 2,
1. The tucks will weigh the same in
55-1/6x=25+1/3x
collect like terms
55-25=1/3x+1/6x
30=(2+1/6)x
30=3/6x
30=1/2x
30=0.5x
x=30/0.5
x=60min
or
1 hour
The tucks will weigh the same in 60minutes(1 hour)
2. How much coal will be in each truck when they weigh the same?
For the train freight car, the weight after 60 minutes is
y=25+1/3(60)
y=25+20
y=55tons
55-25=20tons
There will be 20tons
For the dump truck, the weight after 60 minutes is
y=55-1/6(60)
y=55-10
y=45tons
55-45=10tons
There will be 10tons
PLZ PLZ PLZ PLZ PLZ PLZ PLZ PLZ PLZ HELP FOR BOTH OF THEM
Answer:
7) B, C
8) D
Step-by-Step-Explanation:
The first thing you need to solve for is the the parenthesis
the second one simplifies to x ≤ -7
Write the slope-intercept form of the equation of the line through the point (1,-3) with a slope of 2.
Answer:
The answer is
[tex] \huge y = 2x - 5[/tex]
Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
From the question we have
[tex]y + 3 = 2(x - 1) \\ y + 3 = 2x - 2 \\ y = 2x - 2 - 3[/tex]
We have the final answer as
[tex]y = 2x - 5[/tex]
Hope this helps you
Select the section(s) of the graph where the function is decreasing.
1. blue line
2. red line
3. curved blue line
4. green line
can be more than one
The graph where the function is decreasing is represented by, the blue line, red line and the green line.
What is decreasing function?"If the value of the function f(x) is decreasing on increasing the value of x, then the function is called as decreasing function."
For given situation,
we have been given a piecewise function and its graph.
From the graph of a function,
we can observe that the function f(x) is decreasing for x < -3 , -3 ≤ x ≤ 0, and x > 0
This is represented by, the blue line, red line and the green line
Therefore, the correct options are 1, 2, 4.
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work out the size of angle x
give reasons for your answer
Answer:
80°
Step-by-step explanation:
because a straight parallel line is 180°
Answer:
x=100°
because line AD//EH
therefore alternate angle are equal
so x=100°
Help!! Please;-;
Choose the slope and y-intercept that
correspond with the graph.
Answer:
Y-intercept: -1Slope: -1/3Step-by-step explanation:
The y-intercept is the point where the line crosses the y axis (horizontal line in graphs). We can clearly see that the y-intercept is -1, since the line intersects the y axis at y = -1.
Ok, now for the slope, we will use this equation, where m is the slope we wish to find.
m = rise/run where rise is the change in y and run is the change in x.
To determine the rise and run, we need two coordinate pairs.
9, -4 and 0, -1 will do
Note: The coordinate pairs are x, y, but slope is y/x, it is important that we do not become confused.
Now, we will subtract one y from the other and then do the same for the x's. It is important that we use the same order for the x's as we do for the y's, in order for the answer to be valid.
Y -4 - -1 = -3
X 9 - 0 = 9
Slope is -3/9 or -1/3
Hope that this answer has helped you, please mark it brainliest if it did :)Which number would make this statement true?
<8.9
9.1
8.91
8.09
8.99
Answer:
8.09
9.1 is obviously greater than 8.9, when you compare the numbers.
And the other numbers are all 8 in the ones place (to the left of the decimal). So, you have to look at the number in the tenths place (to the right of the decimal). 8.09 has a "0" in the tenths place, & 8.9 has a "9" in the tenths place, making 8.09 less than 8.9.
If you compared the 2 remaining numbers 8.91 & 8.99, they would both be greater, because since they all have the same number in the tenths place, you have to move on to comparing the next number, which would be in the hundreths place (2 digits to the right of the decimal).
Which transformation(s) can be used to map one triangle onto the other? Select two options reflection only translation only dation, then translation rotation then translation rotation then dilation
Answer: a reflection could i think
Step-by-step explanation:
Answer: A & C
Step-by-step explanation:
If PQ + RS = PS and RS = XY, then PQ + XY = PS.
a. Symmetric Property
b.Segment Addition Postulate
c.Substitution Property
d. Transitive Property
Answer:
B. Substitution Property
Step-by-step explanation:
Transitive property would be TX=GH and GH=PS then TX+PS
The substitution property of equality is one of many equality properties used to simplify expressions and solve equations.
If PQ + RS = PS and RS = XY, then PQ + XY = PS is an expression using substitution property.
What is substitution property?The substitution property states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any expression and y can be substituted in place of x in any expression.
We have,
If PQ + RS = PS and RS = XY, then PQ + XY = PS.
We are substituting RS with XY on PQ + RS = PS.
We get,
PQ + XY = PS
This expression has been solved using the substitution property.
Thus, If PQ + RS = PS and RS = XY, then PQ + XY = PS is an expression using substitution property.
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPP.
Square KLMN with vertices K(0,2), L(1,8), M(7,7), and N(6, 1): 270 counterclockwise about the orgin
Note: Consider we need to find the vertices of the image.
Given:
Square KLMN with vertices K(0,2), L(1,8), M(7,7), and N(6, 1).
It rotates 270 counterclockwise about the origin.
To find:
The vertices of the image after rotation.
Solution:
If a figure rotates 270 counterclockwise about the origin, then the rule of rotation is defined as
[tex](x,y)\to (y,-x)[/tex]
Using this rule, we get
[tex]K(0,2)\to K'(2,0)[/tex]
[tex]L(1,8)\to L'(8,-1)[/tex]
[tex]M(7,7)\to M'(7,-7)[/tex]
[tex]N(6,1)\to N'(1,-6)[/tex]
Therefore, the vertices of the image are K'(2,0), L'(8,-1), M'(7,-7) and N'(1,-6).
3 decagrams = centgrams
Answer:
3,000
Step-by-step explanation:
Just multiply every decagram by 1,000
Samuel graphed the equation y = 2x + 2, and Monika graphed the equationy = -2x + 2. How do their two graphs compare?
A. As you trace their graphs from left to right, Samuel's graph rises and Monika's graph
falls.
B. As you trace their graphs from left to right, Samuel's graph falls and Monika's graph
rises.
C. Samuel's graph is a parabola that opens up, and Monika's graph is a parabola that
opens down.
D. Samuel's graph is a parabola that opens to the right, and Monika's graph is a
parabola that opens to the left.
Answer:
A
Step-by-step explanation:
Because if you look up y=2x+2 that graph rises and if you look up y=-2x+2 it decreases
15. Examine the figure below.
If C is the midpoint of BD, what is the coordinate of point C if point B is at 0?
Answer:
13
Step-by-step explanation:
Given:
BC = 2x + 7
CD = x + 10
Coordinate of point B = 0
Required:
Coordinate of point C
SOLUTION:
Since C is the midpoint of BD, therefore:
BC = CD
2x + 7 = x + 10 (substitution)
Collect like terms
2x - x = -7 + 10
x = 3
BC = 2x + 7
Plug in the value of x
BC = 2(3) + 7 = 6 + 7
BC = 13
Thus, the coordinate of point C would be a distance of 13 units away from the coordinate of point B.
Since the coordinate of B is 0, 13 units away from 0, would be 13.
Therefore, the coordinate of point C = 13
The coordinate of point C if If C is the midpoint of BD will be (0, 13)
From the given diagram, if C is the midpoint of BD, hence;
BC + CD + BD
Given the following parameters
BC = 2x + 7
CD = x + 10
Since C is the midpoint of BD, hence BC = CD
2x + 7 = x + 10
2x-x = 10 - 7
x = 3
Get the measure of BC:
BC = 2x + 7
BC = 2(3) + 7
BC = 13 = CD
Hence the coordinate of point C will be (0, 13)
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A $270 suit is marked down by 10%. Find the sale price.
This question is easy, but the person who answers this gets 100 points! Be fast!
What is (4 x 4) x ((5^2) x 1)
A. 500
B. 400
C. 50
D. 40
Answer:
B. 400
Step-by-step explanation:
4×4 =16
5^2 = 25
25×1= 25
16×25= 400
Find h, k and a, then write an equation for the following transformed function.
Answer:
On the graph h, k, and a are not labeled so do not find a way to find them
Step-by-step explanation:
give me brainliest
Factorise completely 28x2y2-21x2y3
Answer: 7x4y5
Step-by-step explanation:
28x 2y 2 -21x 2y 3
add like terms
28x and -21x
2y and 2y
2 and 3
A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as shown.If the ratios $9:\text{S}$ and $\text{S}:\text{T}$ are both equal to 3 and $\text{S}$ and $\text{T}$ are the side lengths of the shaded squares, what is the total shaded area?
Answer:
[tex]3\sqrt{3} + 72[/tex]
Step-by-step explanation:
I attached an image to aid the understanding of the question.
Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:
[tex]9 \times 8 = 72ft^{2}[/tex]
It remains the area of the shaded square with side S.
From the question, we have the following ratio:
[tex]\frac{9}{S} = \frac{S}{T}[\tex]
But
[tex]\frac{9}{S} = \frac{S}{3}[\tex]
Multiplying through by 3S we have
27 = S² and this gives:
[tex]S = \sqrt{27} = 3\sqrt{3}[/tex]
I did not add ± because length is always positive, so the case of negative is eliminated.
Now the areas of S is [tex]3\sqrt{3}[/tex]
Therefore, the total area of the shaded squares is
[tex]3\sqrt{3} + 72[/tex]
Answer:
17
Step-by-step explanation:
We are given that [tex]$\frac{9}{\text{S}}=\frac{\text{S}}{\text{T}}=3.$\[\frac{9}{\text{S}}=3\][/tex]gives us S=3, so[tex]\[\frac{\text{S}}{\text{T}}=3\][/tex]gives us T=1. There are 8 shaded squares with side length [tex]$\text{T}$[/tex] and there is 1 shaded square with side length [tex]$\text{S},$[/tex] so the total shaded area is [tex]$8\cdot(1\cdot1)+1\cdot(3\cdot3)=8+9=\boxed{17}.$[/tex]