Topic : Linear equations in two variables.
Given :
3x + 2y = -4 ––– (i)x - 2y = 4 ––– (ii)Solution :
Now,
(i) + (ii)
[tex] \qquad \sf \: { \dashrightarrow 3x + 2y + (x - 2y) = - 4 + 4}[/tex]
[tex] \qquad \sf \: { \dashrightarrow 3x + 2y + x - 2y = 0}[/tex]
[tex] \qquad \sf \: { \dashrightarrow 3x \: \cancel{ + 2y} + x \: \cancel{- 2y} = - 4 + 4}[/tex]
[tex] \qquad \sf \: { \dashrightarrow 4x = 0}[/tex]
[tex] \qquad \bf \: { \dashrightarrow x = 0}[/tex]
Now, substituting the value of x in Eq (i) :
[tex]\qquad \sf \: { \dashrightarrow 3x + 2y = -4}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 3(0) + 2y = -4}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 0 + 2y = -4}[/tex]
[tex]\qquad \sf \: { \dashrightarrow 2y = -4}[/tex]
[tex]\qquad \sf \: { \dashrightarrow y = \dfrac{ - 4}{2} }[/tex]
[tex]\qquad \bf \: { \dashrightarrow y = -2}[/tex]
Therefore, The value of x = 0 and y = -2
The solution to the two given simultaneous equations are; x = 0 and y = -2
How to find the solution to simultaneous equations?We are given the simultaneous equations;
3x + 2y = -4 -----(eq 1)
x - 2y = 4 ------(eq 2)
Add eq1 and eq2 to get;
4x = 0
x = 0/4
x = 0
Substitute 0 for x in eq 2 to get;
0 - 2y = 4
-2y = 4
y = -4/2
y = -2
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Graph the radical equation that can be used to calculate the radius, r, of the tank. Use the lowercase "r" and the uppercase "V" when entering the equation. After the equation has been entered, set the value of pi to be 3.14.
and please explain how to use the graph and what should I type and where
Edmentum
Tank is made like Cylinder
So let's find r
Radius=rheight=h[tex]\\ \tt\hookrightarrow V=\pi r^2h[/tex]
[tex]\\ \tt\hookrightarrow r^2=\dfrac{v}{h\pi}[/tex]
[tex]\\ \tt\hookrightarrow r=\sqrt{\dfrac{v}{3.14h}}[/tex]
The equation to find radius of tank is r = √{(V)/(3.14×h)}
What is equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Types of Equations:
Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Quadratic Equation:This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2. Cubic Equation:A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3. Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.let r be radius of cylindrical tank
h be height of tank
V be volume of tank
Volume of cylinder is given by:
V = π×r²×h
r = √{(V)/(π×h)}
r = √{(V)/(3.14×h)}
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The graph represents a linear function. (I need this right now no joking please)
[tex]y=mx+b[/tex] is general equation of linear function
We see that graph is decreasing ⇒ m<0
We have dirt (0;-3) ⇒ b=-3
Then let's try find m
look on dirt (-5;0), x=-5, y=0 ⇒
[tex]0=-5m-3\\-5m=3\\\\m=-\dfrac{3}{5}[/tex]
The answer is D
what is 3/8 x(1 -1/3)
Answer:
1/4x
Step-by-step explanation:
3/8x(1-1/3)
3/8x - 1/8x = 1/4x
I hope that's right.
How can you change the dimensions of the rectangle so that the ratio of the length to the width stays the same, but the perimeter is 185 centimeters? l=25cm h=12cm
Answer:
Width= 30
Length= 62.5
Step-by-step explanation:
First we simplify the length to width ratio
25/12=
2 1/12 ratio of length to width
width=x
length=2 1/12x
Make the equation for this ratio's perimeter being equal to 185
2(2 1/12x) + 2(x)=185
Solve for x
4 1/6x +2x=185
6 1/6x=185
x=30
Substitute the answer in for x to find the length and width
Width= 30
Length= 2 1/12(30)
Length= 62.5
PLEASE HELP I NEED HELP ANSWER THE NEXT QUESTION GIVING BRAINLIEST TO CORRECT ANSWERS AND FIVE STARS WITH 20 POINTS PLEASE HELP ASAP
Answer:
C, D and F
Step-by-step explanation:
volume of a cuboid = W x L x H
(where W = width, L = length and H = height)
Calculate the volume of each of the prisms (cuboids), then compare their volume with the range of 25 - 40 cubic units
Volumes
A: 4 x 4 x 4 = 64 cubic units
B: 3 x 7 x 2 = 42 cubic units
C: 4 x 4 x 2 = 32 cubic units
D: 2 x 6 x 2 = 24 cubic units
E: 3 x 5 x 3 = 45 cubic units
F: 2 x 3 x 6 = 36 cubic units
Therefore, prisms C, D and F have a volume between 25 and 40 cubic units.
find the unknown size of angles
Step-by-step explanation:
y+110=180 (cointerior angle)
y=180-110
y=70
y=z(Alternate angle)
z=70
x=z(corresponding angles)
x=70
Hope this helps.
Please help me!
its my last question.
3/2 ( 4x - 8) +3x = 6x - 12 +3x
= 9x - 12
Rohan draws a circle of radius 10 cm with the help of compass and scale. He also draws two chords, AB and CD in such a way that AB and CD are 6 cm and 8 cm from the centre O. Now, he has some doubts that are given below. Help him out by answering these questions:
It can be deduced that the chord of AB will be 16 cm and the chord of CD will be 12 cm.
How to calculate the chordFrom the information given, we will use Pythagoras theorem to find half of AB. This will be:
= ✓10² - ✓6²
= ✓64
= 8.
Therefore, AB = 8 × 2 = 16cm
The length of CD will be:
= 10² - ✓8²
= ✓36
= 6
The length of CD = 6 × 2 = 12cm.
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Change the equation 8x + 4y = 24 into slope-intercept form
Answer:
y= -2x+6
Step-by-step explanation:
8x+4y=24 move the 8x to the other side
4y=-8x+24 divide by 4
y=-2x+6
Solve the system using substitution
3x - 6y =30
y = -6x + 34
x = 6
y = -2
(explanation in image)
Answer:
3x - 6(- 6x + 34) = 30 3x + 36x - 204 = 30 40x - 204 = 30 40x = 234x = 5.85then solve for y as a linear equationStep-by-step explanation:
Have a nice day !!!! :)A store owner paid $15 for a book. She marked up the price of the book by 40% to determine its selling price. What is the selling price, in dollars, of the book?
\
Answer:
the selling price is 21 dollars
How do I solve this using substitution?
Answer :y=4 x=2
Step-by-step explanation:
Someone please help me with this
Answer:
I think it's y = 1/4+2
Step-by-step explanation:
PLEASE HELP W/ THIS QUESTION I ALLWAYS GET STUCK ON READING TIME!!!
what time does the clock show? Please tell me how to read time I will mark you the brainlyest.
Answer:
2:40
Step-by-step explanation:
Short hand (hours): a little past 2
Long hand (minutes): 40 -- 8*5=40
a school is running a fundraiser. For every $75 worth of wrapping paper sold, the school receives $20. How much wrapping paper must be sold to reach the fundraising goal of $2500?
Answer:
125
Step-by-step explanation:
if the school gets $20 per wrapping paper sold
then in order to earn 2500 the school must sell 2500/20=125
Answer:
9375
Step-by-step explanation
75/20 = x/2500
20x=187500
20x/20 = 187500/20
x=9375
We can calculate E, the amount of euros that has the same value as D.S. dollars, using the equation E= 17/20 D.
How many euros have the same value as 1 U.S. dollar?
How many U.S. dollars have the same value as 1 euro?
Answer:
0.85
1.176
Step-by-step explanation:
E = 17/20 D
Let D = 1,
E = 17/20 × 1
E = 17/20 = 0.85
1 dollar = 0.85 Euro
E = 17/20 D
17/20 D = E
D = 20/17 E
Let E = 1,
D = 20/17 × 1
D = 1.176
1 Euro = 1.176 dollar
[tex]\underline{\boxed{\blue{\Large{\bf{Hello\:Brainlians}}}}}[/tex]
Find the area of the triangle formed by the likes joining the vertex of the parabola x^2=12y to the ends of its latus rectum .
[tex]\boxed{\sf{Note:-}}[/tex]
[tex]\\ \tt\hookrightarrow Spams, plagarised\: from \:web , Short \:answers \:will \:be \:deleted\; on\:the\:spot.[/tex]
[tex]\\ \tt\hookrightarrow Make\:sure\:you\:provide\:step\:by\:step\: solution\: without\: omitting\:any\:step.[/tex]
[tex]\\ \tt\hookrightarrow Attach\:the\: Diagram\:for\: solution.[/tex]
[tex]\boxed{\bf All\:the\:best!}[/tex]
Hi there!
Parabola x² = 12y
→ x² = 4ay
→ 4a = 12
→ a = 12÷4
→ a = 3
So, the co-ordinates of the focus is:-
S(0,a)=(0,3)
→ Let AB be the latus rectum of the given parabola.
→ Coordinates of end-points of latus rectum are (-2a,a), (2a,a)
→ Coordinates of A are (-6,3), while B's coordinates are (6,3).
→ ∆OAB are O(0,0), A(-6,3), B(6,3)
Area of ∆OAB is :-
(Solving part attached as image)
=> 18 unit² is the required answer.
Answer:
18 sq. unit
Step-by-step explanation:
Parabola is x²=12y
On comparing it with
→x²=4ay
→4a=12
→a=12/4
→a=3
Finding the value of x.
→x²=12y
→x²=12×3
→x²=36
→x=√36
→x=6
When we have a=3 and x=6
(-x1,a)=(-6,3)
(x1,a)=(6,3)
Let,
(x1,y1)=(0,0)
(x2,y2)=(6,3)
(x3,y3)(-6,3)
Now,
Area=[tex]=\frac{1}{2} *b*h\\\\=\frac{1}{2} [x1(y2-y3)+x2(y3-y1)+x3(y1-y2)\\\\=\frac{1}{2} [0(3-3)+6(3-0)+(-6)(0-3)\\\\=\frac{1}{2} [18+18]\\\\\\=18.sq.units[/tex]
Find the equation of the lines passing through the point A(3,-4) and (1)parallel, (2)perpendicular to the line 4x+3y=8.If these lines meet the line 2x+y=1 in points B and C ,find the area of triangle ABC.
Solve for x and y!
Show your work and you will get brainliest!
Answer:
x = y = 24.
Step-by-step explanation:
Here we are given a right angled triangle in which one of the angles is 45° . And one of the known side is 24√2 . And we need to find out the value of x and y.
Here we can use the ratio of sine as ,[tex]\qquad\rm\longrightarrow sin45^o =\dfrac{p}{b} [/tex]
Substituting the respective values,
[tex]\qquad\rm\longrightarrow sin45^o =\dfrac{x}{24\sqrt2}[/tex]
Value of sin 45° is 1/√2 . So that,
[tex]\qquad\rm\longrightarrow \dfrac{1}{\sqrt2}=\dfrac{x}{24\sqrt2}[/tex]
Cross multiply ,
[tex]\qquad\rm\longrightarrow x =\dfrac{24\sqrt2}{\sqrt2} [/tex]
Simplify,
[tex]\qquad\rm\longrightarrow \underline{\boxed{\rm \blue{x = 24}}} [/tex]
Again , the third angle will be 45° . we know that the sides opposite to equal angles are equal. Therefore here ,
[tex]\qquad\rm\longrightarrow \underline{\boxed{\blue{\rm y = 24}}}[/tex]
The values of x and y are 24
The triangle is a right angled triangle with an angle measure of 45 degrees.
The above means that:
The values of x and y are equal
So, we have:
[tex]x^2 + y^2 = (24\sqrt 2)^2[/tex]
Evaluate the squares
[tex]x^2 + y^2 = 1152[/tex]
x and y have equal values,
So, we have:
[tex]x^2 + x^2 = 1152\\\\[/tex]
[tex]2x^2 = 1152[/tex]
Divide through by 2
[tex]x^2 = 576[/tex]
Take the square roots of both sides
[tex]x = 24[/tex]
Hence, the values of x and y are 24
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The Shoe Outlet bought boots for $60 and marks up the boots 55% on the selling price. What is the selling price of the boots?
Answer: The markup- 122.225%
Revenue/price- 133.33$
Gross profit- 73.33%
Step-by-step explanation:
The gross profit P is the difference between the cost to make a product C and the selling price or revenue R.
P = R - C
To calculate revenue R based on the cost C and the desired gross margin G, where G is in decimal form:
R = C / ( 1 - G)
The gross profit dollars P is the revenue dollars R from the sale times the gross margin G percentage, where G is in decimal form :
P = R * G
The markup percentage M, in decimal form, is gross profit P divided by cost C.
M = P/ C
M * 100 will change the decimal to a percentage.
The selling price of the boots is $93.
Given information:
The Shoe Outlet purchased the boots for $60 and increased their price by 55%
To calculate the selling price of the boots with a 55% mark-up, to add 55% of the original cost to the original cost.
Calculate the mark-up amount as follows:
Mark-up = 55% of $60
Mark-up = 0.55 * $60
Mark-up = $33
Add the mark-up to the original cost to find the selling price as follows:
Selling Price = Original Cost + Mark-up
Selling Price = $60 + $33
Selling Price = $93
So, the selling price of the boots is $93.
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pls help me!! D:
find x and y
4x-4y=0
y= 2x+6
Answer:
x = -6
y = -6
Step-by-step explanation:
Solve using substitution.
Substitute 2x + 6 for y:
4x - 4(2x + 6)=0
Distribute the 4 to each term in the parentheses:
4x - 4(2x) - 4(6) = 0
4x - 8x - 24 = 0
Combine like terms
-4x - 24 = 0
Add 24 to both sides
-4x = 24
Divide both sides by -4
x = -6
Plug -6 back in for x to solve for y:
y = 2x + 6 = 2(-6) + 6 = -12 + 6 = -6
(x, y) = (-6, -6)
Answer:
x= -6 and y= -6
Step-by-step explanation:
Take 4x-4y=0 as eqn 1
and y=2x+6 as eqn 2
Substitute eqn 2 into eqn 1
4x -4(2x+6)=0
4x-8x-24=0
-4x-24=0
Move -24 to the other side
-4x=24
Divide both sides by -4
[tex] \frac{ - 4x}{ - 4} = \frac{24}{ - 4} [/tex]
x= -6
substitute x= -6 in eqn 2
y=2(-6)+6
y= -12+6
y= -6
Leila is buying a dinosaur model. The price of the model is z dollars, and she also has to pay a 7% tax.
Which of the following expressions could represent how much Leila pays in total for the model?
Answer:
T=z(0.07)+z
Step-by-step explanation:
Dat right der
Draw and label a parallelogram
with a base twice as long as the height and an area less than
60 square inches. Determine the area.
20 length 2 height. 20 times 2 equals 40 square inches\
Appropriate and interesting word sum for :439 and 514 solve it
The word sum for 439 and 514 = 953
Word sum of whole numbersWord sum simply means the addition of two or more whole numbers.
This means that to calculate the word sum of 439 and 514, the both given figures are added up together.
Given, 439 plus 514
That is,
439 + 514 = 953
Therefore, the word sum for 439 and 514 = 953
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{(1, 1), (2, 1), (-2, 1), (-1, 1)}
Function or Not a Function?
=
Use <, >, or = to make the
statements true.
1 km
3,000 m
4L 4,000 mL
Answer:
1 km < 3,000 m and 4L = 4,000 mL
hello help me with this question thanks in advance
Answer:
1) 100/2 = 50°.
2) 50°
3) 50°
Reasons: rhombus, perpendicular bisector
- Toodles!~
[tex]\bold{\huge{\pink{\underline{ Solutions}}}}[/tex]
Answer 18 :-We have,
Rhombus RAMS and Angle SMA = 100°
In rhombus, The diagonals bisect each other at an angle of 90° .Therefore,
[tex]\sf{\angle{ AMR = 1/2}}{\sf{\angle{ SMS}}}[/tex]
[tex]\sf{\angle{ AMR = 1/2 × 100 }}[/tex]
[tex]\sf{\angle{ AMR = 50° }}[/tex]
Thus, Angle AMR is 50°
Hence, Option D is correct
Answer 19 :-We know that,
The sides of rhombus are equal and parallel to each other[tex]\sf{\angle{ AMR = }}{\sf{\angle{ RMS}}}[/tex]
[ Alternative interior angles ]
[tex]\sf{\angle{ RMS = 50° }}[/tex]
Thus, The value of Angle RMS is 50°
Hence, Option B is correct
Answer 20 :-Here, we have to find the value of mAngleMSA
In ΔCMS,
By using Angle sum property
[tex]\sf{ 50° +}{\sf{\angle{MSC + 90° = 180° }}}[/tex]
[tex]\sf{\angle {MSC = 180° - 140°}}[/tex]
[tex]\sf{\angle{MSC = 40° }}[/tex]
Therefore,
[tex]\sf{m}{\sf{\angle{MSA = 40° }}}[/tex]
Thus, The value of mAngle MSA is 40°
Which is true regarding Armando’s use of algebra tiles? He used the algebra tiles correctly. He did not represent the two original factors correctly. The signs on some of the products are incorrect. Some of the products do not show the correct powers of x.
The correct statement about Armando’s use of algebra tiles is some of the products do not show the correct powers of x.
Given
Armando used algebra tiles to represent the product 3x (2x -1 ).
ProductThe number or expression results from the multiplication together of two or more numbers or expressions.
The correct way to find the product function is;
[tex]\rm = 3x (2x -1 )\\\\=3x \times 2x - 3x\times 1\\\\= 6x^2-3x[/tex]
Hence, the correct statement about Armando’s use of algebra tiles is some of the products do not show the correct powers of x.
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How do I award brainliest I’m confused
First person to answer and actually help will get it! I have 2 min. Go!
Answer:
I think its an lucky chance for an mod or something to notice you
Step-by-step explanation:
A 2-column table has 3 rows. The first column is labeled Domain with entries 0, 1, 2. The second column is labeled Range with entries 32, 24, d. In order for the table below to show exponential decay, what must the value of d be in the table below? d = 16
Answer:
D = 18
Step-by-step explanation: