Answer:
(m - 3n)(m + 3n).
Step-by-step explanation:
This is the difference of 2 squares, so we use the identity:
a^2 - b^2 = (a - b)(a + b).
So m^2 - 9n^2
(m - 3n)(m + 3n).
whywould a prism beat a sphere in a competition
Answer:
why?
Step-by-step explanation:
How did the Virginia Declaration of Rights influence the Declaration of Independence?
A. It was the first document that was openly critical of the king.
B. It was the document Jefferson referred to when writing the Declaration of Independence.
C. It suggested that the colonies should be independent from Britain.
D. It was published as a pamphlet and built support for the Declaration.
Answer:
B. It was the document Jefferson referred to when writing the Declaration of Independence.
Step-by-step explanation:
Virginia's Declaration of Rights was drawn upon by Thomas Jefferson for the opening paragraphs of the Declaration of Independence. It was widely copied by the other colonies and became the basis of the Bill of Rights. Written by George Mason, it was adopted by the Virginia Constitutional Convention on June 12, 1776.
Hope I helped answer the question:)
The Virginia Declaration of Rights influenced the Declaration of Independence through its content and circulation as a pamphlet.
Explanation:The Virginia Declaration of Rights influenced the Declaration of Independence in several ways:
It was the document Jefferson referred to when writing the Declaration of Independence. Jefferson drew heavily on the ideas and language of the Virginia Declaration of Rights to craft the Declaration of Independence, including concepts like natural rights, the right to revolution, and the social contract.It suggested that the colonies should be independent from Britain. The Virginia Declaration of Rights asserted that all men are equal and have certain inalienable rights, which laid the foundation for the argument that the American colonies should be independent from British rule.It built support for the Declaration. The Virginia Declaration of Rights was widely circulated as a pamphlet and helped to gather support for the cause of independence, paving the way for the publication and reception of the Declaration of Independence.Learn more about The influence of the Virginia Declaration of Rights on the Declaration of Independence here:https://brainly.com/question/17742394
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What is the solution of the system? 10x-2y=24 6x+2y=8 enter your in the box as an ordered pair.
The solution to the system of equations 10x - 2y = 24 and 6x + 2y = 8 is (2, -2).
To solve the system of equations 10x - 2y = 24 and 6x + 2y = 8, we can use the method of elimination.
Adding the two equations together, the 2y terms will cancel out:
[tex]\[ (10x - 2y) + (6x + 2y) = 24 + 8 \]\[ 10x - 2y + 6x + 2y = 32 \]\[ 16x = 32 \]\\[/tex]
Dividing both sides by 16:
x = 2
Now, we substitute x = 2 into one of the original equations to solve for y. Let's use the first equation:
[tex]\[ 10(2) - 2y = 24 \]\[ 20 - 2y = 24 \][/tex]
Subtracting 20 from both sides:
-2y = 4
Dividing both sides by -2:
y = -2
So, the solution to the system is (2, -2).
the length of a rectangle is (x + 1) cm and its width is 5cm less than its length.
a) Express a square, L cm, in x.
b) Given a rectangle is 24cm, calculate the length and width of the square
Answer:
a) the area of a square is in terms of x is
[tex](x+1)^2[/tex] centimeter square
b)The length of the rectangle is l = (x+1)
l = 7+1 =8 cm
The width of the rectangle is w = [(x+1)-5]
w = (7+1)-5 =3 cm
Step-by-step explanation:
a) the area of a square is in terms of x is
area of square is [tex]l^{2} = (x+1)(x+1)[/tex]
= [tex](x+1)^2[/tex]
b) Given length is l = (x+1) cm and
the width is 5 cm less than its length.
so we have take width is w = (x+1)-5 cm
Given area of triangle is 24 cm
Area of rectangle = length X width
24 = (x+1)(x+1 -5 )
now simplification [tex]24 = (x+1)^2 - 5 (x+1)[/tex]
apply (a+b)^2 = a^2+2 a b+b^2
[tex]x^2+2 x+1-5 x-5 =24[/tex]
[tex]x^2 -3 x -4-24=0[/tex]
[tex]x^{2} -3 x -28 =0[/tex]
now find factors of 28 = 7 X 4 is
[tex]x^{2} -7 x+4 x-28=0[/tex]
[tex]x(x-7)+4(x-7)=0[/tex]
[tex](x+4)(x-7)=0[/tex]
x = -4 and x=7
there fore you have to choose x = 7
The length of the rectangle is l = (x+1)
l = 7+1 =8
The width of the rectangle is w = [(x+1)-5]
w = (7+1)-5 = 3
Verification:-
Given area of rectangle = 24 = 8 X 3
24 =24
so we can not choose x=-4
we have to choose x =7 only
Find the equation of the plane that contains the point (6, 4, -2) and is perpendicular to the line that passes through the points (7, -2, 3) and (1, 4, -5).
Answer:
3x-3y+4z+2=0
Step-by-step explanation:
Answer:
3x-3y+4z+2=0
Step-by-step explanation:
Which of the following could be used as a reference angle for 15 pi / 4
Answer:
[tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].
Step-by-step explanation:
Given the trigonometric expression
[tex]\frac{15\pi }{4}[/tex]
In order to find the reference angle for [tex]\frac{15\pi }{4}[/tex], find an angle that is positive, less than [tex]2\pi[/tex], and coterminal with
Subtract [tex]2\pi[/tex] from [tex]\frac{15\pi }{4}[/tex].
[tex]\frac{15\pi }{4} -2\pi[/tex]
The resulting angle of [tex]\frac{7\pi }{4}[/tex] is positive, less than [tex]2\pi[/tex], and coterminal with [tex]\frac{15\pi }{4}[/tex].
[tex]\frac{7\pi }{4}[/tex]
Since the angle [tex]\frac{7\pi }{4}[/tex] is in the fourth quadrant, subtract
[tex]2\pi-\frac{7\pi }{4}=\frac{\pi }{4}[/tex]
Therefore, [tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].
Keywords: reference angle
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The reference angle = [tex]\frac{\pi}{4}[/tex].
Note that [tex]\frac{15\pi}{4}[/tex] [tex]\frac{15\pi}{4}=3.75\pi[/tex] lies in the 4th quadrant and it is close to [tex]4\pi[/tex].
To find the reference angle of [tex]\frac{15\pi}{4}[/tex] we will subtract it from [tex]4\pi[/tex].
So, the reference angle is:
[tex]4\pi-\frac{15\pi}{4}=\frac{\pi}{4}[/tex]
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James flips a fair numbered cube with faces numbered 1-6 and flips a quarter what is the probability that in one turn James could roll an odd number and flip a heads on the quarter
Answer:
Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex].
Step-by-step explanation:
i) There are three odd numbered faces on the cube, that is the faces having 1, 3, and 5.
Therefore the probability of rolling an odd numbered face is = [tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2}[/tex] since the probability of rolling 1 = probability of rolling 3 = probability of rolling 5 = [tex]\frac{1}{6}[/tex]
ii) The probability of flipping a head on the quarter = probability of flipping a tail on the quarter = [tex]\frac{1}{2}[/tex]
iii) Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]
The probability that James could roll an odd number on a fair six-sided die and flip heads on a quarter in one turn is 1/4 or 25%.
The student is asking about the probability of two independent events happening simultaneously: rolling an odd number on a fair six-sided die and flipping heads on a quarter. To calculate the probability of both independent events occurring, we multiply the probabilities of each event.
The probability of rolling an odd number (1, 3 or 5) on a die is 3 out of 6 possibilities, which simplifies to 1/2 since there are three odd numbers out of six total numbers. The probability of flipping heads on a quarter is 1/2, as there are two sides to a coin and it is fair, meaning each side has an equal chance of landing face up.
Now, to find the combined probability, we multiply the probabilities of the independent events:
Probability of rolling an odd number: 1/2Probability of flipping heads: 1/2Combined probability = (1/2) x (1/2) = 1/4 or 0.25, which means there is a 25% chance to roll an odd number and flip heads in one turn.
What is 2/6 times 3 in its simplest form
Answer:
1
Step-by-step explanation:
[tex] \frac{2}{6} \times 3 = \frac{2}{6} \times \frac{3}{1} [/tex]
[tex] \frac{2}{6} \times \frac{3}{1} = \frac{6}{6} = 1[/tex]
To multiply 2/6 and 3 in its simplest form, multiply the numerators and denominators together. The resulting fraction is 6/6, which simplifies to 1.
Explanation:To multiply fractions, multiply the numerators together and multiply the denominators together. In this case, multiplying 2/6 and 3 gives a result of (2 * 3) / (6 * 1), which simplifies to 6 / 6. Since the numerator and denominator are the same, the fraction is equal to 1 in its simplest form.
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PLEASE SOMEONE HELP ME PLEASE...I NEED EXPERT IN TANGENT LINES ILL GIVE POINTS AND BRAINLESS
Answer:
P=92 cm
Step-by-step explanation:
<B and <D are congruent so you now know that <D also equals 11.5
Add all the sides up then multiply by 2
You are multiplying by two because each point is at the radius (halfway)
11.5 + 11.5 +10.5+12.5 =46
46 x 2=92
Answer:
92 is the answer
Step-by-step explanation:
Notice the dots are only half way. You have the sides 11.5, 10.5, and 12.5. It says the side D and B are congrent which means they equal. So the side is 11.5. 11.5+11.5=23 Whihc is one side of the permiter. 10.5+10.5=21. 12.5+12.5=25. 11.5+11.5=23. When you add them up you get the answer 92. Hope this helps!
17 points sorry that all I have right now
Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000242 mm, while the length of the second strain measures 0.0000000238 mm. How much larger is the first strain than the second?
A.
2.658 × 10-7 mm
B.
2.182 × 10-7 mm
C.
2.182 × 10-8 mm
D.
2.658 × 10-15 mm
Option B
The first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second strain
Solution:
Given that,
The length of one strain of the bacteria measures 0.000000242 mm
The length of the second strain measures 0.0000000238 mm
To find: Difference between the first strain and second strain
From given ,
Length of first strain = 0.000000242 mm
Length of second strain = 0.0000000238 mm
Let us convert them into scientific notation
Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
Count how many places you moved the decimal point. This number is b.
If you moved the decimal to the left b is positive.
If you moved the decimal to the right b is negative.
Write your scientific notation number as a x 10^b
Therefore,
[tex]0.000000242 = 2.42 \times 10^{-7}[/tex]
[ Here we moved the decimal point to right , we have moved 7 times. So exponent is -7 ]
[tex]0.0000000238 = 2.38 \times 10^{-8}[/tex]
[ Here we moved the decimal point to right , we have moved 8 times. So exponent is -8 ]
Now find the difference
[tex]Difference = length\ of\ first\ strain\ - length\ of\ second\ strain[/tex]
[tex]Difference = (2.42 \times 10^{-7}) - (2.38 \times 10^{-8})\\\\\text{Make the exponents same }\\\\Difference = (2.42 \times 10^{-7}) - (0.238 \times 10^{-7})\\\\\text{Take the common term out }\\\\Difference = 10^{-7}(2.42 - 0.238)\\\\Difference = 10^{-7} \times 2.182\\\\Difference = 2.182 \times 10^{-7}[/tex]
Thus first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second
Clara found the product of 3 – 6y2 and y2 + 2. Her work is shown below.
(3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2)
= 3y2 – 12y2
= –9y2
Is the student’s work correct?
No, she did not multiply –6y2 by 2 correctly.
No, she did not add 3y2 and –12y2 correctly.
No, she did not use the distributive property correctly.
Yes, she multiplied the binomials correctly.
Answer:
Option C. is the correct option.
Step-by-step explanation:
Clara found the product of (3 - 6y²) and (y² + 2) and she did it as below
(3 - 6y²)(y² + 2) = 3(y²) + (-6y²)×2 = 3y² - 12y² = -9y²
She did the step wrong as highlighted above. She did not use the distributive property correctly.
Now we will do it in a correct way.
(3 - 6y²)(y²+2) = 3(y² + 2) - 6y²(y² + 2)
= 3y^{2}+6-6y^{4}-12y^{2}=-6y^{4}-9y^{2}+6
Therefore Option C. is the correct answer.
Hope it helps:)
1. What is the Kinetic energy of a 1500 kg car going at a speed of 14 meters/second?
Show your work below
2. What is the KE if m = 2 and v = 5?
3. What is the KE if m = 4 and v = 5?
4. What is the KE if m = 2 and v = 10?
Step-by-step explanation:
1.
Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]
Here m = 1500 kg and v = 14 meter / second
Kinetic energy = [tex]\frac{1}{2} mv^{2}[/tex]= [tex]\frac{1}{2}\times 1500 \times 14^{2}[/tex] joule =147000 joule
2.
Here m = 2 unit and v = 5 units
Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 2 \times 5^{2}[/tex] units =25 units
3.
Here m= 2 units and v = 5 units
Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 4 \times 5^{2}[/tex]=5 0 units
4.
Here m= 2 units and v= 10 units
Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]=[tex]\frac{1}{2}\times 4 \times 10^{2}[/tex]units = 200 units
In △FEG , point H is between points E and F, point J is between points F and G, and HJ¯¯¯¯¯∥EG¯¯¯¯¯ . EH=8 , HF=12 , and FG=30 . What is FJ ? Enter your answer in the box. FJ =
Answer:
[tex]FJ=18\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
△FEG is similar with △FHJ -----> by AA Similarity Theorem
so
[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]
we have
[tex]FE=HF+EH=12+8=20\ units[/tex]
[tex]FH=HF=12\ units[/tex]
[tex]FG=30\ units[/tex]
substitute the given values
[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]
[tex]FJ=12(30)/20\\FJ=18\ units[/tex]
2x-3= 2x-5
A -2
B 0
C 5/3
D no solution
Answer:
D. No solution.
Step-by-step explanation:
2x - 3 = 2x - 5
2x - 2x - 3 = 2x - 2x - 5
-3 = -5 which is absurd so there is No Solution.
Answer:
D no solution
Step-by-step explanation:
2x-3= 2x-5 means : -3=-5 ...false
Write an expression equivalent to (6x + 4y) – 2y by combining like terms. Enter the numbers in the boxes
6x +2y
Solution:
Given expression is (6x + 4y) –2y.
To find the equivalent expression for the given expression.
⇒ (6x + 4y) –2y
⇒ 6x + 4y –2y
Combine like terms together.
⇒ 6x + (4y –2y)
⇒ 6x + 2y
6x +2y is equivalent to (6x + 4y) –2y.
Hence, the expression equivalent to (6x + 4y) –2y is 6x + 2y.
Y=x2-2x-5
Change to vertex form
The vertex form is [tex]y=(x-1)^{2} -6[/tex]
Step-by-step explanation:
The given equation [tex]y=x^{2} -2x-5[/tex] is a parabola. The vertex of the parabola is of the form [tex]y=ax^{2} +bx+c[/tex]
The parameters of the parabola are [tex]a=1, b=-2[/tex] and [tex]c=-5[/tex]
The vertex of the x-coordinate is given by [tex]x=\frac{-b}{2a}[/tex]
Thus, substituting the values of a and b in [tex]x=\frac{-b}{2a}[/tex], we get,
[tex]\begin{aligned}x &=\frac{-(-2)}{2(1)} \\&=\frac{2}{2} \\x &=1\end{aligned}[/tex]
Now, substituting [tex]x=1[/tex] in [tex]y=x^{2} -2x-5[/tex], we get,
[tex]\begin{aligned}y &=1^{2}-2(1)-5 \\&=1-2-5 \\y &=-6\end{aligned}[/tex]
Thus, the vertex is [tex](1,-6)[/tex]
The equation of parabola to be in vertex form is [tex]y=a(x-h)^{2} +k[/tex]
where a is the coefficient of [tex]x^{2}[/tex], h is vertex of the x-coordinate and k is the vertex of the y-coordinate.
Hence, [tex]a=1, h=1[/tex] and [tex]k=-6[/tex]
Thus, substituting the values in the equation of the vertex form,
[tex]y=1(x-1)^{2} -6\\y=(x-1)^{2} -6[/tex]
Hence, the vertex form is [tex]y=(x-1)^{2} -6[/tex]
What is -3-2(5+1)-(1-1)
[tex]-3-2(5+1)-1-1\\-3-(2)(6)-(1-1)\\-3-12-(1-1)\\15-(1-1)\\15-0\\{Answer=-15 \checkmark[/tex]
-7(y+2x)-3(y-x) please expand and then simplify the expression.
Answer:
-10y - 11x
Step-by-step explanation:
First you need to distribute -7 through the parentheses.
-7y - 14x - 3y + 3x
then you need to collect the like terms (terms with the same variable)
-10y - 11x
Answer:-10y - 11x
Step-by-step explanation:
Expanding , we have
-7y - 14x -3y + 3x
collecting the like terms , we have
- 7y - 3y - 14x + 3x
Simplifying , we have
-10y - 11x
Find the sum of all positive whole numbers x such that 2x-7 < 21.
Answer:
x=14
Step-by-step explanation:
2x-7<21
+7=0
2×<21+7=28
2×/2=0
2/28
=14
Answer:
91
Step-by-step explanation:
Trust me, it's an Aops question, and I got mastery on it, or blue if you want.
What is 594 divided by 4 using long division
Answer:
see work attached and shown
Which situation CANNOT be represented by this equation?
3x+4=19
CLEAR CHECK
Penny is selling candles for $3 each at a fund-raiser.
If she starts selling with $4 to help her make change, how many candles, x, will she have to sell to end up with $19?
Penny is selling candles for $4 each at a fund-raiser.
If she starts selling with $3 to help her make change, how many candles, x, will she have to sell to end up with $19?
Penny has already sold 3 candles at a fund-raiser.
If she started selling with $4 to help her make change, what is the price, x, of each candle, if she ends up with $19
Answer:
3x+4=19 x is 5 3(5)=15+4=19
Step-by-step explanation:
Julian needs to create an ad for his company that manufactures mobile phones. He has come up with an idea for the ad, but he needs a quality check before the actual product development begins. Julian is using the
method of advertising testing.
Julian is using the concept testing method of advertising which involves testing ad ideas before product development. It helps in determining consumer reactions and minimizing errors.
Explanation:The method Julian is using is called the concept testing method in advertising. In concept testing, ad ideas and concepts are tested by companies before the actual development of the product. Concept tests are ways for advertisers to determine the reaction of consumers to a proposed product or service before it hits the market, thus minimizing errors and financial risks. For instance, in Julian's case, this would imply presenting his ad idea, which showcases a new mobile phone, to a selected group of people and then collecting their feedback. The feedback can then be used to refine the ad and the product itself, ensuring that the mobile phone meets the expectations and needs of the targeted consumers.
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Estimate, then find the difference and write in simplest form 4 1/2-3 4/5
Answer:
7/10
Step-by-step explanation:
4 1/2=9/2
3 4/5=19/5
9/2-19/5=45/10-38/10=7/10
Which has a positive expression ?
Answer:
The correct answer is C. 3 (-64 ÷ 8) + 25
Step-by-step explanation:
Let's solve the four expressions to find out the positive one, this way:
A. - 4 + (-5) (-6) ÷ (-3)
= -4 + 30 ÷ -3
= - 4 - 10 = - 14
B. 8 [10 ÷ (2) (-2)]
= 8 [10 ÷ -4]
= 8 * - 2.5 = -20
C. 3 ( -64 ÷ 8) + 25
= 3 ( -8) + 25
= - 24 + 25 = 1
D. -2 (-5) (-3) ÷ 10
= - 30 ÷ 10 = -3
As we can see, after solving the four expressions, the only with a positive result is C. 3 ( -64 ÷ 8) + 25
PLEASE HELP < I NEED HELP, TRYING TO MAKE HONOR ROLL
Translate the sentence into an equation.
Nine less than the product of 3 and a number is 4 .
Use the variable w for the unknown number.
Answer: w = 4[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Let the unknown number be w , then
the product of w and 3 = 3w
Nine less than the product of 3 and the number = 3w - 9
completing the equation , we have
3w - 9 = 4
add 9 to both sides
3w = 13
w = 13/3
w = 4[tex]\frac{1}{3}[/tex]
a) Find the value of x. Show algebraic support.
hint: (n - 2)180
Answer:
17
Step-by-step explanation:
The sum of all the angles of this polygon is
(n-2)180
Where m is the number of corners
(5-2)180
3*180
540
Hence
Sum of all angles=540
139+92+71+9x+5x=540
302+14x=540
14x=540-302
14x=238
Dividing both sides by 14
x=17
Which of the following expressions illustrates the associative property of mult
o 4(-1) = (-1)(4)
O
4+ ( + 6) = (4 + 7) +6
O
(-2 - 1)(8) = -2(1 - 8)
O
915 + 3) = 9(5) + 9(3)
Answer:
The correct option is first one.
Therefore,
[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.
Step-by-step explanation:
Associative property:
The associative property states that you can add or multiply regardless of how the numbers are grouped.
For example A x B = B x A
Therefore,
[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.
Answer:
Option (-2-1)(8)=-2(1-8) is correct
The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .
Step-by-step explanation:
Given expression is (-2-1)(8)=-2(1-8)
Associative property of multiplication is given by
(a+b)c=a(b+c)
Comparing the equations (-2-1)(8)=-2(1-8) and (a+b)c=a(b+c) we get that the given expression is in the form of (a+b)c=a(b+c)
Therefore the given equation represents the associative property of multiplication .
Therefore option (-2-1)(8)=-2(1-8) is correct
The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .
Is it possible for two numbers to have a difference of 8 and a sum of 1?
Answer: yes , it is possible
Step-by-step explanation:
Let the first number be x and the second number be y .Then , the sum of the two numbers will be x + y , and their difference will be x - y.
Combining the two , we have :
x + y = 1 ............................... equation 1
x - y = 8 ................................. equation 2
solving the system of linear equation by substitution method. From equation 1 , make x the subject of the formula ,
x = 1 - y ...................... equation 3
Substitute equation 3 into equation 2 ,
1 - y - y = 8
1 - 2y = 8
add 2y to both sides
1 = 8 + 2y
subtract 8 from both sides
1 - 8 = 2y
- 7 = 2y
divide through by 2
y = [tex]\frac{-7}{2}[/tex]
y = - 3.5
substitute y = -3.5 into equation 3 to find the value of x , we have
x = 1 - y
x = 1 - ( - 3.5 )
x = 1 + 3.5
x = 4.5
Let us check :
x + y will be
4.5 + (-3.5) = 1
Also ,
x - y will be
4.5 - (-3.5)
⇒ 4.5 + 3.5 = 8
If Ruby has $10 and Max had $250 who has the most money?
Answer:
Max
Step-by-step explanation:
what is this question
Please help me with 3 please
a. The solution set is (-3,2)
b. The solution set is (2,6)
c. The solution set is (1,1)
d. The solution set is (-0.5,1.5)
e. The solution set is (7.5, -4.5)
f. The solution set is (-2,7)
Step-by-step explanation:
a. x+2y=1 Eqn 1
x=y-5 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{6}{3}\\y=2[/tex]
Putting y=2 in Eqn 2
[tex]x=2-5\\x=-3[/tex]
The solution set is (-3,2).
b. y-x=4 Eqn 1
y=3x Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]3x-x=4\\2x=4[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{4}{2}\\x=2[/tex]
Putting x=2 in Eqn 2
[tex]y=3(2)\\y=6[/tex]
The solution set is (2,6)
c. y = x Eqn 1
y = -x+2 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]x=-x+2\\x+x=2\\2x=2[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]
Putting x=1 in Eqn 1
[tex]y=1[/tex]
The solution set is (1,1)
d. y=5x+4 Eqn 1
x+3y=4 Eqn 2
Putting value of y from Eqn 1 in Eqn 2
[tex]x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8[/tex]
Dividing both sides by 16
[tex]\frac{16x}{16}=\frac{-8}{16}\\x=-0.5[/tex]
Putting x= -0.5 in Eqn 1
[tex]y=5(-0.5)+4\\y=-2.5+4\\y=1.5[/tex]
The solution set is (-0.5,1.5)
e. x-y=12 Eqn 1
y = 3-x Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]
Putting x=7.5 in Eqn 2
[tex]y=3-7.5\\y=-4.5[/tex]
The solution set is (7.5, -4.5)
f. 2x+y=3 Eqn 1
x+y=5 Eqn 2
From Eqn 2;
y = 5-x
Putting in Eqn 1
[tex]2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2[/tex]
Putting x=-2 in Eqn 1
[tex]2(-2)+y=3\\-4+y=3\\y=3+4\\y=7[/tex]
The solution set is (-2,7).
Keywords: linear equation, substitution method
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