x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)
Answer: The correct answer is (1,-1).
Explanation:
The given equations are,
[tex]x-2y=3[/tex] ..... (1)
[tex]5x+3y=2[/tex] ..... (2)
Use elimination method to solve the equations.
Multiply equation (1) by 5.
[tex]5(x-2y)=5(3)[/tex]
[tex]5x-10y=15[/tex] ..... (3)
Subtract equation (3) from equation (2).
[tex]5x+3y-(5x-10y)=2-15[/tex]
[tex]5x+3y-5x+10y=-13[/tex]
[tex]13y=-13[/tex]
[tex]y=-1[/tex]
The y-coordinate is -1.
Put y=-1 in equation (1).
[tex]x-2(-1)=3[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The x-coordinate is 1.
Therefore the intersection point is (1,-1).
Deeside weather the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17? Yes or no.
Simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x² + 8x
Spaceship Earth, a major tourist attraction, is a sphere whose diameter is approximately 50 m. What is the volume of Spaceship Earth? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest hundredth.
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. What is the rectangle’s width and length?
Final answer:
To find the width and length of the rectangle, set the equation (5x + 2)(2x - 1) = 100, simplify to 10x² - x - 102 = 0, factor to find x = 6, then substitute back to find the dimensions: 32 feet by 11 feet.
Explanation:
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. To find the rectangle’s width and length, we need to solve for x using the area of a rectangle, which is the product of its length and width. The equation is:
(5x + 2)(2x - 1) = 100
First, expand the left side of the equation:
10x²- 5x + 4x - 2 = 100
Combine like terms:
10x² - x - 2 = 100
Subtract 100 from both sides to set the equation to zero:
10x² - x - 102 = 0
Now, we can use the quadratic formula, factorization, or a graphing utility to find the values of x that satisfy the equation. For simplicity, we are looking for integer solutions because the setup of the problem suggests that such solutions are likely.
Factoring the quadratic equation, we get:
(10x + 17)(x - 6) = 0
Setting each factor to zero gives us two potential solutions for x:
10x + 17 = 0 or x - 6 = 0
Solving these, we find:
x = -17/10 or x = 6
Since a negative width does not make practical sense for a rectangle, we discard the negative solution and keep x = 6.
Inserting x = 6 into the original expressions for width and length, we find:
Width = 5(6) + 2 = 32 feet
Length = 2(6) - 1 = 11 feet
Therefore, the rectangle's dimensions are 32 feet by 11 feet.
The second step in the process for factoring the trinomial x2-5x-36 is to
Answer:
Find the sum of the factors of 36
Step-by-step explanation:
write the equation of the line that passes throughout (-1,5) and has a slope of 3 in point-slope form
Two competing cable companies have recently restructured their payment plans. Clear TV requires a $30 activation fee and charges $75 per month for their basic plan. Link TV requires no activation fee and charges $82.50 per month for their basic plan. When will the two plans be equal in cost?
the square root of 2.25 is _____. 15 1.5 0.15 irrational
Answer:
The square root of 2.25 is 1.5.
Step-by-step explanation:
We have been given an incomplete sentence. We are asked to bill in the given for our given sentence and complete it.
The square root of 2.25 is _____.
Let us find [tex]\sqrt{2.25}[/tex].
[tex]\sqrt{2.25}=1.5[/tex]
Therefore, the square root of 2.25 is 1.5 and option B is the correct choice.
Find the missing lengths of the sides
Answer:
a) a = 9d, c = 18 yd
Step-by-step explanation:
The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.
Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.
In given figure, we are given the longer leg.
√3x = 9√3
From this we can find the value of x, which is the shorter leg.
Dividing both sides by √3, we get
x = 9
The shorter side, a = 9 yd
Now let's find the hypotenuse.
Plug in x = 9, in 2x, we get
= 2*9
= 18 yd
The hypotenuse "c" = 18 yd.
So the answer is a) a = 9d, c = 18 yd
what are the four main ideas of physical science,
Which expression is a factor of 4ab + 4a − 3b − 3?
b − 1
4a − 3
3b + 1
4a + 3b
(4a − 3) is a factor of 4ab + 4a − 3b − 3. Option B is correct. It is obtained by solving the given expression and taking the common terms.
What is the factored form of an expression?When an expression is written as the result of multiplication of some terms, then that multiplication form is called the factored form of that expression.
From the given expression;
[tex]= \rm 4ab + 4a - 3b - 3\\\\ =4a(b + 1) - 3(b+1) \\\\ = (b+1)(4a - 3)[/tex]
From the expression, (b+1) and (4a—3) are factors.
Hence, option B is correct.
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state if the polygons are similar
Since you didn't provide a picture of the exact thing you're working on I'm not sure if this will help you but it will help anyone who has the same project as me
List the coordinates of the image after a rotation of the figure below of 180° about the origin. 20 points
(__ , __)
(__ , __)
(__ , __)
(__ , __)
Find the measures of the segment and its image:
AD = √___, A'D' = √___
Answer: The co-ordinates of the image quadrilateral areA'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
Step-by-step explanation: We are given to list the co-ordinates of the image after a rotation of the figure below of 180° about the origin.
From the figure, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(3, 1), B(5, 4), C(7, 2) and D(4, 0).
We know that
the co-ordinates of the image of a point (x, y) after rotation of 180° about the origin is given by (-x, -y).
Therefore, after rotating the quadrilateral ABCD through an angle of 180° about the origin, then the co-ordinates of the image A'B'C'D' are
A(3, 1) ⇒ A'(-3, -1),
B(5, 4) ⇒ B'(-5, -4),
C(7, 2) ⇒ C'(-7, -2)
and
D(4, 0) ⇒ D'(-4, 0).
And, the lengths of the line segments AD and A'D' can be calculated using distance formula as follows :
[tex]AD=\sqrt{(4-3)^2+(0-1)^2}=\sqrt{1+1}=\sqrt{2}~\textup{units},\\\\A'D'=\sqrt{(-4+3)^2+(0+1)^2}=\sqrt{1+1}=\sqrt 2~\textup{units}.[/tex]
Thus, the co-ordinates of the image quadrilateral are A'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
1/3 math questions. pls help! 20 pts!
What is the solution of the equation x2 + 10x + 75 = 0?
I need to make a matrix in reduced row echelon form
A real estate agency offers three apartments for rent in New Mexico City. The expected total revenue per month from monthly rentals for the three apartments is $1,600. The individual owners of these apartments bear the monthly maintenance costs of 20% of the rent for the first two apartments and 25% of the rent for the third apartment, which is a total amount of $345. The agency charges a monthly fee equal to 10% of the rent for apartments 1 and 3 and a fee equal to 20% of the rent for apartment 2. The monthly rent plus agency fees totals $1,820. Let x, y, and z represent the monthly rental for the first, second, and third apartments, respectively.
Let the three apartments be A, B & C
The rent of A is $x
The rent of B is $y
The rent of C is $z
So x + y + z = 1600 .......(1)
Now
Maintenance of A is 20% of x = 0.20x
Maintenance of B is 20% of y = 0.20y
Maintenance of C is 25% of z = 0.25z
0.20x + 0.20y + 0.25z = 345
Multiplying by 100 we get
20x + 20y + 25 z = 34500
Dividing by 5 we get
4x + 4y + 5z = 6900 .......(2)
Monthly fee of A is 10% of x = 0.10x
Monthly fee of B is 20% of y = 0.20 y
Monthly Fee of C is 10% of z = 0.10z
Now
0.10x + 0.20y + 0.10 z= 1820 - 1600
0.10x + 0.20y + 0.10z = 220
Multiplying by 100 we get
10x + 20y + 10z = 22000
Dividing by 10
x + 2y + z = 2200 ....(3)
Making a Matrix of equation (1), (2) & (3)
[tex] \left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right] [/tex]
is the required matrix
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
Answer:
C is correct option.
The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
Step-by-step explanation:
We are given expression [tex]\dfrac{6x}{x+3}+10[/tex]
Let us suppose f(x) is total money earned by setting up a food stall at a funfair.
where, x represents the total number of cheeseburger were sold.
Therefore, [tex]f(x)=\dfrac{6x}{x+3}+10[/tex]
We need to collect the information about constant 10.
If we put x=0 into f(x)
f(0)=10
10 is a money earn when no cheeseburger sold.
It means 10 would be initial cost of setting up of Food stall.
Thus, The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
The sum of three consecutive odd integers is 153. what is the value of the largest of the integers?
The value of the largest of the integers will be 53.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of three consecutive odd integers is 153.
Let x be the odd number. Then the other two odd numbers will be x + 2 and x + 4. Then the equation will be
x + x + 2 + x + 4 = 153
3x + 6 = 153
3x = 147
x = 49
Then the other two odd numbers will be
x + 2 = 49 + 2 = 51
x + 4 = 49 + 4 = 53
The value of the largest of the integers will be 53.
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A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.
For which interval is the ball’s height always decreasing?
A. 48
B.0
C.2.5
D.146
2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
What is time interval?" Time interval is the division of time into small equal intervals to have a proper observation of any data."
According to the given graph,
x represents time in seconds along x-axis
y represents height in foot of the ball along y-axis
As per observation,
Height of the ball increasing from 48 to 146 in the time interval
0< x < 2.5.
Height of the ball decreasing from 146 to 0 in the time interval 2.5< x < 5.5.
Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.
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50x = 100 what does x equal??
The Jensen family took a road trip in September.the dad fills up the tank,he records the miles on the SUV as 24,033.he pays $83.58 to fill up the tank. what is the size of the SUV's tank in gallons, rounded to the nearest whole number. One gallon of gas cost $3.79,
Dimension of triangle A are three times the dimensions of triangle
b. The area of triangle A is 252 cm squared. What is the area of triangle B?
Answer:
28 cm2
Step-by-step explanation:
I did this question
Please help asap! 44 pts (:
What is the ratio of pennies to dimes in a dollar
How use zero product property to solve equations
Find the second of 3 consecutive integers if the sum of the first and the third is 26
The time it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours and a standard deviation of 1.1 hours what is the time for a runner with a score of -1.2? Round to the nearest hundredth
explanation and answer
Which trigonometric function is equivalent to sec(-270) ? a. sec(-120) c. sec(-30) b. sec(60) d. sec(90)
Answer: d
Step-by-step explanation: edge 2021
PLEASE GET THIS RIGHT!!!!!!!! The difference between 3.6 and a number is 2.95, as shown below. What number should go in the box to complete the subtraction problem?