Answer:
x = -1
y = -2
Step-by-step explanation:
We are given the following equations:
[tex]y = -2x - 4[/tex]
[tex]y = 3x + 1[/tex]
As we can see, the expressions [tex]{-2x - 4}[/tex] and [tex]3x + 1[/tex] are both equal to [tex]y[/tex]. Therefore, we can equate them:
[tex]-2x - 4 = 3x + 1[/tex]
Now we can solve for [tex]x[/tex] by making [tex]x[/tex] the subject of the equation:
⇒ [tex]-2x - 4 -3x = 3x + 1 - 3x[/tex] [Subtracting [tex]3x[/tex] from both sides]
⇒ [tex]-5x - 4 = 1[/tex]
⇒ [tex]-5x - 4 + 4 = 1 + 4[/tex] [Adding 4 to both sides of equation]
⇒ [tex]-5x = 5[/tex]
⇒ [tex]\frac{-5}{-5}x = \frac{5}{-5}[/tex] [Dividing both sides by -5]
⇒ [tex]x = \bf -1[/tex]
Now that we know the value of [tex]x[/tex], we can calculate the value of [tex]y[/tex] by replacing the [tex]x[/tex] with -1 in any of the equations for [tex]y[/tex] given above:
[tex]y = 3x + 1[/tex]
⇒ [tex]y = 3(-1) + 1[/tex]
⇒ [tex]y = -3 + 1[/tex]
⇒ [tex]y = \bf -2[/tex]
Therefore, the solution to the system of equations is : x = -1, y = -2.
Answer:
x = -1
y = -2
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y = -2x - 4\\y= 3x + 1\end{cases}[/tex]
Use the method of substitution to solve for x:
[tex]\begin{aligned}& \textsf{Substitute}: & 3x+1 & = -2x-4\\& \textsf{Add $2x$ to both sides}: & 3x+1+2x & = -2x-4+2x\\& \textsf{Combine like terms}: & 5x+1 & = -4\\& \textsf{Subtract $1$ from both sides}: & 5x+1 -1& = -4-1\\& \textsf{Simplify}: & 5x & = -5\\& \textsf{Divide both sides by $5$}: & \dfrac{5x}{5} & = \dfrac{-5}{5}\\& \textsf{Simplify}: & x & = -1\end{aligned}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\begin{aligned}& \textsf{Equation}: & y& = 3x+1\\& \textsf{Substitute in $x=-1$}: & y & = 3(-1)+1\\& \textsf{Multiply the numbers}: \quad & y & = -3+1\\& \textsf{Simplify}: & y & = -2\\\end{aligned}[/tex]
Therefore, the solution to the given systems of equations is (-1, -2).
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A minor league baseball park has 7000 seats. Box seats cost $6, grandstand seats cost $4, and bleacher seats
cost $2. When all seats are sold, the revenue is $26,400. If the number of box seats is one-third the number of
bleacher seats, how many seats of each type are there? Give a complete sentence explaining what your answers
mean.
Taking into account the definition of a system of linear equations, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values of the unknowns must give the solution proposed in both equations.
Amount of seats of each typeIn this case, a system of linear equations must be proposed taking into account that:
"B" is the number of box seats."G" is the numer of grandstand seats."BL" is the number of bleacher seats.You know that:
A minor league baseball park has 7000 seats.Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the revenue is $26,400. The number of box seats is one-third the number of bleacher seats,So, the system of equations to be solved is
Equation 1: B + G + BL= 7000
Equation 2: 6B + 4G + 2BL= 26400
Equation 3: B= 1/3BL
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, replacing equation 3 in equation 1 and isolating the variable G, you get:
1/3BL + G + BL= 7000
4/3BL + G= 7000
G= 7000 - 4/3BL
Substituting this expression and equation 3 into equation 2 you get
6×1/3BL + 4×(7000 - 4/3BL) + 2BL= 26400
Solving:
2BL + 4×7000 - 4×4/3BL + 2 BL= 26400
2BL + 28000 - 16/3BL + 2 BL= 26400
2BL - 16/3BL + 2 BL= 26400 - 28000
-4/3BL= -1600
BL= (-1600)÷ (-4/3)
BL= 1200
Remembering that B= 1/3BL and G= 7000 - 4/3BL and replacing the value of BL you get:
B= 1/3BL= 1/3×1200 → B= 400
G= 7000 - 4/3BL= 7000 - 4/3×1200 → G= 5400
In summary, the number of box seats is 400, the number of bleacher seats is 1200 and the number of grandstand is 5400.
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Use the diagram to find the angle measures that satisfy each case. Find the measures of all 4 angles if m<2-m<1=30 degrees
The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
How to use the diagram to find the angle measures that satisfy each case?The diagram that completes the question is added as an attachment
From the diagram, we have
<1 + <2 = 180 degrees --- supplementary angles
Given that
<2 - <1 = 30 degrees
Add the above equations
So, we have
2<2 = 210
Divide both sides by 2
<2 = 105
Substitute <2 = 105 in <2 - <1 = 30
So, we have
105 - <1 = 30
Evaluate
<1 = 85
Also, we have
<3 = <1
<4 = <2
This means that
<3 = 85
<4 = 105
Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105
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i need help this is mad confusing
Answer:
Natural number are the numbers: 1, 2, 3... (The ... means the pattern continues. These were the first numbers that you learned about when you were little.
The whole numbers at the number 0 to the list. 0,1,2,3,...
Integers are the whole numbers and their opposites. Zero is not positive or negative. ...,-3, -2 -1 , 0, 1, 2, 3,.... The list does not include numbers like 1/2 or .75
Rational numbers are numbers that can be written as an integer/ integer. This would include numbers like 1/2 and .75 because you can write .75 as 75/100(an integer over and integer.
Step-by-step explanation:
Do not get frustrated. They are just asking for definitions of different classes of numbers.
The slope of the line that passing through (4,-3)and(8,6)
-3(x+n)=x please help me
Answer:
x=− 3n/4
Step-by-step explanation:
Find the vertical asymptote(s) of f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}
x = −1, 2
x = −2, 2
x = 1, −2
x = −1, 1
Answer:
x = −2, 2
Step-by-step explanation:
[tex]f(x)=\frac{\left(x^{2}+3x+6\right)}{x^{2}-4}[/tex]
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
Vertical Asymptotes:
x=−2,2Horizontal Asymptotes:
y=1
No Oblique Asymptotes
Full Explanation
The line x=L is a vertical asymptote of the function [tex] y=\frac{x^{2} + 3 x + 6}{x^{2} - 4}[/tex] if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
So, find the points where the denominator equals 0 and check them.
x=−2, check: [tex] \lim_{x \to -2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=-\infty [/tex]
Since the limit is infinite, then x=−2 is a vertical asymptote.
x=2, check: [tex]\lim_{x \to 2^+}\left(\frac{x^{2} + 3 x + 6}{x^{2} - 4}\right)=\infty[/tex]
Since the limit is infinite, then x=2 is a vertical asymptote.
Vertical asymptotes: x=−2; x=2
write ____ as a single power of 3
Answer:
[tex]3^{16/5}[/tex]
Step-by-step explanation:
[tex]3^3 \times \sqrt[5]{3} \\ \\ =3^3 \times 3^{1/5} \\ \\ =3^{16/5}[/tex]
help me please if you can asap !
Answer:
Step-by-step explanation
t=2002-1992
t=10
p(10)=0.019(10)^3- 0.287(10)^3+ 3.073(10)+ 55.130
P(10)= 19- 287+ 30.73+ 55.130
p(10)= -182.14
for each final matrix, state the solution.
1 0 0 | 3
0 1 0 | -1
0 0 1 | 8
1 0 -6 | 11
0 1 4 | 7
0 0 0 | -2
1 0 2 | 9
0 1 -8 | 5
0 0 0 | 0
Answer:
Step-by-step explanation:
3TRWRRW
How do you find existence of inverse?
[tex]{\huge\color{black}{\boxed{\fcolorbox{green}{red}{꧁ANSWER꧂}}}}[/tex]
Existence of an Inverse
There are two numbers that f takes to 4, f(2) = 4 and f(-2) = 4. If f had an inverse, then the fact that f(2) = 4 would imply that the inverse of f takes 4 back to 2. On the other hand, since f(-2) = 4, the inverse of f would have to take 4 to -2.
Two planes, which are 2670 miles apart, fly toward each other. Their speeds differ by 90mph. If they pass each other in 3 hours, what is the speed of each?
400mph and 490mph
The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the speed of the fast plane and y represent the speed of the slow plane.
Their speeds differ by 90mph, hence:
x - y = 90 (1)
The planes meet after 3 hours, hence:
3x + 3y = 2670 (2)
From both equations:
x = 490, y = 400
The speed of the fast plane is 490 mph while the speed of the slow plane is 400 mph
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What is the value of the expression below when w=4w=4? 9w-10 9w−10
Answer:
26
Step-by-step explanation:
The value equals 26
9 × 4 = 36
36 - 10 = 26
During the summer, you work 25 hours per week at the Twist Ice Cream Shop and earn $8.00 per hour. You also mow lawns in your neighborhood for $10 per hour and can work as many hours as you want. You want to earn a total of $500 per week. Write and solve an equation to find out how many hours you must mow lawns to reach your goal. Let x= # of hours you mow lawns
The required equation for how many hours I have to work mowing lawns is f(x) = 10x + 200 and the required no. of hours is 30 hours.
What is a function ?A function can be thought of as an output for the given set of inputs.
According to the given question I work for 25 hours per week at the twist ice-cream shop and earn 8.00 dollars per hour.
∴ My total earning in a week will be (25×8) = 200 dollars.
But i want to earn 500 per week so need (500 - 200) = 300 dollars to reach my goal.
I also mow lawns in my neighbourhood for 10 dollars per hour.
∴ I need (300/10) = 30 hours to earn the amount i need which is 500 dollars.
An equation can be written as
f(x) = 10x + 200, where x is the no. of hours and f(x) = 500.
500 = 10x + 200.
10x = 500 - 200.
10x = 300.
x = 300/10.
x = 30.
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Each month, Braxton uses an average of 8 ounces of lotion. Calculate Braxton's total monthly savings if he purchases the brand that has the lowest price per ounce versus the highest price per ounce.
Brand A: 24 ounces for $3.30
Brand B: 40 ounces for $4.60
a $0.18
b $0.75
с $1.30
d $1.50
Option a: Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price
Given,
Braxton’s average monthly usage of lotion = 8 ounces
The amount of two different brands of lotion are given:
Brand A: 24 ounces for $3.30
Brand B: 40 ounces for $4.60
We have to find the monthly savings of Braxton if he purchases the brand that has the lowest price per ounce versus the highest price:
We have to calculate amount for one ounce for the two brands given:
Brand A:
24 ounces for $3.30
Amount for one ounce = 3.30/24
Amount for one ounce = $0.1375
Brand B:
40 ounces for $4.60
Amount for one ounce = 4.60/40
Amount for one ounce = $0.115
Now, we have to calculate the amount for 8 ounces.
Brand A:
8 x 0.1375 = 1.1
$1.1 for 8 ounces of Brand A lotion.
Brand B:
8 x 0.115 = 0.92
$0.92 for 8 ounces of Brand B lotion.
Now, we have to calculate the savings:
Brand A – Brand B
1.1 – 0.92 = 0.18
That is, Broxton have a monthly savings of $0.18 if he purchases the brand that has the lowest price per ounce versus the highest price.
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12 push-ups in 2 days = push-ups per day
Answer:
6 push ups per day
Step-by-step explanation:
→ [tex]12 \div 2 = 6~push~ups[/tex]
Answer: 6 push-ups per day
Step-by-step explanation:
12 push-ups/2 days = 12/2 = 6 push-ups each day for 2 days to have 12 push-ups total.
What Two whole numbers have their first common multiple as 6
Answer:
2, 3
Step-by-step explanation:
The prime factorization of 6 is 2(3), so one possibility is 2 and 3.
whats the answer, i need help cuz i cant figure it out.
Check the picture below.
[tex]\stackrel{AC}{x}~~ + ~~\stackrel{CB}{2x}~~ = ~~\stackrel{AB}{33}\implies 3x=33\implies x=\cfrac{33}{3}\implies \boxed{x=11} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE AC}}{11}\hspace{10em}\stackrel{\textit{\LARGE CB}}{2(11)\implies 22}[/tex]
What is the equation to solve how many centimeters in 14.72 inches. There are 2.54cm in an inch
The equivalent of 14.72 inches in centimeter is 37.3888 cm
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The conversion from inches to cm is given by:
1 in = 2.54 cm
Hence:
14.72 in = 14.72 in * 2.54 cm per in = 37.3888 cm
The equivalent of 14.72 inches in centimeter is 37.3888 cm
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A small deck of twenty cards consists of eight red cards and twelve green cards. Draw five cards at random, without replacement. How many five-card selections are possible?
At random selection, there are 4, five-card selections possible.
What is Random selection?Random selection describes how the sample is drawn from the entire population, whereas random assignment describes how the participants are then assigned to either the experimental or control groups. In an experiment, both random selection and random assignment are possible.Since there are only 20 cards in the deck so there are 4 sections of 5 cards each is possible as 4 × 5 = 20.
Therefore, there are 4, five-card selections possible.
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The units of the subway map below are in miles. Suppose
the routes between stations are straight. Station F, not
shown on the map, is 16 miles west and 4 miles north of
Station A. What is the approximate distance between
Station E and Station F?
The distance from Station E to Station F is
approximately E miles.
(Round to the nearest tenth as needed.)
Distance between EF is 20.09 units.
By considering the given information
E= (-4,2)
F= (16,4)
Distance between EF =
[tex]\sqrt{(16+4)^{2}+(4-2)^{2} } \\=\sqrt{400+4} \\=\sqrt{404} \\=20.09[/tex]
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In coordinate geometry, the distance between two given points is calculated using the distance formula. The formula for calculating the separation between two points
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so does someone help me
Step-by-step explanation:
this is an exercise to take the logical definition of an operation and apply it.
we have first a triangle operation that simply stands for the sum of the 3 included values divided by 3.
in other words, FYI, it creates the mean value of 3 given numbers.
so, we need to calculate
mean value (7, 4, 4) + mean value (8, 2, 11).
(7 + 4 + 4)/3 + (8 + 2 + 11)/3 = 15/3 + 21/3 = 36/3 = 12
the second calculation is based on a table defining a new operation Delta :
2 Delta 2 = 20
2 Delta 5 = 5
2 Delta 3 = 5
5 Delta 2 = 3
5 Delta 5 = 10
5 Delta 3 = 23
3 Delta 2 = 3
3 Delta 5 = 2
3 Delta 3 = 50
so, now we need to use this to calculate
(5 Delta 2) Delta (2 Delta 3)
3 Delta 5
2
the result is 2.
Can someone help with the reason? The first one is given, after that- I have no clue.
Answer:
5x = 8(x - 3)
5x = 8x - 24 → Expand the brackets
-3x = -24 → Collect like terms ,which simply means that you'll transfer 8x to the other side , which will make it -8x
x = 8 → Divide both sides by the coefficient of x (3) : minus cancels minus; then 24 ÷ 3 = 8.
Referring to the figure,
to show the cost for various amounts of long distance calls, which of
the graphs shown shows the data on a 10-by-10 grid with the appropriate
scales?
a. Graph a c. Graph c
b. Graph b d. Graph d
Based on the figure, the graph that shows the data on long distance calls on a 10-by-10 grid with appropriate scales is Graph C.
Which graph is correct?The data is to be shown on a 10-by-10 grid which means that the range of numbers on the x and y axis should be between 0 and 10.
The scales should also be appropriate which means that Time (hours) should represent the x axis and Cost (dollars) should be on the y axis.
Only Graph C has this which makes it the right one.
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Opposites
For problems 12-14, describe the similarities and differences between the expressions.
12. -3 and -(3)
13. -1(7) and -(7)
14. -2(4) and -(2•4)
The similarities between the expressions in all the three problems is that after opening brackets both of the expressions are the same.
How to check if two expressions are similar?Two expressions are similar if their values after solving are equal.
12. -3 and -(3)
Here, when we open the bracket for -(3), we obtain -3 which is the same as the first expression.
13. -1(7) and -(7)
Solving for the first expression, we get -1×7 = -7 and
-(7) = -7.
We can see that both expressions are similar.
14. -2(4) and -(2•4)
Solving -2(4), we get -2×4 = -8
And, -(2·4) = -(8) which is the same as -8
Hence, both expressions are similar.
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what is three fourths divided by five
Which of the following graphs best represents the solution to the pair of equations below? y = x + 1 y = −x − 1 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at negative 1. The lines intersect at 0 comma 1. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at 1. The lines intersect at 0 comma negative 1. A coordinate plane is shown with two lines graphed. One line passes through the y axis at negative 1 and the x axis at 1. The other line passes through the y axis at 1 and the x axis at 1. The lines intersect at 1 comma 0.
The graph that best describes the equations y = x + 1 y = −x − 1 is: A coordinate plane is shown with two lines graphed. One line passes through the y axis at 1 and the x axis at negative 1. The other line passes through the y axis at negative 1 and the x axis at negative 1. The lies intersect at negative 1 and 0.
What is a graph?A graph is a pictorial representation of data used in several disciplines. Graphs makes it easier to understand how a particular data relates with the other.
There many types of graphs, the type used here is the that of a straight line. The graph would have to cut through based on the signs that it has in the equation. That is if it is negative or positive.
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-9x > 18 and x < -2 are equivalent inequalities.
True or False
Answer: True
Step-by-step explanation:
18 less than half a number.
The equation for the given description is 18 - 0.5x = 6
What is Equation?
A assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to symbol, or "=," is used to indicate it.
An identity, in which the variables can take on any value, or a conditional equation, in which the variables can only take on certain values, is a mathematical declaration that two expressions are identical (roots)
According to the given statement;
Since 18 less than half a number is 6
So here we assume the number be x
Now the equation is
18 - 0.5x = 6
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Solve 2l2x-1l-2=12 Show all work
Answer:
Solution
x= 2l (2) 14+l
Step-by-step explanation:
Divide both sides
2l
2
2l
2
x
=
2l
2
14+l
Find the area of the figure (in cm2). (Simplify your answer completely.)
The area of the figure in the image is 800 square centimeters.
How to find the area of the figure?
Here we have a square of sidelength of 30cm, such that in each corner we removed little squares of sidelength of 5cm.
Then the area of the figure will be the difference between the area of the first square and 4 times the area of the smaller square,
The area of a square of sidelength of 30 cm is:
A = 30cm*30cm = 900cm^2
The area of a square of sidelength of 5 cm is:
a = 5cm*5cm = 25cm^2
Then the area of the figure is:
area = A - 4a = 900cm^2 - 4*25cm^2 = 800cm^2
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