Use substitution to determine the solution of the system of equations.
y = −2x − 7
2y − x = 1
A. (−1,0)
B. (212,−28)
C. (−6,−52)
D. (−3,−1)
Answer:
Option D is correct
( -3, -1 )
Step-by-step explanation:
equation 1 is
y = -2x -7
and equation 2 is
2y - x = 1
so from 1 we have y = -2x - 7 put in 2
2 ( -2x - 7 ) -x = 1
-4x - 14 - x = 1
- 5x = 1 + 14
X = 15/-5
X= - 3
put in equation 1
Y = - 2 ( -3) - 7
Y= 6 - 7
Y = - 1
Solution of the given equations D.[tex]\boldsymbol{(-3,-1)}[/tex].
An equation is a mathematical expression that contains an equals symbol.
Given equations are as follows:
[tex]y=-2x-7[/tex]
[tex]2y-x=1[/tex]
Put value of [tex]\boldsymbol{y}[/tex] from the first equation to the second equation.
[tex]2(-2x-7)-x=1[/tex]
[tex]-4x-14-x=1[/tex]
[tex]-5x=15[/tex]
[tex]x=-3[/tex]
Now, put value of [tex]x[/tex] in the equation [tex]2y-x=1[/tex].
[tex]2y-(-3)=1[/tex]
[tex]2y=-2[/tex]
[tex]y=-1[/tex]
Option D. is correct.
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J erk (denoted by J) can be defined as a function of acceleration (denoted by a) and time (denoted by t) using this formula: J= a/t
Acceleration is measured in m/s² and time is measured in s
Select an appropriate measurement unit for j erk.
Units of J: [tex][\frac{m}{s^3}][/tex]
Step-by-step explanation:
The quantity defined in this problem is
[tex]J=\frac{a}{t}[/tex]
where:
a is the acceleration
t is the time
The units of the two quantities are:
a (acceleration) is measured in metres per second squared, [tex][\frac{m}{s^2}][/tex]
t (time) is measured in seconds, [tex][s][/tex]
Therefore, the quantity J is measured in:
[tex][J]=\frac{[\frac{m}{s^2}]}{[s^3]}=[\frac{m}{s^3}][/tex]
which is option B.
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(–5, –6) a solution to this system of e
quations? 12x − 8y = –12 7x − 6y = 1
The functions f(x)=−3/4x+2 and g(x)=(1/4)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answe
Answer:
The solution is x = 1 and y = 1.25.
Step-by-step explanation:
The solution to the graphs [tex]f(x) = -\frac{3}{4} x + 2[/tex] and [tex]g(x) = \frac{1}{4} x + 1[/tex]
Solving for x we get
[tex]-\frac{3}{4} x + 2 = \frac{1}{4} x + 1[/tex] [tex]\Rightarrow[/tex] x = 1 Therefore y = 1/4 + 1 = 1.25
1 and 0
I took the test and got it right
look at the images please helppp
Let's begin with point A:
[tex]A(7,-4)[/tex]
So we need to find the coordinates of points D in order for ABCD to be a rectangle. So:
D can be found by reflecting A across the x axis:
So you just need to multiply the y-coordinate by -1, then:
[tex]D(x,y)=D(7,-1(-4))=D(7,4)[/tex]
Part 2:The length of AD can be found as the change in y from A to D:
[tex]\overline{AD}=4-(-4) \\ \\ \overline{AD}=8units[/tex]
Part 3.B can be found by reflecting A across the y-axisC can be found by rotating A 180 degrees about the originLearn more:Translation and reflection: https://brainly.com/question/12554274
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Last year Luis read 187 books. This year he read 224 books. Next year he wants to read 285 books. If Luis reaches his goal , how many books will Luis have read
antarctica averages 2,400 meters in elevation. what is the average elevation of Antarctica in kilometers
Answer:
2.4 km
Step-by-step explanation:
The conversion factor is that 1 km = 1000 m. So to find km from m we need to divide the value in m by 1000:
2,400 ÷ 1000 = 2.4 km
Answer:
2.4 kilometers
Step-by-step explanation:
There are 1000 meters in 1 kilometer. So to convert from a smaller unit to a larger one you divide. So to calculate:
2400 m * [tex]\frac{1 km}{1000 m}[/tex] = 2.4 km
Given the scale drawing of a one bedroom apartment, what is the actual length of the apartment from the study to kitchen?
Answer: 30 ft
Step-by-step explanation: bc 1/2 inch = 3 feet combined length = 2 + 5= 5 inches therefore (5.0/0.5)(3)= 10(3)=30
Which fractions are equivalent to 40%?
All of them except 8/100 because it results 0.08 or 8%.
The rest:
2/5 = 0.4 = 40%
8/20 = 0.4 = 40%
4/10 = 0.4 = 40%
16/40 = 0.4 = 40%
find the difference and the next three terms -10 -20 -30
Answer:
- 40, - 50, - 60
Step-by-step explanation:
Note the common difference d between consecutive terms of the sequence.
- 20 - (- 10) = - 20 + 10 = - 10
- 30 - (- 20) = - 30 + 20 = - 10
Thus the difference d = - 10
To obtain a term in the sequence subtract 10 from the previous term
- 30 - 10 = - 40
- 40 - 10 = - 50
- 50 - 10 = - 60
The next 3 terms are - 40, - 50, - 60
A radio station uses 1/6 of* its time for the O
news. In a 24 hour day, how many hours
are used for music & entertainment?
Answer:
4 hours is what they use
Step-by-step explanation:
If they use 1/6 of their time each day
A day = 24 hours
1/6 times of that day will be
1/6*24= 4 hours
Simplify the algebraic expression 7x^2 + 6x - 9x - 6x^2 + 15
Answer: x^2-3x+15
Step-by-step explanation:
Combine the like terms.
x^2 -3x+15
Answer:
x2 – 3x + 15 is the correct answer.
Step-by-step explanation:
Dexter rode his bike 9/10 Miles from his house to the store then he rode 4/10 miles his uncle house use the benchmark to estimate how far he rode his bike altogether
Final answer:
Dexter rode an estimated 1.3 miles altogether after traveling 9/10 miles to the store and then 4/10 miles to his uncle's house.
Explanation:
You are asking how far Dexter rode his bike altogether after he traveled 9/10 miles from his house to the store and then 4/10 miles to his uncle's house. To estimate the total distance Dexter rode, we need to add the two distances together.
The sum of 9/10 miles and 4/10 miles is:
9/10 miles + 4/10 miles = 13/10 miles
To make it easier to understand, 13/10 miles can be converted to 1 3/10 miles, which is the same as 1.3 miles as an estimate, considering 10/10 equals 1 full mile. Therefore, Dexter rode an estimated 1.3 miles altogether.
A car drove 24 miles in 0.2 hours. How fast is the car going in miles per hour?
Answer:
120 mph
Step-by-step explanation:
To find miles per hour, divide miles by hours. ("Per" essentially means "divided by".)
(24 miles)/(0.2 hour) = 24/0.2 miles/hour = 120 miles/hour
Un camión pesa 875 kg la diferencia entre el peso del camión vacío y el peso de la carga que lleve no debe ser inferior a 415 kg, si hay que cargar 4 cajas iguales cuanto puede pesar con lo máximo cada una de ellas para poder llevarlas en el camión? Ayuda por favor
Answer:
The weight of each box must be less than 115 kg to be carried in the truck.
Step-by-step explanation:
The weight of the truck is, T = 875 kg.
Let the weight of one box be x kg.
Given:
[tex]875-4x>415[/tex] kg.
Solve the above inequality for x as follows:
[tex]875-4x>415\\-4x>415-875\\-4x>-460\\x<\frac{-460}{-4}\\ x<115[/tex]
As the weight of a box cannot be less than 0, the range of x is (0, 115).
Thus, the weight of each box must be less than 115 kg to be carried in the truck.
Chose all of the terms that describe the set of lines.
OPTIONS: o(╥﹏╥)o
Transversal
Parallel lines
Perpendicular lines
Intersecting lines
Answer: intersecting
Step-by-step explanation:
they cross each other
what things should be written in the conclusion of letter
Answer:
Your signature, and a nice 4-word goodbye
Step-by-step explanation:
Your signature so they know it was YOU who wrote it and a nice 4-word goodbye to show the other person that you care.
Find the diagonal of the rectangular solid with the given measures.
l = 2, w = 3, h = 6
√(46)
7
2√(10)
Answer:
7Step-by-step explanation:
Diagonal = [tex]\sqrt{2^{2} +3^{2}+6^{2} } =\sqrt{49} =7[/tex]
im lost >.< may i haz help?
Answer:
see below
Step-by-step explanation:
A left-arrow on a number line represents subtraction of a positive number or addition of a negative number. The two left arrows, one of length 0.2, the other of length 0.1, indicate the numbers -0.2 and -0.1 are being added. The end result is the dot at the end of the combined arrows, at -0.3.
The only expression that is true and corresponds to this description is the one shown below.
Mr Smith class 1/3 were absent on Monday and Mrs. Brown class 2/5 were absent on Monday. If 4 students from each class were absent on Monday. How many students are in each class?
Answer:
Mr. Smiths class has 12 students and Mrs. Brown's class has 10 students.
Step-by-step explanation:
if 1/3 of the class is absent and that amount is four you would multiply 4 by 3 and get 12. If 2/5 of the class are missing and there 4 students first you would divide 4 by 2 and get 2, then you would take the 2 and multiply it by 5 and get 10.
PLEASEEEE HELPPPPPPPPPPP
Answer:
The correct option is first graph.
Therefore,
The two points for the line y+5=-2(x-4) ( red color )line are
point A( x₁ , y₁) ≡ ( 0 , 3) .......Blue color
point B( x₂ , y₂) ≡ [tex](\dfrac{3}{2},0)[/tex] ............Green color
The Graph is attached below.
Step-by-step explanation:
Given:
[tex]y+5=-2(x-4)[/tex]
Which can also be written as
[tex]y=-2x+8-5\\y=-2x+3[/tex] .....Equation of line
Let the points be point A, and point B
To Find:
point A( x₁ , y₁) ≡ ?
point B( x₂ , y₂) ≡ ?
Solution:
For Drawing a graph we require minimum two points but we will have here three points.
For point A( x₁ , y₁)
Put x = 0 in the given equation we get
y = -2 × 0 +3
y =3
∴ y = 3
∴ point A( x₁ , y₁) ≡ ( 0 , 3)
For point B( x₂ , y₂)
Put y = 0 in the given equation we get
0 = -2x + 3
[tex]x=\dfrac{3}{2}[/tex]
∴ point B( x₂ , y₂) ≡ [tex](\dfrac{3}{2},0)[/tex]
Therefore,
The two points for the line y+5=-2(x-4) ( red color )line are
point A( x₁ , y₁) ≡ ( 0 , 3) .......Blue color
point B( x₂ , y₂) ≡ [tex](\dfrac{3}{2},0)[/tex] ............Green color
The Graph is attached below.
What’s the answer to sin 36/85
look at the image please helppp
Answer:
Option A. one rectangle and two triangles
Option E. one triangle and one trapezoid
Step-by-step explanation:
step 1
we know that
The area of the polygon can be decomposed into one rectangle and two triangles
see the attached figure N 1
therefore
Te area of the composite figure is equal to the area of one rectangle plus the area of two triangles
so
[tex]A=(8)(4)+2[\frac{1}{2}((8)(4)]=32+32=64\ yd^2[/tex]
step 2
we know that
The area of the polygon can be decomposed into one triangle and one trapezoid
see the attached figure N 2
therefore
Te area of the composite figure is equal to the area of one triangle plus the area of one trapezoid
so
[tex]A=\frac{1}{2}(8)(4)+\frac{1}{2}((4+8)(8)=16+48=64\ yd^2[/tex]
Consider the following system of equations made up of Lines 1 and 2.
Line 1: 6x - 7y = 25
Line 2: 2x + 9y = -3
Select all that are true about the system.
3
(0.3) is a solution for Line 1 only
(0, 0) is a solution for Line 2 only.
1-6. 1) is a solution for Line 2 only.
13.-1) is a solution to the system
(3.1) is a solution to the system
Option c: (-6,1) is a solution for Line 2 only
Option d: (3,-1) is a solution to the system
Explanation:
Option a: (0,3) is a solution for Line 1 only
Line 1 is [tex]6 x-7 y=25[/tex]
Let us substitute the coordinate (0,3) in Line 1, we get,
[tex]\begin{array}{r}{6(0)-7(3)=25} \\{-21=25}\end{array}[/tex]
Since, both sides of the equation are not equal, the coordinate (0,3) cannot be a solution to Line 1.
Thus, Option a is not the correct answer.
Option b: (0,0) is a solution for Line 2 only.
Line 2 is [tex]2 x+9 y=-3[/tex]
Let us substitute the coordinate (0,0) in Line 2, we get,
[tex]\begin{array}{r}{2(0)+9(0)=-3} \\{0=-3}\end{array}[/tex]
Since, both sides of the equation are not equal, the coordinate (0,0) cannot be a solution to Line 2.
Thus, Option b is not the correct answer.
Option c: (-6,1) is a solution for line 2 only.
Line 2 is [tex]2 x+9 y=-3[/tex]
Let us substitute the coordinate (-6,1), in Line 2, we get,
[tex]\begin{array}{r}{2(-6)+9(1)=-3} \\{-12+9=-3} \\{-3=-3}\end{array}[/tex]
Since, both sides of the equation are equal, the coordinate (-6,1) is a solution for line 2 only.
Thus, Option c is the correct answer.
Option d: (3,-1) is a solution to the system
Let us substitute the coordinate (3,-1) in line 1 and line 2, we get,
In line 1, we have,
[tex]\begin{array}{r}{6(3)-7(-1)=25} \\{18+7=25} \\{25=25}\end{array}[/tex]
Substituting (3,-1) in line 2, we have,
[tex]\begin{array}{r}{2(3)+9(-1)=-3} \\{6-9=-3} \\{-3=-3}\end{array}[/tex]
Since, from line 1 and line 2, both sides of the equation are equal, the coordinate (3,-1) is a solution to the system.
Thus, Option d is the correct answer.
Option e: (3,1) is a solution to the system
Let us substitute the coordinate (3,1) in line 1 and line 2, we get,
In line 1, we have,
[tex]\begin{array}{r}{6(3)-7(1)=25} \\{18-7=25} \\{11=25}\end{array}[/tex]
Substituting (3,1) in line 2, we have,
[tex]\begin{array}{r}{2(3)+9(1)=-3} \\{6+9=-3} \\{15=-3}\end{array}[/tex]
Since, from line 1 and line 2, both sides of the equation are not equal, the coordinate (3,1) is a solution to the system.
Thus, Option e is not the correct answer.
Answer:
Option C: (-6,1) is a solution for Line 2 only
Option D: (3,-1) is a solution to the system
Step-by-step explanation:
Use the Diagram of ABCD to find X?
Does anyone know this?
Answer:
x = 9
Step-by-step explanation:
x+3=2x-6
3=2x-x-6
9=x
The value of the x for the figure ABCD is 9.
What are quadrilaterals?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Given the quadrilateral ABCD and opposite sides are parallel,
AD ║ BC and AB ║ CD
since the opposite sides of the quadrilateral are parallel so the quadrilateral is a parallelogram,
so AB = CD
AB = x + 3 and CD = 2x - 6
x + 3 = 2x - 6
2x - x = 3 + 6
x = 9
Hence the value of x is 9.
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What did the mathematician do over winter break
Answer:
he hit the slopes
Step-by-step explanation:
;)
Alicia works 40 hours per week as a dental assistant. What is her monthly income? What is her yearly income?
Answer:
How could i answer without her pay rate ?
Step-by-step explanation:
Item 11
A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?
Answer:
[tex]Amount\ of\ sales=\$ 6000[/tex]
Step-by-step explanation:
[tex]Let\ total\ sales=x\\\\Commission=3\%\ of\ total\ sale\\\\Commission=3\%\ of\ x\\\\It\ is\ given\ that\ salesperson\ gets\ \$ 180\ as\ commission.\\\\3\%\ of\ x=180\\\\\frac{3}{100}x=180\\\\x=\frac{180\times 100}{3}\\\\x=60\times 100\\\\x=6000\$\\\\Amount\ of\ sales=\$ 6000[/tex]
While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels
18 miles per hour in still water.
1. Let w represent the speed of the river current in miles per hour. Write an expression for how fast the
motorboat is able to go downstream (with the current) Write another expression for how fast the motorboat is
able to go upstream (against the current).
2. The motorboat travels 49 miles upstream in the same time it takes to travel 77 miles downstream. What is the
speed of the current w? Use the Elimination Method to solve.
Part 1: The speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.
The speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.
Part 2: The speed of the current is 4 miles per hour.
Explanation:
Part (1): The motorboat travels 18 miles per hour in still.
Let w represents the speed of the current.
When the boat travels downstream, the speed of the current will get added to the speed of the boat.
Thus, the expression can be written as [tex](18+w)[/tex] miles per hr
Hence, the speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.
When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.
Thus, the expression can be written as [tex](18-w)[/tex] miles per hr.
Hence, the speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.
Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.
The distance formula is given by [tex]distance $=$ speed $\times$ time[/tex]
Substituting, we have,
[tex]49=(18-w)t\\49=18t-wt[/tex] ---------------(1)
[tex]77=(18+w)t\\77=18t+wt[/tex] ---------------(2)
Solving using elimination method,
[tex]49=18 t-w t\\77=18 t+w t\\-------\\126=36t[/tex]
Dividing both sides by 36, we have,
[tex]t=3.5[/tex]
Substituting [tex]t=3.5[/tex] in [tex]$49=18 t-w t$[/tex], we get,
[tex]49=18(3.5)-w (3.5)\\[/tex]
[tex]49=63-3.5w\\[/tex]
[tex]-14=-3.5w\\[/tex]
[tex]4=w[/tex]
Thus, the speed of the current is [tex]w=4[/tex] miles per hour.
Final answer:
The expression for the speed of the motorboat downstream is (18 + w) miles per hour. The expression for the speed of the motorboat upstream is (18 - w) miles per hour. To solve for the speed of the current, a system of equations can be set up and solved using the Elimination Method.
Explanation:
1. When the motorboat is traveling downstream (with the current), the speed of the motorboat will be the sum of its speed in still water and the speed of the river current. So the expression for the speed of the motorboat downstream is: (18 + w) miles per hour.
When the motorboat is traveling upstream (against the current), the speed of the motorboat will be the difference between its speed in still water and the speed of the river current. So the expression for the speed of the motorboat upstream is: (18 - w) miles per hour.
2. To find the speed of the current, we can set up a system of equations. Let t represent the time taken for both the upstream and downstream trips. The distance traveled upstream is 49 miles and the distance traveled downstream is 77 miles. Using the formula Distance = Speed x Time, we can write the following equations:
(18 + w) * t = 77
(18 - w) * t = 49
We can solve this system of equations using the Elimination Method. First, multiply the first equation by (18 - w), and multiply the second equation by (18 + w) to eliminate the variable w:
[(18 + w) * t] * (18 - w) = [(18 - w) * t] * (18 + w)
Simplify both sides of the equation:
(18 + w)(18 - w)t = (18 - w)(18 + w)t
Expand:
(18² - w²)t = (18² - w²)t
Cancel out the like terms:
324 - w² = 324 - w²
This equation is true for any value of w. Therefore, there are infinitely many possible values for the speed of the current w. The specific value of w would depend on the given values of t and the distance.
Marc was born on his grandmother’s 56th birthday. In how many years will Marcs grandmother be 5 times as Marc will be then?
Answer:
In 14 years Marc's grandmother will be 5 times as Marc will be then
Step-by-step explanation:
1. Information given to us to solve the problem:
Marc's age today = 0
Marc's grandmother age today = 56
2. In how many years will Marc's grandmother be 5 times as Marc will be then?
x = Number of years when Marc's grandmother age will be 5 times as Marc will be then
Let's solve for x, this way:
5 times Marc age in x years = Marc's grandmother age in x years
5 (0 + x) = 56 + x
5x = 56 + x
5x - x = 56 (Subtracting x at both sides)
4x = 56
x = 56/4
x = 14
Let's prove that x = 14 is correct:
5 (0 + 14) = 56 + 14
70 = 70
We proved that x = 14 is correct
In 14 years Marc's grandmother will be 5 times as Marc will be then