Question 3 of 10
What is the solution to the system of equations?
-5
y = 3x + 1
5.
-5.
OA. (-2, 1)
OB. (1, -2)
OC. (-2,-1)
OD. (-1,-2)
5
y=-2x-4
Answers
Option D: The solution of the system of equation is (-1,-2)
What is System of Equation ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
The equations are :
y = 3x + 1 ⇒ y - 3x = 1 (i)
y = -2x -4 ⇒ y + 2x = -4 (ii)
Subtracting (i) from (ii) we get ,
2x +3x = -4 -1
⇒ 5x = -5
⇒x = -1
for x = -1
y = 3x + 1 = 3*(-1) + 1 = -2
The solution of the system of equation is (-1,-2)
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Related Questions
what is 6 ÷ 2(1+2)=
pls help
Answers
Answer:
9
Step-by-step explanation:
Answer:
Use PEMDAS, answer is 9
Step-by-step explanation:
art 1 of 2
Suppose the function f(x)=9.09x represents the number of Chinese yuan equivalent to x British pounds and the function gly)=0.17y represents the
number of U.S. dollars equivalent to y Chinese yuan.
a. Write a composite function that represents the number of U.S. dollars equivalent to x British pounds.
b. Find the value in U.S. dollars of an item that costs 15 British pounds.
Answers
A: The composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x
B: An item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.
What is the composite function?
A composite function is a function that is formed by the composition of two or more functions. It is a new function that is made by plugging the output of one function into another function. The notation for a composite function is f(g(x)) or f(g), where f and g are the two functions being composed.
a. To write a composite function that represents the number of U.S. dollars equivalent to x British pounds, we want to substitute the output of f(x) into g(y). So, we want to find g(f(x))
g(f(x)) = g(9.09x) = 0.17(9.09x) = 1.54x
So, the composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x
b. To find the value in U.S. dollars of an item that costs 15 British pounds, we substitute x = 15 into the composite function:
1.54(15) = 23.10
So, an item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.
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Melissa Josh and Pablo have a total of $66 in the wallet Pablo has three times with Josh has Josh has nine more dollars to Melissa how much money do they have in their wallets
Answers
Answer: Pablo 45 josh 15 Melissa 6
Step-by-step explanation: 15 • 3 + 15 + 6 = 66
If each grey square is 1cm in width and length, then what is the area of the shape? A. 15cm2 B. 12cm2 C. 13cm2 D. 22cm2
Answers
Answer: B. 12cm^2.
Step-by-step explanation:
To find the area of the shape, you need to count the number of squares inside it and then multiply that number by the area of a single square. If each grey square is 1cm by 1cm, then the area of a single square is 1cm x 1cm = 1cm^2. If you count the squares inside the shape, you will see that there are 12 squares. Therefore, the total area of the shape is 12cm^2. The correct answer is therefore B. 12cm^2.
A line passes through point (-4, 8) and has a slope of 5 over 4
Answers
the equation for line will be y = (5/4)x + 13.
What is the slope of line?
Determine the slope of the line using the slope formula given two line-side coordinates. The formula m=(y2-y1)/ describes the slope as the proportion of the change in y values to the change in x values (x2-x1). The coordinates of the first point represent x1 and y1 respectively. At x2, y2, and their respective locations are the second points. It doesn't matter which point you choose to rank as the first and which as the second.
Knowing that formula two, which is used to determine the slope of a line connecting two points, is
The line passes through (-4, 8) so,
8 = (5/4)(-4) + c
8 = -5 + c
c = 13
c = 13
The equation of a line is y = (5/4)x + 13
Hence the equation for line will be y = (5/4)x + 13.
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How do you draw a line segment step by step?
Answers
To draw a line segment, Gather your drawing materials and decide on the starting and ending points of your line segment. Place your pen or pencil on the starting point and use a ruler to guide it to the ending point, drawing a continuous, straight line and Lift the pen or pencil from the paper to complete the line segment.
To draw a line segment, follow these steps:
Gather your drawing materials. You will need a pen or pencil, paper, and a ruler if you want to draw a straight line.Decide on the starting and ending points of your line segment.Place your pen or pencil on the starting point of the line segment.Hold the ruler steady, if you are using one, and use it to guide the pen or pencil to the ending point of the line segment.Keep your hand steady and draw a continuous, straight line from the starting point to the ending point.Lift the pen or pencil from the paper to complete the line segment.If you want to draw a longer or curved line segment, you can use a ruler or a curved drawing tool such as a compass to help you draw it.Learn more about line segments at
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Given f(x) = -2x and g(x) = 10x-3 find f(g(x))
Answers
Answer:
-20x^2 -6x
Step-by-step explanation:
I don't want to explain the whole thing, but here's a pic.
What is the inverse of x^3?
Answers
Answer:
∛x
Step-by-step explanation:
Replace x with y and then solve
[tex]y=x^3\\x=y^3\\\sqrt[3]{x} = y[/tex]
Please help me I suck at mathhh
Answers
Answer:
firstly this is a right angle, so we will use Pythagoras' theorem.C² = A² + B²X² = 10² + 12²X² = 244X = √244X = 15.62X ~ 15.62x – 3 = 3 solve by graphing
Answers
x=3 is the solution of equation 2x-3=3 which represent the line parallel to y axis such that x coordinate is always 3
What is axis?In mathematics, an axis is a line that is used to take or indicate measurements. The coordinate plane's x and y axes are two of its most important axes. The x-axis is represented by a horizontal number line, and the y-axis by a vertical number line. The perpendicular intersection of these two axes yields the coordinate plane. The x-axis and y-axis are also known as the ordinate and abscissa, respectively.
in the question we have:
⇒ 2x - 3 = 3
⇒ 2x = 6
⇒ x = 3
which represent a line parallel to y axis where x is always equal to 3 .To plot graph take any y such that point is (3, y) .
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Find the value of x
Answers
Answer:
x = 30
Step-by-step explanation:
3x + 1 + 89 = 180
3x + 90 = 180
3x = 90
x = 30
3(30) + 1 = 91
91 + 89 = 180
Answer:
x = 30°
Step-by-step explanation:
the two values are on a straight line, so 180 degrees, we solve with an equation
3x + 1 + 89 = 180
3x = 180 - 1 - 89
3x = 90
x = 90 : 3
x = 30°
----------------------------------
check3 x 30 + 1 + 89 = 180
90 + 90 = 180
180 = 180
the answer is goodSimplify A by the power of 7 divided by A by the power of 3
Answers
Answer:
a^4
Step-by-step explanation:
a^7 / a^3 = a^(7-3) = a^4
Find the local linear approximation of f(x) 2In(x) at x = 2.
a. y x- 2 b. y x- 2 + In4 c. y 2ln(x 2) d. y 1
Answers
The local linear approximation of f(x) 2In(x) at x = 2 is y = x - 2 + log (4).
As per the given data, the function f(x) is given by:
f(x)=2 log (x) at x = 2
Here we have to determine the linear approximation of f(x).
A linear approximation is a mathematical phrase that describes using a linear function to approximate a general function.
We know the linear form of the function is
y = f(a) + f'(a) ( x - a )
Here, a = 2
Therefore y = f(2) + f'(2) (x - 2) . . . (1)
Now, f(2) = 2 log (2)
= log [tex](2)^2[/tex]
= log (4)
Again, f'(x) =[tex]\frac{d}{d x}[f(x)][/tex]
[tex]=\frac{d}{d x}(2 \log (x)) \\[/tex]
f'(x) = [tex]2 \cdot \frac{1}{x}=\frac{2}{x} \\[/tex]
Therefore f'(2) = [tex]\frac{2}{2}[/tex] = 1
Plug in the values of f(2) and f'(2) in equation (1) we get,
y = log (4) + 1(x - 2)
y = x - 2 + log (4) (which is the linear approximation of f(x))
Therefore option (b) is correct
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Clara completed 40 math problems in 32 mins what is the unit rate
Answers
Answer:
Varies, see below
Step-by-step explanation:
We need to find the number of math problems per minute. To do that, we divide 40/32 to find that she completes 1.25 problems per minute.
Or, on the flippity flop, we can find the number of minutes per math problem. So we would do 32/40 to get 0.8 minutes per math problem.
Choose the one according to your needs.
The formula for unit rate is:
Unit rate = amount of work done / time
So in this case, the unit rate is:
Unit rate = 40 problems / 32 minutes
So the unit rate is 1.25 problems per minute.
This means that for every 1 minute, Clara completes 1.25 math problems.
What is the solution to this equation 3 x 2 − 12 d − 2?
Answers
The solution to the equation 3 x 2 − 12 d − 2 is 1/3.
Solving the equation for d because the value of d would be the required solution to this equation:
Now
3 x 2 − 12 d − 2 = 0
6 - 12 d - 2 = 0
Sitting the constant terms to the right side of the equation while keeping the term with d to the left-hand side of the equation:
Now
-12d = -6 + 2
-12d = -4
d = -4/-12
d= 1/3
After solving the given equation for d, the solution of the equation is determined to be 1/3.
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David has a score of 89 for each of his first 3 math quizzes. The score on his fourth quiz is 92. What score does he need on his fifth quiz to have an average of 90?
i have to show my work btw
Answers
Answer:
91
Step-by-step explanation:
89+89+89+92+x / 5= 90
359+x / 5= 90 (multiply by 5 both sides)
359+x =450 (subtract 359 from both sides)
X= 91
Colton has a 16 ounce milk. He drinks 9 ounces. Enter the percentage of ounces Colton has left of his milk. Round your answer to the nearest hundredth..
Answers
Answer:
56.25
Step-by-step explanation:
How many types of quadrilaterals can be formed using these sticks?
Answers
You can form two different types of quadrilaterals from the given sticks of 8cm,8cm,5cm,5cm.
A quadrilateral is a polygon with four sides and four angles. Quadrilaterals are two-dimensional shapes, meaning they exist on a flat surface and have length and width, but no depth. Some examples of quadrilaterals include rectangles, squares, parallelograms, and trapezoids.
You can form two different types of quadrilaterals using four sticks of 8cm, 8cm, 5cm, and 5cm in length such as a rectangle of the two 8cm sticks as the length and the two 5cm sticks as the width to create a rectangle, and you can also form a parallelogram by using the two 8cm sticks as the length, and the other two 5cm sticks as the width.
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Your question seems incomplete, but I assume the complete question was:
"How many types of quadrilaterals can be formed using these sticks of 8cm, 8cm, 5cm, 5cm?"
11. (6 points)
Reasoning Complete the following proof by providing
the reason for each statement.
Answers
The reasons for each statement about the given triangle are as follows:
GivenIsosceles triangle theoremSASCPCT( Corresponding parts of a congruent triangles are congruent)The converse of Isosceles triangle theoremWhat are congruent triangles?Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.
Given, A triangle PWZ in that base ∠1 and ∠2 are same and the distance between W and Z from X and Y are the same where XY is the base of another triangle inside the ΔPWZ.
For ΔPWZ
We know PWZ is an isosceles triangle since its two angles are the same.
thus another ΔPXY is on the same base of ΔPWZ and also at the same distance from its point Hence, these triangles are congruent triangles.
Looking at that perspective, we can say that ∠1 and ∠2 are pairs of alternate angles and are congruent.
∠1 ≅ ∠2
The same with ∠3 and ∠4.
∠3 ≅ ∠4
Therefore, As a result, according to the ASA Theorem, the Triangles are congruent. The two angles and the side they encompass are comparable.
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For which problem situation could the equation 45x + 55x = 350 be used?
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?
A car, traveling 45 mph, leaves Dallas heading for Odessa 350 miles away. At the same time, a truck leaves Odessa for Dallas traveling 55 mph on the same road. When will the two vehicles meet?
A 350 mile telephone cable is cut so the shorter piece 45/55 is of the whole cable. How long is each piece?
A 350 mile telephone cable costs $55 per mile for one section and $45 per mile for a different section. What is the total cost of the cable?
Answers
Answer:
Step-by-step explanation:
The equation 45x + 55x = 350 could be used to solve the following problem:
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?
2/3 p + 3 p = 3/5.
]
njwtbiuerwgj
Answers
Answer:
p = 9/55
Step-by-step explanation:
2/3p + 3p = 3/5.
2/3p + 9/3p = 3/5
11/3p = 3/5
Divided both sides by 11/3
p = 9/55
If you can, please give me a Brainliest, thank you!
You deposit $200 in an account. The account earns $15 simple interest in 3 years. What is the annual interest rate?
Answers
Solution:
This graph shows how the distance Daniel runs depends on the number of track practices he attends.
Answers
The rate of change that Daniel runs depends on number of tracks, so the rate of change is 8/5 = 1.6 miles per practice.
What is rate of change?You should be aware that rate of change is the same thing as slope. In slope as y increases, x also increases. vice versa.
Daniel runs depends on the number of track practices he attends.
The rate of change (ROC) is the speed at which a variable changes over a specific period of time. ROC is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, the rate of change is represented by the slope of a line. The ROC is often illustrated by the Greek letter delta (Δ).Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
The formula for rate of change is:
R = (D2 - D1)/T
Rate of change = change in y/ change in x
= 10-2/5-0
=8/5
=1.6
In conclusion the ratio of Daniels run is 1.6
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Please give the answer as soon as possible. asap
Answers
Using the diameter given, the volume of the sphere is 14137.17cm³
What is Volume of a SphereThe volume of a sphere is a measurement of how much space it takes up. It is calculated using the following formula and represents the volume of the sphere:
v = 4/3 * π * r³
Where: r is the radius of the sphere, which is the distance from the sphere's center to its surface, and π is a mathematical constant roughly equal to 3.14.
The formula is based on the observation that a sphere's volume is two thirds that of a cylinder with the same radius and height.
The volume of a sphere is directly proportional to the cube of the radius, which is a crucial point to remember.
In the problem, the diameter given is 30cm, we can calculate the radius from this.
radius = diameter / 2
radius = 30 / 2
radius = 15cm
We can plug in the values to calculate the volume of this sphere;
v = 4/3πr³
v = 4/3(3.14)(15)³
v = 14137.17cm³
The volume is 14137.17cm³
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by making x =1/3, y= -2/5 and x=1/4 find (x *y) + z
Answers
Answer:
7/60
Step-by-step explanation:
solution
(x*y) + z
(1/3*-2/5) + 1/4
-2/15 + 1/4
LCM 60
-8 + 15/60
7/60
Answer:
7/60
Step-by-step explanation:
Looking at the numbers:
x = 1/3
y = -2/5
z = 1/4
We can simply add them into the equation:
(x × y) + z
(1/3 × -2/5) + 1/4 =?
1/3 × -2/5 ≅ -0.1333333 or [tex]\frac{-1333333}{10000000}[/tex]
-0.1333333 + 1/4 = 0.1166667 or [tex]\frac{7}{60}[/tex]
Please draw and explain in easier terms. I have an disorder. The Valley High Marching Band is selling candy bars for a fundraiser. Sierra sold some candy bars. Breanna sold twice as many candy bars as Sierra. Together Sierra and Breanna sold no less than 45 candy bars. Write an inequality to represent this situation. Give three possible solutions for how many candy bars Sierra sold.
Answers
The system of inequality of the situation is y = 2x and x + y ≥ 45 and the possible number of candy bars Sierra sold are 15, 16 and 17
How to write an inequality to represent this situation.From the question, we have the following parameters that can be used in our computation:
Sierra sold some candy bars. Breanna sold twice as many candy bars as Sierra. Together Sierra and Breanna sold no less than 45 candy bars.Represent Sierra with x and Breanna with x
Based on the readings from the question, we have the following inequalities
y = 2x
x + y ≥ 45
Three possible solutions for how many candy bars Sierra sold.Substitute y = 2x in x + y ≥ 45
So, we have
x + 2x ≥ 45
Evaluate
3x ≥ 45
Divide by 3
x ≥ 15
This means that the number of candy bars Sierra sold are at least 15
The possible numbers are 15, 16 and 17
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Dad is getting food ready for my birthday party! Including me, there will be 38 people at the party. Dad is baking cookies for us! He can bake 24 cookies per batch. How many batches should I tell Dad to make so we can each have 4 cookies?
Answers
The number of batches of cookies required for your dad to bake is 6.33 batches.
How many batches should be baked?Number of people at the party = 38
Number of cookies each would have = 4
Total number of cookies needed = Number of people at the party × Number of cookies each would have
= 152 cookies
Number of cookies baked per batch = 24
Equate the number of batches to the number of cookies baked.
Let x = number of batches required
1 : 24 = x : 152
1/24 = x / 152
cross product
1 × 152 = 24 × x
152 = 24x
divide both sides by 24
x = 152 / 24
x = 6.33 batches
Therefore, your dad should bake 6.33 batches of cookies for everyone at the party.
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I will mark you the brainliest!
30 points!
I am giving you all my points please give step by step explanation of
Co-efficient of y in - 2x ^ 2 * y ^ 2 * z is
Answers
The coefficient of y in the expression -2x² * y² * z is 0
How to determine the coefficient of y in the expressionFrom the question, we have the following parameters that can be used in our computation:
An algebraic expression
The algebraic expression is given as
- 2x ^ 2 * y ^ 2 * z
Express the exponents as proper subscripts
So, we have the following representation
-2x² * y² * z
There is no term in the expression with the variable y
Instead, the term has a y² as its variable
This means that the coefficient of y is 0
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HURRY HELP!!!
A grade-school instructor teaches math, English, and history. This year, the teacher has 100 homework papers to correct every week (one per student per class). Suppose that the math and English classes have the same number of students in them, and that the questions on each homework assignment number 10, 20, and 30, respectively. If the teacher corrects 2,100 homework questions every week, how many students are In each class?
(Hint: Use Gauss-Jordan elimination.)
Answers
There are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.
How to evaluate for the number of students for each classesWe shall derive and solve the system of equations as follows:
homework questions corrected per week;
10x + 20y + 30z = 2100...(1)
number of homework papers corrected per week;
x + y + z = 100...(2)
x = number of students in the math class
y = number of students in the English class
z = number of students in the history class.
since the maths and English classes have the same number of students then x = y and: equations (1) and (2) becomes;
10x + 20x + 30z = 2100
30x + 30z = 2100
30(x + z) = 2100 {divide through by 30}
x + z = 70...(3)
x + x + z = 100
2x + z = 100...(4)
Subtract equation (3) from (4) to eliminate z
2x + z - x - z = 100 - 70
x = 30
Now we will substitute this value of x back into the equation (4) such that;
2(30) + z = 100
60 + z = 100
z = 100 - 30 {subtract 60 from both sides}
z = 40
So there are 30 students in the Maths class, 30 students in the English class and 40 students in the history class using Gauss-Jordan elimination to solve the system of equations.
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Solve please please please
Answers
Answer:
ML = 10
Step-by-step explanation:
Given:
LN = ML + 2
JL = 15
LK = 18
We use AAA Similarity Criterion: If two triangles are equiangular, then they are similar. By equiangular, it means that the measurements of the corresponding angles of the two triangles are equal. It is also called the Angle Angle Similarity Theorem.
If lines MN and JK are parallel, then ∠LMN=∠LJK and ∠LNM=∠LKJ and hence ΔMLN∼ΔJLK. Based on the proportionality of the sides, we compose an equation and solve it:
LK/JL = LN/ML
18/15 = LN/ML
6/5 = LN/ML
Since LN = ML + 2, the equation can be written:
6/5 = (ML + 2)/ML
6/5 = 1 + 2/ML
1/5 = 2/ML
ML/5=2
ML=10
