The vector representing D = A - B has following values,
1. x- component of vector D = 9 and y- component of vector D = 9.
2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.
Here, Vector D= A-B __(1)
Components of vector A are,
Ax=5
Ay=5
Components of vector B are,
Bx= -4,
By= -4
1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,
Dx = Ax - Bx
= 5 - (-4)
= 5 + 4
= 9
Dy = Ay - By
= 5 - (-4)
= 5 + 4
= 9
2. Magnitude of vector D, use the Pythagorean theorem,
|D| = √(Dx² + Dy²)
= √(9² + 9²)
= √(162)
≈ 12.73
Direction of vector D, use trigonometry.
Angle θ represents vector D makes angle with positive x-axis is ,
θ = tan⁻¹(Dy / Dx)
= tan⁻¹(9 / 9)
= tan⁻¹(1)
= 45°
Therefore, required value of the vectors are,
1. x- and y-components of vector D are 9 and 9, respectively.
2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.
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The above question is incomplete , the complete question is:
Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.
1. What are the x- and y- components of vector D?
2. What are the magnitude and direction of vector D?
Identify a variable inequality that describes the problem situation. Select the correct answer for each part of the equation.
Vigo earned $127.50 by washing driveways. He spent $70.35 on a new game console controller and then wanted to buy frozen meals that cost $5.99 each. How many frozen meals (x) could he buy while spending no more than his earnings? Also ty if you answer this I appreciate it <3
Answer: 57.15[tex]\geq[/tex] 5.99x
Step-by-step explanation:
127.5-70.35[tex]\geq \\[/tex]x
57.15[tex]\geq[/tex] 5.99x
The rectangular floor of a classroom is 32 feet in length and 34 feet in width. A scale drawing of the floor has a length of 16 inches. What is the perimeter, in inches, of the floor in the scale drawing?
As a result, the floor's perimeter in the size illustration is 38,016 inches.
In maths, what is perimeter?The perimeter of an object is the space surrounding its border. Find the perimeter of different forms by combining the lengths of their sides.
We can start by finding the scale factor that relates the length of the actual floor to the length of the scale drawing.
The length of the actual floor is 32 feet = 384 inches (since there are 12 inches in a foot).
The length of the scale drawing is given as 16 inches.
Therefore, the scale factor is:
384 inches / 16 inches = 24
This means that one inch on the scale drawing represents 24 inches in the actual floor.
To find the perimeter of the floor in the scale drawing, we need to multiply the perimeter of the actual floor by the scale factor.
The perimeter of the actual floor is:
2(32 feet) + 2(34 feet) = 64 feet + 68 feet = 132 feet
Converting to inches, we get:
132 feet x 12 inches/foot = 1584 inches
Multiplying by the scale factor of 24, we get:
1584 inches x 24 = 38,016 inches
Therefore, the perimeter of the floor in the scale drawing is 38,016 inches.
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3.8% of 25. Show your work
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.8\% of 25}}{\left( \cfrac{3.8}{100} \right)25}\implies \text{\LARGE 0.95}[/tex]
Answer:
To find 3.8% of 25, we can convert the percentage to a decimal and then multiply it by 25:
3.8% = 0.038 (converting percentage to decimal)
0.038 x 25 = 0.95
Therefore, 3.8% of 25 is 0.95.
What is 2625/21 please iv been stuck on this for 3 hours bro
In a survey of 200 pet owners in Kathleen's state, the average number of pets per household
was estimated to be 2.75. Using these survey results, Kathleen predicted that about
49,500 pets, in total, would live in 18,000 households in her state. Why is her prediction
flawed? How could she modify her prediction to make it more accurate?
To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations.
Where is Kathleen mistaken?Kathleen's prediction is flawed because she assumed that the average number of pets per household would remain the same for all households in the state, which may not necessarily be true. The sample size of 200 households may not be representative of the entire population of households in the state, and there may be variations in the number of pets per household across different regions or socioeconomic groups.
To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations. Alternatively, she could use data from existing sources, such as census data, to estimate the number of pets per household in different regions of the state and adjust her prediction accordingly. It's also worth noting that factors such as pet ownership trends, cultural attitudes towards pets, and population growth may also impact the accuracy of Kathleen's prediction and should be taken into account.
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Triangle ABC is similar to triangle DEF. The length of BC¯¯¯¯¯ is 44 cm. The length of DE¯¯¯¯¯ is 14 cm. The length of EF¯¯¯¯¯ is 22 cm.
What is the length of AB¯¯¯¯¯?
Enter your answer in the box.
Answer:
28cm
Step-by-step explanation:
[tex] \frac{44}{22} \times 14 = 28[/tex]
WILL MARK BRAINLEST JUST PLEASE ANSWER.
Answer: X=10
m<UXV = 46 degrees
Step-by-step explanation:
Angle WXV is 90 degrees, We know this because Angle VXY is 90 degrees, so it is the same on the other side Angle WXV is split into two angles (WXU, and UXV) to find UXV we subtract 44 from 90, which is 46 Degrees, Now we know 5x-4 is equal to 46, 46+4 is 50, 50/5 is 10, so x is 10
The value of x is, 10
And, The value of angle ∠ UXV is, 46°
Given that;
Angle 44° and ∠ UVX is made a right angle.
Hence, We can formulate;
⇒ 44° + ∠ UVX = 90°
⇒ 44° + (5x - 4)° = 90°
⇒ 44 + 5x - 4 = 90
⇒ 5x + 40 = 90
⇒ 5x = 90 - 40
⇒ 5x = 50
⇒ x = 10
Hence, The value of angle ∠ UXV is,
⇒ ∠ UXV = 5x - 4
= 5 × 10 - 4
= 50 - 4
= 46°
Thus, The value of x is, 10
And, The value of angle ∠ UXV is, 46°
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ALGEBRAIC EXPRESSIONS AND EQUATIONS Solving a linear equation with several occ Solve for w -3(w-1)=-5w+1 Simplify your answer as much as possible. w
To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:
Step 1: Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1
Step 2: Combine like terms on both sides of the equation:
2w = -2
Step 3: Solve for w by dividing both sides of the equation by 2:
w = -1
Therefore, the solution for w is -1.
In HTML format, the answer would be:
<p>To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:</p>
<ol>
<li>Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1</li>
<li>Combine like terms on both sides of the equation:
2w = -2</li>
<li>Solve for w by dividing both sides of the equation by 2:
w = -1</li>
</ol>
<p>Therefore, the solution for w is -1.</p>
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Det - Given the vector ū = (-1,5), find the magnitude and angle in which the vector points (measured counterclockwise from the positive x-axis, 0
The magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.
The magnitude of a vector is the length of the vector, and is calculated using the Pythagorean Theorem. The angle of a vector is the direction in which the vector points, measured counterclockwise from the positive x-axis.
To find the magnitude of the vector ū = (-1,5), we can use the formula:
magnitude = √(x^2 + y^2)
where x and y are the components of the vector.
Plugging in the values of x and y from the vector ū, we get:
magnitude = √((-1)^2 + (5)^2)
Simplifying the expression, we get:
magnitude = √(1 + 25)
magnitude = √(26)
magnitude ≈ 5.10
To find the angle of the vector, we can use the formula:
angle = tan^-1(y/x)
Plugging in the values of x and y from the vector ū, we get:
angle = tan^-1(5/-1)
angle = tan^-1(-5)
angle ≈ -78.69°
Since the angle is measured counterclockwise from the positive x-axis, we need to add 360° to get the angle in the correct quadrant:
angle = -78.69° + 360°
angle = 281.31°
Therefore, the magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.
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Can someone please help me with this? I need help ASAP. Due today!!
Answer:
2*(8*8*3+15*15*3)
Step-by-step explanation:
Small cube V=8*8*3
Large cube V=15*15*3
Doubled height is double of each cube V
so 2*[(8*8*3)+(15*15*3)]
There are 6
red gumballs, 6
blue gumballs, 6
yellow gumballs, 6
green gumballs, and 6
purple gumballs in a gumball machine. If a student randomly selects 1
gumball from the machine, what is the probability that the student selects a red gumball?
Step-by-step explanation:
red gumballs=6 blue gumballs=6
yellow gumballs=6 green gumballs=6
purple gumballs=6
total number of gumballs=30
probability of a student selecting a red gumballs
no of red gumballs 6 1
=------------------------ = ----- = -----
no of total gumballs 30 5
Express (x+10)^2 as a trinominal in standard form
Answer:
x^2 + 10x + 20
Step-by-step explanation: When you multiply binomials, you are practically taking each term and multiplying it with others until you are out of combinations. However, when the product is represented in standard form, it requires the terms to be set within a specific order that prompts the term at the highest order/power placed on the furthest left side of the expression. The first term x^2 can be referred to as a term of the second power, 10x is seen as one to the first power (x^1 = 1st), and 20 as 0, since it is a constant.
If the length of a rectangle is x ^ 2 + 3y and the width is x ^ 2 - 3y , write an expression to represent the area
Answer: x⁴ - 9y²
Step-by-step explanation:
The area of a rectangle is length x width so...
Area = (x² + 3y)(x² - 3y)
Simplify:
Area = x⁴ + 3yx² - 3yx² - 9y²
Area = x⁴ - 9y²
Hope this helps!
PLEASE HELP ASAP I WILL GIVE BRAINLIST!
A group of students are interested in creating a life-sized version of a Rubik's Cube, but they want to determine how much paint they will need to cover the entire cube. Their teacher tells them that, compared to an actual Rubik's Cube, their blocks have a scale factor of k=4.5
. In feet, what is the surface area of their Rubik's Cube?
Answer:
Step-by-step explanation:
OK so i'm not really good at this my self but i'll try my best to help you because I don't really do it for the points I do it because I like to help other people. OK so their blocks have a scale factor of k=4.5. OK so I don't know if this is right but what I would do is there are 8 sides to any cube and you have a scale factor of k=4.5 so I would multiply 4.5 and 8 to get a answer of 36ft.
A zipline cable is attached to two platforms 1000 ft apart at an angle of depression from the taller platform of 12°. What is the length of the cable, rounded to the nearest foot? 1000 ft 20 ft
Answer:
We can use trigonometry to solve this problem.
A is the taller platform, B is the shorter platform, and x is the length of the zipline cable that we want to find.
We can see that the angle between the horizontal and the zipline cable is 12 degrees, so we can use the tangent function to find x:
Therefore, the length of the zipline cable, rounded to the nearest foot, is 209 ft.
At a religious gathering there were 560 persons present . For every 4 adults , there were 3 children 4/5 of the children were boys . How many more boys were there than girls
The religious gathering has 144 more boys than girls.
How to calculate the number of people?First we need to find out how many people and kids are attending the event.
There were 3 kids for every 4 adults. Thus we have to divide the total gathering number by the sum of their ratios which is 4 + 3 = 7
Adult population=> (4/7) x 560 = 320
Children's number=> 560-320 = 240
We know that every 4/5 children is a boy
Thus,
Number of boys: (4/5) * 240 = 192
By deducting the number of boys from the total number of children, we can calculate the number of girls which is
240-192= 48
There are 192 boys and 48 girls
The number of more boys than girls is -
192 - 48 = 144
Therefore, the religious gathering had 144 more boys than girls.
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(Please answer quickly!!!)Simplify negative 4 and 2 over 3 minus 7 and 3 over 4.
3 and 1 over 2 negative 11 and 1 over 12 negative 12 and 5 over 12 negative 28 and 1 over 2
The simplified expression is -12 and 5/12
What is expression ?In mathematics, an expression is a combination of symbols and/or numbers that can be evaluated or simplified to produce a certain value. Expressions can contain variables, constants, operators, and functions, and can be written in a variety of forms, such as algebraic expressions, trigonometric expressions, and exponential expressions.
According to given information :Negative 4 and 2 over 3 can be written as -(4 x 3 + 2) / 3 = -14 / 3
7 and 3 over 4 can be written as 7 x 4 + 3 / 4 = 31 / 4
Next, you need to find a common denominator for the two fractions, which is 12. To convert -14/3 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 4, giving you -56/12. To convert 31/4 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 3, giving you 93/12.
Finally, you can subtract the two fractions by subtracting their numerators and keeping the denominator the same:
(-56/12) - (93/12) = -149/12
To convert this improper fraction back to a mixed number, you can divide the numerator by the denominator and get a quotient of -12 with a remainder of -5.
Therefore, the simplified expression is -12 and 5/12 or -12.41667 (rounded to five decimal places).
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Shaq shot 420 baskets in 14 minutes. Find his basket rate in baskets per minute.
Answer:
30 baskets per minute
Step-by-step explanation:
We know
Shaq shot 420 baskets in 14 minutes.
Find his basket rate in baskets per minute.
We take
420 / 14 = 30 baskets per minute
So, the answer is 30 baskets per minute.
Peter's parents ollow a regular schedule for taking care of their car.they change the plugs every 30 000km,rotate the tyres every 10 000 km,and replace the brake pads blades every 15 000 km.fter how many kilometers will they first have to change the plugs,rotate the tyres,and replace the brake pads all at once for the first time
They will have to change the plugs, rotate the tyre, and replace the brake pads all at once for the first time after 30,000 km.
What is LCM?LCM is the abbreviated form for Least Common Multiple. LCM of two or more numbers is the lowest of all the common multiples of them.
Given,
Plugs are changed every 30,000 km
Rotate the tyres every 10,000 km
Replace the break pads blades every 15,000 km
All the three will be done together for the first time when all the multiples of the three distances intersect for the first time.
It is enough to find the LCM of 30000, 10000 and 15000 to find the least distance travelled when all the things are done together.
Multiples of 30,000 = 30000, 60000, 90000, ...........
Multiples of 10,000 = 10000, 20000, 30000, .......
Multiples of 15,000 = 15000, 30000, 45000, ........
The common multiple for the first time is 30,000.
Hence all the changes will be made to the car together for the first time after 30,000 km.
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All help is appreciated this is due RLLY SOON HAHAH :D
The difference in the medians is ___ times the IQR
Answer:
1/3
Step-by-step explanation:
You want the difference in medians in terms of the IQR.
IQRThe IQR is the difference of the numbers at the ends of the box.
top distribution: IQR = 12 -6 = 6
bottom distribution: IQR = 14 -8 = 6
MediansThe median of each distribution is the location of the line in the box.
top distribution: median = 11
bottom distribution: median = 9
DifferenceThe difference in medians is 11 -9 = 2. The ratio of that to the IQR is ...
2/6 = 1/3
The difference in medians is 1/3 times the IQR.
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Suppose the chemist divided up the total amount of water so that all 8 beakers
held the same amount.
How much water would each beaker hold?
Show how you know.
The amount of water each beaker would hold is x/8
How much water would each beaker hold?From the question, we have the following parameters that can be used in our computation:
Number of beakers = 8
Represent the size with x
So, we have the following quotient expression
Size of each beaker = x/Number of beakers
Substitute the known values in the above equation, so, we have the following representation
Size of each beaker = x/8
Hence, the amount is x/8
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(b) Given a = [2,3,6x], b = [4,2 − x,3], and c = [−1,3,−7], (i) find the unit vectors d in terms of x that are perpendicular to both a and b; (ii) deter- mine the value(s) of x such that d × c has the maximum length. (Please leave your answer in surd form)
(i) The unit vector d that is perpendicular to both a and b is d = (1/|d|) *
[tex][6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]
[tex]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]
2) Value of [tex]X[/tex]
[tex]Xd|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]
It can be found by taking the cross product of a and b, and then dividing by the magnitude of the resulting vector. The cross product of a and b is given by:
[tex]d = a × b = [(3)(3) - (6x)(2-x), (6x)(4) - (2)(3), (2)(2-x) - (3)(4)]= [9 - 12x + 6x^2, 24x - 6, 4 - 2x - 12]= [6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]
The magnitude of d is given by:
[tex]|d| = √((6x^2 - 12x + 9)^2 + (24x - 6)^2 + (-2x - 8)^2)= √(36x^4 - 144x^3 + 216x^2 - 144x + 81 + 576x^2 - 288x + 36 + 4x^2 + 32x + 64)= √(36x^4 - 144x^3 + 796x^2 - 400x + 181)[/tex]
The unit vector d is then given by:
[tex]d = (1/|d|) * [6x^2 - 12x + 9, 24x - 6, -2x - 8]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]
(ii) To find the value(s) of x such that d × c has the maximum length, we can take the cross product of d and c and find the magnitude of the resulting vector. The cross product of d and c is given by:
[tex]d × c = [((24x - 6)(-7) - (-2x - 8)(3)), ((-2x - 8)(-1) - (6x^2 - 12x + 9)(-7)), ((6x^2 - 12x + 9)(3) - (24x - 6)(-1))]= [-168x + 42 + 6x + 24, 2x + 8 + 42x^2 - 84x + 63, 18x^2 - 36x + 27 + 24x - 6]= [-162x + 66, 42x^2 - 82x + 71, 18x^2 - 12x + 21][/tex]
The magnitude of d × c is given by:
[tex]|d × c| = √((-162x + 66)^2 + (42x^2 - 82x + 71)^2 + (18x^2 - 12x + 21)^2)= √(26244x^2 - 21384x + 4356 + 1764x^4 - 6964x^3 + 5988x^2 - 5834x + 5041 + 324x^4 - 432x^3 + 756x^2 - 252x + 441)= √(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848)[/tex]
To find the maximum length of d × c, we can take the derivative of |d × c| with respect to x and set it equal to 0:
[tex]d|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]
Solving for x gives the value(s) of x that maximize the length of d × c. This can be done using a numerical method or by finding the roots of the polynomial in the numerator.
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Use transformations of f(x)=x^(2) to gra h(x)=(x-5)^(2)+2 Use the grapning tool to grapn the runc
To graph the function h(x) = (x - 5)² + 2, we can use transformations of the function f(x) = x².
What a graph of a function represents?A graph of a function is a visual representation of how the output of the function relates to its input.
First, we need to shift the graph of f(x) 5 units to the left, which can be done by subtracting 5 from x in the function:
h(x) = (x - 5)² + 2 = (x - 5)² + 2.
Then, we need to shift the graph of f(x) 2 units up, which can be done by adding 2 to the function: h(x) = (x - 5)² + 2.
Using a graphing tool, you can then plot the points of h(x) to graph it.
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Thomas is putting in a tile floor. He needs to determine the angles that should be cut in the tiles to fit in the corner. The angle in the corner measures 90°. One piece of the tile will have a measure of 24°. Write an equation, and use it to determine the measure of the unknown angle.
The equation can be written as: x + 24° = 90°.
The measure of the unknown angle is 66°.
How to write an equation, and use it to determine the measure of the unknown angle?An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Let the measure of the unknown angle be x.
Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:
x + 24° = 90°
The measure of the unknown angle can be determined as follow:
x + 24° = 90°
x = 90° - 24°
x = 66°
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Solve the system \[ \left\{\begin{array}{rrr} x_{1}+x_{2}+3 x_{3}= & -4 \\ 4 x_{1}+5 x_{2}+5 x_{3}= & 9 \end{array}\right. \] \[ \left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]=[-[]+
x1 = -2, x2 = 1, and x3 = 5.5
This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:
4x1 + 5x2 + 5x3 = 9
- (x1 + x2 + 3x3 = -4)
3x1 + 4x2 + 2x3 = 13
Next, isolate one of the variables. In this case, let's isolate x3:
3x1 + 4x2 + 2x3 = 13
- (2x3) - (-2x3) = 0
3x1 + 4x2 = 13
x3 = \frac{13 - (3x1 + 4x2)}{2}
Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:
x3 = \frac{13 - (3x1 + 4x2)}{2}
x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4
Solve for x2:
x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}
Substitute this expression for x2 into one of the original equations and solve for x1:
x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4
Solve for x1 and then plug this value back into the expression for x2 to find x2:
x1 = -2
x2 = 1
x3 = \frac{13 - (-2 + 4x2)}{2}
x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}
x3 = \frac{13 - 2}{2}
x3 = 5.5
Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.
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Based on the caterer’s experience, 38% of attendees to events will prefer chicken for the main dish. As the caterer plans for an event attended by 780 individuals, the normal approximation will be used for the binomial with a correction for continuity. In this case, what is the standard deviation of the number that she would expect to prefer chicken, when determining the probability that at less than 300 will prefer chicken? Round your answer to 1 decimal place, e.g. 125.7
Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.
what is standard deviation ?The degree of variation or dispersion in a set of data is measured by standard deviation. It calculates how far the data points, on average, deviate from the mean (average) of the data collection. Finding the square root of the data's variation yields the standard deviation. In statistics, the standard deviation is frequently used to characterise the distribution of data and is significant in areas like science, finance, and economics. It can be used to assess the validity of statistical data and to contrast different groups of data.
given
The following formula must be used to determine the standard deviation of attendees who would favour chicken as the main course:
σ = √(np(1-p))
When we change the numbers, we obtain:
σ = √(780 x 0.38 x 0.62) (780 x 0.38 x 0.62)
σ = √(182.616) (182.616)
σ = 13.509
Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.
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Alex goes to a movie on Saturday for $10. While there, he pays $3 for each item he buys at the concession stand.
Which equation best represents this information?
y = 10x + 3
y = 3x - 10
y = 3x + 10
y = 10x - 3
Answer:
y = 3x + 10
Step-by-step explanation:
y represents total he pays
x represents items he buys
total he pays = $3 for each item + $10 movie
y = 3x + 10
I need help figuring out this question
Answer:
(4[tex]x^{2}[/tex]+2)([tex]x^{2}[/tex]-3)
Step-by-step explanation:
4x +2
x -3
uiz Instructions Question 4 How many solutions are possible when you solve this system of equations? 2x+y=7 y=-2x+7
There is only one solution when you solve the system of equations 2x+y=7 and y=-2x+7. The one solutions is (2, 3).
To find the solution, you can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation.
First, solve the second equation for y:
y = -2x + 7
Now, substitute this expression for y into the first equation:
2x + (-2x + 7) = 7
Simplify the equation:
2x - 2x + 7 = 7
Combine like terms:
7 = 7
This equation is always true, which means that there is only one solution for this system of equations. The solution is the point where the two lines intersect, which is (2, 3).
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