The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the step that is the part of the process of algebraically solving the given system of equations:
That would be:
(C) 4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substituted for y).
Proof:
y + 5x = x² + 10(4x - 10) + 5x = x² + 104x - 10 = x² -5x + 10(E) 0 = x2 – 9x + 20 (liked terms are grouped and simplified).
Proof:
4x - 10 = x² -5x + 104x = x² -5x + 10 + 100 = x² -5x -4x + 200 = x² - 9x + 20Solving:
x² - 9x + 20 = 0 x² - 5x - 4x + 20 = 0(x - 5) (x - 4) = 0x = 4 (as question says) OR x = 5Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.
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The complete question is given below:
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.
(A) y = x2 + 5x + 10
(B) y + 5x = x2 + 10 + 4x – 10
(C) 4x – 10 = x2 – 5x + 10
(D) 0 = x2 – 9x
(E) 0 = x2 – 9x + 20
(F) One x-value of a solution to the system is 4.
1. 3k − 8 = 7
2. 8b + 9 = −15
3. 8 = 3x − 13
4. 6p + 22 = 4
5. 84 = 51 + 11c
Add 8 to both sides.
3k = 7 + 8Add 7 and 8 to get 15.
3k = 15Divide both sides by 3.
k = 15 / 3Divide 15 by 3 to get 5.
k=5 ===> Answer===> Exercise 28b + 9 = −15
Subtract 9 from both sides.
8b= −15 − 9Subtract 9 from −15 to get −24.
8b = −24Divide both sides by 8.
b = -24 / 3Divide −24 entre 8 para obtener −3.
b=−3 ===> Answer===> Exercise 38 = 3x − 13
Swap the sides so that all the terms of the variables are on the left side.
3x −13 = 8Add 13 to both sides.
3x = 8 + 13Add 8 and 13 to get 21.
3x = 21Divide both sides by 3.
x = 21 / 3Divide 21 by 3 to get 7.
x = 7 ===> Answer===> Exercise 46p + 22 = 4
Subtract 22 from both sides.
6p = 4 − 22Subtract 22 from 4 to get −18.
6p = −18Divide both sides by 6.
p = -18 / 6Divide −18 entre 6 para obtener −3.
p = −3 ===> Answer===> Excercise 584 = 51 + 11c
Swap the sides so that all the terms of the variables are on the left side.
51 + 11c = 84Subtract 51 from both sides.
11c = 84 − 51Subtract 51 from 84 to get 33.
11c = 33Divide both sides by 11.
c = 33 / 11Divide 33 by 11 to get 3.
c = 3 ===> AnswerSolution 1 :-
>> 3k - 8 = 7
>> 3k = 7 + 8
>> 3k = 15
>> k = 15 / 3
>> k = 5
Solution 2 :-
>> 8b + 9 = -15
>> 8b = -15 - 9
>> 8b = -24
>> b = -24 / 8
>> b = -3
Solution 3 :-
>> 8 = 3x - 13
>> 3x = 13 + 8
>> 3x = 21
>> x = 21 / 3
>> x = 7
Solution 4 :-
>> 6p + 22 = 4
>> 6p = 4 - 22
>> 6p = -18
>> p = -18 / 6
>> p = -3
Solution 5 :-
>> 84 = 51 + 11c
>> 11c = 84 - 51
>> 11c = 33
>> c = 33 / 11
>> c = 3
30 POINTSS ABD BRAINLIEST !! Let p be a prime number. Circle one expression below which could also be a prime number.
2p 7p p - 4 p squared
Give a reason for your answer above
Answer:
p - 4
Step-by-step explanation:
Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.
Let p = 7.
2p = 2*7 = 14 14 = 1*2*7*14
7p = 7*7 = 49 49 = 1*7*49
p - 4 = 7 - 4 = 3 3 = 1*3
p^2 = 7^2 = 49 49 = 1*7*49
Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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Find using appropriate Properties:
6/7 x -2/3 + 3/5 + 5/8 x -6/7
The simplified form of the expression is given as 83x/56 -(97/105)
Finding the value of unknown variablesAlphabets are usually represented as unknown variables in a equation or expression.
Given the following expression shown below
6/7 x -2/3 + 3/5 + 5/8 x -6/7
Collect the like terms to have;
6/7 x+ 5/8 x -2/3 + 3/5 -6/7
Simplify
48x+35x/56 - (70-63 + 90)/105
The final expression will be given as;
83x/56 -(97/105)
Hence the simplified form of the expression is given as 83x/56 -(97/105)
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The area of a painting is 4081 c m squared.
If the width of the painting is 53 cm, what is its length, in centimeters?
Type your numerical answer below (without units). If necessary, round to the nearest integer.
Answer:
49,2
Step-by-step explanation:
i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length
The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.
The area of a rectangle is the product of the length and width of the same rectangle.
Given that:
The area of the painting, A = 4081 cm².
The width of the painting, b = 53 cm.
To find the length of the painting, use the following formula to obtain the area of the rectangle:
Area = length × breadth
Let the length of the painting is l, then
A = l × b
4081 = l × 53
l = [tex]\frac{4081}{53}[/tex]
l = 77
Thus, the length of the painting is 77 cm.
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Solve the following systems of equations algebraically:
[tex]\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.[/tex]
The value of x in the system of equation is 6
How to solve the system of equations?The system of equations is given as:
y = 1/2 * 2^x
y = 5x + 2
Substitute y = 1/2 * 2^x in y = 5x + 2
1/2 * 2^x = 5x + 2
Multiply through by 2
2^x = 10x + 4
Next, we use the trial by error.
Set x = 6
This gives
2^6 = 10 * 6 + 4
Evaluate the product and the exponent
64 = 60 + 4
Evaluate the sum
64 = 64
Hence, the value of x in the system of equation is 6
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the senior class was going on a field trip to disneyland. A total of 350 student went on the trip. they filled seven busses . how many student were on each bus
Answer:
50 ^^
Step-by-step explanation:
So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7
7x2=14
7x3=21
7x4=28
7x5=35
So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50
need more explaining tell me ^^
Sandy jogs 19.7 miles in 4.5 hours. How many miles does she jog per hour
Answer:
4.378 MPH
Step-by-step explanation:
Distance in Miles
MPH= -------------------------
Time in Hours
19.7/4.5 = 4.378 MPH
How do I solve it I am running low on time it says it wrong don’t know
x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.
Solve the inequality:The inequality can be solved as the same way as we solve an algebraic equation.
Combine the terms with variables to one side and constants to other side.To multiply the whole inequality with negative terms we reverse the sign of the inequality.Here in the question the inequality to be solved is given:
- 3x + 7 < 4
By subtracting 7 from both sides of the inequality we get,
⇒ - 3x + 7 - 7 < 4 - 7
⇒ - 3x < - 3
To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,
we get,
⇒ 3 x > 3
Now finally by dividing the whole inequality by 3 we get,
⇒ x > 1
The number line representation can be done by marking values from 1 to numbers greater than 1.
Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.
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Omar recorded the number of hours he worked each week for a year. below is a random sample that he took from his data. 13, 17, 9, 21 what is the standard deviation for the data? standard deviation: s = startroot startfraction (x 1 minus x overbar) squared (x 2 minus x overbar) squared ellipsis (x n minus x overbar) squared over n minus 1 endfraction endroot.
The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 4.47.
How to estimate the standard deviation?Given data set: 13 17 9 21
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]
Mean [tex]$=\frac{60}{4} \\[/tex]
Mean = 15
To find the difference of each data point from the mean as:
Deviation:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
Now we have to square the above deviations we obtain:
4, 4, 36, 36
To estimate the variance of the above sets:
variance [tex]$=\frac{4+4+36+36}{4}$[/tex]
Variance [tex]$=\frac{80}{4}$[/tex]
Variance = 20
The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].
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Answer:
4.4
Step-by-step explanation:
The answer above is correct.
What is the end behavior of the function f(x)=12x2?
dis i know functiin of fx is ♾
Answer:
4th option
Step-by-step explanation:
the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )
f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then
• even degree and positive leading coefficient
f(x) → +∞ as x → + ∞ and
f(x) → + ∞ as x → - ∞
My family was so excited to see the new movie, Thor: Love and Thunder. I decided to go and take my
two boys and four of their friends. The adult ticket price was $11.00 and only 3 of the kids were able to
get the children's ticket price. If the total bill was $62.00, how much was each children's ticket?
Answer:$6
Step-by-step explanation:
If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44
62-44=18
18/3=6
$6 per child ticket
Simplify the expression below
Answer:
C
Step-by-step explanation:
4 is a perfect square. 2 x 2. You can pull the 2 out and everything else would be left under the square root symbol.
What is the value of x to the nearest tenth? The figure is not drawn to scale
Answer:
x=10.5
Step-by-step explanation:
if the two triangles were ratios it would be like
19.3:7.2 to x:3.9
so 75.27 = 7.2x
whcih is 10.45 which is approximately 10.5
Highest Common Factor of 27 and 36.
Answer:
9
Step-by-step explanation:
listing the factors
27 : 1, 3, 9, 27
36 : 1, 2, 3, 4, 9, 12, 18, 36
the common factors are 1, 3, 9
the highest common factor is 9
Hi :)
The highest common factor is also known as the HCF
———————Let's find the HCF of [tex]\boldsymbol{27}[/tex] and [tex]\boldsymbol{36}[/tex].
[tex]\boldsymbol{Factors\:of\:27: 1, 3, 9, 27}[/tex]
[tex]\boldsymbol{Factors\:of\:36:1,2,3,4,6,9,12,18,36}[/tex]
HCF : [tex]\boldsymbol{9}[/tex]
[tex]\tt{Learn\:More;Work\;Harder}[/tex]
:)
Select the correct answer.
Find the inverse of function f.
f(c) = 9x + 7
Answer:
B.) f⁻¹(x) = (1/9)x - 7/9
Step-by-step explanation:
Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.
f(x) = 9x + 7 <----- Original function
y = 9x + 7 <----- Substitute f(x) for "y"
x = 9y + 7 <----- Swap variable positions
x - 7 = 9y <----- Subtract 7 from both sides
(x - 7) / 9 = y <----- Divide both sides by 9
(1/9)x - 7/9 = y <----- Divide each term individually by 9
The inverse function is represented by the symbol f⁻¹(x).
Lauren has an above-ground pool. to keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. when the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? use π = 3.14
1885.5 m^3 of water will fill the container.
To find how many cubic feet of water will it contain:
Given -
Lauren has an above-ground swimming pool. The water level in the pool must be 4 inches above the pool's surface in order for the skimmer to function properly. π = 3.14The pool comprises a 12-foot-radius cylinder with a height of 4.5 feet.
Height of pool = 4.5 ftRadius of pool = 12 ftThe height of the water is 4 inches below the pool top12 inches make 1 ft4 inches = 4/12 ft = 0.33 ftTherefore, height of water = 4.5 - 0.33 = 4.17 ftThe volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed.
The volume of the cylinder formed by the water = volume of water = [tex]\pi r^{2} h[/tex]volume = 3.14 x [tex]12^{2}[/tex] x 4.17 = 1885.5 m^3 of waterTherefore, 1885.5 m^3 of water will fill the container.
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The complete question is given below:
Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14
A cylinder with a radius of 12 feet and a height of 4.5 feet.
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm.which expression represents the volume of the pyramid?(5.2)h cm3(5.2)h cm3(5.2)h cm3(5.2)h cm3
volume of pyramid = 1/3(5.2)h cm3
What is a Prism?Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.
we know that,
The volume of the pyramid is equal to
volume = (1/3) × base area × height
we have height = h cm
area of base = 5.2 cm^2
substitute in the formula
v = 1/3 × 5.2 × h
volume = 1.73h cm^3
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Which type of professional would help the government
determine where to set the price of oranges for U.S.
markets?
O Consumers
O Economists
O Exporters
O Importers
Answer:
Step-by-step explanation:
The answer is Economists
Answer: economists
Step-by-step explanation: got it right
Which of the following expressions can be used to find the area of a square with a side length of m?
The answer is A = m².
We know the general formula for finding the area of a square is :
Area = side²
Now, we are given the side is equal to m.
Hence, the expression which can be used to find the area is :
A = m²
Sarah needs 10 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.50. How much will the fabric cost?
[1 ft = 0.305 m]
Answer:
$4.58
Step-by-step explanation:
Lets convert 10 feet to meters.
1 ft = 0.305m
10ft = 0.305 * 10
10ft = 3.05m
Now we will work out the cost of the fabric.
Given 1m = $1.50
3.05m = 3.05 * $1.50 = $4.58 (nearest cent)
Den pushes a desk 400 cm across the floor. he exerts a force of 10 n for 8 s to move the desk. what is his power output? (power: p = w/t)
The power output is = 5W
Correct option is B.
What is Power ?Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power
Power is characterized as the rate at which a thing performs labor.
According to the given information:P = W/T ..... (1)
Work is calculated as the product of force applied to an item and the distance that object has traveled.
W = F.s
When we plug this value into the equation above, we get:
P = (F. s)/t
where,
power = P =?W
F = 10N Force Exercised
s = Displacement = 400cm = 4m (1 meter = 100 centimeters).
t = Time required = 8s
Using the values in the equation above, we obtain
P = (10 x 4)/8
P = 5W
Hence, the correct option is Option b.
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I understand that the question you are looking for is :
Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.
What is his power output? (Power: P = W/t)
a. 1.25 W
b. 5 W
c. 40 W
d.500 W
Austin is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional, Austin wants to deterrine, for workers in the tech Industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan Austin surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. For the workers with an Unlimited plan, the sample mean is 18.9 with a sample variance of 30.8. For the workers with a Traditional plan, the sample mean is 17.4 with a sample variance of 6.1 Assume that the two populations of vacation days taken are approximately normally distributed. Can Austin conclude, at the 0.10 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-talled test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, (If necessary, consult a list of formulas.) (*) State the null hypothesis and the alternate hypothesis (a) Determine the type of test statistic to use (a) state the null hypothesis H, and the alternate hypothesis (b) Determine the type of test statistic to use. (c) Find the value of the test statistic (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places) (e) At the 0.10 level of significance, can Austin conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan?
The question requires that we have to state the hypothesis:
null hypothesis;H0: u1 < u2, the alternate hypothesis;H1: u1 > u2. The one tail test is what is to be used.
A. How to state the hypothesisH0: u1 < u2
H1: u1 > u2
The one tail test statistic is what is to be used here
B. standard error[tex]\sqrt{\frac{30.8}{17} +\frac{6.1}{15} }[/tex]
= 1.49
The df = 17 + 15 - 2
= 30
test statistic = 18.9 - 17.4 / 1.49
= 1.007
We have the critical value on excel as T.INV(0.9,30)
= 1.310
E. At 0.1, we can conclude that t-value (1.007) does not lies in the rejection area. We fail to reject the null hypothesis. Hence we conclude that the mean vacation with the unlimited plan is greater.
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A semi-circle window can be used above a doorway or as an accent window
in a room to allow more light in large rooms. The semi-circle window in your
home theater room lets too much light in so that the movie experience is not
optimal at any time of the day.
You research and find there are “room darkening” blinds and shades for
semi-circle windows. You can’t quite reach the semi-circle window to
measure but you are able to measure the window beneath. The height of the
rectangle window below is 85 in and the width of the window below the semi-circle is 50 in.
What is the area of the semi-circle window so that you can start your search for the correct size?
Be sure to show and explain your work.
A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].
A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.
A semicircle is a part of a circle, and it is referred to as half of a given circle.
such that:
Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]
and
area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].
Thus from the given question, it can be inferred that;
r = [tex]\frac{50}{2}[/tex]
= 25
r = 25 in
Thus, the area of the semi-circle can be determined as;
area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]
= 982.1429
area of the semi-circle = 982.14 [tex]in^{2}[/tex]
The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].
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If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located?
The distance from the center to where the foci is located is 8 units
How to determine the distanceThe formula associated with the focus of an ellipse is given as;
c² = a² − b²
where;
c is the distance from the focus to center a is the distance from the center to a vertex , major axis is 10 units b is the distance from the center to a co-vertex, minor axis is 6 unitsLet's use the Pythagorean theorem
Hypotenuse square = opposite square + adjacent square
Substitute the values into the formula
c² = 10² - 6²
Find the square
c² = 100 - 36
c² = 64
Find the square root
c = √64
c = 8
Thus, the distance from the center to where the foci is located is 8 units
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what do I check off
Answer:
E. >
Because 65 is greater than 56.
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.
The domain is the water balloon's height increasing will be (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.
What is a slope?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run or horizontal change.Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates. Find the difference between these two points' x-coordinates. Subtract the difference between the x and y coordinates from the difference between the two.The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.
Part A:
As seen from the graphic, increase from 0 to 2 sec.
The domain is (0, 2), where the height of the water balloon increases.
Part B:
The water balloon stays the same from 2 to 4 sec.
The field means that the height of the water balloon remains the same (2, 4).
Part C:
Height decreasing fasted at 4 to 6 sec.
Because the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.
The domain is where the height of the water balloon decreases rapidly (6, 10).
Part D:
The balloon's height will be almost near the ground as resistance will play its role.
But it will almost touch the ground.
The height of the water balloon will be 0 in 16 seconds.
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Which of the following measurements would be MOST likely to have a negative exponent in scientific notation?
a. The distance the Earth is from the sun in meters.
b. The length of a needle in millimeters
c. The length of a football field in inches.
d. The length of an amoeba in meters.
The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
Given four measurements:
The distance the Earth is from the sun in meters.The length of a needle in millimetersThe length of a football field in inches.The length of an amoeba in meters.We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.
A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].
We know that exponent shows continuous growth or continuous decay.
Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.
Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
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What is the slope of the line represented by the equation y- 6 = 2(x+3)?
Answer: 2
Step-by-step explanation:
remember y=mx^2+c
where m = gradient = slope
∴ expand and simplify y-5=2(x+3)
y-5=2x+6
y=2x+11
m=2 ∴ slope: 2
Solve the system of equations by substitution.
3 /8 x +1/3y =17/24
x + 7y = 8
By substitution, the value of x and y are 1 and 1 respectively.
How to solve system of equation?3 / 8 x + 1 /3 y = 17 / 24
x + 7y = 8
x = 8 - 7y
Let's substitute the value of x in equation(ii)
3 / 8(8 - 7y) + 1 / 3 y = 17 / 24
3 - 21 / 8 y + 1 / 3 y = 17 / 24
1 / 3 y - 21 / 8 y = 17 / 24 - 3
8y - 63y/24 = 17 - 72/ 24
-55y / 24 = -55 / 24
cross multiply
-1320y = -1320
divide both sides by -1320
y = -1320 / -1320
y = 1
Hence,
x + 7(1) = 8
x = 8 - 7
x = 1
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