If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
For the values you've given:
- The slope (m) is 35.
- The y-intercept (b) is 550.
From these pieces of information, you can conclude:
1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.
2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.
With these conclusions, you can write the equation of the line in slope-intercept form:
\[ y = 35x + 550 \]
This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.
How does the value of 30,000 x (4 x 3) compare to the value of 300 x (4 x 3)?
Answer:
30,000 x (4 x 3) = 100 times 300 x (4 x 3)
Step-by-step explanation:
Here, the given expressions are:
Expression 1 : 30,000 x (4 x 3)
Expression 2 : 300 x (4 x 3)
Now, simplifying both the expressions, we get
30,000 x (4 x 3) = 30,000 x (12) = 3,60,000
300 x (4 x 3) = 300 x (12) = 3,600
Now, dividing both the expressions, we get:
[tex]\frac{3,60,000}{3,600} = 100[/tex]
or, [tex]\frac{\textrm{Expression 1}}{\textrm{Expression 2}} = 100\\[/tex]
or, {Expression 1} = {Expression 2} x 100
⇒The expression 1 is 100 times the expression 2
Hence, 30,000 x (4 x 3) = 100 times 300 x (4 x 3)
Wahab wants to donate at least $6000 in books and pairs of shoes. Let B represent the number of books and S represent the number of pairs of shoes that Wahab must donate to achieve his goal. 20B+50S≥6000. Wahab donates 100 pairs of shoes. What is the least number of books he should donate to achieve his goal?
Wahab has to donate at least 50 books to reach his goal
Solution:Given that, Wahab wants to donate at least $6000 in books and pairs of shoes.
Let "B' represent the number of books
Let "S" represent the number of pairs of shoes that Wahab must donate to achieve his goal.
20B+50S ≥ 6000 ⇒ this is the inequality for total donation.
Wahab donates 100 pairs of shoes.
Now, as he donated 100 pairs of shoes, S = 100, so substitute this in inequality.
20B + 50(100) ≥ 6000
20B + 5000 ≥ 6000
20B ≥ 6000 – 5000
20B ≥ 1000
B ≥ 50
Hence, wahab has to donate at least 50 books to reach his goal.
If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7 A. g(x) = -2x + 1 B. g(x) = -2x − 6 C. g(x) = -6x + 7 D. g(x) = -2x + 20
Answer:
A. [tex]g(x)=-2x+1[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-2x+7[/tex]
The function [tex]f(x)[/tex] is shifted 6 units below which forms the function [tex]g(x)[/tex]
To find the function [tex]g(x)[/tex], we apply the following translation rules:
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units up.
If [tex]c<0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units down.
Since the function [tex]f(x)[/tex] is shifting 6 units below, thus value of [tex]c<0[/tex] which is taken as -6.
The translation occurring here is given by:
[tex]f(x)\rightarrow f(x)-6[/tex]
Thus,
[tex]g(x)=f(x)-6[/tex]
Substituting [tex]f(x)=-2x+7[/tex]
[tex]g(x)=-2x+7-6[/tex]
∴ [tex]g(x)=-2x+1[/tex]
How do you simplyfy -x squared + 4/2x
Answer:
The solution for the given expression is 0 , 2
Step-by-step explanation:
Given expression as :
- x² + [tex]\frac{4}{2}[/tex] x = 0
or, - 2 x² + 4 x = 0
or, 2 x ( -x + 2 ) = 0
or, ( - x + 2 ) ( 2 x ) = 0
or, 2 x = 0
∴ x = 0
and ( - x + 2 ) = 0
Or, - x = - 2
∴ x = 2
Hence The solution for the given expression is 0 , 2 Answer
30 points!! Please help me ASAP!! I don't understand this.
ABCD is a trapezoid with midsegment (EF). If AD=5x-11, EF=3x+7, BC=2x+7, how many units in length is (EF)?
Answer:
[tex]EF=61\ units[/tex]
Step-by-step explanation:
we know that
In this problem, the length of the mid-segment EF is the sum of the two bases divided by 2
so
[tex]EF=\frac{1}{2}(BC+AD)[/tex]
substitute the given values
[tex]3x+7=\frac{1}{2}(2x+7+5x-11)[/tex]
Solve for x
[tex]6x+14=(7x-4)[/tex]
[tex]7x-6x=14+4[/tex]
[tex]x=18[/tex]
Find the length of EF
[tex]EF=3x+7[/tex]
substitute the value of x
[tex]EF=3(18)+7[/tex]
[tex]EF=61\ units[/tex]
20 FOOT LADDER IS LEANING AGAINST A WALL THE FOOT OF THE LADDER MAKES AN ANGLE OF 58 WITH THE GROUND
The question is incomplete. Here is the complete question:
A 20-foot ladder is leaning against a wall. The foot of the ladder makes an angle of 58 degrees with the ground. Find, to the nearest foot, the vertical distance from the top of the ladder to the ground.
Answer:
17 ft
Step-by-step explanation:
Let the height from the top of the ladder to the ground be 'x' feet.
Given:
The triangle for the given situation is shown below.
Now, from the triangle ABC, AB is the length of the ladder, A is the top of ladder, B is the foot of the ladder and AC is 'x'.
The length of the ladder is, [tex]AB=20\ ft[/tex]
The angle made by the foot of the ladder with the ground is, [tex]\angle ABC=58[/tex]°
Now, using the sine ratio for the angle ∠ABC, we have:
[tex]\sin(\angle ABC)=\frac{AC}{AB}\\\sin(58)=\frac{x}{20}\\x=20\times \sin(58)\\x=20\times 0.8480\\x=16.96\approx 17\textrm{ ft (Nearest foot})[/tex]
Therefore, the vertical distance from the top of the ladder to the ground is 17 feet.
Which of the following situations results in a sum of 1 1/2 ? Select all that apply
A) I cut 3 1/3 inches from my grave. The grass grew 1 5/6 inches over the next week.
B) I used up 1/4 of a pound of coffee and bought 1 1/4 of a pound of coffee from the store
C) I gained 6 1/2 pounds and my wife lost 8 pounds
D) I had 4 1/4 bottles of juice and drank 1 3/4 of them
E) I painted 5/8 of one room and 7/8 of a another
F) I used 3/4 of a pound of ground beef to make burgers and purchased 2 1/4 of a pound of ground beef
Answer:
The answer is: B, C, and F.
Step-by-step explanation:
A. No.
3 1/3 - 1 5/6 =
10/3 - 11/6 =
20/6 - 11/6 =
9/6 = 2/3
B. Yes.
1 1/4 + 1/4 = 1 1/2
C. Yes.
6 1/2 - 8 = 1 1/2
D. No.
4 1/4 - 1 3/4 =
17/4 - 7/4 =
10/4 =
5/2 =
2 1/2
E. No
5/8 + 7/8 =
13/8 =
1 5/8
F. Yes.
2 1/4 - 3/4 =
9/4 - 3/4 =
6/4 =
3/2 =
1 1/2
The following situations result in a sum of 3/2 B, C, and F.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A.
[tex]3\frac{ 1}{3} - 1 \frac{5}{6}[/tex]
10/3 - 11/6
20/6 - 11/6
9/6 = 2/3
No, the following situations don't result in a sum of 3/2.
B.
5/4 + 1/4 = 1 1/2
Yes, the following situations result in a sum of 3/2.
C.
11/2 - 8 = 1 1/2
Yes, the following situations result in a sum of 3/2.
D.
17/4 - 7/4 =
10/4 = 5/2
No, the following situations don't result in a sum of 3/2.
E.
5/8 + 7/8 = 13/8
No, the following situations don't result in a sum of 3/2.
F.
9/4 - 3/4
6/4 = 3/2
Yes, the following situations result in a sum of 3/2.
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f ∠A is 95° and ∠B is 105°, what is ∠C?
A) 75°
B) 85°
C) 95°
D) 105°
The question is missing important data. The quadrilateral having vertices A, B, C and D is a cyclic quadrilateral.
Answer:
B) 85°
Step-by-step explanation:
Given:
A cyclic quadrilateral with ∠A is 95° and ∠B is 105°.
For a cyclic quadrilateral, the sum of the opposite interior angles is equal to 180°
Therefore, sum of angles A and C is 180°.
[tex]\angle A + \angle C=180\°\\95\°+\angle C=180\°\\\angle C=180-95\\\angle C =85\°[/tex]
Therefore, the correct option is option B) 85°
Answer:
A)75
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral are supplementary.
∠B + ∠D = 180°
105° + ∠D = 180°
∠D = 75°
PLEASE HELP!!!!!!!!!!!!!!
Michael earns
Michael earns $9 per hour. He works 28 hours each week. How much does he earn in 6 weeks
The amount of money he earns in 6 weeks is equal to $1512.
Given the following data:
Salary = $9 per hourNumber of hours worked = 28 hours each week.To find the amount of money he earns in 6 weeks:
First of all, we would determine the amount of money he earns each week:
[tex]Weekly\;salary = Salary \times Number \;of \;hours \;worked\\\\Weekly\;salary =9\times 28[/tex]
Weekly salary = $252
In 6 weeks:
Total salary = [tex]252\times6[/tex]
Total salary = $1512
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Write an equation that gives the proportional relationship of the graph.
A. y=1/7x
B. y=5x
C. y=7x
D. y=35x
Answer:
C
Step-by-step explanation:
Write the equation in slope intercept form for the line perpendicular to c(-4,-5) and D(4,9) passing through the midpoint of the line
Slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
Solution:Need to find the slope intercept form for the line perpendicular to C(-4,-5) and D(4,9)
And passing through the midpoints of the line CD.
Lets first calculate slope of CD
Let say slope of CD be represented by [tex]m_1[/tex]
General formula of slope of line passing through points [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is as follows:
[tex]m=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}[/tex]
[tex]\text { In case of line } \mathrm{CD} , x_{1}=-4, \quad y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]
[tex]\text {So slope of line } \mathrm{CD} \text { that is } m_{1}=\frac{(9-(-5))}{(4-(-4))}=\frac{14}{8}=\frac{7}{4}[/tex]
Let’s say slope of required line which is perpendicular to CD be [tex]m_2[/tex]
As product of slope of the lines perpendicular to each other is -1
=> slope of line CD [tex]\times[/tex] slope of line perpendicular to CD = -1
[tex]\begin{array}{l}{=>m_{1} \times m_{2}=-1} \\\\ {\Rightarrow \frac{7}{4} \times m_{2}=-1} \\\\ {\Rightarrow m_{2}=-\frac{4}{7}}\end{array}[/tex]
Now let’s find midpoint of CD
[tex]\text { Midpoint }(x, y) \text { of two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { is given by }[/tex]
[tex]x=\frac{x_{2}+x_{1}}{2} \text { and } y=\frac{y_{2}+y_{1}}{2}[/tex]
[tex]\text { So in case of line } \mathrm{CD} , x_{1}=-4, y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]
And midpoint of CD will be as follows
[tex]x=\frac{x_{2}+x_{1}}{2}=\frac{4+(-4)}{2}=0 \text { and } y=\frac{y_{2}+y_{1}}{2}=\frac{9-5}{2}=2[/tex]
So midpoint of CD is ( 0 , 2 )
As it is given that line whose slope intercept form is required is perpendicular to CD and passing through midpoint of CD , we need equation of line passing through ( 0 , 2 ) and having slope as [tex]m_{2}=-\frac{4}{7}[/tex]
Generic equation of line passing through [tex]\left(x_{1}, y_{1}\right)[/tex] and having slope of m is given by
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=0 \text { and } y_{1}=2 \text { and } m=-\frac{4}{7}[/tex]
Substituting the values in generic equation of line we get
[tex](y-2)=-\frac{4}{7}(x-0)[/tex]
As we required final equation in slope intercept form which is y = mx + c, lets rearrange our equation is required form:
[tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
Hence can conclude that slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]
To find the equation of the line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint (0, 2), follow these steps: 1) Find the slope of the given line. 2) Find the midpoint of the line. 3) Find the negative reciprocal of the slope. 4) Use the slope and midpoint to write the equation of the perpendicular line in slope-intercept form.
Explanation:To find the equation of a line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint of the line, we need to follow these steps:
Let's go through these steps:
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:
slope = (9 - (-5)) / (4 - (-4))
slope = 14 / 8
slope = 7 / 4
The midpoint of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:
midpoint = ((-4 + 4) / 2, (-5 + 9) / 2)
midpoint = (0 / 2, 4 / 2)
midpoint = (0, 2)
The negative reciprocal of a slope is found by changing the sign of the slope and taking its reciprocal.
In this case, the slope is 7 / 4. So, the negative reciprocal is -4 / 7.
Now that we have the slope (-4 / 7) and the midpoint (0, 2), we can use the slope-intercept form of a line to write the equation:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the values, we have:
y = (-4 / 7)x + b
To find the value of b, we can substitute the coordinates of the midpoint (0, 2) into the equation:
2 = (-4 / 7)(0) + b
2 = 0 + b
b = 2
So, the equation of the line perpendicular to the line passing through C(-4,-5) and D(4,9) and passing through the midpoint (0, 2) is:
y = (-4 / 7)x + 2
Let f(x)=8x and g(x)=8x+5+1 .
Which transformations are needed to transform the graph of f(x) to the graph of g(x) ?
Select each correct answer.
horizontal translation 5 units right
vertical translation 1 unit up
vertical translation 1 unit down
horizontal translation 5 units left
horizontal translation 1 unit left
vertical translation 5 units up
One side of a triangle is 2 times the second side. The third side is 5 ft longer than the second side. The perimeter of a triangle is 81 ft. Find the length of each side.
Answer:
19 ft, 24 ft and 38 ft are the lengths of triangle.
Step-by-step explanation:
Let the length of second side be x.
Now given:
Given: Length of first side is 2 times length of second side = 2x
Given:Length of third side is 5 ft longer than the second side = 5+x
Perimeter of triangle = 81 ft.
Need to Calculate length of each side.
Now we know that sum of all three sides of triangle is equal to perimeter of triangle.
Hence,
[tex]x+2x+5+x =81\\4x= 81-5\\4x=76\\x=19 ft[/tex]
Also,
2x= 2×19 =38 ft.
5+x = 5+19 =24 ft.
Hence,
Length of first side = 38 ft.
Length of second side = 19 ft.
Length of third side =24 ft.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 4 /ms2. If the force is changed to 50 N, what will be the acceleration of the object?
The acceleration of the object will be 10 m/s²
Step-by-step explanation:
Direct variation is a relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
If y varies directly with x, then y ∝ xy = k x, where k is the constant of variationFor a moving object, the force acting on the object varies directly with the object's acceleration.
Assume that the force is F and the acceleration is a
∵ F ∝ a
∴ F = k a
∵ F = 20 newtons
∵ a = 4 m/s²
- Substitute these values in the equation above to find k
∵ 20 = k (4)
∴ 20 = 4 k
- Divide both sides by 4
∴ k = 5
- Substitute the value of k in the equation
∴ F = 5 a ⇒ equation of variation
∵ F = 50 Newtons
∵ F = 5 a
∴ 50 = 5 a
- Divide both sides by 5
∴ 10 = a
∴ a = 10 m/s²
The acceleration of the object will be 10 m/s²
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the probability that the card drawn from a standard 52-card deck is queen is
There are 4 queens in a deck of cards.
You have 4 chances out of 52 total cards to get a queen.
The probability is 4 queens / 52 cards = 4/52, which can be reduced to 1/13
13) John and James live 0.7km apart. If John takes 25cm steps, then how many steps would it take
him to walk from his house to James' house? 20 steps
It will take John 2800 steps to walk from his house to James' house
Step-by-step explanation:
First of all we have to convert all the measurements in same unit.
Distance = 0.7 km
As 1 km = 1000 m
0.7*100 = 700m
And
1 m = 100 cm
700*100 = 70000cm
Now,
25 cm = 1 step
[tex]So,\\70000cm = \frac{70000}{25}\\=2800\ steps[/tex]
It will take John 2800 steps to walk from his house to James' house
Keywords: Conversions, Lengths
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Write the difference as a mixed number?
2/6/8 - 1/5/8 ?
Answer:
16/15 or 1 1/15
Step-by-step explanation:
2/6/8=8/3
1/5/8=8/5
----------------
8/3-8/5=40/15-24/15=16/15=1 1/15
A line has a slope of 0 and passes through the point (-1,-6). What is it’s equation in slope intercept form?
Good evening ,
Answer:
D : y = -6
Step-by-step explanation:
A line D has a slope of 0 shouled be parallel to the x-axis then
it’s equation in slope intercept form should be y=a
And since, It passes through the point (-1,-6) then a=-6
finally:
the equation of D is y=-6.
:)
nd
A farmer has 113 sheep.
47 of them are males. How
many more female sheep
are there than male sheep?
Answer:
19 more female sheep.
Step-by-step explanation:
Answer:
66 more female sheep.
Step-by-step explanation:
What you do is subtract 113 subtract 47 which is 66 and if you want to make sure add,66+47.
you 6 moles of a substance which of the following statements is true?
A. you have six times the number of particles that are in 12 grams of carbon-12.
B. you have one third the number of particles that are in 12 grams of carbon-12.
C. you have the same number of particles as in 12 grams of carbon-12.
D. you have three times the number of particles that are in 12 grams of carbon-12.
Answer:
A
Step-by-step explanation:
1)The mole is a unit of measure that contains as many elementary entities as in atoms of 12 grams of Carbon (12 AMU). The Carbon mass is the reference.
2)We have to specify which particle we are using when dealing with mole unit:
particle, atoms, molecules, ions, electrons, etc.
[tex]1\:mol \:C=6*10^{23} \:particles[/tex]
3) So If I have 6 moles of a substance, I am going to have six times the number of particles that are in 12 grams of carbon-12.
[tex]36*10^{23} \:particles[/tex]
Select Is a Function or Is not a Function to correctly classify each relation. Title Is a Function Is not a Function {(2,2),(4,4),(6,6),(8,8)} {(0,3),(3,5),(5,6),(8,4)} {(1,2),(3,3),(4,8),(6,3)} {(3,4),(5,2),(5,6),(7,3)}
Answer:
1 function {(2,2),(4,4),(6,6),(8,8)} written is a function the other following coordinates are not functions due to it not being a straight line as a 'proper' function should be.
Answer:
The answer is:
{(2,2),(4,4),(6,6),(8,8)} is a function
{(0,3),(3,5),(5,6),(8,4)} is a function
{(1,2),(3,3),(4,8),(6,3)} is a function
{(3,4),(5,2),(5,6),(7,3)} is not a function
Step-by-step explanation:
Sorry I don't have an explanation, but I know these are correct because I took the test and got this correct. ;)
Assume AJKL = APQR. If m P= 52°,m2Q = 48°, and mR= 80°, what is
the measure of K?
Answer:
measure of angle K is 48° or m∠K = 48°
Step-by-step explanation:
Given:
ΔJKL= ΔPQR
m∠P = 52°
m∠Q = 48°
m∠R = 80°
When 2 triangles are equal or congruent to each other then their corresponding angles are equal or congruent by congruence property.
Hence ,
m∠P = m∠J
m∠Q = m∠K
m∠R = m∠L
But m∠Q = 48° hence m∠K = 48°
Hence measure of angle K is 48°
A blueprint of a room uses the scale
5 in : 25 ft. A door has a width of 1.5 inches on the blueprint. How wide, in feet is the actual door?
I’ll put you as brainliest
Using the blueprint scale of 5 inches to 25 feet, the width of the door on the blueprint at 1.5 inches translates to an actual width of 7.5 feet.
Explanation:To find the actual width of the door in feet using a given scale, we use proportional relationships.
The scale provided is 5 inches : 25 feet.
This means that every 5 inches on the blueprint correspond to 25 feet in actual size.
To find the actual door's width, we calculate it using the following proportion:
5 inches / 25 feet = 1.5 inches / x feet
Now, we solve for 'x' to find the actual width:
5/25 = 1.5/x
Now, cross-multiply and divide to find 'x':
5x = 25 * 1.5
x = (25 * 1.5) / 5
x = 37.5 / 5
x = 7.5 feet
So the actual door's width is 7.5 feet.
The equation y+ 3 = 5(x - 3) represents a linear function. What is the y intercept of the equation
Answer:
The y intercept is when x=0
When x=0,
y+3= 5(-3)
y+3= -15
y=-18
the y intercept is thus -18.
Step-by-step explanation:
4. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. In a
random sample of 900, approximately how many people will have IQs between 85 and 120?
675 people will have score between 85 and 120
Step-by-step explanation:
Given
Mean = 100
SD = 15
If we have to find percentage of score between two values we have to find the z-score for both values and then area under the curve for both values
z-score is given by:
for a value x:
[tex]z-score = \frac{x-mean}{SD}[/tex]
So,
For 85:
[tex]z-score = z_1 = \frac{85-mean}{SD}\\ = \frac{85-100}{15}\\=\frac{-15}{15}\\=-1[/tex]
[tex]z-score = z_2 = \frac{120-mean}{SD}\\ = \frac{120-100}{15}\\=\frac{20}{15}\\=1.3333[/tex]
Now we have to find the area under the curve for both values of z-score. z-score tables are used for this purpose.
So,
For z1 : 0.1587
For z2: 0.9082
The area between z11 and z2:
[tex]z_2-z_1 = 0.9082-0.1587=0.7495[/tex]
So the probability of score between 85 and 120 is 0.7495
As the sample is of 900 people, the people with scores between 85 and 120 will be:
900*0.7495 = 674.55 people
Rounding off to nearest whole number
675 people will have score between 85 and 120
Keywords: Probability, SD
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Point A(4,3), point B(-1,3) find the equation
Answer:
y = 3Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points A(4, 3) and B(-1, 3).
Substitute:
[tex]m=\dfrac{3-3}{-1-4}=\dfrac{0}{-5}=0[/tex]
The slope m = 0, therefore it's a horizontal line.
The equation of a horizontal line:
[tex]y=a[/tex] where a is any real number
The line passes through points A and B, where ordinates are equal 3.
Therefore the equation is
[tex]y=3[/tex]
Decide whether the two equations are equivalent.
4n + 1= n-8
3n = -9
Answer:
yes
Step-by-step explanation:
just solve for n
20 characters why
Answer:
Yes
Step-by-step explanation:
4n+1=n-8
4n-n+1=-8
3n+1=-8
3n=-8-1
3n=-9
n=-9/3
n=-3
-------------
3n=-9
n=-9/3
n=-3
The two equations are equivalent.
the diagram shows a triangle.
all the measurements are in cm
the perimeter of the triangle is 70cm
the area of the triangle is Acm squared
work out the value of A
Answer:
A = 110.25
Step-by-step explanation:
add all the equations and equal it to 180 because all triangle angles add to 180:
4x+1 + 3x + 3x-1 = 180
10x =70
/10 /10
x = 7
Insert x into each equation and solve:
3(7)-1 = 20
4(7)-1 = 27
3(7) = 21
and then use A = 1/2 base*height formula:
A= 1/2 21* 20
A= 210
Area of triangle A is 210 cm²
Given that;
Perimeter of the triangle = 70cm
Sides of triangle = 3x, 4x + 1, 3x - 1
Find:
Area of triangle A
Computation:
3x + (4x + 1) + (3x - 1) = 70
3x + 4x + 3x = 70
10x = 70
x = 7
So,
Perpendicular = 3x - 1 = 21 - 1 = 20 cm
Hypotenuse = 4x + 1 =28 + 1 = 29 cm
base = 3x = 21 cm
Area of triangle A = (1/2)(b)(h)
Area of triangle A = (1/2)(21)(20)
Area of triangle A = (21)(10)
Area of triangle A = 210 cm²
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how do i solve m - 4/9 = -2 67/90
Answer:
m=-23/10
Step-by-step explanation:
-2 67/90=-247/90
m-4/9=-247/90
m=-247/90+4/9
m=-247/90+40/90
m=-207/90
m=-23/10