Answers
m= 15
b= 45
y= 15x +45
Concept:Overall equation
The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.
Slope, m
The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.
[tex]\boxed{\text{Slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
where [tex](x_1,y_1)[/tex] is the first coordinate and [tex](x_2,y_2)[/tex] is the second coordinate
y-intercept, b
This is the y-value in which the line cuts through the y-axis (vertical axis).
Working:Slope, m
Let's identify two pairs of coordinates on the line.
2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.
The 2 points are: (0, 45) and (5, 120)
Substitute the 2 points into the slope formula:
Slope
= [tex]\frac{120-45}{5-0}[/tex]
= [tex]\frac{75}{5}[/tex]
= 15
Thus, m= 15.
y-intercept, b
From the graph, the line cuts through the y-axis at y= 45.
Thus, b= 45.
Overall equation
Substitute m= 15 & b= 45 into y= mx +b:
∴ The equation of the line is y= 15x +45.
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Related Questions
Find (-18) + (-25) + 13
Answers
Answer: -30
Step-by-step explanation:
Answer:
the answer would be -30!!!
Step-by-step explanation:
i took the quiz.
1.2 A pyramid, with the base similar to an obtuse-angled triangle as indicated by the diagram below. A = 110°, B = 40° and BC = 6 meters. The perpendicular height of the pyramid is 8 meters
1.Calculate the length of AB
2.Calculate the area of the base.
3.Calculate the volume of the pyramid
Answers
a) The length of the side AB is approximately 11.276 meters.
b) The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid is equal to 16.429 cubic meters.
What are the length of a side, the surface area and the volume of a pyramid?a) The picture shows a pyramid with a triangular base, the triangle has one obtuse angle and the length of the side AB can be found by the law of the sine:
6 / sin 110° = AB / sin 30°
AB = 6 × (sin 30° / sin 110°)
AB ≈ 3.193 meters
The length of the side AB is approximately 11.276 meters.
b) First, find the length of the side AC:
6 / sin 110° = AC / sin 40°
AC = 6 × sin 40° / sin 110°
AC ≈ 4.104 meters
Second, determine the area of the triangular base by Heron's formula:
s = 0.5 · (AC + BC + AB)
s = 0.5 · (4.104 m + 6 m + 3.193 m)
s = 6.649 m
A = √[s · (s - AC) · (s - BC) · (s - AB)]
A = √[6.649 · (6.649 - 4.104) · (6.649 - 6) · (6.649 - 3.193)]
A ≈ 6.161 square meters
The area of the base of the pyramid is approximately equal to 6.161 square meters.
c) The volume of the pyramid can be found by using the following expression:
V = (1 / 3) · A · h
Where:
A - Area of the pyramid base, in square meters.h - Height, in meters.If we know that A ≈ 6.161 square meters and h = 8 meters, then the volume of the pyramid is:
V = (1 / 3) · (6.161 m²) · (8 m)
V = 16.429 m³
The volume of the pyramid is equal to 16.429 cubic meters.
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Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.
Answers
Using it's concepts, we have that:
The domain of the relation is of -2 ≤ x ≤ -1.The range of the relation is of -2 ≤ y ≤ 2.Since each value of the input is mapped to only one value of y, it is a function.What are the domain and the range of a relation?The domain of a relation is the set that contains all possible input values for the relation. In a graph, it is given by the values of x.The range of a relation is the set that contains all possible output values for the relation. In a graph, it is given by the values of y.
Hence:
The domain of the relation is of -2 ≤ x ≤ -1.The range of the relation is of -2 ≤ y ≤ 2.When does a relation represents a function?
A relation represents a function when each value of the input is mapped to only one value of the output.
From this graph, we have that each value of x is mapped to only one value of y, that is, there are no vertically aligned points, hence the relation is a function.
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Given that sin(3x-35)°-cos(x+20)° and x is an acute angle, find it's value
Answers
Value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.
As given in the question,
Given data :
sin(3x-35)°-cos(x+20)° = 0 __(1)
As we know x is an acute angle ,
cos (90 - α)° =sinα°
⇒ sin (3x -35)° =cos (90 -(3x - 35))°
⇒ sin (3x -35)°=cos (55 -3x )° ___(2)
Substitute the value of sin (3x -35)° from (2) to (1),
cos(55 -3x)° -cos(x+20)°=0
⇒cos(55 -3x)° =cos(x+20)°
⇒55 -3x=x+20
⇒x=8.75°
Therefore, value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.
The complete question is :
Given that sin(3x-35)°-cos(x+20)° =0 and x is an acute angle, find it's value.
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the graph shows a company’s profit. the shaded region represents values when the profits were greater than projected
Answers
The region represented by the inequality in vertex form is the inequality in the last option y ≥ -(x - 50)² + 625.
What is a quadratic inequality?An inequality with a quadratic expression is referred to as a quadratic inequality.It is of the form y > ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.Let's assume that the equation is y = a(x - h)² + k
y = a(x - 50)² + 625
Put the point (61,504) in the equation
⇒ 504 = a(61 - 50)² + 625
⇒ 504 = a(11)² + 625
⇒ 504 = 121a + 625
⇒ 121a = -625 + 504
⇒ 121a = -121
⇒ a = -1
y = -(x - 50)² + 625
Hence the inequality is y ≥ -(x - 50)² + 625.
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7+ [1 + (3×6+5)] ÷ 2
Answers
Answer: 25
Step-by-step explanation:
Multiplication and Division always come before Addition and Subtraction unless they are in brackets, which has top priority. In this case, the order would be ( ) [ ] ÷ +
( ) :
3 x 6 = 30 + 5 = 35
[ ] :
35 + 1 = 36
÷ :
36 ÷ 2 = 18
+ :
7 + 18 = 25
Answer: 25
maths midpoint theorem
please help
Answers
Step-by-step explanation:
2.
to complete the description :
PQ || MN || BC
the midpoint theorem :
the line segment in a triangle connecting the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
therefore,
MN connects the midpoints of AC and AB, and is therefore half of BC.
PQ connects the midpoints of AN and AM, and is therefore half of MN. and that is half of half of BC = one quarter of BC.
MN = 1/2 × BC
PQ = 1/2 × MN = 1/2 × 1/2 × BC = 1/4 × BC =
= 1/4 × 16 = 4 mm
3.
UV = 10 cm connects the midpoints of PT and PS, and is therefore 1/2 of TS.
in other words, TS = 2×UV = 2×10 = 20 cm.
now we go the other direction from Q :
TS connects to midpoints of QU and QR. therefore,
UR = 2×TS = 2×20 = 40 cm.
VR = UR - UV = 40 - 10 = 30 cm
Chris is studying a type of coral that grows at a constant rate. They measured the age and height of 3
pieces of the coral. Here's what they found:
h = height (cm)
45-
40+
35-
30-
25-
20-
15-
10-
10
5-
●
1 2
●
5 6
a = age (years)
Chris wants an equation they can use to find the height in centimeters (h) of any piece of this coral based
on its age in years (a).
Answers
The required equation Chris wants is is h = 7.5a.
What is an equation ?An equation is a mathematical expression for equation two similar terms in different form.
According to the given question Chris is studying a type of coral that grows at a constant rate.
Given at 2 years the height of the coral is 15 cm,At 4 years the height of the coral is 30 cm and at 6 years the height of the coral is 45 cm.
To find the constant rate of change we divide height by age which is
= 15/2
= 7.5.
Thus an equation can be formed by h= 7.5a where h represents height and a represents age.
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Answer: h=7.5a
Step-by-step explanation: The only reasonable answer
You can buy 5 t-shirts at Baxters for the same price that you can buy 4 t-shirts at bixbys. If one t-shirt costs $11.80 at bixbys, how much does one t-shirt cost at baxters?
Answers
Answer:
4
shirts at Bixby's costing
$
11.50
would cost
XXX
4
×
$
11.50
=
$
46
If
5
shirts at Baxter's cost the same as
4
shirts at Bixby's,
5
shirts at Baxter's would cost
$
46
and
1
shirt at Baxter's would cost
$
46
5
=
$
9.20
(x,y) —> (y,x)
I can’t do this one
Answers
Answer:
I legit don't remember lol
Which expression has the greatest absolute value?
Answers
Answer:
3 because everything is minus
find the area of the figure. use 3.14 for pi
Answers
Answer:
38.13 m²
Step-by-step explanation:
area of triangle = 1/2 base × height
= 1/2 × 4 × 3
= 6 m²
Area of rectangle = length × width
= 6 × 3
= 18m²
Area of semi circle = 180/360 × π × radius²
= 180/360 × 3.14 × 3²
= 14.13 m²
Add all the areas together
6 + 18 + 14.13 = 38.13
it takes 50 people 256 days to build a road how long will it take 80 people
Answers
The answer is that 80 people will build the same road in 160 days.
Given that 50 people take 256 days to build a road.
And we need to find out how many days will 80 people take to build the same road.
Disclaimer: Assuming that the work done by all the people are same.
If the number of people increases, the time taken to build the road decreases in the same proportion. Clearly, the number of people varies inversely to the number of days.
Let x denote the number of days required to build the road for 80 people.
Then the ratio, 80/50 = 256/x
⇒ x = (256×50)/80 = 160
Therefore, 80 people will build the same road in 160 days.
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What is the slope of the line that passes through the points (2, 8) and (-3, 14)?
Answers
Answer:
-6/5
Step-by-step explanation:
(14-8)÷(-3-2) = -6/5
I need help answering question 6. I think it’s A) but my teacher told us D) ? What’s the correct answer??
Answers
the mean weight of a group of 15 boys is 65 kg . one boy joins the group and his weight is 45 kg . what is the average weight of all the boys
I need the answer within 2 to 3 days!
Answers
Answer:
The new average is
63.75kg
Step-by-step explanation:
We have 15 boys with avg. weight of 65kg. That means that the sum of their weights is:
15*65kg = 975kg
We add a boy weighing 45kg. The new sum is
975kg + 45kg = 1020kg
To get the new average, we need to divide by the number of boys. It's no longer 15, because we've added one. It's now 16
avg_weight = 1020kg / 16 = 63.75kg
Translate the sentence into an equation.
Six more than the quotient of a number and 4 is equal to 8.
Use the variable x for the unknown number.
Answers
Answer:
(n ÷ 4) + 6 = 8
Step-by-step explanation:
Pretty sure I answered this before, but here you go.
Quotient means The answer when you divide' So we are working in the division.
n ÷ 4 is the division part
It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)
Lastly it says the answer must be 8 so we add that at the end. So the answer is:
(n ÷ 4) + 6 = 8
24x(4+17)-18x11=
A
296
B 306
C 1,045
D) 5,346
Answers
Answer:
B. 306
Step-by-step explanation:
using pemdas you would do parenthesis, exponents, multiplication or division whatever comes first, and lastly addition or subtraction whatever comes first.
Answer: B
Step-by-step explanation:
Complete the equation and tell which property you used 21× =9×21
Answers
After cross multiplying the given equation the value of x turns out to be 9.
What is cross multiplication?
In mathematics, specifically in abecedarian computation and abecedarian algebra, given an equation between two fragments or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.In cross-multiplication, we multiply the numerator of the first bit with the denominator of the alternate bit and the numerator of the alternate bit with the denominator of the first bit. Cross-multiplication can be used to add or abate unlike fragments snappily.Cross-multiplication is also appertained to as a butterfly system.21 × X =9×21
X = 9
After cross multiplying the given equation the value of x turns out to be 9.
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Which answer choice is equal to -2x2 - 21x - 54?
Answers
Explanation: start by multiplying -2 and 2 giving you -4
-4 -21x -54
Then combine like terms
-21x -58
Assuming there’s no equal sign that’s all you can do
a plank of wood is 220 cm long.I cut it in 14cm pieces. what lenght of wood i will have left over?
Answers
The required Length is 10cm.
What is length?
Length is a measure of distance. In the International System of Amounts, length is a volume with dimension distance. In utmost systems of dimension a base unit for length is chosen, from which all other units are deduced.Length is generally understood to mean the most extended dimension of a fixed object. still, this isn't always the case and may depend on the position the object is in.Varied terms for the length of a fixed object are used, and these include height, which is the perpendicular length or perpendicular extent, and range, breadth, or depth. Height is used when there's a base from which perpendicular measures can be taken. range or breadth generally relates to a shorter dimension when the length is the longest one.220 / 14 gives us 15.
You have to understand that this means 15 whole 14 cm pieces and a Length of 1 piece.
thus 14 * 15 = 210
So 220- 210 = 10
where you know 220- 210 is< 15
Hence, The correct Length is 10cm.
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A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,900 per month for the next three years and then $3,800 per month for two years after that. If the bank is charging customers 9.75 percent APR, how much would it be willing to lend the business owner?
Answers
The amount will be $141647.55.
we need to use the present value of an annuity formula:
the formula used to determine the present value factor of an annuity is:
present value annuity factor = [1 - 1/(1 + i)ⁿ ] / i
we must divide this into 2 parts:
the first part will deal with the $19,00 monthly payment
the second part deals with the $38,000 monthly payment
i = 9.75% / 12 = 0.8125%
n (first part) = 36
n (second part) = 24
the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)³⁶ ] / 0.8125% = 31.1043
the PV annuity factor for second part = [1 - 1/(1 + 0.8125%)²⁴ ] / 0.8125% = 21.7251
loan = ($219,00 x 31.1043) + ($38,00 x 21.7251)//(1 + 0.8125%)³⁶ = $59092.17 + $82555.38 = $141647.55
hence we get the amount as $141647.55
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Mitch drew lines , k, and t so that and k were parallel. He labeled a pair of alternate interior angles 1 and 2. Which diagram did Mitch create?
Answers
Considering the concepts of parallel lines and alternate interior angles, it is found that Mitch created diagram C.
What are parallel lines?Parallel lines are lines that never intersect. For this problem, lines l and k are parallel, that is, they are the horizontal lines.
What are alternate interior angles?When two parallel lines are crossed by a transversal, the alternate interior angles are between the two parallel lines, one in each side.
Since 1 and 2 are alternate interior angles, Mitch created diagram C.
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4.
A standard glass of wine is 5 oz. How many full glasses of wine can you get from a typical 750 ml bottle?
full 5-oz glasses of wine.
Answers
Answer:
5
Step-by-step explanation:
750ml= 25 fluid oz each glass is 5oz
5/25=5oz
44.5 divided by 42.2
Answers
Rectangle A measures 6 cm by 4 cm. Rectangle B is a scaled copy of rectangle A. Select all of the measurements that could be the dimensions of rectangle B
Answers
The scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are 12cm by 8cm and 48cm by 32cm .
It is required to find the measurements that could be the dimensions of rectangle B.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given :
Length=6 cm
width=4cm
According to given question we have,
Divide the length and the width of the rectangle we get=
k=Length/width
k=6/4
k=1.5
This means that a scaled copy of rectangle A must have a value of 1.5
when the dimensions are divided.
Possible rectangles are:
A. 12cm by 8cm
Divide the length and the width of the rectangle we get,
k=12/8
k=1.5
B. 48cm by 32cm
Divide the length and the width of the rectangle we get,
k=48/32
k=1.5
Therefore, the scale copy of a shape is the resulting shape when the original shape is dilated. Possible scaled rectangles of rectangle A are 12cm by 8cm and 48cm by 32cm .
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Some one pls help me will give Brainly
Answers
Answer:
100 miles from shore
Step-by-step explanation:
locate 10 hours on the x- axis, go vertically up to meet the line at (10, 100 )
so after 10 hours they are 100 miles from shore
Answer:
100
Step-by-step explanation:
x-axis shows time - find where this is 10 hours
y-axis shows distance from shore. Find where this corresponds to 10. That is at 100 miles.
What is the area of a triangle ABC with AB=AC=5cm and BC=6cm?
Answers
Answer: 12 cm^2
Step-by-step explanation:
BC ==> Base of triangle
Divide the triangle in two parts:
BC/2=BC'
6/2=BC'
BC'=3
Distance formula: a^2+b^2=c^2
c^2-a^2=b^2
5^2-3^2=b^2
25-9=b^2
b^2=16
b=4 ==> height of triangle
Area of triangle=A. b=base. h=height
A=1/2 * b * h=
A=1/2 * 6 * 4
A=1/2 * 24
A=12 cm^2
Perform the indicated operation
7 1/8 ∙ 5 2/3
Answers
35 1/12
Step-by-step explanation:
6()=69 what’s the awnser
Answers
Answer:
11.5
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
x stands for an unknown value, so we will put the x next to the 6 to solve the equation.
6x = 69
--- ---- <------ fraction bar/divide
6 6
x = 11.5
Check:
6 (11.5) = 69
69 = 69
True statement.
