The slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
We have points on the graph:
(2, 1990) (5, 4225) (9, 7205)
The slope can be found using two points:
[tex]\rm m =\dfrac{4225-1990}{5-2}\\[/tex]
m = 745
The line can be written as:
y = mx + c
y = 745x + c
Plug point (2, 1990)
1990 = 745x + c
1990 = 745(2) + c
c = 500
y = 745x + 500
The pace of increase in money per month is represented by the slope.
Every month, the sum increases by $745.
The initial quantity of money when the business opened is represented by the y-intercept.
The company began with a $500 investment.
Thus, the slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500
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Question 4.
The angle of elevation of the top of a tree from a point on the ground 22 m away is 24⁰°.
Calculate the height of the tree (in metres) correct to 2 decimal places.
22 m
tree
Answer:
9.80 m
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.
__
setupThe geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...
Tan = Opposite/Adjacent
Using the given values, we have ...
tan(24°) = AC/AB = (tree height)/(distance from tree)
tan(24°) = AC/(22 m)
solutionMultiplying by 22 m gives ...
tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m
The height of the tree is about 9.80 meters.
What is the distance between the following points?
Answer:
B
10
Step-by-step explanation:
go up 7 then over 3, add them together and you got 10
Which polynomial is prime?
O x²+x+1
O x²-x-2
O x²-12x + 11
Ox²+2x-8
Answer:
The correct answer is x^2 + x + 1.
Step-by-step explanation:
A prime polynomial is one that cannot be factored. To solve this problem, we can use the process of elimination by eliminating all answer choices that can be factored.
x^2 - x - 2 = (x - 2)*(x + 1)
x^2 - 12x + 11 = (x - 11)*(x - 1)
x^2 + 2x - 8 = (x + 4)*(x - 2)
Since we cannot factor x^2 + x + 1, and we can factor all of the other answer choices, we know that x^2 + x + 1 is the answer.
Hope this helps!
*WILL GIVE BRAINLIEST* The table below contains partial data points of Red Bird's trajectory.
Horizontal distance traveled is 12unit, Equation in standard form is y = -4x² + 120x - 680 and Equation in vertex form is y = -4(x - 15)² + 220
Horizontal Distance Traveled
To find the horizontal distance traveled by Red Bird, we need to calculate the difference between the largest and smallest values of the X-axis data points. In this case, the horizontal distance traveled is:
Horizontal Distance Traveled = Largest X value - Smallest X value
= 17 - 5
= 12 units
The horizontal distance traveled by Red Bird is 12 units.
Equation in Standard Form
To find the equation in standard form, we need to determine the equation of a quadratic function that fits the given data points. Since we have more than three data points, we can use a quadratic regression to find the equation.
Using a regression tool or mathematical software, the equation in standard form for the given data points is:
y = -4x² + 120x - 680
Equation in Vertex Form
To find the equation in vertex form, we can convert the equation from standard form to vertex form by completing the square. The vertex form of a quadratic equation is given by:
y = a(x - h)² + k
To convert the equation to vertex form, we need to rewrite it by completing the square. The steps are as follows:
y = -4x² + 120x - 680
First, factor out the common coefficient -4:
y = -4(x² - 30x + 170)
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (30/2)² = 225:
y = -4(x² - 30x + 225 - 225 + 170)
Now, rewrite the equation by grouping:
y = -4((x - 15)² - 55)
y = -4(x - 15)² + 220
The equation in vertex form is:
y = -4(x - 15)² + 220
So, the equation in vertex form for the given data points is y = -4(x - 15)² + 220.
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Simplify this expression.
(2-5√6)-3√2
A. 6√2-15√6
B. 6√2-15√12
C. 6√2-8√6
D. 6√2-30√3
Answer:
-A.
Step-by-step explanation:
/Correct Me If I'm Not Correct/
"Hope it's Help"
Select the correct answer.
Which equation is equivalent to the given equation?
- 4(x - 5) + 8x = 9x - 3
A.
-5x = -23
B.
5x = 17
C.
-5x = 2
D.
5x = -12
Answer:
A. -5x = -23
Step-by-step explanation:
First you have to simplify the equation - 4(x - 5) + 8x = 9x - 3
-4x + 20 + 8x = 9x -3
9x - 4x = 20 + 3
5x = 23
=> equivalent to answer A.
The equivalent expression is,
⇒ - 5x = - 23
We have to given that,
An expression is,
- 4 (x - 5) + 8x = 9x - 3
Now, We can simplify the expression for equivalent expression,
- 4 (x - 5) + 8x = 9x - 3
Apply distributive property, we get;
- 4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
4x - 9x = - 20 - 3
- 5x = - 23
Therefore, The equivalent expression is,
⇒ - 5x = - 23
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I need help bad I dont understand this
Answer:
12.566 inches
Step-by-step explanation:
2πr/4
2π x8 divided by 4
What is the value of x in the diagram
Answer:
51°
Step-by-step explanation:
the given angle of 102° is the arc angle between the 2 segment end points on the circle arc.
and this arc angle is always a seen from the center of the circle.
by moving the reference point back (to the other side of the circle) to the circle arc that angle is cut in half.
you could move that point to anywhere on the arc of the circle outside of the 2 endpoints, and the angle stays always the same.
FYI - now, if you move that point into the top half-circle between the 2 end points, the perspective flips around, and that angle becomes half of the 360-102 = 258° arc angle.
Consider the following cumulative probability distribution.
1 2 3
4
0.09 0.31 0.48 0.65 0.84
5
1
a. calculate a{xs 4). (round your answer to 2 decimal places.)
pox s 4)
p
b. calculate p{x= 3). (round your answer to 2 decimal places.)
p(x = 3)
#
+
e
10
19
34
m
c. calculate p(2 s x s 4). (round your answer to 2 decimal places.)
p(2 5 x 84)
The solution [tex]P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)[/tex] is mathematically given as
[tex]P(2 \leq X \leq 4)=0.84[/tex]P(X=3)= 0.17[tex]P(2 < =X\leq 4)=0.53[/tex]What is the solution [tex]P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)[/tex]?Generally, the equation for the Probability of P(X=3) is mathematically given as
b)
[tex]P(X=3) = P(X \leq 3)-P(X\leq 2)[/tex]
Therefore
[tex]P(X=3)= 0.65-0.48[/tex]
P(X=3)= 0.17
c)
[tex]P(2\leq X\leq 4) = P(X\leq 4)-P(X\leq 1)\\\\\\P(2\leq X\leq 4) = 0.84-0.31'[/tex]
[tex]P(2 < =X\leq 4)=0.53[/tex]
a)
[tex]P(2\leq X\leq 4)=0.84[/tex]
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A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction
Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
What is the equation of the line that is perpendicular to y = 2x + 9 and has a y-intercept of –3?
Answer:
The image has the ans.
Step-by-step explanation:
Image explains.
How does human behavior explain why the demand line slopes downward?
The decreasing of the prices and increasing of buying are correlated with the human behavior.
What is a Demand Graph ?Demand graph is the curve in the study of economics which tells us about the number of units purchased or the demand of the product with respect to the price.
The demand line slopes downward means the price is decreasing and more people are buying it.
The increase in the buying of the goods on decreasing prices is affected by human behavior as when the price decrease , the middle class people have a tendency to buy more quantity and
even there is need to satisfy unsatisfied wants , If a product was costlier before and the prices have decrease then to satisfy the wants , the people buy it ,
Hence decreasing of the prices and increasing of buying are correlated with the human behavior.
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PLEASE HELP ILL MAKE YOU THE BRAINIEST
Answer:
yes . because the given number satisfy the equation a2+b2=c2
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ (30)^{2} + (40)^{2} = (50)^{2} \\ 900 + 1600 = 2500 \\ 2500 = 2500 [/tex]
Yes. because the given numbers do satisfy the equation a²+b²=c².
After arguing for two weeks, melissa convinced her parents to have her birthday party at flyzone trampoline park. as soon as she gets there, melissa spends time practicing flips on the trampolines. then, she spends 1/2 of an hour eating birthday cake with her friends. in all, melissa spends 1/4 hours at flyzone.
The amount of time that Nora practices flips is; t = 1 ¹/₄
How to Solve Algebra problems?We are told that;
Nora spends time practicing flips on the trampolines. Let this be t.
Then, she spends 1/2 of an hour eating birthday cake with her friends.
Thus, total amount of time spent on flips and eating with her friends is;
t + ¹/₂ = 1 ³/₄
t = 1 ³/₄ - ¹/₂
t = 1 ¹/₄
Complete Question is;
After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?
Solve this equation for (t) to find the amount of time Nora practices flips
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Given: ΔABC (to the right)
AB=15
BD=9
AD⊥BC
m∠C=30°
Find Perimeter of ABC
Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of its 3 sides.
Given the following:
AB = 15 BD = 9m∠C=30°Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:
AD = √(15² - 9²)
AD = 12 units
Use the trigonometric ratios to find DC and AC:
sin 30 = AD/AC
sin 30 = 12/AC
AC = 12/sin 30
AC = 24 units
tan 30 = AD/DC
tan 30 = 12/DC
DC = 12/tan 30
DC ≈ 20.8 units
BC = BD + DC = 9 + 20.8
BC = 29.8 units.
Perimeter of triangle ABC = BC + AB + AC
Perimeter of triangle ABC = 29.8 + 15 + 24
Perimeter of triangle ABC = 68.8 units.
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Which image is a reflection of the orange letter K in Quadrant I?
I'll give you brainliest if you actually answer my question
The answer is the green K in quadrant IV
what is the Cartesian co-ordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The K in the fourth quadrant is a reflection of K in the first quadrant because it first flips the K and but there is no change in the position of the x-axis quite clearly.
Hence, The answer is the green K in quadrant IV
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y2-y1
m =
X2-X1
Find the slope of the line that passes
through these two points.
Simplify completely.
(1,5)
(4,6)
m =
[?]
Answer:
[tex]\sf m=\dfrac{1}{3}[/tex]
Step-by-step explanation:
The slope of a line can be found using the following formula:
[tex]\sf m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (1, 5) and (4, 6):
where:
x₁ = 1, x₂ = 4
y₁ = 5, y₂ = 6
Substitute these values into the formula:
[tex]\sf \sf m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{6-5}{4-1}\\\\m=\dfrac{1}{3}[/tex]
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4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received.
How many slices of pizza did Harris eat?
Kenji is using walnuts to bake muffins and granola for his restaurant. each batch of muffins
1
pound of walnuts. he needs 2 pounds of walnuts to make granola. kenji can use up
2
to 8 pounds of walnuts and still have enough for baking tomorrow.
uses
let b represent the number of batches of muffins kenji makes.
write an inequality that represents the situation.
Answer:
Step-by-step explanation:
1/2b + 2 ≤ 8
b ≤ 12
Answer:
Step-by-step explanation:
1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth
a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.
b). if X = 2 m, find the actual dimensions of the carpet.
c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?
Answer:
look above
Step-by-step explanation:
hopeit hepls
While traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent.while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro = 1.3687 us dollars
Answer:
$44.69
Step-by-step explanation:
150 x 1.3687 = $205.305 = $205.31
250 - 205.31 = $44.69
(Hope this helps ^-^)
Answer
44.70 US dollars
Step-by-step explanation: Edg right? If thats what youre reffering too then this is correct
Solve the equation 9x2 + 8x - 5= 3x² to the nearest tenth
Answer:
x=13
Step-by-step explanation:
9*2+8x-5=3x^2
9*2 = 18
18-5=13
13+8x=3x^2
3x^2 = 9x
13+8x=9x
-8x -9x
13=x
x=13
Stock for the jones corporation starts with a value of $39.63 and gains $0.30 in value per month. stock for the overton company starts with a value of $24.45 and gains $0.80 in value per month. when are the two stocks nearly equal in value?
Using linear functions, it is found that the two stocks will be nearly equal in 30 months.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Each of the stocks can be modeled by these following functions:
S1(t) = 39.63 + 0.3t.S2(t) = 24.45 + 0.8t.They will be equal when:
S1(t) = S2(t).
Hence:
39.63 + 0.3t = 24.45 + 0.8t
0.5t = 15.18
t = 15.18/0.5
t = 30.36.
Rounding, approximately 30 months.
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1 Pound brown sugar is equivalent to _____ cups.
Answer:
3 1/2 or 3.5 cups is equal to 1 pound
Step-by-step explanation:
1 Pound brown sugar is equivalent to ___3 1/2 or 3.5__ cups.
Hope This Helped
Answer:
3½ cups
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Prove: Every point on the perpendicular bisector of a segment is equidistant from the ends of the segment.
Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Which equation matches the graph of the greatest integer function given
below?
A. y = [x]-2
B. y = [x] +2
C. y -[x]+3
D. y = [x]-3
The equation that matches the graph of the greatest integer function is y = [x] - 2
How to determine the equation?The parent function of an step function is represented as:
y = [x]
From the given graph, we can see that the lines are shifted 2 units down.
This means that:
(x,y) = (x,y - 2)
So, we have:
y = [x] - 2
Hence, the equation that matches the graph of the greatest integer function is y = [x] - 2
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ABC Car Share Inc. offers car sharing for a $199 yearly fee plus $14/hr for the
use of its car share. What is the total cost for a person who purchases a car
share and uses it for 72 hours total time?
OA. $1307
OB. $1107
C. $1207
OD.
$1407
SUBMIT
Answer:
C
Step-by-step explanation:
199+(14*72) = 1207
annual fee plus cost for each hour used
Maria orders t-shirts for her volleyball camp. Adult-sized T-Shirts cost $6.25 each and youth-sized T-Shirts cost $4.50. Maria has $550 to purchase both adult-sized and youth-sized T-Shirts. If she purchases 45 youth-sized T-Shirts, determine algebraically the maximum number of adult-sized T-Shirts she can purchase.
Answer:
55
Step-by-step explanation:
45 * 4.50 = 202.5
550 - 202.5 = 347.5
347.5/6.25 = 55.6 (55 full t shirts)
HURRY please answer this
Which expression is represented by the model?
Problem Solving
Nicholas is 32 years older than Martina. 9 years ago the sum of their ages was 56. How old is each now?
Answer:
make variables and solve with A
that's the song pota pota pota
Step-by-step explanation:
Answer:
I believe your answer is Nicholas is 53 and Martina is 21
Step-by-step explanation:
44+12=56
9 years later
53 and 21