Answer:
This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.
One potential confusion students may have follows from the subtle difference between what the car is doing and the idea of slope as the ratio between the change in vertical distance on the graph and the change in horizontal distance on the graph. Because the car is traveling one mile on a down-hill slope, the situation could be represented as a right triangle with a hypotenuse of 5,280 ft and a leg of 250 ft; using the Pythagorean Theorem they would find that the other leg is approximately 5,274 ft. Following through on this interpretation, a student might conclude that the car travels a horizontal distance of approximately 5,274 ft for every 250 ft in vertical distance and arrive at a slope of approximately -0.047. While this is, in some sense, the slope of the hill, it is not the slope of the function as described. This interpretation yields numbers that are very close to the situation described in the task, yet conceptually different since the distance traveled by the car would now be expressed in terms of horizontal distance traveled as opposed to distance along the slope of the hill to compute the elevation. If students do indeed pursue this line of reasoning, the task provides an opportunity to compare and contrast the graph of the function and what it represents with a drawing of the hill and the vertical and horizontal distances traversed with each mile down the slope.
Step-by-step explanation:
From the given function in terms of D the elevation of the car above sea
level can be determined.
Responses:
The slope is the decrease in the elevation per unit increase in distance from the top of the hill.The y-intercept is the elevation of the top of the hill above sea level.The x-intercept is the distance from the top of the hill top when the elevation of the car is at sea level.How can the linear function for the slope and intercept be interpreted?Given:
The function that gives the elevation of the car above sea level, from the top of the hill is given as follows;
Elevation above sea level = 7500 - 250·D
Where;
0 ≤ D ≤ 6
Required:
The meaning of the slope and intercepts of the graph of the function.
Solution:
From the given linear function, of the elevation of the car, we have;
The slope which is -250 = The decrease in the elevation when the distance of the car from the top of the hill increases by 1 mile.The y-intercept, which is 7,500, is the elevation above sea level when the car is 0 mile from the top of the hill, which is when the car is at the top of the hill.The x-intercept is the point at which the elevation, which is the distance the car will be from the top of the hill when it is at sea level.Learn more about linear functions here:
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A motorist is pumping gas into his car at a rate of StartFraction 5 over 12 EndFraction of a gallon every StartFraction 1 over 24 EndFraction of a minute. At this rate, how many gallons of gas will he have pumped into his car in One-half of a minute?
1
5
10
20
it is 5
Step-by-step explanation:
The measures of the angles of Triangular garden are in the ratio 2:5:5. What are the measures of the angles? Classify the triangle based on its sides :)
2x + 3x + 5x = 180
10x = 180
x = 18
2x = 36, 3x = 54, 5x = 90
They add up to 180 (definition of sum of angles of a triangle.)
Name <2 in many different ways as possible.
Answer:
2 to two too
Step-by-step explanation:
thats how much i think
Please give me the correct answer.Only answer if you're good at math.
Answer:
The first hour is 14 euros and each hour after that is 2 euros.
a jewellery shop is having a sale
a bracelet is now reduced to 420 pounds
this is 70% of the original price
A) workout the original price of the bracelet
a ring is now reduced to 840 pounds
this is a saving of 40% of the original price
b) workout the original price of the ring
Answer:
a) £600
b) £1400
Step-by-step explanation:
a)
original price = x
reduced price = £420
reduced price is 70% of original price
Since the discounted price, £420, is 70% of the original price, x, then
70% of x = 420
0.7x = 420
x = 420/0.7
x = 600
Answer: £600
b)
original price = x
discounted price = £840
discount percentage = 40%
The original price is x, and x is 100% of the original price since 100% is the whole amount. The discount is 40% of the original price. 100% - 40% = 60%. That means the discounted price is 60% of the original price.
60% of x = 840
0.6x = 840
x = 840/0.6
x = 1400
Answer: £1400
she’s not skinner than you...she’s just a picky eater.
go get that big mac you been wanting ❤️
Answer:
ok
Step-by-step explanation:
Answer:
huh????
Step-by-step explanation:
Three girls (Zeva, Abby and Jenny) went to a hair salon. Each girl had their hair styled (curly, straight, and wavy) and colored (blonde, red, and black). From the clues below, which chart correctly matches the girl, the hairstyle and the color?
Answer:
You need to make the question again and include the chart.
Step-by-step explanation:
1. What is the circumference of a tire with a diameter of 12 inches?
A36
B48
C24
D6
2. What is the radius of a circle with a diameter of 20 inches?
A10
B60
C30
D40
3. What is the circumference of a circle with a radius of 12?
A24
B72
C6
D36
4. What is the circumference of a circle with a radius of 7 feet?
A28
B42
C14
D3.5
5. What is the radius of a circle with a diameter of 36 inches?
A6
B18
C12
D16
6. What is the circumference of a circle with a diameter of 30 centimeters?
A60
B90
C50
D15
7. Is the diameter of a tire less than, greater than, or equal to its circumference?
Aequal
Bnot enough information
Cless than
Dgreater than
8. What is the diameter of a tire with a radius of 11 inches?
A22
B33
C5.5
D121
9. Your favorite CD has a radius of 9 centimeters. What is the circumference of the CD?
A18
B4.5
C27
D54
10. Which is true about the radius and diameter?
AThe radius and diameter can sometimes be equal.
BThe diameter is two times the size of the radius.
CThe diameter is half the size of the radius.
DThe radius is two times the size of the diameter.
Answer:
1) A. 36
2) A. 10
3) B. 72
4) B. 42
5) A. 6
6) B. 90
7) C. less than
8) A. 22
9) D. 54
10) B. The diameter is two times the size of the radius.
Step-by-step explanation:
1) 12 x 3.14 = 36
2) 20/2 = 10
3) 12 x 2 x 3.14 = 72
4) 7 x 2 x 3.14 = 42
5) 36/3.14 = 12/2 = 6
6) 30 x 3.14 - 90
8) 11 x 2 =22
9) 9 x 2 x 3.14 = 54
4.6 isosceles and Equilateral triangles
Answer:
Step-by-step explanation:
5555
The red arcs mean those angles are the same.
When two angles are the same the corresponding sides are also the same.
5. X = 8
6. X = 11
7. 2x-16 = 8
Add 16 to both sides:
2x = 24
Divide both sides by 2:
X = 12
8. X + 19 = 8
Subtract 19 from both sides:
X = -11
-1/4m + 5 = 16; m =
what does m =
You have $35 in your bank account and deposit $2.50 each week. At the same time, your cousin has $115 but is withdrawing $7.50 each week. When will the accounts have the same balance? How much will they have?
What are the variables and equations, and how do you solve?
Answer:
$55
Step-by-step explanation:
Let w = the no. of weeks
35 + 2.50w = amount you will have in the account after w weeks
115 - 7.5w = amount cousin will have in the account after w weeks
You need to set these expressions equal to each other.
35 + 2.50w = 115 - 7.5w Multiply thru the equation
by 10 to remove the fractions
350 + 25w = 1150 - 75w
100w = 800
w = 8 weeks
35 + 2.50w = 35 + 2.5(8) = 35 + 20 = $55
115 - 7.50w = 115 - 7.50(8) = 115 - 60 = $55
Help me? I’m giving brain
Answer:
4.31 as said
Step-by-step explanation:
Answer:
it could be 4.30 because when u divide those two the answer is 4.3057142857, and because the number in the hundreths place is just a 0 its probably just 4.30 i could be wrong sorry
please please please please help me
Sim porque positivo não fecha
Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $51,800?
Answer:
3.8 months
Step-by-step explanation:
Question: Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $51,800?
First step! What is 5.3% of 36k?
1,908
Second Step! Divide
51,800/1,908= 27.1488469602
Third Step! Round
27.1488469602= 27.1
27.1 weeks.
7 weeks in a month.
12 months in a year.
27.1/7= 3.8
3.8 months
The number of years for the amount of compound interest to reach $51,800 is given by b = 7 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the number years be represented as b
where the amount after b years is = $ 51,800
The initial principal amount P = $ 36,000
The number of times the compound interest is applied = quarterly = 4
Now , the equation is
A = P ( 1 + r/n )ⁿᵇ
On solving for the number of years b , we get
b = ln ( A / P ) / n [ ln ( 1 + r/n ) ]
b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln ( 1 + 0.053/4 ) ] )
On further simplification , we get
b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln (1 + 0.01325 ) ] )
b = 6.911 years
On rounding to the nearest year , we get
b = 7 years
Therefore , the value of b is 7 years
Hence , the number of years is 7 years
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The formular r= √A/P- 1 gives the interest rater that will allow principal P to grow into amount A in two years, if the interest is compounded annually. Suppose you have 5425
to deposit into an account. Find the interest rate you would need to have $470 in the account at the end of the second year.
The interest rate is 29.43%
How to determine the interest rate?The given parameters are:
Amount, A = $470
Principal, P = $5425
The formula of rate is given as:
r= √A/P- 1
Substitute known values
r= √470/5425- 1
Evaluate the difference
r= √470/5424
Evaluate the quotient
r= √0.08665
Evaluate the exponent
r= 0.2943
Express as percentage
r = 29.43%
Hence, the interest rate is 29.43%
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pls help i will give you like and brainliest if you are correct!!!
Answer:
+9.2=7.6x
x+9.2=38x
______
5
Solution
=1.393939393
1\2+ 1/4 rasultado y explicasion
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Simplemente agregue usando la calculadora y debería obtener esta respuesta. ;)
cubed root of 1080 in simplest radical form
mary works for a commission of 12% on all goods she sell for the month if her basic salary is 3000 per month and she sells $2500 worth of goods for a certain month calculate mary's gross salary for that particular month
Answer:
3300
Step-by-step explanation:
Formula
Gross Salary = Basic + Commission
Givens
Basic = 3000
% = 12%
Solution
Gross = 3000 + 12/100 * 2500
Gross = 3000 + 30000/100
Gross = 3000 + 300
Gross = 3300
The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft? What is the length of the field?
80 ft
100 ft
120 ft
140 ft
Answer:
The answer is 120 feet.
Step-by-step explanation:
The area of the field (A) is:
A = w · l (w - width, l - length)
It is known:
A = 12,000 ft²
l = w - 20
So, let's replace this in the formula for the area of the field:
12,000 = w · (w - 20)
12,000 = w² - 20
⇒ w² - 20w - 12,000 = 0
This is quadratic equation. Based on the quadratic formula:
ax² + bx + c = 0 ⇒
In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000
Thus:
So, width w can be either
or
Since, the width cannot be a negative number, the width of the field is 120 feet.
The length of the field is 120 feet.
Option C is the correct answer.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
Let's start by using the given information to set up two equations:
Let x be the length of the field in feet.
Then, the width of the field is x - 20 feet.
The area of the field is given as 12,000 square feet:
x (x - 20) = 12,000
Expanding the left side of the equation, we get:
x² - 20x = 12,000
Bringing all the terms to one side, we get:
x² - 20x - 12,000 = 0
Now, we can solve this quadratic equation using factoring,
Completing the square, or the quadratic formula.
Here, we will use factoring:
x² - 20x - 12,000 = 0
(x - 120) (x + 100) = 0
The solutions are x = 120 and x = -100, but a negative length doesn't make sense, so we reject that solution.
Therefore,
The length of the field is 120 feet.
To check, we can substitute x = 120 into the equation for the width:
Width = x - 20 = 100 feet
Area = Length x Width
= 120 ft x 100 ft
= 12,000 sq ft
Thus,
The length of the field is 120 feet.
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Find the slope for the line that runs through points (2,5) and (-3, 7). Write your answer as a fraction using the slash as your fraction bar.
A) 2/5
B) 5/2
C) -2/5
D) -5/2
Answer:
c.
Step-by-step explanation:
5-7 = -2
2 - -3=5
-2/5
Ariane borrows $300 on a 5−year loan. She is charged 5% simple interest per year. How much interest is she charged for 5 years? What is the total amount she has to pay back?
Answer:
Interest = $75
Total to pay back = $375
Step-by-step explanation:
The total amount she will have to pay back is found by the formula:
= Amount borrowed * (1 + rate * years)
= 300 * ( 1 + 5% * 5)
= $375
The interest is therefore:
= Amount to be paid back - Amount borrowed
= 375 - 300
= $75
Find the value of x.
Answer:
x = 25
Step-by-step explanation:
One can use the Line Tangent to a Circle theorem to solve this problem. The Line Tangent to a Circle theorem states that when two non-parallel lines are tangent to a circle (the lines touch the circle at a single point), then the distance between the intersection point and the point of tangency is the same for both lines. This theorem does go by other names, but the actual theorem content is the same.
Using this one can form the equation;
BA = CA
Substitute,
2x + 3 = 53
Inverse operations,
2x + 3 = 53
-3 -3
2x = 50
/2 /2
x = 25
I don´t like math can I get some help with this math maze.
Answer:
Go down down and to the right
Can someone help me on this
Answer:
P = 44
Step-by-step explanation:
perimeter of a square = 4a
where a = side lenght
equation:
⇒ 4a
solve by substituting 11 for a
⇒ 4a
⇒ 4 x 11
⇒44
2. Find the slope and the y-intercept
of the graph of the linear equation
y = 1/8x + 3
A) Slope: 8; y-intercept: 3
B) Slope: 1/3; y- intercept: 1/8
C) Slope: 1; y-intercept: 1/8
8
D) Slope: 1/8; y-intercept: 3
Answer:
D) Slope: 1/8; y-intercept: 3
Step-by-step explanation:
An equation in the form y = mx + b has certain characteristics that help us determine the slope and y-intercept of the line easily.
The variable "m" gives us the slope of the line, while the variable "b" gives us the y-intercept of the line.
Taking y = 1/8x + 3, we can see that the m-value is 1/8 and the b-value is 3.
Therefore, the slope of this line is 1/8 and the y-intercept is 3.
The answer is D) Slope: 1/8; y-intercept: 3.
find the value of the variable if necessary round your answer to the nearest tenth
Answer:
x = 24.7
Step-by-step explanation:
Here, we want to find the value of x
To do this, we are to use the appropriate trigonometric ratio
From what we have;
9 faces the angle given as it is the opposite, x is below and it is the adjacent
The trigonometric identity that links opposite to adjacent is the tan which is the ratio of former to latter
Thus, we have that;
tan 20 = 9/x
x = 9/tan 20
x = 24.7
Alexander is going to invest $1,900 and leave it in an
account for 7 years. Assuming the interest is
compounded monthly, what interest rate, to the nearest
tenth of a percent, would be required in order for
Alexander to end up with $3,100?
3,100= 1,900 +84x
right since 84 months in 7 years
so 14.3% right?
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Simplify -6w+(-8)+1+(-7w)
Answer:
[tex]-13w-7[/tex]
Step-by-step explanation:
1) Remove parentheses.
[tex]-6w-8+1-7w[/tex]
2) collect like terms.
[tex](-6w-7w) +(-8+1)[/tex]
3) Simplify.
[tex]-13w-7[/tex]
Therefor, the answer is -13w - 7.