Final answer:
The quadratic function represents the gas mileage of a car in relation to its speed. By calculating the vertex of the parabola, it is determined that the best gas mileage for the given new car model occurs at a speed of 42 mi/h, which can lead to more efficient driving.
Explanation:
Understanding Gas Mileage and Speed
The question revolves around the mathematics found in the relation between speed and gas mileage for cars. Specifically, a quadratic function M(s) = -1/28s²+3s-31 represents the gas mileage M, in miles per gallon (mi/gal), at a given speed s in miles per hour (mi/h) for a new car model. To analyze this model, one may want to find the speed that provides the best gas mileage, which typically requires finding the vertex of the parabolic graph that this equation represents.
To find the speed that gives the maximum gas mileage, we would complete the square or use the vertex formula for a parabola given by s = -b/(2a), where a and b are the coefficients of the quadratic term and the linear term, respectively. For our function, a = -1/28 and b = 3. Plugging these into our formula gives a speed of s = -3 / (2 * -1/28) = 42 mi/h. This suggests that the best gas mileage for this car model occurs at a speed of 42 miles per hour.
It is essential to understand the relationship between speed and gas efficiency because it can help reduce fuel consumption and costs, as well as lessen environmental impact. By finding the optimal speed for gas mileage, drivers can make informed decisions about their driving habits for financial and ecological benefits.
A cone has a diameter of 18 units and height of 8 units. What is its volume?
Answer:
289
Step-by-step explanation:
btw i need the point pls dont use this
Final answer:
The volume of a cone with a diameter of 18 units and height of 8 units is approximately 678.58 cubic units, calculated using the formula V = 1/3πr²h.
Explanation:
The student is asking about the volume of a cone with a given diameter and height. To calculate the volume (V) of a cone, you can use the formula:
V = ⅓πr²h
where π (pi) is approximately 3.14159, r is the radius of the base of the cone, and h is the height of the cone.
The diameter is given as 18 units, so the radius (r) is half of the diameter, which is 9 units. The height (h) is given as 8 units. By substituting these values into the formula, the calculation for the volume is:
V = ⅓π(9 units)²(8 units)
V = ⅓π(81 units²)(8 units)
V = ⅓π(648 units³)
V = 216π units³
When we calculate this using the approximate value of π, the volume is:
V = 216 × 3.14159 units³
V = 678.58464 units³
The volume of the cone is approximately 678.58 cubic units.
Nendell saw at a diner if he bought one of each item and spent $7.50, how much did the drink cost
In science class Krissy labeled 26 vertebrae bones on a diagram of an adult human Doug labeled 1 bone in the throat and 6 bones of the inner ear for both ears. Most adult humans have 206 bones. Write an equation to solve for the number of bones left in the diagram that need to be labeled
Brian has reduced his cholesterol level by 12% by following a strict diet and regular exercise. If his original level was 220, what is his approximate cholesterol level now?
Final answer:
By reducing his cholesterol level by 12% from the original 220 mg/dL, Brian's current approximate cholesterol level is 193.6 mg/dL.
Explanation:
Brian has reduced his cholesterol level by 12% by following a strict diet and regular exercise. If his original level was 220, to calculate his current cholesterol level, we need to find 12% of 220 and then subtract that from 220. Here's how:
Calculate 12% of 220: (12/100) * 220 = 26.4.
Subtract the reduction from the original level: 220 - 26.4 = 193.6.
Therefore, Brian's approximate cholesterol level now is 193.6 mg/dL.
Someone please help me!
Cherries cost $5 for 2 pounds and $7.50 for 3 pounds.
Question:
a. What is the cost per pound?
b. Is it constant?
c. If you were to graph this situation, would you put weight or cost on the x-axis? Which one would you put on the y-axis?
d. Plot the two points described.
e. How much would 5 pounds of cherries cost? What did you do to solve this problem?
Draw your answer below:
A) 5/2 = 2.50, it costs $2.50 per pound
B) yes because 7.50 / 3 = 2.50 as well
C) weight would be on x-axis and cost on the Y axis
D) draw a graph and put the dots on (2,5) and (3,7.50) and draw a straight line
E) 2.50 *5 = $12.50, multiply cost per pound by pounds.
-4w less than or equal to 20
There are two containers of milk. There is twice as much milk in the first container as in the second. After using 2 gal. of milk from the second container and 3 gal. of milk from the first container, the second container had 4.5 times less milk than the first. How many gallons of milk were in both containers originally?
Let us say that:
V1 = initial gallons in first container
V2 = initial gallons in second container
From the problem statement, we can create the equations:
V1 = 2 V2
V1 – 3 = 4.5 (V2 – 2)
Combining the two:
2 V2 – 3 = 4.5 (V2 – 2)
2 V2 – 3 = 4.5 V2 – 9
2.5 V2 = 6
V2 = 2.4 gallons
V1 = 2 V2 = 4.8 gallons
So there are 4.8 gallons in the 1st container while 2.4 gallons in the 2nd container.
-9x is greater than or equal to -3(x-4)
Use the distributive property to express 16+48
Final answer:
The sum of 16 and 48 can be expressed using the distributive property by factoring out the common factor of 16, yielding 16 + 48 = 16(1 + 3).
Explanation:
The question involves using the distributive property, a concept in mathematics, to express the sum of two numbers, specifically the numbers 16 and 48. To apply the distributive property, we look for a common factor that can be factored out. In this case, the common factor of both 16 and 48 is 16. Therefore, we can express the sum as:
16 + 48 = 16(1 + 3)Here, we've factored out the number 16 that is common to both terms in the sum. The distributive property allows us to then multiply 16 by each term inside the parentheses to get back the original expression.
This is an example of how the distributive property can simplify expressions and aid in mental calculations, such as understanding that 48 can be divided evenly by 16, resulting in 3.
Help me I want to understand this finnall part
Explain how you can use a model to find 6x17
Answer:
The required model is shown below:
Step-by-step explanation:
Consider the provided information.
We need to use partial products model to solve 6×17
The partial product is the product of parts of each factor.
Here Multiplicand is 6 and Multiplier is 17
We can rewrite 17 as 1 ten and 7 ones. i.e 17=10+7
Therefore,
6×17 = 6(10+7)
6×17 = 6×10+6×7 [Distributive property]
6×17 = 60+42 = 102
Hence, the required model is shown below:
‘Mathnificent’ is a math tutoring service. The first year it was open, it had 5 students. If 3 new students enroll each year, which of the following equations represents how many students will be enrolled in x years?
A. y = 5x - 3
B. y = 5x + 3y
C. y = 3x - 5
D. y = 3x + 5
Final answer:
The equation representing the number of students enrolled after x years is y = 3x + 5, taking into account the initial number of students and the annual enrollment of new students.(Option D)
Explanation:
To determine the equation that represents the number of students enrolled in Mathnificent tutoring service in x years, we start with the initial condition that there were 5 students in the first year. Since 3 new students enroll each year, we add 3 to the number of students for each subsequent year. The total number of students after x years can be represented by adding the product of 3 (the number of new students enrolling each year) and x (the number of years) to the initial number of students, which is 5.
The correct equation to represent this scenario is y = 3x + 5. This equation indicates that there is a constant rate of new students enrolling each year (3), and we are adding these to the initial count (5).
Which set of rational numbers is arranged from least to greatest?
−3.5, negative 1 over 4, 2, 1 over 3
−3.5, negative 1 over 4, 1 over 3, 2
2, 1 over 3, negative 1 over 4, −3.5
negative 1 over 4, 1 over 3, 2, −3.5
Is 22/15 less than 14/31?
Is 19/35 greater than 27/19
Is 15/25 greater than 22/44
Is 30/25 less than 29/30
malcolm buys a 5/6 pound bag of black beans and a 3/4 pound bag of pinto beans. how many pond of beans does malcolm buy in all
5/6 + 3/4
5/6 = 10/12
3/4 = 9/12
10/12 + 9/12 = 19/12 = 1 7/12 pounds total
Answer: the answer is 1 7/12 pounds
Step-by-step explanation:
Because 5/6+3/4=1 7/12
The formula f=n/4+37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. Use the formula to estimate the temperature when n = 18 chirps/min. Round to the nearest whole number, if necessary. 41 42 37 46
[tex]f=\dfrac{n}{4}+37\\\\\text{substitute the value of n = 18 to the expression}\\\\f=\dfrac{18}{4}+37=4.5+37=41.5\approx42[/tex]
Answer: f = 42.
By using substitution of value n, temperature F in degree Fahrenheit is 42.
What is substitution method?"The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables."
Given
Formula to estimate the temperature F in degree Fahrenheit
f = [tex]\frac{n}{4} +37[/tex]
n = 18 chirps/min
Substituting n in the formula
f = [tex]\frac{n}{4} +37[/tex]
⇒ f = [tex]\frac{18}{4}+37[/tex]
⇒ f = 4.5 + 37
⇒ f = 41.5 ≅ 42 (nearest whole number)
Thus, temperature F in degree Fahrenheit is 42.
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points A is 5,623m above sea level.points B is below sea level at -1,245m. what is the distance between the two points?
Round 846 divided by 11 to the nearest tenth
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=
Answer:
The value of f(-2) is, -2
Step-by-step explanation:
The graph which is shown on the coordinate plane passes through the two points i.e, (2,0) and (0, -1).
First find the equation for this line:
Using Point-Slope form for the equation of line: [tex]y-y_{1}=m(x-x_{1})[/tex] ..[1]
where m is the slope given by ;
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First find the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1-0}{0-2}[/tex]
⇒ [tex]m=\frac{-1}{-2} =\frac{1}{2}[/tex]
Now, substitute the value of m=[tex]\frac{1}{2}[/tex] , [tex]x_{1}[/tex]= 2and [tex]y_{1}[/tex]=0 in equation [1];
[tex]y-0=(\frac{1}{2})(x-2)[/tex] or
[tex]y=\frac{1}{2}\cdot (x-2)[/tex]
In this graph x represents the input of the process and Y the output of the process and f the function of the variable x i.e, y=f(x)
∴ [tex]y=f(x)=\frac{1}{2}(x-2)[/tex] ....[2]
now, we put the value of x=-2 inequation [2] to solve for f(-2).
[tex]f(-2)=\frac{1}{2}(-2-2) =\frac{1}{2} \cdot (-4)[/tex]
Simplify we get;
[tex]f(-2)=-2[/tex]
I really need help on this.
Joshua has a baseball card collection.84 cards make up 70% of his collection how many cards are in his total collection
What is the equation of this line in standard form? A. −6x+7y=−11 B. −6x+5y=13 C.
−6x+7y=11 D. −7x+6y=−11
Answer:
The answer is 6x-5y=-13
Step-by-step explanation:
Which two sets of angles are corresponding angles?
∠e and ∠h; ∠f and ∠g
∠e and ∠i; ∠f and ∠h
∠e and ∠g; ∠f and ∠h
∠e and ∠i; ∠f and ∠g
What is 57.15% rounded to the nearest whole percent?
The number we would get when we round 57.15% to the nearest whole number is: A. 57%.
What is Nearest Whole Percent?Nearest whole percent means the number has no fractional part of decimal.
Given the number, 57.15%, to round it to the nearest whole number, digits 1 and 5 would be removed since the last number closer to the whole number is less than 5.
Thus, we would have 57%.
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2a + 4b = d for b
I trying to solve for b.
I don't understand how to isolate the variable.
Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 14x + 8 as ordered pairs.
For the equation y = 14x + 8, the ordered pairs with x values of 1, 2, 3, and 4, calculated by substituting these x-values into the equation, are (1,22), (2,36), (3,50), and (4,64).
Explanation:The equation in question is a linear equation, y = 14x + 8 , and you've been asked to use the x-values: 1, 2, 3, and 4 to write the solutions as ordered pairs. To find the corresponding y-values, substitute these x-values one by one into the equation.
For x = 1, y = 14*1 + 8 = 22, so the ordered pair is (1,22) For x = 2, y = 14*2 + 8 = 36, so the ordered pair is (2,36) For x = 3, y = 14*3 + 8 = 50, so the ordered pair is (3,50) For x = 4, y = 14*4 + 8 = 64, so the ordered pair is (4,64)
These points plotted on a graph represent the dependence of y on x.
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To determine the solutions of the equation y = 14x + 8 for x-values 1, 2, 3, and 4, each x-value is substituted into the equation to find the corresponding y-values, resulting in ordered pairs (1,22), (2,36), (3,50), and (4,64).
Explanation:To find solutions of the equation y = 14x + 8 using the x-values 1, 2, 3, and 4, we will substitute each x-value into the equation and solve for y to obtain the corresponding y-value.
These ordered pairs represent solutions for the given linear equation and show the dependence of y on x.
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given that 4,12,x,y,324,972 is a geometric sequence. find the sum of x and y
The sum of x and y in the given geometric sequence is 144, with x being 36 and y being 108, based on the common ratio of 3.
To solve the problem, we first need to recognize that a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a constant called the common ratio. We are given a sequence 4, 12, x, y, 324, 972, and we need to find the common ratio and subsequently x and y.
Step-by-Step Solution:
Find the common ratio (r) using two known consecutive terms.
Once r is found, apply it to determine the missing terms x and y.
Calculate the sum of x and y.
Given the sequence 4, 12, x, y, 324, 972, let's use the first two terms to find the common ratio. The ratio of the second term to the first term is 12 / 4 = 3. Thus, the common ratio (r) = 3.
Now, let's find x by multiplying the second term (12) by the common ratio: x = 12 x 3 = 36.
To find y, multiply x by the common ratio: y = 36 x 3 = 108.
The sum of x and y is then: x + y = 36 + 108 = 144.
Add the two expressions. 8k + 4 and 3k + 8
Enter your answer in the box.
THE ANSWER IS 11K + 12
Which property was applied to create this equivalent expression? 7x+(5+6×)--->(7x+5)+6x
Answer:
Associative property is applied
Step-by-step explanation:
7x+(5+6×)--->(7x+5)+6x
In the given expression , the terms are grouped in different order
In associative property, we can group the numbers in any order
(a+b)+c -------> a+(b+c)
first two terms are grouped on the left side
last two terms are grouped on the right side
7x+(5+6×)--->(7x+5)+6x
In the given expression, the terms are grouped in different order
So Associative property is applied
Answer:
Associative property of Addition.
Step-by-step explanation:
We are given the following information in the question:
We are given the expression:
[tex]7x + (5+6x) = (7x+5)+6x[/tex]
We have used the associative property of addition.
Associative property of addition:
The associative property states that we can add regardless of how the numbers are grouped. By grouped it is meant how you use parenthesis are used. In other words, if we are adding, it does not matter where you put the parenthesis. Whatever may be the order of addends, the sum will always be same.