To pass a truck going 55 mph while you go 60 mph, it will take about 8.94 seconds if using the correct passing techniques. This calculation is based on the relative speed and the total distance required to pass the truck.
First, consider the difference in speeds between the car and the truck. Assuming the truck is going 55 mph as stated in the reference information, and the car speeds up to 60 mph:
Calculate the relative speed:Therefore, it will take approximately 8.94 seconds to pass the truck completely.
What is the relationship between the “solution” to a quadratic equation and the graph of a quadratic equation? How many possible real solutions might there be when you solve a quadratic equation and how do these possible solutions affect the position the parabola on a coordinate plane?
Solutions of a quadratic equation represent points where the graph of the equation (a parabola) intersects the x-axis, and there could be zero, one, or two real solutions.
Explanation:The relationship between the 'solution' of a quadratic equation and the graph of a quadratic equation is that the solutions of a quadratic equation correspond to the points where the graph of this equation, also known as a parabola, intersects with the x-axis on a two-dimensional (x-y) graph. A quadratic equation can have zero, one, or two real solutions. These solutions are represented graphically by where the curve of the parabola intersects the x-axis.
When the parabola intersects the x-axis twice, there are two distinct real solutions. If the parabola is tangent to the x-axis, then there is exactly one real solution, also known as a repeated root, whereas if the parabola does not intersect or touch x-axis at all, then there are no real solutions, indicating that the roots are complex or imaginary.
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How many solutions does the equation have?
2x + 3 = 4x + 2
A. no solutions
B. 1 solution
C. many solutions
What is the value of f(−1) when f(x)=2x+2 ?
Enter your answer in the box.
f(−1)=
The table below shows the average yearly balance in a savings account where interest is compounded annually. no money is deposited or withdrawn after the initial amount is deposited. which type of function best models the given data?
a. linear function with a negative rate of change
b. linear function with a positive rate of change
c. exponential decay function
d. exponential growth function
The given data represents the average yearly balance in a savings account where interest is compounded annually. The function that best models the data is an exponential growth function.
Explanation:The given data represents the average yearly balance in a savings account where interest is compounded annually. Since the balance is increasing over time, the function that best models the data is an exponential growth function. Option d, exponential growth function, is the correct answer.
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What is the answer of 6=1-2n+5
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.
Which equations can be used to solve for y, the length of the room? Check all that apply.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
the correct answer is
B)y2 – 5y = 750
C)750 – y(y – 5) = 0
E)(y + 25)(y – 30) = 0
I JUST took the test
How many times can 5/8 go into 12?
PLEASE HELP ASAP!!!
Draw a Venn diagram to illustrate this conditional:
Cars are motor vehicles.
The Venn diagram that illustrates the given conditional statement is:
Option: a
Step-by-step explanation:Cars are motor vehicles.
This means that all the cars are motor vehicles but converse need not be true.
i.e. all the motor vehicles cant be cars.
i.e. Cars are contained in Motor Vehicles.
Hence, the correct Venn diagram is: Option: a
( Option: b represent the statement
Some cars are Motor vehicles and some motor vehicles are cars.
Option: c represent the statement
Motor vehicles are Cars.
Option: d represent the statement:
Some motor vehicles are cars and some cars are motor vehicles.)
During the first quarter of the year, 351,875 people downloaded an app for their smartphones. During the second quarter of the year, 101,949 fewer people downloaded the app than during the first quarter. How many downloads occurred during the two quarters of the year?
a. Round each number to the nearest hundred thousand to estimate how many downloads occurred during the first two quarters ofthe year.
Imagine a 10 kg block moving with a velocity of 20 m/s to the left. Calculate the kinetic energy of this block
When it is 10:00 am solar time at location x, at which location is 11:00 am solar time being observed?
There are a total of 360 degrees and a total of 24 hours, therefore there are 15 degrees per hour.
Location x is located at 45 degrees, so therefore the location after 1 hour must be at 60 degrees.
Answer:
D
Answer:
it is letter D
Step-by-step explanation:
its letter D when I was doing it, in go formative
A rectangular box has a length of 7 ft a width of 3 ft and a height of 2ft what is the volume
2x+4=3y can someone solve it?
Choose all the numbers that are perfect squares.
64
24
12
49
144
84
4
Justin is constructing a line through point Q that is perpendicular to line n. He has already constructed the arcs shown. A line n and an arc with center Q is drawn. Center Q lies above the line n. The arc cuts the line on two points A and B. A is left of B. Another arc is made with a center at A. The arc cut the line segment A B near point B. The arc is symmetric to line A B. He places his compass on point B to construct an arc. What must be true about the width of the compass opening when Justin draws the arc?
I believe that this problem has the following choices:
It must be equal to BQ .
It must be wider than when he constructed the arc centered at
point A.
It must be equal to AB .
It must be the same as when he constructed the arc centered
at point A.
The correct answer is the last one:
It must be the same as when he constructed the arc centered at point A.
Answer:
The compass must be the same width as it was when he constructed the arc from point A.
Step-by-step explanation:
In order to construct a perpendicular line to a given line, we need to construct a point above and a point below the line such that the segment through them meets the line at a right angle.
When he constructed the arc from point A, it gave him one piece to creating these points. An arc from point B, intersecting the arc from point A at two points, will give him the two points he needs.
In order for the arc from point B to intersect the arc from point A, however, the width of the compass must be the same as it was when he constructed the arc from point A.
Find two positive numbers whose product is 36 and whose sum is a minimum.
To find two positive numbers whose product is 36 and whose sum is a minimum, set up an equation using the arithmetic mean and geometric mean inequality. Solve for the two numbers.
Explanation:To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the arithmetic mean and geometric mean inequality. Let the two numbers be x and y. Since the product of the numbers is 36, we have xy = 36. Using the arithmetic mean and geometric mean inequality, we know that the minimum value of the sum of two positive numbers is attained when the two numbers are equal. Therefore, x = y. Substituting this into the equation xy = 36, we have x^2 = 36. Taking the square root of both sides, we get x = √36 = 6. So, the two positive numbers are x = 6 and y = 6.
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The two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.
Explanation:To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the Arithmetic Mean-Geometric Mean Inequality.
Let x and y be the two numbers.
According to the inequality, the minimum sum occurs when the numbers are equal.
So, we have x = y = √36 = 6.
Therefore, the two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.
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A rectangle's length is 5 units more than the width. the perimeter is 9 times the width. what are the length and the width of the rectangle described?
What is the slope of the line whose equation is 12=4x−6y ? Enter your answer in the box.
Answer:
Slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
Step-by-step explanation:
The slope line form is denoted by
y = mx + c
Where m is the slope and c is the y- intercept .
As given
The equation of the line is given by .
12=4x−6y
It is also written as
6y = 4x - 12
[tex]y = \frac{4x}{6} -\frac{12}{6}[/tex]
Simplify the above
[tex]y = \frac{2x}{3} -2[/tex]
(Compare with y = mx + c )
Thus
[tex]m = \frac{2}{3}[/tex]
Therefore the slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
Find the value of x and the value of y.
The sum of the squares of two consecutive odd integers is 1570. find the integers
Final answer:
Two consecutive odd integers whose squares sum to 1570 are found by setting up a quadratic equation. Solving this equation gives us 27 and 29 as the required integers.
Explanation:
The question requires us to find two consecutive odd integers whose squares add up to 1570. Let's consider the smaller integer to be n, which means the next consecutive odd integer would be n + 2 (since there is always a difference of 2 between consecutive odd numbers). Our equation based on the given information will be:
[tex]n^2 + (n + 2)^2[/tex] = 1570
To solve for n, we will expand the equation and simplify:
[tex]n^2 + n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n - 1566[/tex] = 0Divide the entire equation by 2: n2 + 2n - 783 = 0Solving the quadratic equation, we find that n = 27 and n = -29.
As we are looking for positive integers, we take n = 27. Therefore, the two consecutive odd integers are 27 and 29.
Which answer is the solution set to the given inequality |x+7| < 17
Landscapers plan to spread a layer of stone on a path. The number ss of bags of stone needed varies directly with the depth dd (in inches) of the layer. They need 20 bags to spread a layer of stone that is 2 inches deep. How deep will the layer of stone be when they use 15 bags of stone?
2/20 = x/15
cross multiply
20x/30
x = 30/20 = 1.5
it will be 1.5 inches deep
2/20 = x/15
cross multiply
20x/30
x = 30/20 = 1.5
it will be 1.5 inches deep
This circle is centered at the point (4,5) and the length of its radius is 3. What is the equation of the circle
What is the measure of each interior angle of a regular 10 sided polygon?
An investment grows by 20% over a 20 year period. What is its effective annual percent growth rate?
The effective annual percent growth rate is 3.97%.
Explanation:The effective annual percent growth rate can be calculated using the formula:
Effective Annual Growth Rate = (1 + Growth Rate)^(1/n) - 1
Given that the investment grows by 20% over a 20-year period, the growth rate would be 0.20.
Substituting the values into the formula:
Effective Annual Growth Rate = (1 + 0.20)^(1/20) - 1
Simplifying further:
Effective Annual Growth Rate = (1.20)^(0.05) - 1
Effective Annual Growth Rate = 0.0397 or 3.97%
Final answer:
The effective annual percent growth rate for an investment that grows by 20% over a 20-year period is approximately 0.949%.
Explanation:
To calculate the effective annual percent growth rate, we need to use the formula for compound interest:
A = P(1 + r)^n
where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of years the money is invested for.We can rearrange this formula to solve for r:
r = (A/P)^(1/n) - 1
Given that the investment grows by 20% over 20 years, this means A = 1.20P, as it has increased by 20%. With P as the original amount and n as 20 years, the calculation is:
r = (1.20)^(1/20) - 1
Now we compute the value:
r = (1.20)^(0.05) - 1
r ≈ 0.00949
Converting this into a percentage:
r ≈ 0.949%
Therefore, the effective annual percent growth rate is approximately 0.949%.
Find the value of x and y
x+4y=21, 4x-16=y
A segment has endpoints with coordinates - 3 and 4. What is the length of the segment?
Answer: 7 units
Step-by-step explanation: In this problem, the given numbers -3 and 4 represent the coordinates of the endpoints of a segment and we are asked to find the length of the segment.
To find the length of a segment, we take the greater endpoint coordinate minus the lesser endpoint coordinate.
In this case, the greater endpoint coordinate is 4 and the lesser endpoint coordinate is -3.
So, we have 4 - (-3) which can also be thought of as 4 + 3 which equals 7.
Therefore, the length of this segment is 7 units.
When u.s. students took the timss, 53 percent of them: a. overestimated their math skills. b. were realistic about their math skills?
A proof uses logical reasoning that starts with accepted ideas and proceeds through logic to reach a conclusion.
Which type of reasoning does a mathematical proof use?
deductive or inductive
Solution for 5y-4=9y+8 equation