The range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
Given that, a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula [tex]d = v + \frac{v^2}{20}[/tex].
Here,
[tex]75=v+\frac{v^2}{20}[/tex]
[tex]75=\frac{(20v+v^2)}{20}[/tex]
[tex]v^2+20v=20\times75[/tex]
[tex]v^2+20v=1500[/tex]
[tex]v^2+20v-1500=0[/tex]
[tex](v+50)(v-30)=0[/tex]
[tex]v-30=0[/tex]
[tex]v=30[/tex]
First thing is to realize what 'not to exceed' means. More than 75 feet exceeds 75 feet, but exactly 75 feet or anything less does not. So you want to determine v such that [tex]d\le75[/tex].
[tex]d=v+\frac{v^2}{20}[/tex]
is the given model. This is a reasonably good model presuming you have a better than average reaction time, dry pavement, new tires, etc. Be that as it may, you need to determine v such that:
[tex]v+\frac{v^2}{20} \le75[/tex]
Multiply by 20, we get
[tex]20v+v^2\le1500[/tex]
Add -1500 to both sides
[tex]v^2+20v-1500\le0[/tex]
[tex](v+50)(v-30)\le0[/tex]
So, [tex]v\le-50[/tex] or [tex]v\le30[/tex]
Thus, the range is [tex]-50\ge v\le30[/tex]
Therefore, the range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
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Kerry can travel at speeds in the range [tex]{(-\infty, 30]} mi/h[/tex].
To find the range of speeds Kerry can travel while ensuring her stopping distance doesn't exceed 75 feet, we need to solve the inequality [tex]v + \frac{v^2}{20} \leq 75[/tex], where v represents her speed in miles per hour.
First, we rearrange the inequality:
[tex]v^2 + 20v - 1500 \leq 0[/tex]
Next, we factor the quadratic equation:
[tex](v - 30)(v + 50) \leq 0[/tex]
This gives us two critical points: v = 30 and v = -50.
Since speed cannot be negative, we discard v = -50.
Now we test the intervals created by the critical point:
- For v < 30, the inequality holds.
- For v > 30, the inequality does not hold.
What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?
A. x = −6
B. x = −4
C. y = −6
D. y = −4
we know that
The given line is parallel to the x-axis
so
the equation of the line that is parallel to the given line and passes through the point [tex](-4,-6 )[/tex] will be equal to the y-coordinate of the point
The y-coordinate of the point is [tex]-6[/tex]
therefore
the equation is
[tex]y=-6[/tex]
the answer is the option C
[tex]y=-6[/tex]
Please help with this problem.
What is the value of y?
Enter your answer in the box.
If, while training for a marathon, you ran 76 miles in 2 2/3 months, how many miles did you run each month? (Assume you ran the same amount each month)
Algebra 1: Factoring Polynomials Factor the common factor out of each expression: 40n^4m^2+40n^3m^3-32n^3
24 loaves of bread cost $48. How much do 10 loaves cost
The ratio of the number of boy campers to the number of girl campers with 8 to 7. If there were a total of 195 campers, how many boy campers were there? How many girl campers?
The minimum wage in 2003 was $5.15. This was w more than the minimum wage in 1996. Write an expression for the minimum wage in 1996.
An equation with an exponent is called an exponential equation. true or false?
Write an equation that is linear but not standard form
Answer:
what she said is write so use it
Step-by-step explanation:
A linear equation not in standard form can be represented as y = mx + b, where 'm' is the slope and 'b' is the y-intercept. An example is y = 0.5x + 3, which graphs as a straight line with a slope of 0.5 and crossing the y-axis at the point (0, 3).
A linear equation that is not in standard form could be written as y = mx + b. This form is known as the slope-intercept form of a linear equation, where m represents the slope of the line and b represents the y-intercept, the point where the line crosses the y-axis. For example, if we choose a slope of 0.5 and a y-intercept of 3, the equation would be y = 0.5x + 3.
Simplify the expression.
(1/4)^(-3/2)
Please show how to do the problem.
How do I solve this ?
Solve each inequality and give the solution in interval notation:
Simplify by collecting like terms: 2x-4-6x+8
The solution of the mathmatical exression by combining like terms,
⇒ - 4x + 4
Given that,
An expression to simplify,
⇒ 2x - 4 - 6x + 8
Now, simplify the mathmatical exression by combining like terms,
⇒ 2x - 4 - 6x + 8
Combine like terms,
⇒ 2x - 6x - 4 + 8
⇒ - 4x + 4
Therefore, the solution of expression is,
⇒ - 4x + 4
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P and q are on a number line. If p has a coordinate -5 and pq =7 , what could the coordinate of p be
an object falls d meters in t seconds. what is the independent variable
A company sold 160 units in the last quarter of the year. Which of the following graphs represents the company's sales performance?
The question does not provide specific graphs to choose from for the company's sales performance. Nonetheless, a correct graph would show a point at 160 units for the last quarter of the year.
Explanation:Unfortunately, the question as presented does not include any graphs to choose from. Ideally, the correct graph would have the last quarter of the year on the x-axis and the number of units sold on the y-axis. It would display a single point at 160 units for the last quarter. However, without specific graphs to choose from, a more detailed answer cannot be provided.
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The graph which represents the company's sales performance is graph B.
Which of the following graphs represents the company's sales performance?
The last quarter of the year begins October 1st and ends December 31st.
Total units sold by the company in the last quarter of the year = 160 units
Graph 1:
October = 40 units
November = 60 units
December = 40 units
Total = 140 units
Graph 2:
October = 40 units
November = 65 units
December = 55 units
Total = 160 units
Graph 3:
October = 40 units
November = 50 units
December = 50 units
Total = 140 units
Graph 4:
October = 40 units
November = 60 units
December = 50 units
Total = 150 units
Therefore, last quarter of the year in graph B represents the company's sales.
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24 minutes. Working together, how long will it take for them to paint the wall?
Answer: 8
Step-by-step explanation:
In the expression 4^9 the number 9 is called the
Match each step to its justification to solve 2x+5=19
The steps :
given subtraction property of equality subtract division property of equality divide Further ExplanationOne variable linear equation is an equation that has a variable and the exponent number is one. Can be stated in the form:
[tex]\large{\boxed{\bold{ax=b}}}[/tex]
or
ax + b = c, where a, b, and c are constants, x is a variable
Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one
Can be stated in the form:
[tex]\large{\boxed{\bold{ax+by=c}}}[/tex]
ax + by = c
x, y = variable
There are 2 general steps to solving a linear equation of one variable:
1. add or subtract both segments with the same number so that it is expected that in one segment there are only variable modifiers or constant numbers 2. Change the equation into a simple form so that the coefficient of the variable is 1This can be done by dividing or multiplying by equal numbers
An equation will remain equivalent if both segments are multiplied or divided by the same number
In the equation
2x + 5 = 19
The right steps to complete it according to the images included are:
1. 2x + 5 = 9 ⇒ given 2. both segments are subtracted by the number 52x + 5 -5 = 9-5 ⇒subtraction property of equality
3. 2x = 14 ⇒subtract 4. both segments are divided by 2 so that the coefficient x = 1[tex]{\displaystyle {\frac {2x} {2}}=~\frac{14}{2}[/tex]
⇒division property of equality
5. x = 7 ⇒ divideLearn more
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Keywords: variable, linear equation
3 -2 is equivalent to _____.
A -6
B -9
C 1/9
D 1/6
Thanks!
what is the answer to qx + x = r
The value of x in the equation qx + x = r can be found by combining like terms and then isolating x. The solution is x = r / (q+1).
Explanation:The equation given is qx + x = r. This equation belongs to the domain of algebra and can be simplified using the principles of solving linear equations. Let's work step-by-step to evaluate the solution to this equation:
First, we can combine like terms on the left side, meaning we can add qx and x together since they are similar terms. By factoring out x, we get x(q + 1) = r. Then, in order to solve for x, we have to divide r by the sum of q + 1. The resulting equation is x = r / (q + 1).That is the solution to the equation.
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True or false: it is possible to determine a vector if only one of its components is known.
What is the greatest common factor for 200 and 205
If x represents the width of a rectangle and if its length is twice its width how long is the rectangle
If x represents the width of a rectangle and if its length is twice its width then rectangle is 2x long.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that x represents the width of a rectangle.
Length is twice its width
Length=2width
Length=2x
Length is nothing but how long the rectangle.
As the width of rectangle is x and length is 2x.
The area of rectangle is length times of width
Area of rectangle=Length×Width
=2x×x
=2x²
Hence, x represents the width of a rectangle and if its length is twice its width then rectangle is 2x long.
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18 tens 20 ones = Hundreds
t−12/2=3/t2−3
solve for T
–3
–1
1
3
Select the equation that most accurately depicts the word problem. The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.
you don't list the options but it should look something like this:
68=2L+2(9)
The set of whole numbers is closed under division
True or false
Answer:
true
Step-by-step explanation:
11+22+33+...+1010 is divided by 5. what is the remainder? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4