Find the distance from point A(−1, 7) to the line y= 3x. Round your answer to the nearest tenth.
I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.
We will get that the distance is 3.22
So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)
That distance is:
[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]
Now we want to minimize this, which is equivalent to minimize d^2, then we can define:
D = d^2
and write:
[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]
Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).
Remember that for a parabola like:
a*x^2 + b*x + c
The vertex is at:
x = -b/2a
Then for our parabola, the vertex will be at:
x = -(-44)/(2*10) = 44/20 = 2.2
Thus the minimum distance is given by:
[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]
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In the diagram ABC = WRS. What is the perimeter of WRS?
the top of a certain mountain in California has an altitude of 14,721 ft above sea level. The bottom Death Valley is 282 ft below sea level. using 0 as sea level, find the difference between these two elevations. what is the difference between these two elevations?
Solve for x.
5(x - 3) + 4(x + 3) = 3(x - 1)
x = 0
x = 1/4
x = 1/2
x = 1
Solve. 5m+72=−2m+52 Drag and drop the answer into the box.
Rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x).
Answer:
[tex]x^2+x-1-\frac{6}{x+4}[/tex]
Step-by-step explanation:
Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]
a(x) = dividend
b(x) = divisor
q(x) = quotient
r(x) = remainder
Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]
We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]
So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]
Thus a(x) = dividend = [tex]x^3+5x^2+3x-10 [/tex]
b(x) = divisor= [tex]x+4[/tex]
q(x) = quotient=[tex]x^2+x-1[/tex]
r(x) = remainder=-6
Substitute the value in the rational form.
[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]
Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is [tex]x^2+x-1-\frac{6}{x+4}[/tex]
What is the greatest common factor of 125,50 and 275
Luis ate three of the eight pizza slices. he paid $2.70 as his share of the cost. how much did the whole pizza cost?
The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base
Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8
Which graph models the equation 2x + 3y = 6?
Answer: i did the test and i got B and i was right so its B
Step-by-step explanation:
Given: x - 5 > -2.
Choose the solution set.
{x | x R, x > -7}
{x | x R, x > -3}
{x | x R, x > 3}
{x | x R, x > 7
x-5>-2
x> -5+2
X>3
Answer is: {x | x R, x > 3}
hey i need help solving these and not just the answer i really would like to know how
rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____
To rewrite the expression as a multiple of a sum of two numbers with no common factor, find the prime factorizations of the given numbers and then multiply them together which brings the result as 39.
Explanation:To rewrite the expression as a multiple of a sum of two numbers with no common factor, we need to find two numbers that have no common factors and multiply them together. Let's find the prime factorizations of 15 and 24:
15: 3 × 524: 2 × 2 × 2 × 3Now we can rewrite the expression as:
15 + 24 = (3 × 5) + (2 × 2 × 2 × 3) = 3 × (5 + 8) = 3 × 13 = 39
So, 15 + 24 can be written as a multiple of 3 × 13, which is 39.
How much in Federal taxes does Curtis annually pay?
he pays 29.59 a week
multiply that by 52 weeks in a year
29.59 * 52 = 1538.68 a year
Answer is A
the scatter plot shows how many desks and computers were found in 12 different offices
how many offices had 11 computers
1
2
3
4
Answer:
It's three. Look at 11 on the Y axis (computers) and count how many dots are at 11. There's a total of three computers based on the dots at 11.
Step-by-step explanation:
A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
The number of offices that have 11 computers is 3.
What is a scattered plot?A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
We have,
Horizontal axes = number of desks
Vertical axes = number of computers
Each dot in the scatter plot indicates offices.
Number of offices = 12 dots = 12
We need to find the number of dots that is with 11 computers.
We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.
Thus the number of offices that have 11 computers is 3.
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For a normal distribution, the z value for an x value that is to the right of the mean is always:
In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.
Explanation:In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.
For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.
In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.
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21: stan bought a monster truck for $2,000 down and payments of $450 a month for five years. what's the total cost of the monster truck?
Answer:
The total cost of the monster truck = 29000 $
Step-by-step explanation:
Stan bought a monster truck for $2,000 down and payments of $450 a month for five years.
Initial payment = 2000 $
Monthly payment = 450 $
Number of years paid = 5
Number of months in 5 years = 12 x 5 = 60
Total amount paid = 2000 + 60 x 450 = 29000 $
The total cost of the monster truck = 29000 $
the table shows the sales of admission tickets to a science museum. A table labeled Science Museum Admission Revenue. It contains a row for Tickets Sold with the amounts 128, 264, 308, 514, 520, 650, 722, and a row for Sales with the amounts 1088, 2244, 2618, 4369, 5525, and 6137. The equation y = 9.75x represents the number of dollars, y, earned by an art museum for selling x tickets. Which statements about the costs of the admission tickets at the museums are true? Select each correct answer. It costs $9.75 per ticket for admission to the art museum. It costs $8.75 per ticket for admission to the science museum. Art museum tickets are more expensive than science museum tickets. Given the same number of ticket sales, the science museum earns more revenue. 1 2 3 4 5
Answer: It costs $9.75 per ticket for admission to the art museum.
Art museum tickets are more expensive than science museum tickets.
Step-by-step explanation:
From the given table of Science Museum Admission Revenue, we can see that the sales amount by selling 128 tickets = $1088
Therefore, the cost of each ticket for science museum =[tex]\frac{1088}{128}=\$8.5[/tex]
∴ It costs $8.5 (not 8.75) per ticket for admission to the science museum.
Also,The equation [tex]y = 9.75x[/tex] represents the number of dollars, y, earned by an art museum for selling x tickets.
At x=1, y=9.75
∴ It costs $9.75 per ticket for admission to the art museum.
Clearly, 9.75>8.5
∴ Art museum tickets are more expensive than science museum tickets.
If the number of ticket sales will be same then art museum will earn more revenue.
Since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Price per ticket to a science museum:
Given the table showing the sales of admission tickets to a science museum:
Thus,
The unit rate/price per ticket sold at the science museum using a pair of values from the table, say, (128, 1088) is: y/x
Thus:
unit rate/price per ticket = [tex]\frac{1088}{128} = 8.5[/tex]That is, a ticket to a science museum costs $8.5.
Price per ticket to an art museum:
The equation, y = 9.75x is given as the equation modelling the situation.
Where x = number of tickets soldy = amount in dollarsThus, this means that the price per ticket to the art museum is: $9.75.
Therefore, since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
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Which of the following has the ability to turn light energy into chemical energy? A. a generator B. an automobile C. a tree D. water
Tiana's checking account charges a $7.75 monthly service fee and a $0.16 per-check fee. If Tiana writes 17 checks per month, should she switch to a checking account that charges a $10.50 monthly service fee and no per-check fee? A. No, because her monthly fees are currently greater than $10.50. B. No, because her monthly fees are currently less than $10.50. C. Yes, because her monthly fees are currently less than $10.50. D. Yes, because her monthly fees are currently greater than $10.50.
the answer to this question is B
Answer:
Option B. is correct.
Step-by-step explanation:
Tiana's checking account charges a $7.75 monthly service fee and $0.16 per check fee.
If Tiana writes 17 checks per month, her total charges =
0.16 × 17 = 2.72 + 7.75 = $10.47
Her total account charges $10.47 for 17 checks.
In the question it is asking that she should switch to a checking account that charges a $10.50 monthly service fee and no per check fee.
Answer : No, because her monthly fees are currently less than $10.50.
You forget the last two digits of your password for a website. What is the probability that you randomly choose the correct digits?
Use the graph of f to estimate the local maximum and local minimum. (explain)
Answer:
The graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
Step-by-step explanation:
Consider the provided graph.
it is not always possible to find maximum or minimum for the whole function, but locally it is.
To find the local maximum and minimum we need to choose an interval first.
Local maximum: f(c) ≥ f(x) for all x in the interval
Local minimum: f(c) ≤ f(x) for all x in the interval
For better understanding refer the figure 1
Now consider the provided graph:
The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.
Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.
Also the graph of the function has local maximum at (0,0) as at x = 0
The value of function f(x)≤f(c) for every x in the domain.
Hence, the graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. How soon did the second train overtake the firstIf 50x represents the distance the slower train travels, then the faster train travels?
For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.
Here's how to solve a similar problem based on the given examples:
Let the first train's speed be 50 mph and the second train's speed be 55 mph.
The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).
The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.
Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.
So, the second train will overtake the first train after 5 hours.
Answer for 6-9 please asap
1. In ΔPQR, PQ = PR and M is the midpoint of QR . Prove that PM bisects ∠QPR.
ANSWER FORMAT: ΔPQM = Δ (?) because... (reason)
2. In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC
at point H and the angle bisector of ∠C meets
AB
at point K. Prove that BH = CK.
ANSWER FORMAT: ΔBCK = Δ (?) because... (reason)
3. In ∆ABC the median
AM
is extended to ray
AM
and point P on
AM
is taken so that
PM = AM. What is the distance from point P to vertices C and B if AB = c and AC = b?
To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
Rewrite and simplify ln(4500) in terms of ln5 and ln6
Simplified form of the given logarithmic expression ln(4500) will be ln(4500) = 3ln(5) + 2ln(6)
Given logarithmic expression in the question is,
ln(4500)We have to convert this expression in terms of ln(5) and ln(6).
Since, Factored form of 4500 = 5×5×5×6×6
= 5³×6²
Therefore, ln(4500) = ln(5³×6²)
= ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]
= 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]
Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.
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Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .
A small airplane used 5 2/3 gallons of fuel to fly 2 hour trip. How many gallons were used each hour