Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?
a. 9.8
b. 10
c. 73.5
d. 75
Answers
For this case, the first thing we must do is define variables.
We have then:
x: time in minutes
y: distance traveled.
We then have the following equations:
For Kathleen:
[tex] y = (\frac{1}{15}) x + 5
[/tex]
For Arnob:
[tex] y = (\frac{2}{15}) x
[/tex]
By the time Arnob reaches Kathleen we have:
[tex] (\frac{1}{15}) x + 5 = (\frac{2}{15}) x
[/tex]
From here, we clear the value of x.
We have then:
[tex] (\frac{2}{15}) x - (\frac{1}{15}) x = 5
[/tex]
[tex] (\frac{1}{15}) x = 5
x = (15) * (5)
x = 75 min
[/tex]
Answer:
it takes Arnob to catch up to Kathleen 75 minutes:
d. 75
Related Questions
How to factorise 4b squared + 19b
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b (4b+19)
41/18 as a mixed number
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making 10 pounds of Apple Jam requires five pounds of Apple how many pounds of Apple are needed to make eight pounds of apple jam
Answers
Now we want 8lb. of jam.
Set up a proportion:
2/1=8/x
Solve for x by cross-multiplying.
2x=8
x=4 lb. of apple
What is the minimum value of P = x - 2y over the feasibility region defined by the constraints shown?
a) 8
b) -2
c) -16
d) -14
Answers
After that plug each of those points into p = x -2y, to see which one gives the lowest number.
the answer is -14
hope this helps : )
Can someone help me?
In the circles shown, Line AC is congruent and equal to Line RT and Line AB is congruent and equal to Line RS. Which shaded region has a larger area?
Answers
Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Quadratic formula: x =
Answers
-2 = -x + 2x - 4
+4 +4
2 = x
However, for quadratic equation, there needs to be 3 numbers:
ax^2+bx+c=0
Putting the equation in this form, we can say that
(0)x^2+(1)x+(-2)=0
Taking that and putting it into the quad formula makes:
x=(-1+-sqrt((1)^2-4(0)(-2)))/2(0)
That makes it a divide by 0 problem, making it unsolveable
Answer:
D on edge
Step-by-step explanation:
You are spreading fertilizer on a golf course at the rate of 40 pounds per 10000 square feet. If the course is 320 acres, how many tons of fertilizer will be needed?
Answers
Today you deposited $5000 into a savings account paying 12% interest. how much shouldyou have in 15 years
Answers
unicorns
Math Help! I NEED IT ASAP!!!! PLEASE!! WILL UPVOTE,LIKE PAGE,LIKE POSTS AND PICS!!
Sorry this took me forever to post, I had to do someting
_________________________________________________
5.What is each number in standard form?
Drag the answers into the boxes to match each number.
1.5.78×10−115.78×10−11
2. 5.078×10−65.078×10−6
3. 5.708×10−85.708×10−8
Answer Choices:
A.0.000005078
B.0.0000000000578
C.0.000000578
D.0.0000000005078
E.0.00000005708
F.0.00000000005708
_________________________________________________
Answers
2. 5.078 × [tex]10^{-6} [/tex] = A) 0.000005078
3. 5.708 × [tex]10^{-8} [/tex] = C) 0.0000000578
Find the point on the terminal side of θ = 3pi/4 that has a y coordinate of 1.
Answers
y/x = -1
1/x = -1
x = -1
Point is (-1, 1).
Answer:
B
Step-by-step explanation:
hope this helps
what is 5√28 + √63 in simplest radical form
Answers
The simplest radical form of the expression 5√28 + √63 will be 29√7.
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c.
Then the simplest radical form of the expression will be
[tex]\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}[/tex]
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5√28 + √63
Simplify the expression, then we have
⇒ 5√28 + √63
⇒ 5√(4 x 7) + √(9 x 7)
⇒ 5 x 4√7 + 9√7
⇒ 20√7 + 9√7
⇒ 29√7
The simplest radical form of the expression 5√28 + √63 will be 29√7.
More about the simplest radical form link is given below.
https://brainly.com/question/7440652
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Consider a triangle where A=30 degrees, a=1.5cm and b=2cm
How many possible triangles have the above properties? Write either 0 or 1 or 2.
I don't understand this question at all. ...?
Answers
Use the Law of Sines to find sin(B).
The solution to the problem is as follows:
sin(A)/a = sin(B)/b
sin(30)/1.5 = sin(B)/2.6
(sin(30)*2)/1.5 = sin (B)
sin (B) = 0.8666667
B = sin^-1(0.8666666667)
B = 60.1 degrees
B = 60 degrees (2 s.f.)
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With the given conditions of angle A being 30 degrees, side a being 1.5 cm, and side b being 2 cm in a triangle, only one possible triangle satisfies these properties according to the Law of Sines.
Explanation:The question relates to determining the number of possible triangles given certain conditions. Specifically, it refers to a triangle with an angle A of 30 degrees, a side a of 1.5 cm opposite to A, and another side b of 2 cm. To decide the number of possible triangles that fit these criteria, we make use of the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
In the given scenario, since side a (1.5 cm), opposite to angle A (30 degrees), is shorter than side b (2 cm), it is possible that two different triangles could exist, often referred to as the ambiguous case in the Law of Sines. However, the fact that side a is shorter than side b coupled with angle A being acute (30 degrees) leaves us with only one possible triangle. This is because the side opposite the smallest angle (A) cannot form a valid triangle if it's longer than the other given side. Therefore, there is just one solution to this problem.
Learn more about Possible Triangles here:https://brainly.com/question/13495187
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A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
Answers
ince the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%, that means there is a 90% confidence interval. 9 / 10 = .90 = 90% 90% = 1.645 1.645 * .9 = 1.4805 Margin of Error - 1.4805
and The margin of error is the distance from x-bar, the center of the confidence interval ,to the end of the interval. This distance is 6% of 80% which is given by: 80×6100=4.8 Therefore the margin of error is 4.8% and the confidence interval is: ({80 - 4.8}%, {80 + 4.8}%)
Answer:
Margin of error: 6%; Confidence Interval Percentage: 90%; Confidence Interval: 74% and 86%
Step-by-step explanation:
Margin of error: 6% -- It's already given in the question.
Confidence interval is at 90%. 9/10=.90
The exam creator is saying that they are 90% confident that the seniors test scores will be between 74% and 86%.
0.8 - 0.06 = 0.74
0.8 + 0.06 = 0.86
The confidence interval is (0.74, 0.86)
Which ratio forms a proportion with 14/42?
1/4
7/21
12/40
28/80
Answers
7/21
Hope it helps
Answer: 7/12
Explaintion: Write at least 20 characters to explain it well.
Find all the cube roots of -125i in polar form. Convert all results to a+bi form. ...?
Answers
z = -125i
z = 125<270, where angle is in degrees.
z^(1/3) = 125<((270 + k(360))/3)
= 125<(90 + 120k)
For k = 0:
z^(1/3) = 125<90 = 125i
For k = 1:
z^(1/3) = 125<210 = 125(-sqrt(3)/2 - i/2) = -125sqrt(3)/2 - 125/2*i
For k = 2:
z^(1/3) = 125<330 = 125(sqrt(3)/2 - i/2) = 125sqrt(3)/2 - 125/2*i
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Final answer:
To find all cube roots of -125i in polar form, convert them to a+bi form by expressing -125i in polar form, finding the cube roots, and converting them to a+bi form.
Explanation:
To find all the cube roots of -125i in polar form and convert them to a+bi form, follow these steps:
Express -125i in polar form: -125i = 125∠-90°.
Find the cube roots by taking the cube roots of the magnitude and adding multiples of 360°/3 to the argument.
The cube roots of -125i in a+bi form are 5∠-30°, 5∠90°, and 5∠210°, which correspond to -2.5-4.33i, 0+5i, and 2.5-4.33i respectively.
Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
Answers
8x - 4y = 12
-4y = -8y + 12
y = 2y -3
We now have two equations:
y = mx - 6
y = 2x - 3
Recall that parallel lines have the same slope, and the slope is "m" for an equation in slope-intercept form y=mx+b.
The slope in y = 2x - 3 is 2, so for the equation y = mx -6 to be parallel, it must also have a slope of 2.
Therefore, m = 2.
The value of [tex]m[/tex] is [tex]2[/tex].
Given:
The given equations are:
[tex]y=mx-6[/tex] ...(i)
[tex]8x-4y=12[/tex] ...(ii)
To find:
The value of [tex]m[/tex] that will create a system of parallel lines with no solution.
Explanation:
The slope-intercept form of a line is:
[tex]y=mx+b[/tex] ...(iii)
where, [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
The slope of line (i) is [tex]m[/tex].
Equation (ii) can be rewritten as:
[tex]-4y=-8x+12[/tex]
[tex]y=\dfrac{-8x+12}{-4}[/tex]
[tex]y=2x-3[/tex]
The slope of this line is [tex]2[/tex].
We know that the slopes of parallel lines are equal. So, [tex]m=2[/tex].
Learn more:
https://brainly.com/question/14874024
What multiplication fact could you use to find a number that can be divided evenly by 8 and9?
Answers
What are the solutions of 4x2 + x = −3?
Select one:
Answers
Answer:
The correct answer is c.
Step-by-step explanation:
Given the equation
[tex]ax^{2}+bx+c=0[/tex]
The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):
[tex]\frac{-b|\sqrt{b^{2}-4ac}}{2a}[/tex]
The solutions of [tex]4x^{2}+x=-3[/tex] are the same that the solutions of [tex]4x^{2}+x+3=0[/tex]
With [tex]a=4\\b=1\\c=3[/tex] we replace this in the quadratic equation ⇒
[tex]\frac{-1|\sqrt{(1)^{2}-4(4)(3)}}{(2)(4)}[/tex] ⇒
[tex]\frac{-1|\sqrt{1-48}}{8}[/tex] ⇒
[tex]\frac{-1|\sqrt{-47}}{8}[/tex]
Given that [tex]i^{2}=-1[/tex] (imaginary numbers property)
[tex]\frac{-1|\sqrt{47i^{2}}}{8}=\frac{-1|i\sqrt{47}}{8}[/tex]
The solutions are [tex]\frac{-1+i\sqrt{47}}{8}[/tex]
and [tex]\frac{-1-i\sqrt{47}}{8}[/tex]
The correct answer is c.
Answer: C
Step-by-step explanation: I just took the test and got it right <3
Solve for c.
3abc + b = 5
c = (5 - b)/(3ab)
c = -5/3ab
c = 2 - ab\
how does one work this out
Answers
3abc + b = 5
Subtract b from both sides:
3abc + b - b = 5 - b
3abc = 5 - b
Divide both sides by 3ab:
3abc/3ab = (5 - b)/3ab
c = (5 - b)/3ab
Write the equation for 5x + 2y = 3 in slope-intercept form.
Answers
in other words, isolate y.
5x-2y=3
Subtract 5x from both sides
-2y=(-5x+3)
Divide both sides by -2
y=5/2x-3/2
Answer:
y=5/2x-3/2
Answer:
Slope-Intercept Form states that in the equation of a straight line y=mx+b the slope is the number represented by m that is multiplied on the x, and b is the y intercept i.,e the point where line cut the vertical y-axis.
Given equation: 5x+2y=3 ......[1]
To convert this equation into slope intercept form;
Subtraction Property of equality states that you subtract the same number from both sides of an equation.
Subtract 5x from both sides in equation [1];
[tex]5x+2y-5x=3-5x[/tex]
Simplify:
[tex]2y=3-5x[/tex] or we can write this as;
[tex]2y=-5x+3[/tex] ......[2]
Division property of equality states that you divide the same number from both sides of an equation:
Divide by 2 from both sides of an equation in [2]
[tex]\frac{2y}{2} =\frac{-5x+3}{2}[/tex]
On simplify:
[tex]y=-\frac{5}{2}x+\frac{3}{2}[/tex]
Therefore, the given equation in slope intercept form is: [tex]y=-\frac{5}{2}x +\frac{3}{2}[/tex]
Which answer describes the type of sequence? 3, 9, 15, 21, ...
geometric
arithmetic
neither arithmetic nor geometric
Answers
Answer:
The sequence is arithmetic
Step-by-step explanation:
we know that
In an arithmetic sequence, the difference between consecutive terms is always the same and is called common difference
In this problem we have
[tex]3,9,15,21,...[/tex]
Let
[tex]a1=3, a2=9,a3=15,a4=21[/tex]
[tex]a4-a3=21-15=6[/tex]
[tex]a3-a2=15-9=6[/tex]
[tex]a2-a1=9-3=6[/tex]
The sequence is arithmetic
The common difference is equal to [tex]6[/tex]
Factor completely: 5ab(x + 6) − 4(x + 6) ...?
Answers
= ( x + 6 ) ( 5 a b - 4 )
Answer:
D is your answer :)
Step-by-step explanation:
A recipe for oatmeal raisin cookies call for 1 2/3 cups of flour to make 4 dozen cookies. How many cups of flour are needed to make 6 dozen cookis?
Answers
Mark wants to create a scale drawing of the poster shown below:
A rectangle is shown. The length of the rectangle is labeled 4 centimeters. The width of the rectangle is labeled 10 centimeters.
What are the dimensions of the poster at one-half its current size?
2 cm by 10 cm
2 cm by 5 cm
8 cm by 20 cm
8 cm by 5 cm
Answers
4/2=2
10/2=5
so the answer is
2cm by 5cm
4+4 = 8 cm /2 = 4 cm /2 = 2 cm
10+10= 20 cm /2 = 10 cm /2 = 5 cm
the right answer is B, 2 cm by 5 cm
which decimal is equivalent to the fraction 9/11?
Answers
9/11 is .81
Which situation shows a constant rate of change?
A. The height of a monkey swinging from branch to branch over time
B. The height of a bouncing ball over time
C. The number of points scored in a basketball game compared with the number of minutes played
D. The amount a person pays for gas compared with the number of gallons purchased
Answers
The correct answer is:
D) The amount a person pays for gas compared with the number of gallons purchased
Explanation:
A constant rate of change means that for every x, y increases the same amount.
In the situation "The amount a person pays for gas compared with the number of gallons purchased ," the independent quantity, or x-value, is the number of gallons, and the dependent quantity, or y-value, is the amount paid. Since gas has a set price per gallon, for every gallon purchased, the total amount paid goes up the same amount. This means it has a constant rate of change.
If 100 envelopes cost 70 cents, how much would 250 cost?
Answers
100 envelopes / 70 cents = 250 envelopes / x
The value of x from the equation is 175.
To find out how much 250 envelopes would cost, set up a proportion using the given information that 100 envelopes cost 70 cents. Cross-multiply and solve for the unknown cost, which is $1.75.
Explanation:To find out how much 250 envelopes would cost, you can use the concept of proportions. Since 100 envelopes cost 70 cents, you can set up a proportion to find the cost of 250 envelopes: 100/70 = 250/x, where 'x' represents the unknown cost. Cross-multiplying, you get 100x = 70 * 250. Dividing both sides by 100, you find that x = 175.
Therefore, 250 envelopes would cost 175 cents.
In decimal form, 175 cents is equal to $1.75.
Write the number21,989.098 in expanded form and word form
Answers
20,000+1,000+900+80+9+0.09+0.008
Word Form:
what is 72/60 in simplest form
Answers
So 72/60 = 6/5
Thus, 6/5 is the simplest form.
So, first find out how many times 60 can go into 72
This is 1 so right now we have. 1 12/60 right?
Now this still isn't simplest form so what number can go into bolth 12 and 60?
12 right?
Okay, so 4 x 3 = 12 so now we have 1 3/60
Now lets deal with 60 15 x 4 = 60. now we have 1 3/15
We can still make it smaller so we know 3 can go into 3 and 15 so lets use 3
1 ~ 3 = 1 so we have 1 1 / 15
5 x 3 = 15
So your answer is....
1 1 / 15
Hope This Helped
Cheers,
Belive1234
Using the rule of thirds to evaluate the composition of a well-crafted painting, the eye should be attracted to A. one or more points of interest. B. the top of the painting. C. the lighter values in the painting. D. the midpoint of the composition.
Answers
Answer: A: one or more points of interest.
Step-by-step explanation:
The rule says that an image should be divided into 9 equal squares by two horizontal and two vertical lines and that the important objects of the image should be placed between the lines (in the centers of the squares) or in the intersections of the lines.
In this way, the eye is dragged to the different points that the artist wants the viewer to focus on the image, then the correct option is option A: one or more points of interest.