An athlete run in 22 minutes is 19.232 laps
Given,
An athlete runs at a speed of 9 miles per hour.
and, If one lap is 349 yards.
To find the how many laps does he run in 22 minutes?
Now, According to the question:
Firstly, Convert the mph into yard per minute,
Remember that:
I mile = 1,760 yard
1hour = 60 minute
Convert the speed in miles/hour to yards/minute
9 [tex]\frac{miles}{hour}[/tex] = 9[tex]\frac{1760}{60}[/tex] = 264 yard/ min
We know that
The speed is equal to divide the distance by the time
Let
s → the speed
d → the distance in yards
t → the time in minutes
Using the formula :
Speed = distance/ time
Solve the distance:
d = speed x time
Speed = 264 yard/ minute
Time = 22 minute
Therefore,
Distance = 264 x 22
Distance = 5,808 yards
Divide the distance by 302 yards to find out the number of laps
= 5,808/ 302 = 19.232 laps
Hence, An athlete run in 22 minutes is 19.232 laps
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im not sure the steps to this math problem, from step one to step three
The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]What is the length of the arc ? ( Precalc )
We're going to use the following formula:
[tex]L=2\cdot\pi\cdot r\cdot\frac{\theta}{360}[/tex]If we replace our values:
[tex]L=2\cdot\pi\cdot3\cdot\frac{60}{360}=\pi[/tex]Therefore, the length is pi.
Which expression is undefined? O A. 11 B.- 3 C.6-6) D. -4+0
Answer:
Option C
Step-by-step explanation:
Undefined expression:
Division by 0, or fraction in which the denominator is 0. In this question, this is in option C, since 3/(6-6) = 3/0.
I NEED HELP WITH THIS ASAP ILL MARK YOU BRAINLIEST Put each set of numbers from greatest to least
Every number is equivalent to:
[tex]\begin{gathered} 7.18\times10^{-3}=0.00718 \\ \sqrt{\frac{25}{49}}=\frac{5}{7}=0.7143 \\ \frac{7}{10}=0.7 \\ 0.\bar{8}=0.8888 \\ \frac{3}{4}=0.75 \\ 80\text{ \% = 0.8} \end{gathered}[/tex]So, each number from greatest to least is:
[tex]0.\bar{8},80\text{ \%, }\frac{3}{4},\sqrt{\frac{25}{49}},\frac{7}{10},7.18\times10^{-3}[/tex]Question 34: Find the polar coordinates that do NOT describe the point on the graph. (Lesson 9.1)
Notice that the polar coordinates of the point on the simplest form are (2,30). Then, the only option that does not match a proper transformation of coordinates is the point (-2,30)
Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9
We have the expression:
[tex]5m+n\text{.}[/tex]We must evaluate the expression for:
• m = 7,
,• n = 9.
Replacing the values of m and n in the expression above, we get:
[tex]5\cdot7+9=35+9=44.[/tex]Answer
44
Find the interest earned on a $50,000 deposited for six years at 1 1/8 % interest, compounded continuously
To calculate the interest earned, we can use the following equation:
[tex]I=P((1+i)^n-1)[/tex]Where P is the value of the deposit, i is the interest rate and n is the number of periods of time.
First, we need to calculate the equivalent value of 1 1/8 % as:
[tex]1\frac{1}{8}\text{ \% = }\frac{1\cdot8+1}{8}\text{ \% = }\frac{9}{8}\text{ \% = 1.125\% = 0.01125}[/tex]So, replacing P by $50,000, i by 0.01125, and n by 6, we get:
[tex]\begin{gathered} I=50,000((1+0.01125)^6-1) \\ I=50,000(0.694) \\ I=3,471.3577 \end{gathered}[/tex]Answer: $ 3,471.3577
in the diagram of BED below, FC||ED,BF=6,FE=18, and BC=22. What is the length of BD
we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
18/6=DC/11
solve for DC
DC=3*11
DC=33
Find the length of BD
BD=BC+DC
BD=11+33=44 units
therefore
the answer is 44 units
Bella competed in the 5,000 m race at the Olympics she finished in the race 14.2 minutes after the race Bella wrote the equation c equals 18.1 m to model the relationship between the number of calories she burned c and the number of minutes she ran m.how many calories did Bella burn in the first 10 minutes of the 5,000 meter race.
Answer
She burnt 181 calories in that first 10 minutes of the 5,000 meter race.
Explanation
Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as
c = 18.1m
The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.
That is, find c when m = 10 minutes
Recall,
c = 18.1m
c = 18.1 (10)
c = 181 calories.
Hope this Helps!!!
helppppppppppppppppppppppppppppppp
Answer:
b=4
I believe this is correct.
Step-by-step explanation:
-(2)^3+7(2)^2-2(2)+12=
-8+28-16
-8+12
4
Gretchen is planting a rectangular garden. she wants to use 9 square feet for tulips.if garden has length of 8 feet by 3 feet, how much room will she have left for rest of her flowers
Given: the garden has a shape of a rectangle
The garden has a length of 8 feet by 3 feet
So, the area of the garden =
[tex]8\cdot3=24ft^2[/tex]she wants to use 9 square feet for tulips.
So, the remaining for rest of her flowers = 24 - 9 = 15 square feet
When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.Suppose you are buying a new truck at a price of $26,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $2,600 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $23,400) at an APR of 6.5%.What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)
Solve by applying the zero product property.m^2= 27-6m
To apply the zero product property we first need to write all the terms of the equation on side:
[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]Now we need to factorise the expression on the right:
[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:
[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]Therefore, the solutions of the equation are m=-9 and m=3
For each situation, an inequality is written. Which one has an incorrect inequality?АThree less than a number is greater than negative four and less than negative one; - 4 75DAll real numbers that are greater than or equal to - 7 1/2or less than or equal to zerox < 0 or x>-7 1/2
Option D has an incorrect inequality.
Since option D Says:
"All real numbers that are greater than or equal to - 7 1/2 or less than or equal to zero"
Greater than or equal is represented with the symbol ≤ or ≥.
So the correct inequality is for this statement is:
x ≤0 or x>-7 1/2
Not
x < 0 or x>-7 1/2
Note that the x and 0 part doesn't have an equal sign.
Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
HELP PLEASE will give BRAINLIEST!!! You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is
y = 3/2x +6. There is a tree in your yard at the point (6, 2). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the
tree from the zip line? Round your answer to the nearest tenth.
Answer:
Hello lovely. Assume that the attached graph represents your situation, with the red line representing the zip line and the blue dot representing the tree. The tree is at point (6, 2). You will need to choose a reference point to calculate the distance between the tree and the zip line. We'll use the point (0, 6), or the y intercept
To calculate the distance between two points, we use the formula d=√((x2 – x1)² + (y2 – y1)²).
Substitute
d=√((0 – 6)² + (6 – 2)²).
Simplify
d=√((-6)² + (4)²).
d=√(36 + 16).
d = √52
The distance is approximately equal to 7.2 feet
is this right triangle shown a right triangle? 50 cm2 40mc2 20cm2 Explain your reasoning.
Solution:
Note that :
[tex]2500=50^2\ne\text{ }40^2+20^2=2000[/tex]and If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, this statement is not true. We can conclude that it is not a right triangle.
Solve the inequality: y-5-20Which of the following is the graph of the solution?
Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
Write the sequence {15, 31, 47, 63...} as a function A. A(n) = 16(n-1)B. A(n) = 15 + 16nC. A(n) = 15 + 16(n-1)D. 16n
To find the answer, we need to prove for every sequence as:
Answer A.
If n=1 then:
A(1) = 16(1-1) = 16*0 = 0
Since 0 is not in the sequence so, this is not the answer
Answer B.
If n=1 then:
A(1) = 15 + 16*1 = 31
Since 31 is not the first number of the sequence, this is not the answer
Answer D.
If n=1 then:
16n = 16*1 = 16
Since 16 is not in the sequence so, this is not the answer
Answer C.
If n = 1 then:
A(1) = 15 + 16(1-1) = 15
A(2) = 15 + 16(2-1) = 31
A(3) = 15 + 16(3-1) = 47
A(4) = 15 + 16(4-1) = 63
So, the answer is C
Answer: C. A(n) = 15 + 16(n-1)
A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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The product of two consecutive positive even integers is 48. Find the greatest positive integer.
From that statement we can create the following equation,
[tex]n\cdot \left(n+2\right)=48[/tex]solving for n,
[tex]\begin{gathered} n^2+2n=48 \\ n^2+2n-48=0 \\ n_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-48\right)}}{2\cdot \:1} \\ n_{1,\:2}=\frac{-2\pm \:14}{2\cdot \:1} \\ n_1=\frac{-2+14}{2\cdot \:1},\:n_2=\frac{-2-14}{2\cdot \:1} \\ n=6,\:n=-8 \end{gathered}[/tex]We can only use the positive number for this problem, therefore n = 6
From the above, the set of numbers is 6 and 6+2=8, since 6*8=48.
Answer: the greatest integer is 8
[tex]4\sqrt[3]{16} /2\sqrt[3]{2}[/tex]
The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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In exercises 1 and 2 , identify the bisector of ST then find ST
Given: The line segment ST as shown in the image
To Determine: The bisector of ST and the value of ST
Solution
It can be observed from the first image, the bisector of ST is line MW
[tex]\begin{gathered} ST=SM+MT \\ SM=MT(given) \\ MT=19(given) \\ Therefore \\ ST=19+19 \\ ST=38 \end{gathered}[/tex]For the second image, the bisector of ST is line LM
[tex]\begin{gathered} ST=SM+MT \\ SM=3x-6 \\ MT=x+8 \\ SM=MT(given) \\ Therefore \\ 3x-6=x+8 \\ 3x-x=8+6 \\ 2x=14 \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} SM=3(7)-6=21-6=15 \\ MT=7+8=15 \\ ST=SM+MT \\ ST=15+15 \\ ST=30 \end{gathered}[/tex]For first exercise, the bisector is MW, ST = 38
For the second exercise, the bisector is LM, ST = 30r
hello, while doing the question please don't put A decimal Answer ( ex: 1.5) because my teacher told me that's incorrect, you can add or subtract depending on the question, or check if you need to simplify! Thank you:)
Notice that the unit segment is divided in 8 parts. Then, each mark is equal to 1/8.
The kitten that weighs the most is placed over the 5ft mark. Then, its weight is:
[tex]\frac{5}{8}[/tex]The kitten that weighs the least is placed over the third mark. Then, its weight is:
[tex]\frac{3}{8}[/tex]Substract 3/8 from 5/8 to find the difference on their weights:
[tex]\frac{5}{8}-\frac{3}{8}[/tex]Since both fractions have the same denominator, we can substract their numerators:
[tex]\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{2/2}{8/2}=\frac{1}{4}[/tex]Therefore, the difference in pounds between the heaviest and the lightest kittens, is:
[tex]\frac{1}{4}[/tex]5 6 7 8. One times a number equals 4 1
hello
to solve this problem, we need to find the property of equality
let the unknown number be represented by x
[tex]4=1\times x[/tex]to solve for x, divide both sides of the equation by 1
[tex]\begin{gathered} 4=1x \\ \frac{4}{1}=\frac{1x}{1} \\ x=4 \end{gathered}[/tex]the number here is 4
the property used to get the answer is division property of equality
Which choice could be used in proving that the given triangles are similar? A) PO 6 DE 4 II B) PO 4 EF 9 PO 4 DE 6 D) PR 6 DE 6 allo
Hi, can you help me answer this question please, thank you!
From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answer:
translated 8 units down and then reflected across the y-axis
Watch help videoA group of friends wants to go to the amusement park. They have no more than $305to spend on parking and admission. Parking is $19, and tickets cost $26 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.<
p = number of people who can go to amusement park
Amount they want to spend is no more than $305. This means there expenses will be less than or equals to $305.
parking = $19
cost per person = $26
Therefore,
[tex]19+26p\leq305[/tex][tex]\begin{gathered} 26p\leq305-19 \\ 26p\leq286 \\ p\leq\frac{286}{26} \\ p\leq11 \end{gathered}[/tex]the length of a rectangle is two more than the width. if the perimeter is 28, find the length and the width of the rectangle, let w represent the width and l represent the length.
You have that the perimeter of a rectangle is 28. In order to find the values of length and width of the rectangle, you take into account the following formula for the perimeter of a rectangle:
[tex]P=2w+2l[/tex]where w is the width and l is the length. You have that the length l is twice the width w of the rectangle, that is l=2w. By replacing this expression for l into theformula for the calculation of the perimeter you obtain:
[tex]P=2w+2(2w)=2w+4w=6w[/tex]Thus, you have that P = 6w. You solve this equation for w, and also replace the value of P, just as follow:
[tex]\begin{gathered} P=6w \\ w=\frac{P}{6}=\frac{28}{6}=\frac{14}{3}=4.66 \end{gathered}[/tex]Then, the width is 4.66. The length is:
[tex]l=2w=2(4.66)=9.33[/tex]length = 9.33
