Mathematics High School

Two runners ran as a team in a 5,000-m relay race. the first runner ran 500 m farther than the second runner. how many meters did each run?

Answers

Answer 1
Let a = runner 2, a + 500 = runner 1.

a + (a + 500) = 5000
2a + 500 = 5000
2a = 4500
a = 2250

Runner 1 ran 2,750 meters. Runner 2 ran 2,250 meters.  
Answer 2
Let x be the distance first runner ran.
Since first runner ran 500m more than 2nd runner so, x-500.

The total distances they ran must add to 5000.

So,
x + x - 500 = 5000, or
2x = 5500, or
x = 2750.

So the first runner ran 2,750 m. And the second runner ran x - 500 = 2750 - 500 = 2,250 m.
Let's check 2750+2250 = 5000.
The answer's correct .

Related Questions

x2+y2-4+2y-11=0 what are the center and radius of the circle?

Answers

[tex] x^2 + y^2 - 4x + 2y - 11 = 0 [/tex]

You need to complete the square for both x and y.

[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]

[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]

[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]

The center is (2, -1).
The radius is 4.

This is probably easy but I'm not smart and don't know what else to do I know this is the correct formula it's just confusing to me because there're three numbers and I'm just really dumb.

Answers

Side rectangle = 3 × 1 = 3
Right side rectangle = 4 × 1 = 4
Left side rectangle = 4 × 1 = 4

Both triangles = 4 × 3 = 12 
Both triangles = 6

3 + 4 + 4 + 12 = 23

I think the answer is 23 cm

Hope this helped☺☺

First off, don't put yourself down. You'll get it eventually. It takes a different amount of time for everyone :) ♡

Area of a right triangular prism = 1/2(2B) + Ph
The 1/2 and 2 cancel each other out: B + Ph.

Base of the triangular prism: 3 × 4 = 12 cm²

Perimeter of the base (use the Pythagorean Theorem →a² + b² = c²← to figure out the missing side; hypotenuse): 3² + 4² = c²
                                                    9 + 16 = c²
                                                    √25 = 5
                                                    3 + 4 + 5 = 12 cm

Height of triangular prism: 1 cm

Plug these numbers into the formula (B + Ph):
(12 + 12×1) = 24 cm²

The area of the right triangular prism is 24 cm².

Help! Thanks in advance!
Screenshotted question!

Answers

The answer is (2g)-3

Solve the system of equations using the substitution method.

{2x+8y=4 x=−3y+5



Enter your answers in the boxes.

Answers

Hi!
I believe the answer is (14,-3)
have a great day & good luck!

Four girls and eight boys are running for president or vice president of the student council. find each probability: find the prbability that two girls are elected

Answers

The probability is 1/11.

The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.

The probability that a girl is elected for the second office is 3/11.  This is because after one girl is elected, there are 3 girls left out of 11 students left.

Together, this gives us
4/12(3/11) = 12/132 = 1/11

The probability that two girls are elected president and vice president from a group of 4 girls and 8 boys is calculated using a hypergeometric distribution, resulting in a probability of 1/11.

The question is asking for the probability that two girls are elected president and vice president of the student council when there are four girls and eight boys running for these positions. This is an example of a hypergeometric distribution problem, as we are selecting without replacement from a finite population divided into two groups.

To find the probability, we need to determine the number of successful outcomes divided by the total number of possible outcomes. The successful outcome is that the two elected individuals are both girls. Since there are 4 girls, there are 4 choose 2 ways to select 2 girls, which equates to 6 possible successful outcomes. The total number of ways to choose 2 individuals from 12 candidates (4 girls + 8 boys) is 12 choose 2, resulting in 66 possible outcomes.

The probability can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.

Probability = Successful outcomes / Total outcomes = 6 / 66 = 1 / 11

12q^2-17q-7
A. (3q+1)(4q-7)
B. (3q-1)(4q+7)
C. (3q+7)(4q-1)
D. (3q-7)(4q+1)

Answers

the correct answer is B

PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?

$121.01

$87.45

$62.61

$113.72

Answers

The correct answer for your problem would be $62.61

Answer:

$62.61

Step-by-step explanation:

Data:

The price of home entertainment = $ 2 254

Time to pay = 18 months

interest rate  = 22.48 %

monthly payment  = $ 2254/ 18

                              =  $ 125. 22

                              =   - 22.48 (2254)/18

                              = $ 62.61

Consider this system of linear equations:

22x − y = -23 (equation 1)

11x + 12y = 1 (equation 2)

Answers

To solve this problem you must apply the proccedure shown below:

 1. You have the folllowing system of equations given in the problem above:

 22x − y = -23 (equation 1)
 11x + 12y = 1 (equation 2)

 2. If you multiply the equation 2 by -2, and then sum the equation 1+equation 2, you obtain:

 -25y=-25
 y=1

 3. Then, you must substitute y=1 into the equation 1, then you have:

 x=-1

 4. As you can see, when you solve it, the solutions are:

 x=-1
 y=1
 
Using subtraction method or elimination method

22x − y = -23
-
(11x + 12y = 1) *2

22x − y = -23
-
22x + 24y = 2
  0   -25y  = -25
y = 1

22x - 1 = -23
x = 1


Can anyone help me with this problem?

Answers

[tex]\tan\Theta=\dfrac{|BC|}{|CA|}[/tex]

Use Pythagorean theorem:
[tex]|AB|^2=|BC|^2+|CA|^2\\\\9^2=6^2+|CA|^2\\\\81=36+|CA|^2\ \ \ \ |-36\\\\|CA|^2=45\to|CA|=\sqrt{45}\\\\|CA|=\sqrt{9\cdot5}\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5[/tex]
[tex]\tan\Theta=\dfrac{6}{3\sqrt5}=\dfrac{2}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{2\sqrt5}{5}[/tex]

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.


T.A. =


Answers

Hello,
Please, see the attached file.
Thanks.

Answer:

Step-by-step explanation:

Identify a counterexample to disprove 6n>n^2/6,where n is a real number.

Answers

A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.

The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.

Substituting 7 for n, we get:

6 x 7 > 72/6

42 > 49/6

42 > 8.167

This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:

6 x 12 > 122/6

72 > 144/6

72 > 24

This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.

The square root of 136 is between which two whole numbers?

Answers

The square root of 136 is between 11 and 12. Hope I helped!
The square root is between 11 and 12 but closer to 12. 
Hope this helps! 

triangle XYZ is obtuse which list could represent the angle measures of triangle XYZ?

A. 20 60 100
B. 30 60 90
C. 50 50 80
D. 60 60 60

Answers

An obtuse triangle must have an angle greater than 90degrees (cannot equal 90). Therefore, A. would be the correct answer. This is because A. is the only set of angles that includes an angle greater than 90. Also, all angle measures add up to equal 180degrees.

When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x^2

Answers

Leading coefficient = -3
Constant = 2

When you order them in standard form, you need to put them in ascending order of the exponents. Therefore the -3x^2 would come first, which makes the number attached (-3) the lead coefficient. 

Also, since the number (2) without an x attached would be last (due to the power of x technically being 0), than that is the constant. 

Find the slope of the line on the graph

Answers

find 2 points on the graph where the blue line crosses an X and Y that we know

1st point ( -4,0)
 2nd point (0,3)

slope = change in y over change in x

change in y = 3-0 = 3

change in x = 0 - -4 = 0+4 = 4

slope = 3/4




A bakery has 49 donuts and 28 muffins for sale. What is the ratio of muffins to donuts? Please answer ASAP 99 Points :V

Answers

Hey there! :D

In a ratio, the first thing or item mentioned is first in the ratio. Let the muffins stand for x, and the donuts stand for y. It asks for the ratio of muffins to donuts. 

x:y 

Plug in the numbers. 

28:49

Both numbers are divisible by 7. 

28/7= 4 49/7=7

4:7 <=== simplified ratio

I hope this helps!
~kaikers 
Muffins: 28
Donuts: 49

Muffins to donuts: 28/49

Answer = 28/49 = 4/8 = 1/2

~Hope this helped~

The expression 8x + 2y

Answers

You can do 2(4x + 1y)

The trapezoids are similar. the area of the smaller trapezoid is 131 m2. find the area of the larger trapezoid to the nearest whole number. (1 point)

Answers

The answer is 3,726 m2

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.

2r
r²
r√2

Answers

r^2
.......................
The answer is r squared. Hope it helped!

A ball is rolling in a circular path that has a radius of 10 inches as shown in

Answers

the complete question in the attached figure

we know that
[circumference]=2*pi*r
for r=10 in
[circumference]=2*pi*10-----> 62.8 in

if 360° (full circle) has a length of --------> 62.8 in

 54°------------------------------> X
x=54*62.8/360-----> x=9.42 in

the answer is 9.42 in

Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.

22
110
220
440

Answers

Sum: S
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]

S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110

Answer: Second option 110

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]\sum_{7}^{16}(2i-12)\\\\=\sum_{7}^{16}2(i-6)\\\\=2\sum_{7}^{16}(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2(\frac{10\times (10+1)}{2})\\\\\=\frac{n(n+1)}{2}\\\\=2\times \frac{10\times 11}{2}\\\\=10\times 11\\\\=110[/tex]

Hence, the value of summation is 110.

Therefore, Second option is correct.

The Freshman class has 27 more boys than girls. If there are 283 freshman, how many are girls?

Answers

You can write an equation to represent this situation. Let x represent the number of girls.

283 = x + (x + 27)

Here, we are adding the number of girls with 27 more people than this amount of girls. This will allow us to add the number of girls, x, with the number of boys, x + 27, to get a total of 283.

This equation can be simplified if we add the like terms together: the x's.

So, 
283 = 2x + 27. 

Since this is a multi-step equation, we must use the reversed order of operations; undo addition first.

283 - 27 = 2x + 27 - 27
256 = 2x + 0
256 = 2x

Now, we must undo multiplication by dividing.
256/2 = 2x/2
128 = 1x


So, x, the number of girls, is equal to 128.

Hope this helps you! :)

Can somone help me with this 1 problem? In the figure shown, △RST is an isosceles triangle with RS≅RT. Which is the measure of ∠T?

A.21°

B.40°

C.70°

D.110°

Answers

In an isosceles triangle, the angles opposite to the two equal sides are also congruent.
Based on your information, T and S are congruent. So we know that the measure of angle T is 3x+7. But we need to solve for x. Let's add all the angle values together and set it to 180 because the angles of a triangle sum to 180.
1) 2(3x+7) + 2x - 2 = 180
2) 6x + 14 + 2x - 2 = 180
3) 8x + 12 = 180
4) 8x = 168
5) x = 21
6) m<T = 3x + 7 = 3(21) + 7 = 63 + 7 = 70
I got C, but it is always helpful to double check work. Hope this helps!
Final answer:

In an isosceles triangle, base angles are congruent, meaning ∠R would equal ∠T. However, no angle measures are provided, making it impossible to determine the measure of ∠T with the given information.

Explanation:

The given figure is an isosceles triangle, triangle RST, where RS is congruent to RT. In an isosceles triangle, the base angles are congruent, meaning that they have the same measure. Therefore, if we know the measure of one of the base angles, we know the measure of the other. The problem, however, does not provide the measures for any of the angles. This makes determining the measure of ∠T impossible with the given information. We would need to know either the measure of angle R or S or the measure of the angle at the vertex, angle T, to find the measure of ∠T. Without additional information, we cannot definitively choose between options A, B, C, or D.

Learn more about Isosceles Triangles here:

https://brainly.com/question/32587870

#SPJ11

Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5

Answers

The question is incomplete.

This is the complete question as I found in internet:

Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10

these are the points:

-1,5

1,5

0,-5

0,5

Answer: (0, -5)

Explanation:


point          x           y        5x - 2y = 10 ?


-1,5         -1           5         5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution

1,5            1          5         5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
 
0,-5           0        -5           0 -2(-5) = 10 ⇒ a solution

0,5             0         5          0 - 2(5) = - 10 ≠ 10 ⇒ not a solution

Answer:

(10,5/2) answer is A

Step-by-step explanation:

just took test.

Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, D, Sarah travels after hiking for an additional h hours?
A. D = 3h + 5
B. D = 3(h - 5)
C. D = 3h - 5
D. D = 5h + 3

Answers

the answer is a D=3h+5

Answer: A. [tex]D=3h+5[/tex]

Step-by-step explanation:

Given: The rate of increasing speed  = 3 miles per hour

The distance she traveled before stopping = 5 miles

Let h represents the number of additional hours for hiking.

Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-

[tex]D=3h+5[/tex]

Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?

Answers

We will call:

S: Runner Sophia.
T: Runner Tyler.

At the beginning the distance between both runners is 400m

At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m

and so on.

So, for example at t = 1s, the distance between both runner is:

D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)

So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:

[tex]d=vt[/tex]

Then, the distance between both runners, at any time, is given by:

[tex]D = 400-5t+4t[/tex]

So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:

[tex]0 = 400 - 5t+4t[/tex]
∴ [tex]400-t = 0[/tex]
∴ [tex]t = 400s[/tex]

Answer: 400 seconds

Step-by-step explanation:

5x = 400 + y

4x = y

take 4x and add it to the top so it looks like this:

5x = 400 + 4x

cancel 4x if you don't know how to do it  you do it like this you take +4x and instead you do -4x to cancel.

and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400

x = 400

_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal

Answers

the answer is c- skew lines
Hey There! I'll be glad too help you.



Skew lines are lines that never intersect and are not coplanar.



So the answer would be C. ^-^

find the greatest common factor 6x^2a + 6xa^2

Answers

The greatest common factor is 6xa

If you multiply 6xa with a and x ---->  6xa(x+a), you'll get 6x^2a + 6xa^2 

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. A. 44.4 cm, 11.1 cm B. 44.4 cm, 3.2 cm C. 11.1 cm, 4.9 cm D. 24 cm, 4.9 cm

Answers

it will probably be A Hopes This Helps.

PLS HELP ME ASAP WITH 3, 4, AND 5! PLS! (Read directions carefully :)

(BRAINLIEST WILL BE GIVEN HOPEFULLY!)

(Random answers gets moderated!)

Answers

3) It is a matter of reading the value from the graph. I read the graph as ...
a. d(0) = 20
b. d(2) = 18
c. d(4) = 12
d. d(6) = 10
e. d(9) = 15
f. d(3) = 15, or d(9) = 15

4) The domain is the horizontal extent: 0 to 12.
The range is the vertical extent: 10 to 20.

5)
a. f(7) = -2*7 +5 = -9
b. f(-3) = -2(-3) +5 = 11
c. -2x +5 = 17; -2x = 12; x = -6, so f(-6) = 17
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