Arman, Babken, and Cecilia decided to compete in a 100m run. When Arman crossed the finish line, Babken was 10m behind him. When Babken crossed the finish line, Cecilia was 10m behind him. How far was Cecilia behind Arman when he crossed the finish line?

Answer:

s=25

Step-by-step explanation:

8(5s-13)-16(2s+6)=0

40s-104-32s-96=0

40s-32s-104-96=0

8s-104-96=0

8s-200=0

8s=0+200

8s=200

s=200/8

s=25

Answer: s=25

Step-by-step explanation:

Using Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \sf\longmapsto P^2=17^2-11^2[/tex]

[tex]\\ \sf\longmapsto P^2=289-121[/tex]

[tex]\\ \sf\longmapsto P^2=168[/tex]

[tex]\\ \sf\longmapsto P\approx 13[/tex]

Answer:

H=17B=11P=?Using Pythagorean theorem

Step-by-step explanation:

Answer:

[tex]p\leq 4[/tex]

Step-by-step explanation:

we know that

The solution of the graph shows the interval (-∞,4]

All real numbers less than or equal to 4

In a number line the shaded area is at left of x=4 (closed circle)

The number 4 is included in the solution

therefore

the inequality that represent the graph is

[tex]p\leq 4[/tex]

Answer:

C, B

Step-by-step explanation:

4x * 1 = 4x

4x * y = 4xy

4x + 4xy

Next

5 * x = 5x

5 * 3 = 15

5x + 15

Answer:

17(c)

18(b)

Step-by-step explanation:

17) (4x*1)+(4x*y)

4x+4xy

18) (x+3)5

(5*x)+(3*5)

5x+15

Answer:

right 2, down 9

Step-by-step explanation:

move point A' two places to the right, and down nine to get to point A

The explicit equation for the nth term of the geometric sequence 3584, 896, 224 is:

[tex]a_n=3584(0.25)^{n-1}\\\\\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]

Solution:

Given that we have to find the explicit equation for nth term of geometric sequence

Given sequence is:

3584, 896, 224

A geometric sequence has a common ratio

Let us find the common ratio. Divide each term by the previous term.

[tex]r=\frac{896}{3584} = 0.25\\\\r = \frac{224}{896} = 0.25[/tex]

Thus the common ratio is 0.25

The formula for nth term of geometric sequence is given as:

[tex]a_n=ar^{n-1}[/tex]

Where,

[tex]a_n[/tex] is the nth term of sequence

a is the first term of sequence

r is the common ratio

Here in given sequence 3584, 896, 224

first term = a = 3584

common ratio = r = 0.25

Therefore,

[tex]a_n=3584(0.25)^{n-1}[/tex]

[tex]\text{Where } n\geq 1 \text{ ,n = 1, 2, 3, 4, .........}[/tex]

"n" is a natural positive number greater than or equal to 1

Thus the explicit equation to find nth term is found

Answer:

Step-by-step explanation:

each side is 21 inches long.

4x+3=21

subtract 3 from both sides

4x=18

x=4.5

Answer:

4.5

Step-by-step explanation:

Since its an equilateral triangle, all the sides are equal.

SO, you can set up the equation:

3 ( 4x + 3 ) = 63

Start by disributing

12x + 9 =63

Subtract 9 from each side to isolate the variable

12x = 54

Divide both sides by 12

x = 4.5

Answer:

4850 students

Step-by-step explanation:

if 2619 women make up 54% of the entire student body, then we know that 0.54x=2619, since 54%=0.54 and we can call x the entire student body. solve:

0.54x=2619

÷0.54    ÷0.54

x=4850

henceforth, the total enrollment is 4850 students.

hope this is helpful!

Answer:

4850 students

Step-by-step explanation:

Let b = total enrollment.

Then 54% of b = 2619.  Find b by dividing both sides of

0.54b = 2619 by 0.54:

b = 4850

The total enrollment is 4850.

Final answer:

The 5 in 11.205 is in the thousandths place and represents 0.005, while the 5 in 5.32 is in the units place, representing 5. The 5 in 5.32 is one thousand times the value of the 5 in 11.205, and vice versa.

Explanation:

The relationship between the 5 in 11.205 and the 5 in 5.32 can be described in terms of their place values. In the number 11.205, the 5 is in the thousandths place, which means it represents 5 thousandths or 0.005. In the number 5.32, the 5 is in the units place, which means it represents 5 ones or simply 5.

To compare their values, we can say that the 5 in 5.32 is one thousand times the value of the 5 in 11.205 because 5 divided by 0.005 equals 1000. Alternatively, we could say the 5 in 11.205 is one thousandth the value of the 5 in 5.32.

These comparisons are based on the understanding of place value in decimal numbers, where each position to the left or right of the decimal point represents a power of 10. Therefore, the value of a digit is determined by its position relative to the decimal point.

2 + 2 = 4 because 4 is a sum of 1-digit numbers

2 + 2 ≠ 22 because 22 is the sum of 1-digit and 2-digit numbers

Step-by-step explanation:

Lets explain some important notes:

∵ 2 + 2 is the addition problem of two 1-digit numbers

∴ There sum will be 4 which is also 1-digit number

∴ 2 + 2 must be 4

∵ 22 is a two digit number

∴ Its value is 20 + 2 ⇒ not 2 + 2

∴ 2 + 2 can not be 22

2 + 2 = 4 because 4 is a sum of 1-digit numbers

2 + 2 ≠ 22 because 22 is the sum of 1-digit and 2-digit numbers

Learn more:

You can learn more about the place value of numbers in brainly.com/question/13174282

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Answer:

-3x-16

Step-by-step explanation:

(2x-6)-(5x+10)

2x-6-5x-10

2x-5x-6-10

-3x-6-10

-3x-16

Answer:

0.8

Step-by-step explanation:

To calculate the cost of any item per pound, divide the cost of the item by its weight in pounds: cost ÷ pounds = cost per pound.

Hope This Helped!!

Answer:

0.8 is the unit price per pound

Step-by-step explanation:

If you divide the price ($16) by the amount (20 pounds) then you will get the unit price per pound (0.8)

So, 16 ÷ 20 = 0.8

1.[tex](-7,-3)[/tex]

2.[tex][5,\alpha )[/tex]

3.[tex](-4,-\alpha )[/tex]

4.[tex](-1,0)[/tex]

Explanation

a shaded circle in number line indicates that the number in the shaded point is also included in the interval. In the interval notation this limit is expressed using a square bracket.

A circle that is not shaded in a number line indicates that the number is not included in the interval. In interval notation a bracket is used to represent that point on the number line.

An arrow shows the extension to negative or positive infinity. The symbol [tex]\alpha[/tex] is used to represent infinity and is always included in bracket.

Final answer:

The cube root of 27x18 is 3x6, determined by taking the cube root of each term, with 27 yielding 3 and the x18 exponent reduced by a factor of 3 to x6.

Explanation:

The question posed is, "What is the cube root of 27x18?" To solve this, we need to break down the expression and compute the cube root of both terms separately. The cube root of 27 is 3 because 33 = 27. For the variable x raised to the 18th power, taking the cube root means we divide the exponent by 3, which gives us x6. Therefore, the cube root of 27x18 is 3x6.

Answer: total comes to 4X - 12Y + 4

Step-by-step explanation:

Answer:

7x - 4y - 8 -3x - 8y + 12

Step-by-step explanation:

7x - 3x = 4x

-4y - 8y = 12y

-8 + 12 = 4

4x - 12y + 4

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Answer:$18.00

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 of 9

" of " in math means multiply

1/2 * 9 = 9/2 or 4 1/2 or 4.5

Answer:

Step-by-step explanation:

Provide problems and we're here to help.

Answer:

write the problem, decide whether you use add or sub.,add or sub. the constant on both sides, eliminate the coefficients of the variable, last solve for the variable.

Step-by-step explanation:

m∠S = 45°

Solution:

Given ∠R = 3x°, ∠S = 2x°, ∠T = 3x°.

Sum of the angles of a triangle = 180°

⇒ m∠R + m∠T + m∠S = 180°

⇒ 3x° + 3x° + 2x° = 180°

Adding all the angles.

⇒ 8x° = 180°

Divide both sides of the equation by 8, we get

⇒ x° = 22.5°

Substitute x = 22.5° in m∠S.

⇒ m∠S = 2 × 22.5°

⇒ m∠S = 45°

Hence, m∠S = 45°.

Answer:

Step-by-step explanation:

10=z+6

subtract 6 from both sides

4=z

z=4

Answer:

The answer is 4

Step-by-step explanation:

To get the answer for this equation, take 6 and subtract from both sides.. meaning 6-6 and they will cancel and then subtract 6 from 10 and that will give you your answer of 4.

Answer:

[tex]\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]

Step-by-step explanation:

If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.

Moreover,

[tex]a=2\\ \\b=4[/tex]

The equation of such ellipse is

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

Hence, the equation of the ellipse is

[tex]\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]

Answer:

70

Step-by-step explanation:

To evaluate k( -5), substitute x = - 5 into k(x)

k(−5)=(6×-5)+100=−30+100=70

The function that correctly represents the pattern in the given table is y = 2x + 1, which means that, for each input X, you multiply by 2 and then add 1 to obtain output Y.

The table of values given indicates a linear relationship between X and Y. If we look closely, we can see that for every unit increase in X, Y increases by 2 units. This pattern indicates that the function is characterized by the equation y = 2x + 1.

So, the correct answer is C) y = 2x + 1. This means that Y is twice the value of X plus 1. In simpler terms, we multiply the input variable (X) by 2 and then add 1 to determine the output (Y).

None of the other given function expressions correctly describe the pattern observed in the table.

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The expression for the function is y=2x. Y is double x.

The function that relates the values of X and Y in the given table is y = 2x. This means that the value of Y is twice the value of X. For example, when X=3, Y=6 because 2*3=6. This pattern holds true for all the other values in the table.

Option A) y= 2x is the correct expression for this function as it shows that Y is double X. Therefore, the answer to this question is A) y= 2x. Y is double x.

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Answer:

4/21

Step-by-step explanation:

1. distribute

24p-8+9=3p+6-1

2. combine like terms on each side

24p+1=3p+5

3. solve for p

21p=4

p=4/21

Answer:

Step-by-step explanation:

7,014,999,999 rounded to the nearest hundred thousand

7,015,000,000 <===

The values of x and y needs to be 39 degrees and 21 degrees respectively to show that ABCD is a parallelogram.

We know that opposite angles of a parallelogram are equal and we are asked to find the value of x and y.

We are given that angle A = 3y angle B = 3x , angle C = y + 78 and angle D = 4x - 21

Now as we know that the opposite angles are going to be equal.So,

angle A = angle C

3y = y + 78

2y = 78

y = 39

So, the value of y is going to be 39 degrees.

Similarly, we can also find the value of x.

angle B = angle D

3x = 4x - 21

-x = -21

x = 21

So, the value of x is going to be 21 degrees.

Hence, the values of x and y needs to be 39 degrees and 21 degrees respectively to show that ABCD is a parallelogram.

Answer:

40

Step-by-step explanation:

Answer:

1=R, 2=O, 3=A, 4=D

Step-by-step explanation: