Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. Write a system of equations to represent the situation

solutions:

1) G ≅ F

2) DA ≅  ES

Explanation:

Q)1

ΔBIG ≅ ΔFNS

pairs that are congruent:

From the list given,

→ G ≅ F is not necessarily congruent.

Q)2

ΔDAL ≅ ΔEKS

pairs that are congruent:

From the list given,

DA ≅  ES  is not necessarily congruent.

Usually the congruence is done according to naming

So

<B=F

<I=<N

<G=<S

#2

Check the naming

So

DA=EK

So option D

Answer:

im not vary shur

im so sorry but u may be in a hier grade than me

Answer:

\( - 4x < 32 \\ or \: - x < \frac{32}{4} \\ or \: - x < 8 \\ or \: x < - 8 \\ \\ therefore \: x \: < - 8.\)

Thank you ☺️

Answer:

part 1: $532.95. Part 2: 16

Step-by-step explanation:

Part 1: 15 * 15.35 = 230.25

30 * 10.09 = 302.70

230.25 + 302.70 = $532.95

Part 2: R = letters in the word desk

there are 4 letters in the word Desk

\(2^{R}\) = \(2^{4}\) = 2 * 2 * 2 * 2 = 4 * 4 = 16 subsets

I think Simon can put 144 items on a wreath because 60 bows+36 silk roses+48 silk carnations=144 items but items of each wreath is not specified (how many wreath are there?).  I hope it helped somehow?

Answer:

The Slope= -13/3

y-intercept= (0,5/3)

Step-by-step explanation:

m= change in y/change in x

m= y2-y1/x2-x1

m=6-(-7)/ -1-(2)

m=-13/3

Answer:

Yes-

Step-by-step explanation:

It repeats .121212 infinitely... I assume. You didn't say if it repeated or not.

Answer:

Yes

Step-by-step explanation:

Every repeating decimal satisfies a linear equation with integer coefficients, and those equations have solutions that are always rational numbers.

Therefore, every repeating decimal is a rational number.

Answer:

its -1

Step-by-step explanation:

cuz

Answer: it’s -1

Step-by-step explanation:

I just did the test

Answer:

(3,1)

Step-by-step explanation:

The width of the confidence interval will decrease with a decrease in sample size, while the level of confidence will remain the same.

The width of the confidence interval will decrease with a decrease in sample size. This is because when the sample size is smaller, there is less data and therefore the margin of error is larger. The formula for the margin of error is:

ME = z * (σ/√n)

Where z is the z-score for the desired confidence level, σ is the sample standard deviation and n is the sample size. Therefore, when the sample size is reduced, the margin of error increases and the width of the confidence interval decreases.

For example, suppose we have a 95% confidence interval of ±5 with a sample size of 50. The margin of error in this case is:

ME = 1.96 * (σ/√50)

If the sample size was decreased to 25, the margin of error would increase to:

ME = 1.96 * (σ/√25)

Therefore, the width of the confidence interval would decrease from ±5 to a smaller value. The level of confidence would remain the same at 95%.

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Angle A is congruent to angle c because they are both right angles. By the angle sum theorem, angle ADB is congruent to angle CBD.

A triangle is a closed polygon with three-line segments that intersect at each of its three angles. When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.

Side DB is congruent to side BD because they are the same segment.

Angle A is congruent to angle c because they are both right angles.

By the angle sum theorem, angle ADB is congruent to angle CBD.

By angle- side triangle congruence theorem, triangle BCD is congruent to triangle DAB.

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The asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the vertical asymptote t = 1, the horizontal asymptote y = 0 (x-axis), and the horizontal asymptote x = 0 (y-axis).

To find the asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t, we need to examine the behavior of the equations as t approaches certain values.

Let's first consider the vertical asymptotes. Vertical asymptotes occur when the denominator of either the x or y equation approaches zero. In this case, the vertical asymptote will occur when the denominator of the x equation, (t-1), approaches zero. Solving for t, we find that t = 1 is the value that makes the denominator zero. Therefore, the vertical asymptote is the line t = 1.

Next, we will determine the horizontal asymptotes. Horizontal asymptotes are defined by the behavior of the x and y equations as t approaches positive or negative infinity. To find the horizontal asymptotes, we need to examine the limits of x and y as t approaches infinity and negative infinity.

As t approaches infinity, the x equation, 1/(t-1), approaches zero since the numerator remains constant while the denominator grows larger. Therefore, the x-coordinate tends to zero as t approaches infinity.

Similarly, as t approaches negative infinity, the x equation approaches zero. Therefore, the x-coordinate tends to zero as t approaches negative infinity.

For the y equation, as t approaches infinity, the y equation, 2/t, approaches zero since the numerator remains constant while the denominator grows larger. Therefore, the y-coordinate tends to zero as t approaches infinity.

As t approaches negative infinity, the y equation approaches zero as well. Therefore, the y-coordinate tends to zero as t approaches negative infinity.

Hence, we have identified that the horizontal asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the x-axis (y = 0) and the y-axis (x = 0).

To summarize, the asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the vertical asymptote t = 1, the horizontal asymptote y = 0 (x-axis), and the horizontal asymptote x = 0 (y-axis). These asymptotes provide valuable information about the behavior of the graph as t approaches certain values, helping us understand the overall shape and characteristics of the parametric curve.

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Answer:

Step-by-step explanation:

Answer:

Remember that the slope of perpendicular lines are negative reciprocals of each other.Step-by-step explanation:y = 1 - 2x     the slope is -2     the value of the x term.So the slope of the new line using point (- 1, 2)  is  1/2.Now use y = mx + b where y = -1, x = 2, and m = 1/2 .y = mx + b-1 = 1/2(2) + b                solve for "b", the y-intersect-1 =  1 + b-2 = bThe line that is perpendicular to y = 1 - 2x  is  y = 1/2x - 2

Step-by-step explanation:

The equilibrium point is (60, 2400), the consumer surplus at the equilibrium point is $48,000, and the producer surplus at the equilibrium point is $36,000.

(a) The equilibrium point occurs when the quantity demanded by consumers equals the quantity supplied by producers. To find this point, we need to set the demand function equal to the supply function and solve for x.

Demand function: D(x) = 3000 - 10x

Supply function: S(x) = 900 + 25x

Setting D(x) equal to S(x):

3000 - 10x = 900 + 25x

Simplifying the equation:

35x = 2100

x = 60

Therefore, the equilibrium point occurs at x = 60.

(b) Consumer surplus at the equilibrium point can be found by calculating the area between the demand curve and the equilibrium price. Consumer surplus represents the difference between the price consumers are willing to pay and the actual market price.

At the equilibrium point, x = 60. Plugging this value into the demand function:

D(60) = 3000 - 10(60)

D(60) = 3000 - 600

D(60) = 2400

The equilibrium price is $2400 per unit. To find the consumer surplus, we need to calculate the area of the triangle formed between the demand curve and the equilibrium price.

Consumer surplus = (1/2) * (2400 - 900) * 60

Consumer surplus = $48,000

(c) Producer surplus at the equilibrium point represents the difference between the actual market price and the minimum price at which producers are willing to sell their goods.

To find the producer surplus, we need to calculate the area between the supply curve and the equilibrium price.

At the equilibrium point, x = 60. Plugging this value into the supply function:

S(60) = 900 + 25(60)

S(60) = 900 + 1500

S(60) = 2400

The equilibrium price is $2400 per unit. To find the producer surplus, we need to calculate the area of the triangle formed between the supply curve and the equilibrium price.

Producer surplus = (1/2) * (2400 - 900) * 60

Producer surplus = $36,000

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Answer:

The answer to the division problem (5/8) ÷ (4 1/6) is 3/20.

Step-by-step explanation:

To divide a fraction by a mixed number, we first need to convert the mixed number into an improper fraction. The mixed number is 4 1/6. To convert it, multiply the whole number (4) by the denominator (6) and add the numerator (1):

4 * 6 + 1 = 24 + 1 = 25

Now we have the improper fraction 25/6. The division problem is now:

(5/8) ÷ (25/6)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:

(5/8) * (6/25)

Now, multiply the numerators together and the denominators together:

(5 * 6) / (8 * 25) = 30 / 200

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10:

(30 ÷ 10) / (200 ÷ 10) = 3 / 20

So, the result of the division (5/8) ÷ (4 1/6) is 3/20.

The quotient obtained from the division of given fractions is 3/20.

Given that, 5/8 divided by \(4\frac{1}{6}\).

Here, \(4\frac{1}{6}\) = 25/6

Dividing fractions is nothing but multiplying the fractions by reversing one of the two fraction numbers or by writing the reciprocal of one of the fractions. By reciprocal we mean, that if a fraction is given as a/b, then the reciprocal of it will b/a.

Here, 5/8 ÷ 25/6

= 5/8 × 6/25

= 1/4 × 3/5

= 3/20

Therefore, the quotient obtained from the division of given fractions is 3/20.

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ANSWER. Part b

Line segment PM = 2.2 length

ML = 2.2

ON = 2

NK = 2

Answer:60

Step-by-step explanation:

a) Timothy's bike costs $20.It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost

To find the cost of Timothy's bike, we need to calculate 20% of Katie's bike cost.

20% of $100 can be calculated by multiplying $100 by 0.20:

20% * $100 = $20.

Therefore, Timothy's bike costs $20.

To calculate 20% of $100, we multiply $100 by the decimal equivalent of 20%, which is 0.20:

20% * $100 = 0.20 * $100 = $20.

In this scenario, Timothy's bike is priced at 20% of Katie's bike cost. This means that Timothy's bike is relatively less expensive compared to Katie's bike. It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost of Timothy's bike based on the given percentage relationship.

Based on the given information, Timothy's bike costs $20, which is 20% of Katie's bike cost.

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Answer:

i use logical reasoning

Answer:

x<1/-3

Step-by-step explanation:

Distribute -3 to (x+3)

-3x-9+5<-3

add like terms (-9+5=-4)

-3x-4<-3

add 4 to both sides

-3x<1

divide both sides by -3

x<1/-3

Hey there again,

I don't understand what it means by the sign change but I can still help.
A'  (3,4)
B'  (5,2)
C'  (2,3)

Answer:

x = 3

Step-by-step explanation:

Given the 2 equations

x + y = 3 → (1)

2x - y = 6 → (2)

Adding the 2 equations term by term eliminates the y- term, that is

3x = 9 ( divide both sides by 3 )

x = 3

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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Can you explain more? if your looking for the slope of both it is 5/9 for the fist one and 2/3 for the second. If your looking for y and x -intercept for the first one x intercepts at (-2,0) and y intercepts at (0, 4/3) and, for the second one x intercepts at ( -13/5, 0) and y intercepts at (0, 13/9)

Method 1: Factoring

m^2 + 7m + 10

We need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5.

m^2 + 2m + 5m + 10

(m + 2)(m + 5)

n^2 + 9n + 18

We need to find two numbers that multiply to 18 and add up to 9. These numbers are 3 and 6.

n^2 + 3n + 6n + 18

(n + 3)(n + 6)

p^2 - 6p + 8

We need to find two numbers that multiply to 8 and add up to -6. There are no such numbers, so we cannot factor this quadratic.

Method 2: Quadratic Formula

m^2 + 7m + 10

a = 1, b = 7, c = 10

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)

m = (-7 ± sqrt(9)) / 2

m = -5 or -2

n^2 + 9n + 18

a = 1, b = 9, c = 18

n = (-b ± sqrt(b^2 - 4ac)) / 2a

n = (-9 ± sqrt(9^2 - 4(1)(18))) / 2(1)

n = (-9 ± sqrt(9)) / 2

n = -3 or -6

p^2 - 6p + 8

a = 1, b = -6, c = 8

p = (-b ± sqrt(b^2 - 4ac)) / 2a

p = (6 ± sqrt(6^2 - 4(1)(8))) / 2(1)

p = (6 ± sqrt(16)) / 2

p = 2 or 4

Therefore, the solutions to the quadratics are:

m^2 + 7m + 10 = (m + 2)(m + 5) or m = -5 or -2

n^2 + 9n + 18 = (n + 3)(n + 6) or n = -3 or -6

p^2 - 6p + 8 = (p - 2)(p - 4) or p = 2 or 4

Answer:

57, 58, 59, 60

Hope this Helps :)

Since in the 24 hour clock military time is based off of 0 meaning 0001-2359, then the time of 4pm would be written as 1600 hours.

Military time is commonly used by the armed forces emergency services and hospitals. Military time is a way of expressing time in which the day runs from midnight to midnight and is divided into 24 hours, and it is commonly used in many organizations that operate on a 24-hour schedule.

Here the use of clock is based on a 24 hour clock where midnight is 0000 hours and noon is 1200 hours.

If the noon is 1200 hours according to the military time then 4 hours later than the noon that is 4 pm will be 1600 hours,

as 1 pm will be 1300 hours, 2 pm will be 1400 hours and 3 pm will be 1500 hours,

Similarly 4pm will be 1600 hours according to the military time.

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The probability of getting 2 or fewer seeds to germinate out of 6 is 0.14307 or 14.3%.

The probability of getting the seeds that will germinate out of six seeds, as per data, 75% of the seeds of the given type germinate is,

6C₀ (1 − 0.75)⁶ + 6C₁(1 − 0.75)⁵(0.75)¹ + 6C₂(1 − 0.75)⁴(0.75)².

So, 2 or less seeds germinate as the question suggests that we need to find the probability.

Now, let us solve the problem:

Calculation of probability of germination p = 0.75,

q = 1 - p

  = 1 - 0.75

  = 0.25

Hence, the probability of germination is 0.75, and the probability of non-germination is 0.25.

Calculation of the number of seeds to be germinated,

Now we need to find out the probability of germination of 2 seeds or less.

Therefore, we will calculate the probability of germination of 0, 1, or 2 seeds out of 6 seeds.

Using Binomial Distribution formula,

P (x ≤ 2) = P (x = 0) + P (X = 1) + P (X = 2)

           = {6C₀ * (0.75)⁰ * (0.25)⁶ + 6C₁ * (0.75)¹ * (0.25)⁵ + 6C₂ * (0.75)² * (0.25)⁴}

           = (1) * (0.00024414) + (6) * (0.001831) + (15) * (0.008789)

           = 0.00024414 + 0.010986 + 0.13184

           = 0.14307

Thus, the probability of getting 2 or fewer seeds to germinate out of 6 is 0.14307 or 14.3%.

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Answer:

Tim needs to finish 59/90

Step-by-step explanation:

Add together what Evan Claire and Jaya ran  

9/10 + 7/9+ 2/3

The common denominator is 90

9/10 (9/9) +7/9 *10/10  + 2/3 *30/30

81/90 + 70/90 + 60/90

211/90

We need 3 km = 3 *90/90 = 270 /90

270/90 - 211/90 = 59/90