Zach loves to compete in triathlons. At a race a few months ago, he finished in 280 minutes. Yesterday, he completed another triathlon and finished in 294 minutes. What was the percent of increase in Zach's finishing time?

Answer: 15

Step-by-step explanation:

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Answer:

What is the largest y-value that satisfies this system?

1/2(x-3)(x-2)=y

2(x-1/2)=y

Step-by-step explanation:

the first one has a binomial times a binomial which you have to do the generic rectangle if you did you would get

x² - 5x + 6 = y you keep parenthesis and the 1/2 and bring down to get

1/2(x² - 5x + 6) = y then distribute

1/2x² - 5/2 + 3 = y

2(x - 1/2) = y the distribute and get

2x - 1 = y

so the first one has the largest y-value

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

let the denominator of the fraction be x , then the fraction is

[tex]\frac{x-5}{x}[/tex]

increasing the numerator and denominator by 4

[tex]\frac{x-5+4}{x+4}[/tex] = [tex]\frac{x-1}{x+4}[/tex]

this fraction is then equal to 3 times ( triple ) the value of the fraction, so

[tex]\frac{x-1}{x+4}[/tex] = [tex]\frac{3(x-5)}{x}[/tex] ( cross- multiplying )

3(x - 5)(x + 4) = x(x - 1) ← expand factors on left using FOIL

3(x² - x - 20) = x(x - 1) ← distribute parenthesis on both sides

3x² - 3x - 60 = x² - x ( subtract x² - x from both sides )

2x² - 2x - 60 = 0 ( divide through by 2 )

x² - x - 30 = 0 ← in standard form

(x - 6)(x + 5) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 5 = 0 ⇒ x = - 5

however, x > 0 , then x = 6

original fraction

= [tex]\frac{x-5}{x}[/tex] = [tex]\frac{6-5}{6}[/tex] = [tex]\frac{1}{6}[/tex]

Answer:

  x ∈ {2, 3, 4, 5, 6}

Step-by-step explanation:

You want the positive integer solutions of ||x²-2x|-|3x-20|| = |x²+x-20|.

Each of the absolute value functions has turning points where the argument is zero. Those turning points are ...

  x²-2x   ⇒   x(x-2) = 0   ⇒   turning points at x=0 and x=2

  3x-20   ⇒   x -20/3 = 0   ⇒   turning point at x=20/3

  x²+x-20   ⇒   (x+5)(x-4) = 0   ⇒   turning points at x=-5 and x=4

In numerical order, the turning points are ...

  x ∈ {-5, 0, 2, 4, 20/3}

These divide the domain of the equation into 6 intervals. Since we are concerned only with positive integer solutions, we are only interested in the intervals ...

  [0, 2), [2, 4), [4, 20/3), [20/3, ∞)

In this domain, x²-2x < 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...

  |-(x² -2x) +(3x -20)| = -(x² +x -20)

The difference in the absolute value bars is negative, so we get the equation ...

  -(-x² +2x +3x -20) = -x² -x +20

  2x² -4x = 0 . . . . . . . add x²+x+20

  x = 0 . . . . . x = 2 is not in the domain

There are no positive integer solutions in this domain.

In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 < 0. This means the equation becomes ...

  |(x² -2x) +(3x -20)| = -(x² +x -20)

The difference in the absolute value bars is negative, so we get the equation ...

  -(x² -2x +3x -20) = -x² -x +20

  0 = 0 . . . . . . . . . . . . add x² +x -20

  2 ≤ x < 4 . . . . . . . . all x-values in the domain are solutions

The positive integer solutions are x = 2, x = 3.

In this domain, x²-2x > 0, 3x-20 < 0, and x²+x-20 > 0. This means the equation becomes ...

  |(x² -2x) +(3x -20)| = x² +x -20

The difference in the absolute value bars is positive, so we get the equation ...

  (x² -2x +3x -20) = x² +x -20

  0 = 0 . . . . . . . subtract x² +x -20

  4 ≤ x < 6 2/3 . . . . . . . . . all values of x in the domain are solutions

The positive integer solutions are x = 4, x = 5, x = 6.

In this domain, x²-2x > 0, 3x-20 > 0, and x²+x-20 > 0. This means the equation becomes ...

  |(x² -2x) -(3x -20)| = x² +x -20

The difference in the absolute value bars is positive, so we get the equation ...

  x² -2x -3x +20 = x² +x -20

  -6x +40 = 0 . . . . . . . subtract x² +x -20

  x = 6 2/3 . . . . . . . add 6x, divide by 6

There are no positive integer solutions in this domain.

The positive integer values of x are {2, 3, 4, 5, 6}.

The other coordinate is x = [tex]\sqrt{3} /2[/tex].

Given:

A point (x, y) is on the unit circle. If its y-coordinate is 1/2 and the point lies in Quadrant I.

we know that :

In unit circle radius r = 1.

[tex]x^{2} +y^{2} = r^{2}[/tex]

[tex]x^{2} +(1/2)^2 = 1^2[/tex]

[tex]x^{2} +1^2/2^2 = 1[/tex]

[tex]x^2 + 1/4 = 1[/tex]

[tex]x^{2} = 1-1/4[/tex]

[tex]x^{2} = 4- 1 / 4[/tex]

[tex]x^{2} =3/4[/tex]

[tex]x =[/tex] ±[tex]\sqrt{3/4}[/tex]

[tex]x =[/tex] ±[tex]\sqrt{3} /2[/tex]

since x is in first quadrant it has only positive value

[tex]x =\sqrt{3} /2[/tex].

Therefore the other coordinate is x = [tex]\sqrt{3} /2[/tex].

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The outcomes in the collection for event E is four and they are  (1, 4) (2,3) (3,2) (4, 1).

Two number cubes, each of which has its faces numbered from 1 to 6 is rolled.

The cubes will be rolled and the sum of the numbers landing face up will be recorded.

The total sample space for two cubes = 6² = 36

Let the event E represent the event of rolling a sum of 5

Total possible outcomes for a sum of 6 is (1, 4) (2,3) (3,2) (4, 1)

We need to find the probability of event E, P(E)

P(E) = possible outcomes/ sample space

P(E) = 4/ 36 = 1/9

Therefore, the outcomes in the collection for event E is four and they are  (1, 4) (2,3) (3,2) (4, 1).

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Answer:

[tex]x^{2}[/tex] -x -6

Step-by-step explanation:

You combine the like terms 2x and -3x which is -x

Answer:

Step-by-step explanation:

1 is correct

2 is correct

3 is wrong

4 is correct

5 is correct

6 is wrong

7 is wrong

For 7:

360 - 90 - 61 - 65

= 144

For 6:

180 - 144

= 36

For 3:

180 - 115 - 36

= 29

Answer:

15.13 units

Step-by-step explanation:

The coordinates of the polygon before and after dilation is below

preimage      image

J (2, 4)           J' (4, 8)

K (4, 4)           K' (4, 4)  

P (3, 2)            P' (6, 4)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                           image

J (2, 4)   → (2 * 2, 4 * 2) →   J' (4, 8)

K (4, 4)  → (4 * 2, 4 * 2) →    K' (8, 8)  

P (3, 2)  → (3 * 2, 2 * 2) →    P' (6, 4)

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Solving the proportion using the multiplication property of equality gives

The both ratio showing fractions of one-fifth on the left hand side of the equation is equal to the right hand side of the equation which have t as the numerator and 3 as the denominator

The fractions will be solves by cross multiplying as below

1/5 = t/3

5 * t = 3 * 1

5t = 3

dividing through by 5

5t / 5 = 3 / 5

t = 3/5

plugging in t back to the initial equation gives

1/5 = t/3

1/5 = 3/5 / 3

1/5 = 1/5

Therefore t = 3/5

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The y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing  presentation handouts

In this question, we have been given a function 2x+y=20 that represents the relationship between the remaining budget balance(y) dollars in dollars if printing x presentation handouts.

We write given equation in slope-intercept form,

y = -2x - 20

when x = 0,

y = -20

So, y-intercept is -20

This means, the remaining budget balance is -20 dollars if no printing  presentation handouts (x = 0).

Therefore, the y-intercept of this situation is -20 and it means, the remaining budget balance is -20 dollars if no printing  presentation handouts

Given question is incomplete.

The complete question is:

A company has a small budget for printing presentation handouts for an important meeting. The function 2x+y=20 represents the relationship between the remaining budget balance, y, in dollars if printing x presentation handouts. What is the y-intercept of this situation and what does it represent?

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The median of the given data is 88.5

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Given the numbers of pairs of shoes sold during the 10 days of the sale were:

86 84 100 97 96 88 89 60 78 99

We have to determine the median for the given data

The data given must be arranged in ascending order.

60, 78, 84, 86, 88, 89, 96, 97, 99, 100

median = middle most value

∴ 88,89 are middle values

∴ Median =(88+89)/2

= 177/2

= 88.5

Therefore the median of the given data is 88.5

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The expression (3⁴)² in repeated multiplication is (3⁴) * (3⁴)

From the question. the expression is given as

(3⁴)²

The task is that we rewrite the expression as products i.e. repeated multiplication

This in other words means that:

We rewrite the (3⁴)² as repeated multiplication

To do this, we apply the exponent rule of indices

This rule states that:

a^m = a * a * a .... in m places

So, we have

(3⁴)² = (3⁴) * (3⁴)

Hence, the equivalent expression is (3⁴) * (3⁴)

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Answer:

7 :D

Step-by-step explanation:

Lets go step by step!

When we do something to one side, we must do it to the other!

2x - 5 < 9

2x - 5 + 5 < 9 + 5

2x < 14

2x/2 < 14/2

x < 7

Your answer is 7 :D

Have an amazing day!

Please rate and mark brainliest!

Answer:

x=7

Step-by-step explanation: Okay so,

2x−5=9

First, you take the 5 and add it to the 9:

2x=9+5=

2x=14

Then you divide 2x by 2 and what you do to one side you do to the other, so you also divide 14 by 2:

2x/2=14/2=

x=7

Hope this helps!

Answer:

The answer would be -1/3.

Step-by-step explanation:

If you plug the coordinates into slope formula (y 2 - y 1 )/ (x 2 - x 1) , you'd have 3-5 over 8-2, and once you solve that, you'll have -1/3 as your slope. Hope this helps ! :D

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The length of side BC is 15.6 cm and the size of angle EDC in degrees is 56.5°

From the question, we are to determine the length of BC

From the given information,

m ∠ABC = 30°

AC = 9 cm

By using SOH CAH TOA, we can write that

tan (m ∠ABC) = AC / BC

tan (30°) = 9 / BC

BC = 9 / tan (30°)

BC = 15.588

BC ≈ 15.6 cm

To determine the measure of angle EDC,

First we will determine the length of CD

From the diagram,

BD = BC + CD

20 = 15.588 + CD

CD = 20 - 15.588

CD = 4.412

Now, using SOH CAH TOA

cos (m ∠EDC) = CD / DE

cos (m ∠EDC) = 4.412 / 8

cos (m ∠EDC) = 0.5515

m ∠EDC = cos⁻¹(0.5515)

m ∠EDC = 56.5300°

m ∠EDC ≈ 56.5°

Hence, the length of BC is 15.6 cm and the measure of EDC is 56.5°

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Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.

In the given question, we have to find the speed of each.

Two trains going in opposite directions leave at the same time.

One train tavels 15 mph faster than the other.

In 6 hours the trains are 630 miles apart.

Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.

Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.

So, find the distance covered by the first vehicle in 6 hours by using the formula

Distance = Speed × Time

So the distance D(1) is;

D(1) = s*6

D(1) = 6s

So the distance D(2) is;

D(2) = (s+15)*6

D(2) = 6s+90

Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.

D(1)+D(2) = 630

Puttimg the value of D(1) and D(2)

6s+6s+90=630

Simplifying

12s+90=630

Subtract 90 on both side we get

12s=540

Divide by 12 on both side we get

s=45 mph

So the value of speed of the faster vehicle

s+15 = 45+15

s+15 = 60 mph

Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.

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Answer:

Step-by-step explanation:

It is clear that after smelting the amount of iron obtained is 12\20 = 60%.

Therefore when 45t is smelted the amount obtained = 60% x 45t

= 27t

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

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The linear equation of the table is, t = -5/3a +19

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

y = mx + c

where

y = dependent variable

m = slope

x = independent variable

c = y - intercept

Here we have the table with the values of t and the value of a.

Now, we need to find the linear equation for this table.

In order to find the linear equation, we need the values of slope and the y intercept values.

To find the value of slope we have to take two point from the given table.

They are (6,9) and (9,4).

Now, apply the value on the slope formula, then we get,

m = (4 - 9) / (9 - 6)

m = -5/3

Now, we have to use the slope m and the point (6,9), to find the value of y intercept,

Then we get the value of c as,

9= -5/3(6)+c

9=-10+c

c=19

Therefore, the linear equation of the table is, t = -5/3a +19

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According to the given dot plot, the striking deviation is at the value of 4, making the correct answer option C: 4.

What is the striking deviation?

A striking deviation is a noticeable or significant difference or deviation from the norm or expected value in a data set. It refers to an observation or value that stands out from the others due to its higher frequency, magnitude, or significance. In statistics, striking deviations can be identified through various measures, such as standard deviation, variance, or graphical representation, such as dot plots or box plots.

To determine the striking deviation in the given dot plot, we need to look for the value with a noticeably larger number of dots compared to the others. We can do this by comparing the frequency of dots for each value. From the given graph, we can see that the frequency of dots at 4 is significantly higher than the other values. This means that 4 has a higher occurrence or significance in the data set compared to the other values.

Therefore, the striking deviation is at the value of 4, making the answer option C: 4.

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Answer:

There are 80 lunch items altogether.

Step-by-step explanation:

If the ratio of hotdogs to hamburgers is 10:30 then all we have to do is multiply the whole ratio by 2 to get 20:60.

So it there are 20 hotdogs and 60 hamburgers then there are 80 lunch items altogether because 20+60=80.

;)

The weight of each of his checked bags will be; 15.5 kg.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that; Number of checked bags = 2

Backpack weight = 4 kg

The total weight of Carl's baggage 35kg

Let w be the weight of each checked bag.

Weight of 2 checked bags = 2w

It can be found as; Weight of 2 checked bags + Backpack weight =  Total weight of Carl's baggage

Then;

2w + 4 = 35

Subtract 4 from both sides;

2w + 4 = 35

2w  = 31

Divide 2 from both sides;

w = 15.5

Therefore, the weight of each of his checked bags will be; 15.5 kg.

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The equation of line passes through the points (2, 0) and (0, -1) will be;

⇒ y = 1/2 x - 1

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (2, 0) and (0, -1).

Now,

Since, The equation of line passes through the points (2, 0) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 0) / (0 - 2)

m = - 1 / - 2

m = 1 / 2

Thus, The equation of line with slope 1 / 2 is,

⇒ y - 0 = 1 / 2 (x - 2)

⇒ y = 1/2 x - 1

⇒ y = 1/2 x - 1

Therefore, The equation of line passes through the points (2 , 0) and

(0, - 1) will be;

⇒ y = 1/2 x - 1

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Answer: 25*tan(35°)

Step-by-step explanation: For this problem, since the triangle is a right triangle, you must use the formula, tangent(Ф) = opposite/adjacent. In this case, Ф = 35 degrees. The side opposite to the angle Ф is x, and the side adjacent to Ф is 25. Therefore,

tangent(35°) = x/25

After multiplying the 25 over,

x = 25*tan(35°)

am answering from two to ten

For the given amplitude , period and displacement , equation of the modelling the displacement d as a function for the given time t for the initial movement in negative direction is equal to

d(t) = -13sin(8πt + (-8πt₀)) .  

As given in the question,

It is given that object moves in simple harmonic motion ,

Amplitude = 13cm

Period 'T' = 0.25 seconds

f = 1/T

 = 1/ 0.25

 = 100/25

 = 4 / sec

displacement d from rest position is 0.

t  = t₀

Equation of modelling the displacement d as function of time given time t

is given by :

d(t) = A sin(2πft + -2πft₀)

⇒d(t) = -13sin[2π(4t) + -2π(4t₀)]

⇒d(t) = -13sin[8πt -8πt₀]

As initial movement in negative direction.

Therefore, for the given amplitude , period and displacement , equation of the modelling the displacement d as a function for the given time t for the initial movement in negative direction is equal to

d(t) = -13sin(8πt + (-8πt₀)) .  

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A graph of the line that passes through the points (3, -7) and (-3, 5) is shown in the image attached below. Also, the equation of this line is y = -2x - 1.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, the points on the line include the following:

Substituting the given points into the formula, we have;

Slope, m = (5 - (-7))/(-3 - 3)

Slope, m = (5 + 7)/(-6)

Slope, m = 12/-6

Slope, m = -2

At point (3, -7), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y + 7 = -2(x - 3)

y + 7 = -2x + 6

y = -2x + 6 - 7

y = -2x - 1

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