The table shows the race time for Jon, who competed in three different youth triathlons.

A 4-column table with 4 rows titled Jon's Youth triathlon results. Column 1 is labeled Month with entries May, June, August. Column 2 is labeled Swim times (minutes) with entries 10.06, 9.5, 8.25. Column 3 is labeled Bike times (minutes) With entries 15.05, 13.0, 12.75. Column 4 is labeled Run times (minutes) with entries 24.25, 23.7, 22.01.

What is Jon’s total time for the June triathlon?

9 . 5
1 3 . 0
+ 2 3 . 7

for the first one x = 12

second one is 2

Answer:

x = 12

x = 2

Step-by-step explanation:

Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.

The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.

The circumcenter, centroid, and orthocenter are all collinear.

The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1

i.e, CSOC = 21.

Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.

The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.

Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.

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It is not a function. which is the correct answer would be option (B)

Given that,

A function is shown in the figure with its domain and range.

To determine the inverse function.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

Since the two preimages of the value 5 are present in the domain

So that is why the inverse function of a given function is not possible.

Therefore, It is not a function.

Hence, the correct answer would be option (B)

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 The rationalized expression in general term is given by: (-8 -4√2) / 3

  Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

  As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

(8√2 / 6-3√8 ) Multiply by  ( 6+3√8)/( 6+3√8)

(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)

8√2(6+3√8) / (6-3√8)²  Expand the denominator using the FOIL method.

8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)

8√2(6+3√8) / -36

48√2 + 24√2√8 / -36  ::::.   √8 = 2√2

48√2 + 96 / -36

-12(4√2 + 8) / 12x3

(-8 -4√2) / 3 is the result.

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The equation of the line in standard form of 2y = -4x - 12 is 4x + 2y = -12.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.

Given the equation 2y = -4x - 12, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

2y = -4x - 12

4x + 2y = -12

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A Figure ABCD is a rhombus. The angles of A and C are equal by alterenate interior angle. The value of x in the figure ABCD rhombus is 9 degree.

We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.

The Solution to an equation is finding values of the variable in the considered equation for which the equation considered evaluates to be true.

For a solution, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, thus solution to a system is the intersection of all its equation at single point

WE know that the diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.

Since the side lengths of a rhombus are equal, so the angles of A and C are equal by alterenate interior angle.

Now, 5x-8 = 3x + 10

i.e. 5x - 3x = 10 + 8

i.e. 2x = 18

i.e. x = 9

Therefore the value of x in the figure ABCD is 9 degree.

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rob has 8 dimes and 17 nickels in $1.65

There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.

Let n represent nickels & d dimes

given: n + d = 25 #1 (number of coins)

given: .05n + .10d = 1.65 #2 (amount in dollars)

n = 25 - d #3 (rewrite of #1)

.05(25 -d) + .10d = 1.65 (substitute #3 in #2)

1.25 - .05d + .10d = 1.65 (multiply out the left side)

.05d = .40 (collection of like terms)

d = 8 (divided both sides by.05)

n + 8 = 25 (substitute answer for d in #1)

n = 17 (subtract both sides by 8)

There are 8 dimes and 17 nickels.

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Answer:

for real even great Britain cant get this because ya

Step-by-step explanation:

Answer:

Lucia is 12 years old now

The sum of the finite series  [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]  is 20

Given a finite series:

[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]

Recall the properties of summation notation:

Σₙ b. f(n) = b Σₙ f(n) where b is a constant.

Σ (a + b) = Σ a +  Σ b

[tex]\sum\limits^p_{n=1} {b} =b.p[/tex]  where b is a constant

Using the above summation properties, we can write:

[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]

=7 . 8 - (1+2+3+ ...+8)

= 56 - 8/2 (1+8)

= 56 - 4 . 9

= 56 - 36 = 20

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months}\dotfill &10 \end{cases} \\\\\\ A=50\left(1+\frac{0.03}{1}\right)^{1\cdot 10} \implies A=50(1.03)^{10}\implies A \approx \text{\LARGE 67.20}[/tex]

well, let's check how long till you'd have $100 first

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months} \end{cases}[/tex]

[tex]100=50\left(1+\frac{0.03}{1}\right)^{1\cdot t} \implies 100=50(1.03)^t\implies \cfrac{100}{50}=1.03^t \\\\\\ 2=1.03^t\implies \log(2)=\log(1.03^t)\implies \log(2)=t\log(1.03) \\\\\\ \stackrel{\textit{about 23 months and 13 days}}{\cfrac{\log(2)}{\log(1.03)}=t\implies \text{\LARGE 23.45}\approx t}[/tex]

Answer:

x= -3

Step-by-step explanation:

[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]

Answer:

[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]

Step-by-step explanation:

Given absolute value equation:

[tex]2|2x+3|=|x-3|[/tex]

The absolute value of a number is its positive numerical value.

Therefore, the expressions inside the bars should be set to both positive and negative.  Rewrite the absolute value equation as four equations without absolute value bars and simplify:

[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]

[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]

[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]

From inspection of the equations:

so there are only two unique equations to be solved.

Equation 1

[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]

Therefore, the solutions are:

[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]

The following volume quantities are listed below:

a) 2 pints, 1 qt

b) 12 pints, 6 qt

c) 5 pints, 2.5 c

d) 6.75 pints, 3.375 fl oz

In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.

Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:

Now we proceed to convert each quantity to pints and quarts by cross multiplication:

a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt

b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt

c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c

d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz

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Answer:

630 rock cards

Step-by-step explanation:

aight so 40 % of 1400 is 560 , and 15% of 1400 is 210 . add those and you get 770 . so you got 770 water and rare . you subtract that by 1400 and you got 630 !!

Answer: 476 rock type pokemon cards

Step-by-step explanation: Let's do this! 40% of 1400 is 560, and 15% of 560 is 84. 560 - 84 = 476.

Answer:

3/7.

Step-by-step explanation:

1/3 / 7/9

Invert the 7/9 and multipliply:

= 1/3 * 9/7

= 9 / 21

= 3/7

Answer: 7+8y

Step-by-step explanation:

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

The formula for estimating the nth term of an arithmetic sequence is:

a n = a₁ + (n-1)d

The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7

A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.

A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.

The formula for estimating the nth term of an arithmetic sequence exists:

a n = a₁ + (n-1)d

The four quantities in the formula exist a n, a₁, n, d.

The first 5 terms are a n = -2n + 3

a₁ = -2 + 3 = 1

a2 = -4 + 3 = -1

a3 = -6 + 3 = -3

a4 = -8 + 3 = -5

a5 = -10+3 = -7

Therefore, the first 5 terms of the sequence  be 1, -1, -3, -5, -7.

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The example that illustrates public scientific communication is D. a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.

Communication simply had to do with how messages are passed from the sender to the audience or the other party.

In this case, the example that illustrates public scientific communication is a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.

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Answer:

It will take 22 hours

Step-by-step explanation:

10925 ÷ 500 = 21.9 = 22 hours

The equation written in standard form is expressed as 3x - y = -11

The standard form of a linear equation is expressed as Ax + By = C

Given the equation below;

y - 8 = 3(x+1)

Expand

y- 8 = 3x + 3

Collect the like terms

y-3x = 3 + 8

y - 3x = 11

-3x + y = 11

3x - y = -11

Hence the equation written in standard form is expressed as 3x - y = -11

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Answer:

Thus the value of the car decreases by $2,750 every year.... Making it $19,250 in the first year and $16,500 in the second

Step-by-step explanation:

12.5/100×22,000

2750

Answer:

Associative.

Step-by-step explanation:

The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.

e.g

[tex](a - b) \times c = c \times (b-a)[/tex]

Answer:

35, the population size is 2.

Answer: $7 per book

Step-by-step explanation:

$77 for 11 books, so we do 77 ÷ 11 = 7

Answer:

0.744-0.741-0.7412-0.7041-0.70411

Step-by-step explanation:

Answer:

Step-by-step explanation:

Decending order- From greatest to least

To order them start with the dight with the highest number in the place that isn't equal. In this case it the 4 in the hundredths place so are top 3 numbers are 0.741, 0.7412, and 0.744. As this point you continue to look at the greatest number when the dights aren't equal so the top three would be ordered 0.744,0.7412

0.744,0.7412, and 0.741. As for the bottom 2 numbers you do the same thing with the top three numbers so the rest of the list is 0.70411 and 0.7041

The maximum​ displacement, the​ frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.

A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

Therefore, the instantaneous speed is different from velocity, which is the rate at which the distance traveled along a particular path changes over time. The temporal rate of change of the position vector can also be used to describe velocity.

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Answer: n=-7

Step-by-step explanation:

5n - 7n = 14

(5-7)n=14

-2n=14

-2n/(-2)=14/(-2)

n=14/(-2)

n=-7

The equation is,

→ 5n - 7n = 14

Solving for the value of n,

→ 5n - 7n = 14

→ -2n = 14

→ n = -(14//2)

→ [ n = -7 ]

Thus, the value of n is -7.