Solve for the missing side length in this triangle ​

The men’s world record mile run time in 1940 would have been 10.454 seconds

Here, the equation of the linear function that best fits the data (the line of best fit) is Finishing time = 10.878 - 0.0106(Year after 1900)

Let k be the finishing time in seconds and t be the number of years after 1900

So, the equation of regression line becomes,

k = 10.878 - (0.0106) t

To find the the men’s world record mile run time in 1940 first we find the the number of years (t)

t = 1940 - 1900

t = 40 years

So, the finishig time (k) would be,

k = 10.878 - (0.0106) × 40

k = 10.454 seconds

Therefore, the finishing time was 10.454 seconds

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On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

the prime factors of

32 are 2 × 2 x 2 x 2 x 2

64 are - 2 x 2 × 2 x 2 x 2 x 2

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Answer:

354acres

Step-by-step explanation:

Total acre = 59000

Percentage of old oak acre trees is 0.6%

Therefore, the acres of old trees are calculated:

59000 * (0.6÷100) = 354acres

[tex]\cfrac{45p^5q^4-60p^3q^2 - 15p^2q^3}{15p^2 q^3}\implies \cfrac{45p^5q^4}{15p^2 q^3}-\cfrac{60p^3q^2}{15p^2 q^3}-\cfrac{15p^2q^3}{15p^2 q^3}\implies 3p^3q-\cfrac{4p}{q}-1[/tex]

In the given equation x = 9 is the value that satisfies the equation.

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because [tex]3*3 = 9[/tex]. The symbol for square root is "√" and it can also be represented as "sqrt".

In the given equation [tex]x = 9[/tex] is the value that satisfies the equation.

To find the value of x in the equation [tex]3 \sqrt{x} = 9[/tex], we first need to square both sides of the equation to eliminate the square root.

[tex]3 \sqrt{x} = 9[/tex]

Squaring both sides:

[tex](3 \sqrt{x} )^2 = 9^2[/tex]

[tex]x = 9^2 / 3^2 = 9^2 / 9 = 9[/tex]

Therefore, x = 9 is the value that satisfies the equation.

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The provided phrase, x3+4x2+ 7x+ â' 2 has four terms. and coefficient are 1 , 4 ,7 for the expression

What does the phrase mean?

Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.

What kind of phrase would that be?

A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.

The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.

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If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

If p(x) is a polynomial function with p ( 3/4 ) = 0

Then we need to find which of the given statements are true.

A. The function has a factor of (4x + 3).

If x=3/4 then 4(3/4)+3 which is not equal to zero

B. The function has a factor of (4x – 3).

If x=3/4 then 4(3/4)-3 which is equal to zero

C. The function has a factor of (3x + 4).

If x=3/4 then 3(3/4)+4 which is not equal to zero

D. The function has a factor of (3x – 4).

If x=3/4 then 3(3/4)-4 which is not equal to zero

Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

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The proportion equation for c in terms of j is written as c = 0.9j

In order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.

This would tell us the price that one of the bottles of juice is been sold for.

Hence we would have

9.90 / 11

= 0.9

Hence the equation would be: c = 0.9j

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Answer:

1. The answer is 40 degrees

2. Adjacent angles are sometimes congruent.

3. UPR is vertical to TPQ

4. The answer is 132 Degrees

Answer:

Step-by-step explanation:

it B.

just put in the calculator and it gives  you the reduced fraction

Answer:

B. 3/4

Step-by-step explanation:

Find the GCD (or HCF) of the numerator and denominator

GCD of 15 and 20 is 5

Next, divide both the numerator and denominator by the GCD

15 ÷ 5 = 3

20 ÷ 5 = 4

Finally, put them back into a fraction

[tex]\frac{3}{4}[/tex]

Therefore, 15/20 simplified to the lowest terms is 3/4.

Thus, complete scale is: 1 inch = 57.7 miles

This can be solved by the concept of cross-multiplication method.

A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.

Since the international yard was adopted in the 1950s and 1960s, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.

Correct order is:

d. 27 / 1557 = 1/d

e. 27 . d = 1 . 1557

a. 27d = 1557

f. 27d / 27 = 1557 / 27

b. d = 57.7

c. scale: 1 inch = 57.7 miles

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Bacteria are important in the nitrogen cycle because they convert gaseous nitrogen into ammonia.

The nitrogen cycle is a biogeochemical process through which nitrogen is changed into a variety of forms before returning to the atmosphere after first entering the soil and then organisms.

Given:

The cycle's most crucial component is bacteria.

The nitrogen is changed between states by bacteria so it can be utilised.

Different bacteria assist nitrogen change states when it is absorbed by the soil so that it may be absorbed by plants.

Then, the plants provide the nitrogen for the animals.

Hence, Bacteria convert gaseous nitrogen into ammonia.

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On solving the provided question, we can say that - the value of x in triangle ABD is = 60

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here, in triangle ABD

x = 60

as its acute angle

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The number of subscriber is increasing by factor 1,12 every month. The number of subscribers m months since the beginning of the year can expressed by the growth model equation S(m) = 150 . e^(0.12m)

The problem can be solved using exponential growth model.

1) The relation between growth rate and doubling time is given by:

doubling time = 70 / growth rate

In this case, doubling time = 6 months.

Hence,

growth rate = 70/6 = 11.67% = 0.1167 ≈ 0.12

Growth factor is defined as:

Growth factor = 1 + growth rate

                       = 1 + 0.12 = 1,12

2) The growth model of the number of subscribers is given by:

S(m) = So . e^(r.m)

Where:

S(m) = number of subscriber after m months

So= initial number of subscriber

r = growth rate

t = time period

Substitute So = 150 and r = 0.12

S(m) = 150 . e^(0.12m)

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Answer:

Approximately - 9.7%

Step-by-step explanation:

By using the percent change formula, you will be able to calculate the percent decrease.

(b-a)/a times 100 <-- (percent change formula)

(120-133)/133 times 100

-13/133 times 100

-9.7744%

Answer:

  9.8% decrease

Step-by-step explanation:

You want the percent decrease from 133 to 120.

The amount of change as a percent can be found using the formula ...

  percent change = ((new value)/(old value) -1) × 100%

Here, the new value is 120, and the old value was 133. The change is ...

  percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%

  = -0.09774 × 100% ≈ -9.8%

The change from 133 to 120 is a 9.8% decrease.

__

Additional comment

When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)

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Check the picture below.

let's bear in mind that the -(1/3)x has a negative slope, namely going down, so a reflection over the x-axis will yield the same points pretty much, but instead of the IV Quadrant, on the I Quadrant, above, whilst the slope remains the same, it simply turns positive.

A) Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE

B)The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.

To find the speed and direction of the wind, we can use the fact that the ground speed vector (GS) is the sum of the air speed vector (AS) and the wind speed vector (WS).

Given that:

AS = 480 miles per hour at a bearing of N82°E

GS = 518 miles per hour at a bearing of 79°E

We can use the law of cosines to find the wind speed (WS) and the angle between AS and WS.

WS = √(GS² - AS² + 2AS * GS * cos(GS - AS))

WS = √(518² - 480² + 2(480)(518)cos(79 - 82)) = √(268816 - 230400 + 466560cos(-3)) = √(28672) = 168 miles per hour

Then we can use the angle between AS and WS to find the direction of the wind:

Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE

To find the resulting ground speed and direction of the plane if the pilot increased the air speed to 500 miles per hour, we can use the same method as before.

Given that:

AS' = 500 miles per hour at a bearing of N82°E

GS' = √(AS'² + WS² - 2AS'WS * cos(direction of WS - direction of AS'))

GS' = √(500² + 168² - 2(500)(168)cos(80.5 - 82)) = √(250000 + 28672 + 118400cos(1.5)) = √(284872) = 535.5 miles per hour

The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.

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a) Bearing from A to B is 253°.

b) Bearing from B to A is 287°.

What is a bearing?

A bearing is an angle measured clockwise from north in mathematics. Typically, bearings are expressed as a three-figure bearing.

a)

The bearing of 73° and the co-interior angle formed must total 180°. The counter-clockwise angle from B to A is 107°.

However a bearing must always be measured clockwise from north. 107° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 107° from 360°.

360° – 107° = 253° and so, the bearing of A from B is 253°.

b)

The bearing of 107° and the co-interior angle formed must total 180°. The counter-clockwise angle from A to B is 73°.

However a bearing must always be measured clockwise from north. 73° is counter-clockwise from north.

The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.

To work the bearing, subtract 73° from 360°.

360° – 73° = 287° and so, the bearing of B from A is 287°.

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The equation that represents the situation is

2p + 194.99 = 284.97

Option B is the correct answer.

The price of each game is $44.99.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Game system price = $194.99

Total price = $284.97

194.99 + 2 games = $284.97

Games = p

Now,

The price of each game.

194.99 + 2p = 284.97
2p = 284.97 - 194.99

2p = 89.98

p = 44.99

Thus,

The equation is 194.99 + 2p = 284.97.
The price of each game is $44.99.

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As a result, using the values provided, we can turn these data into a bar graph.

A graph is a type of non-linear data structure that consists of nodes, also called vertices, and edges. Any two edges can connect the nodes, which are also known as vertices in a graph. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 5, and 4, 50.

Here,

The gene contributes to the development of pigment.

Yes, factors such as temperature, light cycle, and the presence of mutagens can affect the color of the fur.

In the evolution chart, Mcl provided has ullets that it runs. In mature solutions, the dominating truit moderate is thus always present.

Therefore, using the supplied numbers, we may convert these data into a bar graph.

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The point slope form is not okay to use to find the height of the trees

From the question, we have the following parameters that can be used in our computation:

The point slope form of a linear equation is represented as

y - y₁ = m(x - x₁)

Where

Slope = m

The point slope form does not show the initial value

So, this form is not okay for the required parameters

The slope-intercept form is given as

y = mx + c

Using the given parameters, we have

y = 3/4x + 3

Subtract 3 from both sides

y - 3 = 3/4x

Rewrite as

y - 3 = 3/4(x - 0)

This equation can be rewritten in any of the following forms

Hence, the incorrect equation is y - 15= 3/4(x-15)

We have the slope-intercept form to be

y = 3/4x + 3

Set x = 1 and 2, and then solve for y

So, we have

y = 3/4 * 1 + 3 = 3.75

y = 3/4 * 2 + 3 = 4.5

So, the equivalent equations are

y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)

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A linear system has one solution if the slopes of the equation of lines are different.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

A linear equation is equal to the equation of a line, which has the form:

y = mx +b

where m = slope

If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

Example:

2x + 5y = 34  .. .. (equation 1)

x + 5y = 32  .........(equation 2)

Change the equation 1 and equation 2 into slope-intercept form:

y = (-2/5) x + 34/5   ..... (equation 1a)

y =  (-1/5) x + 32/5   ..... (equation 2a)

The slope of equation is (-2/5) while equation 2 is (-1/5), which is different from equation 1.  Hence, the system of linear equation has one solution.

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Anytime one makes a traffic manoeuvre, such as changing lanes or passing another vehicle, a person put both himself and other drivers on the road in danger.

What are the methods for passing risky situations?

Avoid driving at intersections with railroads, railroad crossings, and entrances to shopping centres.

Only pass to the left if there are two lanes on the road. It is frequently illegal and dangerous to pass on the right. Only when the car in front of you flashes its left turn signal is there an exemption.

When there is a long line of traffic and an oncoming car is right ahead, it is advisable to wait until the incoming vehicle has passed before making a passing motion.

Therefore, it is best to wait until one can see fully ahead because there might be an approaching car right around the bend.

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Answer:

Holy has $85 dollars remaining.

Step-by-step explanation:

(There is no model given in the question, so I'll tell you what the model should be equal to)

If she has $125 to spend, and she spends $35 of that money on gas, she will have $85 left.

$125 - $35 = $85

A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

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In the graph, there is a strong positive relationship between the variables. Option D

We know that the term correlation has to do with how two or more variables are related. The way that the variables are related can be seen from the graph that is shown.

There is a strong positive correlation if we notice that the straight-line of the graph is moving in the positive direction. As we can see from the graph that we have, there is a positive correlation among the variables.

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Answer:

x = 9

Step-by-step explanation:

The equation is y = mx + b

m = The slope

b = y-intercept

The slope here is undefined, and there is no y-intercept, so the equation is

x = 9