A baseball Dimond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?

At hour 9, the temperature recorded was = 75 degrees

At hour 13, the temperature recorded was = 95 degrees

The rate of change = Change in the temperature / Change in the time

⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour

⇒ The rate of change = 20 degrees / 4 hours

⇒ The rate of change = 5 degrees per hour

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The Equation of perpendicular bisector line l is found to be [tex]y = 2x+ 11[/tex]

Given Line XY is formed by points  X(-9, -7) and Y(-3,5) therefore, it passes through these two respective points.

Let the slope of this line be n

The Slope of line passing through X and Y points is given by

n = [tex](y_{2} - y_{1} )/(x_{2} -x_{1} )[/tex]

⇒ n = {5 - (-7) }/ {(-3) - |(-9)}

⇒ n = 12/6

⇒ n = 2               (equation 1 )

Given that line l is perpendicular bisector of XY

Let the slope of l  = m

We know that the product of the slopes of any two perpendicular lines is -1

Therefore, n x m = -1

⇒ m = -1 \ n

putting the value of n from the above equation 1 we get

⇒ m = - 1/2

Additionally, because l is the perpendicular bisector hence it goes through the mid point of the line XY

Mid point of two lines = [tex](x_{2} + x_{1} )/2[/tex] and [tex](y_{2} + y_{1} )/2[/tex]

Mid point of XY = [tex]\frac{-9 + (-3)}{2}[/tex] and [tex]\frac{-7 + (5)}{2}[/tex]

                          = (-6, -1)

The equation of perpendicular bisector l is given my the following formula:

[tex]y = nx + c[/tex]

here we have n = slope of line

we have n = 2 from equation 1

∴ y = 2x + c (equation 2)

Also equation (2) is satisfied by the point (-6,-1)

Hence we can express it as:

-1 = 2(-6) + c

⇒ c = 11

Therefore the required equation of perpendicular bisector l is

[tex]y = 2x + 11[/tex]

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The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.

Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.

Similar Triangles Definition

Angle - Angle (AA)

Side - Angle - Side (SAS)

Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.

If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:

LEFT: y and 35 as the legs and unknown hypotenuse.

RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.

The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.

Since these two are seen as similar triangles,

y/35 = 6/7.9

⇒y = 26.58

⇒ y ≈ 27 ft

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If a trader is given a 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, then

(I) The discount amount will be ¢6750000

(II) The final amount that the trader will have to pay to buy the goods will be ¢38250000.  

As per the question statement, a trader is given 15 Percent discount on goods bought from a factory and the original price of the item bought from the factory is ¢45000000.

We are required to calculate the discount amount, and the final amount that the trader will have to pay to buy the goods.

To solve this question, we simply need to calculate 15 percent of 45000000, and then subtract the calculated discount amount from ¢45000000.

Therefore, 15 percent of ¢45000000 = ¢[(15/100) * 45000000]

                                                   = ¢(15 * 450000)

                                                   = ¢6750000

That is, on 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, the discount amount is ¢6750000.

And, considering the discount of ¢6750000 on the factory price of ¢45000000, the final amount that the trader will have to pay to buy the goods = ¢(45000000 - 6750000)

           = ¢38250000.

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Answer:

you can ask questions for clarification

The equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph:

The two points are:

(0, -3) and (1, -5)

The equation of the line:

y - (-5) = [-5 - (-3)]/[1] (x - 1)

y + 5 = -2(x - 1)

y = -2x -3

Thus, the equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).

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Answer:

Here is your Answer and I'm from South Africa

If we look at the series, one third of the current term gives the numerical value of the next term.

If we need to express it algebraically, we can write the following equation.

Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.

In geometric sequences, any term can be written in terms of the first term. Below is an example.

Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.

Answer:

m/4 = 3x - 30

Step-by-step explanation:

Hello!

Let's subtract the second equation from the first equation:

Now, solve for m.

Multiply both sides by 12 to get rid of the denominators

Plug in 12x - 120 for m in m/4

The value of m/4 is 3x - 30.

Answer: 21

Step-by-step explanation:

Answer:

$4,000 in the 10% per year account

$11,000 in the 12% per year account

The value of b for the given line is 1

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.

Given that : y = 3x + b; (2, 7)

y =3x + b

7 = 6 + b

1 = b

The value of b for the given line is 1

The line's equation is a linear equation of degree one.

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Reason:

The equation is in y = mx+b form where

m = 20 = slope

b = 0 = y intercept

The slope is the rate of change. It tells us how fast y increases.

slope = rise/run = 20 = 20/1

rise = 20 = increase the earnings by 20 dollars

run = 1 = each time the number of hours go up by 1

The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.

In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.

Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.

Lets use the numbers given

12 x 1 = 12        15 x 1 = 15

12 x 2 = 24       15 x 2 = 30

12 x 3 = 36       15 x 3 = 45

12 x 4 = 48       15 x 4 = 60

12 x 5 = 60

Based on this, the least common multiple is 60

6 x 1 = 6          15 x 1 = 15

6 x 2 = 12       15 x 2 = 30

6 x 3= 18

6 x 4 =24

6 x 5 =30

Based on this, the least common multiple is 30

9 x 1 = 9           15 x 1 = 15

9 x 2 = 18         15 x 2 = 30

9 x 3= 27         15 x 3 = 45

9 x 4 =36

9 x 5 =45

Based on this, the least common multiple is 45

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Answer:

a -7

b 18

c -13

d -5

e 0

f -7

g 0

h -6

Step-by-step explanation:

too lazyy

If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

What is dividend, divisor and quotient?

The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.

Let x be the quotient after dividing 782 by 1523.

[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]

Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

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Answer:

y = 15/4 mm

x = 36/5 mm

Step-by-step explanation:

In similarity triangles, the corresponding sides are in same ratio.

          [tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]

                               [tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]

The answer to this question represents the possible choices that we have when solving a division.

When solving this division operation, and we use technology, we get the following result:

Then, we can conclude that:

We can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.

In this case, we can see the integer part of the answer, 20, and a fraction:

And we know that:

the parameters we are estimating using the OLS method must be themselves linear

What are the Gauss Markov assumptions?

Gauss Markov Assumptions

Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.

What are the properties of Gauss Markov Theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

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The teacher requires 1.5 gallons of paint for the whole class

Quantity of paint available with the teacher = 1 gallon

Fractions: In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Portion of the class covered by 1 gallon of paint = 2/3 class

Let x represent the whole class

Formulating the equation:

The portion of the class covered out of the whole class*Total class = Paint required for the portion of the class

So, for 2/3x = 1

x = 3/2

x = 1.5 gallon

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To calculate the total number of miles the delivery truck drove, we add the lengths of the three routes together.

-> It drove 123 + 10 + 15 = 148 (miles).

Answer:

p=2+1.1m

Step-by-step explanation:

p=price, m=miles

Let the age of Maisie be x

From the first statement, Ellie is six years older than Maisie implying:

From the second statement, Zoe is twice as old as Eli implying:

From the last statement, the sum of their ages is 50 implying:

Solving for x:

We open the bracket and collect like terms

Hence, Zoe's age is:

Answer:

Zoe's age = 28

Answer:13x9x6=702

Step-by-step explanation:

Answer:-2

Step-by-step explanation: Substitute the given y-value into 4x−3y=18 and solve for x

Answer:

both angles 1 and 2 measure 135°

Step-by-step explanation:

angle 1 = angle 2 = 135°

Hope this helps

The fraction is 47/200. The decimal is 0.235.

A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.

For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.

For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.

So here the given percentage is 23.5%.

The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.

Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.

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Answer:

g(8)=17

Step-by-step explanation:

Given :
g(a)=a²+2a-63

Substitute a = 8 :

g(8)=8^2+2(8)-63

= 64+16-63

=17