Use a coordinate grid to write a coordinate proof of the following statement.
If the vertices of a triangle are A(0,0), B(2 a, b) , and C(4 a, 0) , then the triangle is isosceles.
a. Plot the vertices on a coordinate grid to model the problem.

Angle 213.7°  the bearing of D from towns  A, B, C and D .

What is an angle in math?

The bearing of B from D is angle ADB, which is

∠ADB = arctan(30/45) ≈ 33.7°

The bearing of D from B is that angle plus 180°, so is

180° +33.7° = 213.7°

We use angle ADB because the reference direction for bearings is North.

The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).

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The speed of the wind today is 6 miles per hour.

We know that speed = distance / time        .........(1)

You ride your bike to a store, 4 mi away, to pick up things for dinner.

Here, distance = 4 miles

When there is no wind, you ride at 10 mi/h.

So, using above formula (1),

⇒ 10 = 4 / t

⇒ t = 10/4

⇒ t = 2.5 hours

This means,  it takes 2.5 hours for you to get to the store on a day without wind.

Today your trip to the store and back took 1 hour.

We need to find the speed of the wind.

Let 's' be the speed of the wind.

So using above formula (1),

⇒ (10 - s) = 4 / 1

⇒ 10 - s = 4

⇒ s = 6 mi/h

Therefore, the speed of the wind today is 6 miles per hour.

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The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Then the expression will be given as

⇒ 470(32 - n)

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

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Answer:

$6.95

Step-by-step explanation:

Kole: $ 6.50

His sister : $6.50+$0.40

= $6.90

Half of his sister: $6.90/2 =$3.45

$10-($6.50 +$3.45)

=$10-$3.05

=$6.95

The spinner's point has a 11.11% chance of landing on red.

A pie chart is a type of chart which displays data as a circular graph.

We comprehend that the pie's total value is always 100%. It is also assumed that a circle has a circumference of 360°. As a result, the sum of all pieces of data equals 360°. Based on these, there appear to be primarily two pie chart formulas:

Now, the stated data of the pie chart are-

When a circle is wholly rotated, the center forms a 360-degree angle.

A complete rotation at the central point of the circle yields 360 degrees.

The total color percentage is 100%.

Divide a red value by 3.6 because 360 ° / 100% = 3.6.

The spinner's pointer displays an overall percentage of red of 40%.

P = 40/3.6 (probability of each pointer landing on red).

P = 11.111.. = 11.11 (pointer landing on red) (approx.)

As an outcome, the pointer has a 11.11% chance of landing on the red.

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Step-by-step explanation:

2x=1.2-0.8

2x=0.4

x=0.4/2=0.2

Answer:

C,D, and E

Step-by-step explanation:

-29/4 is an improper fraction version of -7 1/4

-7- 1/4 = -7 1/4

-(7 + 1/4) is -29/4

Just make -29/4 into a mixed number, which is -7 1/4

Answer:

Step-by-step explanation: the answer is the last 3 ones because if you add them together, you get -7 1/4.  Remember that -(number) = -1(number). So, -(1) = -1(1).

45 because it's 45 and I'm smart with a PhD in maths

The point slope form finds the equation of a straight line that passes through a given point and is inclined to the x-axis. Each point on a line must satisfy the line's equation. Two-variable linear equations symbolize lines. The point slope formula is utilized when we know the line's slope and a point. The next section explains the point slope form and how to calculate its formula.

The equation of a straight line that is inclined at a particular angle to the x-axis and passes at a given point may be found by using the point slope form. This form is used to get the equation of the line. An equation may be said to be the equation of a line if it can be shown to be fulfilled by every point along the line. This indicates that a line is represented by a linear equation that has two variables. Whereas the Point slope formula is only used in situations in which both the slope of the line and a point on the line are known. In the next part, let's get more in-depth knowledge about the point slope form as well as how to derive the formula that is used to express the point slope form.

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Given statement is False and the True statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.'

The correct answer is an option (B)

In this question, we have been given a statement 'In a frequency​ distribution, the class width is the distance between the lower and upper limits of a class.'

We need to determine whether the given statement is True or False.

We know that, the class width is the distance between the lower limits of consecutive classes.

So, the given statement is False.

The correct statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes. '

Therefore, given statement is False and the True statement is 'In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.'

The correct answer is an option (B)

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Answer:

last one is the correct one

Mark please

The geometric mean between pair of numbers 4√3 and 10√3 is 10.95

We know that for a sequence of numbers x1, x2, . . . , xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 4√3 and 10√3

We need to find the geometric mean between pair of numbers, 4√3 and 10√3.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{4\sqrt{3}\times 10\sqrt{3} } \\\\\Pi=\sqrt{4\times 10 \times \sqrt{3}\times \sqrt{3} } \\\\\Pi=\sqrt{40 \times 3 } \\\\\Pi=\sqrt{120}\\\\ \Pi=2\sqrt{30}\\\\\Pi=10.95[/tex]

Therefore, the geometric mean between pair of numbers 4√3 and 10√3 is 10.95

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Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

[tex]\frac{14}{2}[/tex] [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

neverminding the amount of $3000, we know the compound interest is 1.1%, we also know that the compounding period is daily, so hmmm let's assume there are 365days in a year, so

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1~\hfill \begin{cases} r=rate\to 1.1\%\to \frac{1.1}{100}\dotfill &0.011\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, so let's assume 365} \end{array}\dotfill &365 \end{cases} \\\\\\ \left(1+\frac{0.011}{365}\right)^{365}-1 ~~ \approx ~~ 0.01106055 ~~ \approx ~~ 1.106055\% ~~ \approx 1.11\%[/tex]

Answer:

6?

Step-by-step explanation:

24=10x-6x

24=4x

6=x

When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. The height of Kara's building is 186.6 ft.

In math, height can be defined as the vertical distance from the top to the base of the object. Height is the distance between an object's highest and lowest points.

The measurement of an object's height from the base to the top is known as the height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Mount Everest's summit serves as an illustration of height.

Ignoring the height of Kara,

h = 50 tan 75°

substituting the value of tan 75°, we get

= 50 × 3.7321

Height of building = 186.6 ft.

Therefore, the approximate height of Kara's building is 186.6 ft.

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=====================================================

Explanation:

Multiply the given values. This is because,

total mass = (number of paperclips)*(mass per paperclip)

So,

(5.0 x 10^−4)(6.85 x 10^4)

(5.0 * 6.85) x (10^−4 * 10^4)

34.25 x 10^(-4+4)

34.25 x 10^0

(3.425 x 10^1) x 10^0

3.425 x 10^(1+0)

3.425 x 10^1

3.4 x 10^1

We round the first value to 2 sig figs because it is the smaller sig fig count of 5.0 and 6.85; the 0 in 5.0 is significant.

Notice how I rewrote 34.25 into 3.425 x 10^1. I did this to get the number in the form a x 10^b, where [tex]0 \le a < 10[/tex], which fits scientific notation form.

The value 3.4 x 10^1 simplifies to 34. So an estimate of the total mass is about 34 mg. But we'll stick with scientific notation since your teacher instructed it.

Answer:

I would say y=3x+6

Step-by-step explanation:

Answer: 1 ) other angle = 32.0°

2 ) A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Step-by-step explanation for first picture:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

x + 58° = 90°

x = 90° - 58°

x = 32.0°

Step-by-step explanation for second picture:

( number on x line, number on y line )

A = ( 2, -2 )

B = ( -2, 5 )

C = ( -4, 2 )

reflection

A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Answer : second option

The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.

According to the statement

We have to find that the Numeric value.

So, For this purpose, we know that the

The Number value is the value refers to the worth of each digit depending on where it lies in the number.

From the given information:

The given value is a -2½.

And we have to find that the in which option the given value in the question is placed.

For example, if the value in the given question is a 1 then the in which option we have given value is 1.

Then

according to the statement,

In option B the value is similar to the those value which is given in the question.

So, The numeric value of the question is present in the in the option B. Thus, Option B is a correct option.

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Answer: 5, 7, 13, 15, 18

Step-by-step explanation:

To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.

Let's factor x2−5x+6

x2−5x+6

The middle number is -5, and the last number is 6.

Factoring means we want something like

(x+_) (x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -5

Multiply together to get 6

Can you think of the two numbers?

Try -2 and -3:

-2+-3 = -5

-2*-3 = 6

Fill in the blanks in

(x+_) (x+_)

with -2 and -3 to get...

(x-2) (x-3)

Since you cannot divide by 0, the discontinuities at these points exist as a vertical asymptote. Therefore, the vertical asymptote exists at x= two and x= 3.

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If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

Given:

0.145t² + 0.019t + 5.5 = 0

Using almighty formula or quadratic formula

t=-b±√b²-4ac/2a

Where:

b²=19²

a=145

c=5500

Let plug in the formula

t=-19±√19²- 4(-145) (5500)/2(-145)

t=-19±√361+(3,190,000)/-290

t=-19±√3,190,361/-290

t=-19±1,786.158/-290

Hence,

-19-1,786.158/-290; -19+1,786.158/-290

t=6.2; 6.09

Therefore If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

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The number 6 comma 107 comma 200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex].

Scientific notation is used to represent a very large number or a very small number in Simple way.

Steps to find scientific Notation of a number

Step (i) Move the decimal point until a number between 1 and 10 is created.

Step (ii) Count the number of times the decimal is moved .

Step (iii) If the decimal is moved n times then multiply the term by n times of 10.

In the given question

the number 6107200.

Step (i) We will move the decimal 6 place towards left.

number becomes 6.107200

Step (ii) The decimal is moved 6 place towards left.

Step (iii) we will multiply by [tex]10^{6}[/tex].

[tex]=6.1072*1000000[/tex]

So , the number becomes [tex]6.1072*10^{6}[/tex]

Therefore , the number 6107200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex]

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The line's equation is y=3x-4.

What is Equation of line?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation where the slope of line is m and b is the y- intercept. The slope is defined as

m = (y-y1)/(x-x1)

Given:

For two lines to be perpendicular to each other, they must have slopes that are negative reciprocals of each other (i.e. the negative reciprocal of n is -1/n). The slope of the given line is –1/3 which means the slope of a line perpendicular to it would be 3.

From the given slope equation of the line

y=3x+b,

where b is the y-intercept. Since we know the line passes through the point (2,2).

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

y-2 = 3*(x-2)

y=3x-6+2

y=3x-4

The value of b = -4

Therefore, the equation of the second line is y=3x-4.

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