Triangle ABC is a right triangle on the coordinate system and its vertices are (−2, 5),
(−2, 1), and (1, 1). What is the area of triangle ABC?

The equation of the line is y = (3/2)x - 1/2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).

Now,

The equation of a line.

y = mx + c

The line passes through points (3, 4) and (5, 7).

m = (7 - 4) / (5 - 3)

m = 3/2

Slope = 3/2 _____(1)

Now,

(3, 4) = (x, y)

4 = 3/2 x 3 + c

4 = 9/2 + c

c = 4 - 9/2

c = (8 - 9) / 2

c = -1/2

y-intercept = -1/2 ____(2)

Now,

y = mx + c

From (1) and (2),

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

Thus,

The equation of the line is y = (3/2)x - 1/2.

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The complete question.

Find the equation of a line that [passes through the point (2, 4), and (5, 7).

Answer:

10-16i

Step-by-step explanation:

use distrubutive property and treat i like a variable

Answer:

y > 0

Step-by-step explanation:

\(y = e^{4x}\)

This is an exponential function;

Consider as x → ∞, y → ∞;

If x = 0. y = e⁰ = 1;

As x → -∞, y → 0;

y ranges from 0 to ∞ therefore, i.e. y > 0

Answer:

Step-by-step explanation:

Simplifying square roots

Example

Let's simplify \sqrt{75}

75

​

square root of, 75, end square root by removing all perfect squares from inside the square root.

We start by factoring 757575, looking for a perfect square:

75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5

2

×375, equals, 5, times, 5, times, 3, equals, start color #11accd, 5, squared, end color #11accd, times, 3.

We found one! This allows us to simplify the radical:

\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} \\\\ &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} \\\\ &=5\cdot \sqrt{3} \end{aligned}

75

​

​

=

5

2

⋅3

​

=

5

2

​

⋅

3

​

=5⋅

3

​

​

So \sqrt{75}=5\sqrt{3}

75

​

=5

3

​

square root of, 75, end square root, equals, 5, square root of, 3, end square root.

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Practice

PROBLEM 1.1

Simplify.

Remove all perfect squares from inside the square root.

{\sqrt[]{12}}=

12

​

=root, start index, end index, equals

Explain

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Simplifying square roots with variables

Example

Let's simplify \sqrt{54x^7}

54x

7

​

square root of, 54, x, start superscript, 7, end superscript, end square root by removing all perfect squares from inside the square root.

First, we factor 545454:

54=3\cdot 3\cdot 3\cdot 2=3^2\cdot 654=3⋅3⋅3⋅2=3

2

⋅654, equals, 3, dot, 3, dot, 3, dot, 2, equals, 3, squared, dot, 6

Then, we find the greatest perfect square in x^7x

7

x, start superscript, 7, end superscript:

x^7=\left(x^3\right)^2\cdot xx

7

=(x

3

)

2

⋅xx, start superscript, 7, end superscript, equals, left parenthesis, x, cubed, right parenthesis, squared, dot, x

And now we can simplify:

\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\cdot 6\cdot\left(x^3\right)^2\cdot x} \\\\ &=\sqrt{3^2}\cdot \sqrt6 \cdot\sqrt{\left(x^3\right)^2}\cdot \sqrt x \\\\ &=3\cdot\sqrt6\cdot x^3\cdot\sqrt x \\\\ &=3x^3\sqrt{6x} \end{aligned}

54x

7

​

​

=

3

2

⋅6⋅(x

3

)

2

⋅x

​

=

3

2

​

⋅

6

​

⋅

(x

3

)

2

​

⋅

x

​

=3⋅

6

​

⋅x

3

⋅

x

​

=3x

3

6x

​

​

Practice

PROBLEM 2.1

Simplify.

Remove all perfect squares from inside the square root.

\sqrt{20x^8}=

20x

8

​

=square root of, 20, x, start superscript, 8, end superscript, end square root, equals

Explain

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More challenging square root expressions

PROBLEM 3.1

Simplify.

Combine like terms and remove all perfect squares from inside the square roots.

2\sqrt{7x}\cdot 3\sqrt{14x^2}=2

7x

​

⋅3

14x

2

​

=2, square root of, 7, x, end square root, dot, 3, square root of, 14, x, squared, end square root, equals

Explain

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Since the equation is a true one, then it is an identity.

It should be noted that the information given is represented as 9(a−4)+3(2a+5)=7(3a−4)−6a+7.

After using the distributive law, the value that will be gotten will be:

15a - 21 = 15a - 21.

Therefore since the equation is a true one, then it is an identity.

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Answer:

9

Step-by-step explanation:

9x8=72 72+18=90

The value of y is π/9 or 7π/9 for the range 0 ≤ y ≤ π.

cosec 3y /( cot 3y + tan 3y) = 0.5

Trigonometry formula is:

cosec Ф = 1/ sin Ф

cot Ф = cos Ф/ sinФ

tan Ф = sinФ/ cos Ф

\(\frac{\frac{1}{sin 3y} }{\frac{cos 3y}{sin 3y} +\frac{sin 3y}{cos 3y} }\)  = 0.5

\(\frac{\frac{1}{sin 3y} }{\frac{cos 3y^{2} + sin 3y^{2} }{sin 3y cos 3y} }\) = 0.5

sin² 3y + cos ² 3y = 1

1/ sin 3y × sin 3y cos 3y = 0.5

cos 3y = 0.5 = 1/2

cos π/ 3 = 1/2

For 0≤ y ≤π

0 ≤3y ≤ 3π

So 3y = 2kπ + π/3 , k = 0, 1

y = π/ 9 or 7π/ 9

Therefore the value of y is π/9 and 7π/ 9 for the given range.

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The value of Z in the similar triangles is 6

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

The triangle

Using the corresponding sides of similar triangles, we have

z/12 = (14 - z)/16

Cross multiply the equation

This gives

16z = 168 - 14z

So, we have

30z = 168

Divide

z = 5.6

Approximate

z = 6

Hence, the value of Z is 6

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Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

10 + 10 = 21

dont ask howwwwww

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

x = -8 and y = 3

Step-by-step explanation:

Solve the system of equations by substitution:

x + y = 6

y = 5x

Substitute the value of y from the second equation into the first equation:

x + (5x) = 6

6x = 6

x = 1

Now, substitute the value of x into the second equation to find y:

y = 5(1)

y = 5

So, the solution to the system of equations is x = 1 and y = 5.

Solve the system using substitution:

y = -6x + 36

6y - x + 6 = 0

Substitute the value of y from the first equation into the second equation:

6(-6x + 36) - x + 6 = 0

-36x + 216 - x + 6 = 0

-37x + 222 = 0

-37x = -222

x = 6

Now, substitute the value of x into the first equation to find y:

y = -6(6) + 36

y = -36 + 36

y = 0

So, the solution to the system of equations is x = 6 and y = 0.

Solve by the substitution method:

5x + 9y = -13

-6x + y = 51

Rearrange the second equation to isolate y:

y = 6x + 51

Substitute the value of y from the second equation into the first equation:

5x + 9(6x + 51) = -13

5x + 54x + 459 = -13

59x + 459 = -13

59x = -472

x = -8

Now, substitute the value of x into the second equation to find y:

y = 6(-8) + 51

y = -48 + 51

y = 3

So, the solution to the system of equations is x = -8 and y = 3.

Answer:

1) x=1, y=5
2) x=6, y=0

3) x = -8, y = 99

Step-by-step explanation:

1)
x + 5x = 6

6x = 6

x = 1

y = 5

2)

y = -6x + 36

6y - x + 6 = 0

6(-6x + 36) - x + 6 = 0

-37x + 222 = 0

x = 6

y = 0

3)

5x + 9y = -13

-6x + y = 51

y = 6x + 51

5x + 9(6x + 51) = -13

59x + 459 = -13

x = -8

y = 99

Answer: C. At the α=0.05 significance level, they should conclude that more than 50% of adults support the tax increase.

Step-by-step explanation:

Given: Null hypothesis: \(H_0:p=0.5\)

Alternative hypothesis: \(H_a: p>0.5\)

p-value = 0.033

If the p-value is greater than alpha (p > . 05), then we fail to reject the null hypothesis.

If α=0.01 , then p-value > α i.e. we fail to reject the null hypothesis.

Conclusion: Exactly 50% of adults support the tax increase.

If α=0.05 then p-value < α i.e. we reject the null hypothesis.

Conclusion: more than 50% of adults support the tax increase.

Thus, Correct option: C .

Answer: At the a = 0.05 significance level, they should conclude that more than 50% of adults support the tax increase.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

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Complete question -

Seven times a number in algebraic expression

Answer:

5 4/9

Step-by-step explanation:

Answer:

Exact Form:

49 /9

Decimal Form:

5. 4   repeating

Mixed Number Form:

5  4 /9

Step-by-step explanation:

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

Answer:

b=−1

Step-by-step explanation:

Answer:

7/11 or

7

--

11

Step-by-step explanation:

Hope this helps :)

Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

Hope this helps :)

Pls brainliest...

Answer:

180 miles

Step-by-step explanation:

You must find 40% of 450 and you can make the of into an x (multiplication symbol) like so:

40% x 450

Now, percent's are fractions, and 100% is equal to one whole or 1. To make 40% a fraction, simply just place a decimal in front of the 4, like so:

.40 or 0.40 or 0.4 or .4

Now place that in the equation:

0.40 x 450

Solve:

 450.00

x     0.40

___________

  180.00

       ^

(!Important! !Always bring down the decimal in the exact place it was at in first place!)

Check:

180 = 40%

450 = 100%

(To get 450 you must multiply 100 by 4.5, therefore you multiply 40 by 4.5 to get 180)

Answer:

Michael ran 180 miles in bad weather.

Answer:

\(5 { \times 54}^{2} \)

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

tăng lên 5.000 nghìn đồng

Step-by-step explanation:

mỗi chuyến bay có 0.5% hành khách mất hành lí

mỗi người đòi bồi thường 1.000.000 đồng

do đó vẽ mỗi người tăng lên :0.5%×1.000.000=5.000

The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

b because 90

                  15

                  15

               -_____

                  76.50

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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