The point stope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1 = (x-12). What is
the standard form of the equation for this line?

Answer:

15/100*1800=15*1800/100=15*18=270

Step-by-step explanation:

1800-270=1530 therefore answer is 1530

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].

In this question we need to find the exact values of three trigonometric functions associated with the terminal side of an angle. The following definitions are used:

Sine

[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]     (1)

Secant

[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]     (2)

Tangent

[tex]\tan \theta = \frac{y}{x}[/tex]     (3)

If we know that x = - 7 and y = 2, then the exact values of the three trigonometric functions:

Sine

[tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex]

Secant

[tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex]

Tangent

[tex]\tan \theta = -\frac{2}{7}[/tex]

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].

The statement reports typing errors, correct form is shown below:

Let (x, y) = (- 7, 2) be a point on the terminal side of θ. Find the exact value of sin θ, sec θ and tan θ.

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Answer:

John is 19 and his sister is 23.

Step-by-step explanation:

See attached image.

All the parts shown in the figure are solved.

A mathematical technique that is used to determine the possible arrangement of the objects when the sequence of selection does not matter.

Part 1

(a) When two dices are rolled the basic outcomes will be =?

Each dice has 6 outcomes and therefore 6* 6 =36

Therefore total 36 basic outcomes.

(b) Yes both the events are equally likely .

Part 2

(a) There can be 11 types of sum from 2 -12 obtained when two dices are rolled

Sum

2 1+1                                                  

3 1+2, 2+1                                          

4 1+3, 2+2, 3+1                                  

5 1+4, 2+3, 3+2, 4+1                            

6 1+5, 2+4, 3+3, 4+2, 5+1                    

7 1+6, 2+5, 3+4, 4+3, 5+2, 6+1          

8 2+6, 3+5, 4+4, 5+3, 6+2          

9 3+6, 4+5, 5+4, 6+3                          

10 4+6, 5+5, 6+4                                  

11 5+6, 6+5                                          

12 6+6    

(b) They are not equally likely as the sum obtained is dependent on both the dice rolling.

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Answer:

Volume = 7WH - (1/2)W^2H

Step-by-step explanation:

The base consists of the length (L) and the width (W).  It is rectangular, so the perimeter would be the sum of all four sides:

Perimeter = L + W + L +W,

or      Perimeter = 2L + 2W

We are told that 2L + 2W = 28cm     [The perimeter is 28 cm]

------

The volume of the box is given by:  

Volume = L*W*H     [Length x Width x Height]

=====

Let's rearrange the first equation and use it in the second:

2L + 2W = 28cm

2L = 28cm - 2W

L = (28cm - 2W)/2

L = (14 - W)

Now use this definition of L (14 - W) in the second equation:

Volume = L*W*H

Volume = (14 - W)/2)*W*H

Volume = (7-(1/2)W)*W*H

Volume = 7WH - (1/2)W^2H

This can also be written as:  Volume = WH(7 - (1/2)W)

The measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a diagram shown in the picture.

The measure of an angle is 30 degrees shown.

The triangle is a right-angled triangle

30-60-90

Two parallel lines are shown which are intersected by a transversal.

The adjacent angle is 60 degrees.

The measure of angle θ:

θ = 90 - 60

θ = 30 degrees

Thus, the measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.

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Answer:

B)20

Step-by-step explanation:

convert 900in to ft=75

1500/75=20boxes

Answer:

the correct answer is 2 act

Step-by-step explanation:

there is same base (act)

then 5+3=8

and 8-6 = 2act

Answer:

5/7 or D

Step-by-step explanation:

i just know

The steps are shown below: -5<x<1

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

|x +2 | <-3

If we take the module is positive,

x+2 -2 < -3-2

x < -5

If we take the module is negative,

-( x+2)  < -3

-x -2 < -3

-x -2 +2 < -3 +2

-x< -1

x>1

Combining the inequalities,

-5<x<1

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Answer:

40

Step-by-step explanation:

the formula for area of a parallelogram is a = bh

you know area (a) = 160 and height (h) = 4, so:

160 = 4 * b

divide both sides of this equation by 4,

b = 40

the base is 40 meters long

Answer:

7 yds  1 ft 1 inch

Step-by-step explanation:

Quick Solve!

Side #1:

144 inches + 24 inches + 7 inches = 175 inches

Side #2:

72 inches + 18 inches = 90 inches + 6 inches = 96 inches

Conclusion:

175 inches + 96 inches = 271 inches

Answer:

⇒ 7 yds  1 ft 1 inch

Answer:

7 yards 1 foot 1 inch

Step-by-step explanation:

Adding both of them together, you get:

6 yards 3 feet 13 inches

Since 1 foot = 12 inches, and 13 inches exceeds that, add a foot to the previous 3 feet and subtract 12 from the 13 inches

Therefore: 6 yards 4 feet 1 inch

Since 1 yard = 3 feet, and 4 feet exceeds that, add a yard to the previous 6 yards and subtract 3 feet from the remaining 4 feet

Hence:

7 yards 1 foot 1 inch

Answer:

26 gm

Step-by-step explanation:

Tin is   1   out of (9+1)   = 1/10 th

1/10th * 260 gm  =   26 gm

Answer:

D

Step-by-step explanation:

factor the denominators of both fractions

x² - 16 ← is a difference of squares

= (x - 4)(x + 4)

8x + 2x² ← factor out 2x from each term

= 2x(4 + x) = 2x(x + 4)

then expression is

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

with LCD of 2x(x + 4)(x - 4)

Answer:

Zero Slope

Step-by-step explanation:

Horizontal lines like line L have ZERO SLOPE

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 16 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

If two polygons are similar, their corresponding sides ratios will be equal to each other.

[tex]\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2} [/tex]

[tex]\qquad \tt \rightarrow \: 2x = 12 + 20[/tex]

[tex]\qquad \tt \rightarrow \: 2x = 32[/tex]

[tex]\qquad \tt \rightarrow \: x = 16[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Yes, it is possible to have a perfect square binomial. The detailed information is given below.

In trinomial, there are three terms and in binomial, there are two terms.

Let the perfect square of the binomial will be given as

⇒ (a + b)²

There are only two terms a and b and has a square on it. So the expression (a + b)² is a perfect square binomial.

Open the bracket, then we have

(a + b)² = a² + b² + 2ab

There are only three terms a², 2ab and b² and derived from a perfect binomial square. So the expression a² + b² + 2ab is a perfect square trinomial.

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Answer: a

Step-by-step explanation:

[tex]a^{2}=a \cdot a\\a^{2}+ab=a(a+b)[/tex]

Therefore, the HCF is a.

Answer:

a

Step-by-step explanation:

Factorizing both terms :

The HCF of the terms is a.

Answer: Answer below.

Step-by-step explanation: If x is pi, and y is 1/pi, then multiplying x by y is 1; yes. So, for y, 1 is being divided by pi. The opposite of division is multiplication. If you multiply 1/pi by pi, the pi in the denominator cancels. Just how if it is 5x = 10, dividing by 5 cancels it on the left side, and gets you x = 2.

This is general for everything. If you multiply 2 by 1/2, you get 1. This is because dividing is also like multiplying by its reciprocal. 1/2's reciprocal is 2/1, and multiplying leaves you with 1. Go and use a calculator, it's correct. Actually, any problem a/b × b/a = 1.

Answer:

2/5

Step-by-step explanation:

Step-by-step explanation:

[tex] = 4x - 8y + 6 {x}^{2} + 3x - 5y[/tex]

[tex] = 6 {x}^{2} + (4x + 3x) + ( - 8y - 5y)[/tex]

[tex] = 6 {x}^{2} + 7x - 13y[/tex]

The answer is B.

Answer:

b.) 6x² + 7x - 13y

Explanation:

Given Expression

= 4x - 8y + 6x² + 3x - 5y

collect like terms

= 6x² + 4x + 3x -8y - 5y

combine similar terms

= 6x² + 7x - 13y

The exponential model best represents the data is B. f(x) = 5(0.2)^x

From the table of values, we have the following points:

(x, y) = (0,5) and (1,1)

An exponential model is represented as:

y = ab^x

Substitute (x, y) = (0,5)

5 = ab^0

5 = a

This gives

a = 5

So, we have:

y = 5b^x

Substitute (x, y) = (1,1)

1 = 5b^1

This gives

5b = 1

Divide by 5

b = 0.2

Substitute b = 0.2 in y = 5b^x

y = 5(0.2)^x

Hence, the exponential model best represents the data is B. f(x) = 5(0.2)^x

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Answer:

This is the answer to your question

The surface area of the composite figure is given by 730 sq.in

Composites are solid figures made up of basic shapes like rectangle , square and even of three dimensional figures like cube , cuboid etc.

It is given in the question to determine the area of the composite figure

Area of Cube is

Area = 6 * side²

Area = 6 * 4² = 96 sq.in

The surface area of the cuboid is equal to

Sum of surface area of all the sides

As the opposite sides are same

7x10x2 + 15x10x2 + 7x15x2

650 sq.in

As the surface area of the base of the cube is counted twice

Therefore it will subtracted from the total

96 + 650 - 4*4

=730 sq.in

Therefore the surface area of the composite figure is given by 730 sq.in

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The length, width and height of the rectangular prism is ∛10

The volume is given as:

Volume, V = 10m^3

For a minimised volume, we have:

Length = Width = Height

This means that:

V = L^3

So, we have:

L^3 = 10

Take the cube root of both sides

L = ∛10

Hence, the length, width and height of the rectangular prism is ∛10

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The correct answer is option D which is p ³+ 2; when p = 3 the number of plants is 29.

The complete question is given below:-

liana cubed the number of flowering plants in her garden, then added 2 vegetable plants. Let p represent the original number of plants in her garden. Which shows an expression to represent the total number of plants in her garden and the total number of plants if p = 3? 3 p minus 2; when p = 3 the number of plants is 7 3 p + 2; when p = 3 the number of plants is 11 p cubed minus 2; when p = 3 the number of plants is 25 p cubed + 2; when p = 3 the number of plants is 29

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is liana cubed the number of flowering plants in her garden, then added 2 vegetable plants.

If she cubed the number of the plants will be:- P³

Now she added two vegetable plants:- 2

Then the equation will be: - p³ + 2. Now we will put the value of p = 3 in the equation.

Total number of the plants = ( 3 )³ + 2 = 27 + 2 = 29

Therefore the correct answer is option D which is p³+ 2; when p = 3 the number of plants is 29.

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2. 7/10 ÷ 1/5 = 7/2

7/10 × 5 = 1/2

hope it helps u

An isosceles triangle is one with two equal-length sides. The ΔBCD is an isosceles triangle.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

Given ΔABC is an isosceles triangle with side AB = AC. Therefore, as per the base angle theorem,

∠A = ∠C = 36°

Also, in ΔABC, the sum of the angles can be written as,

∠ABC + ∠BAC + ∠BCA = 180°

∠ABC + 36° + 36° = 180°

∠ABC = 108°

For ∠ABC we can write,

∠ABC = ∠ABD + ∠CBD

108° = 72° + ∠CBD

∠CBD = 36°

Now, in ΔBCD, the measure of ∠CBD and ∠DCB both equals to 36°. Therefore, we can write, that the ΔBCD is an isosceles triangle.

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Answer:

Please see the question below.

Step-by-step explanation:

In the expression "[4 x 3⁵ - 9 x (-7)]" I'm unclear if the "x" is a multiplication sign, or the variable x.  I'll assume it is the variable x in my answer.

4 x 3⁵ = 972x

- 9 x (-7) = 63x

3³ (-4² +2²)  = 27 (20) = 540

-11 = -11

========

Putting it all together:

972x + 63x + 540 -11

1035x + 529

Total number of plants is p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.

Equation is mathematical statement formed when two algebraic expressions are equated using an equal sign.

It is given that  

Let p represent the original number of plants in her garden.

then  total number of plants in her garden =  p³ +2

the total number of plants if p = 3 is

=3³ +2

= 29

p³ +2 ; when p = 3 the number of plants is 29 , Option D is the right answer.

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