MATHEMATICS HIGH SCHOOL

What is the slope of the line?
6x - 2y = 10

Answers

Answer 1
Answer:

The slope of the Line is 3

What is the slope of a line?

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) may be easily determined by finding the difference among the coordinates of the points. The slope is normally represented by the letter 'm'.

Conclusion: The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

The general equation of a line having a slope is y = mx + c

we have to arrange the equation 6x - 2y = 10 in y = mx + c form

6x -2y = 10

2y = 6x - 10

y = 3x - 5

The slope of the line is represented by m, the value of m in equation y = 3x - 5 is 3

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Answer 2
Answer: We need to rearrange the equation so that it is in slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

To do this we just solve for y.

Subtract 6x from both sides.

-2y = 10 - 6x

Divide both sides by -2.

y = -5 + 3x

m=3

The line has a slope of 3.





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Three roads intersect to form a large triangular area as shown below.-5 miles
300
What is the length, to the nearest tenth of a mile, of side x of the triangle?
O A. 2.5 miles
O B. 2.9 miles
O C. 4.0 miles
O D. 4.3 miles

Answers

Answer:

b i think

Step-by-step explanation:
I think your correct answer is B

Select the term that best describes the statement.All lines are straight or a triangle has four sides.

A.) conjunction
B.) disjunction
C.) negation
D.) conditional

Answers

Answer:

Option B is correct.

Step-by-step explanation:

Given the statement

All lines are straight or a triangle has four sides.

we have to choose the correct word for the above statement.

Conjunction statement is a compound statement formed by joining two statement with connector AND and Disjunction statement with connector OR.

Negation statement is the opposite of given statement.

Conditional statement is if-then statement.

The given statement is the compound statement formed by joining two statements with connector OR

⇒ The given statement is disjunction

Option B is correct.
the answer I would go with is A.

If cot(theta)= 4/3, find csc(theta) (Picture provided)

Answers

Answer:

D

Step-by-step explanation:

If \cot \theta=(4)/(3), then we can consider right triangle with adjacent leg 4 un. and opposite leg 3 un.. By the Pythagorean theorem,

\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\n \n\text{hypotenuse}^2=4^2+3^2,\n \n\text{hypotenuse}^2=16+9,\n \n\text{hypotenuse}^2=25,\n \n\text{hypotenuse}=5\ un.

So,

\csc \theta=\frac{\text{hypotenuse}}{\text{opposite leg}}=(5)/(3).

Answer:

The correct answer is option d

Step-by-step explanation:

Trigonometric ratio

Cot θ = Adjacent side/Opposite side

It is given that,

Cot θ  = 4/3

Adjacent side = 4

Opposite side = 3

Csc θ = Hypotenuse/Opposite side

To find the Hypotenuse

Hypotenuse² = Opposite side² + Adjacent side ² = 3²+ 4²

Hypotenuse = √(3²+ 4²) = 5

To find Csc θ

Csc θ = Hypotenuse/Opposite side = 5/3

The correct answer is option d

Csc θ = 5/3

1.) A ladder is leaning against the side so that the distance on the ground betweenthe base and the house is 7 feet.
If the ladder is 15 feet long, then what is the angle at which the ladder is leaning?

Answers

The angle at which the ladder is leaning is 62.18°.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.

For the given situation,

The length of the ladder = 15 feet

The distance between the house and the ladder base = 7 feet

The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.

we know that, cos θ = (Base)/(Hypotenuse)

The figure below shows the relationship between the sides.

⇒ cos θ = (7)/(15)

⇒ θ = cos^(-1)((7)/(15) )

⇒ θ = 62.18

Hence we can conclude that the angle at which the ladder is leaning is 62.18°.

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Answer:

62.182°

Step-by-step explanation:

Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.

What is the product?2a-7 over a times 3a^2 over 2a^2-11a+14
a) 3 over a -2
b) 3a over a-2
c) 3a over a+2
d) 3 over a+2

Answers

Answer:

The correct option is b.

Step-by-step explanation:

We have to find the product of (2a-7)/(a)  and  (3a^2)/(2a^2-11a+14).

Multiply both terms.

(2a-7)/(a)* (3a^2)/(2a^2-11a+14)

Cancel out the common factor a from numerator and denominator.

(2a-7)/(1)* (3a)/(2a^2-7a-4a+14)

(2a-7)/(1)* (3a)/(a(2a-7)-2(2a-7))

(2a-7)/(1)* (3a)/((2a-7)(a-2))

Cancel out the common factor (2a-7) from numerator and denominator.

(1)/(1)* (3a)/(a-2)

(3a)/(a-2)

Therefore, the correct option is b.
this question involves factoring and multiplying equations so just follow along my procedures in the image

How do I determine whether each binomial is a difference of two squares

Answers

A binomial is a difference of two squares if it can be written as a^2 - b^2. Note the subtraction sign. For example 9x^4 - 16 = (3x^2)^2 - 4^2 so it is a difference of two squares.
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