JK is J(-3 9) and K(5 -1), if LM is perpendicular to JK, what is the slope of LM?

Answer:

D

Step-by-step explanation:

Using the sine ratio in the right triangle

sin51° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] ( multiply both sides by y )

y × sin51° = 9 ( divide both sides by sin51° )

y = [tex]\frac{9}{sin51}[/tex] ≈ 11.6 ( to 1 dec. place ) → D

Answer:

Step-by-step explanation:

take 23 degree as reference angle

using tan rule

tan 23=opposite/adjacent

0.42=25/x

x=25/0.42

x=59.52

x=60

Answer:

(5/2)² must be added to the equation to complete the square.

Step-by-step explanation:

The given equation is

x^2+5x+10=0

writing it in in square form

(x)² + 2(x) (5/2) + (5/2)²-(5/2)² + 10= 0

We multiply (5/2) to the mid term because we have to make 2x equal to 5x.

As the square formula tells that square of first element plus 2 into first element multiplied by second element plus square of second element.

Making 2x equal to 5x gives (5/2) as the second element.

Therefore add square of the second element but also subtract square of second element to make it equal to the given original equation.

Now we can solve it.

(x)² + 2(x) (5/2) + (5/2)²-(5/2)² + 10= 0

(x + 5/2)²-(5/2)² + 10= 0

(x + 5/2)²- 25/4+ 10= 0

(x + 5/2)²- 25*5 +10*5/4*5= 0

(x + 5/2)²-  125+50/20= 0

(x + 5/2)²-  175/20= 0

(x + 5/2)²=  175/20

Answer:

(-5,-4) quadrant is in III quadrant

The expression on the left matched with an equivalent expression on the right are;

3x + 0 = 3x

5/3 - x + 1/3 = -3/2x + 2 + 1/2x

2x - 3 = x - 3 + x

2x - 6 = -6 + 2x

3/5 - 13/5 = -6.9 + 4.9

3x + 0 = 3x

5/3 - x + 1/3

combine like terms

= 5/3 + 1/3 - x

= (5+1)/3 - x

= 6/3 - x

= 2 - x

-3/2x + 2 + 1/2x

combine like terms

-3/2x + 1/2x + 2

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

= -2/2x + 2

= -x + 2

2x - 3 = x - 3 + x

2x - 6 = -6 + 2x

3/5 - 13/5

= (3-13)/5

= -10/5

= -2

-6.9 + 4.9

= -2

Ultimately, an expression is said to be equivalent when the value on the right hand side is equal to the value on the left hand side.

Read more on equivalent expression:

https://brainly.com/question/15775046

#SPJ1

Answer:

Step-by-step explanation:

87 = x + 90

Isolate the variable by subtracting 90 on both sides

87 = x + 90

-90      -90

x=-3

-4x = 16

Isolate the variable by dividing by -4 on both sides

-4x=16

/-4   /-4

x = -4

43 = 6x - 5

Answer:

[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan\theta=\frac{6}{5}\text{ and } \cos\theta <0[/tex]

And we want to find the value of sin(2θ).

First, recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the hypotenuse is:

[tex]h=\sqrt{6^2+5^2}=\sqrt{61}[/tex]

Next, note that tangent is positive and cosine is negative. Tangent is positive in QI and QIII. Cosine is negative in QII and QIII.

Hence, we can conclude that θ must be in QIII.

In QIII, sine is negative, cosine is negative, and tangent is positive.

And with respect to θ, our opposite side is 6, adjacent side is 5, and the hypotenuse is √(61).

We can rewrite our expression as:

[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]

Using the above information, substitute:

[tex]\displaystyle =2\left(-\frac{6}{\sqrt{61}}\right)\left(-\frac{5}{\sqrt{61}}\right)[/tex]

Simplify. Hence:

[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]

Answer:

20

Step-by-step explanation:

6×2=12 + 8 = 20

so you answer for number 3 is twenty

Answer:

Triangle 2

Step-by-step explanation:

That is Pythagorean Theorem, which is only for right triangles. The second triangle has the little square, so you know it is 90 degrees.

Answer:

use this <3 (helps calculate scientific notation) https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php

Step-by-step explanation:

Answer:

Add 48 to get a perfect square

Explanation:

A perfect square would be of the number 651249 which means that you have to add 48 to get a perfect square.

Answer:

4 hours

Step-by-step explanation:

You divide 12 by 3 and the answer is 4.

hope this helped

Hi there! For this question, you need to know the ratio of sine and cosine.

Define A = angle

opposite and adjacent side changes only if we focus on another angle.

From the picture, if we focus on angle S, the opposite would be 36. But if we focus on angle R (flip to make RT as base), see that the opposite would be 14.

Answer

The bold one is simplest form while the non-bold is non-simplest.

Questions can be asked through comment.

Hope this helps, and Happy Learning ! :)

Answer:

Step-by-step explanation:

hope it helps

#carryonlearning

Answer:

Step-by-step explanation:

• AB, BC, and AC form a triangle. Enter a possible value of AC....

So it asks for only a possible value of AC as there are many possible values.

Given AB = 8 cm and BC = 6 cm, they are in the ratio of 3:4.

Line segments of 3, 4 and 5 length will form a right-angled triange.

A possible value of AC = 5*2 = 10cm

• Points A, B, and C lie on the same line, and C lies between A and B.

So AC+CB = AB

AC+6 = 8

AC = 2cm

Enter this value of AC in the second

response box.

Answer:

Step-by-step explanation:

if ABC forms a triangle, AB=8 and BC=6

a possible value of AC=10cm

if ABC is a line segment n C is between A n B

AC + BC = AB

AC = 8 - 6 = 2cm

Answer:

b

Step-by-step explanation:

Answer:

[tex](6 {x}^{2} - 5x + 10) - 2 {x}^{2} - x + 13 \\ 6 {x}^{2} - 5x + 10 - 2 {x}^{2} + x - 13 \\ = 4 {x}^{2} - 4x - 3[/tex]

Answer:

y ≈ 61

Step-by-step explanation:

Using the Sine rule in the triangle

[tex]\frac{y}{sin117}[/tex] = [tex]\frac{21}{sin18}[/tex] ( cross- multiply )

y × sin18° = 21 × sin117° ( divide both sides by sin18° )

y = [tex]\frac{21sin117}{sin18}[/tex] ≈ 61 ( to the nearest whole number )

Answer:

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex] where h and k are the center of the circle and r is the radius. Filling in:

[tex](x-2)^2+(y-3)^2=16[/tex]

Answer:

-1, 1, 3, 5, 7

Step-by-step explanation:

Answer:

The solution to the equation is:

Step-by-step explanation:

To find the solution to the equation, you only must operate the equation until you clear the x variable, with the next steps:

And we solve:

As you can see, the solution of the equation is x = 2.5 or x = 5/2

Answer:

C)  x = 3

Step-by-step explanation:

factor out a 2 to get:

2(x² - 6x + 9) = 0

(x-3)² = 0

x = 3

Answer and Step-by-step explanation:

First, to find the zeros of the function, we can take out a common factor from the equation, and then factor.

The equation has a common factor of 2 (so distribute of the 2 from all of the numbers).

2([tex]x^2 - 6x + 9[/tex])

Now, we factor. Find two numbers that multiplies to [tex]9x^2[/tex] and adds up to -6x.

-3x and -3x.

Now, we substitute these two for -6x.

[tex]2(x^2 - 3x-3x+9)[/tex]

Factor.

[tex]2(x - 3)(x-3)[/tex]

Finally, we set all of the values to 0 and solve for x.

2 ≠ 0

x - 3 = 0    x = 3

x - 3 = 0    x = 3

That means the answer is C. x = 3

(Not shown, but the multiplicity of this x value is 2, because there are two

x = 3)

#teamtrees #PAW (Plant And Water)

Answer:

90.8

Step-by-step explanation:

20/13 = x/59

13x = 1180

x=90.76

x=90.8

Answer:

12,5

Step-by-step explanation:

First, you need to find how many kilobytes do you download every seconds.

You simply divide 48 kilobyte / 5 seconds and you get 9,6 kB/s.

Now you know that your download speed is this you can find the amount of time needed for downloading 120 kilobytes.

You simply divide [tex]\frac{120 kilobytes}{9,6 kilobytes/s} = 12.5 s[/tex].

12,5 seconds.

Answer:

the domain is xl-5<×< 3 is the range of 16

The domain is all real numbers. The range is {y|y ≤ 16}.

The domain of a function is all the of values of the input or independent variable into the function

Since the x-intercepts of the function are at (-5, 0) and (3, 0), and also, the graph opens downwards, the values of x are in the interval (-∞ ≤ x ≤ -5) ∪ (-5 ≤ x ≤ 3) ∪ (3 ≤ x ≤ ∞). This is (-∞ ≤ x ≤ ∞).

So, the domain is the set of all real numbers.

The range of a function is all the output values of the function

Since the vertex of the parabola is at (-1, 16) and its y-intercept is at (0, 15), the maximum value of y is 16. So, the values of y are in the range y ≤ 16.

So, the range of the function is {y|y ≤ 16}

So, the domain is all real numbers. The range is {y|y ≤ 16}.

Learn more about domain and range of a function here:

https://brainly.com/question/10197594

Answer:

Step-by-step explanation:

Cos(Sec - 1 ) = 1 - cosC

Cos and Sec are reciprocals which when multiplied together is 1

-1 * Cos = -Cos

SO: 1 - Cos = 1 - Cos

Hope this helps!

Answer: 28

You add 36 and 20 and divided it by 2

I have added the complete question in the attachment

Answer:

15

Step-by-step explanation:

From the diagram in the attachment

27⁰ represents 3 pupils they love PE

135⁰ represents those that love mathematics. But the number was not given.

We have;

27⁰ = 3

135⁰ = ?

We cross multiply to find the unknown

135⁰x3 = 27⁰?

405 = 27⁰?

Divide through by 27

405/27 = ?

15 = ?

Therefore 15 pupils said mathematics was there favorite

Answer: 340 students

Step-by-step explanation:

The number of students walking to school is 119 and this is 35% of the total number of students.

Assume the total number is denoted by "x".

That would mean that the following formula captures the situation:

119 = 35% * x

119 = 0.35x

x = 119/ 0.35

= 340 students