The line of which equation passes through points (0,6) and (4,-1)

Answer: Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches

Step-by-step explanation:

Let the shorter leg bw represented by x.

Therefore, the longer leg will be x+2.

The hypothenuse is 10inches

We should note that in Pythagoras theorem, the square of the longer and shorter side equals the square of the hypothenuse. This will be:

x² + (x+2)² = 10²

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4

2x² + 4x = 96

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

x² + 8x - 6x - 48 = 0

x(x + 8) -6(x + 8) = 0

x - 6 = 0

x = 0+6.

x = 6

Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches

Step-by-step explanation:

Halfway from x = -7 and x= 3 is --2, Similarly, y is -1. The center is at (-2, -1). The radius is the distance from the center to one of the diameter endpoints: sqrt ( 5 squared plus 4 squared ), or sqrt(41).

The equation of the circle is

(x + 1) squared plus (y + 1) squared = 41

Answer:

First don't forget the [ tex ] [ /tex ] in order to execute the latex code.

Step-by-step explanation:

[tex] \sin A=\frac{5}{\sqrt{89}}sinA= 89 [/tex]

[tex] \cos AcosA [/tex] = [tex] \cos [/tex]

The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Given that:

[tex]\sin A=\dfrac{5}{\sqrt{89}}[/tex]

So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.

There must be existing a right triangle with same measure of angle A such that:

Perpendicular's length = P = 5 units

and Hypotenuse' length = H = [tex]\sqrt{89}[/tex] units.

Using Pythagoras theorem, we get:

Base' length = B as:

[tex]P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8[/tex]

(took positive root as B is representing length, a non-negative quantity).

Thus, Base is of 8 units length.

Thus, we get:

[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}[/tex]

Rationalizing, we get:

[tex]\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}[/tex]

Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is [tex]\dfrac{8\sqrt{89}}{89}[/tex]

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

10 feet

Step-by-step explanation:

a²+b²+=c²

a=8ft

b=6ft

Answer:

(-9, 9)

Step-by-step explanation:

[tex]6x^{2} +1 = 487[/tex]                                             (Given)

       -1       -1                                     (Getting "x" alone)

[tex]6x^{2} = 486[/tex]                                        (Cont. Getting "x" alone)

÷6      ÷6                                                           ↓

[tex]x^{2} = 81[/tex]                                                              ↓

[tex]\sqrt{x} ^2 = \sqrt{81}[/tex]                           (9 and -9 squared are both equal to 81)

↓             ↓                                                        ↓

x = 9      x = -9                                            (Answer)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

31

Step-by-step explanation:

62 / 2 = 31

Answer:

31

Step-by-step explanation:

angle is half of arc

Step-by-step explanation:

Cumulative frequency can also defined as the sum of all previous frequencies up to the current point.

So, 48+24=72

So, the missing cumulative frequency is . 72

Answer:

the missing cumulative frequency is . 72

Step-by-step explanation:

9514 1404 393

Answer:

  A

Step-by-step explanation:

A vertical line intersects the graph in more than one place. As a consequence, we say the graph "fails the vertical line test." When the test fails, the graph is not a graph of a function.

Answer:

To answer this question I need the values of the rhombus. like the p and the q.

Step-by-step explanation:

Answer: 287

ksjfhfjkskkdjffj

Answer:

287

Step-by-step explanation:

since we are rounding to a whole number, the number would be depending on .3

3 is less than 5 so round down

287

Answer:

8

Step-by-step explanation:

18+46=64

87.5% of 64=56

64-56=8

56 take the bus

8 dont take the bus

Answer: m is the slope and b is the y-intercept.

Step-by-step explanation:

it is understandable that the x has a coefficient of 1, so the m is 1 . and the y-intercept( b ) is −4 .

Answer:

I think it its

Step-by-step explanation:

C if its wrong sorry

Answer:

1) 4

2) 15/2

3) 75

Step-by-step explanation:

Answer:

1. If BD = 2, then CE = 2*BD = 2*2 = 4

2. If AC = 15, the AB = 1.2*15 = 7.5

3. If m∠ADB = 75°, then m∠AEC = m∠ADB = 75° as corresponding angles

4. If AE = 6x + 8 and BD = 18, then x is:

5. If BD = x + 1 and CE = x + 10 then:

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Ratio = Width: Height

Ratio = 720 : 540

Cancelling 0

Ratio = 72 : 54

Cancelling by 9

Ratio = 8 : 6

Cancelling be 2

Ratio = 4 : 3

Answer:

15x + 12

Step-by-step explanation:

3(5x + 4)

15x + 12

3 · 5x = 15x

3 · 4 = 12

Combine them:

15x + 12

Answer:

3(5x + 4)

15x + 12

3 · 5x = 15x

3 · 4 = 12

15x + 12

Answer:

x = 4.5

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle, then

the segment is half the length of the 3rd side, that is

5x = 0.5 × 45 = 22.5 ( divide both sides by 5 )

x = 4.5

look at png sorry i need to type 20 characters but the chart explains everything

simplify your answer but adding/subtracting like terms

Answer:

D.B

Step-by-step explanation

40+35= 75+105= 180

(edited)

Answer: ummm... i think it is.. 3-2

Step-by-step explanation:

Answer: 11/38

Step-by-step explanation: x - y v q r 2÷x029 2%.091 57rq x2 = 11/38

9514 1404 393

Answer:

  260π in²

Step-by-step explanation:

The slant height is the hypotenuse of a right triangle with legs 10 and 24. Using the Pythagorean theorem, we find it to be ...

  l² = 10² +24² = 100 +576 = 676

  l = √676 = 26

The given formula tells you the lateral area is ...

  A = πrl = π(10 in)(26 in)

  A = 260π in² . . . . . cone's lateral area

_____

Additional comment

The name of the constant relating diameter to circumference (π) is "pi". It is the 16th letter of the Greek alphabet. "Pie" is something else entirely.

Answer:

260[tex]\pi in^{2}[/tex]

Step-by-step explanation:

Answer:

-12 degrees

Step-by-step explanation:

the graph

Answer:

i believe 95 ft ² but I'm not sure sorry

Answer:

95

Step-by-step explanation:

this seems to be a triangular prism. Hopefull this works?

6*1/3 (5+5+5)=95

Answer:

C) 180

Step-by-step explanation:

y = 105 (because of alternate interior angles)

105 + x = 180

x = 75

x + y

105 + 75

180

Answer:

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