using the 45o −45o −90o Triangle theorem.

Solve this triangle.​

Answer:

[tex]hypotenuse = \sqrt{ {height}^{2} + {adjacent}^{2} } \\ = \sqrt{ {11}^{2} + {60}^{2} } \\ = \sqrt{3721} \\ = 61 \: inches[/tex]

hypotenuse=

height

2

+adjacent

2

=

11

2

+60

2

=

3721

=61inches

Triangle ABC has the three sides AB, BC, and AC.

Let's find the slope of each line. We'll use the slope formula

Let's start with the slope of line AB.

A = (-3, -4) = (x1,y1)

B = (16, -2) = (x2,y2)

m = slope

m = (y2-y1)/(x2-x1)

m = (-2-(-4))/(16-(-3))

m = (-2+4)/(16+3)

m = 2/19

The slope of line AB is 2/19. I'll keep it in fraction form.

We'll use this later, so let p = 2/19.

---------------

Repeat those steps to find the slope of BC

B = (16, -2) = (x1,y1)

C = (13, -10) = (x2,y2)

m = (y2-y1)/(x2-x1)

m = (-10-(-2))/(13-16)

m = (-10+2)/(13-16)

m = -8/(-3)

m = 8/3

The slope of line BC is 8/3.

Let q = 8/3 so we can use it later.

---------------

Now find the slope of line AC.

A = (-3, -4) = (x1,y1)

C = (13, -10) = (x2,y2)

m = (y2-y1)/(x2-x1)

m = (-10-(-4))/(13-(-3))

m = (-10+4)/(13+3)

m = -6/16

m = -3/8

The slope of line AC is -3/8

Let r = -3/8.

---------------

To recap everything so far, we have

We can see that,

Of those slope multiplications, q and r multiply to -1 is what we should focus on. If two slopes multiply to -1, then their lines are perpendicular. This applies to any perpendicular lines where neither line is vertical, and neither is horizontal.

The fractions 8/3 and -3/8 are negative reciprocals of one another. We flip the fraction and flip the sign from positive to negative, or vice versa. This is another way to see we have perpendicular slopes.

So in short, we've shown that BC and AC are perpendicular, and therefore triangle ABC is a right triangle.

----------------------------------------------------------------

To solve this problem a completely different way, we could follow this outline:

Through step 1, you should find that,

Let a = sqrt(73), b = sqrt(292), c = sqrt(365). You should find that a^2+b^2 = c^2 is a true statement based on those values, and therefore we have a right triangle. The longest side is AB = sqrt(365), making angle C to be the 90 degree angle. The diagram is shown below. I used GeoGebra to make the diagram.

Answer:

9. 5 Hours

Step-by-step explanation:

8:30 AM to 12:00 PM = 3.5 hours

12:00 PM to 6:00 PM = 6 hours

Total = 6 + 3.5 = 9.5 hours  

Hope this answer helps you :)

Have a great day

Mark Brainliest

Answer:

There is a vertical Asymptote at x = 5 because [tex]\lim_{x \to 5^{-} } G(x) = \infty\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]

There is a vertical Asymptote at x = -5 because [tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]

Step-by-step explanation:

The exact question is as follows :

Given - G(x) = -7(x-5)^2(x+6)/(x-5)(x+5)

To find - Which statement make correctly uses limits determine a vertical Asymptote of G(x)

Solution -

Vertical Asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.

Here the given function is the rational function

Denominator of G(x) = (x - 5)(x + 5)

So,

Put denominator = 0, we get

(x - 5)(x + 5) = 0

⇒x = 5, -5

∴ we get

G(x) has vertical Asymptotes at x = 5 and x = -5

Now,

At  x= 5

[tex]\lim_{x \to 5^{-} } G(x) = \infty\\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]

And

At x = -5

[tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]

∴ we get

There is a vertical Asymptote at x = 5 because [tex]\lim_{x \to 5^{-} } G(x) = \infty\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]

There is a vertical Asymptote at x = -5 because [tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]

Answer:

Step-by-step explanation: A

Answer:

5 inches

Step-by-step explanation:

Well two bags hold 250 cubic inches, which means one bag will hold 125 cubic inches.

Then you cube route 125 because its cubic inches.

[tex]\sqrt[3]{125}[/tex] = 5

So I would think its five inches but I may be wrong <3

Answer: [tex]32.909\ \text{ounce}[/tex]

Step-by-step explanation:

Given

3.25 cm long segment of rope weighs [tex]61.40\ gm[/tex]

Using unitary method

1 cm of a segment measures

[tex]\dfrac{61.40}{3.25}=18.892\ gm[/tex]

[tex]1\ cm\equiv 18.892\ gm[/tex]

converting cm to inch and gm to ounce

[tex]\dfrac{1}{2.54}\ in.\equiv \dfrac{18.892}{28.3495}\ \text{ounce}\\\\1\ in.\equiv \dfrac{18.892}{28.3495}\times 2.54\ \text{ounce}\\\\1\ in.\equiv 1.692\ \text{ounce}[/tex]

for 19.45 in., weight is

[tex]\Rightarrow 19.45\ in.\equiv 1.692\times 19.45\\\\\Rightarrow 19.45\ in\equiv 32.909\ \text{ounce}[/tex]

Answer:

i got it right⬇

Answer:

20%

Step-by-step explanation:

$187.50 - 20% = $150.00

Answer:

x≥26667

Step-by-step explanation:

let x= her sales

so the money she gets from her sales is .03x

if we wants at least 2900 we can write

2100+.03x≥2900

Solve for x

.03x≥800

x≥26666.6667

round up (because you can make a fraction of a sale) to get

x≥26667

4247.43327 Or short 4247.4!

Step-by-step explanation:

Answer:

STATEMENT NO. 4 IS CORRECT.

Step-by-step explanation:

Because every rectangle has two pair of parallel lines so it can be called a parallelogram.

Answer:

79

Step-by-step explanation:

79, 85, 89, 68 have a mean of 80.25 according to calculator.net. the number itself Is close to the number you want, in this case 80, i input 80, but it gave me a score of 80.2, so i tried again with 81, it gave me a score of 80.4, so the third attempt was successful with 79 being the input and 80 the output

calculator.net is approved on my school computer so there is a chance it is on yours as well.

Answer:

x=5

Step-by-step explanation:

to find volume: length x width x height

the first rectangular prism volume: 15*5*5= 375 in³

because they have the same volume, you would set the other rectangular prism equal to 375: 25*3*x=375

75*x=375

divide both sides by 75: x=5

Answer: 2/3

Step-by-step explanation:

there are 24 pets total (count all of the dots on the plot)

16 students have 2 or more pets (count the dots from point 2 until 6)

your fraction is 16/24

16/24 is 2/3 simplified

hope this helps

Answer:

Essential Elegance Candle

Step-by-step explanation:

Ratios are Lavender:Vanilla

For the Essential elegance candle the ratio is 3:6 which can be simplified to 1:2 whereas the Glory Candle is 4:10 which can be simplified to 2:5 on either one the vanilla is the bigger number but in terms of ratio it would be the essential elegance since 1/2>2/5

Answer:

C: 18 4/15

Step-by-step explanation:

7 2/3 + 10 3/5

Convert fractions so that they share a common denoninator:

7 10/15 + 10 9/15

17 19/15

18 4/15

Answer:

Hello! answer: 21.4

Hope that helps!

Answer:

Yes it is a function

Hope its help you ☺

Answer:

Area = 634.21 square metre

Step-by-step explanation:

Area of shaded region = Area of the circle - Area of the sector

[tex]Area \ of \ the \ circle = \pi r^2 = 225 \pi\\\\Area \ of \ the \ sector = \pi r^2 \frac{ \theta}{360} = \pi \times 225 \times \frac{37}{360}[/tex]

[tex]Area \ of \ shaded \ region = 225 \pi - (225 \pi \times \frac{37}{360})[/tex]

                                   [tex]= 225 \pi (1 - \frac{37}{360})\\\\= 225 \pi \times 0.89722\\\\=634.21 m^2[/tex]

Answer: 30.5

Step-by-step explanation:

Answers:

=========================================

Explanation:

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as [tex](x,y) \to (7x, 7y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Answer: angle f is 31.788 and angle d is 58.212

Step-by-step explanation:I need one more brainliest for next rank I’d appreciate it

Answer:

c, a, b

Step-by-step explanation:

Given

See attachment for matrices

(a)

[tex]D = \left[\begin{array}{cc}\cos\theta &\sin\theta\\ -\sin\theta& \cos\theta\\\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D |= (\cos\theta * \cos\theta - \sin\theta *- \sin\theta)[/tex]

[tex]|D | = \cos^2\theta + \sin^2\theta[/tex]

Using trigonometry ratio, we have:

[tex]|D | = 1[/tex]

(b)

[tex]\left[\begin{array}{ccc}2&0\\0&2\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 2 * 2 - 0 * 0[/tex]

[tex]|D| = 4 - 0[/tex]

[tex]|D| = 4[/tex]

(c)

[tex]\left[\begin{array}{ccc}0&i\\-i&0\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 0 * 0 -(-i * i)[/tex]

[tex]|D| = 0 +i^2[/tex]

[tex]|D| = i^2[/tex]

In complex numbers

[tex]i^2 = -1[/tex]

So:

[tex]|D| = -1[/tex]

So, the order of the determinants is: c, a, b

Answer:

53 pushes

Step-by-step explanation:

Total Volume of soap = 474 mL

Volume per push = 8mL

Mimimum volume required = 50mL

The equation which represents the number of push, x that can be made :

Total volume = minimum volume + (volume per push * number of pushes)

Total volume = 50 + (8 * x)

474 ≤ 50 + 8x

474 - 50 ≤ 8x

424 ≤ 8x

53 ≤ x

The number of pushes that can be made = 53

Answer:

The probability he rolls a 2 or lower and the coin lands on heads is 16.66%.

Step-by-step explanation:

Since Kane rolls a dice and flips a coin at the same time, to determine what is the probability he rolls a 2 or lower and the coin lands on heads the following calculation must be performed:

Given = 6 sides = 2/6

Coin = 2 sides = 1/2

2/6 x 1/2 = X

0.333 x 0.5 = X

0.1666 = X

0.1666 x 100 = 16.66

Therefore, the probability he rolls a 2 or lower and the coin lands on heads is 16.66%.

Answer:

77 ft.

Step-by-step explanation:

7*8+7*3=77

Given :

If, A = { x : x is a letter in the word 'MATHEMATICS' } .

To Find :

The members of A and find  n (A).

Solution :

We have given a set, A = { x : x is a letter in the word 'MATHEMATICS' } .

Now, we know in set theory recurring element is written once only i.e all unique elements should be there in the set.

So,

A = { M, A, T, H, E, I, C, S }

Now, number of element in set A is 8.

Therefore, n(A) = 8 .

Answer:

Step-by-step explanation:

take 45 degree as reference angle

using sin rule

sin 45=opposite/hypotenuse

1[tex]\sqrt{2}[/tex]=x/16

x=16/[tex]\sqrt{2}[/tex]

x=8[tex]\sqrt{2}[/tex]

Answer:

children = 67

Step-by-step explanation:

two equations can be derived from this question

x + y = 85 equation 1

3x + y = 121 equation 2

where x = number of adults

y = number of children

subtract equation 1 from 2

2x = 36

x = 18

substitute for x in equation 1

y = 85 - 18 = 67

Answer:

Step-by-step explanation:

AN Example of every way to write a ratio is:

which one you choose will depends on the problem or situation

Answer:

(5, -7).

Step-by-step explanation:

Solution is the point of intersection.

(5, -7).