Sketch and solve the following triangles.

1. The legs of a right triangle measure 5cm and 12cm. What is the measure of its hypotenuse?

2. In ∆ABC and C is a right angle, if c = 12 and b = 10, find cos A.

3. In ∆ABC and C is a right angle, the opposite of ∠A = 12. if the hypotenuse = 13, find tan θ.

4. If sin A = [tex] \frac{15}{17} [/tex] What is tan A?

5. If cot θ = [tex] \frac{7}{24} [/tex] What is sec θ?

[tex]\large\tt{(Nonsense \: will \: be)} \\ \large \tt{( \: reported!)} [/tex]




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Answer:

first one is the second choice

question 2 is correct, the answer is the 4th option

Step-by-step explanation:

no other words

Answer:

6500

Step-by-step explanation:

(3)1% of 5000 = (3)50= 150

150x 10= 1500

1500+5000=6500

Answer:

in the thousandths

Step-by-step explanation:

because it would go

hundreds,tens,ones (decimal) tenths, hundredths,then thousandths

Answer:

Thousandths place and 0.009

Step-by-step explanation:

Answer:

x > -2.5

Step-by-step explanation:

1) 5.1 (3 + 2.2x) > -14.25 - 6 (1.7x + 4)

2) 15.3 + 11.22x > -14.25 - 10.2x - 24

3) 15.3 + 11.22x > -38.25 - 10.2x

4) 11.22x + 10.2x > -38.25 - 15.3

5) 21.42x > -53.55

6) x > -2.5

Alternate forms

x > -5/2x or x > -2 1/2

Answer:

I would roll with option B.

Step-by-step explanation:

If I understand it correctly, I would opt for option B here's why:

Suppose the pizza or pie is $20 each.

For option A,  If me and two of my friends order individually we would each only get 10% discount. So 10% of 20 is $2 so we would each pay $18 for each pizza ($54 in total for all of us).

For option B, if we order in same check that means we get 30% of our total order. Our total order is $60 (b/c each pizza is $20 so 20*3= 60). Taking 30% off of $60 is getting discount of $18 bucks which means we would pay $42 only.

Hence, comparing option A and option B, we can clearly see that opting for option B, will save 54-42 = $12.

Answer:

[tex]\displaystyle \sec A=\frac{65}{63}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \csc A=\frac{65}{16}[/tex]

Where A is in QI.

And we want to find sec(A).

Recall that cosecant is the ratio of the hypotenuse to the opposite side. So, find the adjacent side using the Pythagorean Theorem:

[tex]a=\sqrt{65^2-16^2}=\sqrt{3969}=63[/tex]

So, with respect to A, our adjacent side is 63, our opposite side is 16, and our hypotenuse is 65.

Since A is in QI, all of our trigonometric ratios will be positive.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

[tex]\displaystyle \sec A=\frac{65}{63}[/tex]

Answer:

Step-by-step explanation:

cosec A =60/16

hypotenuse/opposite = 60/16 =15/4 (in simplest form)

therefore hypotenuse = 15 , opposite = 4  

then adjacent =? (let be x)

using pythagoras theorem to find adjacent

opposite^2 + adjacent^2 = hypotenuse^2

4^2 + x^2 = 15^2

16 + x^2 = 225

x^2 = 225 - 16

x^2 = 209

[tex]x=\sqrt{209}[/tex]

sec A =hypotenuse/adjacent

[tex]=\frac{15}{\sqrt{209} }[/tex]

[tex]=\frac{15}{\sqrt{209} } * \frac{\sqrt{209} }{\sqrt{209} }[/tex]

=[tex]\frac{15\sqrt{209} }{209}[/tex]

Answer:

0.017325

x

Step-by-step explanation:

The line the puck traveled is the hypotenuse of a right triangle.

Using the Pythagorean theorem:

Travel = sqrt( 4^2 + 30^2)

Travel = sqrt( 16 + 900)

Travel = sqrt(916)

Travel = 30.265 feet ( round the answer as needed)

5 belong to whole number. b I don't know

Answer:

option c

Step-by-step explanation:

2x² - 4x = 3

2x² - 4x - 3 = 0

a = 2, b = - 4, c = -3

      [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{4 \pm \sqrt{16 + 24 }}{4} \\\\x = \frac{4 \pm \sqrt{40}}{4} \\\\x = \frac{4 \pm \sqrt{4 \times 10} }{4} \\\\x = \frac{4 \pm 2\sqrt{10} }{4} \\\\x = 1 \pm \frac{\sqrt{10}}{2}[/tex]

Answer:

121

Step-by-step explanation:

(4 - 3+2·5)²

Multiply

(4-3+10)²

Now add and subtract

(1+10)²

11²

121

Answer:

[tex]it \: is \: a \: polygon \: having \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ base = 5cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ height = 3cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ area \: of \: polygon \: = base \times height \\ \\ area \: of \: polygon \: = (5 \times 3)cm \\ \\ area \: of \: polygon = 15cm ^{2} [/tex]

Answer:

Step-by-step explanation:

Lucy=65

Eva= X points

Total:

Points =  65 + 65 = 130

Answer:

2.4

Step-by-step explanation:

If I round 2.39 to the nearest tenth it will be 2.4.

Have a nice day!

Answer:

[tex]\frac{3y+2}{6y^2}\\[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{3y+2}{3y}/\frac{6y^2+4y}{3y+2} \\= \frac{3y+2}{3y} * \frac{3y+2}{6y^2+4y}\\= \frac{3y+2}{3y} * \frac{3y+2}{2y(3y+2)}\\= \frac{3y+2}{3y} * \frac{1}{2y}\\= \frac{3y+2}{6y^2}\\[/tex]

Answer:

B maybe

Step-by-step explanation:

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

Explanation:

Focus solely on triangle ABD.

Let x be the length of AD. This is the unknown horizontal leg of the triangle. The vertical leg is known, so we'll say b = 16.

The hypotenuse is 20, so c = 20.

Use the pythagorean theorem to find x

a^2 + b^2 = c^2

x^2 + 16^2 = 20^2

x^2 + 256 = 400

x^2 = 400 - 256

x^2 = 144

x = sqrt(144)

x = 12

Segment AD is 12 cm long.

Answer:

2

Step-by-step explanation:

Answer:

[tex]n=1.3\times 10^{12}[/tex]

Step-by-step explanation:

Given that,

The radius of a cell, r = 10⁻³ cm

The density of the cell, d = 1.1 g/cm³

The weight of the Koala, m = 6 kg = 6000 grams

The density of an object is given by:

[tex]d=\dfrac{m}{V}[/tex]

For n cells,

[tex]nd=\dfrac{m}{V}\\\\n=\dfrac{m}{dV}[/tex]

Put all the values,

[tex]n=\frac{6000}{\frac{4}{3}\cdot\pi\cdot\left(10^{-3}\right)^{3}\cdot1.1}\\\\n=1.3\times 10^{12}[/tex]

So, there are [tex]1.3\times 10^{12}[/tex]cells in the average koala.

Step-by-step explanation:

Assuming figure to be trapezoid,

Perimeter=6+4+7+4yd

=21 yd

Area of trapezoid=((6+7)/2) x ((4)^2-(0.5)^2)

=(13/2)x(16-0.25)

=6.5 x 15.75

=102.375 Sq yards

Answer:

let's write it as an equation

speed in m/sec (s) = 33.3 -9.81s

speed in m/sec (2.8) = 33.3 -9.81*2.8 = 5.832

9.81 is the deceleration due to earth's gravity.

the speed changes that ammount per second.

85%

Hope this helps! :)

______________

Answer:

68/80×100%=85%

hope it helps!!!

Answer:

The fourth (last) function is the correct one.

Step-by-step explanation:

Look at the parent function y = √x,  Its graph goes through (0, 0).  On the other hand, if y = √(x - h), the graph goes through (h, 0) if h is positive, and the graph is translated h units to the right from the graph of y = √x.  If h is negative, the graph is translated h units to the left.

In the four possible answers given, the values of h are {-4, 9, 5, -9}, in that order.  h = -9 results in the graph that is positioned 9 units to the left of the graph of y = √x.  This graph is furthest to the left.  Thus the fourth choice is the correct one.

Answer:

18 sq.m

Step-by-step explanation:

Area of the part with cement = area of backyard - area of grass part

Backyard:

length = l = 6m  ; Width = w = 4 m

Area of backyard = l * w = 6*4 = 24 sq. m

Grass part:

l = 3 m ; w = 2 m

Area of the grass part = 3*2 = 6 sq.m

Area of the part with cement = 24 - 6 = 18 sq.m

Answer:

true. true. false.

Step-by-step explanation: i’m in love with the shape of u. we push and pull like magnet whatever

Answer:

Option A

Step-by-step explanation:

From the graph attached,

Distance of point A of rectangle ABCD = 5 units

Distance of point E of rectangle EFGH = 5 units

Similarly, all the vertices of the rectangles ABCD and EFGH are equidistant from the y-axis.

Therefore, rectangle ABCD and rectangle EFGH may overlap each other by reflecting each other across y-axis.

Let's check by the rule of reflection,

Rule for the reflection of a point (x, y) across y-axis is given by,

(x, y) → (-x, y)

Following this rule,

A(-5, 5) → E(5, 5)

B(-3, 4) → F(3, 4)

C(-4, 1) → G(4, 1)

D(-6, 2) → H(6, 2)

Therefore, rule for the reflection is applicable in this question.

Option A will be the answer.