What is the length of leg s in the right triangle shown?

What Is The Length Of Leg S In The Right Triangle Shown?

Answers

Answer 1

Answer:

D. 5

Step-by-step explanation:

Applying,

cos∅ = adjacent/Hypotenuse

From the diagram,

Given: ∅ = 45°, adjacent = s, hyptenuse = 5√2

Therefore,

cos45° = s/5√2

make s the subject of the equation

s = cos45°×5√2

s = (1/√2)(5√2)

s = 5

Hence the right answer is D. 5


Related Questions

Find the mode of the data.
Length (inches) of fish in tank:
2, 3, 1, 4, 5, 2, 2
Mode: [?] in.

Answers

Answer:

The mode is 2

Step-by-step explanation:

Mathematically, the mode of a given data set represents the most recurring number or the number with the most count

Looking at the given dataset, we can see that the number 2 recurred 3 times

Compared with the other numbers, it has the most count

this means it is the mode of the given or displayed dataset

There are 1,099 souvenir paperweights that need to be packed in boxes. Each box will hold 11 paperweights. How many boxes will be needed?

Answers

Answer:

1099/11=99.9

since you can't have 99 boxes, you round to 100 boxes.

you will need 100 boxes.

Solve each triangle. Round your answers to the nearest tenth.
show work If possible ​

Answers

Answer:

∠ABC = 76°

BC = 20.1

CA = 28.0

Step-by-step explanation:

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB  = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating that the sum of angles of a triangle is equal to 180°.

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> [tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]

=> [tex]\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}[/tex]

Substitute the necessary values

[tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]      ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

[tex]\frac{sin60}{25} = \frac{sin44}{BC}[/tex]

Cross multiply

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = [tex]\frac{17.3675}{0.8660}[/tex]

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

[tex]\frac{sin60}{25} = \frac{sin76}{CA}[/tex]

Cross multiply

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = [tex]\frac{24.2575}{0.8660}[/tex]

CA = 28.01

=> CA = 28.0 to the nearest tenth

If you are given a parallelogram with the top right and left corners each measuring 72* and the bottom right corner measuring 108*. What is the measurement of the missing corner, the bottom left corner of the parallelogram?

Answers

Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

Given

The top left and right corners measures [tex]72^{\circ}[/tex] and the bottom right corner measures [tex]108^{\circ}[/tex].

Suppose the missing corner measures [tex]x[/tex]

So, the sum of the four angles of parallelogram is [tex]360^{\circ}[/tex]

[tex]\therefore x+72^{\circ}+108^{\circ}+72^{\circ}=360^{\circ}\\\Rightarrow x=360^{\circ}-252^{\circ}\\\Rightarrow x=108^{\circ}[/tex]

Therefore, the missing angle is [tex]108^{\circ}[/tex].

A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (seconds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x

Answers

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x

A 20 ft. ladder is used against a 15 ft. wall. What is the measure of the angle made by the ladder and the ground (nearest whole degree)? How far is the ladder from the wall on the ground (to the nearest tenth)?

Answers

Step-by-step explanation:

Given that,

The length of a ladder, H = 20 feet

The height of the wall, h = 15 ft

We know that,

[tex]\sin\theta=\dfrac{h}{H}[/tex]

h is perpendicular and H is hypotenuse

So,

[tex]\sin\theta=\dfrac{15}{20}\\\\\theta=\sin^{-1}(\dfrac{15}{20})\\\\\theta=48.59^{\circ}[/tex]

Now using Pythagoras theoerm,

[tex]b=\sqrt{H^2-h^2}\\\\b=\sqrt{20^2-15^2}\\\\b=13.2\ ft[/tex]

Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.

A parabola is defined by the equation x2 = 3/4 y. In which direction will the parabola open?

Answers

I’m pretty sure it’s positive so a upward one that looks like :u

Write the equation of the line in slope-intercept form

Answers

Answer:

y = 4/1 + 0

Step-by-step explanation:

we rise 4 units up and move 1 unit to the right

and the y intercept is 0 because its exactly in the center of x and y axis

From 1980 to 1990 the consumer price index increased from 82.4 to 130.7 if a bottle of dish soap cost 0.74 in 1980 and the price of dish soap increased at the same rate as the cpi from 1980 to 1990 by approximately how much did the price of the bottle of dish soap increase from 1980 to 1990

Answers

Answer:

$0.43

Step-by-step explanation:

Rate of increase = [(CPI in 1990 / CPI in 1980)^1/t] - 1

(130.7 / 82.4)^1/10

1.586165^0.1 = 1.047213 - 1  = 4.72%

Price of dish soap in 1990 = value in 1980 ( 1 + rate of increase)^10

0.74( 1.047213)^10 = 1.174

Price increase 1.174 - 0.74 = 0.43

what is the value of X in the isosceles trapezoid below?

Answers

Solve using your rules:

180 = 9x + 4x + 37

That means 143 = 13x

Thus x = 11

Answer:

11

Step-by-step explanation:

What is -1.2 repeating as a mixed number​

Answers

Answer:

[tex]-1\frac{2}{9}[/tex]

Step-by-step explanation:

         _

y = - 1.2

                 _

y × 10 = - 1.2 × 10

                _

10y = - 12. 2

                _

10y = - 12. 2

-         _

y = - 1.2

____________

9x = 11

9x ÷ 9 = 11 ÷ 9

[tex]x = -1\frac{2}{9}[/tex]

   _

- 1.2 = - 1 2/9

Simply
7p2 x 3p
14p4

Answers

Answer:

[tex]{ \tt{ = \frac{7 {p}^{2} \times 3p}{14 {p}^{4} } }} \\ = { \tt{ \frac{21 {p}^{3} }{14 {p}^{4} } }} \\ = { \tt{1.5 {p}^{ - 1} }}[/tex]

Find the average rate of change (-4,-7)(-2,3)

Answers

The average rate of change is m=5.
Hope this helped.

Match each vertex in ABC to its corresponding vertex in the dashed triangle.

Answers

A -> A

B -> E

C -> D

Theyre similar triangles, ABC = AED

The corresponding vertex of the similar triangles are

A ≈ A

B ≈ E

C ≈ D

The triangles ABC and AED are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ABC

Let the second triangle be represented as AED

The measure of AB = 3

The measure of AD = 8

The measure of AC = 4

The measure of AE = 6

Now , for the similar triangles , corresponding sides of similar triangles are in the same ratio

So ,

AB / AE = AC / AD

Substituting the values in the equation , we get

3/6 = 4/8

1/2 = 1/2

Therefore , the triangles are similar

Hence , the triangles ABC and AED are similar triangles

To learn more about similar triangles click :

https://brainly.com/question/29378183

#SPJ2

if a:b=1:3 and b:c=5:8 what's a:c

need steps pls​

Answers

Answer:

a:c=1:8

Step-by-step explanation:

a:b=1:3

therefore a=1 and b=3

b:c=5:8

therefore b=5 and c=8

then,

a:c=1:8

Answer:

a : c = 5 : 24

Step-by-step explanation:

[tex]a : b = 1 : 3\\\\\frac{a}{b} = \frac{1}{3} \ => b = 3a\\\\b : c = 5 : 8 \\\\ \frac{b}{c} = \frac{5}{8} \ => \ \frac{3a}{c} = \frac{5}{8}[/tex]                  [tex][substituting \ b = 3a ][/tex]

                 [tex]\frac{a}{c} = \frac{5}{24}[/tex]

    [tex]=> a : c = 5 : 24[/tex]

What angle is Framed below
60​

Answers

Answer:

is there supposed to be an image?

have a good day :)

Step-by-step explanation:

What is the ordered pair for Point T?
A. (1,5)
B. (0,5)
C. (5,0)
D. (5, 5

Answers

Answer:

B.(0,5)

Step-by-step explanation:

Ordered pairs are written as (x,y)

x value of T is 0

y value of T is 5

Ordered pair for point T is (0,5)

examine the matrices below and use to answer questiom 12 and 13

x={3 -5} y= {6 7}
{-4 2} {-4 -3}



number 2 question
calculate x and y

A {9 12}
{0 1}

B {9 -12}
{0 -5}

c {9 -2}
{-8 -1}

D {9 2}
{-8 -1}

Answers

Answer:

d

Step-by-step explanation:

Which of the following is the area of a triangle pictured below

Answers

Answer:

(2) 22.44 cm^2

Step-by-step explanation:

A = bh/2

A = (8.8 cm)(5.1 cm)/2

A = 22.44 cm^2

Answer:

22.44 cm^2

Step-by-step explanation:

8.8 - 7.6 = 1.2

1.2 · 5.1 = 6.12 / 2 = 3.06

7.6 · 5.1 = 38.76 / 2 = 19.38

19.38 + 3.06 = 22.44 cm^2

Lisa invested $2500 in a bank account. The account has an annual interest rate of 3.5%. How much money will be in the account after 15 years? Use the formula A(t) = P*e^rt to solve the problem. (round to the nearest hundredth)​

Answers

Answer:

A = $ 4188.38

Step-by-step explanation:

A= $2500

r = 3.5% = 0.035

t = 15years

n = 1

     [tex]A = P(1 + r)^t[/tex]

        [tex]= 2500 ( 1 + 0.035)^{15}\\\\= 2500 (1.67535)\\\\= \$ 4188.38[/tex]

If the sum of the measures of 21 and 22 is 180°, what is the sum of the measures of 23 and 24?

Answers

Answer:

180

Step-by-step explanation:

it is a quadrilateral that has 360 degrees in total. So if 1 and 2=180 then 3 and 4=360-180=180. Hope this is right.....

Copy and complete the statement using < or >
-7 or -8

Answers

Answer: -7

Step-by-step explanation:

Well since where going below degrees the answer would be -7 because it is closer to 1

En un curso, el 40 % de los alumnos reprobó un examen. Si el curso tiene 45 alumnos. ¿Cuántos alumnos aprobaron

Answers

Answer:

Cantidad de aprobados= 25

Step-by-step explanation:

Dada la siguiente información:

Reproado= 45%

Aprobado= 55%

Cantidad de alumnos= 45 alumnos

Para calcular la cantidad de aprobados, debemos utiliar la siguiente formula:

Cantidad de aprobados= cantidad de alumnos*porcentaje aprobados

Cantidad de aprobados= 45*0.55

Cantidad de aprobados= 25

Answer this wuestion for me man

Answers

Answer:

The length of ribbon is [tex]\sqrt{32}[/tex].

Step-by-step explanation:

Length of the side of square = 4 inches

let the length of the diagonal is x.

By use of Pythagorean theorem

[tex]x^2 = 4^2 + 4^2 \\\\x =\sqrt {16 + 16}=\sqrt{32}[/tex]

Which of the following represents a constant from the expression given?

15x2 + 2x + 9

Answers

Answer:

9

Step-by-step explanation:

15x^2 + 2x + 9

A constant does not have a variable with it

15x^2 is the quadratic term

2x is the linear term

9 is a constant term

Answer:

The answer is 9.

someone already explained  it lol

I need help I’m stuck

Answers

The answer is b and have a nice day

What’s the answer????????????

Answers

Answer:33

Step-by-step explanation:

trust

what is the correct answer​

Answers

The Answer is:

A. x = 4

what is the algebraic expression for 12 times a number x, plus a second number y ?​

Answers

12x + y is the answer

Answer:

12x + y

Step-by-step explanation:

PLEASE ANSWER I NEED HELP SEE THE ATTACHMENT

Answers

Answer:

[tex]p=\frac{50}{360} 2\pi [8cm+(8-9)cm]+2(4.5cm)[/tex][tex]=19.0~cm[/tex]

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

hope it helps...

have a great day!!

Answer is 19cm I think
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