Congruent angle pairs : find value of x and the value of y

Answer:

α = 27.9794744° ≈ 28.0 m (nearest tenth)

Step-by-step explanation:

Step 1:

Opposite (O) = 42.5 (the side opposite to the reference angle, α)

Adjacent (A) = 80

Hypotenuse (H) = the longest side opposite to the right angle

2. We are given the adjacent (A) and opposite (O) lengths, we would use TOA. Which is:

Tan α = Opp/Adj

Plug in the values

Tan α = 42.5/80

3. Make α stand alone

α = [tex] tan^{-1}(\frac{42.5}{80}) [/tex]

4. α = 27.9794744° ≈ 28.0 m (nearest tenth)

Answer:

A.) Paul

B.) Plain

C.) Paul

Step-by-step explanation:

Paul: Shirt - Striped; Jumper - Spotted; Towel - Plain

Kerry: Shirt - Plain; Jumper - Striped; Towel - Spotted

Sandra: Shirt - Spotted; Jumper - Plain; Towel - Striped

Hope this helps! Have a nice dayy! :)

Answer:

a) 17

b) 21st term

Step-by-step explanation:

a) 20 - 3 = 17

b) 20 - 21 = -1

Answer:

r=42 degrees

This is because of vertically opposite angles

s=68

This is because 180( angles in a triangle) minus ( 70 + 42) is equal to 68 degrees

Answer:

r = 42° , s = 68°

Step-by-step explanation:

r and 42° are vertical angles and are congruent , then

r = 42°

The sum of the 3 angles in a triangle = 180° , then

s = 180° - (70 + 42)° = 180° - 112° = 68°

Answer:

(-2,4) radius = 2

Step-by-step explanation:

[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]

(h,k) point  r is the radius

Answer:

1,946,075.95 AED

Step-by-step explanation:

Firstly, we write the general formula for an exponential increase as follows;

V(t) = A( 1 + r)^t

where V(t) is the value after some number of years t

A is the investment amount which is 100,000 AED

r is the rate of increase which is 16% = 16/100 = 0.16

t is the number of years which is 20

substituting these values;

V(20) = 100,000( 1 + 0.16)^20

V(20) = 100,000(1.16)^20

V(20) = 1,946,075.95 AED

Answer:

365

Step-by-step explanation:

tn = t1 + (n - 1)(d)

t(47) = -3 + (47 - 1)(8)

t(47) = -3 + (46)(8)

t(47) = -3 + 368

t(47) = 365

Answer:

k=20t/a

Step-by-step explanation:

20t=ak

20t/a=k

k=20t/a

Answer:

h(5x) = 75x² + 7

Step-by-step explanation:

h(x) = 3x² + 7

h(5x) = 3(5x)² + 7

h(5x) = 3(25x²) + 7

h(5x) = 75x² + 7

[tex]h(5x) = 75x^2 + 7[/tex]

To find h(5x), you simply need to substitute 5x in place of x in the function [tex]h(x) = 3x^2 + 7[/tex] and then simplify the expression.

[tex]h(x) = 3x^2 + 7[/tex]

Now, replace x with [tex]5x: h(5x) = 3(5x)^2 + 7[/tex]

Simplify: [tex]h(5x) = 3(25x^2) + 7[/tex]

Now, calculate [tex]3 * 25: h(5x) = 75x^2 + 7[/tex]

So, [tex]h(5x) = 75x^2 + 7[/tex]

To know more about substitute:

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Answer:

He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots.

Step-by-step explanation:

He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots. The true factorized form of the fourth grade polynomial is:

[tex]r(x) = (x^{2}+1)\cdot (x^{2}-9)[/tex]

[tex]r(x) = (x- i)\cdot (x+i)\cdot (x+3)\cdot (x-3)[/tex]

Given:

The expression is:

[tex]13+23+12+7[/tex]

To find:

The value of the given expression by using Commutative and Associative properties of numbers.

Solution:

We have,

[tex]13+23+12+7[/tex]

Applying parenthesis and brackets, we get

[tex]=[13+(23+12)]+7[/tex]

[tex]=[13+(12+23)]+7[/tex]             [Commutative properties of numbers]

[tex]=[(13+12)+23]+7[/tex]             [Associative properties of numbers]

[tex]=(25+23)+7[/tex]

Using Associative properties of numbers, we get

[tex]=25+(23+7)[/tex]               [Associative properties of numbers]

[tex]=25+30[/tex]

[tex]=55[/tex]

Therefore, the value of the given expression 55.

Answer:

The domain: All real numbers.

The range: y>0

Step-by-step explanation:

Domain means all possible x values, and by looking at the graph it covers all real numbers.

Range means all possible y values, and since the x axis is a horizontal asyntope, the graph will never touch the x axis, which is why the range is y>0.  

Answer:

AngleRST and AngleRSV

Step-by-step explanation:

You first draw the diagram with statement given

Answer:

a) RTS & RSV b) RST & TSU d) TSU & USV

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i did the test

Answer:

a=3/2   b=-1 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

I still think your equations are wrong...

4000/4000 not 400/400 since the total investment is to be $8000

not $800

Step-by-step explanation:

2000 A+ 6000B=520

4000A+4000B        =480

~~~~~~~~~~~~~~~~~~~~~

2000 A+ 6000B=520

-2000A - 2000B   =-240  

4000B = 280

B=7%

A=5%

Answer:

[tex]3^x+5x+3[/tex]

Step-by-step explanation:

Given that,

[tex]f(x)=3^x+10x[/tex]

and

[tex]g(x)=5x-3[/tex]

We need to find (f-g)(x).

We know that,

(f-g)(x) = f(x)-g(x)

[tex]=3^x+10x-(5x-3)\\\\=3^x+10x-5x+3\\\\=3^x+5x+3[/tex]

So, the value of (f-g)(x) is [tex]3^x+5x+3[/tex].

Answer:

The literals are; a, b, and c

The constants are; c, and 3

The variables are; x, and y

Step-by-step explanation:

The literals (numbers) are letters which represent numbers in an expression or equation, and to which mathematical operations, including, addition, subtraction, division, and multiplication can be applied

The given equation is a·x² + b·x + c - y + 3 = 0

The literals are;

'a', 'b', and 'c'

The constants are the values that remain the same always in an equation and does not change

The constants are;

'c', and '3'

The variables are the values that vary in relation to one another

The variables are;

'x', and 'y'

Answer:

the first option on the screen

Answer:

We know that the lateral area of any prism is the sum of the areas of its side faces. Thus, the lateral area of a triangular prism is the sum of the side faces, that is the three rectangular faces. The formula to find the lateral area of a triangular prism is, (a + b + c) h or Ph.

so

20×6= 120 sq in

Answer:

120 sq in.

Step-by-step explanation:

LA = ah

LA = 20 × 6

A = 120

Answer:

b.

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

(c)

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

Step-by-step explanation:

b. The volume of solid formed is given by the washers formula as follows;

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

Therefore, we have, the integral expression whose solution is the volume formed by rotating 'R', about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is given as follows;

[tex]V = \pi \cdot \int\limits^\pi_0 {\left([2 + cox(x)]^2 - [csc(x)]^2} \right) \, dx[/tex]

(c)  We have;

x = arcos(y - 2), x = arcsin(1/y)

At x = 0, y = 2 + cos(0) = 3

csc(0) = ∞

At x = π, y = 2 + cos(π) = 2 + -1 = 1

csc(π) = ∞

Therefore, we get;

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

B) An equation that involves integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis is;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) An equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x= -1 is;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

B) The volume of solid formed is gotten from applying the washers formula;

[tex]V = \pi \int\limits^a_b ({[f(x)]^{2} - [g(x)]^{2}}) \, dx[/tex]

This means that the integral expression whose solution is the volume formed by rotating R about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is expressed as;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) From answer above, we have;

x = cos⁻¹(y - 2), x = sin⁻¹(1/y)

Now,

At x = 0; y = 2 + cos(0) = 3

csc(0) = 1/0 = ∞

Also,

At x = π; y = 2 + cos(π)

y = 2 + (-1)

y = 1

Also, csc(π) = ∞

Thus, we have;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

Read more about finding the integral volume of solid at; https://brainly.com/question/21036176

Answer:

You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.

Example look at the pic please 7,225 cm = ___ m

Meters are larger than centimeters, so you expect your answer to be less than 7,225.

Using the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to m.

Cancel similar units, multiply, and simplify.

7,225 centimeters = meters

Answer:

Sample Response: If you move from smaller to larger units, divide by a power of 10 or move the decimal to the left. If you move from larger to smaller units, multiply by a power of 10 or move the decimal to the right.

Answer:

515,857,549,048

Step-by-step explanation:

I guess you are to write in numerals

Five hundred fifteen billion = 515,000,000,000

eight hundred fifty-seven million = 857,000,000

five hundred forty-nine thousand = 549,000

forty-eight = 48

Total = 515,000,000,000 + 857,000,000 + 549,000 + 48

= 515,857,549,048

Therefore,

Five hundred fifteen billion, eight hundred fifty-seven million, five hundred forty-nine thousand, forty-eight = 515,857,549,048

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are acute, scalene, obtuse, equilateral, isosceles and right angled triangle.

For a right angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the square of the remaining two sides.

For an obtuse triangle, the square of the longest side is greater than the sum of the square of the remaining two sides.

For an acute triangle, the square of the longest side is less than the sum of the square of the remaining two sides.

In triangle JKL:

J² + L² = 3² + 4² = 25

K² = 6² = 36 > 25 (J² + L²)

Hence triangle JKL is an obtuse triangle

In triangle XYZ:

X² + Y² = 4² + 4² = 32

Z² = 5² = 25 < 32 (X² + Y²)

Hence triangle XYZ is an acute triangle.

Answer:

obtuse & acute

Step-by-step explanation:

Answer:

= 24 3/4x

Step-by-step explanation:

3* 8 1/4x

Here 8 1/4 is a mixed fraction.

Convert it to improper fraction

8 1/4 = 33/4

So, 3*33/4 x

99/4 x

= 24 3/4x

That is

Hope this will helpful.

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Answer:

1 degree c

Step-by-step explanation:

Answer:

if you like please mark me brainlaist

Step-by-step explanation:

thanks

Answer:

[tex]3ft^2[/tex]

Step-by-step explanation:

SA = [tex]6a^{2}[/tex]        

SA = [tex]6(3)^2[/tex]      Solve for the exponent first

SA = 6(9)       Multiply

SA = 54 square feet