Select all pairs of complementary angles in the diagram.

The solution to the given system of equations is the point (1, 5).

Here we have the system of equations:

g(x) = 3x + 2

f(x) = |x - 4| + 2

To solve this, first you can see where the graphs intercept on the graph (the intercept point is the solution to the system)

But we can also solve it analytically. To do it, we have:

g(x) = f(x)

3x + 2 =  |x - 4| + 2

3x =  |x - 4|

Notice that the only solution of the above equation is x = 1, so we know that it is the x-value of the solution.

To get the y-value, we just evaluate one of the two given functions on x = 1.

f(1) = |1 - 4| + 2= 3 + 2 = 5

Then the solution to the system is the point (1, 5).

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The number of tiles (y) at any x stage is given by the equation y = 2x - 1

An equation is an expression that shows the relationship between two or more variables and numbers.

From the table, the number of tiles increases by 2 for every additional stage. Let y represent the number of tiles and x represent the stage, hence:

y = 1 + (x - 1)2

y = 2x - 1

The number of tiles (y) at any x stage is given by the equation y = 2x - 1

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Answer:

C

Step-by-step explanation:

Use the pythagorean theorem.

32^2+b^2=48^2

1024+b^2=2304

Subtract 1024

b^2=1280

Square root

b=sqrt(1280)

Now simplify sqrt(1280)

sqrt(1280) = sqrt(256*5)

You can take the square root of 256 since it is a perfect square so take it out of the radical.

sqrt(256*5)=16sqrt(5)

So the answer is c, 16[tex]\sqrt{5}[/tex]

Answer:

C. 16/5

Step-by-step explanation:

pythagorean theorem

a^2 + b^2 = c^2

divide 48 and 32 by 16

a= 2 c= 3

4 + b^2 = 9

b^2 = 5

b = √5

then multiply 16 with √5

which =

16√5

Answer:

Step-by-step explanation:

Kiran can know for sure that it is incorrect by substituting x with 1/4

Solving for the equation gives 4(1/4 + 3) = 7
distributing gives 1 + 3 = 7
obviously this is incorrect

b)
Andre's error is that he didnt distribute 7
Distributing 7 results in
4x + 12 = 7
then subtracting 12 from both sides
4x = -5
x = -5/4

Answer:

x=-1.25

Step-by-step explanation:

well he was wrong about the 4x = 1.

4(x+3)=7

4x+12=7    1. - 12 on both sides

4x=-5   2. 4 on both sides

x=-1.25

Answer:

increase of 300%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hypotenuse: This the longest side of right angle triangle and it is opposite to 90°

[tex]1) Sin \ P = \dfrac{Oppossite \ side \ of \ \angle P}{hypotenuse}\\\\ =\dfrac{4\sqrt{10}}{14}[/tex]

[tex]Cos \ P =\dfrac{adjacent \ side \ of \angle P}{hypotenuse}\\=\dfrac{6}{14}[/tex]

[tex]7)\sf Cos \ X = \dfrac{adjacent \ side \ of \angle X}{hypotenuse}\\\\Cos \ X =\dfrac{8}{18}\\\\Cos \ X = 0.4\\\\X = Cos^{-1} \ 0.4[/tex]

X = 66°

8) Here, opposite side is given and we have to find hypotenuse. So, use Sin.

[tex]Sin \ 65 =\dfrac{10}{x}\\\\0.9 *x = 10\\\\x =\dfrac{10}{0.9}[/tex]

x = 11.1

10) Here, opposite side is given and we have to find hypotenuse. So, use Sin to find x

[tex]Sin \ X =\dfrac{6}{9}\\\\Sin \ X = 0.67\\\\x= Sin^{-1} \ 0.97[/tex]

x = 42°

Answer:

8(5+8)

Step-by-step explanation:

The GCF of 40 and 64 is 8. Then you divide 40 and 64 by 8.

B) 153 yd²

hope this helps :)

Answer:

A: y=-2x-2

B: y=-2x+2

Step-by-step explanation:

Answer:

2 to 6, 2/6, or 2:6

Step-by-step explanation:

a ratio is a comparison of two values expressed as a quotient

There were 16 total players at the baseball game of which 12 of the players chose a bottle of water.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let p represent the total number of players, 2 of the players chose a bottle of water which accounted for 3/4 of the total players, hence:

(3/4)p = 12

p = 16

There were 16 total players at the baseball game.

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The factors of the expression are [tex]\rm (4x+1)(-2x^2-3)[/tex]

First group the first two terms and the last two terms together respectively.

The factors of the expression are given by;

[tex]\rm -8x^3 -2x^2 - 12x - 3\\\\-2x^2(4x+1)-3(4x+1)\\\\(4x+1)(-2x^2-3)[/tex]

Hence, the factors of the expression are [tex]\rm (4x+1)(-2x^2-3)[/tex].

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product of two perpendicular line slopes must equals - 1 ;

As you know the coefficient of x is the slope of the line

Thus if we suppose that line has a slope of m , we have :

m × 2 = - 1

m = - 1 / 2

__________________________________

y = ax + b

y = - 1 / 2 x + b

The line passes through the point ( - 2 , - 2 ) thus :

- 2 = - 1 /2 × ( - 2 ) + b

- 2 = 1 + b

b = - 3

__________________________________

y = - 1/2 x - 3

Which mean the option c is the correct answer.

Answer:

y = -1/2(x) - 4

Step-by-step explanation:

[tex]y=-\frac{1}{2}(x)-4[/tex]

Area of top rectangle

Area of horizontal rectangle (Left):-

Area of right rectangle:-

Area of triangle:-

Total:-

Answer:

6

Step-by-step explanation:

if you plug in and add it all up you get 6

[tex] \mathcal{SOLUTION: }[/tex]

Therefore, the value of 6! is 720.

━┈─────────────────────┈━

[tex] \mathcal{SOLUTION: }[/tex]

Therefore, the value of the given expression is 12.

━┈─────────────────────┈━

ฅ^•ﻌ•^ฅ

_______________∞_______________

Answer:

I believe 6in squared is the correct answer

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

6*?=24 in

6*4=24in

if it is 3 in on the smaller one, it also will be 2 so it will be 6.

Answer:

13

Step-by-step explanation:

693/11 = 63 miles per hour

819/63 = 13

Formula for the circumference of a circle = pi x 2 x radius

Circumference = 3

pi = 3.14

radius = r

---To find the radius, we will need to solve for it. Start by plugging in what we know.

3 = 3.14 x 2 x r

---Simplify by multiplying 3.14 by 2

3 = 6.28 x r

---Divide both sides by 6.28 to solve for r

r = 3 / 6.28 = 0.4777

---Round the decimal to the nearest tenth

r = 0.5

Hope this helps!

r=0.5

Hope it helps.

Do comment if you have any query.

Answer:

when DAE is at 16° and EDC is at 64° then ABC is at 45° and BCD is at 55°.

Answer:

exponential equation

thia is the form of quadratic equation

Answer:

[tex]w = 10 \sqrt{2} [/tex]

[tex]y = 20[/tex]

Step-by-step explanation:

Use the Sine Rule to solve for the unknown sides.

A rectangle with proportions close to the Golden Ratio of approximately 1:1.618 is believed to be aesthetically pleasing.

A rectangle with sides that are in the golden ratio, or roughly 1:1.618, is referred to as a golden rectangle. This ratio has been employed in art, architecture, and design for ages since it is seen to be aesthetically beautiful.

To build a golden rectangle, start with a square and then add a smaller square to one of its sides to form a rectangle. The smaller rectangle is then used to repeat this procedure until you obtain a rectangle whose sides are in the golden ratio.

The layout of credit cards is one instance of a situation in real life that makes use of a golden rectangle. Golden rectangles are a popular shape for credit cards because of their attractive proportions and visual balance. A golden rectangle may also be used in credit card designs to help the card stand out from other cards and be simpler to recognize. The dimensions of several paintings, sculptures, and structures are more instances of how golden rectangles are used in the design.

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The expression that is equivalent to the given expression is 125y⁵.

The given expression is:

[tex]\frac{5y^{3} }{(5y)^{-2} }[/tex]

Some important power rules applicable to this problem are:

1)[tex](ab)^m=a^mb^m[/tex]

2)[tex]\frac{1}{a^{-n} } =a^n[/tex]

So, [tex]\frac{5y^{3} }{(5y)^{-2} } =\frac{5y^{3} }{5^{-2} y^{-2} }[/tex].....by power rule (1)

[tex]=(\frac{5}{5^{-2} } )(\frac{y^3}{y^{-2} })[/tex]

[tex]=5^3y^5[/tex].....by power rule(2)

[tex]=125y^5[/tex]

Hence, the expression that is equivalent to the given expression is 125y⁵.

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Answer:

Step-by-step explanation:

we are given A spinner has six equal-sized sections numbered 1, 1, 2, 2, 3, and 4 Sample space:

the sample space of an experiment or random trial is the set of all possible outcomes or results of that experimentso, we will only unique outcomesso, sample space is S={1,2,3,4}................Answer

Answer:

45.7% or if rounded, 46%

Step-by-step explanation:

1st, you add up the total of people in the House of Representatives.

238+201=439

Then divide the number of Democrats 201 by the total number 439 to get .457  which is 45.7% or if you need to round 46%

To double check, multiply the total number 439 X 45.7% to get 200.6

Answer:

The given shape is Trapezium

Area of Trapezium= 1/2h(L1+L2)

=1/2×7×(11+3

=1/2×7×14

=49

Your answer is 49

Answer:

Angle B = 24°

Step-by-step explanation:

Given:

that means, Angle A = 5 ( Angle B + 7.2 )

Now,

Let Angle B = x (say)

•.• Angle A = 5 ( x + 7.2 )

Therefore, As it is given that the angles are supplementary , the sum of Angle A and Angle B will be equal to 180°.

Angle A + Angle B = 180°

[tex]⇢x + 5(x + 7.2) = 180[/tex]

[tex]⇢x + 5x + 36 = 180[/tex]

[tex]⇢6x = 180 - 36[/tex]

[tex]⇢6x = 144[/tex]

[tex]⇢x = \frac{144}{6} [/tex]

Now, substituting the value of x. . .

Thus, Angle B comes out 24°