Simplify the following surd expressions-

Domain is basically an input while Range is an output. Domain is the set of all x-values while Range is the set of y-values.

[tex]\large \boxed {domain} = > \large \boxed{range}[/tex]

From input to output. That means from if we substitute domain in the equation, we would get range.

[tex]f(x) = 4x + 2 \\ f(0) = 4(0) + 2 = 0 + 2 = 2 \\ f(3) = 4(3) + 2 = 12 + 2 = 14 \\ f(6) = 4(6) + 2 = 24 + 2 = 26[/tex]

We input the value of x that are given and we get the value of f(x) which is the output at the specified domain.

[tex] \large \boxed{2, 14, 26}[/tex]

Answer:

The length of the first piece is 0.51 m

The length of the second piece is 0.31 m

The length of the third piece is 0.28 m

Step-by-step explanation:

The question is a simultaneous equation with word problem

The total length of the wood = 0.9 m

The number of pieces the wood is cut into = 3

The length of the first piece = 0.2 m + The length of the second piece

The length of the third piece = The length of the second piece - 0.23 m

Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;

x = 0.2 + y...(1)

z = y - 0.23...(2)

x + y + z = 0.9...(3)

Therefore, by substitution, we have;

0.2 + y + y + y - 0.23 = 0.9

3·y - 0.03 = 0.9

3·y = 0.9 + 0.03 = 0.93

y = 0.93/3 = 0.31

y = 0.31

The length of the second piece = y = 0.31 m

From equation (1), we have;

x = 0.2 + y = 0.2 + 0.31 = 0.51

x = 0.51

The length of the first piece = x = 0.51 m

From equation (2), we have;

z = y - 0.23

z = 0.51 - 0.23 = 0.28

z = 0.28

The length of the third piece = z = 0.28 m.

Answer:

Choice 2 and 4 should be the answer

Step-by-step explanation:

For choice 2: both started away from home and finished at home.

For choice 4, Peter is farther away from home than Camilla, but they reached home at the same time which proves that Peter is faster.

Answer:

47/24

Step-by-step explanation:

24x1 = 24

24+23 = 47

47/24

Answer:

47/24

Step-by-step explanation:

just add 24 to the 23 and you'll get your answer.

Answer:

60 degress

Step-by-step explanation:

How I got it:

1. Find out the angel of each side. 360 divded by 6 = 60

2. Get the answer of 60

Advice:

-Make an polygon using paper and rotate it. (Use protractor and ruler if your gonna do it)

Answer:

the answer will be a because its on top of it

Answer:

E, I hope this helps :D

Answer:

34

Step-by-step explanation:

Answer:

x=34

Step-by-step explanation:

2x=x+34

-x   -x

x=34

TADA! :D

Answer:

Step-by-step explanation:

b/c this is an isosceles triangle  we know that either leg is the same length.. so we can use many trig functions  :)

SOH CAH TOA to remember how trig functions fit on the triangle...

we know the hypotenuse and the angle and we want to find the adjacent leg ( which for this triangle is also the opposite leg )

use Cos = Adj / Hyp

Hyp*Cos(45) = adj

16* [tex]\sqrt{2}/2[/tex] = adj

8*[tex]\sqrt{2}[/tex] = adj

each leg is the same  [tex]8\sqrt{2}[/tex]

Answer:

D

Step-by-step explanation: So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

Answer:

The product of a rational number and an irrational number is irrational.

Step-by-step explanation:

The product of a rational number and an irrational number is irrational. For example, let p= 1 be a rational number and q= 3.567be an irrational number if multiplied together the result would be 3.567, which is an irrational number.

Hope this helped!

Answer:

mark of the fifth exam = 60

Step-by-step explanation:

Mean = sum of all marks / number of exam

Mean = 70

Number of exam = 5

Let x =

Mean = sum of all marks / number of exam

70 = (65 + 80 + 76 + 69 + x) / 5

Cross product

70 × 5 = (290 + x)

350 = 290 + x

350 - 290 = x

x = 60

mark of the fifth exam = 60

Answer:

x = -0.22   or x = -2.28

Step-by-step explanation:

2x^2 + 5x + 1 = 0

You use the quadratic formula: -b ±√5² - 4 x 2 x 1 ÷ (2 x 2)

-5 +√17 ÷ 4 = -0.22

-5 - √17 ÷ 4 = -2.28

Answer:

160

Step-by-step explanation:

the length betwenn side to side woukd be 160

Answer:

The answer is 100

Step-by-step explanation:

a² + b² = c²

80²+60²=c²

6,400+1,200=c²

√6,400=√c²

subtract 1,200 - 6,400= 5,200

c2=72.1

Answer:

here you go I hope this is right

Answer:

x-intercept: -1/7

y-intercept: 1/4

Step-by-step explanation:

change equation into standard form:  7x - 4y = -1

set 'x' to zero and solve for y:  0 - 4y = -1

                                                        y = 1/4

set 'y' to zero and solve for x:  7x - 0 = -1

                                                        x = -1/7

Answer:

[tex]y=1/3x[/tex]

Step-by-step explanation:

It's positive, and it goes up once for every three times it goes to the right.

Answer:

192 in 2. multiply all of the numbers together

Step-by-step explanation:

6x4x8=192

Answer:

false, true and false

Step-by-step explanation:

Answer:

The image if the point is (-7, -9)

Step-by-step explanation:

∵ The given point is (9, -7)

∴ x = 9 and y = -7

∵ The given point is rotated 270° counterclockwise about the origin

→ By using the third rule above

∴ The image of the point is (y, -x)

→ That mean change the sign of x-coordinate, then switch them

∵ x = 9 and y = -7

∴ The image if the point is (-7, -9)

Answer:

65-n

Step-by-step explanation:

"less than" means you will subtract the second number by the first, therefore 65 less than a number is 65-n.

Answer:

1/4 of ur pens

Step-by-step explanation:

Answer:

The first angle is the smallest

Step-by-step explanation:

Step one:

given data

Angle 1= x+37

Angle 2= 90

angle 3= x+67

We know that the sum of angle in a triangle is 180

so

x+3+90+x+67= 180

collect like terms

2x+160= 180

2x=180-160

2x= 20

divide both sides by 2

x= 10

Step two:

so

Angle 1= 10+37= 47 °

Angle 2= 90= 90

angle 3= 10+67= 77 °

Answer:

B. [tex]y= \left \{ {{x^{2}+4,\,x< 2 } \atop {-x+4,\,x \ge 2}} \right.[/tex]

Step-by-step explanation:

The piecewise function consists in two functions:

(i) A vertical parabola directed in the +x direction and centered at [tex]V(x,y) = (0, 4)[/tex] for all [tex]x \in (-\infty, 2)[/tex]. That is:

[tex]y = x^{2}+4[/tex], [tex]x < 2[/tex]

(ii) A line with negative slope for all [tex]x \in [2, +\infty)[/tex].

[tex]y = -x+4[/tex], [tex]x \ge 2[/tex]

The correct answer is B.