Convert 2 centimeters into feet. Round your answer to the nearest hundredth.

Answer:

[tex]y = \frac{1}{2}x +2[/tex]

Step-by-step explanation:

From the table of function given, you would observe that if you subtract 2 from half of the x-variable values, you'd get the y-variable values.

For example, half of -8 = -4. If you add 2 to -4, you'd get: -4 + 2 = -2. Same applies to other x-values on the table.

Thus, an expression for the function represented by the table values can be written as,

[tex]y = \frac{1}{2}x +2[/tex]

Answer:

10 times.

Step-by-step explanation:

We need to find that the value of 3 in 546300 is how many times more than 3456.

The place value of 3 in 546300 is 300 and the place value of 3 in 3456 is 3000.

Now dividing 3000 by 300 as follows :

[tex]\dfrac{3000}{300}=10[/tex]

It means that the value of 3 in 546300 is 10 times more than the value of 3 in 3456.

Answer:

[tex]-|9|[/tex]   and [tex]-|-9|[/tex]

Step-by-step explanation:

Given

Expression = -9

Required

Select all equivalent expressions

To do that, we examine each of the options.

First Option

[tex]-|9|[/tex]

This can be rewritten as

[tex]-|9| = -1 * |9|[/tex]

[tex]|9| = 9[/tex]

So, the expression becomes

[tex]-|9| = -1 * 9[/tex]

[tex]-|9| = -9[/tex]

Hence, |-9| is equivalent to -9

Second Option

[tex]|-9|[/tex]

[tex]|-9| = 9[/tex]

So, the expression is not equivalent to -9

Third Option

[tex]-|-9|[/tex]

This can be rewritten as

[tex]-|-9| = -1 * |-9|[/tex]

[tex]|-9| = 9[/tex]

So, the expression becomes

[tex]-|-9| = -1 * 9[/tex]

[tex]-|-9| = 9[/tex]

Hence, -|-9| is equivalent to -9

Fourth Option

[tex]-(-9)[/tex]

This can be rewritten as

[tex]-(-9) = -1 *(-9)[/tex]

[tex]-(-9) = -1 *-9[/tex]

[tex]-(-9) = 9[/tex]

Hence, -(-9) is not equivalent to -9

Fifth Option

The distance from 0 to 9

This is calculated as thus;

[tex]Difference = 9 - 0[/tex]

[tex]Difference = 9[/tex]

Hence, the difference from 0 to 9 is not equivalent to -9

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use tan

tan∅ = opposite/ adjacent

From the question

x is the opposite

10 is the adjacent

Substitute the values into the above formula and solve for x

That's

[tex] \tan(20) = \frac{x}{10} [/tex]

x = 10 tan 20

x = 3.63970

We have the final answer as

Hope this helps you

Answer:

23

Step-by-step explanation:

18+5=23

The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

A line section that can connect two places is referred to as a segment.

As per the given line segment, AC and CD have been drawn below,

Since, AD = AC + CD

AD = 18 + 5 = 23

Hence "The value of AD for the given line segment such that AC = 18 and CD = 5 will be 23".

For more about line segments,

https://brainly.com/question/25727583

#SPJ2

Answer: $428.00

Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.

Answer:

So how many days do we need to solve for?

Step-by-step explanation:

Answer:

608 squared centimeters.

Step-by-step explanation:

To find the surface area of the net of the triangular prism, we can find the area of each individual shape and add them up.

For the net, we have 3 rectangles and 2 (congruent) triangles.

The left rectangle has a length of 16 and a width of 10. Thus, it's area is A=16(10)=160 squared centimeters.

The middle rectangle has a length of 16 and a width of 12. Thus, it's area is A=16(12)=192 squared centimeters.

The right rectangle has a length of 16 and a width of 10. Thus, it's area is identical to the left rectangle. It's area is 160 squared centimeters.

Now, for the two triangles, it's important to note they are the congruent since they belong to one triangular prism. Thus, we only need to figure out the area of one and then multiply by 2 to get the area of both of them.

One triangle has a base length of 12 and a height of 8. In other words, its area is (1/2)(12)(8)=48. Two of them will be 48(2) or 96.

Now, let's add all the areas together to find the surface area of the triangular prism. Thus, the area is:

96+160+160+192=608 squared centimeters.

Answer:

608 cm^2

Step-by-step explanation:

Find the area of the large rectangle

length is 10+12+10 = 32 and width is 16

A = 32*16 =512 cm^2

Then we have 2 triangle

The area of 1 is

A = 1/2 bh where b = 12 and h = 8

A = 1/2 ( 12 *8)

 = 1/2 (96)

But we have 2 triangles

2 * 1/2 (96)

96 cm^2

Add the area of the large rectangle and the two triangles

512+96 =608 cm^2

Answer:

Lol hi emelio

Step-by-step explanation:

Answer:

The piecewise function would be as follows :

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Step-by-step explanation:

This piecewise function is composed of one segment, and a ray. Let's start by identifying the properties of this segment.

Segment : As you can see the segment extends from 0 to 2 on the x - axis. This is at y = 25. Therefore our first expression would be 'C(g) = 25 at {0 < g < 2}.'

Ray : As this is ray, we have C(g) = 10g, as the slope is apparently 10. As you can see the rise is 10, over a run of 1, given the points (2, 25) and (3, 35) lie on the plane. The ray starts at the coordinate (2, 25), leaving us with the inequality g > 2.

So now that we have the expressions 'C(g) = 25 at {0 < g < 2}' and 'C(g) = 10g at {g > 2}' we can combine them to create the following piecewise function,

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Answer:

331.52 ounces

Step-by-step explanation:

For this problem, we need to know the conversion from gallon to ounces.  The conversion is for every one gallon, there are 128 ounces.  Using this, we simply will perform the conversion.

2.59 Gallons * ( 128 ounces / 1 Gallon) == 331.52 ounces

So in 2.59 gallons, there are 331.52 ounces.

Cheers.

Answer:

C

Step-by-step explanation:

We know that A is not true because the angle is formed by rays, not line segments. We know this because the ends of the lines are arrowheads, which indicates that they are rays. You might be saying that A is true because BA and BC form the angle but actually, even if you removed points A and C, you would still have the angle. B is not correct because according to the diagram, the vertex is point B, not point A. The vertex of an angle is the common endpoint of the two rays that form the angle, therefore it would be point B. D is not correct because angles can have multiple names, the letters do not have to be in alphabetical order. Therefore, C is correct.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(2 + i)(i + 2i)}[/tex]

Use the distribute property to multiply each term of the first binomial by each term of the second binomial.

⇒[tex] \sf{2(i + 2i) + i(i + 2i)}[/tex]

⇒[tex] \sf{2i + 4i + {i}^{2} + 2 {i}^{2} }[/tex]

Collect like terms

⇒[tex] \sf{3 {i}^{2} + 6i}[/tex]

Hope I helped!

Best regards!

Answer: Hi!

121 ÷ 3 = 40.3

987 ÷ 9 = 109.7

675 ÷ 5 = 135

432 ÷ 7 = 61.7

Hope this helps you!

Answer:

40 1/3

109 2/3

135

61.7

Step-by-step explanation:

Hey there!

Well lets divide all given expressions,

121 ÷ 3 = 40 1/3

987 ÷ 9 = 109 2/3

675 ÷ 5 = 135

432 ÷ 7 = 61.7 rounded to the nearest tenth

Hope this helps :)

Answer:

x = 18

Step-by-step explanation:

ΔABC ≅ ΔDEC

∠ B ≅ ∠E

40 = 2x + 4

-2x = 4 - 40

-2x = -36

2x = 36

x = 36/2

x = 18

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{a}{9} = - 4}[/tex]

Apply cross product property

⇒[tex] \sf{a = - 4 \times 9}[/tex]

Multiply the numbers

⇒[tex] \sf{a = - 36}[/tex]

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(0,5) and (8,0)

So the distance between them is

d = 9.4339811

We have the final answer as

Hope this helps you

Answer:

Answer: {4,5}. 13) ∪ . Put the sets together in one large set. {1,2,3,5} ... {2,3,1,5}. There are no duplicates to remove, but I can write this in a nicer order.

Step-by-step explanation:

Answer: 93 and 4/5

Step-by-step explanation:

6 7/10 divided by 1/14

= 67/10 divided by 1/14

= 67/10 x 14/1

= 67/5 x 7/1

= 469/5

Answer:

[tex]\huge \boxed{8t + 56}[/tex]

Step-by-step explanation:

[tex]8(7 + t)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]8(7) + 8(t)[/tex]

[tex]56 + 8t[/tex]

Answer:

4×(-5)=-20

Step-by-step explanation:

Answer:

[tex]\huge \boxed{-20}[/tex]

Step-by-step explanation:

[tex]4*(-5)[/tex]

[tex]\Rightarrow 4* -5[/tex]

Multiplying.

[tex]\Rightarrow -20[/tex]

Answer:

0

Step-by-step explanation:

First, simplify for both sides

6/15 -> 2/5

2/5 -> 2/5

x+2/5 = 2/5

Subtract 2/5 from each side.

(x+2/5)-2/5-> x

2/5-2/5 -> 0

x = 0

Answer:

We conclude that the population mean is greater than 10.

Step-by-step explanation:

The complete question is: A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis [tex]H_0= \mu \leq 10[/tex] and [tex]H_A=\mu >10[/tex].

We are given that a random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3.

Let [tex]\mu[/tex] = population mean

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq 10[/tex]    {means that the population mean is less than or equal to 10}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 10    {means that the population mean is greater than 10}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 12

             s = sample standard deviation = 3  

            n = sample of observations = 10

So, the test statistics =  [tex]\frac{12-10}{\frac{3}{\sqrt{10} } }[/tex]  ~  [tex]t_9[/tex]

                                    =  2.108  

The value of t-test statistics is 2.108.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean is greater than 10.

Answer:

Approximately 36.5885

Approximately 4.2426

Step-by-step explanation:

Please reference the drawing I've provided (sorry it's kind of awful. Drawing on a computer is hard :(

Problem 1)

So, the trapezoid can be split into a right triangle and a rectangle. To find the perimeter, we just need to find all the side lengths and add them.

We already know the dimensions of the rectangle. So, we need to find the dimensions of the right triangle.

We know that the height is 9 since it's opposite to the rectangle. Importantly, we know that the angle opposite to 9 is 60°.

This means that the other angle is 30°. So, the right triangle is a "special right triangle." In the 30-60-90 triangle, the hypotenuse is 2x, the side opposite to 60° is x√3, and the side opposite to 30° is x.

So, we know that 9 is the side opposite to 60°. Substitute and solve for x:

[tex]9=x\sqrt{3}\\ x=\frac{9}{\sqrt{3} } \\ x=\frac{9\sqrt3}{3}=3\sqrt3[/tex]

So, x is 3√3. This means that the side opposite of angle 30 or d is 3√3.

And since x is 3√3, this means that the hypotenuse is 2(3√3) or 6√3.

Therefore, the perimeter of the figure would be:

[tex]9+6+6+3\sqrt3+6\sqrt3\\=21+9\sqrt3\\\approx36.5885[/tex]

Problem 2:

For the bookcase, we simply need to find the value of c.

The braces that will be built is simply the hypotenuse of the right triangles. Therefore:

[tex]a^2+b^2=c^2\\[/tex]

Plug in 3 for a and b:

[tex]3^2+3^2=c^2\\c^2=9+9=18\\c=\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt2\approx4.2426[/tex]

Therefore, each of the braces will be approximately 4.2426 feet long.

Edit: Grammar

Answer:

The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

Step-by-step explanation:

Let x represent the number of  1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. Each of 1 point free throw is 1 point, each of 2 point free throw is 2 points and each of the 3 point free throw is 3 points. This is represented by the equation:

x + 2y + 3z = 33             (1)

Also, The player scored 17 times, therefore it is represented by:

x + y + z = 17                   (2)

The player scored  3 more 2-point field goals than 1-point free throws, it is represented by:

y = x + 3                      

-x + y = 3                         (3)

Solving equation 1, eqn 2 and eqn 3 simultaneously:

x = 5, y = 8, z = 4.

The number of 1 point throw is 5, the number of 2 point throw is 8 and the number of 3 point throw is 4

Answer:

No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

Step-by-step explanation:

Equations : x + y + z = 17 [ Total times taken to score ]

1x + 2y + 3z = 33 [ Total Score ]

Also, y = x + 3

Putting the value of 'y' in both equations :

x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

Solving these equations :

From (i), z = 14 - 2x

Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

42 - 3x = 27 → 3x = 15 → x = 5

y = x + 3 = 5 + 3 → y = 8

z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

Let's take as x and y the age of the man and of his son

We will do a system, so we can satisfy all the request:

1. sum of ages = 2 (difference)

2. product = 675

[tex]\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.[/tex]

semplify the first equation

x + y = 2x -2y

now let's choose one of the incognite (x) and we solve for it

x - 2x = - 2y - y

- x = - 3y

x = 3y

Let's substitute this solution in the second equation

[tex]\left \{ {x=3y} \atop {(3y)*y=675}} \right.[/tex]

note: x = 3y, so in the second equation x * y = 3y * y

Now let's solve the second equation

3y * y = 675

3y² = 675

y² = 675 / 3 =

y² = 225

y = 15

Son's age is 15

Man's age is 15 * 3 = 45 (See the first equation [x = 3y])

Complete Question

Apabila a =2 b = 3 dan c =12 tentukan nilai dari bentuk :

a⁶× b⁴ × c²

(ab)² ×c³

Answer:

1) a⁶× b⁴ × c² = 746496

2) (ab)² ×c³ = 62208

Step-by-step explanation:

a =2, b = 3, c =12

a) a⁶× b⁴ × c²

2⁶× 3⁴ × 12²

= (2 × 2 × 2 × 2 × 2 × 2) × (3 × 3 × 3 × 3) × (12 × 12)

= 64 × 81 × 144

= 746496

b) (ab)² ×c³

(2 × 3)² × 12³

= 6² × 12³

= (6 × 6 )× (12 × 12 × 12)

= 36 × 1728

= 62208