A box has a volume of 5m³. The box will be enlarged by a scale factor of 2. What will the volume of the new box be?

Answer:

a = 4,

b = 12

c = 10

d = 15

Step-by-step explanation:

Since the product of each column is equal, therefore,

b*5 = 60

b = 60 ÷ 5 = 12

c*6 = 60

c = 60 ÷ 6 = 10

Since the sum of each column are equal, therefore,

12 + 10 + a = 5 + 6 + d

22 + a = 11 + d

Think of a number you can add to 22, and another number you can add to 11, which will make both sides equal. Add both numbers, whenmultiplied together should give you 60.

Factors of 60 are:

(a, d)

(1, 60) => 22 + a = 11 + d => 22+1 = 11+60 (incorrect)

(2, 30) => 22 + a = 11 + d => 22+2 = 11+30 (incorrect)

(3, 20) => 22 + a = 11 + d => 22+3 = 21+20 (incorrect)

(4, 15) => 22 + a = 11 + d => 22+4 = 11+15 => 26 = 26 [CORRECT]

(5, 12) => 22 + a = 11 + d => 22+5 = 11+12 (incorrect)

(6, 10) => 22 + a = 11 + d => 22+6 = 11+10 (incorrect)

Therefore,

a = 4,

d = 15

Answer:

given,

base= 10

height= 8

now, area of triangle =

[tex] \frac{1}{2} \times b \times h[/tex]

or, area =

[tex] \frac{1}{2} \times 10 \times 8[/tex]

therefore the area of a triangle is 40 sq units.

hope its helpful..

Answer:

A, 40 sq.units

Step-by-step explanation:

Area of Triangle:   1/2·b·h

Substitute:  h= 8, b= 10

                  A = 1/2 (10)(8)

Simplify:   A = 1/2(80) = 40

Area= 40 sq. units

Answer:

The answer is 2 root 10.

hope it helps..

Answer:

x = ±2[tex]\sqrt{10}[/tex].

Step-by-step explanation:

40 - x^2 = 0

Subtract 40 from both sides

-x^2 = -40

Divide both sides by -1

x^2 = 40

Find the square root of both sides

x = ±[tex]\sqrt{40}[/tex]

x = ±[tex]\sqrt{2 * 2 * 2 * 5}[/tex]

x = ±[tex]\sqrt{2^2 * 2 * 5}[/tex]

x = ±2[tex]\sqrt{2 * 5}[/tex]

x = ±2[tex]\sqrt{10}[/tex]

Hope this helps!

Answer:

power index

Step-by-step explanation:

Prime factor index form is expression of a number as product of its prime number. Here the prime factor is listed only once. It is necessary to insert the required power index to solve for the HCF

Answer:

Thurka got 8 questions right and 4 wrong.

Step-by-step explanation:

Thurka got "x" questions right and "y" questions wrong, therefore the sum of these questions must be equal to the total number of questions in that exam, which would be 12, therefore:

[tex]x + y = 12[/tex]

Since for each right question Thurka got 5 marks and for each wrong one 2 marks, then the total score can be written as:

[tex]5*x - 2*y = 32[/tex]

Solving the system of equations would give us the number of right and wrong questions.

[tex]\left \{ {{x + y=12} \atop {5*x-2*y=32}} \right.[/tex]

[tex]\left \{ {{2*x + 2*y=24} \atop {5*x - 2*y=32}} \right.[/tex]

[tex]7*x = 56\\x = \frac{56}{7} = 8[/tex]

[tex]y = 12 - x = 12 - 8 = 4[/tex]

Thurka got 8 questions right and 4 wrong.

Answer:

y = 6

Step-by-step explanation:

You should always multiply by the easiest choice(which I see is multiplying the 7 and the 3 to get 21

7(9x + 3y = -18)

-3(8x + 7y = 10)

63x + 21y = -126

-24x -21y = -30

39x          = -156

and solve to get x = -4

then plug -4 into x any of the equations to get y = 6

( 8(-4) + 7y  = 10

  -32 + 7y  =  10

      7y = 42

        y = 6)

Answer:

The first equation should be multiplied by - 7 and the second equation by 3 .

Step-by-step explanation:

answer on edge

Answer:

AB ║ CD, reason If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel

Step-by-step explanation:

Statement,                                      Reason

Triangle ACD is isosceles,             Given

∠1 ≅ ∠3,                                           Given

∠3 ≅ ∠4,                                          Base angles of isosceles triangle

∠1 ≅ ∠4,                                           Substitution

∠1 and ∠4, are alt int. ∠s,                Definition

AB ║ CD,                                          Have congruent alternate interior angles

If two lines (AB and CD) and a transversal AD, form alternate interior angles, (∠1 and ∠4) that are congruent, then the two lines are parallel

The two-column proof that shows that Segment AB║Segment CD is shown in the image attached below (See attachment).

Given the image showing an isosceles triangle, ΔACD.

The two-column proof that shows segment AB || Segment CD has been provided in the table shown in the image attached below.

We know already that:

ΔACD is isosceles

∠1 ≅ ∠3

∠3 and ∠4 base angles of the isosceles triangle, therefore, ∠3 ≅ ∠4.

By substitution, ∠1 ≅ ∠4

∠1 and ∠4 are alternate interior angles, therefore, based on the Converse of Alternate Interior Angles Theorem: AB║CD

The complete two-column proof is in the image attached below.

Learn more about Alternate Interior Angles Theorem on:

https://brainly.com/question/19486848

Answer:

Step-by-step explanation:

The figures that come to a point (cone, pyramid) only have one base. The others have two:

  cylinder

  rectangular prism

  triangular prism

Answer:

B-cylinder

C-rectangular prism

E-triangular prism

Step-by-step explanation:

Got it right on edge unit test

Answer:

6 ft

Step-by-step explanation:

We can use ratios to solve

30 ft tall             x ft tall

------------------  = ------------------

10 ft shadow       2 ft shadow

Using cross products

30 * 2 = 10x

60 = 10x

Divide by 10

60/10 = 10x/10

6 =x

Answer:

An arrow that goes from 0 to negative 3 and from negative three to 4.5

Give me brainliest,5stars,and thanks plz!

Answer:

arrow goes from negative 3 to negative 1.5 and from 0 to negative 3

Step-by-step explanation:

Step-by-step explanation:

M(8.-2), M'(x,y) , [tex]$$\overrightarrow{v}[/tex] =(-5,1)

[tex]$$\overrightarrow{MM'} = $$\overrightarrow{v}[/tex]

--> x - 8 = -5 --> x= 3

---> y+2 = 1 --> y =-1

so M'(3,-1) and its reflection y-axis is (-3,-1)

The correct representation of given transformations is [tex]\bold{M(8,-2)\rightarrow M'(3,-1)\rightarrow M''(-3,-1)}[/tex]

"A translation is a geometric transformation where a geometrical figure is moved from one location to another location without changing its size, shape or orientation."

"A vector is a quantity or phenomenon that has magnitude and direction."

To find the vector from point P(a ,b) and Q(m, n)

[tex]\overrightarrow{PQ}= < m-a,n-b >[/tex]

We have been given that, the translation of M (8,-2) along vector<-5, 1 >

Let (x, y) represents the translated point along <-5, 1>

This means, <-5, 1> = <x-8, y-(-2)>

⇒ x - 8 = -5

⇒ x = -5 + 8

⇒ x = 3

Also, y + 2 = 1

⇒ y = 1 - 2

⇒ y = -1

So, the translated point is (3, -1)

The reflection of (3, -1) along y-axis is (-3, -1) .

Hence the correct representation of transformations is[tex]\bold{M(8,-2)\rightarrow M'(3,-1)\rightarrow M''(-3,-1)}[/tex] that is, option (C)

Learn more about geometric transformation here:

https://brainly.com/question/15222136

#SPJ2

Answer:

The answer is 2/10 :P

Step-by-step explanation:

We have To list all the possibilities first ! : 1 head, 2 head, 3 head, 4 head, 5 head, 1 tail, 2 tails, 3 tails, 4 tails and 5 tails ! ;)

We have in total 10 possibilities !

So if we want to work out the probability that she will get a 2 and a head, the answer has to be 2/10 because we have 10 possibilities !

I hope I helped you ! :P

Answer: C) $95

Step-by-step explanation:

4% is 4/100.  Thus, simply divide 3.80 by 4/100 to get $95.00.

Hope it helps <3

If you stretch on the y-axis then you are increasing/decreasing values at a every x.

The new function is therefore:

[tex]g(x)=3\cdot2^x[/tex]

Hope this helps.

Answer: D.) Cultural knowledge

Step-by-step explanation:

Answer:

solution,

Sum of exterior angles=360°

[tex]3x + 2x + 40 + 4x + x + 50 = 360 \\ or \: 3x + 2x + 4x + x + 40 + 50 = 360 \\ or \: 10x + 90 = 360 \\ or \: 10x = 360 - 90 \\ or \: 10x = 270 \\ or \: x = \frac{270}{10} \\ x = 27[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

1st Option

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

Step 1: Find the missing leg

2² + b² = 6²

b² = 36 - 4

b = √32

Step 2: Find cosA

cosA = √32/6

cosA = 4√2/6

cosA = 2√2/3

Answer:

This is a basic cubic function- thus the domain is all real numbers. You could think about domain as the possible x values for a graph. Since this cubic function extends from x=negative infinity to x=positive infinity, the range is all real numbers, or (-infinite, infinite) if you are told to write in interval notation.

Hope this helps!

The domain of [tex]y= x^{3}[/tex] are all real numbers, or  R due to the fact that [tex]x^{3}[/tex]  is a polynomial, which means its domain is R too.

Solution:

The domain of a particular expression is all real numbers except in the place where expression is undefined. The domain of any graph includes all the x-values that are solutions.

Interval Notation:

(-

Set-Builder Notation:

{x|x ∈R}

Determine the domain from the graph:

Thus, the domain of is:

(−∞,∞), {x|x∈R}

Learn more about the domain of polynomial:

https://brainly.com/question/12324899

Answer:

  783.7 square units

Step-by-step explanation:

The formula for the surface area of a cylinder is ...

  A = 2πr^2 + 2πrh = 2πr(r +h)

Using the given numbers, the area is ...

  A = 2(3.14)(6)(6 +14.8) = 783.7 . . . square units

Answer:

About 783.7 square cm.

Step-by-step explanation:

The formula for the surface area of a cylinder is (2 * pi *r^2) + (2 * pi * r * h).

(2 * 3.14 * 6^2) + (2 * 3.14 * 6 * 14.8) = (2 * 3.14 * 36) + (2 * 3.14 * 6 * 14.8) = 6.28 * 36 + 6.28 * 88.8 = 226.08 + 557.664 = 783.744.

So, the surface area of the cylinder is about 783.7 square centimetres.

Hope this helps!

Answer:

P = 0.4688 = 46.88%

The probability that a randomly selected high school student plays organized​ sports is 0.4688.

Step-by-step explanation:

We are given that a survey of 900 randomly selected high school students determined that 422 play organized sports.

​(a) What is the probability that a randomly selected high school student plays organized​ sports?

We know that the probability of an event is given by

P = Number of desired outcomes/total number of outcomes

For the given case, the desired outcomes are those students who play organized sports and the total number of outcomes are 900 randomly selected high school students who were surveyed.

So the probabilty is

P = 422/900

P = 0.4688

P = 46.88%

​(b) Interpret this probability

There is a 46.88% chance of randomly selecting a high school student who plays organized sports or in other words, if we randomly choose a high school student then there is a 46.88% probability that the selected student plays organized sports.

Answer:

D. $56,250

Step-by-step explanation:

Calculate the increase.

45000 × (1 + 25%)

45000 × 1.25

= 56,250

They made $56,250 this month.

Answer:

D

Step-by-step explanation:

Answer:

None of the listed

Step-by-step explanation:

[tex]Solve-for ;x -in\\ 2x+2y =18\\x = 9-y\\Substitute , 9-y -for ,x- in -2x-2y=-6\\-2(9-y)-2y =-6\\18+2y-2y=-6\\18 = -6\\The -statement- is -false \\Answer ; No -Solution[/tex]

Answer:

[tex]a_{n} = 12 -3(n-1)[/tex]

Step-by-step explanation:

[tex]a_{1} = 12\\a_{n} = a_{n-1} - 3[/tex]

we have to find formula for nth term of series for this problem

[tex]a_{1} = 12\\a_{2} = a_{2-1} - 3 = a_{1} -3 = 12 -3 = 9\\a_{3} = a_{3-1} - 3 = a_{2} -3 = 9 -3 = 6[/tex]

Thus, we see series is 12, 9 ,6

Thus, we can see that series is decreasing by unit of 3.

and we know that when there is in increase or decrease in series by a a constant number then series is arithmetic progression series.

Hence, this is a decreasing AP series

In AP

nth term is given

nth term = a+(n-1)d

where a is the first term

d is the common difference

common difference is given by = nth term - (n-)th term

lets take 2nd and 1st term to get common difference.

d = 9-12 = -3

(note: this was obvious by looking at series itself that d is -3 as series was decreasing by 3 unit)

a = 12

thus, nth term = a +(n-1)d

nth term = 12 +(n-1)(-3)

nth term = 12 -3(n-1)

writing this in form of [tex]a_{n}[/tex]

[tex]a_{n} = 12 -3(n-1)[/tex]  Answer

Answer:

13

Step-by-step explanation:

There are 6 ways to choose the first number and 5 ways to choose the second number to paint so the total number of ways is 6 * 5 = 30 but we are over counting by a factor of 2 since 1 and 6 is the same as 6 and 1 so it's 30/2 = 15, not 30. The only choices that have a product of 6 are 2 and 3 or 1 and 6 so the answer is 15 - 2 = 13.

Answer:

13 ways

Step-by-step explanation:

Total number of distinct ways to pair two faces

= C(6,2) = 6! / (2!4!) = 15

Total number of ways to pair two faces so that the product equals six

=cardinality {1*6, 2*3} = 2

Therefore

number of ways to paint two faces such that the product is not six

= 15 - 2

=13

Answer:

area of sector:

[tex] \frac{theta}{360} \times \pi \: {r}^{2} [/tex]

[tex] \frac{165}{360} \times \frac{22}{7} ( {8}^{2} )[/tex]

[tex] \frac{11}{24} \times \frac{1408}{7} [/tex]

[tex] \frac{1936}{21} [/tex]

[tex]92.19 \: {in}^{2} [/tex]

Answer:

the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]

Step-by-step explanation:

Use the fraction of the area of the circle associated with the red sector. Use a proportion to find the appropriate fraction knowing that a full circle [tex](360^o)[/tex] corresponds to the area:

[tex]Area=\pi\,R^2=\pi\, (8\,in)^2= 64\, \pi\,\,in^2[/tex]

then the proportion goes like:

[tex]\frac{64\,\pi\,\,in^2}{360^o} =\frac{sector}{165^o} \\ sector=\frac{64\,\pi\,165^o}{360^o}\,\,in^2\\sector\approx 92.15\,\,in^2[/tex]

Therefore, the area of the sector can be rounded to [tex]92.2\,\,in^2[/tex]

Answer:

15

Step-by-step explanation:

4x=60

60 divided by 4 = 15

Hello!

Answer:

(x + 1).

Step-by-step explanation:

Begin by using the rational root theorem to find possible factors of this equation.

We get the following:

±1, ±3, ±1/2, ± 3/2

We can use synthetic division to check numbers to see if they are a factor of the equation. After checking the possible numbers, -1 was found to produce a remainder of 0 when calculated:

-1 | 2    1     -4     -3

  +      -2     1       3

    2    -1     -3      0

Therefore, x = -1 is a possible root of this equation. Writing this as a factor would become:

x = -1

x + 1 = 0

(x + 1) is the factor.

I hope this helped you!

Answer: 0.705

Hello!

________________________

Sheila either walks or cycles to school the probability that she walks to school is 0.705

Step-by-step explanation:

Probability she walks and is  not late = 0.65 * 0.60 = 0.39.

Probability she cycles and is not late =  0.35*0.9 = 0.315

Therefore P(not late) =  0.39 + 0.315 = 0.705

Hope this helped you!

Answer:

Domain: (−∞,∞)

Range: (−∞,∞)

Step-by-step explanation:

trust me

Answer:

A- 5 banners

B- 2 banners

C- 2 banners

D- Shade banner 2