Explore rectangular and triangular prisms and their two-

Write 165 as a sum of powers of 2 :

165 = 128 + 37

165 = 128 + 32 + 5

165 = 128 + 32 + 4 + 1

165 = 2⁷ + 2⁵ + 2² + 2⁰

This translates immediately into the decimal expansion of a binary number,

165 = 1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

so that

165₁₀ ≡ 1010 0101₂

Answer:

10100101₂

Step-by-step explanation:

Let us solve it now.

2 |165

2 |82  -  1

2 | 41   - 0

2 |20   -  1

2 |10    - 0

2 | 5   - 0

2 |2      - 1

2 | 1     - 0

    0    - 1

Now write the remainders from bottom to top.

165 = 10100101₂

To find the perimeter and area on a coordinate plane, first find each distance between points and then find perimeter and area with these lengths.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

Let's suppose if we have coordinates (a, b) (c, d), (e, f), and (g, h) on a coordinate plane.

We can use the distance formula to get the length of each side and then adding all the side lengths to get the perimeter of the figure, which is represented by the coordinates on a coordinate plane.

The distance formula can be used:

If we want the distance between (a, b) and (c, d)

[tex]\rm Distance = \sqrt{(c-a)^2+(d-b)^2}[/tex]

Similarly, we can find the distance for all the coordinates.

Let's assume the figure is a rectangle on a coordinate plane:

Then area = length×width

Thus, to find the perimeter and area on a coordinate plane, first find each distance between points and then find perimeter and area with these lengths.

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Answer:

x = [tex]-3 + \sqrt{(4+x)(4-x)}[/tex]

y = [tex]-3 - \sqrt{(4+x)(4-x)}[/tex]

Step-by-step explanation:

[tex]x^2 + y^2 + 6y=7\\[/tex]

⇒ [tex]\left(x-a\right)^2+\left(y-b\right)^2[/tex]

[tex]\left(x-0\right)^2+\left(y-\left(-3\right)\right)^2 =4^2[/tex]

What happened in this math problem:

The numbers are complex numbers, and the sum of the complex numbers (-4 +i) and (10 - 5i) is 6 - 4i

The expressions are given as:

(-4 +i) and (10 - 5i)

The sum is represented as:

Sum = (-4 +i) + (10 - 5i)

Open the brackets

Sum = -4 +i + 10 - 5i

Collect like terms

Sum = -4  + 10 +i - 5i

Evaluate the like terms

Sum = 6 - 4i

Hence, the sum of the complex numbers (-4 +i) and (10 - 5i) is 6 - 4i

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Answer:

343 cubic inches

Step-by-step explanation:

7 times 7 times 7 is 343

Answer:

Answer:

0.6 ...........................

Seen can close the lid on the cube container with a 6 in. marker inside it which has the side length of 4 inches.

The cube shape is the three-dimensional solid which has 6 equal side. The diagonal of a cube can be calculated with the following formula;

d=6∛a

Here, (a) is the length of the side of the cube.

Sean has a plastic container which is in the shape of a cube. The side lengths of the cube container is 4 in. Thus, the diagonal of the cube is,

d=6∛a

d=6∛(4)

d=6 x 1.587

d=9.522 inches.

The diagonal of the cube container is 9.522 inches, which is more than the length of the marker.

9.522 in >6 in

Hence, Seen can close the lid on the cube container with a 6 in. marker inside it, which has the side length of 4 inches.

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Answer: 36 square units

Step-by-step explanation:

Divide the figure into 2 shapes: a rectangle and a triangle. Count the squares to find the dimensions of each figure. The rectangle has a width of 4 units and a length of 6 units. The triangle has a base of 6 units and a height of 4 units.

The formula for the area of a rectangle is length * width. The area of the rectangle is 4*6 = 24 square units.

The formula for the area of a triangle is (base * height)/2. The area of the triangle is (4*6)/2 = 24/2 = 12 square units.

Add the areas of both the rectangle and triangle. 24+12 = 36 square units.

Answer:

In terms of pi: 164.5pi cm squared

Substituting pi for 3.14: 516.53 cm squared

Step-by-step explanation:

3.5^2 = 12.25pi

12.25*2 = 24.5pi

7pi*20 = 140pi

140 + 24.5 = 164.5pi

164.5*3.14 = 516.53

The part of the trip does Annie still have to travel to reach her destination is 24.64.

Annie traveled 2/7 parts of her trip in the first hour, and then 1/8 parts in the second hour. she plans to rest when she has completed half of her trip.

what part of the trip does Annie still have to travel to reach her destination.

We have to determine part of the trip does Annie still have to travel to reach her destination

Annie traveled 2/7 parts of her trip in the first hour, and then 1/8 parts in the second hour.

She plans to rest when she has completed half of her trip.

2/7 Annie traveled in the first hour = 2/7*60 = 17.1428hours

and 1/8 in one hour,

1/8*60=7.5minutes

The distance traveled in the first hour+distance traveled in the second hours=total distance travelled.

Therefore the total distance =7.5+17.14=24.64

The part of the trip does Annie still have to travel to reach her destination is 24.64

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Answer:

18 ft.

Step-by-step explanation:

While you don't have the table provided, this is still a relatively simple problem to solve.

As we know, there are 3 feet per 1 yard (this can be written as 3 ft. = 1 yd. if that's easier to comprehend). So, if we're trying to find how many feet are in 6 yards, you'll write out your equation as 3*6=?. To find what ? is, you'll do the multiplication: 3*6-18.

So, with this, there are 18 feet in 6 yards.

Answer:

≈ 4.7 mm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the missing side , then

x² + 5.2² = 7²

x² + 27.04 = 49 ( subtract 27.04 from both sides )

x² = 21.96 ( take square root of both sides )

x = [tex]\sqrt{21.96}[/tex] ≈ 4.7 mm ( to the nearest tenth )

Answer:

see photo attached for your reference.

Step-by-step explanation:

15.50 (to the nearest hundredth)

Answer:

The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height. Let us know the basics of the area of a triangle. If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.

Answer:

A

Step-by-step explanation:

That is the original and unchanged version of the quadratics.

Hope this helped! :)

Option A is true because the sum of angles in a triangle is 180, so we can rule that one out immediately.

We can solve for x for the other 3 options by setting up this equation:

7x+2 + 4x+7 + 8x = 180 | Simplify

19x + 9 = 180 | Subtract 9

19x = 171 | Divide by 19
x=9

Now we can substitute x into all the values:
<J = 7x+2 = 65
<L = 4x+7 = 43
<K = 8x = 72

Looking at the options again, we can see that A, B, and D are true, leaving C to be false.

Answer:

the answer is 54.6/1 i really im not sure

Step-by-step explanation:

Answer:

573440 kg

Step-by-step explanation:

Given,

Density of copper ( D ) = 8960 kg / m³

Length of cube ( l ) = 4 meters

To find : Mass of solid cube of copper ( m )

Formula : -

Volume of cube = l³

Volume of cube

= l³

= 4³

= 4 x 4 x 4

= 64 meter³

So,

V = 64 meter³

Formula : -

D = m / V

m = D x V

   = 8960 x 64

m = 573440 kg

Hence,

The mass of a solid cube of copper is 573440 kg.

The measure of the angles are 91.375°and 88.625°. Both the angles are obtained by the supplementary angle principal.

Supplementary angles are two angels whose total is 180 degrees. When a straight line is crossed by a line, two angles develop on each of the examined straight line's sides.

Two sets of additional angles make up those two-two angles. That is, if supplementary angles are placed next to each other, the exterior sides of their exterior sides will form a straight line.

The given data in the problem is;

∠1 = 9y-2

∠2 = 7y+16

The sum of the supplementary angle is 180

⇒9y-2 +7y+16 = 180

⇒16y +14 =180

⇒16y= 166  

⇒ y=10.375

The measure of the angle 1 is;

∠1 = 9y-2

∠ 1 = 9 ×10.375 -2

∠ 1 = 91.375°

The measure of the angle 2 is;

∠2 = 7 × 10.75 +16  

∠2 = 88.625°

Hence, the measure of the angles are 91.375°and 88.625°.

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Using it's concept, the theoretical probabilities of each color are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, considering the nine regions, and the numbers of each color, we have that:

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The equation, representing  the cost of each book, c, which Jade buys is c = 50/4. The cost of each book represented by c in this situation is $12.5

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus, [tex]a \div b[/tex] = a divided in b equal parts.

Also, we can write: [tex]a \div b = a \times \dfrac{1}{b}[/tex]

(it is so because as a = a times 1 so [tex]a/b = 1 \times (a/b) = (1/b) \times a[/tex] )

For this case, we're given that;

4 books = $50 in cost

Dividing 4 books in 4 groups equally gives 1 book per group.

Dividing $50 in 4 groups equally, which would correspond to those 4 groups of books, would give cost per group, and therefore cost of each book.

We've got:

[tex]\text{Cost of each book} = c = \dfrac{50}{4} \: \rm (in \: dollars)[/tex]

Dividing further, we get:

[tex]c = 50/4 = 12.5 \: \rm dollars[/tex]

Thus, the equation, representing  the cost of each book, c, which Jade buys is c = 50/4. The cost of each book represented by c in this situation is $12.5

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Answer:

Bottom right.

Step-by-step explanation:

It is not the top left because that is 1/2,

It is not the bottom left because that is 2/3,

It is not the top right because that is 3/5,

It is the bottom right because it is 3/4.

Step-by-step explanation:

I hope you will understand

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$23000\\ P=\textit{original amount deposited}\\ r=rate\to 3.70\%\to \frac{3.70}{100}\dotfill &0.037\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]23000=P\left(1+\frac{0.037}{12}\right)^{12\cdot 4}\implies 23000=P\left( \frac{12037}{12000} \right)^{48}\implies \cfrac{23000}{~~ \left( \frac{12037}{12000} \right)^{48}~~}=P \\\\\\ \cfrac{23000}{~~ \frac{12037^{48}}{12000^{48}}~~}=P\implies \cfrac{23000\cdot 12000^{48}}{12037^{48}}=P\implies 19840.43\approx P[/tex]

Answer:

[tex]\frac{5}{6}-\frac{1}{9} = \frac{45}{54} -\frac{6}{54} = \frac{13}{18}[/tex]

Step-by-step explanation:

An easy way to find a common denominator is to multiply the denominators against each other, like this:

[tex](\frac{9}{9})\frac{5}{6}-\frac{1}{9} (\frac{6}{6})[/tex]

Now, simplify:

[tex]\frac{45}{54}-\frac{6}{54}[/tex]

Then, subtract:

[tex]\frac{39}{54}[/tex]

Simplify:

[tex]\frac{13}{18}[/tex]      (Divide numerator and denominator by 3)

Hope this helps!!

Answer:

h=6cm

Step-by-step explanation:

V=lwh

126=3×7×h

h=6cm