Three students were scheduled to give book reports in 1 hour.
After the first report, 2/3 hour remained (HINT: this means the first persons' report was 1/3 of an hour)


The next report took 1/6 hour. What fraction remained?

Answer:

3.2

Step-by-step explanation:

→ State Pythagoras theorem

x² + y² = z²

→ Substitute in

3² + 1²

→ Simplify

10 = z²

→ Evaluate

√10 = 3.2

Answer:

3.2

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

a = 3

b = 1

[tex]3^{2}[/tex] + [tex]1^{2}[/tex]  = 9 + 1 = 10

[tex]c^{2}[/tex] = 10

c = [tex]\sqrt{10}[/tex]

c = 3.16227766017

Round to the nearest tenth

c = 3.2

Answer:

1) 54+2x=5x−6−18x Distributive Property

2) 60=−15x Division Property of Equality

3) −4=x Division Property of Equality

Explanation:

1.) This answer is Distributive Property because the parenthesis in the original equation were removed through the process of distributing.

3(–2 – 6x) was distributed by multiplying 3 • –2 and 3 • –6x to get –6 – 18x

2.) This answer is Division Property of Equality because for all real numbers x, y, and z, if x = y and z ≠ 0, then x/z = y/z. This is true in this equation because of 60/–15 = −15x/–15.

3.) Division is used to get the value of x, which is –4.

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The surface area and the volume of solid prism are 432in² and 576in³ respectively.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles

The surface area of a rectangular prism is expressed as;

A = 2( wl + hl + hw )

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given the data in the question;

The surface area of the solid is;

A = 2( wl + hl + hw )

A = 2( (8in × 12in) + (6in × 12in) + (6in × 8in) )

A = 2( 96in² + 72in² + 48in² )

A = 2( 216in² )

A = 432in²

Therefore, surface area of the rectangular prism is 432in²

The volume of the solid is;

V = w × h × l

V = 8in × 6in × 12in

V = 576in³

Therefore, volume of the rectangular prism is 576in³

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Answer:

[tex]\sf y =\dfrac{-3}{4}x+16[/tex]

Step-by-step explanation:

Where m is the slope and b is the y-intercept.

   3x + 4y = 64

Subtract 3x from both sides,

           4y = -3x + 64

Now, divide both sides by 4,

      [tex]\sf \dfrac{4y}{4}=\dfrac{-3x}{4}+\dfrac{64}{4}\\\\y = \dfrac{-3}{4}x + 16[/tex]

The least number of visits he needs to make in order to earn a free movie ticket is approximately 15 visits.

Points received for signing up = 85 rewards points

Points received for each visit to the movie theater = 10.5 points

Points needed for a free movie ticket = 240 points

Number of visits = x

85 + 10.5x ≤ 240

10.5x ≤ 240 - 85

10.5x ≤ 155

x ≤ 155 / 10.5

x ≤ 14.761

Approximately,

x ≤ 15 visits

Therefore, Jordan needs at least 15 visits to earn a free movie ticket.

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Answer:

15

Step-by-step explanation:

40/100×25

=10

25-10=15

The value of n is 1/2 and it is not an even number or odd number

From the question, the steps are given as

n + n + 1 = 2n + 1

n + n + 1 = 2n+2-1

n + n + 1 = 2(n+1) -1

Also, from the question, we have the result of the expression to be

2

This means that

n + n + 1 = 2

Substitute n + n + 1 = 2(n+1) -1 in the equation n + n + 1 = 2

So, we have

2(n + 1) - 1 = 2

Add 1 to all sides of the equation

So, we have

2(n + 1) = 3

Divide both sides of the equation by 2

So, we have

n + 1 = 3/2

Subtract 1 from all sides

n = 1/2

The above implies that the number n is neither an even number, nor an odd number

This is so because the result is a fraction

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c.(4x+8y)=60

it is equivalent

Answer:

A and C

Step-by-step explanation:

Substitute 4x + 8y = 12

A:

12+3=15

15=15 ✓

B:

12=10 ×

C:

5(12)=60

60=60 ✓

D:

Multiply 4 to x+2y=6 to make it 4x+8y=12

x+2y=6

4x+8y=24

12=24 ×

Answer:

22

Step-by-step explanation:

AB + BC = AC

4x -6 + 4 = 2x + 10  Combine like terms

4x -2 = 2x + 10  Subtract 2s from both sides of the equation

2x -2 = 10  Add 2 to both sides

2x = 12  Divide both sides by 2

x = 6

Plug in 6 for x in AC

2x + 10

2(6) + 10

12 + 10

22

Answer:

x = 9

Step-by-step explanation:

To solve for x, you must isolate the variable.

First, start by adding 2 to BOTH sides to eliminate the 2.

3=1/3x. then divide each side by 1/3

3÷1/3 = x

3/1 × 3/1 = x

9 = x

Step-by-step explanation:

divide volume by product of length and width

54cm³= 3cm x 2cm

54/6= 9cm

Answer:

Step-by-step explanation:

246 degrees

Answer:61.5

Step-by-step explanation:

123/2=61.5

61.5+57=118.5

180-118.5=61.5

Answer: irelating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten:

Step-by-step explanation:

Answer:

its the 3rd option

Step-by-step explanation:

you solve parenthesis then multiply then had to minus which gave you the total

Answer:

A

Step-by-step explanation:

using the sine ratio and the exact values

sin30° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

calculate the height of the wall below x , call it h

the hypotenuse is the length of the ladder

using the sine ratio in the lower right triangle.

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2h = 18 ( divide both sides by 2 )

h = 9

lower part of the wall is 9 meters

using the sine ratio in the right triangle on the right

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9+x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2(9 + x) = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

9 + x = 9[tex]\sqrt{3}[/tex] ( subtract 9 from both sides )

x = 9[tex]\sqrt{3}[/tex] - 9 = 9([tex]\sqrt{3}[/tex] - 1)

Answer:

[tex]\textsf{A)} \quad x=9(\sqrt{3}-1)[/tex]

Step-by-step explanation:

Interior angles of a triangle sum to 180°.  Therefore, if the ladder makes an angle of 30° with the ground, the angle it makes with the wall is 60°.

Therefore, the two triangles are congruent as their corresponding angles are the same and the length of their longest side (hypotenuse) is the same.

30-60-90 Triangle Theorem

A 30-60-90 triangle is a special right triangle where the measures of its angles are in the ratio 1 : 2 : 3 and the measure of its sides are in the ratio 1 : √3 : 2.

The formula for the sides is  b : b√3 : 2b  where:

Therefore, as the length of the hypotenuse is 18:

[tex]\implies 2b=18[/tex]

[tex]\implies b=9[/tex]

[tex]\implies b\sqrt{3}=9\sqrt{3}[/tex]

To find x, subtract the length of the shortest leg of the right triangle from the length of the other leg of the right triangle:

[tex]\implies x=9\sqrt{3}-9[/tex]

[tex]\implies x=9(\sqrt{3}-1)[/tex]

L = lbs lost by Leila

N = lbs lost by Nina

since we know that Leila lost "L" lbs and Nina lost 43lbs more than that, so Nina lost then "L + 43", and we also know their total weight was 95lbs hmmmm so

[tex]\stackrel{Leila's}{L}~~ + ~~\stackrel{Nina's}{(L+43)}~~ = ~~\stackrel{total}{95}\implies 2L+43=95\implies 2L=52 \\\\\\ L=\cfrac{52}{2}\implies L=26\hspace{15em}\underset{Nina~lost}{\stackrel{26~~ + ~~43}{\text{\LARGE 69}~lbs}}[/tex]

Answer: 6400kg=6.4*10⁶ g

Step-by-step explanation:

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Answer - 6.4 × 10^6

Step by step Explaination-

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Firstly, we'll discuss the units of digits -

1. We'll convert 6400 kilograms into grams. Multiply the value in kilograms by the factor '1000'.

2.  Standard form may be a means of writing variety thus it's easier to browse. it's typically used for terribly large or small numbers.

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The possible values of the number will be -62/4 or -31/2.

Multiplication of numbers may be defined as the tool or arithmetic operation which can be used to increase the count of a number. For example, if there is a number 4, then in order to increase the number it will be multiplied with some other number like 9. Now, the number will be 4×9 = 36. We are given that the product of -4 with a number gives the answer as 62. Let us assume the number as x and form the equation in accordance with the data given in the question.

-4×(x) = 62

Now, to find x we divide -4 on both the sides and we get

x = -62/4

This number can also be simplified by dividing both numerator and denominator with 2 and we get

x = -31/2.

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The measure of m∠ABD in the figure shown is 19°.

Given:

∠BCD = 71°

In the figure, ΔABC is an isosceles triangle where AB = BC.

According to the Isosceles Triangle Theorem, an isosceles triangle has equal angles on either side of its equal sides.

So, ∠BAD = ∠BCD = 71°

The sum of angles in a triangle sums to 180°.

∠ABC + ∠BAD + ∠BCD = 180°

∠ABC + 71° + 71° = 180°

∠ABC + 142° = 180°

∠ABC = 180° - 142° = 38°

DB is the angle bisector of ∠ABC.

Now, ∠ABD = ∠CBD = 38°/2 = 19°

The measure of ∠ABD is 19°.

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Answer:

x-0.5,1,2,3,4,5,6

y-12,6,3,2,1.5,1

Step-by-step explanation:

Substitute the x value inside the formula. E.g. y=6 over 0.5, then solve.

Plot the points on the graph and join the up.

Answer:

Step-by-step explanation:

answer-x=π/7+y/7

Step-by-step explanation:

yes

By using the properties of the 30-60-90 right triangles, the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

Right triangles are triangles where one of its internal angles is a right angle, that is, has a measure of 90°. 30-60-90 triangles are right triangles whose internal angles have measures of 30°, 60° and 90°, respectively.

This kind of right triangles have the following features:

If we know that the short leg has a length of L, then the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

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Answer:

x = 147

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 7 , then

sum = 180° × 5 = 900°

sum the interior angles and equate to 900

x + 141 + 112 + 129 + 106 + 139 + 126 = 900

x + 753 = 900 ( subtract 753 from both sides )

x = 147

Answer:

what is the symbol between the 2 fractions?

Answer:

First question mark is 4, second question mark is 64

Step-by-step explanation:

For the first question mark, 7 is half of 14, and half of 8 is 4, so they would be the same ratio, and then for the second, 12 to 24 is just one half, meaning you would need to find double 32, which is just 64

There will  be no interval of time when Josue has more in savings than Arianna, they have same savings is after 4 weeks

Step one:

For Josue

initial savings balance= $70

weekly savings = $9

Let J represent amount of money Josue has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=9t+70-------1

For Arianna

initial savings balance= $30

weekly savings = $19

Let A represent the amount of money Arianna has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=19t+30---------2

Step two

equation 1 and 2 to find t

9t+70=19t+30

9t-19t=30-70

-10t=-40

divide both sides by 10

t=4

t=4 weeks

so after 4 weeks Josue and Arianna will have the same amount of money

For Josue t=4

J=9(4)+70-------1

J=36+70

J=$106

For Arianna t=4

A=19(4)+30---------2

A=76+30

A=$106

The two equations above shows that after 5 weeks their savings will be $106.

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