Simplify the expression below.

Answer:

Number = 14

Step-by-step explanation:

It is given that,

Twice the sum of a number and seven is three times the number

Let the number be x. Twice of the number is 2x. Three times of the number is 3x.

So,

2(x+7)=3x is the equation that models the given scenario

Opening brackets on LHS,

2x+14=3x

Subtracting 2x on both the sides

2x-2x+14=3x-2x

14=x

So, the number is 14.

The number is 14.

The calculation is as follows:

Based on the above information, the calculation is as follows:

2(x+7)=3x  

2x+14=3x

x = 14

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Answer:

[tex]\sqrt{384}[/tex]

Step-by-step explanation:

[tex]\sqrt{384}[/tex] is equivalent  to [tex]\sqrt[8]{6}[/tex]

An equivalent expression to the given expression [tex]8\sqrt{6}[/tex] is  [tex]\sqrt{384}[/tex]

"It is a mathematical statement which consists of numbers, variables and some mathematical operations."

"The expressions that work the same even though they look different."

For given question,

We have been given an expression [tex]8\sqrt{6}[/tex]

We know, for a positive real number a, [tex]\sqrt{a^2}=a[/tex]

So, we can write 8 as [tex]8=\sqrt{8^2}[/tex]

So, given expression becomes [tex]\sqrt{8^2}\sqrt{6}[/tex]

We know, for any positive real numbers m, n, [tex]\sqrt{m} \sqrt{n}=\sqrt{mn}[/tex]

[tex]\sqrt{8^2}\sqrt{6}[/tex]

= [tex]\sqrt{8^2\times 6}[/tex]

= [tex]\sqrt{64\times 6}[/tex]

= [tex]\sqrt{384}[/tex]

So, an expression [tex]8\sqrt{6}[/tex] is equivalent to expression [tex]\sqrt{384}[/tex]

Therefore, an equivalent expression to the given expression [tex]8\sqrt{6}[/tex] is  [tex]\sqrt{384}[/tex]

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Answer:

$0.14

Step-by-step explanation:

Hello!

To find the price per ounce you divide the total cost by the number of ounces

11.99/84 = 0.1427

Round to nearest hundredth

0.14

The answer is $0.14

Hope this helps!

Answer:

according to circle theorem the angle in the center is twice of the angle of the angle form by the cords of the circle.

Since, the center circle is 90 theta is 45 degrees

Step-by-step explanation:

*Another approach

Answer:

Option (4)

Step-by-step explanation:

From the given circle O,

AC and BD are the diameters intersecting at point O.

∠AOB ≅ ∠COD [Vertical angles]

Therefore, length of intercepted arcs by these central angles will be same.

[tex]m(\widehat{AB})=m(\widehat{CD})[/tex]

(3x - 70) = (x + 10)

3x - x = 70 + 10

2x = 80

x = 40

Since, [tex]m(\widehat{AB})+m(\widehat{BC})=180[/tex] [Since AC is a diameter]

(3x - 70) + [tex]m(\widehat{BC})[/tex] = 180°

3(40) - 70 + [tex]m(\widehat{BC})[/tex] = 180°

[tex]m(\widehat{BC})[/tex] = 180° - 50°

           = 130°

Therefore, Option (4) will be the correct option.

Answer:

130 degrees

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

The exterior angle is the sum of the opposite interior angles.

120 = x + the other angle next to x but not the one next to 120

Since it is an isosceles triangle

120 = x + x

120 = 2x

60 = x

Hope that helped!!! k

Answer:

(-53)/80

Step-by-step explanation:

Simplify the following:

-23/30 + 5/48

Put -23/30 + 5/48 over the common denominator 240. -23/30 + 5/48 = (8 (-23))/240 + (5×5)/240:

(8 (-23))/240 + (5×5)/240

8 (-23) = -184:

(-184)/240 + (5×5)/240

5×5 = 25:

(-184)/240 + 25/240

-184/240 + 25/240 = (-184 + 25)/240:

(-184 + 25)/240

-184 + 25 = -159:

(-159)/240

The gcd of -159 and 240 is 3, so (-159)/240 = (3 (-53))/(3×80) = 3/3×(-53)/80 = (-53)/80:

Answer: (-53)/80

Answer:

This is  called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.

Step-by-step explanation:

Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.

From the figure we can see that

AE≅ CE

AD≅DB

BF≅CF  

BECAUSE  all the given points are the midpoints which divide the lines into two equal halves.

If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)

(1)

If we join C with L we find out that the the line DE is half in length to the line BC.

AS

AE= CE  (midpoints dividing into equal line segements.)

LE= DE

Triangle CEL= Triangle DEF

so

DL= BC

But DE = 1/2 DL

therefore

DE= 1/2 BC (2)

Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side

Answer:

-18x square y -+36xy square + 54 xy - 1

Step-by-step explanation:

collect the terms, calculate the product, collect the terms, then distribute

Answer:

68.5

Step-by-step explanation:

Subtract 4 from 73.

You get 69.

Then, subtract 0.5 more.

Your answer is 68.5.

Hope it helps!

Answer:

21 feet

Step-by-step explanation:

The pool has dimension 15 feet by 17 feet, which is in the form of a rectangle.

The area of the pool = length × width

                                   =  17 × 15

                                   = 255 square feet

Area of the pool and cement walkway = 483 square feet

Area of walkway = area of pool and walkway - Area of pool

                            = 483 - 255

                            = 228 square feet

Let's assume that the cement walkway has equal thickness across its perimeter, so that;

the dimension of the pool and the cement walkway = 23 feet × 21 feet

The width of the cement walkway is 21 feet.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line parallel to 3x - y = 14 we must first find the slope of 3x - y = 14.

So we have

y = 3x - 14

Comparing with the general equation above

Slope / m = 3

Since the lines are parallel their slope are also the same

So slope of parallel line = 3

Equation of the line using point ( - 4 , -7) and slope 3 is

We have the final answer as

Hope this helps you

Answer:

(27+x)/6

Step-by-step explanation:

(2x)/3 + (9-x)/2

Get a common denominator of 6

(2x)/3 *2/2 + (9-x)/2*3/3

4x/6  +3(9-x)/6

Distribute

4x/6 + (27-3x)/6

Combine like terms

(27+4x-3x)/6

(27+x)/6

Answer:

The next number going up or down?

Step-by-step explanation:

Down

20

5

Up

180

Answer:

60

Step-by-step explanation:

The sequence is to first add 20 and then divide by 2. To find the next number in the sequence, add 20. This means the next number in the sequence is 40+20=60.

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

Answer:

448,648

Step-by-step explanation:

33,200/.074 = 448,648

Answer: 448648

Step-by-step explanation:

33,200 copies represent 7.4% of the total amount

-----------------------------------------------------

#1  33,200 ÷ 7.4%

- this is because how we get 33,200 by calculation is use the total amount and times 7.4% to get 33,200. So we are just working backwards. Since it was times before, then we divide after.

 33,200÷7.4%

=33,200÷0.074

≈448648 (you can't round up when the real amount is less the exact amount)

Answer: 2000

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Write down the expression exactly as it is given.

[tex] \dfrac{3y - 9}{x} = [/tex]

Now write the expression again, but replace x with 3, and replace y with 6.

[tex] = \dfrac{3 \times 6 - 9}{3} [/tex]

Now simplify the numerator using the correct order of operations.

[tex] = \dfrac{18 - 9}{3} [/tex]

[tex] = \dfrac{9}{3} [/tex]

Now divide 9 by 3.

[tex] = 3 [/tex]

Answer: 3

Answer:

B) -4 and E) 4

Step-by-step explanation:

Answer:

13 and 14.

Step-by-step explanation:

So we have two consecutive integers.

Let's call the first integer a.

Since the integers are consecutive, the other integer must be (a+1) (one more than the last one).

We know that the sum of the greatest integer (or a+1) and twice the lesser integer (a) is 40. Therefore, we can write the following equation:

[tex](a+1)+2(a)=40[/tex]

The first term represents the greatest integer. The second term represents 2 times the lesser integer. And together, they equal 40.

Solve for a. Combine like terms:

[tex]a+1+2a=40\\3a+1=40[/tex]

Subtract 1 from both sides. The 1s on the left cancel:

[tex](3a+1)-1=(40)-1\\3a=39[/tex]

Divide both sides by 3:

[tex]\frac{3a}{3}=\frac{39}{3}\\a=13[/tex]

Therefore, a or the first integer is 13.

And the second integer is 14.

And we can check:

14+2(13)=14+26=40

Let the two consecutive integers be x and x + 1.

According to the question,

★ Greatest integer = x + 1

★ Lesser integer = x

The sum of the greatest integer and twice the lesser integer is 40. [ Given ]

⇒ ( x + 1 ) + 2 ( x ) = 40

⇒ x + 1 + 2x = 40

⇒ 3x + 1 = 40

⇒ 3x = 40 - 1

⇒ 3x = 39

⇒ x = 39/3

⇒ x = 13

★ x + 1 = 13 + 1 = 14

Answer:

The density is 3.8 g

Step-by-step explanation:

D=M/V (Density= Mass divided by Volume)

5.7 divided by 1.5 is 3.8

Answer:

Hey again! Just remember about the number lines. If it's easier, you can use a calculator to divide the fractions to make them easier to visualize in decimal form.

The answer to this one is:

-2.4

-2.25

-11/5 (which is -2.2)

-15/10 (1.5)

-1.6

Answer:

The answer is

Step-by-step explanation:

To find the distance between two points we use the formula

where

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

From the question the points are

(-1, 4) and (1,-1)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

B and the first d and second one.

Step-by-step explanation:

The age is a big factor and b can showing the preference per age

Answer:

5 seconds

1220 ft

Step-by-step explanation:

Step 1: Know when the stone reaches the maximum height

We know the maximum or minimum height of a parabola is at the vertex so we need to find the vertex

Step 2: Calculate the vertex

The t coordinate of the vertex can be calculated with [tex]\frac{-b}{2a}[/tex]

b = 160

a = 16

[tex]t=\frac{-(160)}{2(-16)}\\t=\frac{-160}{-32}\\t=5[/tex]

Step 3: We know the t coordinate we can find the height at that time

[tex]h_{(t)} =-16(5)^{2} +160(5)+20\\h_{(t)}=16(25)+ (800)+20\\h_{(t)}=400+ 800+20\\h_{(t)}=1220[/tex]

Therefore the stone reaches its maximum height of 1220 ft in 5 secs

Answer:

The maximum height of 420 feet is reached after 5 seconds.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

[tex]f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)[/tex]

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

[tex]f(x)=a(x-h)^2-k[/tex]

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

[tex][-2,\infty)[/tex]

This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.

Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:

[tex]0.5x+1.5=0\text{ and } x-1=0\\0.5x=-1.5 \text{ and }x=1\\x=-3\text{ and }x=1[/tex]

Therefore, the graph crosses the x-axis at x=-3 and x=1.

So, from the three equations, we gathered the following information:

1) The graph curves upwards.

2) The roots of zeros of the function is (-3,0) and (1,0).

3) The y-intercept is (0,-1.5).

4) The vertex is (-1,-2). This is also the minimum point.

5) Therefore, the range of the graph is all values greater than or equal to -2.

6) The end behavior of the graph on both directions go towards positive infinity.

Therefore, our correct answer is A.

B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.

C is not correct because the graph goes towards positive infinity since it shoots straight up.

And D is not correct because the y-intercept is (0,-1.5).

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

\begin{gathered}f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)\end{gathered}

f(x)=0.5x

2

+x−1.5

f(x)=0.5(x+1)

2

−2

f(x)=(0.5x+1.5)(x−1)

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

f(x)=a(x-h)^2-kf(x)=a(x−h)

2

−k

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

Answer:

a c d

Step-by-step explanation:

Derrick's value = 0

Ari's value = 0.5

Wesley's value = 2.1

============================

Explanation:

Derrick doesn't shade anything, so his value is 0.

Ari shades half of one model, so 1/2 = 0.5 is his value

Wesley shades 2 full models, plus 1/10 = 0.1 of another one, leading to 2+0.1 = 2.1 as his value.

The fractional amount of the model shaded by each of the boys are :

The size of each model cut out = 1/100 = 0.01

DERRICK :

ARI :

WESLEY

Therefore, the amount shaded by each of the boys represented as a decimal are :

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