Choose all properties that were used to simplify the following problem:

(Possible answers)
1 associative property of addition
2 associative property of multiplication
3 multiplicative inverse
4 commutative property of multiplication
5 multiplicative identity
6 distributive property
7 commutative property of addition
Multiple choice!

The value of the line segment TU is 12 units.

A line segment is a fixed-length section of the a line to two ends.

According to the question;

TU = x + 8 and ST = 3x are the lengths.

SU is the total length of the line segment.

Now, it is clear that SU is divided into parts such that;

SU = ST + TU

As, T is the mid point of the line SU;

The,

ST = TU

Equating the values;

3x = x + 8

Solving the equation;

3x -x = 8

x = 4

Put the value of x in TU;

TU = x + 8

TU = 4 + 8

TU = 12

Therefore, the value of the line segment TU is found as 12 units.

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The common side length of the paintings is 8 feet

The area of a shape is the amount of space on the shape

The given parameters are

Area of painting 1 = 24 square feet

Area of painting 2 = 32 square feet

Express the areas as the product of their factors

So, we have

24 = 2 * 2 * 2 * 3

32 = 2 * 2 * 2 * 4

Multiply the common factors

Common factors =2 * 2 * 2

Evaluate the product

Common factors = 8

This represents the common side length

Hence, the common side length of the paintings is 8 feet

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The x-intercepts of the parabola are  (-1,0) and (-5,0) and the coordinates of the vertex are  ( -3 , - 4 ).

A parabola is a graphical representation of a function of the form y=g(x) where g(x) is a quadratic polynomial of x.

The given equation of the parabola is y = x² + 6x + 5

to find the x-intercepts we have to take the value of y at zero.

∴  x² + 6x + 5 = 0

or,  x² + 5x + x + 5 = 0

or, x (x + 5) + 1 ( x + 5 ) = 0

or, (x+5)(x+1)=0

either x=-5 or x=-1

Therefore the x-intercepts of the graph is (-1,0) and (-5,0)

Now to find the vertex of the parabola:

y =  x² + 6x + 5

or, y = x² + 2·x·3 + 3² - 4

or, y = (x + 3)² - 4

Therefore from the above equation we can say that the vertex of the parabola is at ( -3 , - 4 ).

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Answer:

C) Positively skewed, and the mean is to the right of the median.

Step-by-step explanation:

A histogram is a graphical representation of the distribution of numerical data.

A histogram is:

Since the long tail of the given histogram is on the positive side of the peak, the histogram is positively skewed (right-skewed).

The mode is the value that occurs most often in a set of data.

In a histogram, the mode is the highest point.

The median and mean fall to the right of the mode in a right-skewed (positively skewed) histogram, and the mean is always to the right of the median: mode < median < mean.

The median and mean fall to the left of the mode in a left-skewed (negatively-skewed) histogram, and the mean is always to the left of the median: mean < median < mode.

So the correct definition of the given histogram is:

Answer:

Gradient: 9

Y-intercept: -2

Step-by-step explanation:

The equation of a line is expressed in this format:

y = mx + c

Where m is the gradient (slope) of the line, and c is the y intercept.

The equation in the question is already in this format, meaning the values can be read directly from it without needing any rearranging.

m = 9, c = -2.

Step-by-step explanation:

Are you asking for the number?

Answer:

A = 80

B = 10

Step-by-step explanation:

a + b = 90

a = 8b

above are  the two equations that we will used to find A and B.

substitute in 8b for a in the first equation.

a + b = 90

8b + b = 90  Combine like terms

9b = 90  Divide both sides by 9

b = 10

If b is 10, than a must be 80.

Answer:

B

Step-by-step explanation:

3/20 15%,20%, 25%, 1/3 33%

All my work and answer is provided in the attached screenshot to my answer! :)

Have a great day!

The equation that shows the relation between the number of hours worked and tickets sold is t = 23h (fourth option)

Examining the table, it can be seen that the number of tickets sold increases by 23 for every hour that Gwen works.

Tickets sold when Gwen works for 2 hours = 23 x 2 = 46

Tickets sold when Gwen works for 2 hours = 23 x 3 = 69

Because the tickets sold increase by a constant number, the equation would be modelled as a linear function.

Linear equations have the form : a + bx

Ticket sold = (number of hours x ticket sold in the first hour)

t = 23h

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By using the definition of perimeter and addition and subtraction of sides, the perimeter of the composite figure is 22 centimeters.

According to the image attached aside, we find a composite figure created by adding three quadrilaterals. The perimeter is the sum of the lengths of all sides of the composite figure, that is, we need to add the lengths of the eight sides of the figure.

p = AB + BC + CD + DE + EF + FG + GH + AH

GH = AB - EF - CD

GH = 7 cm - 3 cm - 1 cm

GH = 3 cm

AH = BC - DE + FG

AH = 3 cm - 2 cm + 1 cm

AH = 2 cm

p = 7 cm + 3 cm + 1 cm + 2 cm + 3 cm + 1 cm + 3 cm + 2 cm

p = 22 cm

The perimeter of the composite figure is 22 centimeters.

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A numerical expression to represent the greatest total number of fish that could be in both aquariums is; Number in Tiger barb + number in giant danios

The Greatest number of fishes that could be in both aquariums is; 14

We are given that;

Tiger barbs = 30 gallon aquarium

Giant danios = 20 gallon aquarium

Greatest number of fishes that could be in both aquariums;

Tiger barb = volume / length

Tiger barb = 30 / 3

Tiger barb = 10 fishes

Giant danios = volume / length

Giant danios = 20 /5

Giant danios = 4 fishes

Hence, the greatest total number of fishes in both aquarium is :

Number in Tiger barb + number in giant danios

= 10 + 4 = 14

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Complete question is;

There are tiger barbs in a 30-gallon aquarium and giant danios in a 20-gallon aquarium

Use the rule to solve this problem. The rule for the number of fish in an aquarium is to allow 1 gallon of water for each inch of length.

Giant Danio=5 inch length

Tiger barb=3 inch length

What is the correct numerical expression that represents the greatest total number of fish that could be in both aquariums?

The equation with nontrivial linear combination is (16)4x + ( -48 )2x²+ (-8 )(8x-12x²) = 0

We can solve this problem following some steps.

Let's assume the value is A for blank one and it is B for blank two.

Now we can rewrite the equation as,

(16)4x + (A) 2x²+ (B)(8x-12x²) = 0

Or, 64x + 2Ax² + 8Bx - 12Bx² = 0

After rearrangement, we can write this equation as,

x ( 64 + 8B) + x²( 2A - 12B) = 0

We can consider the whole equation as zero, only when the coefficient of both x and x² is zero, To complete a nontrivial combination, we have to write,

∴ ( 64 + 8B) = 0 [ Coefficient of x ]

Or , 8B = -64

Or, B = -64/8 = -8

Again following the previous concept we can also write, ( 2A - 12B ) = 0

[ Coefficient of x² ]

Now, we should put the value of B = -8

∵ ( 2A - 12B ) = 0

Or, 2A + 96 = 0

Or, 2A = - 96

Or, A = - 48

So, the value of A is -48, and the value of B is -8

Now we can conclude,

(16)4x + ( -48 )2x²+ ( -8 )(8x-12x²) = 0

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Answer:O 18+3

O-18+3

O-18+(-3)

Step-by-step explanation:O 18+3

O-18+3

O-18+(-3)

Answer:

x = 6

Step-by-step explanation:

As stated, the scale factor from two figures is 1/4

To find the value of x we can simply use the following equation

[tex] \frac{(1.5)}{x} = \frac{1}{4} [/tex]

cross multiply expressions

x = 6

Answer:

15 + (n + 12)

Step-by-step explanation:

Answer:-

Step-by-step explanation:

Step 1 1.2r = 0.6r-3

Step 2 .6r = -3

Step 3 -3 divided by .6 = -5

Answer: -5

The answer to the given question is length is 17m and width is 6m

Given that a rectangle's length is 7 meters less than its width.

And also given the perimeter of the rectangle is 46 meters.

We know that the rectangle's perimeter is twice the sum of its length and width.

l - length of the rectangle

w - width of the rectangle

P - perimeter of the rectangle

Then we have P = 2 × (l + w)

Given that a rectangle's length is 7 meters less than its width.

⇒ l = 4 × w - 7

Given the perimeter of the rectangle is 46 centimeters.

⇒ 2 × ( l + w) = 46

⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)

⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)

⇒ 5w - 7 = 23

⇒ 5w = 23 + 7

⇒ 5w = 30

⇒ w = 6 (dividing both sides by 5)

Using the width value in the length equation, we get

l = 4 × 6 - 7

⇒ l = 24 - 7

⇒ l = 17

Therefore, The rectangle is 17 meters in length and 6 meters in width.

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The digit 3 in 5,630, is not 10 times the value of the digit 3 in 342. It's false.

It should be noted the question has to do with place value. In this case, the digit 3 in 5,630 gives a value of 30.

On the other hand, the digit 3 in 342 is 300.

Therefore, we can see that the digit 3 in 5,630, is not 10 times the value of the digit 3 in 342.

Therefore, the correct option is false.

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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342. True or. false?

Answer: an=2(n-1)+1

Step-by-step explanation:

1,3,5,7, …

As the terms progress in the sequence, each term get increased by 2 to get to the next term. Hence, the change is linear and can be modeled with the function y=2(x-1)+1 where y=term value, x=term number and 1 is the first term in the sequence.

y=2(x-1)+1

an=2(n-1)+1 ==> n=term number while an=term value. an=nth term

Answer:

Jay paid £573.76 for the smart phone originally.

A light bulb will consume 3,600 watts - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.

We are given that:

Consumption in 3 days 12 hours = 12,600 watts

12 hours = 12 / 24 days = 0.5 days

Days = 3 + 0.5 days = 3.5 days

Now, by using the unitary method, we get that the consumption by a light bulb in 1 day will be equal to:

3.5 days = 12,600 watts

1 day = 12,600 / 3.5 watts

1 day = 3,600 watts

Therefore, a light bulb will consume 3,600 watt - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.

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Observe that

[tex]\dfrac{(n!)^2}{(2n+1)!} = \dfrac{n!(2n-n)!}{(2n+1)(2n)!} = \dfrac1{(2n+1)\binom{2n}n}[/tex]

Starting with a well-known series

[tex]\displaystyle 2\arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]

we take some (anti)derivatives to find a sum that more closely resembles ours.

Let [tex]f(x)=2\arcsin^2(x)[/tex]. Then

[tex]\displaystyle f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{n \binom{2n}n}[/tex]

[tex]\displaystyle x f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{n \binom{2n}n}[/tex]

[tex]\displaystyle x f''(x) + f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{\binom{2n}n}[/tex]

[tex]\displaystyle x^2 f''(x) + x f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{\binom{2n}n}[/tex]

Noting that both sides go to zero as [tex]x\to0[/tex], by the fundamental theorem of calculus we have

[tex]\displaystyle \sum_{n=1}^\infty \frac{2^{2n} x^{2n+1}}{(2n+1)\binom{2n}n} = \frac14 \int_0^x (t^2 f''(t) + t{}f'(t)) \, dt[/tex]

so that when [tex]x=\frac12[/tex], and rearranging some factors and introducing a constant, we recover a useful sum.

[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac12 \int_0^{1/2} (x^2 f''(x) + x f'(x)) \, dt[/tex]

Integrate by parts.

[tex]\displaystyle \int_0^{1/2} x^2 f''(x) \, dx = \frac14 f'\left(\frac12\right) - 2 \int_0^{1/2} x f'(x) \, dx[/tex]

[tex]\displaystyle \int_0^{1/2} x f'(x) \, dx = \frac12 f\left(\frac12\right) - \int_0^{1/2} f(x) \, dx[/tex]

Then our sum is equivalent to

[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac18 f'\left(\frac12\right) - \frac14 f\left(\frac12\right) + \int_0^{1/2} \arcsin^2(x) \, dx[/tex]

The remaining integral is fairly simple. Substitute and integrate by parts.

[tex]\displaystyle \int_0^{1/2} \arcsin^2(x) \, dx = \int_0^{\pi/6} u^2 \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} - 2 \int_0^{\pi/6} u \sin(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 2 \int_0^{\pi/6} \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1[/tex]

Together with

[tex]f\left(\dfrac12\right) = 2 \arcsin^2\left(\dfrac12\right) = \dfrac{\pi^2}{18}[/tex]

[tex]f'\left(\dfrac12\right) = \dfrac{4\arcsin\left(\frac12\right)}{\sqrt{1-\frac1{2^2}}} = \dfrac{4\pi}{3\sqrt3}[/tex]

we conclude that

[tex]\displaystyle \sum_{n=0}^\infty \frac{(n!)^2}{(2n+1)!} = \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} \\\\ ~~~~~~~~~~~~~~~~~~ = 1 + \left(\frac18\cdot\frac{4\pi}{3\sqrt3}\right) - \left(\frac14\cdot\frac{\pi^2}{18}\right) + \left(\frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{\frac{2\pi}{3\sqrt3}}[/tex]

The volume of Daves storage box is 19200 and the surface area is 4400

The given parameters are

Length = 32 cm

Width = 20 cm

Height = 30 cm

The volume is

Volume = Length * width * height

So, we have

Volume = 32 * 20 * 30

Evaluate

Volume = 19200

The surface area is

A =2 *(LW + LH + WHW)

So, we have

A = 2 * (32 * 20 + 20 * 30 + 32 * 30)

Evaluate

A = 4400

Hence, the volume of Daves storage box is 19200 and the surface area is 4400

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Answer:

1hour 15

Step-by-step explanation:

The glider begins its flight a mile above the ground.

Distance above the ground after 45 minutes =

Change in height of the glider

Next, we determine how long the entire descent last.

Expressing the distance moved as a ratio of time taken

Therefore: Total Time taken =45+30=75 Minutes

=1 hour 15 Minutes

Answer:

yes

Step-by-step explanation:

to solve this you must first find her rate

6 / 20 is her rate

you want to know how many she can do in ten minutes so we must find how many seconds are in 10 minutes

10 * 60 = 600

175 / 600 is the rate needed fro the test

now make them have the same denominator

6 / 20 is also 180 / 600

175/600 is less than 180/600 so yes she will finish the test in time

The smallest angle on the line will be 36°

A line segment seems to be a straight line that connects two places. A line segment does indeed have a predetermined length. A ruler can be used to determine the shortest distance between the two points.

A straight angle in geometry is an angle with a vertex point of 180 degrees. It basically generates a straight line with sides that point in opposite directions first from the vertex. It is also known as "flat angles."

We know the the sum of the straight angle is = 180°

So,

(5a + 18) + (48 - a) + (8a -30 ) = 180°

5a - a + 8a + 18 +48 - 30 = 180°

12a + 36 = 180°

12a = 180 - 36

a = 12°

So putting the value of a in the equation:

(5a + 18) = 5 *12 + 18 = 78°

(48 - a) = 48 - 12 = 36°

(8a -30 ) =  96 - 30 = 66°

36° < 66° <78°

So the smallest angle on the line will be 36°

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The value of the x in the linear equation is a 3/4.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

8 - (6 - 8x) = 4x + 5

Now we have to solve this

Then

8 - (6 - 8x) = 4x + 5

8 - 6 + 8x = 4x + 5

Now, rearrange the above written terms for the value of the x

2 + 8x = 4x + 5

4x = 3

x =3/4.

So, The value of the x in the linear equation is a 3/4.

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Answer:

4,000

Step-by-step explanation: