Which radicals are already in the simplest form?

The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

We know that the parallelopiped has sides

Thus, we proceed as follows

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So, we have

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2)

Since (a × b) = (5, -7, -2)

Thus, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14

So, the volume is 14 cubic units

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Answer:

Step-by-step explanation:

10,14,18

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

Here, given that,

A chef makes small and large snacks to sell at a local art show.

He cannot make more than 30

snacks before the show, with no more than 6 large snacks.

The chef must make at least 10 small snacks to earn a profit.

Let,

x represent the number of small snacks

and y represent the number of large snacks.

Given x ≥ 0 and y 20

So, we get,

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

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Answer:

  (a, b, c) = (-3, -2, -4)

Step-by-step explanation:

You want to solve the system of 3 equations in 3 variables shown in the attached figure.

The easiest solution is one provided by a suitable calculator (attached). It tells you ...

The "work" is entering the problem into the calculator.

We notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...

  (4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)

  7b +3c = -26 . . . . . simplify

Multiplying the third equation by 4 and adding that to the first equation gives ...

  4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)

  21b +2c = -50 . . . . . simplify

Now, we have two equations in two unknowns.

Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...

  3(7b +3c) -(21b +2c) = 3(-26) -(-50)

  7c = -28 . . . . . simplify

  c = -4 . . . . . . . divide by 7

Using this in the first "ad hoc" equation, we can find b:

  7b +3(-4) = -26

  7b = -14 . . . . . . . . add 12

  b = -2 . . . . . . . . divide by 7

And the values of b and c can go into the last of the original equations to give ...

  -a +4(-2) +2(-4) = -13

  -a = 3 . . . . . add 16

  a = -3 . . . . . multiply by -1

The solution is (a, b, c) = (-3, -2, -4).

__

Additional comment

The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.

The third equation suggests we could make a substitution for 'a':

  a = 4b +2c +13

That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.

The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.

Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.

The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x

An equation is an expression that shows the relationship between two or more numbers.

Let x represent the height of the trapezoid.

a) One base of trapezoid measures five feet greater than its height. Hence:

First base = x + 5

The other base is one foot less than twice its height, hence:

Second base = 2x - 1

Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x

b) The height is increased by 4 feet. New height = x + 4

First base = (x + 4) + 5 = x + 9

Second base = 2(x + 4) - 1 = 2x + 7

Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x

The area of the trapezoid is 1.5x² + 2x.

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A) Total mass of 3500 books is 2,800 kilograms.

B) The average mass of one apple is 130 grams.

A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:

Total mass = (3500 books) * (800 grams/book)

= 2,800,000 grams

= 2,800 kilograms

Therefore, the Total mass of 3500 books is 2,800 kilograms.

B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:

Average mass = (1.04 tonnes) / (8000 apples)

= 130 grams/apple

Therefore, the average mass of one apple is 130 grams.

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identification of the expression 4x- 2y + 6 = 2x is

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, a linear expression 4x-2y + 6 = 2x

Coefficient:

Coefficients are the numbers by which the variables in an equation are multiplied

Thus, the Coefficient terms for this equation = 4x, -2y, 2x

Constants:

the constant is the part of the expression that does not vary with the value of x and y.

Thus, constant terms for this equation = 6

variable terms:

These are the terms that vary at the different values of x and y.

Thus, variable terms for this equation = 4x, -2y

Like terms:

Terms that have identical variable parts (same variable(s) and same exponent(s))

thus, Like terms for this expression = 4x, 2x

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Answer:

y=1x-6

Step-by-step explanation:

First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.

-Hope this helped

There is a $1,000 additional interest earned on a $100,000 CD (Commercial Paper) for 9 months than for 6 months.

The additional interest earned for a 9-month CD over a 6-month CD can be computed using the subtraction operation.

Firstly, the interests on the 9-month CD and 6-month CD are worked out separately, using the interest formula: Principal x Rate x Time.

The interest for the 6-month CD is subtracted from the interest for the 9-month CD.  The result is the difference or additional interest earned.

Commercial Deposit = $100,000

Annual Percentage Rate = 4%

Monthly Percentage Rate = 0.333% (4%/12)

Interest for 9 months = $3,000 ($100,000 x 4% x 9/12)

Interest for 6 months = $2,000 ($100,000 x 4% x 6/12)

The difference in interest earned = $1,000 ($3,000 - $2,000) or ($100,000 x 4% x 3/12)

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APY = 4%

Explanation:

Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.

(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512

This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.

Answer:

105/512

Step-by-step explanation:

hope this helps

Hello there!

Answer:

16

Step-by-step explanation:

[tex] |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0[/tex]

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

Therefore , the solution of the given problem of function comes out to be 2.

A function connects various inputs together or produces a single output from each input. Simply explained, a function is a collection of equations that are linked to a single, identifiable output. A statement, rule, or law which explains the connection between two variables is known as a function in mathematics (the dependent variable). When a rule of this type is applied, there is just one output. by photographer Alex Federspiel. 

Here,

=> (1−α)(1−β)(1+α)(1+β)

​=>(1−α−β+αβ)​ /(1+α+β=αβ)

=> (1−(α+β)+αβ ) / ( 1+(α+β)+αβ)

=>(1 + 2/3 + 1/3 )/ (1 -2/3 + 1/3)

​=> 2 x 3 /2  =3

=> (1−α)(1+β)+(1−β)(1+α) / (1+α+β+αβ)

=> 3(2−2αβ)/2

​

=>3(1−αβ)

=>3(1− 1/3 )

=>2

Therefore , the solution of the given problem of function comes out to be 2.

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The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.

The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.

To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.

When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.

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By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.

It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)

First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.

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A remainder is the remaining amount of a number than comes out of a division. I'm not sure how to explain it better, so I'll give you an example:

Let's say you want to divide 5 by 2. We know that 5 can't be divided by 2 evenly, it won't give you a whole number. Instead it will give you a decimal 2.5.

In this case, 1 is the remainder and I will explain why! Do the long division for 5/2. 2 fits into 5 two times, so you multiply 2 * 2, which gives you 4. If you subtract that number from 5, you get 1. We know that 2 can't fit into one, therefore, 1 is the remainder. once you start getting into decimals, you can fit numbers into other numbers, which is why technically you can fit 2 into 5, but you can't fit it in evenly, if that makes sense!

I hope this example helps see what a remainder is. It's just the number in a long division that the divisor (in my example, 2 is the divisor) can't fit in!

Answer: x = 8.6 y=10.5

Step-by-step explanation:

Answer:

Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.

Answer:

Step-by-step explanation:

3

Answer:

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

If you buy a sweater, the second one is at 40% discount.

Divide the discount between the two to get:

You get a discount of 20% for each sweater.

Answer:

Discount percentage = 20%

Step-by-step explanation:

Discount of the sweaters,

→ first sweater = 0%

→ other sweater = 40%

The average discount percent is,

→ (first sweater + other sweater)/2

→ (0% + 40%) ÷ 2

→ (0 + 40)/2

→ 40/2

→ 20% off

Hence, the answer is 20% off.

Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

The function's zeros are

0=x+2 x=-2

and

0=x+7 x=-7

Consequently, the graph at y=0 where the function crosses those two points .

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The three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

First we have to write the equivalent ratios for 75%.

Since, 75% can be written as,

75/100

Simplifying this, 15/20

Again simplifying this, 3/4

Hence, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4.

Now to write the equivalent ratios for 100%.

Since, 100% can be written as,

100/100

Simplifying this, 20/20

Again simplifying this, 4/4

Hence, the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

Therefore,  the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

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The percentage of people aged 20 to 34 that  have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%

Percentage simply means a proportion of the number as a fraction of 100

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

This implies that  X ~ Normal(x=110, б² = 25)

The z-score probability distribution for the normal distribution is given by;   Z  =   (x-ц)/б ~ N(0,1)

Recall that  population mean = 110 and standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X  125)

 P(X < 150) = P(  <  ) = P(Z < 1.60) = 0.9452

 P(X  125) = P(    ) = P(Z  0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

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Answer:

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

Two copies of one tenth translates as:

Answer:

Two copies of 1/10 = 1/5

Step-by-step explanation:

Given statement,

→ two copies of one tenth.

Forming the expression,

→ 2 × (1/10)

Let's simplify the expression,

→ 2 × (1/10)

→ (2 × 1)/10

→ 2/10

→ 1/5

Hence, the answer is 1/5.

Answer: can you put them in order so i can read it better?

Step-by-step explanation:

Answer: To find the factor pairs for -240, we can use the following steps:

Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)

For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).

The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).

Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).

Step-by-step explanation:

12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.

9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,

= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].

= [8×8 - 4×4] cm².

= 64 - 16 cm².

= 48 cm².

10. Similarly the figure in (10) is twice the area of the two trapezoids.

11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.

12. The total area is the sum of the areas of the trapezoid and the parallelogram.

13. The larger figure is a rectangle with a right-angle triangle on top.

We have to subtract two rectangles from this to obtain the area of the shaded region.

14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.

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The statements that would support her request include:

A well-known marker brand's manufacturer intends to introduce a new shade. It mailed surveys to 5,000 of its customers asking them which general color family they preferred in order to decide which color to add.

The percentage difference is not statistically significant enough to support the majority claim. The survey did not include families of every color, which might have led to nonresponse bias.

It's possible that the mail-in survey had an undercoverage bias. Also, the results were not random because only current clients were polled.

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Answer: the other guy is correct except for the "since only existing customers...".

Step-by-step explanation:

Just took the test, the others he mentioned were right

The density of the material is 1533.3 grams per quarts.

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.

The formula to find the density is Density=Mass/Volume

Density =6900/4.5

Density= 1533.3 grams per quarts

Therefore, the density of the material is 1533.3 grams per quarts.

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