The sun is a even number

The value of the expression is $-56x² + 266x + 261

Algebraic expressions are simply described as mathematical expressions that consists of coefficients, certain variables, terms, constants and factors.

Algebraic expressions are also identified with arithmetic operations, such as;

From the information given, we have;

$49x^2+14x(19-7x)+(19-7x)^2

expand the bracket, we get;

49x² + 266x - 98x² + 361 - 7x²

Now, collect the like terms, we get;

49x² - 98x² - 7x² + 266x + 361

Add or subtract the values

$-56x² + 266x + 261

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The power of the kettle if it takes 90 seconds to boil given the inverse proportionality is 3 kilowatts.

Let

number of seconds that it takes for a kettle to boil = n

power of the kettle = p

n = 270/p

If n = 90 seconds

n = 270/p

90 = 270/p

90 × p = 270

90p = 270

divide both sides by 90

p = 270/90

p = 3 kilowatts

Ultimately, the power of the kettle is 3 kilowatts.

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In the above triangle,

1) the sum of side 1 and 2 is: 4x² + 3x + 4
2) the length of side 3 is: 5x³-6x²-12

1) To find the sum of side 1 and side 2, we simply need to add them together.

Side 1 = 3x² - x - 1

Side 2 = x² + 4x +  5

Side  1 + Side 2 = (3x²  - x - 1) + (x²  + 4x +  5)

= 3x² + x² - x + 4x - 1 + 5

= 4x² + 3x + 4

Therefore, the sum of side 1 and side 2 is = 4x² + 3x + 4

2)  We can derive the expression of the thried side by removing the expression in  (1) above form the perimeter.

That is;

(5x³-2x² + 3x - 8) - (4x² + 3x + 4)

First we distribute the negative sign

= 5x³-2x² + 3x - 8 + -1 (4x² + 3x + 4)

= 5x³-2x² + 3x - 8 + -1 (4x²) -1( 3x) -1( 4)

= 5x³-2x² + 3x - 8 + -4x² - 3x - 4

Combining like terms we have

= (5x³) (-2x²+-4x²) + (3x +- 3x) + (-8 +   - 4)

= 5x³-6x²-12

Hence the missing side (thrid side is) 5x³-6x²-12

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The maximum volume of the cylindrical can such that the sum of its height and its circumference is 45 cm is  337.5 cm³

Let's denote the radius of the cylindrical can as r, and its height as h.

The circumference of the base of the can is 2πr, so the sum of the height and the circumference can be written as:

h + 2πr = 45..(1)

We want to find the maximum volume of the can, which is given by:

V = πr²h..(2)

From (1), h = 45 - 2πr

Substitute h value in equation above

V = πr²(45-2r)

V = 45πr² - 2π²r³

To find the maximum volume, we have to find the differentiation of V

dV/dr = 90πr - 6π²r² = 0

Solving for r, we get:

r = 15/π cm

Now plug in r value in h

V = π(15/π)²(15)

= 337.5 cm³

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Answer: The correct answer would be n/255 = 115/360 (N= 81.46)

Step-by-step explanation:

n/255 = 115/360

155/360 = (255)

n = 81.46 ft squared

The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect since, one group only received a placebo accurately describes the benefit of comparison in the experiment shown in the design web.  Thus option A is correct.

A scientific experiment inside that carry out a sequence of tasks and closely monitor their results to discover new information. An investigation is a method that used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that hasn't been tried before.

Although one sample only obtained a placebo inside the investigation depicted in the design web, which is difficult to compare the severity of allergic rhinitis in both groups to establish whether the drug had a substantial impact.

Hence, option A is the correct option.

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8% will be the value of sales tax that has been charged on a tie will be.

The tie cost is $22.50

The cost after the tax is $24.30.

The change in the cost will be:

= cost after-tax - cost before tax

=24.30-22.50

=1.8

The percentage change will be

Next, assemble a ratio of the sales tax to the pre-tax cost of the tie.

=Sales tax/Pre-tax value

= (1.8/22.50)*100

=8%

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Answer:

The answer to your problem is, 6.1 inches

Step-by-step explanation:

So we know that 1 inch of there model in real life is 50 feet.

Divide:

305 / 50

= 6.1 but we are going to use 6

Since it is 6 there model is 6 inches.

But remember we still have that 0.1 which we need to full fill for that:

Note that 6.1 will be in inches.

So it is done.

Thus the answer to your problem is, 6.1 inches

We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.

We also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.

Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.

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Answer:

Step-by-step explanation:

tax

C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

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

Explanation:

If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.

Count the dots over the x axis labels of "0.4" through "0.6"

That makes 5+1+1 = 7 dots total.

There are 7 instances where the difference of proportions is 0.4 or larger.

This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.

This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.

Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.

Answer:

Step-by-step explanation:

The mean of data is 5.5

Given that

The number of data is = n = 4

The given Numbers are 5, 6, 8, 13

We know

Mean x bar = (sum of data)/(number of data)

                   = (5 + 6 + 8 + 3)/4

                   = 22/4

                   = 5.5

Thus,  x bar = 5.5

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Answer:

c

Step-by-step explanation:

Answer:  C

Step-by-step explanation:

A.  incorrect.  Acute is when all the angles in the triangle are less than 90, not including 90 ex. (35, 65,80)

B.  incorrect.  Obtuse is when you have 1 angle greater than 90, not including 90.  ex( 100,20, 60)

C. correct, Right is when you have have 1, 90 degree angle.  That symbol in the corner of the triangle means the lines are perpendicular, which means it forms  right angle or 90 degree angle

D, incorrect because C is true

Answer: To solve a two-step inequality, undo the addition or subtraction first, using inverse operations, and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.

Step-by-step explanation:

The missing values from ratio table are 17 and 28.

We have table as

3      1

48    16

51      x

78    26

84     y

So, the ratio are in proportion then

48 / 16 = 51 /x

3 = 51/x

x= 51/3

x = 17

and, 3/1 = 84/y

y= 84/3

y= 28

Thus, the values are 17 and 28.

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The  probability that the student does not own a trampoline is given by the relation P ( A' ) = 5/12

Given data ,

Let the probability that the student does not own a trampoline be P ( A ' )

Given that there are 14 students who own a trampoline out of 24 students in total, the probability of owning a trampoline is 14/24. Therefore, the probability of not owning a trampoline is:

1 - 14/24 = 10/24 = 5/12

So, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12

Hence , the probability is 5/12

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Answer:6720m^2

Step-by-step explanation:

Step-by-step explanation:

Upper problem:

The transformation is a translation of 3 units down.

Lower problem:

The transformation is a translation of 2 units left and 5 units down.

Step-by-step explanation:

For a RIGHT triangle   tan Φ = opposite leg / adjacent leg

 for this triangle

         tan 71 = x / 5.7

       5.7 * tan 71 = x    =   16.6  units

Answer:

x=3/2

x=-2

Step-by-step explanation:

The value of x in the given diagram is 12.

option C.

The value of x in the given diagram is calculated by apply the principle of intersecting chord theorem as shown below;

The intersecting chord theorem states that angle formed at the circumference is twice the angle at the tangent.

the angle at circumference = 360 - (6 + 20x)

tangent angle = 4x + 9

360 - (6 + 20x) = 2 (4x + 9)

360 - 6 - 20x = 8x + 18

-28x = -336

x = 336/28

x = 12

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The measure of angle ABC is 30 degrees. Option B

It is important to note the properties of a circle, they include;

Also note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.

From the information given, we have that;

<ADC = 60 degrees

This is the angle at the circle

Then,

<ABC is the angle at the circumference

<ABC = <ADC/2 = 60/2 = 30 degrees

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Answer:height = 5 inches  and the base = 10 inches.

Step-by-step explanation:

If the graphs of the linear equations in a system are parallel: A. There is no solution.

The general form for the equation of a line is:

y = mx + c

where:

m is slope

c is y-intercept

Usually, for two equations to have a solution, they must intersect each other.

However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.

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There are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

The organization or positioning of a group of items or components in relation to one another is referred to as an arrangement. It can be used in a variety of situations, such as mathematics, art, or event planning, and can relate to the arrangement, positioning, or grouping of things.

The number of different ways you can arrange 7 books in a specific order is given by the permutation formula:

P(7,7) = 7!

where "!" denotes the factorial operation.

Thus, the number of ways you can arrange your 7 favorite books along a small shelf, assuming that the order of the books makes a difference to you, is:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

Therefore, there are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

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The height of the triangle is h = 18.18 inches

Given data ,

In an equilateral triangle, all three sides are equal in length.

Let the length of each side be s

Now , the perimeter of the equilateral triangle is given as 63 inches, so we have:

Perimeter of the triangle = 3s = 63 inches

Dividing both sides by 3, we get:

s = 63/3 = 21 inches

Let's now plot an altitude from one of the equilateral triangle's vertex to the side's midway. As a result, two right-angled triangles will be formed, each with the hypotenuse "s" and sides "s/2" and "h"

From the Pythagoras theorem , we get

(h²) + ((s/2)^2) = s²

Substituting the values we found earlier for "s", we get:

(h²) + ((21/2)²) = 21²

Simplifying further, we have:

(h²) + (10.5²) = 21²

(h²) + 110.25 = 441

Subtracting 110.25 from both sides, we get:

h² = 330.75

On taking square roots on both sides , we get

h = √(330.75)

h ≈ 18.18 inches

Hence , the height of the equilateral triangle is 18.18 inches

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Answer:

It's linear

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

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