Select the correct answer.
CAMERY
Which expression is equivalent to the given expression?
2x214x + 24
OA. 2(x-8)(x + 3)
OB.
(2x12)(x - 2)
OC. 2(x - 3)(x - 4)
OD. 2(x - 5)(x - 2)

Answer:

8, 26 and 19

Step-by-step explanation:

Perimeter is the length of all sides of a polygon. It is simply the length of the boundary around a closed shape. Perimeter of a triangle = Sum of all three sides.

Hence,

[tex]\Rightarrow[/tex] n + 3n + 2 + 4n - 13 = 69 (acc. to Q)

[tex]\Rightarrow[/tex] n + 3n + 4n + 2 - 13 = 69

[tex]\Rightarrow[/tex] 8n - 11 = 69

[tex]\Rightarrow[/tex] 8n = 80

[tex]\Rightarrow[/tex] n = 80/10

[tex]\Rightarrow[/tex] n = 8

Length of all three sides:

Answer:

-4

Step-by-step explanation:

Split the problem into two cases: one positive and one negative

|4x+7| =9

4x+7=9

(4x+7) =9

Subtract 7 from both sides

4x+7 - 7 = 9 - 7

Solution

x = 1/2

x = -4

The sequence 1620,540,180,60,20, . . . .. is a geometric sequence with common ratio 1/3.

To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic sequence, then:

  a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric sequence, then:

  a(n) = a(n-1) . r

where r is the common ratio.

The given sequence is:

    1620,540,180,60,20, . . .  .

In this sequence:

a(1) = 1620

a(2) = 540

a(3) = 180

First we check the difference between 2 consecutive terms:

a(2) - a(1) = 540 - 1620 = -1080

a(3) - a(2) = 180 - 540 = -360

Since the difference is not constant, then the sequence  is not an arithmetic one.

Now we check the ratio,

a(2) : a(1) = 540 : 1620 = 1/3

a(3) : a(2) = 180 : 540 = 1/3

and so on

Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 1/3

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Question

The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.

What is the predicted population in the year 2014?

Answer:

3541

Mari put 1/2  of a bottle of water at the water fountain .

Let the capacity of the bottle holding water be 100 .

It is given that Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.

The amount of water is given by :

 2/3 of 100 - 1/6 of 100 =  2/3 × 100 - 1/6 × 100

                                       = 100( 2/3 - 1/6)

                                        = 100(1/2)

                                        = 50

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It looks like you want to find

[tex]\displaystyle \int_1^4 x f''(x) \, dx[/tex]

Integrate by parts:

[tex]u = x \implies du = dx[/tex]

[tex]dv = f''(x) \, dx \implies v = f'(x)[/tex]

Then

[tex]\displaystyle \int_1^4 x f''(x) \, dx = x f'(x) \bigg|_{x=1}^{x=4} - \int_1^4 f'(x) \, dx[/tex]

By the fundamental theorem of calculus,

[tex]\displaystyle \int_1^4 f'(x) \, dx = f(4) - f(1)[/tex]

so that

[tex]\displaystyle \int_1^4 x f''(x) \, dx = 4 f'(4) - f'(1) - f(4) + f(1) = 12 - 7 - 8 + 4 = \boxed{1}[/tex]

The number falls between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375

first we convert fraction into decimal number

[tex]-\frac{25}{4}[/tex]  = - 6.25

and for remove percentage we divide by 100

- 400 % = - 4

from choose the option,

[tex]-\frac{43}{8}[/tex]  = 5.375

- 720 % = - 7.2

[tex]-\frac{20}{3}[/tex] = - 6.6

then, choose  [tex]-\frac{43}{8}[/tex]  

therefore, number lies between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375

A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.

Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12.

All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that b ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:

Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.

A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.

A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.

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Answer:

x=7

Step-by-step explanation:

AB is 1 part of the line

BC is the other part of the line

the total length of the line is 50 units

when you add AB to BC you should get 50

5x+2x+1=50

7x+1=50

7x=49

x=7

Answer:

when sixteen times a number is decreased by seventeen the result is 26

If a cargo van delivers only 50-pound and 80-pound packages and the total weight of the packages cannot exceed 1,500 pounds, then a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip is x + y ≥ 20; 80x + 50y ≤ 1,500.

A system of inequalities is a term used in mathematics that is a set of two or more than two inequalities in one or more than one variable.

Consider,

the number of 80-pound packages = x

the number of 50-pound packages = y

As the van can carry a minimum of 20 packages, the sum of x and y can be given as,

x + y ≥ 20

The weight of 80-pound boxes can be given as 80x and the weight of 50-pound boxes can be given as 50x. As the total weight of the packages cannot be more than 1500 pounds,

80x + 50y ≤ 1500

If we consider x to be 19,18 or 17 and the remaining to be y, it will exceed the limit of 1500 pounds. If x is considered to be 16,

80(16) + 50 (4) = 1480

Hence, the maximum number of 80-pound packages that the van can carry per trip is 16.

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Answer:

The simplified answer would be: -22n

Please correct me if I am wrong, hope this helps! ;)

Answer:

-22n.

Step-by-step explanation:

'+-' = '-'   so,

– 8n+– 8n+– 6n

= -8n - 8n -6n

= -22n.

Answer:

x=-9

Step-by-step explanation:

x=-9

Thank you so much!

Answer:

the answer is D

hope this helps!

Answer:

4.6667

Step-by-step explanation:

answer=

Children =5

Adults = 3

3/8 are adults

Answer: 180

Step-by-step explanation: 3 times 6 is 18 so just add a zero

Answer: 180

Step-by-step explanation:

3x60

60+60+60

Restaurant A offers the best value as one hamburger is $1.29

The first step is to calculate the price of one burger in restaurant A

11= 14.19

1= x

cross multiply

11x= 14.19

x= 14.19/11

x= 1.29

The next step is to calculate the price on one burger in restaurant B

2= 2.64

1= x

Cross multiply

2x= 2.64

x= 2.64/2

x= 1.32

Hence the price of the hamburger at Restaurant A is $1.29 and the price at Restaurant B is $1.32.

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Answer:

(A) Restaurant A for $1.29

Step-by-step explanation:

Got it right on my quiz.

Answer:

No decimal: 905

One decimal: 905.3

Solution=0.76

How to solve 11/12 - 7/45?

[tex]\frac{11}{12} -\frac{7}{45} \\=\frac{(11*45-7*12)}{540} \\=\frac{411}{540} \\=0.76[/tex]

What is a fraction?

       Ex: 1/2 = 0.5

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Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.

An obtuse-angled triangle or obtuse triangle is one in which one of the angles is an obtuse angle or greater than 90°. The sum of the obtuse triangle's interior angles is only 180°. This means that the angle sum property of any triangle remains unchanged.

An obtuse-angled triangle is one in which one of the interior angles is greater than 90°. If one angle in an obtuse triangle measures more than 90°, the sum of the remaining two angles is less than 90°.

Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.

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For the given subscriptions, we have that:

a) The mean is of $6.42.

b) The median is of $5.

c) The modes are of 5 and 10.

d) Marshall would have to add a subscription of $12.25.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For this problem, the observations are given as follows:

10, 5, 10, 4, 12, 5, 6, 2.75, 3.

Hence the mean is:

M = (10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3)/9 = $6.42.

With another observation, we want a mean of $7, hence:

(10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3 + x)/10 = 7

57.75 + x = 70

x = 12.25.

Hence, for item d:

Marshall would have to add a subscription of $12.25.

The median of a data-set is the middle value, which is the value that 50% of the data-set is greater and 50% is lesser.

The ordered data-set in this problem is:

2.75, 3, 4, 5, 5, 6, 10, 10, 12.

The middle value is of 5, which is the median.

The mode of a distribution is the observation that appears the most times in the distribution.

In this problem, those observations are 5 and 10, both of which appears twice, hence the distribution is bimodal.

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ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

The right angle triangle JKL with base JL and perpendicular KJ has been drawn.

Height = KJ = a

Since J(0,0) so K(0,a)

Hence "ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units".

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Answer:

Step-by-step explanation:

where?

Answer: 2n+5-3

Step-by-step explanation:

Break this quote down:

"three less than the product of a number and two, increased by five"

To this:

"three less than the product" ==> product-3

Now break this quote down

Product: "product of a number and two, increased by five"

To this:

"product of a number and two" ==> 2*n

"increased by five" ==> +5

"product of a number and two, increased by five" ==> 2*n+5

Product: 2*n+5

Product-3: 2*n+5-3=2n+5-3

we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

Because one of these solutions does not have a meaning in the given contest.

So we have a square with an area of 16 square units, then the side length of that square will be given by:

S^2 = 16 square units

Now, there are two solutions for the above equation, these are:

S = 4 units

S = -4 units.

But being a solution of the equation does not mean that the solutions have sense in the context of the problem.

When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"

That does not make sense, remember that math is just a language, and it should be used to communicate things to others.

So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.

That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

Because one of these solutions does not have a meaning in the given contest.

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Answer:

No

Step-by-step explanation:

12/24 = (1 * 12) / (2 * 12) = 1/2

24/72 = (1 * 24) / (3 * 24) =  1/3

1/2 ≠ 1/3

Step-by-step explanation:

Simon only used 125ml milk

250÷2=125

Craig used 375ml milk

250x1.5=275

The equation that is not a power equation is p = v²×i

From the question, we are to determine which of the given equations is not a power equation

Where the Voltage, V, and the Current, I, are given, the power, P is given by

P = IV

When the Voltage and the Resistance, R, are given

P =  V²/R

When the Current and the Resistance are given,

P = I²R

∴ P =  V²/R, P = IV, and P = I²R are power equations.

Hence, the equation that is not a power equation is p = v²×i

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