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Answer:

The product of the Width and Length is x^2 + 4x + 3 cm^2.

Step-by-step explanation:

The volume of a box = 5x^3 + 20x^2 + 15x cm^3.

Volume of a Box = W*L*H       [Width(W), Length(L), and Height(H)]

W*L*(5x) = 5x^3 + 20x^2 + 15x cm^3

W*L = (5x^3 + 20x^2 + 15x cm^3)/5x cm

W*L = x^2 + 4x + 3 cm^2

We know the area of the base of the box (W*L).  It is x^2 + 4x + 3 cm^2.

To find the actual width and length, we need to know one of the variables, L or W.  Without that, all we can say is that their product (W*L) is x^2 + 4x + 3 cm^2.

Answer:

10

Step-by-step explanation:

multiply -4 and 3 to get -12

multiply -12 and -2 to get 24

multiply 2 and 7 to get 14

multiply 14 and 1 to get 14

subtract 14 from 24 to get 10

Answer:

12 is the answer

Step-by-step explanation:

FIRST do 23 - 11 and you will find your answer

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

[tex]y+6=x^2-x[/tex]

Complete the square by adding (b/2)^2

[tex]y+6+0.25 = x^2-x+0.25[/tex]

Rewrite as square binomial

[tex]y+6.25 = (x-0.5)^2[/tex]

Isolate y

[tex]y=(x-0.50)^2-6.25[/tex]

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

[tex]y=-(x^2-x-6)[/tex]

Add 6 to both sides (on the left side add -6 since -1 was factored out).

[tex]y-6=-(x^2-x)[/tex]

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]

Rewrite as square binomial

[tex]y-6.25=-(x-0.5)^2[/tex]

Add 6.25 to both sides

[tex]y=(x-0.50)^2+6.25[/tex]

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

Answer:

a) y-intercept (0,  -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)

b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The ordered pair which will satisfy both the inequalities will be the solution to the system of inequalities. Therefore, let's substitute each solution in the given inequalities,

A.) (–3, 4)

          4 > (-3)² + 1

Since the first inequality is not satisfied this is not a part of the solution.

B.) (–2, 6)

          6 > (-2)² + 1

          6 > 5

          6 < (-2)² - (-2) + 1

          6 < 7

Since both the inequalities are satisfied this is the solution to the given system of inequalities.

C.) (0, 2)

          2 > 0 + 1

          2 > 1

          2 < (0)² - (0) + 1

          2 < 1

Since the second inequality is not satisfied this is not a part of the solution.

B.) (2,4)

          4 > (2)² + 1

          4 > 5

Since the first inequality is not satisfied this is not a part of the solution.

Hence, the correct option is B.

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Answer:

72  sq cm

Step-by-step explanation:

For any rectangle, the diagonal is the hypotenuse of the right triangle formed by the base of the rectangle(b) and the height (h) of the rectangle

By the Pythogorean formula

[tex]d^{2} = b^{2} + h^{2}[/tex]

where d is the diagonal

For a square, all sides are equal so b = h = a and we get the formula

[tex]d^{2} = a^{2} + a^{2} = 2a^{2}[/tex]

[tex]a^{2} = d^{2} /2[/tex]

In this case we have d =12 so

[tex]a^{2} = 12^{2} /2 = 144/2 = 72[/tex]

But for a square of side a, the area is [tex]a^{2}[/tex] so 72 is the area

Answer:

72 square cm

Step-by-step explanation:

       [tex]\sf \boxed{\bf Area = \dfrac{d^{2}}{2}}[/tex]  , here d is the length of the diagonal

                  [tex]\sf =\dfrac{12* 12 }{2}\\\\ = 6*2\\\\= 72 \ cm^2[/tex]

The decimal: 0.4545...

Can be written in fraction form as 45/99.

Here we have the number:

N = 0.4545...

Notice that the repeating digits are two, 4 and 5.

Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:

100*0.4545... = 45.4545...

Now if we subtract the original number, we get:

45.4545... - 0.4545... = 45

This means that:

(100 - 1)*0.4545... = 99*0.4545... = 45

Then we can multiply and divide our number by 99, so we get:

[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]

So the fraction is 45/99

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Answer:

1.596

Step-by-step explanation:

So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.

[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]

Answer:

x = -1.596

Explanation:

[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]

take log on both sides

[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]

[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]

[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]

[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]

calculate

[tex]\rightarrow \sf x= -1.596322539[/tex]

[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]

Answer:

8ax - 8bx + 4a - 4b

Step-by-step explanation:

(a - b)(2x - 3) + (6x + 7)(a - b)

2ax -3a -2bx +3b + 6ax - 6bx + 7a -7b

8ax + 4a - 8bx - 4b

Answer:

A. 0.2

Step-by-step explanation:

First make the table.

                                          10-grade  11-grade  12-grade  Total

Woodson high school    |     110     |     120    |      80     |   310   |

Valley high school          |     180    |     150    |     120     | 450   |

Riverside high school     |     160    |     140    |     200    | 500   |

Total                                 |     450   |     410    |     400    | 1260 |

Question: In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?

First, find 12-grade and riverside high school number. 200. Take the total lined up with total number, which is 1260, and divide 200 divided by 1260.

200/1260=0.2

The answer is 0.2.

Hope this helps!

If not, I am sorry.

Answer:

its .4

Step-by-step explanation:

i got it wrong when i tried it says it is .4 or the third option c

Answer:

6/7, -6/7

Step-by-step explanation:

True. All natural numbers N are integers Z, but not all integers are natural numbers.

Natural numbers:

Integers:

Since natural numbers are all positive, N is positive integers but not all integers are natural numbers.

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We happen to have

[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]

which is to say, the base-8 representation of 1/7 is

[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]

This follows from the well-known result on geometric series,

[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]

if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have

[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]

Uniformly multiplying each term on the right by an appropriate power of 2, we have

[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]

Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.

[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]

That is,

[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]

[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]

[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]

etc. so that

[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]

and thus the base-16 representation of 1/7 is

[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]

and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.

Given the egg has hatched, the egg was kept warmer than room temperature.

                      Cool      Room temperature        Warm             Total

Hatched           5              16                                21                  42

Unhatched        18           10                                 4                   32

Total                 23            26                                25                    74

To fill the blank we need to analyse the temperature carefully if see the table then cool hatched eggs are 5 , unhatched cool eggs are 18, eggs on room temperature and hatched are 16, eggs on room temperature and unhatched are 10, warm hatched eggs are 21 and warm unhatched eggs

So we can notice that hatched eggs are more in room temperature.

Hence hatched eggs are more in room temperature.

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Answer:

Given the egg has hatched the egg was kept warmer than room temperature.

Hope this helped!

Answer:

its D. 2 and 3

Step-by-step explanation: supplementary angles are angles that add up to 180 (or that make a straight line) the angle pairs that make a straight line are 1 and 2, 2 and 3, 3 and 4, and 4 and 1.
So D would be correct

At  150 minutes the length of the first candle is 3 times that of the other.

The complete question is

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in 5 hours and the second one burns in 2 hours. Both the candles are lit together. After how many minutes the length of the first candle is 3 times that of the other?

When two algebraic expression are equated using an equal sign an equation is formed.

First candle burns for 5 hours

Second candle burns for 2 hours

Let the length of candle be l.

After t time (in minutes), length of first candle =l−(lt/300)

Length of second candle =l− (lt/120)

From the data given

l -  (lt/120) = 3 * (l−(lt/300))

On simplifying

4t = 600

t = 150 minutes

Therefore after 150 minutes the length of the first candle is 3 times that of the other.

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Answer:

Perimeter of a rectangle: 2L + 2W

2(7u - 8) + 2(10u + 3)

= 14u - 16 + 20u + 6

= 34u - 10

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle.

P = 2 ( length + width)

The perimeter of the rectangle is represented by the expression

(34u - 10) centimeters.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The width of a rectangle = (10u + 3) centimeters.

The length of the rectangle =  (7u - 8) centimeters.

The perimeter of a rectangle is given as,

P = 2 ( length + width)

P = 2 ( 7u - 8 + 10u + 3)

P = 2 (17u - 5)

P = (34u - 10) centimeters.

Thus,

The perimeter of the rectangle is represented by the expression

(34u - 10) centimeters.

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Now out of these points, steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.

The steps to copy a line segment are given below:

1. Let's start with a line segment AB that we have to copy.

2. Now mark a point C. Below or above AB, which will be one endpoint of the new line segment.

3. Now, put the compass tip on point A of the line segment AB.

4. Spread the compass up to point B, so that the compass width is equal to the length of AB.

5. Without changing the compass width, now place the compass tip on point C that you made in step 2.

6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.

7. Draw a line from C to D.

Now out of these points, steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.

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Answer:

This is an extremely easy question bro!

1. 3²

2. 3 (Base) ² (Exponent)

3. Expanded form: (9 * 1)

   Standard form: 9

Step-by-step explanation:

Well, there's none.

The statement that must be true about square WXYZ are as follows;

Therefore, the statement that must be true about square WXYZ are as follows;

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The correct value of the given function at x = 5 is y =3.

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

Here, the given equation :

         y = x - 2

put x = 5 in the given equation, we get

        y = 5 - 2

        y = 3

Thus, the correct value of the given function at x = 5 is y =3.

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The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.

It follows from the task content that the variables are;

let x be the amount of 30% strawberry concentrate.

let y be the amount of 55% lemon concentrate.

The equations of the linear system according to the task content are as follows;

From the first equation; x = 2-y;

Hence, upon substitution; we have;

0.30(2-y) + 0.55y = 0.8

0.25y = 0.2.

y = 0.2/0.25 = 0.8L.

Hence, x = 2- 0.8 = 1.2L.

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Answer:

$42.95

Step-by-step explanation:

If Chris lost $8.59 playing poker in one week, in five weeks he would lose $42.95.

$8.59 lost per week.

5 weeks.

$8.59 x 5 = $42.95.

Hope this helps!

If not, I am sorry.

[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]

Solution : ] 3 , + ♾️ [

PLEASE GIVE BRAINLIEST

Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .

Ounce is defined as 1/16 part of a pound.

It is given that

price of a 2-ounce box is $1.10,

a 16-ounce box is $8.98

a 32-ounce box is $17.98.

As Jeff wants to purchase total 48 ounce chocolates , the box which is more cheaper has to be determined  

The price of 1 ounce in a 2 ounce box is $1.1 /2 = $ 0.55

The price of 1 ounce in a 16 ounce box is $8.98 /16 = $ 0.56

The price of 1 ounce in a 32 ounce box is $17.98 /32 = $ 0.56

Therefore Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .

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The rules describes the transformation is (x, y)(x, y).

The correct option is (B)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

If the figure is rotated 360 degrees then the coordinates remains unchanged.

This is because when from where it started it stops there again.

As the 360 degree rotation is complete circle rotation.

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[tex]6x+3=5x-8[/tex] (given)

[tex]x+3=-8[/tex] (subtract 5x from both sides)

[tex]x=\boxed{-11}[/tex] (subtract 3 from both sides)