simplify 6/4-√5
___+___

Answer:

Equation for the perimeter of prism's square face: 16x + 12

Step-by-step explanation:

Volume of Square prism = Length * Width * Height

                                         = 144 x^3 + 216 x^2 +81 x

taking 9x common = 9x( 16 x^2 + 24 x + 9)

                               = 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )

                                = 9x ( 4x+3)^2

so the length is 9x, width is 4x+3 and height is 4x+3

Now, Perimeter of prism's square face = 2* Width + 2 * Height

                                                                = 2* (4x+3) + 2* (4x+3)

                                                                = 8x +6 + 8x + 6

                                                                = 16x +12

Final answer:

Factoring the volume expression of the square prism reveals the square's base area. Once identified, the perimeter can be found by multiplying one side length by four.

Explanation:

The volume V of a square prism can be expressed as the product of the area A of its square base and its height h, so V = A × h. Given the polynomial expression for the volume, we can factor it to find the square base area. The given volume is 144x³ + 216x² + 81x. Factoring out the greatest common factor of 9x, we get 9x(16x² + 24x + 9). Recognizing this as a perfect square trinomial, we can further factor it to 9x(4x + 3)². Therefore, the area A of the base is (4x + 3)². To find the perimeter P of the square base, we take four times one side of the square, which is P = 4(4x + 3). Simplifying, we get P = 16x + 12.

Answer:

1/3.

Step-by-step explanation:

Since there are 12 friends and 4 bread loaves, you would divide 4/12 by 4 which is 1/3.

Answer:

  (a) reduction

  (b) 1/2

Step-by-step explanation:

The image figure A'B'C'D' is smaller than the original figure ABCD, so the dilation is a reduction.

Each of the points A'B'C'D' is half as far from the origin as the original points ABCD, so the scale factor is 1/2.

_____

Draw lines C'C and D'D. You will see they meet at the origin, which is the center of dilation. Then look at how far the points are along those lines. C' is one grid square diagonal along the line; C is 2 grid square diagonals along that line, so is twice as far from the origin. That is, C' is 1/2 the distance of C, so represents a reduction by a scale factor of 1/2.

The same distance considerations are observed along the line D'D. The point D' is the diagonal of a 2x1 rectangle from the origin (A distance of √5.) The point D is the diagonal of a 4x2 rectangle from the origin, so is twice as far. Once again D' is 1/2 the distance of D, so represents a reduction by a factor of 1/2.

Answer:

  D.  N = w² + 8w + 12

Step-by-step explanation:

The current size is w by w+4, so the area is ...

  A = w(w+4)

When each dimension is increased by 2, the new size is (w+2) by (w+4+2). The latter dimension can be simplified to (w+6). Now, the new area is ...

  N = (w+2)(w+6) = w² +8w +12 . . . . . . . matches choice D

Answer:

p = w - 8

Step-by-step explanation:

I can find 1p or p by subtracting 8 on both sides of the equation.

We need to isolate the variable p here, so we subtract 8 from both sides.

Answer:

Part A) The graph in the attached figure

Part B) [tex]y=2.40x[/tex]

Step-by-step explanation:

Let

y------> the price of gas

x-----> the volume of gas purchase

we know that

The relationship between the cost of gas and the volume purchase represent a direct variation and remember that a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the constant of proportionality k is equal to

[tex]m=k=2.40\frac{\$}{gallon}[/tex]

and the y-intercept b is equal to zero because the line passes through the origin

[tex]b=0[/tex]

therefore

the linear equation is

[tex]y=2.40x+0\\y=2.40x[/tex]

using a graphing tool

see the attached figure

Answer:

see attachment for answers and correction

Step-by-step explanation:

Your answer is correct for Wyatt.

The missing blanks for Abigail are filled with the integer part and the fractional part of the mixed number Abigail started with.

___

Beware signs. In this problem -6 + 1/4 is not the same as -6 1/4.

Answer:

  465.988 mph

Step-by-step explanation:

The two speed vectors form two sides of a triangle. Their included angle is 45°, so the law of cosines can be used to find the resultant magnitude x.

  x^2 = 500^2 +50^2 -2·500·50·cos(45°) ≈ 217,144.66

  x ≈ √217,144.66 ≈ 465.988 . . . . miles per hour

_____

You may find you need to round the answer to the nearest whole number.

Answer:

A) The y-coordinates have the same value.

Step-by-step explanation:

Answer:

D) Both points are 4 units above the y-axis.

Step-by-step explanation:

Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE?

A) The y-coordinates have the same value. TRUE. The y-coordinates have the value 4.

B) The x-coordinates have the same absolute value. TRUE. 3 and -3 have the same absolute value, |-3| = |3| = 3.

C) The x-coordinates are opposite numbers. TRUE. 3 and -3 are opposite numbers.

D) Both points are 4 units above the y-axis. NOT TRUE. Both points are 4 units above the x-axis.

Answer:

30°

Step-by-step explanation:

If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.

If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.

Thus, the measure of the angle ELM is 180°-42.5°=137.5°.

Consider triangle EML. In this triangle,

m∠MEL=180°-137.5°-12.5°=30°.

Thus, m∠MEJ=30°.

Answer:

30°

Step-by-step explanation:

x=(a-b)/2 because of secants exterior angles

x=(85-25)/2 Substitution

x=60/2 Algebra

x=30° Answer

Answer:

Step-by-step explanation:

It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...

  XZ² = YZ² + XY²

Solving for XY, you find ...

  XY² = XZ² - YZ²

  XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25

  XY = 4.5

The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...

  Sin = Opposite/Hypotenuse

  sin(X) = 6/7.5

  Cos = Adjacent/Hypotenuse

  cos(X) = 4.5/7.5

  Tan = Opposite/Adjacent

  tan(X) = 6/4.5

_____

Comment on the triangle and ratios

The side lengths of this triangle are in the ratios ...

  XY : YZ : XZ = 3 : 4 : 5

If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.

The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.

Answer:

65

Step-by-step explanation:

Let "a" represent the number of adult tickets sold. Then the number of child tickets sold is 151-a and the total revenue for the day is ...

9.10·a + 5.10·(151-a) = 1030.10

4a = 260 . . . . . . subtract 770.10

a = 65 . . . . . . . . . divide by 4

The number of adult tickets sold on Monday was 65.

_____

Check

65 adult tickets and 86 child tickets will produce a revenue of ...

65·9.10 + 86·5.10 = 591.50 + 438.60 = 1030.10 . . . . answer checks OK

Answer: 65 adult tickets were sold that day

Step-by-step explanation:

Let's call:

c: number of child tickets sold on Monday.

a: number of adult tickets sold on Monday.

Set up the following system of equations:

[tex]\left \{ {{c+a=151} \atop {5.10c+9.10a=1030.10}} \right.[/tex]

You can solve it by Substitution method, as following:

- Multiply the first equation by -5.10

- Add both equations.

- Solve for a.

Then:

[tex]\left \{ {{-5.10c-5.10a=-770.1} \atop {5.10c+9.10a=1030.10}} \right.\\---------\\4a=260\\a=65[/tex]

Answer: Y=-13/4 + 4

Hope this helps! :)

Answer:  [tex]\bold{x=\dfrac{1\pm \sqrt5}{2}}[/tex]

                both zeros are irrational numbers

Step-by-step explanation:

Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.

[tex]\dfrac{1}{x}=x-1\qquad \text{Restriction: }x\neq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=\dfrac{-(-1)\pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}\\\\\\x=\dfrac{1\pm \sqrt5}{2}[/tex]

Answer:

f(x) = 3(x -4)^2 +1

Step-by-step explanation:

Usually you start by factoring the leading coefficient from the first two terms:

f(x) = 3(x^2 -8x) +49

Now, you add the square of half the x-coefficient inside parentheses, and subtract the same quantity outside.

f(x) = 3(x^2 -8x +(-4)^2) -3(-4)^2 +49

= 3(x -4)^2 -48 +49

f(x) = 3(x -4)^2 +1 . . . . . . . . the vertex form you desire

The center of the circle is (-4, 5) while the radius is 11 units.

Answer:

8/3

Step-by-step explanation:

Let S represent the value of 2.666...(repeated). Then 10S will have the value 26.666...(repeated). Subtracting S from 10S, we have ...

10S -S = 26.666... - 2.666... = 24

9S = 24

S = 24/9 = 8/3

The improper fraction equivalent of 2.666...(repeated) is 8/3.

_____

In general, if the number of repeated digits is n, you do this procedure multiplying the number by 10^n before you do the subtraction. The result is a fraction with (10^n)-1 as a denominator. That is, for a 2-digit repeat, the denominator will be 99; for a 6-digit repeat, 999999.

Knowing this, you can immediately recognize that 0.6...(repeated) = 6/9 = 2/3. Then your number 2.666...(repeated) is 2 2/3 = 8/3.

The repeating decimal 2.6 (2.66...) can be simplified as a fraction by setting it equal to a variable, multiplying by a power of 10 to eliminate the decimal, subtracting the original equation, and solving for the variable. This process results in the simplified fraction 8/3.

The number 2.6 repeated refers to the number where the digit 6 repeats indefinitely. To simplify it as a fraction, we can do the following steps:

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Answer:

A D and E are the answers

Step-by-step explanation:

The general formula is n * CD so all you do is multiply n times the original length.

A is true. 3/2 * 12  = 36/2 = 18 True.

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

B is not true 4*12 = 48 not 3

B would be true if n = 1/4

1/4 * 12 = 3

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

C is not true 8*12 = 96 not 20

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

D is true 2 * 12 = 24

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

E is true 3/4 * 12  = 36/4 = 9

A D and E are the answers

Answer:

Step-by-step explanation:

Call the point of intersection of AA' and BC point X. Then ...

  CX = AC·cos(90°-x) = AC·sin(x)

and the area of AA'C is ...

  area = AC·CX·sin(90°-x) = AC²·sin(x)cos(x) = (1/2)AC²·sin(2x)

Obviously, area is maximized for 2x = π/2, or x = π/4 when AC is fixed.

___

On the other hand, ...

  AC = AB·tan(x)

so the area of the triangle is ...

  area = (1/2)AC²·sin(2x) = (1/2)(AB·tan(x))²·sin(2x) = AB²·sin(x)³/cos(x)

For fixed AB, area approaches infinity as x approaches 90°.

_____

Comment on the attachments

The attached diagrams show AC=1 and B free to move. Values of x around 45° are shown. The number in the middle of the figure is the approximate area of ΔAA'C.

3(20×9)+3((24-9)×8)+(10×8)+(9×10)+((20-8)×10)+((24-9)×10)

=3(180)+3(15×8)+80+90+(12×10)+(15×10)

=540+3(120)+170+120+150

=920+360

=1280

Answers

[tex] {1280cm}^{2} [/tex]

Answer:

[tex]S=1964 in^{2}[/tex]

Step-by-step explanation:

The surface of a rectangular prims is defined as

[tex]S=2lw+2wh+2lh[/tex]

Where [tex]l[/tex] is length, [tex]w[/tex] is width and [tex]h[/tex] is height.

In this case, we have a figure formed by two rectangular prism. We are gonna call Surface 1 to the bottoming prism.

Its diemensions are:

[tex]l=24in\\w=10in\\h=8in[/tex]

So, the Surface 1 is

[tex]S_{1}=2(24)(10)+2(10)(8)+2(24)(8)= 480+160+384=1024in^{2}[/tex]

Now, the dimensions of Surface 2 are

[tex]l=9in\\w=10in\\h=20in[/tex]

Replacing all values, its surface is

[tex]S_{2}= 2(9)(10)+2(10)(20)+2(9)(20)=180+400+360=940in^{2}[/tex]

Therefore, the total surface of the whole figure is

[tex]S=1024+940=1964 in^{2}[/tex]

Answer:

252 square inches

Step-by-step explanation:

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches. The area of a triangle is ...

A = (1/2)bh

so one face of Georgia's pyramid will have an area of ...

A = (1/2)(9 in)(14 in) = 63 in^2

Then all four faces will have a total area of ...

(63 in^2) · 4 = 252 in^2

_____

Comment on the pattern

The pattern shown includes the base of the pyramid. The problem text says the base is not included. We have assumed that the base is not included. (For Georgia's pyramid, a different pattern would be more to the point: see attachment.)

252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The square pyramid will not have a bottom.

We have to find the lateral surface area as the base area is not included.

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches.

The area of lateral face is A = (1/2)bh

A = (1/2)(9 in)(14 in)

= 63 square inches

There are four faces so, 4×63 = 252 square inches

Lateral surface area is  252 square inches

Hence, 252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

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Answer:

Step-by-step explanation:

The function to be analyzed is:

[tex]y = \frac{4}{x-1}+5[/tex]

This function has a vertical and a horizontal asymptote. The vertical asymptote is located where discontinuity exist. That is:

[tex]x = 1[/tex]

Besides, the horizontal asymptote coincides with the limit of function, which is:

[tex]\lim_{x \to \pm \infty} \left(\frac{4}{x-1} + 5\right)[/tex]

[tex]\lim_{x \to \infty} \frac{4}{x-1} + \lim_{x \to \infty} 5[/tex]

[tex]L = 0 + 5[/tex]

[tex]L = 5[/tex]

The horizontal asymptote is:

[tex]y = 5[/tex]

The function and the asymptotes are presented in the image attached below.

Answer: 37.2 meters

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, to calculate the height of the light pole (x), you can apply the proccedure shown below:

-Apply [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

-Substitute values.

-Solve for the  height of the light pole (x).

Then you obtain the following result:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(60\°)=\frac{x}{43}\\\\x=43*sin(60)\\x=37.2[/tex]

Answer:

37.2 meters

Step-by-step explanation:

Since this is the right triangle, the side that is 43 m is the hypotenuse.

Note: the side opposite of 90 degree angle is hypotenuse.

Also, we want the height of the pole, which is the side that is "opposite" to the angle 60 degree given.

Now, which trigonometric ratio relates "opposite" and "hypotenuse"??

It is SINE. Now we can write and solve (let the height of the pole be h):

[tex]Sin(\theta)=\frac{Opposite}{Hypotenuse}\\Sin(60)=\frac{h}{43}\\h=Sin(60)*43\\h = 37.24[/tex]

The light pole is 37.24 meters tall, to the nearest tenth, it is 37.2 meters

Try suggested solution, note, the answers are marked with green colour.

The probability for drawing marbles without replacement varies with each draw as both the available and desired outcomes decrease. By applying this rule, the probabilities can be calculated for drawing 5 marbles with all, exactly two, or none being red.

To answer these questions, we first need to know the total number of marbles in the bag. The bag contains 5 red, 8 white, and 10 blue marbles, yielding a total of 23 marbles. When answering probability questions when drawing without replacement, the denominator (total possible outcomes) decreases with each draw, while the numerator (desired outcomes) remains constant if the kind of object drawn remains the same and decreases otherwise.

For the first question, we're drawing 5 marbles all of which are red. The probability is calculated as follows: (5/23) * (4/22) * (3/21) * (2/20) * (1/19). This is because with each draw, both the total number of marbles and the number of red marbles decrease by 1.

For the second question, we're drawing 5 marbles, 2 of which are red. This can happen in various ways (e.g., red, red, not red, not red, not red, etc.). Each of these sequences has a probability and we sum these probabilities. Assuming we draw 2 red then 3 not red, the probability is: (5/23) * (4/22) * (18/21) * (17/20) * (16/19). The 18 in the third fraction is derived from the total number of non-red marbles (8 white + 10 blue).

For the last question, we're drawing 5 marbles, none of which are red. The probability is: (18/23) * (17/22) * (16/21) * (15/20) * (14/19), similar to the previous example, we only consider non-red marbles.

Learn more about Probability here:

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The probable question may be:

A bag contains 5 red marbles, 8 white marbles, and 10 blue marbles. You draw 5 marbles out at random, without

replacement. What is the probability that all the marbles are red?

The probability that all the marbles are red is _____

What is the probability that exactly two of the marbles are red?

The probability that exactly two of the marbles are red is _______

What is the probability that none of the marbles are red?

The probability of picking no red marbles is __________

Answer:

  0.01000188

Step-by-step explanation:

The third term is ...

  8C2·x^6·y^2 = 28 x^6 y^2

Putting in the given values for x and y, we get ...

  28·3^6·7^2·10^-8 = 1000188×10^-8 = 0.01000188

_____

8C2 = 8!/(2!·(8-2)!) = 8·7/(2·1) = 28

Answer: [tex]\frac{32}{35}[/tex]

Step-by-step explanation:

We need to convert the mixed numbers into fractions.

The new numerator will be the sum of the numerator of the fractional part and the product obtained by multiplying the denominator of the fractional part by the whole number part.

The new denominator will the the same denominator of the fractional part.

Then:

[tex]2\ \frac{2}{7}=\frac{2+(2*7)}{7}=\frac{16}{7}[/tex]

[tex]2\ \frac{1}{2}=\frac{1+(2*2)}{2}=\frac{5}{2}[/tex]

Dividing the fractions, we get:

[tex]\frac{\frac{16}{7}}{\frac{5}{2}}=\frac{16*2}{7*5}=\frac{32}{35}[/tex]

Answer:

4.25 Liters

Step-by-step explanation:

Edge of Cubical tank

= 20 cm

= 20 (0.01 m)……………..1 meter = 100 cm

= 0.2 m

Volume of Tank

= ( Edge ) ^ 3

= ( 0.2 m ) ^3

= 0.008 m^3

= 8 liters…………….. 1 m^3 = 1000 Liters

Volume required to fill the tank

= 8 - 3.75

= 4.25 Liters

Answer:

50

Step-by-step explanation:

20% is the same as 0.2 times something.

So you can create the equation 0.2x = 10. The solution of this equation is x=50.

Answer:

  A.  The dilated line lies on the original line.

Step-by-step explanation:

Dilation changes sizes, but not slopes or angles. The dilated line is guaranteed to have the same slope as the original.

The center of dilation is "invariant" (doesn't move) as a result of the dilation. Here, the point (3, 0) is the center of dilation. It is the x-intercept of the original line, so will also be on the dilated line.

The dilated line has the same slope as the original and goes through a point that the original line goes through. Hence it lies on the original line.

_____

How do you do this question?

1. make use of the properties of dilation, as we have done above.

2. plot some points on the original line—(0, 3) and (3, 0) are the intercepts—apply the dilation, and see where the line goes. (You will find (0, 3) ⇒ (-6, 9), and (3, 0) ⇒ (3, 0). Both are on the original line.)

Answer: 132 Square Feet

Step-by-step explanation:

Answer:

132

Step-by-step explanation: