The cost per minute of a conference phone call, originally $2. 80, increased by 20%. What is the new price? $3. 00 $3. 20 $3. 26 $3. 36.

Answer:

  a. length: 20-2x; width: 12-2x; height: x

  b. V = 4x^3 -64x^2 +240x

  c. cubic trinomial

  d. 262.7 cubic inches maximum for a 2.4 inch square

  e. 15 × 7 × 2.5 inches for 262.5 in³ volume

Step-by-step explanation:

If the square cut from each corner has side length x, the dimensions are ...

__

The volume is the product of length, width, and height.

  V = LWH

  V = (20 -2x)(12-2x)(x) = 4(x-10)(x-6)x = 4(x^2 -16x +60)x

  V = 4x^3 -64x^2 +240x

__

The volume function is a cubic trinomial.

__

The maximum volume will be found where the derivative of the volume function is zero.

  V' = 12x^2 -128x +240 = 0

  x^2 -32/3x +20 = 0 . . . . divide by 12

  (x -16/3)^2 = 76/9 . . . . . complete the square

  x = (16 -√76)/3 ≈ 2.4 . . . . size of the square

  V = 4(2.4)(10 -2.4)(6 -2.4) ≈ 262.7 . . . cubic inches

The maximum box volume is about 262.7 cubic inches when the square is about 2.4 inches on each side.

__

A graphing calculator shows there to be two solutions for a volume of 262.5 cubic inches. The rational solution is x = 2.5 inches. The box dimensions would be ...

Answer:

3,000 words

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

just did the test

The values of a, b, h, and k, given the equation below;

[tex]\rm \dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\\ \dfrac{(x-0)^2}{3^2}+ \dfrac{(x-3)^2}{5^2}=1[/tex]

Given

An ellipse has vertices along the major axis at (0, 8) and (0, –2).

The foci of the ellipse are located at (0, 7) and (0, –1).

It can be seen that the major axis is parallel to the y axis.

The major axis points are;

(h, k +a) = (0, 8)

(h, k -a) = (0, -2)

Here, k + a = 8

k - a = -2

Subtracting the equations;

k + a - k + a = 8 + 2

2a = 10

a = 10/2 = 5

The foci are;

(h, k +c) = (0, 7)

(h, k -c) = (0, -1)

Here, k + c = 7

k - c = -1

Subtracting the equations;

k + c -k + c = 7+ 1

2c = 8

c = 8/2 = 4

The foci are given by;

[tex]\rm c^2=a^2-b^2\\\\b=\sqrt{a^2-c^2} \\\\b = \sqrt{5^2-4^2}\\\\b = \sqrt{25-16} \\\\ b =\sqrt{9}\\\\ b=3[/tex]

The equation is;

[tex]\rm \dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\\ \dfrac{(x-0)^2}{3^2}+ \dfrac{(x-3)^2}{5^2}=1[/tex]

To know more about ellipse click the link given below.

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Answer:

4/18 and 15/18

Step-by-step explanation:

trust me bro

Answer:4/18 and 15/18

Step-by-step explanation:trust the progres kk

Answer:

c. 13 23/45

d. -9/5

Step-by-step explanation:

explanation for c:

(5+8)+(1/9 +2/9) and then add the numbers so it will be

13+23/45 ----> 13 23/45

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

explanation for d:

convert decimal into fraction------> -6/5-3/5

calculate the difference -------> -9/5 and now you got your answer!!

Answer:

Step-by-step explanation:

The total amount is $2.41.

If the are 23 pennies, then the amount excluding the pennies is:

This amount comprises quarters, nickels and dimes.

Each of them is multiple of 5:

Any amount made by the combinations of these has to be multiple of 5 cents. But the sum is $2.18, which is not multiple of 5 cents.

It means Henry can't make it.

Answer:

The probability of choosing a red marble is 35%.

Step-by-step explanation:

Total marbles: 17

[tex]\frac{6}{17} = 0.35[/tex]

Answer:

80%

Step-by-step explanation:

Based on the given conditions: (18 - 10)÷10

Calculate the sum or difference: 8/10

Cross out the common factor: 4/5

Convert to percentage: 80%

Answer: 80%

Answer:

80%

Step-by-step explanation:

Based on the given conditions, formulate: (18-10) ÷ 10

Calculate the sum or difference: 8/10

Cross out the common factor: 4/5

Convert to percentage: 80%

Answer: 80%

Hope this helps

Answer:

6 hours.

Step-by-step explanation:

since that is true we can use trial and error. if every km took an hour it would take six hours up and 4 hours down but they said they were twice as fast going down so that means it would take 2 hours going down. 6 add 2 is 8 which is our total meaning that 6 hours is the right answer

Answer:

2 1/2   (2.5)

Step-by-step explanation:

Multiply all the numbers then divide by 1/2

Answer:

22/3=8/3=2.66

if 12 servings =2.6 cup of flour

...18 servings=???????

18×2.6/12=3.9

the answer is 3.9

Check the picture below.

so let's simply get the area of each of the triangular faces and the base and sum them all up.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{front and back}}{2\left[ \cfrac{1}{2}(100)(40) \right]}~~ + ~~\stackrel{\textit{left and right}}{2\left[ \cfrac{1}{2}(50)(40) \right]}~~ + ~~\stackrel{base}{(100\cdot 50)}} \\\\\\ 4000~~ + ~~2000~~ + ~~5000\implies 11000~m^2[/tex]

Answer:

The equations which represents the situation are

1) 2Y+X=5

2) 5X-Y=3

Step-by-step explanation:

~Cornasha_Weeb

Answer:

x= 1

Step-by-step explanation:

The value of y = -5x

Plug it in the equation of y + 4x = -1

So it becomes, -5x + 4x = -1

Combine like terms which are -5x and 4x which equals to -x

Eliminate the negative sign because x cannot be negative. Apply that to -1. It becomes 1.

Hope you find this helpful!

Answer:

Step-by-step explanation:

Equation 1: y = -5x

Equation 2: y + 4x = -1

Step 1. Substitute y in equation 2 using equation 1

You would get, -5x + 4x = -1

Step 2. Combine like terms

-x = -1

Step 3. Cross out the negatives

x = 1

Step 4. Substitute x in Equation 1 to get y

y = -5(1)

y = -5

Hope this helps :)

Have a great day!

Answer:

18 buttons

Step-by-step explanation:

2 buttons per shirt times the number of shirts (9) gives an answer of 18

Answer:

g= h(3j+7)

     ---------

          4

Step-by-step explanation:

4g = h(3j + 7)

4g = h*3j+h*7

Not sure for (b)

Step-by-step explanation:

(a)55+80+x=180 (angles inside the triangle)

135+×=+180

x=180-135

x=45

Answer:

1a) A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound.

1b)An ionic compound formed by acid-base reactions and without those ions is called a salt. Water is definitely one of the most important inorganic compounds to all living things. It is a compound comprised of two hydrogen atoms and one oxygen atom.

The four major classes of biological macromolecules are carbohydrates, lipids, proteins, and nucleic acids.

2a)Regulates body temperature. Moistens tissues in the eyes, nose and mouth. Protects body organs and tissues. Carries nutrients and oxygen to cells.

2b)If a cell is seriously deprived of water,

this lack of water would most likely affect

the cell's enzymes because:

• The cytoplasm and plasma

membrane would not function

properly

Both the plant and animal cell needs

water in order to perform their basic

functions which include transport of

materials, waste distribution, production

of genetic information, and many more.

As a result of this, we can see that there

would be a serious problem if any

of these cells are deprived of water

which would lead to the cytoplasm and

plasma membrane to partially shut

down because they would not be able to

engage in protein synthesis and other

important functions.

3a)Carbohydrates provides energy rich for organic compounds made of elements carbon, hydrogen and oxygen. The lipids contain the element nitrogen. The carbohydrates contain the only elements carbon, hydrogen, and oxygen.

3b)Organic nitrogen occurs in many forms, including amino acids, proteins, nucleic acids, nucleotides, and urea.

3c)A carbohydrate has only Carbon, Hydrogen and Oxygen, with the hydrogen and oxygen in the ratio 2:1. A protein is made of amino acids. ... So without nitrogen atoms the compound can not be a protein.

Answer:

[tex]tan(A) = \frac{4}{3}[/tex]

Step-by-step explanation:

Here we see tan(B) has opposite side of 12 and adjacent of 9

using the formula:

[tex]tan(A) = \frac{opposite }{adjacent}[/tex]

[tex]tan(A) = \frac{12}{9}[/tex]

[tex]tan(A) = \frac{4}{3}[/tex]

Answer:

[tex]\textsf{tan(A)}=\frac{4}{3}[/tex]

Step-by-step explanation:

The trig ratio for tan is:  [tex]\textsf{tan}(x)=\mathsf{\frac{O}{A}}[/tex] where

For angle A:

O = 12

A = 9

[tex]\implies \textsf{tan(A)}=\frac{12}{9}\\\\\implies \textsf{tan(A)}=\frac{4}{3}[/tex]

Answer:

c

Step-by-step explanation:

t(a+2)= 3+a+2/a+2-3= 5+a/a-1

Step-by-step explanation:

4

........................

[tex] \rightarrow \: \sf \dfrac{10}{100} \times 1500[/tex]

[tex] \\ \\ [/tex]

[tex] \rightarrow \: \sf 10 \times 15[/tex]

[tex] \\ \\ [/tex]

[tex] \rightarrow \: \sf 150[/tex]

Answer:

True

Step-by-step explanation:

We know that [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex], [tex]sin\theta<0[/tex] in Quadrant III, and [tex]cos\theta<0[/tex] in Quadrant III. Thus, x is indeed negative since [tex]cos\theta<0[/tex].

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad D(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 2}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\stackrel{M}{\downarrow }}{(-2~~,~~2)}\implies \begin{cases} \cfrac{x+2}{2}=-2\\[1em] x+2=-4\\ \boxed{x=-6}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=2\\[1em] y+8=4\\ \boxed{y=-4} \end{cases}[/tex]

Answer: D

Step-by-step explanation:

If you look at the quadratic formula, we see that b=5, a=5, and c=3.

So ax^2 + bx + c = 0 -> 5x^2 + 5x + 3 = 0

The different groups of 5 can be formed from the 10 volunteers is,

⇒ 252

Permutation and Combination form the principles of counting and they are applied in various situations.

A permutation is a count of the different arrangements which can be made from the given set of things. In permutation the details matter, as the order or sequence is important.

Here given that,

A blood bank needs 5 people to help with a blood drive. 10 people have volunteered.

Here, We get;

The different groups of 5 can be formed from the 10 volunteers is,

⇒ ¹⁰C₅

⇒ 10! /5! 5!

⇒ 10×9×8×7×6 / 5×4×3×2

⇒ 252

Thus, The different groups of 5 can be formed from the 10 volunteers is,

⇒ 252

To know more about the permutation and combination

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