simplify 12e^5 divided 3e^3

Answer:

[tex]30x^2y^4z^4[/tex]

Step-by-step explanation:

If we multiply 6x by 5x, we get [tex]30x^2[/tex].

If we multiply y by [tex]y^{3}[/tex], we get [tex]y^{4}[/tex].

z stays the same, since it's not being multiplied by anything.

Hope this helped!

Answer:

Step-by-step explanation:

Multiply each term:

30x^2y^4z^4

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Answer:

D. ​Population, because it is a collection of salaries for all teachers in the school.

Step-by-step explanation:

In research, population refers to a complete set of subjects that share a characteristic and that the researcher is interested in. On the other hand, a sample is a subset of a population and it's usually the one the researcher takes to make a study with.

In this example, we have "The salary of each teacher in a school" since we are taking ALL the teachers of this school, this would be a population. If we were working with the salary of only a portion of the teachers of said school, it would be a sample.

Thus, the right answer is  D. ​Population, because it is a collection of salaries for all teachers in the school.

Answer:

315.1° (1 d.p.)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

s= 15 (nearest integer), 14.8 (to nearest 10ths)

Step-by-step explanation:

here you need to apply the cosine rule,

[tex] {s}^{2} = {u}^{2} + {t}^{2} - 2ut \cos(s) [/tex]

substituting the values,

u= 13, t=5 and angle S as 60 and solving will give you the answer 14.76 (2 dp)

Answer:

The information given are;

[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]

Where;

r(V) = The radius of the doughnut (cm)

V = The volume of the doughnut (cm³)

The data are;

V,          r(V)

-30,     -0.8

-20,     -0.7

-10,      -0.55

0,          0

10,         0.55

20,        0.7

30,        0.8

From the table of values, the identified key features are;

a) There is a direct relationship between the radius and the volume of the doughnut

b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above

c) The data values are symmetric and continuous about the y and x-axis

2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and  V where V = -30 and-20 at one end and 20 and 30 at the other end

b) The x and y-intercept are

The x -intercept = (0, 0)

The x -intercept = (0, 0)

c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)

d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R

Step-by-step explanation:

Answer:

the chemist should use 60 liters of 55% solution and 40  litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.

Step-by-step explanation:

From the given information,

Let x be the litres of 55% pure solution

Let y be the litres of 30% pure solution

Also;

Given that our total volume of solution is  100 litres

x+y =100  ---- (1)

The total solution of pure by related by the sum of the individual pure concentrations to make up the concentration of final solution.

(0.55)(x)+(0.30)(y) = 0.45(100) ---- (2)

From equation (1)

Let ; y = 100 - x

Replacing the value for y = 100 - x into equation (2)

(0.55)(x)+(0.30)(100-x) = 0.45(100)

0.55x + 30 - 0.30x = 45

0.55x - 0.30x = 45 - 30

0.25x = 15

x = 15/0.25

x = 60 liters of 55% solution

From ; y = 100 - x

y = 100 - 60

y = 40  litres of 30% solution.

Therefore, the chemist should use 60 liters of 55% solution and 40  litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.

Answer:

Step-by-step explanation:

To calculate the horizontal distance d we use cosine

cos ∅ = adjacent / hypotenuse

From the question

d is the adjacent

the hypotenuse is 145m

So we have

cos 55 = d / 145

d = 145 cos 55

d = 83.16

d is 83.2 meters to 3 significant figures

Hope this helps you

Answer:

0.09

Step-by-step explanation:

11.52 / 128

First, divide both numerator and denominator by 2:

2.88 / 32

Divide both numerator and denominator by 4:

0.72 / 8

Divide 0.72 by 8, you get 0.09.

Answer:

1. 2.997

2. 29.93

Step-by-step explanation:

1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.

2. Same thing, gotta multiply all given values

Answer:

Length 37 cm, width 25 cm.

Step-by-step explanation:

Let the original dimensions be length x and width x - 12 cms.

The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.

So , from the areas, we have:

x(x - 12) - (x - 2)(x - 14) = 120

x^2 - 12x  - (x^2 - 16x + 28) = 120

-12x + 16x - 28 = 120

4x = 148

x = 37 cms

So the length was 37 cm and the width was 37-12 = 25 cm.

Answer:

The answer is below

Step-by-step explanation:

The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).

From the sector, AB = AC = radius of the sector (r) = 12. Therefore:

[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]

From the triangle: AC² = AB² + BC²

AC² = 12² + 12² = 144 + 144

AC² = 288

AC=√288 = 12√2

[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]

Answer:

55

Step-by-step explanation:

35+90=125

180-125=55

The interior angles of a triangle should always add up to 180 degrees

Answer:

B=55 degrees

Step-by-step explanation:

if the shape is a triangle then the sum of the angles of the triangle is 180

angles :A+B+C=180

35+B+90=180

B=180-125

B=55 degrees

Answer:

[tex]0.2 = \frac{x}{5} - 1.4[/tex]

Move 1.4 to the left side of the equation

That's

[tex]0.2 + 1.4 = \frac{x}{5} \\ \\ \frac{x}{5} = 1.6[/tex]

Convert the decimal to fraction

That's

1.6 = 8/5

[tex] \frac{x}{5} = \frac{8}{5} [/tex]

Multiply through by 5

We have

[tex] \frac{x}{5} \times 5 = \frac{8}{5} \times 5 \\ \\ \\ x = 8[/tex]

Hope this helps you

x = 65° and y = 77.5°.

The triangle with the 50 degree angle and x, is an isosceles triangle. That means that the other unlabeled angle is also equal to x degrees.

x + x + 50 = 180

2x + 50 = 180

2x = 130

x = 65°.

Since x = 65 degrees, and the two angles make a 90 degree angle, the other unlabeled angle will be 90 - 65 = 25 degrees.

Since the other triangle is also isosceles, that triangle has two angles that measure y degrees and one angle measuring 25 degrees.

y + y + 25 = 180

2y + 25 = 180

2y = 155

y = 77.5°.

Answer:

  C.  100

Step-by-step explanation:

You can rearrange the equation to say ...

  (Height)(Width) = Constant

Multiply any of the coordinate values shown, and you will see the constant is 100.

  4×25 = 5×20 = 10×10 = 20×5 = 100

The constant is 100.

Answer: The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.

Answer:

spinner B

Step-by-step explanation:

there's 8 sides to the spinner and half of them have A on it.

Answer:

C

Step-by-step explanation:

f-g means to subtract g from f:

(4^x - 8) - (5x+6)

Remove the parenthesis and change the equations sings for g:

4^x-8 -5x -6

Combine like terms:

4^x - 5x - 14

The answer is A.

Answer: D

Step-by-step explanation:

In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.

[tex]x+3=0\\x=-3[/tex]

So, you should use -3. The only options with -3 are B and D.

The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.

Hope this helps! If you still have questions, please ask.

Answer:

44

Step-by-step explanation:

Answer: C

1/4

Step-by-step explanation:

Given a graph for the transformation of f(x) in the format g(x) = f(kx),

This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.

Therefore, the value of k will be 1/4.

Answer:

k=4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3 times the sum of 4 and 2 = 3*(4+2)

                                            = 3 * 6

                                           = 18

18 - 9 = 9

Answer:

1/x^12

Step-by-step explanation:

X^-12....simply move x^-12 to the other side of the division and change the sign of the exponent.

The simplified form of the expression x Superscript negative 12 is 1/ x¹².

The rule of the exponent is defined as the simplified form of the exponents

where a is the base and b and n are the exponent.

Here given in the question is the expression that x superscript negative 12.

As we now superscript is to write the number in exponent position.

here -12 is written in the superscript of x.

then the mathematical expression will be converted as

x superscript negative 12 = x⁻¹²

As we know from the rule of exponent that a⁻ⁿ = 1/aⁿ where a is the base and n is the exponent.

x⁻¹² can be rewritten as x⁻¹² = 1/ x¹²

Therefore the simplified form of the expression x Superscript negative 12 is 1/ x¹².

Learn more about the rule of exponent

here: https://brainly.com/question/11975096

#SPJ2

Answer:

C

Step-by-step explanation:

4:10 ≠ 6:8

Answer:

180

Step-by-step explanation:

Given the ratio = 7 : 3 : 2 = 7x : 3x : 2x ( x is a multiplier ), then

7x = 2x + 75 ( Natasha gets 75 more sweets than Henry )

Subtract 2x from both sides

5x = 75 ( divide both sides by 5 )

x = 15

Thus

total number of sweets = 7x + 3x + 2x = 12x = 12 × 15 = 180

Explanation:

f(x) = x^3

f(x+4) = (x+4)^3 .... shifts graph 4 units to the left

f(x+4) - 6 = (x+4)^3 - 6 ... shifts 6 units down

The change from x to x+4 means the xy axis has moved four units to the right (since each input is now 4 units larger). If we hold the curve y = x^3 to be completely still while the xy axis moves 4 units to the right, then the illusion of the curve moving 4 units to the left happens.

The -6 at the end does what you'd expect it to do, and there is no opposites going on here. Whatever the y value is, subtract 6 from it to get the new y value. Effectively this moves the graph down 6 units.

Answer:

Increases

Step-by-step explanation:

It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.

Answer:  y = 23x - 62

Step-by-step explanation:

Parallel lines have the same slope.

y = 23x + 4

  m=23   b=4

Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m).  I will choose the latter.

 y = mx + b

 7 = 23(3) + b

 7 = 69 + b

-62 = b

m = 23, b = -62  -->  y = 23x - 62

Answer: Degree of polynomial (highest degree) =4

Maximum possible terms =9

Number of terms in the product = 5

Step-by-step explanation:

A trinomial is a polynomial with 3 terms.

The given product of trinomial: [tex](x^2 + x + 2)(x^2 - 2x + 3)[/tex]

By using distributive property: a(b+c+d)= ab+ac+ad

[tex](x^2 + x + 2)(x^2 - 2x + 3)=(x^2 + x + 2) x^2+(x^2 + x + 2) (-2x)+(x^2 + x + 2)(3)\\\\=x^2(x^2)+x(x^2)+2(x^2)+x^2 (-2x)+x (-2x)+2 (-2x)+x^2 (3)+x (3)+2 (3)\\\\\\=x^4+x^3+2x^2-2x^3-2x^2-4x+3x^2+3x+6[/tex]

Maximum possible terms =9

Combine like terms

[tex]x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6[/tex]

Hence, [tex]\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6[/tex]

Degree of polynomial (highest degree) =4

Number of terms = 5

Answer:

Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an  x2 term, an x term, and a constant term.

The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.

The maximum number of terms in the product of the trinomials is 5.

There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.

Explanation:

This is the response on Edge 2020-21. Hope this helps, have a great day!