Use the two examples that you provided in question 5 to describe how those trace elements have been introduced into our diets and/or personal hygiene habits.

Answer:

5y^7x^2

Step-by-step explanation:

5y (xy^3)^2

apply product rule: xy^3

5y(x^2(y ^3)^2)

multiply exponents: (y^3)^2

5y(x^2y^6)

Add exponents: y and y^6

5y^7x^2

Using exponent properties, the equivalent expression is:

[tex]\frac{y^{18}}{z^{18}}[/tex]

The original expression is:

[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]

When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:

[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]

The negative exponent at the numerator goes to the denominator, hence:

[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]

The negative outer exponent means that we have to exchange the numerator and denominator, hence:

[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]

Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:

[tex]\frac{y^{18}}{z^{18}}[/tex]

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Answer:

y^18/x^18

Step-by-step explanation:

In this problem, we need to use multiplication and subtraction method to solve it.

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x(y) means to multiply x with y

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Note that {a = 7} and {b = 6}

First, we need to multiply 4 with {a = 7}, we get:

4(7) = 28

Then, we need to subtract {b = 6} from 28, we get:

28 – 6 = 22

Finally, this simplifies as:

4(7) – 6 = 22

Hope this helps :)

The value of 'x' is -8 in the given equation 121 = 4(5-3x) + 5.

So, 121 = 4(5-3x) + 5:

Therefore, the value of 'x' is -8 in the given equation.

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Answer:

Step-by-step explanation:

3−4x/3 this is for x

y = -4/3x + 3 this is for why I’m not sure which one your trying to solve for

Answer:

7. Slope = -5

Y-intercept = -3/4

8. Slope = 1/4

Y-intercept = 5

Step-by-step explanation:

y = mx + b

Slope = m

Y-intercept = b

When x = -2:

f(-2) = -3 (-2) + 1

f(-2) = 6 +1

f(-2) = 7

y = 7

When x = 0:

f(0) = -3 (0) + 1

f(0) = 0 +1

f(0) = 1

y = 1

When x = 3:

f(3) = -3 (3) +1

f(3) = -3 (3) + 1

f(3) = -9 +1

f(3) = -8

y = -8

So, the Range is {7, 1, -8}

Answer:

The function is increasing from x = 0 to x = 1.

Step-by-step explanation:

The value of g(0) is less than g(1), meaning g(x) increased from x=0 to x=1.

[tex]2(x-3)\geqslant -3(-3+x)\implies 2x-6\geqslant 9-3x\implies 2x\geqslant 15-3x \\\\\\ 5x\geqslant 15\implies x\geqslant \cfrac{15}{5}\implies x\geqslant 3[/tex]

Answer:

1. straight

2. right

3. obtuse

4. acute

Step-by-step explanation:

This shows that a reasonable domain for this function is x > -5/6

The domain of a function is a value of the independent variable of the function for which it exists.

Given the equation below:

f(x) = 12x + 10

Since the function represents the expression used calculate a person's daily paycheck, then the function f(x) must be greater than zero;

12x + 10 > 0

12x > -10
x > -10/12
x > -5/6

This shows that a reasonable domain for this function is x > -5/6

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True

the sum of interior angles is equal to exterior

A point that is Interior to an Angle is found on the Exterior of the Angle

The statement is false

How do we explain?

A point that is interior to an angle is located within the angle, not on the exterior. The interior of an angle refers to the region enclosed by the angle's sides.

A point that is interior to an angle is located within the angle, not on the exterior. When we refer to the interior of an angle, we are referring to the space enclosed by the angle's sides and vertex.

In geometric terms, an angle consists of two rays that share a common endpoint called the vertex. The interior of the angle is the region between these two rays while on the other hand, the exterior of an angle refers to the space outside the angle, beyond its sides.

In conclusion, a point that is interior to an angle is found within the angle itself, not on the exterior.

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Answer:

−[tex]x^{2}[/tex] + 9x + 1

Step-by-step explanation:

Answer: So after applying concept of parallelism m<10 = 119

Step-by-step explanation:

As we have given m<119

In terms of parallelism

m< 4 = m<8

and m<8 = m<10

Therefore

m< 10 = m<4 = 119

So after applying concept we get m<10 = 119.

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Answer:

see explanation

Step-by-step explanation:

the 2 expressions are difference of squares and factor in general as

a² - b² = (a + b)(a - b)

Then

4w² - 36

= (2w)² - 6²

= (2w + 6)(2w - 6)

and

25[tex]x^{4}[/tex] - 64y²

= (5x²)² - (8y)²

= (5x² + 8y)(5x² - 8y)

Answer:

The variable is x and the constant is 6.  The coefficient of the variable is 3.

Step-by-step explanation:

The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

The fraction expression is given as

-2 1/3 + (-1 3/4) =

Express the terms of the expression as an improper fraction

So, we have

-2 1/3 + (-1 3/4) = -7/3 + (-7/4)

Remove the bracket in the above expression.

So, we have

-2 1/3 + (-1 3/4) = -7/3 - 7/4

Take the LCM in the above expression.

So, we have

-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12

Evaluate the difference

-2 1/3 + (-1 3/4) = -49/12

Express the fraction as a mixed fraction

-2 1/3 + (-1 3/4) = -4 1/12

Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

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Number of shoes needed to wrap around the equator = 7.57 x10⁷

The length of a size 7 shoe = 1.4 x 10-¹ m

The circumference of the Earth around the equator =  1.06 x 10^7 m

We know that here, the circumference around the equator will be equal to the number of shoes times the length of each shoe.

So to find the number of shoes, we should divide the circumference of the Earth by the length of one shoe.

Hence, number of shoes end-to-end needed to wrap around the equator = 1.06 x 10⁷ / 1.4 x 10-¹

             = 7.57 x10⁷

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Answer:

23716 cubic feet

Step-by-step explanation:

7^2=49

11^2=121

2^2=4

49x121=5929

2929x4=23716

Answer:

1. = 96

2. = -158

Step-by-step explanation:

When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative

After d days the total number of lily in the ponds are . It is an simple example of geometric progression.

The formula to calculate the sum of the first n terms of a geometric progression is given by: Sn = a[(rn – 1)/(r – 1)]. Where r is the common ratio and a is the first number of the progress.

Lilly pond starts with 1 Lilly pad, so a = 1and every day amount doubles, so r = 2. Total number of day is d, so n = d.

Therefore, the total number of lilly in the pond is = 1x[(2d-1)/(2-1)] = 2d-1.

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I'm assuming the equation is

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]

Let me know if the equation is different so I can update the solution.

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Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").

If we multiply both sides by 4, then all the denominators of 4 will cancel.

We'll have these steps:

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]

Therefore "y = 32."

Hope this helps.

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Answer:

Step-by-step explanation:

Take 1325-35=1290. 1290/30= 43. She will be able to learn 43 Yoga for 43 months.

An example of a systematic random sample will be selecting 4 balls from a bag containing. The correct option is B.

A probability sampling technique called systematic sampling involves picking people from the population at regular intervals, such as every 15th person on a list of the population. This can mimic the advantages of straightforward random sampling if the population is arranged in random order.

Here we have two options a.) selecting all the students in a class of 30.

b.) Select 4 balls from a bag containing 30 balls.

Out of the two options, a systematic random sample will be Select 4 balls from a bag containing 30 balls.

Therefore, the correct option is B.

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