write an expression for - add 5 to the quotient of z and 6, then subtract 8 from the result

Answer:

\(3a^{b} *\sqrt{3} +2a*\sqrt{3b}\)

Step-by-step explanation:

\(\sqrt{3^{2}*3a^{2b} } +a*\sqrt{2^{2} *3b} \\\sqrt{3^{2} *a^{2b} *3} +a(\sqrt{2^{2} *\sqrt{3b} } )\\\)

Result:

\(3a^{b} *\sqrt{3} +2a*\sqrt{3b}\)

Step-by-step explanation:

(x-2)^2 + (y-9)^2   = r^2

this is of the form fora circle with center  h,k and radius r

(x-h)^2 + (y-k)^2 = r^2

for the equation given   center =   2, 9    and radius = r

Answer:

Step-by-step explanation:

To construct a confidence interval for the standard deviation of the pH of rainwater in this region, we will use the following formula:

Lower bound: sqrt((n-1)s^2 / X^2)

Upper bound: sqrt((n-1)s^2 / Y^2)

where n is the sample size, s is the sample standard deviation, and X and Y are the values of the chi-squared distribution that correspond to the lower and upper bounds of the confidence interval, respectively.

First, we need to calculate the sample size and the sample standard deviation:

n = 12

s = 0.309

Next, we need to find the values of X and Y from the chi-squared distribution. Since we want a 90% confidence interval, and there are (n-1) = 11 degrees of freedom, we can find the values of X and Y that correspond to the 5th and 95th percentiles, respectively, using a chi-squared table or a calculator:

X = 3.816

Y = 20.483

Now we can substitute these values into the formula to find the lower and upper bounds of the confidence interval:

Lower bound: sqrt((n-1)s^2 / X^2) = sqrt((11)(0.309^2) / (3.816)^2) = 0.152

Upper bound: sqrt((n-1)s^2 / Y^2) = sqrt((11)(0.309^2) / (20.483)^2) = 0.554

Therefore, we can say with 90% confidence that the standard deviation of the pH of rainwater in this region is between 0.152 and 0.554.

Interpretation: We are 90% confident that the true standard deviation of the pH of rainwater in this region falls between 0.152 and 0.554. This means that if we were to take many random samples of rainwater from this region and calculate the standard deviation for each sample, about 90% of the resulting confidence intervals would contain the true standard deviation of the population.

Answer:

Step-by-step explanation:

50:100 and 1:2

15:20 and 3:4

15:16 and 5:2

10:5 and 2:1

Hope this helps!

Answer:

17.36

Step-by-step explanation:

18×22=396

396–83.52=312.48

312.48÷18=17.36

the denominator will be zero when. \(x=-2\)or \(x=-7.\) Therefore, the domain of the expression is all real numbers except \(x=-2\) and \(x=-7\).

In mathematics, factoring refers to the process of finding the factors of a given number or expression. Factors are numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these are the numbers that can be multiplied in pairs to obtain 12 (e.g. 2 x 6 = 12).

In algebra, factoring involves breaking down an algebraic expression into simpler expressions that can be multiplied together. This is done by finding common factors or using techniques such as difference of squares, perfect squares, or grouping. Factoring is an important tool in algebra, as it can help simplify complex expressions and solve equations.

To simplify a rational expression, follow these steps:

Step 1: Factor both the numerator and denominator if possible. For example, in the expression you provided, the numerator can be factored as\((2x+5)(x+4)\)and the denominator can be factored as \((2x+15)(x+2)\).

Step 2: Cancel out any common factors in the numerator and denominator. In this case, both the numerator and denominator have a common factor of (2x+5), which can be cancelled out.

Step 3: Simplify the remaining expression. After cancelling out the common factor, the simplified expression becomes:

\((2x+5)(x+4) / (2x+15)(x+2) = (x+4) / (x+2)(2x+15)\)

Domain restrictions occur when a value of x makes the denominator equal to zero, because division by zero is undefined. In this case, the denominator will be zero when x=-2 or x=-7. Therefore, the domain of the expression is all real numbers except x=-2 and x=-7.

It is important to identify any domain restrictions before simplifying a rational expression to ensure that the final expression is valid for all values of x in its domain.

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After considering all the given data we conclude that after performing simplification on the given sub question the values are A)-15x⁶y⁸ , B) -15x⁶y⁸ (x² + y²) and C) -7.5xy⁴

To proceed and evaluate the given expression we have to consider operating with the help of power rule which will enable the simplification by using multiplying  two powers with the same base, and finally use summation of their exponents.
In a system of function when a  large numbers is expressed in terms of powers is referred to as exponents. The exponent is a number that has a dedicated spot as a superscript over a number. 
Let us apply simplification on the given expressions one by one.
A) (-3x²y⁶)(5x⁴y²) = -15x⁽²⁺⁴⁾y⁽⁶⁺²⁾ = -15x⁶y⁸

B) -15x⁸y⁸ - 15x⁶y⁸  = -15x⁶y⁸ (x² + y²)

C) -15x⁸y¹² / 2x⁶y⁸  = -7.5x²y⁴
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The complete question is
Simplify
A) (−3x2y6)(5x4y2).
B) −15x8y8 −15x6y8
C) −15x8y12/ 2x6y8

Answer:

  c) BC/tan(20°)

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you remember the relations between trig functions and angles. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

In the case of the present triangle, these relations mean ...

  sin(B) = AC/BC   ⇒   AC = BCsin(70°)

  cos(C) = AC/BC   ⇒   AC = BCcos(20°)

  tan(B) = AC/BA   ⇒   AC = BAtan(70°)

  tan(C) = BA/AC   ⇒   AC = BA/tan(20°)

__

The answer choice that is not on this list is ...

  c) BC/tan(20°) . . . . . . not equivalent to AC

_____

Additional comment

The interior angle at C is the supplement of the given angle 160°. These angles form a linear pair.

  C = 180° -160° = 20°

The interior angle at B is the complement of the interior angle at C.

  B = 90° -20° = 70°

The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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Answer:

4.0 g/ml

Step-by-step explanation:

\( Volume_X \) = water displaced by X

Water displaced by object X = Final fluid level - Original fluid level

Water displaced by object X = 90 ml - 65 ml = 25 ml

\( Volume_{X} = 25 ml \)

Density of rock:

100 grams => 25 ml

x grams => 1 ml

Cross multiply

x*25 = 1*100

25x = 100

25x/25 = 100/25

x = 4

Density of object X = 4 g per 1 ml = 4.0 g/ml

Answer:

24

Step-by-step explanation:

I'm pretty sure that it would be division so 120 divided by 5 is 24

Answer:

-147 is the correct answer

Step-by-step explanation:

-27+(-120)

-27-120 [As we know that + - equals to -]

-147 Ans

Step-by-step explanation:

a1. The shape will be a vertical or horizontal line.

a2. The shape will be shaped like a diagonal line increasing as we go right.

a3. The shape will be shaped like a diagonal line decreasing as we go right.

a4. The shape will be shaped like a U facing upwards.

a5.The shape will be shaped like a U facing downwards.

a6. The shape will look like a S shape and it increases as we go right.

a7. The shape will look like a S shape and it decreases as We go right.

a8. The shape look like a W shape and it facing upwards.

a9. The shape look a W shape facing downwards.

We are given function.

\(x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8\)

b. We can test by the Rational Roots Test,

This means a the possible roots are

plus or minus(1,2,4,8).

c. If we apply Descrates Rule of Signs,

d. Use Desmos to Graph the Function. Some roots are (-2,1,4).

e.

\((x {}^{2} + 1) (x - 1)(x - 4)(x + 2)\)

f. The complex zeroes are

i and -i

Polynomial \(f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8\) in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Shape of the graph for the following polynomial:

Finding zeros of the polynomial given:

\(f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8\)

By factor theorem, if f(t) = 0, t is a zero of the polynomial.

Taking t = 1.

f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0

(x - 1) is a factor of the polynomial f(x).

Divide f(x) by (x-1) using long division to find the other factors.

f(x)/(x-1) = \(x^{4} -2x^{3}-7x^{2} -2x-8\) is also a factor of f(x).

Factorizing it further:

g(x) = \(x^{4} -2x^{3}-7x^{2} -2x-8\)

g(-2) = 16 + 16 - 28 + 4 - 8 = 0

(x + 2) is a factor of g(x) and thus f(x).

g(x)/(x+2) = \(x^{3} - 4x^{2} +x - 4\) is a factor of f(x).

Factorizing it further:

k(x) = \(x^{3} - 4x^{2} +x - 4\)

k(4) = 64 - 64 + 4 - 4 = 0

(x - 4) is a factor of k(x) thus of f(x).

k(x)/(x-4) = \(x^{2} +1\)

Factorizing it further:

l(x) = \(x^{2} +1\) = (x + i)(x - i)

Zeros of f(x) = 1, -2, 4, ±i

Rational zeros :  1, -2, 4

Positive real zeros: 1, 4

Negative real zeros: -2

Complex zeros: ±i

Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).

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Answer: 28

Step-by-step explanation: In this problem, we're given information about the parts of a segment and we're asked to find the value of x.

To find the value of x, we can use the segment addition postulate.

Looking at the diagram, it should make since that RS + ST = RT.

So 4x + 3x + 11 = 60 or 7x + 11 = 60.

Subtracting 11 from both sides and solving for x, we get x = 7.

Since RS is 4x, we can substitute a 7 in for x to get 4(7) or 28.

Option (c) 28 is your correct answer.

RS + ST = RT

substitute the value in equation

=> 4x + 3x + 11 = 60

=> 7x + 11 = 60

11 will move to RHS to sub from 60 to get 49.

=> 7x = 60 - 11

=> 7x = 49

=> x = 49÷7

∴ x = 7

Now, finding distance between RS by putting 7 in x value.

Distance between RS = 4x

= 4(7)

= 28

Therefore, the distance between RS is 28.

Answer:

        x   |   y

1. |   0    |   2

2.|  -2    |   5

3.|    1    |   0.5

4.|    4   |   -4

Step-by-step explanation:

3x + 2y = 4

manipulate the literal equation

3x + 2y = 4

y = (4 - 3x)/2

now substitute in the given values and solve

x = 0

y = (4 - (3 * 0))/2

y = 2

x = -2

y  = (4 - (3 * -2))/2

y = 5

x = 1

y = (4 - (3 * 1))/2

y = 0.5

x = 4

y = (4 - (3 * 4))/2

y = -4

which means that:

        x   |   y

1. |   0    |   2

2.|  -2    |   5

3.|    1    |   0.5

4.|    4   |   -4

Answer:

73.74 degrees

Step-by-step explanation:

Answer: r=11

Step-by-step explanation:

A=πr^2

A=121π

121π=πr^2

r^2=121

r=11

yessssss I cannnnnnn helppppp youu

\( \frac{ - 12}{c} = 6 \\ \)

Inverse both sides

\( - \frac{c}{12} = \frac{1}{6} \\ \)

Multiply both sides by - 12

\(( - 12) \times - \frac{c}{12} = ( - 12) \times \frac{1}{6} \\ \)

\(c = - 2\)

There u go have a great day ❤

Answer:  C = -2

Step-by-step explanation:  Well if you times 2x3 that = 12.  So -2= c.

I am really sorry if this is wrong. I tried my best.  :-)

Hope you have a wonderful day !

Answer:

Number 1: 84.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability that a red card is drawn at least once by the third draw is 0.88.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let, a card is drawn from a standard deck of 52 cards and then placed back into the deck.

In a standard 52 card deck the red cards are 26.

So,

P(red) =  n(red cards) / n(total cards)

          = 26 / 52

P(red) = 0.50

Now, X ≈ Bin (n = 3, P = 0.50)

P(X = x) = (n  x) p^x (1 - p)^n-x

(n  x) = \(\frac{n!}{x!(n-x)!}\)

P(X ≥ 1) = 1 - P(X < 1)

            = 1 - P(X = 0)

            = 1- (3  0)(0.5)^0(0.5)^3

            = 1 - 0.125

             = 0.875

P(X ≥ 1)  = 0.88

Hence, the probability that a red card is drawn at least once by the third draw is 0.88.

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Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

Answer:

d

Step-by-step explanation:

becuase 0.54166666666 is equal to it

Answer:

13/24

Step-by-step explanation:

Could i have branliest and heart please

Answer:

27

Step-by-step explanation:

Input 5 for all x-values.

If that is an equal sign...

1/9*(3^5)

With PEMDAS, exponents are done before multiplication.

1/9*243

= 27

Answer:

a) 62.5

b) -62.5

Step-by-step explanation:

Given:

x² + y² + z² = 1 is T = 500xyz²

Required:

Locate the highest and lowest temperatures.

Here,

S = (x² + y² + z² = 1)

T = 500 xyz²

Let's take Lagrange multiplier:

∇T = λ∇S

Thus,

500 yz² = λ(2x)........... 1

500 xz² = λ(2y).............2

500 xy² = λ(2z)..............3

Where, x² = y², 2y² = z²

Therefore,

x²+ y²+z² = 1

=> x² + x² + 2x² = 1

Solve for x:

x = ±½ = y

z = ±\( \frac{1}{\sqrt{2}} \)

From the above calculations,

x, y, z = ±½, ±½, ±\(\frac{1}{\sqrt{2}} \)

Calculate for the highest temperature:

Tmax = T(½, ½, \(\frac{1}{\sqrt{2}}) \) = 500 * ½ * ½ * ½ = \( \frac{500}{8} = 62.5 \)

Calculate for the lowest temperature:

Tmin = T(-½, ½, \(\frac{1}{\sqrt{2}}) \) = 500 * -½ * ½ * ½ = \( - \frac{500}{8} = -62.5\)

The highest temperatures is 62.5 and lowest temperatures is -62.5 on the sphere

Given-

The given equation is,

\(x^2+y^2+z^2=1\)

The equation for the temperature is,

\(T=500(xyz)^2\)

By the Lagrange multiplier

\(\bigtriangledown T=\lambda \bigtriangledown S\)

we can rewrite the  temperature equation by the above multiplier as,

\(500yz^2=\lambda (2x)\)

\(500xz^2=\lambda (2y)\)

\(500xy^2=\lambda (2z)\)

Here let,

\(x^2=y^2\)

\(2y^2=z^2\)

therefore,

\(2x^2=z^2\)

Put this values in the given equation of the question we get,

\(x^2+x^2+2x^2=1\)

\(4x^2=1\)

\(x^2=\dfrac{1}{4}\)

\(x= \pm\dfrac{1}{2}\)

Therefore,

\(y= \pm\dfrac{1}{2}\)

\(z= \pm\dfrac{1}{\sqrt{2} }\)

Use positive value for the highest temperatures and negative values for the lowest value of temperatures in the temperature equation.

Highest temperature is,

\(T=500(xyz)^2\)

\(T_h=500(\dfrac{1}{2} \times\dfrac{1}{2}\times\dfrac{1}{2} )\)

\(T_h=\dfrac{500}{8}=62.5\)

Lowest temperature is,

\(T_l=500(\dfrac{-1}{2} \times\dfrac{-1}{2}\times\dfrac{-1}{2} )\)

\(T_l=-62.5\)

Hence, the highest temperatures is 62.5 and lowest temperatures is -62.5 on the sphere

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A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

A line of best fit which best represents the student's data has been drawn on the distance vs. time graph shown in the image attached below.

If only the variables D and t are to be used, the quantities which the student should graph in order to produce a linear relationship between the two quantities are D and t² because D = 1/2gt².

A graph of D and t² has been plotted in the image attached below.

Finally, we would calculate the value of g by using the slope of this graph.

Slope = Δy/Δx

Slope = 0.5/0.1

Slope = g = 5 m/s².

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Answer: A line of best fit which best represents the student's data has been drawn on the distance vs. time graph shown in the image attached below.

If only the variables D and t are to be used, the quantities which the student should graph in order to produce a linear relationship between the two quantities are D and t².

A graph of D and t² has been plotted in the image attached below.

The value of g based on the slope of this graph is equal to 5 m/s².

Step-by-step explanation:

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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