Simplify the expression.

-6(2 + x) =

Based on the equation for gravitational force, the value of radius (r) is equal to r = √(GM₁M₂/F).

A gravitational force can be defined as a universal force of attraction which acts between two (2) physical objects, especially by pulling them together.

Mathematically, the gravitational force between two (2) planetary objects is given by this formula:

F = GM₁M₂/r²

Where:

Making r the subject of formula, we have:

Fr² = GM₁M₂

Divide both sides by F, we have:

r² = GM₁M₂/F

Taking the square root of both sides, we have:

r = √(GM₁M₂/F)

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Answer: The equation given is not in slope-intercept form, which is y=mx+b. The equation for the line which passes through the given points is y = 7/10x - 3/5.

The measure of m∠MSP as represented in the image attached is 74 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and right angle.

From the image shown:

m∠MSN + m∠MSP = 180° (sum of angles in a straight line)

106 + m∠MSP = 180°

m∠MSP = 74°

The measure of m∠MSP as represented in the image attached is 74 degrees.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's use those two points off the curve in order to get it, check the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{1}{3 +3}\implies {\LARGE \begin{array}{llll} \cfrac{1}{6} \end{array}}[/tex]

Using Venn sets, the number of elements in the sets are given as follows:

For this problem, we consider that the sets A, B and C are the sets represented in the problem, and use the information given to find the number of elements in each set.

For the set A, we have that:

Hence 12 elements belong only to set A and 10 belong to both A and C, hence set A has 22 elements.

For the set B, we have that:

In total, there are 31 elements, of which:

31 - 31 = 0, hence set B has only 1 element, that is also present in set C.

For the set C, we have that:

Hence it has 10 elements that are also in set A, and 9(the intersection with B is included in C - A as n(AnB) = 0) are not, hence set C has 19 elements.

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The number of expert trails in the park is 15.

Percentage can be described as the fraction of an amount expressed as a number out of hundred. The sign :used to represent percentages is %.

The first step is to determine the total number of intermediate and expert trails

Intermediate and expert trails = (1 - percentage of beginner trails) x total number of trails

(1 - 0.375) x 48

0.625 x 48= 30

The second step is to divide the total number of intermediate and expert trails by 2 since they are an equal number.

30 / 2 = 15

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Answer:

Hello,
If you want f(x) read this.

Step-by-step explanation:

I am going to use Horner's method.

[tex]\begin {array}{c|c|c|c}&x^2&x&1\\---&--&--&--\\&4&5&-9\\x=2&&8&26\\---&--&--&--\\&4&13&\boxed{17}\\x=2&&8&42\\---&--&--&--\\&4&\boxed{21}&59\\x=2&&8\\---&--&--&--\\&\boxed{4}&29\\\end {array}\\\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\So\ \boxed{F(x)=4x^2+21x+17}\\\\Proof:\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\\\=4x^2-16x+16+21x-42+17\\\\=4x^2+5x-9\\[/tex]

I hope this is what you want.

The two integers where the value of square root of 11 lies is between 3 and 4.

It should be noted that the information is to find the two integers where the value of square root of 11 lies.

It should be noted that the square root of 11 is 3.33.

It should be noted that 3.33 lies between 3 and 4.

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Between which two integers is the value of square root of 11.

Answer:

  700 mL

Step-by-step explanation:

Lena wants to know how much of solution B she uses to obtain a mixture of solution A with 20% alcohol and solution B with 17% alcohol that contains 400 mL less of solution A, and has 179 mL of alcohol in it.

Let b represent the number of mL of solution B in the mixture. Then (b-400) will be the number of mL of solution A. The number of mL of alcohol in the mix is ...

  0.20(b -400) +0.17b = 179

Simplifying the equation gives ...

  0.37b -80 = 179

  0.37b = 259 . . . . . . add 80

  b = 700 . . . . . . . . divide by 0.37

Lena uses 700 mL of solution B (17%) for the resulting mixture to have 179 mL of pure alcohol.

__

Additional comment

That means there will be 300 mL of solution A, and the contributions from each solution are ...

f(1) = -2

The relationship between x and y-values can be represented through a function.

Function Notation

Function notation is one way to write out an equation. In this notation, f(x) represents the y-value at a specified x-value. Thus, f(1) equals the y-value when x is 1. Many times f(x) will be replaced with variable y. So, another way to write the function above is y = -x - 1.

Solving For f(1)

To find f(1), plug 1 into the equation for x.

Now, you can easily solve the equation.

You need to deposit $1459.667 every month;

Let the amount needed to be deposited each month be 'x' ;

Monthly interest rate, i = 5%/12 = 0.4167% = 0.004167

Total amount  = $600,000

Total time (in months) = 20 × 12 = 240 years;

Therefore, according to question;

600,000 = x . [(1 + i)ⁿ -1]/i

600,000 = x. [(1 + 0.004167)²⁴⁰ - 1]/0.004167

x = 1459.667

The additional amount you must repay over and above the principal borrowed is called interest. This is how lending institutions turn a profit.

Typically, interest is expressed as an annual percentage of the principal.

Monthly interest is the interest that is paid every month or after every 30 days.

We compute the monthly interest rate by dividing the annual interest rate by 12 to calculate the monthly interest on a loan or investment.

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According to the solving the LHS = RHS this shows the equality symmetric property.

52 = 52.

LHS is an informal shorthand again for the left-hand side of the an equation in mathematics. Likewise, RHS refers to the right-hand side. Because equality is symmetric, both sides share the same value, expressed differently.

Given the "equality" (=) relation and a = b, if b = a holds true for all a and b, equality is said to be symmetric. For all of a and b, the assertion is TRUE (no counterexample can be found). This is known as the equality symmetric property.

-21-17+25+65=52

Proving that both LHS = RHS :

-21-17+25+65=52

-21-17+25+65=52

- 38 + 90 = 52

52 = 52

So,

LHS = RHS

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Answer:

2/5= 0.4 and 4/5= 0.8

Step-by-step explanation:

The simplification of  (39x⁵z⁴)⁰ • 18x²y  is 18x²y.

Making anything simpler is known as simplification. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

To simplify an equation:

Rewrite the given equation using the commutative property of multiplication.

18(39x⁵z⁴)⁰x²y

Use the power rule (xy)ⁿ=xⁿyⁿ for distributing the exponent.

18(39⁰(x⁵)⁰(z⁴)⁰)x²y

Anything raised to 0 is 1.

18(1(x⁵)⁰(z⁴)⁰x²y

Multiply (x⁵)⁰(x⁵)⁰ by 11.

18((x⁵)⁰(z⁴)⁰)x²y

Multiply the exponents in (x⁵)⁰.

18(x⁰(z⁴)⁰)x²y

Multiply x⁰ by x² by adding the exponents.

18(x²(z⁴)⁰)y

Simplify 18(x²(z⁴)⁰)y

18x²y

Therefore, simplification of given equation is 18x²y.

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The distance of Proxima Centauri, which is 4.3 light years away can also be expressed in miles is equivalent to 253.7 x 10¹¹ miles from solar system.

A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun

Given that a star named Proxima Centauri is 4.3 light-years away. Therefore, we can write that -

Distance [D] = 4.3 light years

The Proxima Centauri is 4.3 light - years away. As given in the question that  light-year is the distance that light travels in one year and 1 light year is equal to 5,900,000,000,000 miles. Therefore in 4.3 light years, there will be -  

D [miles] = 4.3 x 59x 100,000,000,000 = 253.7 x 10¹¹ miles

Therefore, the Proxima Centauri is 253.7 x 10¹¹ miles away.

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Answer:

2

90

Step-by-step explanation:

54 / 3 = 18

so 18 licks per 1 lollipop.

18 + 18 = 36 (aka 2 lollipops).

18 x 5 = 90 (equivalent to 5 lollipops).

Answer:

36/2

90/5

Step-by-step explanation:

54/3=18 36/2=18 and 90/5= 18

The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power

We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. This is written as;

(9⁻² * 3⁵)⁻²

According to laws of indices, we know that;

(a²)³ = a²*³ = a⁶

Thus;

(9⁻² * 3⁵)⁻² = (9⁻²)⁻² * (3⁵)⁻²

⇒ 9⁴ * 1/3¹⁰

⇒ 9⁴/3¹⁰

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Answer:

126

Step-by-step explanation:

→ Find the sum of the angle

x + x - 35 + x - 46 + 0.5x = 3.5x - 81

→ Equate to 360

3.5x - 81 = 360

→ Add 81 to both sides

3.5x = 441

→ Divide both sides by 3.5

x = 126

Answer:

25

62.5

1.25

hope this helps

Answer:

Step-by-step explanation:

$12.50=10b

so 20$=(20)10/12.5=16

50$=(50)10/12.5=40

1$=(1)10/12.5=0.8

From the given sets we get A’∩ (B∪C’) = {2,8,9}.

Given the universal set U= {1,2,3,4,5,6,7,8,9}

A = {1,5,6,7}

B = {1,2,7}

C= {2,3,4,6,7}

A’ (A not) means to remove all the elements of set A from the universal set U

A∪B (union of A and B) means to write all the elements of both the sets but to not repeat the single element

A∩B (intersection of A and B) means to write only the common elements of both the sets

A’ = {2,3,4,8,9}

C’ = {1,5,8,9}

First we need to find out B∪C’ which means the union of B and C’

B∪C’ = {1,2,5,7,8,9}

Now we need to find A’ (B∪C’) = {2,8,9}

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Answer:

if you want to multiply its 1.83 x 47 = 86.01

Step-by-step explanation:

Answer:

No, it is less than both of the fractions.

Step-by-step explanation:

Multiply the two fractions

[tex]\frac{8}{9}[/tex] x [tex]\frac{3}{7}[/tex] = 0.380952381

Figure out the value of the two fractions

[tex]\frac{8}{9}[/tex] = 0.8888888889

[tex]\frac{3}{7}[/tex] = 0.4285714286

Reduce/Simplify:

0.380952381 = 0.38

0.8888888889 = 0.89

0.4285714286 = 0.43

          =  [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]

Step-by-step explanation:

Given that

            [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

To find

So, according to the question

we have,

            [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

We know that,

    ∵ log(m.n) = logm + logn

Now using this property to solve that logarithmic equation

          =  [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

          =  [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]

We know that,

    ∵ log(mⁿ) = nlogm

Now using this property to solve that logarithmic equation

          =  [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]

          =  [tex]logx+({\frac{-1}{2} )log(x^2 + 3 )[/tex]

          =  [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]

This is the the solution of given logarithmic equation.

Logarithmic equation.

Answer:

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The capacity of the given container is 6.3 liters.

So, 4(3/5) + 1(7/10):

Therefore, the capacity of the given container is 6.3 liters.

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Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

Z = (x - μ)/δ

Where:

If 15 percent of the rainbow trout are longer than 15 inches, then we have:

P(x > 15) = 0.15

From the z-table, the z-value which corresponds to a mean of 0.15 is given by:

z-value = -1.036

Substituting the given parameters into the formula, we have;

Z = (x - μ)/δ

-1.036 = (15 - μ)/2.4

-1.036 × 2.4 = 15 - μ

-2.4864 = 15 - μ

μ = 15 + 2.4864

Mean, μ = 17.4864

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Complete Question:

The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?

A. 26 inches

B. 18 inches

C. 30 inches

D. 33 inches

E. 34 inches

Using the normal distribution, it is found that:

a) There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.

b) A capacity of 415 million gallons is needed.

c) An amount of 236 million gallons of water use is exceeded with 95% probability.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 310, \sigma = 45[/tex]

For item a, the probability is one subtracted by the p-value of Z when X = 350, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (350 - 310)/45

Z = 0.89

Z = 0.89 has a p-value of 0.8133.

1 - 0.8133 = 0.1867.

There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.

For item b, the capacity should be the 99th percentile, which is X when Z = 2.327, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2.327 = (X - 310)/45

X - 310 = 45 x 2.327

X = 415. (rounded)

A capacity of 415 million gallons is needed.

For item c, the amount of water use is the 5th percentile, which is X when Z = -1.645, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

-1.645 = (X - 310)/45

X - 310 = -1.645 x 45

X = 236.

An amount of 236 million gallons of water use is exceeded with 95% probability.

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The value of the expression is 29

The expression is given as

(2 - 5i)(p + q)

Where

p = 2

q = 5i

Substitute these values in (2 - 5i)(p + q)

So, we have

(2 - 5i)(p + q) = (2 - 5i)(2 + 5i)

Apply the difference of two squares

(2 - 5i)(p + q) = 4 - (-25)

Evaluate the difference

(2 - 5i)(p + q) = 29

Hence, the value of the expression is 29

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