Using the distributive property, remove the parentheses
10c^4(9-8c^2)
Also simplify

Answer:

6

Step-by-step explanation:

logx 27  * log3 x^2

The first step is to convert to base 10

(log 27/logx) * (log x^2/log3)

27 = 3^3 so we can rewrite this

(log 3^3/logx) * (log x^2/log3)

log a^b  = b log a

(3 log 3/logx) * (2log x/log3)

We can cancel the log x in the numerator and denominator and the log 3 in the numerator and denominator

3 * 2

6

Step-by-step explanation:

First , Subtract y from both sides:

−3x = −10 −y

Second, Divide both sides by −3

x = [tex]\frac{-10-y}{3}[/tex]

That's ur answer

Hope this helped u!!!

Good luck!!

Answer:

The correct answer is $81.28

Step-by-step explanation:

In order to find this, we simply treat the word of as a multiplication symbol.

0.8% of 125% of $8128

Now change the percentages to decimals

0.008 * 1.25 * 8128 = 81.28

Answer:

Step-by-step explanation:

To solve this kind of problem, we must remember that the word "of" means multiplication in math language, and all percentages numbers can be expressed as a fraction where the denominator is 100. Applying all this, we have

[tex]0.8\%\times 125\%\times 8128\\\frac{0.8}{100}\times \frac{125}{100} \times 8128\\ 0.008(1.25)(8128)=81.28[/tex]

Therefore, all those percentages of 8128 results in 81.28

Answer:

3 7/10

Hope that helped!

Answer:

3.7 converted into a fraction is [tex]\frac{37}{10}[/tex]

Step-by-step explanation:

Unable to determine the subject of the question due to lack of information.

The arithmetic operations described pertain to the addition and multiplication of numbers and the result of their signs. For instance:

When two positive numbers add or multiply, the result is also positive (e.g., 3 + 2 = 5 and 2 x 3 = 6).

When two negative numbers add or multiply, the result is negative when adding and positive when multiplying (e.g., -4 + (-2) = -6 and (-4) x (-3) = 12).

For numbers with opposite signs, in addition, subtract the smaller number from the larger number and give the result the sign of the larger number, while in multiplication, the result will have a negative sign (e.g., -5 + 3 = -2 and (-3) x 2 = -6).

Regarding quantum numbers, the sets of quantum numbers provide information about the state of an electron in an atom. Each set of numbers must follow specific rules:

The principal quantum number n must be a positive integer.

The azimuthal quantum number l must be an integer ranging from 0 up to n - 1.

The magnetic quantum number mē must range from -l to +l.

The spin quantum number ms must be either +1/2 or -1/2.

Therefore, for the given quantum numbers a. {4, 2, -2, 1} is not an allowed set because the spin quantum number must be either +1/2 or -1/2, not 1. Similarly, set b. {3, 1, 0, -1/2} is a possible set because it follows all the designated rules for quantum numbers.

Answer:

The mass of aluminum is 26.982 g/mol.

Step-by-step explanation:

The molar mass of an element is the mass in grams of 1 mole of the element. It is determined by taking the atomic weight of the element on the periodic table, and writing it as g/mol.

The mass of aluminum will depend on the quantity and context. Given quantities in chemical compounds range from 26.98g in AlPO4 to 80.94g in Al2S3 (for 1 mol). For specific quantities or other situations, the mass should be calculated proportionally.

The mass of aluminum can be determined using the specific heat and molecular absorption principles. A known quantity of aluminum in a compound like AlPO4 contains 1.000 mol or 26.98 g Al, while an Al2Cl6 molecule contains 1.994 mol or 53.74 g Al. When considering an Al2S3 molecule, it contains 3.00 mol or 80.94 g Al, which is the greatest mass of Al among the examples.

To calculate the mass for a different quantity of aluminum, you need to adjust these figures proportionally. For instance, if you have only half a mol of Al2S3, the mass would not be 80.94g, but half of that. Also, regarding mass of atoms, it is often represented in atomic mass units (amu) or in kilograms.

These examples give a clear idea of how to determine the mass of aluminum in different situations. The specific condition determines which calculation or table to use.

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The recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.

To determine how many grams of carbohydrates are recommended per day based on a daily value of 12%, you can use the following calculation:

First, calculate what 1% of the daily value would be:

1% of daily value = 36 grams / 12% = 3 grams

Now, to find the recommended daily intake, simply multiply this by 100 since you want to find the recommended intake for 100% of the daily value:

Recommended daily intake = 3 grams/1% * 100% = 300 grams

So, the recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.

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Answer:

117 Girls

Step-by-step explanation:

If 64% of the kids are boys, then 36% are girls   64% + 36% = 100%

.36 x 325 = 117  girls

Proof

.64 x 325 = 208 boys

208 + 117 = 325

There are 117 girls at the zoo.

To determine how many children at the zoo are girls, we start by understanding that 64% of the 325 children are boys. Let's go through the steps to find out the number of girls.

Calculate the number of boys by multiplying 64% by 325.

Percentage to decimal conversion: 64% = 0.64. So, 0.64 × 325 = 208 boys.

Subtract the number of boys from the total number of children to find the number of girls: 325 - 208 = 117 girls.

Therefore, there are 117 girls at the zoo.

Answer:

$17,600,000

Step-by-step explanation:

First, we need to count the amount of money we pay for each episode. If each episode costs you $200,000 to make, that would be subtracted from your total amount. If there are 150,000 viewers per episode, we can multiply 150,000 by 11, because there are 11 episodes. There are 1,650,000 people watching your show! Since the advertiser pays you $12 per person, we can simply multiply 12 times the number of people. You have earned $19800000. However, we need to subtract how much it took us to make the episodes, so we multiply the number of episodes, 11, by $200,000 and subtract the product from our total amount. Your amount of profit is $17,600,000.

Hope this helps! (Brainliest please!)

Answer:

$99 000

Step-by-step explanation:

(a) No. of episodes

There are 11 episodes per season.

No. = 0.5 × 11

No. = 5.5 episodes

=====

(b) No. of viewers

There are 150 000 viewers per episode

No. = 5.5 × 150 000/1

No. = 825 000 viewers

=====

(c) Payment

The advertiser pays $12 per 100 viewers.

Pay = 825 000 × 12/100

Pay = $99 000

The advertiser will pay you $99 000.

Answer:

75 weeks

Step-by-step explanation:

Let the number of weeks be x

10x + 45 = 789          Subtract 45 from both sides

10x = 789 - 45           Combine

10x = 744                   Divide by 10

x = 744/10                  Divide

x= 74.4 weeks.          It will not hurt her to save the extra week to get the phone

Answer:

Option D is correct.

Explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

Step-by-step explanation:

Geometric sequence states that a sequence of numbers in which the ratio between consecutive terms is constant,

we can write a formula for the nth geometric sequence in the form of:

[tex]a_n = a_1r^{n-1}[/tex] .....[1] where [tex]a_1[/tex] is the first term and  r is the common ratio between successive term.

Given the sequence: 64, 32, 16 , 8......

Here, first term ([tex]a_1[/tex]) = 64.

Common ratio(r) = 0.5

Since,

[tex]\frac{32}{64} =0.5[/tex]

[tex]\frac{16}{32} = 0.5[/tex] ,

[tex]\frac{8}{16} = 0.5[/tex] ......

Substitute the value of a and r in [1] we get;

[tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

therefore, the explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

Answer:

d.  2x^2    -3x  -8

Step-by-step explanation:

if f(×)=2x^2-5 and

g(×)=3×+3

(f-g)(×)=

I like to line them up vertically

2x^2-5

-(3x+3)

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

Distribute the minus sign

2x^2-5

-3x-3

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

Line up the powers

2x^2+ 0x   -5

           -3x-3

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

2x^2    -3x  -8

Answer:

The two equations are [tex]y=\frac{1}{2}x+5[/tex]    and  [tex]y=\frac{1}{2}x[/tex]                                                                                                                                                                            

Step-by-step explanation:

we have given that : Part I=  [tex]y=\frac{1}{2}x+5[/tex] equation of line

slope intercept form is y=mx+c

the slope of the line Part I is m=1/2

taken another equation of line Part II= [tex]y=\frac{1}{2}x[/tex]

whose slope of line Part II is m=1/2

since, both equation have same slope therefore these two equation  Part II and Part I are parallel

It is also shown by the graph attached.

Let the Length of River D be : P

Given : River C is 100 Miles Longer than River D

⇒ Length of River C = P + 100

Given : The Sum of Both Rivers is 5570 Miles

⇒ P + (P + 100) = 5570

⇒ 2P + 100 = 5570

⇒ 2P = 5570 - 100

⇒ 2P = 5470

⇒ P = 2735

⇒ Length of River D is : 2735 Miles

⇒ Length of River C is : (P + 100) = (2735 + 100) = 2835 Miles

Answer:

1.What was the net price paid by Rowly

by 5/4/2  percentage 137000 cents,138400 cents,141200 cent

2.What was the amount of trade discount

by 5/4/2 percentage 7000 cents,5600 cents,2800 cents

Step-by-step explanation:

list price= $1,400

percentage discounts=5%

4%

and

2%

we have to find net price=?

we will calculate discount one by one

5% of 1400=[tex]\frac{5}{100}[/tex]×1400

5% of 1400=70

amount of trade discount for 5 %=70 dollar

we know that

1 dollar=100 cent

we will convert dollar into cents

7o dollar=70*100=7000 cent

Net amount  paid for 5% discount=1440-70=1370 dollar

1370 dollar=1370*100=137000 cent

4% of 1400=[tex]\frac{4}{100}[/tex]×1400

4% of 1400=56

amount of trade discount for 4 %=56 dollar

56 dollar=56*100=5600 cent

Net amount  paid for 4% discount=1440-56=1384 dollar

1384 dollar=1384*10138400 cent

2% of 1400=[tex]\frac{2}{100}[/tex]×1400

2% of 1400=28

amount of trade discount for 2%=28 dollar

28 dollar=28*100=2800 cent

Net amount  paid for 2% discount=1440-28=1412 dollars

1412 dollar=1412*100=141200 cent

Answer:

x = 91.5

Step-by-step explanation:

for 30.5 miles travelled gas used is 1 gallon ← unit rate

To calculate distance travelled multiply gas used by 30.5

For 3 gallons used

distance travelled = 3 × 30.5 = 91.5 miles

⇒ x = 91.5

Answer:

the desired equation is y = (1/6)x + 3/2.

Step-by-step explanation:

From the graph you can see immediately that the y-intercept is (0,3/2).

This is "b" in y = mx + b.

Focus on point (-3,1).  Substitute -3 for x in y = mx + 3/2 and then 1 for y:

1 = m(-3) + 3/2

Clear this result of fractions by mult. all three terms by 2:

2 = m(-6) + 3.  Solving for m, -6m = 2 - 3, or -6m = -1.  Then m = 1/6, and the

desired equation is y = (1/6)x + 3/2.

900 = 2 · 2 · 3 · 3 · 5 · 5

Next numbers:

2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 5 = 900 · 15 = 13,500

2 · 2 · 2 · 2 · 3 · 3 · 3 · 3 · 5 · 5 · 5 · 5 = 13,500 · 15 = 202,500

202,500 · 15 = 3,037,500

3,037,500 · 15 = 45,562,500

....

Given : Water Level in the Pool decreases by 6.35 × 10⁻¹ cm each Day

⇒ In One Day : The Level decreases by 6.35 × 10⁻¹ cm

⇒ In [8.64 × 10⁻⁴] Seconds : The Level decreases by 6.35 × 10⁻¹ cm

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = (\frac{6.35 \times 10^-^1}{8.64 \times 10^4})}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 0.73 \times 10^-^5}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 7.3 \times 10^-^6}[/tex]

First Blank : 7.3

Second Blank : 10⁻⁶

Answer: a = c^(1/2) which is the first answer choice of the list

Work Shown:

a = b^(2/3) ... given equation

a = (c^(3/4))^(2/3) ... replace b with c^(3/4)

a = c^((3/4)*(2/3)) .... multiply exponents

a = c^(1/2) .... Simplify; note the 3's cancel, also 2/4 turns into 1/2

Answer:

C

Step-by-step explanation:

The general functional notation is:

[tex]f(x)=A[/tex]

Where it means that [tex]f[/tex] is a function of [tex]x[/tex], and the answer is [tex]A[/tex].

From the problem, we know that the depth is a function of distance, and at that specific distance, the depth is 30 ft.

So we see that depth is a function of distance from shore, and the answer is 30 ft.

Matching this to our explanation of functional notation above, we can say that:

Depth(distance from shore) = 30 ft

Answer C is right.

Answer:

Depth distance from shore equals 30 ft

Step-by-step explanation:

Confirmed from pretest

[tex]\bf \stackrel{\textit{solving for \underline{y}}}{3y+12=2x}\implies 3y=2x-12\implies y=\cfrac{2x-12}{3}\implies y=\cfrac{2x}{3}-\cfrac{12}{3} \\\\\\ y=\cfrac{2}{3}x-4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Symbols (or letters) in an equation can be important.

Step-by-Step Explanation:

The symbol [or letter (x, m, n, etc.)] is usually not important because the symbol represents a number. Sometimes it is important because each symbol (or letter) can represent another number.

for example: n+3 = 4-m (the symbol/ letters are different because they represent a different number).

for another example: n+3 = 4 (the symbol/ letter is only one letter).

The choice of letter or symbol to represent an unknown number in mathematics is arbitrary. It doesn't impact the mathematical operation or relationships, as the fundamental principles of algebra apply universally to any symbol.

It doesn't matter what letter or symbol is used to represent an unknown number because the essence of algebra and mathematical expressions is based on abstraction and generality. Mathematical symbols are placeholders for values and can be interchanged without changing the underlying mathematical relationships. Here's why it doesn't matter:

1. Universality of Symbols: Mathematical symbols and variables are universally understood and follow consistent rules. Whether you use "x," "y," "a," "b," or any other symbol, the principles of mathematics remain the same.

2. Abstraction: Algebra allows us to work with general concepts rather than specific numbers. The choice of symbols is arbitrary and doesn't affect the mathematical operations. The symbols represent placeholders for any number that satisfies the given conditions.

3. Flexibility: Different symbols can be used for different contexts or problems. For example, "x" is often used for unknowns in equations, "a" for constants, and "y" for dependent variables in functions. However, this is a convention, and other symbols can be used interchangeably.

4. Consistency: The rules of algebra, such as the commutative, associative, and distributive properties, hold true regardless of the symbols used. Algebraic manipulations and equations remain valid irrespective of the choice of symbols.

In summary, mathematical symbols are versatile and interchangeable because they serve as placeholders for values. The principles of algebra and mathematics are symbol-independent, allowing for flexibility in representation while maintaining the same underlying mathematical relationships.

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Answer:

Step-by-step explanation:

OK... You have to use this formula: Y2 - Y1

                                                          X2 - X1

Y2 - Y1

X2 - X1

-5 - 7

2 - - 2

-12

-2

Simplify by dividing both -12 & -2 by 2: -6

                                                                 -1

It's either -6 or it's just -6 by itself... Really sorry if I'm wrong...

                -1  

Well, a linear equation should look like this: y = ax + b.

So if the slope is 0, then y = a*0 + b = b.

If y = b, then the line is a horizontal line like this:    ______________

Now, we look at the points that were given in the question: (-2, 7), (2, -5)

If the slope is 0, then the value of y, should not change, but the value of x will constantly be changing. So it means that as x increases, y is always the same.

If we look at the y place on the points: The y values are the bold numbers:

(-2, 7), (2, -5)

As you can see, 7 is not the same as -5. So the line's slope is not 0. The slope would be a negative number. Why? Well, 7 is above the x-axis and -5 is below the x-axis. For the x values, -2 is smaller than 2, so the point (-2, 7) is located at the top left quadrant and the point (2, -5) is located at the bottom right quadrant.

So to answer your question, the slope is not zero. The slope is negative.

Answer:

1. 2x-3

2.-4x+12

3.9x+3

4.-15x-12

5.2x-5

6.-11x

7.23x+42

8.-21x

9.-2x-12

10.4x-8

Step-by-step explanation:

Answer:

C) y + 1 = -2/3(x - 4)

Step-by-step explanation:

The given line passes through the points A (4, -1) and B (-2, 3)

Let's find the slope now.

Slope (m) = (y2 - y1)/(x2 - x1)

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

= (3 + 1)/-6

= 4/-6

Slope (m) = -2/3

The equation of line y - y1 = m (x - x1)

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

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

Answer:  C) y + 1 = -2/3(x - 4)

Thank you.

Answer:

answer is c)

Step-by-step explanation:

:)

Answer:

[tex]\dfrac{9}{100}=0.09\ or\ \dfrac{9}{10}=0.9[/tex]

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\text{We have}\ \sqrt{81}:\\\\\sqrt{81}=9\ because\ 9^2=81.\ \text{Therefore}\\\\\dfrac{\sqrt{81}}{100}=\dfrac{9}{100}\\\\\text{If is}\ \sqrt{\dfrac{81}{100}},\text{then:}\\\\ \text{Use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{\dfrac{81}{100}}=\dfrac{\sqrt{81}}{\sqrt{100}}=\dfrac{9}{10}=0.9\\\\\sqrt{81}=9\ because\ 9^2=81\\\sqrt{100}=10\ because\ 10^2=100[/tex]

Kevin needs to answer at least 26 questions correctly out of 32 to exceed an 80% success rate, which means he needs to get 2 more questions right than he previously did.

Kevin correctly answered 75% of his 32 test questions, which is 24 questions. To achieve more than an 80% correct rate, Kevin needs to answer more than 80% of 32, which is more than 25.6 questions. Since Kevin can't answer a fraction of a question, he must answer at least 26 questions correctly. To find the number of additional questions he needs to answer correctly to exceed 80% when he has already answered 24 correctly, we subtract 24 from 26, resulting in 2 more questions that Kevin needs to answer correctly to exceed an 80% success rate.

Answer:

Solving the system of equations using the substitution method, the solution is: x=2 and y=-2

Step-by-step explanation:

(1) y=7x-16

(2) y=2(2x-5)

Substituting "y" of the equation (1) in the equation (2)

(2) 7x-16=2(2x-5)

Applying the distributive property to eliminate the parentheses on the right side of the equation:

7x-16=2(2x)-2(5)

Multiplying:

7x-16=4x-10

Solving for x: Subtracting 4x and adding 16 both sides of the equation:

7x-16-4x+16=4x-10-4x+16

3x=6

Adding like terms:

Dividing by 3 both sides of the equation:

3x/3=6/3

x=2

Replacing x by 2 in the equation (1):

(1) y=7(2)-16

y=14-16

y=-2

Solution: x=2 and y=-2

Answer:

Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )Step-by-step explanation:

Answer:   $ 22

Step-by-step explanation:

[tex]\boxed{\$ 22}[/tex] of sales tax should be paidon the new price.

Further Explanation:

Calculation:

The given listed price of furniture in the month of May is [tex]\$550.[/tex]

The sales tax is of [tex]3\%[/tex] on the listed price of the furniture.

The price of the month May is increased by [tex]33\dfrac{1}{3}\%.[/tex]

The increased price of the furniture can be obtained as follows,

[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\%  \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32 \\\end{aligned}[/tex]

The new price of the furniture in dollars is [tex]\$ 733.32.[/tex]

The sales tax is of  [tex]3\%[/tex] on the listed price.

The sales tax on the new price can be obtained as follows,

[tex]\begin{aligned}{\text{Sales tax}}&= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]

[tex]\boxed{\$ 22}[/tex] of sales tax should be paid in dollars on the new price.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Sales Tax

Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month, 33 1/3%, paid, dollars, new price.