Simplify. 7√50x^15y^21 Assume x and y are nonnegative.

A.5x7y102xy−−−√B.35x7y102xy2−−−−√C.35x7y10xy−−√D.35x7y102xy−−−√

we are given that the English Aplhabet has 26 letters. we let g represent the number of letters in the Greek alphabet. From the statement given, English alphabet which is 26 = 20 + 1/4 *g. The expression which is similar to this is in option A. 1/4g + 20 = 26.

Answer:

Step-by-step explanation:

(  -2x³ + x - 5) × ( x3 - 3x - 4)

= ( -2x³)×( x3 - 3x - 4) +(x)×( x3 - 3x - 4) - (5)( x3 - 3x - 4)

= - 2x^6  +6x^4 +8x³ + x^4 - 3x² -4x - 5x³ +15x + 20

= - 2x^6  +7x^4 +3x³-3x²+11x +20

To know which of the following expressions are polynomials, let us look at the definition of a polynomial:

Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".

For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.

We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.

Now lets, look at the

[tex]30y^2[/tex] since it has got one term it can not be a polynomial.

[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.

[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.

[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.

The correct polynomial expressions are 30y²+x and 30y². Option A and D is the correct answer.

Polynomials are expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and exponentiation.

30y²+x: This expression is a polynomial because it consists of a constant term (30), a variable term (y²) raised to a non-negative integer exponent, and an additional variable term (x).

30y²: This expression is a polynomial because it consists of a constant term (30) and a variable term (y²) raised to a non-negative integer exponent.

These expressions are considered polynomials because they consist of variables, constants, and non-negative integer exponents, and they involve the appropriate mathematical operations of addition and multiplication.

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The complete question is, "Which expressions are polynomials? Select each correct answer.

a.  30y²+x

b. 30y²+x (¹/²)

c. (30y²) ÷ x

d. 30y²"

The multiples for 6 : 6, 12, 18, 24, 30,36, 42, 48

The multiples for 8 : 8, 16, 24, 32, 40, 48, 56, 64

Hope this helps

C

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.

Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.

This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.

Given fraction;

[tex]\frac{1}{3+\sqrt{2}}[/tex]

Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;

The conjugate of the denominator (3 + √2) is 3 - √2;

Apply the rationalization of fraction;

[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]

Hence option C is correct.

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You can see that this line passe through the points (-4,-2) and (4,3).

The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope is

[tex]\dfrac{3-(-2)}{4-(-4)}=\dfrac{5}{8}.[/tex]

Then the equation of the line is

[tex]y-3=\dfrac{5}{8}(x-4),\\\\y=\dfrac{5}{8}x+\dfrac{1}{2}.[/tex]

Answer: correct choice is C.

Hello,

Please, see the attached files.

Thanks.

Answer:

hey i think the answer is 7

Step-by-step explanation:

After the 15% discount, Maria pays 85% of the cost. That cost is the sum of the fixed cost and the variable (per visit) cost.

... (updated cost) = 0.85×($150 +$30×a)

... (updated cost) = 127.50 +25.50a . . . . in dollars

The term sin(x+[7pi/4]) can be rewritten in terms of sin(x) and cos(x) using the formula for sine of the sum of two angles. Given A = x and B = 7pi/4, the equation can be simplified to sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2).

To rewrite the term sin(x+[7pi/4]) in terms of sin(x) and cos(x), we can use the formula for sine of the sum of two angles. The formula is given by:

sin(A + B) = sinAcosB + cosAsinB

Substituting our given values into this formula, where A = x and B = 7pi/4, we get:

sin(x + [7pi/4]) = sin(x)cos(7pi/4) + cos(x)sin(7pi/4)

Note that cos(7pi/4) = √2/2 and sin(7pi/4) = -√2/2. Therefore:

sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2)

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Answer,

C. 1650

Explanation,

495/6 = 82.5

82.5 x 20 = 1650

Hope this helps :-)

If arc ADB is that portion of the circle that is not arc AB, then its measure is ...

... 360° -49° = 311°

_____

The sum of the measures of the arcs of a circle is 360°.

Answer:

See the attached

Step-by-step explanation:

An exponential function has the variable in the exponent.

Answer:

Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]

Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]

Step-by-step explanation:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is initial value and b is growth factor.

It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.

We need to check whether the given function is an exponential function or not.

The given function is

[tex]f(x)=8e^x[/tex]

It is an exponential function with initial value 8 and growth factor e≈2.718.

Similarly,

[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.

[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.

We are given: Triangle ABC sides, AB = x, BC = y and CA = 2x.

Another triangle MNO whose vertices M,N and O correspond to A,B,C respectively.

Therefore, AB corresponding to sides MN , BC corresponding to sides NO and CA corresponding to sides OM.

Also, we are given " A similarity transformation with a scale factor of 0.5 Maps ABC to MNO".

That means triangle ABC is dilated by a factor of 0.5.

Each side of the triangle MNO is 0.5 times(half) of Triangle ABC.

We could also say that each side of Triangle ABC is two times of sides of triangle MNO.

We are given side OM = 5 units.

CA = Times of OM = 2 * 5 = 10 units.

CA = 2x = 10 units or 2x=10.

Dividing both sides by 2, we get

[tex]\frac{2x}{2}=\frac{10}{2}[/tex]

x=5.

AB = x.

Therefore, AB = 5 units.

Answer:

Step-by-step explanation:

Answer:125a6

-64q12

-c^30d^9f^18g^3

Step-by-step explanation:

Got it right on edgy

The value of F(8) is 64.

Given that,

Based on the above information, the calculation is as follows:

[tex]F(8) = 8 \times 8[/tex]

= 64

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Answer: 40,000,000

Population: 400,000,000

40X1010

Step-by-step explanation:

Answer:

[tex]P_4 = 7604.08[/tex]

Step-by-step explanation:

If the population increases at a rate of 4% per annum, then:

In year 1:

[tex]P_1 = P_0 + 0.04P_0[/tex]

Where [tex]P_0[/tex] is the initial population and [tex]P_n[/tex] is the population in year n

In year 2

[tex]P_2 = P_1 + 0.04P_1[/tex]

It can also be written as:

[tex]P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)[/tex]

Taking out common factor [tex]P_0[/tex]

[tex]P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)[/tex]

Taking out common factor (1 + 0.04)

[tex]P_2 = (1 + 0.04) (P_0 + 0.04P_0)[/tex]

Taking out again common factor [tex]P_0[/tex]

[tex]P_2 = (1 + 0.04) (1 + 0.04) P_0[/tex]

Simplifying

[tex]P_2 = P_0 (1 + 0.04) ^ 2[/tex]

So

[tex]P_n = P_0 (1 + 0.04) ^ n[/tex]

This is the equation that represents the population for year n

Then, in 4 years, the population will be:

[tex]P_4 = P_0 (1 + 0.04) ^ 4\\P_4 = 6500(1 + 0.04) ^ 4\\P_4 = 7604.08[/tex]

Answer:

1a. 42 liters

1b. 345 miles

2a. 10 h 20 min 41.4 sec

2b. 361.6 km

5a. $8

5b. 444.5 km

5c. 46 h 13 min 20.9 sec

5d. $160

Step-by-step explanation:

Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, value 1 and related value 1. You are asked to find value 2 that corresponds to related value 2.

Solving the Proportion

Expressed as a proportion, this looks like ...

... (value 1)/(related value 1) = (value 2)/(related value 2)

If you multiply both sides of this equation by related value 2, you can find value 2.

... (related value 2)/(related value 1)×(value 1) = value 2

Another way to think about it

I like to think of the related values as making a fraction. If the related value 2 is larger than related value 1, the fraction is greater than 1 and the value 2 will be larger than value 1. (This realization can serve as a check on your answer.)

1a. related value 2 = 168 km. This is the value for which you want to find value 2, the number of liters of gasoline. related value 1 has the same units as related value 2 (km), and value 1 has the same units as value 2 (liters).

Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...

... (168/468)×(117 L) = 42 L

1b. (10 h)/(4 h)×(138 mi) = 345 mi

2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h

2b. (4 h)/(5 h)×(452 km) = 362.6 km

You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.

5a. (2 lb)/(50 lb)×$200 = $8

5b. (7 h)/(6 h)×381 km = 444.5 km

5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h

5d. (20 kg)/(11 kg)×$88 = $160

Answer:

  C.  -20

Step by step explanation:

It appears you want the value of the expression -5² +8|-1| +(-3).

The order of operations tells us that the first step is to evaluate expressions in parentheses. Here, the absolute value symbols effectively serve as parentheses, so we start there.

|-1| signifies the absolute value of -1, its magnitude, or positive value. That simplifies to 1. So, your expression is ...

  -5² +8·1 -3

The next step is to evaluate the term with an exponent: -5² = -(5·5) = -25.

  = -25 +8·1 -3

Now, we perform the multiplication:

  = -25 +8 -3

And finally, the addition/subtraction

  = -17 -3

  = -20

__

Additional comment

The expression you show in the problem statement looks like the first term is negative fifty-two. That is very different from negative five squared. An exponent is indicated using a caret (^), as -5^2, or using a superscript font, as -5². Please be careful to use appropriate math symbols where exponents are involved.

Answer:

b. Your answer is appropriate.

c. The decimals can be eliminated by multiplying by 100. (You can also add 0.14 to the problem, adding .01 to each individual price and 0.14 to the total. This will make the second equation be 12x +25y = 246, which makes the numbers slightly easier to work with.) Unfortunately, there don't seem to be any common factors that would reduce the size of the numbers.

Step-by-step explanation:

a. We assume you're finding quantities of shirts and pants for a purchase of 14 total items costing $245.86. If so, your equations are appropriate.

b. The solution for one variable or the other can be found in 6 arithmetic operations using your suggested method. Any other method takes as many or more. (Multiplying the first equation by -11.99 and adding to the second gets you the equivalent of substituting for x in as many operations.)

Graphing can be quick and easy with the right tool. Since you know the solutions are integers, just about any graphing tool will get you close enough.

Another method (using only 5 arithmetic operations) is to calculate the average price of an item as 245.86/14, then figuring the ratio of the difference from the lower price to the total difference in price. Multiplying this ratio by the number of items gives the number of the higher-priced item (pants). (245.86/14 -11.99)/(24.99 -11.99)·14 = 6 This method treats the problem as a "mixture" problem, finding the numbers of each consitutuent that make the average come out what it is.

c. See above for how to simplify the numbers. Done properly, the answer is not changed. (Some people don't work well with decimals or fractions, so like to see those eliminated from the problem. Some folks work better with small integers than with large ones, so like to see the numbers be made as small as possible.)

The population of the first town decreases at a rate of 600 people per year, and is predicted to be 2,100 in 2016. The town with an initial population of 75,000 grows at a linear rate, represented by the function P(t) = 75000 + 2500t, with the population expected to reach 100,000 after 10 years.

For the first part of your question regarding the town's decreasing population, we need to establish a rate of decrease. The town's population went from 5,900 in 2010 to 4,700 in 2012—this is a decrease of 1,200 over two years, or 600 people per year. Therefore, we can predict that the population will continue to decrease by 600 people per year. In 2016, this suggests the population would be 4,700 (population in 2012) - 600*4 (4 years from 2012 to 2016), which equals 2,100. For identifying the year when the population will reach 0, we use the same rate and find it by using the formula (current population / rate of decrease) + current year. As for the part about the town with an initial population of 75,000 growing at a constant rate, we can model this as a linear function such as P(t) = 75000 + 2500t. This equation states that the population at any given year is the initial population plus the annual growth times the number of years since the model began. In terms of the graph of this function, the y-intercept represents the initial population, while the slope is the constant rate of growth. The model expects the population to reach 100,000 after (100,000 - 75,000) / 2,500  = 10 years.

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I have memorized facts about fractions like these, so can tell you ...

[tex]\dfrac{5}{9}=0.5\overline{5}\\\\-\dfrac{3}{8}=-3\times 0.125=-0.375\\\\-\dfrac{3}{11}=-0.27\overline{27}[/tex]

_____

A fraction with 9 as a denominator is a repeating 1-digit decimal with the decimal digit being the numerator of the fraction.

A fraction with 11 as a denominator is a repeating 2-digit decimal with the two digits being 9 times the numerator of the fraction.

1/8 = 0.125, so any multiple of 1/8 is that multiple of 0.125.

To convert 5/9 - 3/8 - 3/11 into a decimal, you find a common denominator (792), subtract the numerators, resulting in -73/792, and then divide the numerator by the denominator to find the decimal, which is -0.0922.

The problem is asking us to write the rational number 5/9 - 3/8 - 3/11 as a decimal. To do this, we need to first subtract these fractions and then convert the result into a decimal.

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x = [tex]\frac{y}{c}[/tex] - b

divide both sides by c

x + b = [tex]\frac{y}{c}[/tex] ( subtract b from both sides )

x = [tex]\frac{y}{c}[/tex] - b

The equation solved for x is x = y/c - b.

Two or more expressions with an equal sign are defined as an equation.

The given equation is y = c(x + b).

y = c(x + b)

y/c = x + b

y/c - b = x

Or, x = y/c - b

Hence, the equation solved for x is x = y/c - b.

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To convert the density of the textbook to slug/in³, we first convert the density from g/cm³ to kg/m³ and then use the given conversion factors to convert it to slug/in³.

To convert the density of the textbook to slug/in³, we need to use the given conversion factors: 1 slug = 14.59 kg and 1 in = 2.54 cm. First, we need to convert the density from g/cm³ to kg/m³ by dividing by 1000. Then, we can convert from kg/m³ to slug/in³ using the given conversion factors. Let's calculate:

Given density = 3 g/cm³

Step 1: Convert g/cm³ to kg/m³

Density in kg/m³ = 3 g/cm³ / 1000 = 0.003 kg/m³

Step 2: Convert kg/m³ to slug/in³

Density in slug/in³ = 0.003 kg/m³ × (1 slug / 14.59 kg) × (1 in³ / (2.54 cm)³)

Performing the calculations gives us the density of the textbook in slug/in³.

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Quite often, the CD will earn more interest—even if you have to pay a penalty for early withdrawal.

_____

For example, my local credit union offers 0.10% interest on passbook savings and 1.46% interest on a 4-year CD. One of my local banks offers 0.01% interest on passbook savings, and 0.60% on a 4-year CD.

A CD (Certificate of Deposit) generally offers a higher interest rate than a passbook savings account, which may lead to a greater return on investment. But it has a drawback where money cannot be withdrawn without penalty until a set time period ends.

The primary advantage of a CD (Certificate of Deposit) over a passbook savings account is typically a higher interest rate. A CD is a type of timed deposit, meaning that the money is typically put in the bank for a fixed amount of time. During this time, the interest rate is usually higher than that of a typical savings account, allowing for a greater return on the initial investment. Unlike a passbook savings account, however, you cannot withdraw money from a CD without penalty until the time period ends, which in this case is four years. This is an important consideration for Beth and Mark.

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