what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)

Answer:

I just had to do this problem and,

B is (10, -4) and D is (58/9, -2)

Step-by-step explanation:

A. f(-5) = -(-5)^2-4(-5)+4 = -1

  f(5) = -(5)^2-4(5)+4 = -41

-1 + -41 = -42

B. -1 - -41 = 40

Answer:

D. $455.80

Step-by-step explanation:

True Balance = Bank Statement - Outstanding Checks

= $592.53 - ($49.80 + $86.93)

= $455.80

The question asked is related to probability, which is a topic in Mathematics. After calculating the probability of selecting a good quart of milk four times in a row (considering that the quantity decreases each time a good quart is selected), the probability equates approximately to 0.3 or 30%.

The given question is a statistical problem related to probability and involves the concept of independent events. In this case, each quart of milk being good or spoiled is an independent event, meaning the outcome of one event doesn't affect the other.

In the cooler, there are 20 quarts of milk in total, 15 of which are good (20 - 5 spoilt quarts equals 15 good ones). Hence, the probability of selecting a good quart of milk at first is 15/20, or 0.75.

After removing one good quart, there are now 14 good quarts out of 19. Hence, the probability of drawing a second good quart is 14/19. We can calculate the probabilities for the third and fourth quarts in the same way, resulting in 13/18 and 12/17 respectively.

Since these are independent events, the probability of all these events happening is the product of their individual probabilities. Therefore, the answer is 0.75* (14/19)* (13/18)* (12/17), which is approximately 0.3 or 30%.

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n standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

We have,

In scientific notation, a number is expressed as the product of a coefficient between 1 and 10 and a power of 10.

Given [tex]1.2\times10^{-2}[/tex],

We can rewrite it by moving the decimal point two places to the left to obtain 0.012.

The coefficient 0.012 is between 0.01 and 0.1, which is equivalent to 1/100 or 1 divided by 10 raised to the power of 2.

Thus, we can write it as 1.2 multiplied by 10 raised to the power of -2.

Thus,

In standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

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48/12 = 4 feet

24/2 = 2 feet

 4 *2 = 8 square feet

Answer:

                     8 feet squared

The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ

Here,

The expression is [tex]16 - x^{2}[/tex]

We have to find the value of expression after substitute 4 sinθ for x.

What is substitution method?

Substitution method is algebraic method to solve the linear equations.



Now,

The expression is [tex]16 - x^{2}[/tex]

By putting x = 4 sinθ in above equation, we get;

[tex]16 - x^{2}[/tex]  = 16 - ( 4 sinθ)^2

            = 16 - 16 sin^2θ

            = 16 ( 1 - sin^2θ )

            = 16 cos^2θ

Since,  1 - sin^2θ = cos^2θ

Hence, The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ

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To simplify the expression 16 - x² after substituting 4 sin θ for x, you end up with 16 cos² θ, using the Pythagorean trigonometric identity.

To simplify the expression 16 - x² after substituting 4 sin θ for x, where 0° < θ < 90°, we follow these steps:

The substitution gives us 16 - (4 sin θ)².

To further simplify:

Final answer:

To find the expression with a quotient greater than 1, we convert the mixed numbers into improper fractions and perform the division for each expression. The expression that gives a quotient greater than 1 is 5 3/4 divided by 7 3/8.

Explanation:

To find the expression that has a quotient greater than 1, we need to divide the given fractions. Let's examine each expression:

4 2/3 divided by 5 1/4: To divide mixed numbers, we convert them into improper fractions and then perform the division. In this case, the quotient is less than 1.

3 1/8 divided by 2 2/5: Similar to the first expression, we convert the mixed numbers into improper fractions and divide. The quotient is also less than 1.

1 6/7 divided by 2 1/3: Again, convert the mixed numbers into improper fractions and perform the division. The quotient is less than 1.

5 3/4 divided by 7 3/8: Convert the mixed numbers into improper fractions and divide. The quotient is greater than 1, so this is the expression we're looking for.

Therefore, the expression with a quotient greater than 1 is 5 3/4 divided by 7 3/8.

In the given equation of the provided problem, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.

To solve for A in each of the given equations, we'll isolate the variable A on one side of the equation. Let's go through each equation:

R = x(A + B)

To solve for A, we'll start by expanding the expression on the right side:

R = xA + xB

R - xB = xA

Divide both sides of the equation by x to solve for A:

A = [tex]\frac{R - xB}{x}[/tex].

Therefore, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

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The numerator of the equivalent fraction with denominator 12 for 1/2 is 6. This comes from multiplying both the numerator and denominator of 1/2 by the same number (6).

To find the numerator of the equivalent fraction with denominator 12 for 1/2, we simply multiply both parts of the fraction by the same number such that the denominator becomes 12. We know that 2 * 6 equals 12, so we multiply the numerator 1 by 6 as well, which gives us the numerator 6.

Therefore, the fraction 1/2 is equivalent to 6/12.

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[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

We will calculate the unit conversion factor used to convert its engine displacement from cubic-centimeters to cubic-inches.

The relationships between inch and cm are as follows:

[tex]\boxed{ \ 1 \ inch = 2.54 \ cm\ }[/tex]

Inches and cm represent units of length.

Made into fractions, 1 inch as the denominator and 2.54 cm as the numerator.

[tex]\boxed{ \ \frac{1 \ inch}{2.54 \ cm} \ }[/tex]

As a unit conversion factor of volume, the numerator and the denominator in cubic.

[tex]\boxed{ \ \frac{(1 \ inch)^3}{(2.54 \ cm)^3} \ }[/tex]

[tex]\boxed{ \ \frac{1 \ inch^3}{16.387 \ cm^3} \ }[/tex]

Thus, we get the unit conversion factor

[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

Let's use this unit conversion factor to calculate its engine displacement in new units.

[tex]\boxed{= 1,043 \ cm^3 \times 0.061 \ \frac{inch^3}{cm^3}}[/tex]

Note for cm³ units that have been crossed out.

The conversion result is [tex] \ \boxed{ \ 63.623 \ inch^3\ }[/tex]

Keywords: the motorcycle engine, Kawasaki Ninja 1000, 1043 cubic-centimeters (cm³), to calculate, its engine displacement, in cubic-inches (in³), what unit conversion factor