Determine if the ordered pair is a solution of the equation. Is (0,0) a solution of y = x? options: True False

8.2% = 0.082

50 * 0.082 = 4.1

the answer is 4.1

Final answer:

To convert 6 7/9% to a decimal, we change the mixed number to an improper fraction, divide by 100 and round to the nearest thousandth, resulting in approximately 0.068.

Explanation:

To find the decimal equivalent of 6 7/9%, we must first convert the mixed number to an improper fraction and then to a decimal. To convert 6 7/9% to an improper fraction, we multiply the whole number 6 by the denominator 9 and add the numerator 7 to get 7 + (6 × 9) = 7 + 54 = 61. Then we place 61 over the original denominator to obtain 61/9. The percentage sign indicates that we are dealing with a part out of 100, so we must divide 61/9 by 100 or, equivalently, multiply by 1/100.

Therefore, the calculation to convert the percentage to a decimal is: (61/9) × (1/100) = 61/900. Using a calculator, or performing the division manually, gives us approximately 0.0677777....

Finally, to round this to the nearest thousandth, we would look at the fourth decimal place (which is 7 in this case). Since 7 is greater than 5, we round up the third decimal place, resulting in 0.068.

Answer:

[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following integration:

[tex] \displaystyle \int \frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]

in order to do so we can consider using u-substitution

let our

[tex] \displaystyle u = {x}^{ \frac{1}{2} } \quad \text{and} \quad du = \frac{ {x}^{ - \frac{1}{2} } }{2} [/tex]

to apply substitution we need a little bit arrangement

multiply both Integral and integrand by 2 and ½

[tex]\displaystyle 2\int \frac{1}{2} \cdot\frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]

factor out [tex]x^{\frac{1}{2}}[/tex]:

[tex]\displaystyle 2\int \frac{1}{2 {x}^{ \frac{1}{2} } } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]

recall law of exponent:

[tex]\displaystyle 2\int \frac{ {x}^{ - \frac{1}{2} } }{2 } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]

apply substitution:

[tex]\displaystyle 2\int \frac{5}{ 1+ {x}^{ } } du[/tex]

rewrite x as [tex]\big(x^{\frac{1}{2}}\big)^{2}[/tex]:

[tex]\displaystyle 2\int \frac{5}{ 1+ ( {x ^{ \frac{1}{2} } })^{ 2 } } du[/tex]

substitute:

[tex]\displaystyle 2\int \frac{5}{ 1+ ( u)^{ 2 } } du[/tex]

recall integration rule of inverse trig:

[tex] \displaystyle 2 \times 5 \tan^{-1}(u)[/tex]

simplify multiplication:

[tex] \displaystyle10 \tan^{-1}(u)[/tex]

substitute back:

[tex] \displaystyle10 \tan^{-1}( {x}^{ \frac{1}{2} } )[/tex]

simplify if needed:

[tex] \displaystyle10 \tan^{-1}( \sqrt{x} )[/tex]

finally we of course have to add constant of integration:

[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]

and we are done!

Final answer:

The standard form of the equation y = (3/8)x - 4 is 8y - 3x = -32.

Explanation:

The standard form of the equation y = (3/8)x - 4 is written as 8y - 3x = -32.

To convert a linear equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), you need to multiply the entire equation by the common denominator of the coefficients.

In this case, the common denominator is 8, so multiplying both sides of the equation by 8 gives us 8y = 3x - 32. Moving all the terms to one side, we have 8y - 3x = -32, which is the standard form of the equation.

To transform the equation y = 3/8x - 4 into standard form, subtract 3/8x from both sides and then multiply through by 8 to eliminate the fraction, resulting in -3x + 8y = -32.

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A should not be negative. To convert the equation y = 3/8x - 4 to standard form, you need to manipulate the equation so that it fits the standard form criteria.

Step-by-step, we start by moving the x-term to the left side of the equation:

Therefore, the standard form of the given equation is -3x + 8y = -32.

25 * 2.5 = 62.5 *2 = 125

8x5 = 40

125 +40 = 165 square feet

Answer:

c

Step-by-step explanation:

To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.

To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.

First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).

Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.

To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.

This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.

Answer:

25

Step-by-step explanation:

>First jump = 4.25 m

>Best jump = 1.12 * First jump

Best jump = 1.12 * (4.25 m)

Best jump = 4.76 m

>Best jump = 0.85 * Winning jump

Hence,

Winning jump = Best jump / 0.85

Winning jump = 4.76 m / 0.85

Winning jump = 5.6 m

ASA

Is the answer i got on my work

Answer:

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

Step-by-step explanation:

we have

[tex]-3x^{2} -4x-4=0[/tex]

Rewrite (Multiply by [tex]-1[/tex] both sides)

[tex]3x^{2}+4x+4=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+4x+4=0[/tex]

so

[tex]a=3\\b=4\\c=4[/tex]

substitute

[tex]x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}[/tex]

[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]

Simplify

[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

Final answer:

There were 113 people who bought a ticket but did not show up to the concert, calculated by subtracting the number of attendees (587) from the total tickets sold (700).

Explanation:

To determine how many people bought a ticket but did not attend the concert, you would subtract the number of people who attended from the total number of tickets sold. In this case, 700 tickets were sold and only 587 people attended. So, the calculation would be:

700 tickets sold - 587 attendees = 113 people who did not attend

Thus, 113 people bought a ticket but did not show up to the concert.

The acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

To find the acceptable circumferences for a woman's basketball, we need to consider the ideal circumference and the allowable variation. The ideal circumference is 28.75 inches and the actual circumference can vary by at most 0.25 inches. So, the acceptable circumferences can be found by adding and subtracting the maximum allowable variation from the ideal circumference:

Acceptable circumference = 28.75 ± 0.25 inches

This means the acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.

To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.

(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i

You may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.

Final answer:

To solve a complex number, understand it as a sum of a real number and an imaginary number and use operations like conjugation. For division, multiply by the conjugate to simplify. Complex numbers ensure all polynomial equations have solutions.

Explanation:

To solve a complex number, one must understand that a complex number z is the sum of a real number and an imaginary number, which is written as z = a + ib. The terms a and b represent the real and imaginary parts respectively, often notated as Re(z) and Im(z).

To divide by a complex number, you multiply the numerator and the denominator by the conjugate of the denominator, simplifying to a form without imaginary numbers in the denominator. This can be expressed as z/z' = (aa' + bb')/(a'² +b'²) + i(ba' - ab')/(a'² + b'²). The conjugate of a complex number z is written as z* or z*.

Complex numbers are crucial in solving polynomial equations as they ensure that every polynomial equation has a solution. This is shown by the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. For instance, the equation x² - 2x + 5 = 0 has no real solutions but two complex solutions, x = 1±2i.

Answer:

c: 18

Step-by-step explanation:

300/6 = 50 mph

250/5 =50mph

 so they drove 50 miles per hour

 so 50 *3 = 150 miles in 3 hours