Four friends race their bikes down the street. Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds. Which order shows the friends’ times from fastest to slowest?

Answer:

Step-by-step explanation:

Area of shaded region = Area of Square ABCD− Area of 4 quadrants of circle

Side of square =14cm

Area of Square =(side)

2=(14) 2=196cm 2Radius of circle  = half of the side of square = 214=7cmArea of quadrant of circle = 41πr 2

Area of 4 quadrants of circle =4( 41 πr 2)= 722×7×7=154cm 2  Area of shaded region =196−154=42cm 2

Answer:

8 and 12

Step-by-step explanation:

The inverse of the function is x²+8x+13

In mathematics, an inverse function is a arithmetic operator that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y provides the result x, and contrariwise, i.e., f(x) = y if and only if g = x.

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).-

Swap x and f(x).-

The result is the inverse of the original function .

y=√x+3-4

y+4=√x+3

on squaring with sides we get

y²+16+8y=x+3

y²+8y+13=x

swapping x And y we get y=x²+8x+13

f inverse x =x²+8x+13

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Answer:

0.0068

Step-by-step explanation:

i had this question

Answer: x=1308.8

Step-by-step explanation:

The value of log₄(256) is 4

In order to solve logarithm with different bases change of base rule is used, according to which a logarithm operation can be rewritten as a fraction of logarithms having a new base

                                logₐb = (logₓb) / (logₓa)

log₄(256) = (log₁₀256) / (log₁₀4)

= (log₁₀4⁴) / (log₁₀4)

As per the power rule of logarithms, the logarithm of an exponential number is equal to exponent times of the logarithm it means when an logarithmic term has an exponent it is transferred to the front of the logarithm and the logarithm is multiplied with it.

                                 (∵ logₐMⁿ = n logₐM)

=(4log₁₀4) / (log₁₀4)

= 4

Hence, it is seen that the value of the above question, log₄256 is 4.

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The required simplification of rational expression is (4 + x) / (x - 3).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Simplifying the rational expression: x² + 2x - 8 / x² - 5x + 6

Given a rational expression,

x² + 2x - 8 / x² - 5x + 6

On simplifying, we get,

For numerator, x² + 2x - 8: (x - 2)(x + 4)

For denominator, x² - 5x + 6: (x - 2)(x - 3)

Now, x² + 2x - 8 / x² - 5x + 6 = (x - 2)(4 + x) / (x - 2)(x - 3)

= (4 + x) / (x - 3)

Restriction is that the denominator, x - 3 should not be 0.

Hence, the required simplification of rational expression is (4 + x) / (x - 3)

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The simplest form of the expression is 3xy .

We have given an expression  ∛81 x⁵ y³ / ∛3 x² .

On simplifying , we get

   [tex]\frac{(81x^5y^3)^{1/3}}{(3x^2)^{1/3}} = \frac{(3^4x^5y^3)^{1/3}}{(3x^2)^{1/3}}\\\\= \frac{3^{4/3}x^{5/3}y}{3^{1/3}x^{2/3}} \\\\= 3xy[/tex]

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Step-by-step explanation:

42086

14

12

10+

4

2

422

+ 9

2 4 6

8 10 12 14 16 x

42595

Answer:

-1/2

Step-by-step explanation:

[tex]-\frac{1}{6}[/tex] ÷ [tex]\frac{2}{6}= -\frac{1}{6}[/tex] x [tex]\frac{6}{2} \\[/tex] = [tex]\frac{-6}{-12} =- \frac{1}{2}[/tex]

I assume you mean the polynomial

[tex](ax^6 + bx^8 + cx^3 + d) (x^5 + ex^4 + f) (x^2 + gx + h)[/tex]

The degree of this polynomial is the exponent of the largest power of [tex]x[/tex] in the expansion of the product.

This term is the product of the largest power terms in each factor. These are

[tex]ax^6 + bx^8 + cx^3 + d \implies bx^8[/tex]

[tex]x^5 + ex^4 + f \implies x^5[/tex]

[tex]x^2 + gx + h \implies x^2[/tex]

So, the largest power term in the polynomial is

[tex]bx^8 \cdot x^5 \cdot x^2 = bx^{15}[/tex]

and the degree is 15.

Answer:

Judah's hourly wage is $7/hr.

Step-by-step explanation:

x=(86+12)/14

x=98/14

x=7

If Melinda hit a total of 1,645 tennis balls and she hits 32 balls per minute, it means she has been in the tennis practice for 50 minutes

How many of the hits of 1645 are attributable to only practice?

Out of the 1645 tennis balls so far hit by Melinda only 1,600 are attributable to the tennis practice because she  has already hit 45 tennis balls before the tennis practice commenced

number of tennis balls in tennis practice=1645-45

number of tennis balls in tennis practice=1600

number of minutest at practice=1600/32

number of minutest at practice=50 minutes

In essence, Melinda has been at the practice for 50 minutes

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Answer:

90

Step-by-step explanation:

Espero que te ayude :)

Answer:

90

Step-by-step explanation:

1800 x 0.05 = 90

Hope this helps :)

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

x² + 7x + 5 is the domain of all real numbers.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².

we have to calculate (f + g)(x)

Which is equivalent to:

(f + g)(x) = f(x) + g(x)

Taking the two functions and substituting them into this expression, we get,

f(x) + g(x) = (7x + 5) + (x²)

simplifying the above function, we get

f(x) + g(x) = x² + 7x + 5

Therefore, (f + g)(x) = x² + 7x + 5.

We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.

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Lin knows that there are 4 quarts in a gallon. To figure out how many gallons are in six quarts, she should divide six by four.

This is further explained below.

Generally,  The unitary method is an approach to problem-solving that involves first determining the value of a single unit and then determining the component values by multiplying the value of the single unit by itself.

6 qs=0.25* 6gallons

6=1.5gallons

In conclusion, in order to calculate how many gallons are in six quarts, she needs to divide six by four.

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Answer: 440-25h = m

Step-by-step explanation:

She makes 25 dollars per hour (25h=m)

If u subtract the amount that the console costs the equation becomes

440-25=m

Im assuming u are in 7th grade math which is what i was in last year so i hope this helps! :)

Answer:

If in the next 6 days she rides an average of 8 miles per day, she will meet her goal.

Step-by-step explanation:

What is the average number of miles she would have to ride each day to meet her goal?

We know that Mayerlin wants to ride her bicycle for 56 miles this week, and she already has ridden 8 miles, so the distance left is:

56mi - 8mi = 48mi

Now, to find the average distance that she needs to ride each day in order to meet her goal, we need to take the quotient between the distance left and the number days that she has left (6 days), then we will get:

D = 48mi/6 = 8mi

This means that if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.

given coordinates                           dilated coordinates

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

Given data

p' ( 4, 6 )

Q' ( 2, 2 )

R' ( 6, 2 )

S' ( 6, 6 )

The given coordinates is gotten by ( x, y ) and the coordinates is gotten to be ( x, -y ). Applying the rule is solve as follows:

given coordinates                           dilated coordinates

( x, y )                                                     ( x, -y )

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

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The perimeter of rectangular classroom with its length five times its width is 108 ft.

Rectangle is two - dimensional shape with four sides such that the pair of two opposite sides are equal and parallel to each other.

Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -

Width [W] = 9 ft

Length [L] = 5W = 5 x 9 = 45 ft

The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -

[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft

Therefore, the perimeter of rectangle with its length five times its width is 108 ft.

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Answer:3.8

Step-by-step explanation:

3.8

Answer:

29

Step-by-step explanation:

firat 4 78374748383838

The statements about the diagram that can be concluded, includes;

The first statement that cannot be concluded is the option;

[tex] \overleftrightarrow{AB}[/tex]

intersects [tex]\overleftrightarrow{CD}[/tex]

[tex] \overleftrightarrow{AB}[/tex] is on plane T, [tex]\overleftrightarrow{CD}[/tex] is on plane S

[tex]\overleftrightarrow{AB}[/tex] is offset from [tex]\overleftrightarrow{CD}[/tex] by [tex] \overline{BC}[/tex]

Therefore;

[tex]\overleftrightarrow{AB}[/tex] cannot intersect [tex]\overleftrightarrow{CD}[/tex]

The second statement that cannot be concluded is the option;

[tex] \overleftrightarrow{HC} \perp \overleftrightarrow{ CD}[/tex]

The angle [tex] \angle {DCH} [/tex] appears more to be obtuse than 90° such that [tex] \overleftrightarrow{HC} [/tex] cannot be [tex] \perp [/tex] to [tex]\overleftrightarrow{ CD}[/tex]

The third statement that cannot be concluded is the option;

[tex] \overleftrightarrow{FA} \perp \overleftrightarrow{ CD}[/tex]

The reason the above statement cannot be concluded is that [tex] \overleftrightarrow{FA} [/tex] and [tex] \overleftrightarrow{ CD}[/tex] are lines that do not intersect.

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The distance between points is 9.11 .

What is the Distance Between Two Points?

the distance between points V(1,3) and W(6, -1)

[tex]d = \sqrt{( x_{2}- x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

so x₁ = 1 , x₂ = 3 and y₁ = 6 , y₂ = -1

[tex]vw = \sqrt{( 3-1 )^{2} + ( -1 - 6 )^{2} }[/tex]

[tex]vw = \sqrt{( 2 )^{2} + ( -7)^{2} }[/tex]

[tex]vw = \sqrt{4 + 79}[/tex]

[tex]vw = \sqrt{83}[/tex]

vw = 9.110433 ≈ 9.11

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The values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

The figure that completes the question is added as an attachment

The opposite sides of a parallelogram are congruent

This means that

5x - 20 = 7x - 38

4y + 11 = 6x - 31

So, we have

5x - 20 = 7x - 38

Collect the like terms

7x - 5x = 38 - 20

Evaluate the like terms

2x = 18

Divide through by 2

x = 9

Substitute x = 9 in 4y + 11 = 6x - 31

So, we have

4y + 11 = 6 x 9 - 31

Evaluate the product

So, we have

4y + 11 = 23

This gives

4y = 12

So, we have

y = 3

Hence, the values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

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If you are aware of the line's length or have access to a ruler, bisecting (or cutting in half) a line is not difficult. However, you can still cut the line in half with a straightedge and compass even if you don't know how long it is.

Draw the section of the line you need to divide. You must use a straightedge to create the line segment if it is not already present. Put the compass needle on either terminal to accomplish this. Approximately half of the length should be covered by the compass when it is opened.

Using the compass, aim to keep the needle on the endpoint and refrain from changing the compass's setting. To do this, position your straightedge on the intersection of the arcs above the line and line them up with the intersection below the line. The line is bisected at a 90-degree angle by the line you draw connecting the two arc intersections.

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The answer for the given logarithmic function is 3

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

loga[tex]b^{n}[/tex] where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logabc where a is the base is given as logab+logc

loga b/c where a is the base is given as logab-logac

Now it is given to us to find the value of log₅125

where 5 is the base and 125 is the argument

125 = 5x5x5 which is [tex]5^{3}[/tex]

hence 125 can be written as 5^3

Thus the logarithmic function becomes

log₅125=log₅[tex]5^{3}[/tex]

thus it can be written as3log₅5

Now we know that log₅5 can also be written as log5/log5

And hence log5/log5 becomes 1

Thus 3log₅5 = 3*1 =3

Hence the answer to the given logarithm is 3

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