Given the speeds of each runner below, determine who runs the fastest.
Ron runs 12 feet per second.
Brooke runs 329 feet in 24 seconds.
Jessica runs 1 mile in 591 seconds.
Tony runs 645 feet in 1 minute.

We will use the angle properties to determine the constituent angles.

We are given that a line segment ( BD ) is an angle bisector of < ABC. We will go ahead and represent this piece of information graphically as follows:

We will define the following angle as follows:

The angle bisector ( BD ) divides the angle into two equal halves as follows:

We are given expressions for both angles as follows:

We know from the property of angle bisector that the two constituent angles are equal i.e:

Now we can use the value of ( x ) calculated above and determine either of the constituent angles as follows:

Then we can use the angle bisector property relation again to determine the angle ABC as follows:

Answer:

Answer: 85 cm

Step-by-step explanation:

Answer:

dihuyyh

Step-by-step explanation:

The correct description of the values in both the domain and range of the function are;

Domain is on the interval (0, 100) which are possible values of number of copies of the book produced.

Range is on the interval (700, 1700) which are the possible total cost of publishing the book

The formula for total cost is;

Total cost = fixed cost + variable cost or

We are given the function; C = 10N + 700  

Where;

C is the total cost of publishing the book (in dollars).

N is the number of copies of the book produced.

a) Domain is possible values of N.

For the first printing, the company can produce up to 100 copies of the book.

Thus, the domain is on the interval (0, 100) but only integers.

The range is the possible cost.

Possible cost maximum = 10(100) + 700 = 1700

Thus, the range is on the interval (700, 1700) where any cost in that interval is not continuous, but follows a discrete sequence.

b)  Reasonable values of the domain are [0, max] where the maximum value is the largest book sales ever in the market area,  maybe 50 or 75

Reasonable values for the range are [700, max] where the maximum cost is 700 + 10 *50 or 75,

or 1200 or 1450.  

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Answer:

3 options.

Chicken - White

Chicken - Italian

Chicken - Wheat

Explanation:

This question can be better explained with a graphic:

You have an index card with the word "chicken", and 3 index cards with the words "white", "wheat", and "Italian", which are the options of bread.

Also we have represeted the red yarn with 3 black lines that connect the options.

We can see from the image that we have 3 options of sandwiches:

Chicken - White

Chicken - Italian

Chicken - Wheat

The decimal equivalent of 7 over 16 is 0.4375 .

Fractions and decimals are two ways to represent the same numbers. A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. A fraction is represented as a numerical value that is defined as a part of a whole.

We will convert the given fraction 7/16 to a decimal number.

To convert any fraction to a decimal, we just need to divide its numerator by denominator.

Here the fraction is 7/16 which means we need to perform 7 ÷ 16 = 0.4375.

So, 7/16 as a decimal is 0.4375.

Thus, 7/16 as a decimal is equal to 0.4375

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Draw the graph of x-axis which is lesser than 5 .

What is  Graph inequality ?

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Answer:$16,000 in interest

Step-by-step explanation: well, you just take 4% of 80,000 which is $3200. (80,000x0.04=3200). Then because it is 5 years, just multiply the 3200 by 5 (there isn't compound interest.) 3200*5=16,000.

Given the expression:

To solve this expression for x, means that you have to isolate the term "x" in one side of the equal sign and all other terms mus be in the other side of it.

To "pass" a term from one side of the = sign to the other you have to perform the inverse operation to both sides of the equation (this way the equality remains valid)

So, the term "fy" is adding, the inverse operation is to subtract it, first step is to subtract this term of both sides of the equation:

+fy and -fy cancel each other so that:

Next, the term "x" is being multiplied by "d" but you need to reach the point were x is alone.

To cancel this multiplication you have to divide it by "d", and to keep the equality valid you have to perform the operation in both sides of the = sign:

d/d=1, then we get that x is equal to:

Answer:

31

Step-by-step explanation:

800/25=32

992/32=31

Answer:

£31

Step-by-step explanation:

let me know if you want a through explanation

Recall that a rotation of 180 degrees around the origin transforms the coordinates following the rule:

(x, y) --> (-x, -y)

and also recall that a reflection across the y-axis will convert the following:

(x, y) --> (-x, y)

Therefore, we cansider the succession of transformations given as:

(x, y) --> (-x, -y) --> (x, -y) (since the y value stays the same in the reflection around the y axis, but the x changes to its opposite)

Then, this transformation (from beginning to end)

(x, y) --> (x, -y) is equivalent to a reflection around the x-axis (which keeps the x coordinate intact and flips the y-coordinate to its opposite. So, please select the option that reads: Reflection around the x-axis.

3.2 x 10^-3 = 0.0032 ( we have to move the decimal point 3 units to the left since the exponent of 10 is -3)

Express all the options in decimal form

2.1 x 10^-3 = 0.0021

4.2 x 10^-4 = 0.00042

5.2 x 10^-2 = 0.052

5.2 x 10^-1= 0.52

0.052 > 0.0032

0.52> 0.0032

So, correct options are:

5.2 x 10^-2

5.2 x 10^-1

If we invest $12,000 in an account that pays simple interest of 3.4%

each year. 4080 is the interest earned after 10 years.

Simple interest is the cost of borrowing money without accounting for the effects of compounding.

Given that if we invest $12,000 in an account that pays simple interest of 3.4% each year. The interest earned after 10 years we have to calculate.

A=P(1+rt)

A= Final Amount

P=Principle amount=12000

r = rate of interest=3.4%

t is time =10 years

Substitute these values in Formula.

Convert 3.4% to decimal number by dividing with 100.

A=12000(1+0.034(10))

A=12000(1+0.34)

A=12000(1.34)

A=16080

So intial amount-Final amount

12000-16080

4080

Hence the interest earned after 10 years is 4080.

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answer: b) - 28.05

For this case we have the following function given:

We also know that the domain is given by:

and in order to find the range we need to use the domain given:

So then the range for this case would be given by:

By using the slope formula the required value of r is 7 .

Given : ( 2 , 5 ) and ( 5 , r )

The slope given is  2/ 3

We know that when two values of x and y are given and we are supposed to find the slope of the equation we use the slope formula.

And thus by using the slope formula we get the below :

y₂ - y₁ = m ( x₂ - x₁ )

= > r - 5 = 2/ 3 ( 5 - 2 )

On cross multiplying we get :

3 r - 15 = 10 - 4

Add 15 to both sides of the equation and we will get

3 r = 10 - 4 + 15

3 r = 21

Divide both sides by 7 and we get :

r = 7

Thus by using the slope formula the required value of r is 7 .

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Answer:

y = -6/3 + 12

Step-by-step explanation:

Step 1: Plot the point

Step 2: Simplify the given function then graph it

3y = -6x + 9 becomes:

y = -6/3x + 3

Step 3: Using the slope of -6/3 (because parallel lines will ALWAYS have the same slope) find 1 more point on the graph.

Step 4: Draw a line thru those points and find the y-int

y = ax + b, x and y are variables, a is the slope and b is the y-int

y = -6/3 + 12

Since equality is false there is no solution.

Answer:

Discriminant = 9.

Step-by-step explanation:

Discriminant

[tex]\boxed{b^2-4ac}\quad\textsf{when}\;ax^2+bx+c=0[/tex]

[tex]\textsf{when $b^2-4ac > 0 \implies$ two real roots}.[/tex]

[tex]\textsf{when $b^2-4ac=0 \implies$ one real root}.[/tex]

[tex]\textsf{when $b^2-4ac < 0 \implies$ no real roots}.[/tex]

Given function:

[tex]x^2+x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned} \implies b^2=4ac&=(1)^2-4(1)(-2)\\&=1-4(-2)\\&=1+8\\&=9\end{aligned}[/tex]

Therefore, the discriminant of the given function is 9.

As the discriminant is greater than zero, this implies that there are two real roots.

Given the image we have a Parallelogram. Because it is a four-sided plane figure with opposite sides parallel.

ANSWER

a) Parallelogram

Answer:

  1.147×10^-2 cm

Step-by-step explanation:

You want the difference between the two values 1.87×10^-2 and 7.23×10^-3 expressed in scientific notation.

Addition and subtraction of numbers in scientific notation requires that the multipliers have the same exponent. That exponent can be chosen so no adjustment of the exponent is required in the answer.

  [tex]1.87\times10^{-2}-7.23\times10^{-3}= 1.87\times10^{-2}-0.723\times10^{-2}\\\\=(1.87-0.723)\times10^{-2}=\boxed{1.147\times10^{-2}}[/tex]

This measurement is in centimeters.

__

Additional comment

A calculator or spreadsheet can accept input and display results in scientific notation.

The difference in the diameter of of G and H is 1.147x 10⁻² cm

What are mathematics operations?

• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.

• The operation's arity is determined by the number of operands.

• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.

• A zero-arity operation, also known as a nullary operation, is a constant.

• The mixed product is an example of an arity 3 operation, also known as a ternary operation.

it is given that :

the diameter of cell G is = 1.87 x 10⁻² cm

the diameter of cell H is = 7.23 x 10⁻³ cm

Now, to find the difference between the diameter of two cells simply subtract the diameter of cell G and H :

difference in the diameter of of G and H = 1.87 x 10⁻² cm - 7.23 x 10⁻³ cm

difference in the diameter of of G and H=1.87 x 10⁻² cm - 0.723 x 10⁻² cm

                                                                  = 1.147x 10⁻² cm

Therefore, the difference in the diameter of of G and H is 1.147x 10⁻² cm

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Answer:

3a x 7a= 21a^2

Step-by-step explanation:

7a x 13a=91a^2

Answer:

its was 100.6

Step-by-step explanation:

i hope this helps

From the graph we can conclude:

The cars travels for 2 hours, then stops for 1 hour and finally travels again for 2 hours.

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

Those are supplementary angles, hence:

11.

Answer:

27 ounces of flour

Step-by-step explanation:

[tex]\frac{7}{3}[/tex] x [tex]\frac{9}{9}[/tex] = [tex]\frac{63}{27}[/tex]

7/3 = 63/x

isolate the so that it is on the top, so multiply by x on the right and on the left

this gives you:

x*7/3 = 63

try to isolate x and multiply by 3 to get rid of the denominator

x*7 = 63 * 3

x*7 = 189

finally isolate x by dividing by 7 and getting rid of the 7 multiplying with it

x= 189/7

x = 27

you need 27 ounces of flour if you have 63 ounces of sugar

According to the given equation (y = (3/4)x -2) the value of y for x:

Y = {-5 , -2 , 1 , 4}

A coordinate plane is just a two-dimensional plane that is created when two number lines cross. These number lines include the x-axis, a horizontal number line, and indeed the y-axis, a vertical number line.

In a coordinate plane, which is a two-dimensional number line, the vertical line is known as the y-axis and the horizontal line as the x-axis, as you might recall from pre-algebra. These parallel lines cross one another at their zero points. The origin is where we start from.

Equation:

y = (3/4)x -2

X = {-4 , 0 , 4 , 8}

for each value of x the value of the y :

For x = -4

y = (3/4)x -2

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

y = -5

For x = 0

y = (3/4)x -2

y = (3/4)(0) -2

y = 0 -2

y = -2

For x = 4

y = (3/4)x -2

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

y = 1

For x = 8

y = (3/4)x -2

y = (3/4)(8) -2

y = 6 -2

y = 4

According to the given equation (y = (3/4)x -2) the value of y for x:

Y = {-5 , -2 , 1 , 4}

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If Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

The number of lemon limes in the bag = 2 lemon-lime

Number of watermelon in the bag = 3 watermelon

Number of grape gumballs in the bag = 5 grape gumball

Sample space is the set of all the possible outcomes the experiment

Here there are 2 lemon-lime, 3 watermelon and 5 grape gumball

Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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Answer:Option B is the correct answer

We need to find the slope of a segment that joins the points (5, -2), and (-5, -8)

Therefore we use the formula for the slope:

Therefore the value of the slope is 0.6 = 6/10 = 3/5

You may need to enter the answer in a particular format (all three values above are the same, but expressed differently)

Then if we want the expression for the equation of the line, we use this slope, and either one of the points that they give us. for example the point (5, -2)

We write the general form of the equation of a line in slope-intercept form:

and use for "m" 3/5, and require that the point (5, -2) be part of the line:

Therefore, the equation of the line (in slope intercept form) is: