Illustrative Mathematics

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using for distance in kilometers and for number of hours, an equation that represents this situation is .

What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?

Write another equation that relates and in this context.

The reflection of (-2, -2) and (-1, 1) are

preimage    image

(-2, -2)         (-4, -2)

(-1, 1)             (-5, 1)

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is over line x = -3

However, reflection over line x = -3 which is (-3, 0) is  done as follows

from -2 to -3 = -2 - -3 = 1 unit

reflecting 1 unit over x = -3

-3 - 1 = -4

(-4, -2)

(-2, -2) ⇒ (-2 - -3, -2) ⇒ (1, -2) ⇒ (-3 - 1, -2) → (-4, -2)

from -1 to -3 = -1 - -3 = 2 units

reflecting 2 units over x = -3

-3 - 2 = -5

(-5, 1)

(-1, 1) ⇒ (-1 - -3, 1) ⇒ (2, 1) ⇒ (-3 - 2, 1) → (-5, 1)

The calculation is simply saying put

(-2, -2) this point is just before the reflection line, the image will formed at the point just after the reflection line -3 which is -4 hence (-4, -2)

(-1, 1) this point is a line before the reflection line, the mirror image will be formed skipping a line (-4) to get to -5 hence the point  (-5, 1)

the y coordinate is constant for both situations

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The correct option is option (B) .

In other words Histograms , Pareto charts and scatter plots have a common thing that they are all visual tools to display data.

Histogram :

It show continuous data in ordered rectangular columns. There are usually no gaps between columns.

Scatterplot :

A scatterplot is an x-y plot that shows the relationship between two variables. Used to plot data points on vertical and horizontal axes.

Pareto Chart :

A Pareto chart is a common tool used by manufacturers to analyze quality and defect data, providing a quick visual representation of the frequency and cumulative percentage of occurrences of a particular problem.

Hence , all of three have a common thing that is they visualize tools to represent the data

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Answer:

A. TPR

B. NM

C. 6

Step-by-step explanation:

1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.

2.  If you flip PRT then TR will match with NM

3. 4x-3=21

4x-3+3=21+3

Simplify: 4x=24

4x/4=24/4

x=6

The Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8  troy ounces.

Weight of a single gold alloy pendant = 15/32 troy ounces.

Jeweler makes the number of Pendants  from the total weight of gold alloy = 45/8 ÷ 15/32.

Dividing Fractions by Fractions

We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,

x/y ÷ a/b

⇒ x/y × b/a (reciprocal of a/b is b/a)

⇒ xb/ya

Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.

45/8 ÷ 15/32 = 45/8 × 32/15 = 12

∴ The value of 45/8 ÷ 15/32 = 12.

Hence the Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

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Answer:

m = 37

Step-by-step explanation:

The interior and corresponding exterior angle of a triangle are always supplementary.

Therefore, we can set the sum of the two given angle measures to 180°:

[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]

and solve algebraically for m.

[tex]2m-12 + 3m+7 = 180[/tex]

[tex](2m + 3m) + (-12+7) = 180[/tex]

[tex]5m-12+7 = 180[/tex]

[tex]5m - 5 = 180[/tex]

[tex]5m = 185[/tex]

[tex]m=37[/tex]

The value of m is 37.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Given:

m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.

int. m <Z + ext. <Z= 180

2m - 12 + 3m + 7 = 180

5m - 5 = 180

5m = 185

m = 185/ 5

m = 37

Hence, the value of m is 37.

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Answer:

skewed  to the right

Step-by-step explanation:

look at the graph

divide it in half

if both the sides are not equal then it is skewed

then to find out which way it is skewed look which side has more.

Answer: 6,001 milliliters

Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.

Answer:

I believe 6 liters is more.

as x -> -infinity, y -> -infinity and as x-> infinity, y-> infinity

So, last option is correct

Answer:

y = 1/2 x + 3/2

Step-by-step explanation:

A perpendicular slope is the opposite reciprocal, so it is 1/2

2 = 1/2(1) + b  To solve for b  

2 = 1/2 + b  Subtract 1/2 from both sides

1 1/2 = b

y = 1/2 x + 3/2

Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem

The minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot

The length of the planks that lumber stores sell = 8 foot

The error tolerance of the plank = 4%

Then the 4% of the length 8 is

= 8 × (4/100)

Divide the terms

= 8 × 0.04

Multiply the terms

= 0.32

Therefore the error tolerance will be ±0.32

The minimum length that you can buy = 8 - 0.32

= 7.68 foot

The greatest length that you can buy = 8 + 0.32

= 8.32 foot

Hence, the minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot

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Answer:

m∠1 = 126°

m∠2 = 154°

Step-by-step explanation:

First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)

We know that the measures of the interior angles of a triangle add to 180°.

Therefore,

m∠A + 96° + 30° = 180°

m∠A + 96° = 150°

m∠A = 54°

From this value, we can solve for m∠1, since it is supplementary to ∠A:

m∠A + m∠1 = 180°

54° + m∠1 = 180°

m∠1 = 126°

To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.

First, the measures of the interior angles of a triangle add to 180°:

28° + m∠1 + m∠B = 180°

28° + 126° + m∠B = 180°

m∠B = 26°

Finally, we can solve for m∠2 because it is supplementary to ∠B.

m∠B + m∠2 = 180°

26° + m∠2 = 180°

m∠2 = 154°

Step-by-step explanation:

any particular result with 2 dice has a probability of

1/6 × 1/6 = 1/36

a 3 on one die or both simply means at least one 3.

so, if all the 36 different outcomes we are looking at

3 1

3 2

3 3

3 4

3 5

3 6

1 3

2 3

4 3

5 3

6 3

the 3 3 combination can be counted only once !

so, we have 11 desired outcomes out of the possible 36.

so, the probability of getting at least one 3 is

11/36

the sum of at least 10 means the corresponding cases

4 6

5 5

5 6

6 4

6 5

6 6

in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.

so, we have 6 desired outcomes of the 36.

the probability of that is

6/36 = 1/6

The required speed is 45 mph in each direction.

What is speed?

The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

We know that distance=rate*time

d=rt

45=rt

45=(r+30)(t-2)

rt=(r+30)(t-2)    

This shows,

rt=rt+30t-2r-60

0=30t-2r-60

if 45=rt, then r=45/t

substitute in the equation

0=30t-2(45/t)-60

multiply both sides by t

0=30t²-90-60t

on solving this quadratic equation, we get  t= 3 s, t=-1 s

consider positive value

t=3 hours

45=rt

45=r*3

r=45/3 =15 mph to new site

r+30=15+30=45 mph returning

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The answer is -9.

-2 -(+7) = -2 -7

-2 -7 = -9

well, we know the price is $18, now, if we jack it up by 70%, well, what's 70% of 18?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 18}}{\left( \cfrac{70}{100} \right)18}\implies 12.6~\hfill \underset{price}{\stackrel{18~~ + ~~12.6}{\text{\LARGE 30.60}}}[/tex]

The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

What is transformation of function?

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up.

Given,

function g(x) = (x − 4)3 + 5 and compares to function f(x) = x3,

The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

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The group that travels faster when groups of hikers left camp at the same time and each traveled at a constant rate is group B.

From the information, two groups of hikers left camp at the same time. each traveled at a constant rate.

Since group A covered 3/4 mile in 1/2 hour, the speed will be:

= Distance / Time

= 3/4 ÷ 1/2

= 1.5 miles per hour.

It took Group B 3/4 hour to travel 1/3 mile. The speed will be:

= Distance / Time

= 3/4 ÷ 1/3

= 2.25 miles per hour.

Group B had a faster speed.

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Complete question

Two groups of hikers left camp at the same time. each traveled at a constant rate

group A covered 3/4 mile in 1/2 hour

It took Group B 3/4 hour to travel 1/3 mile

Which group so travelling at a faster rate?

The number of students that chose band as an elective is 50

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic

let the total number of seats for choir be x and that for band be y

if there are 4 times as many seats as there in band then mathematically,

x = 4y.--------------------1

If there are 250 students, then, there would be 250 seats for the combined class.

so,

x + y = 250--------------2

substitute x = 4y in equation 2

4y + y = 250

5y = 250

y = 250/5

y = 50

In conclusion, 50 students can choose band.

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Banerjee Company is  liable for FUTA tax this year and the net FUTA tax for the year is $528.60.

a. Yes. Banerjee Company liable for FUTA tax this year.

b. FUTA tax

FUTA tax =0.6%

Hence,

Net FUTA tax = (Wages paid  × tax rate ) +(Taxable wages × Tax rate)

Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)

Net FUTA tax = $140.40 + $388.30

Net FUTA tax =$528.60

Therefore $528.60 is the Net FUTA tax.

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Answer:

create a line between (0,0) and (1,3)
the unit rate is 3/2 or 1.5

Step-by-step explanation:

pls mark

AS per the combination method, Mr. Walters receive both payments in the same month in the 6th time.

Combination method:

A way of adding equations together in such a way that the variables are set aside, one by one is called as combination.

Given,

Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He received both payments in May 2019.

Here we need to find the next time he would receive both payments in the same month.

While looking into the given question we have identified he following things,

Dividend payment = 5 months

Royalty payment = 6 months

Both payment received = May 2019.

So, according to the combination method,

The value of n = 6 and the value of x = 5

So, the next time he would receive both payments in the same month is

=> 6 C 5 = 6! / 5! (6 - 5)!

Which results the value as 6.

Therefore, on 6th time from this payment he will receive both in the same month.

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The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

Given that,

The list of numbers are 3,6,9,7,4,6,7,0,7

The mean, median, mode, and range must be determined.

The "mean" is the standard "average," which is calculated by adding up all the numbers and dividing the result by the total number of numbers.

The value that sits in the middle of a set of numbers is known as the "median." Before you can find the median, your numbers must be listed in numerical order from smallest to greatest. This means that you might need to redo your list.

The "mode" value is the one that shows up the most often. There is no mode for the list if no number on the list is repeated.

A list of numbers' "range" is just the range between the largest and lowest values. It conveys "spread," which is the degree to which the values are scattered (or how concentrated they are).

Mean=(3+6+9+7+4+6+7+0+7)/9

Mean = 49/9

Mean = 5.4

Median is 0,3,4,6,6,7,7,7,9

The median is 6

Mode is 7

Range is

Greater number is 9 and the smallest number is 0

Difference is 9-0=9

Range is 9.

Therefore, The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

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Anlges on the same side of the transversal add up to 180 degrees.

What is Transversal?

A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.

Solution:

Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.

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Answer:

=30

Step-by-step explanation:

The library’s December record is 29442  

Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.

There are 4 basic operations in mathematics as given below.  

1. Addition  =>  (+)

2. Subtraction  => (-)

3. Division  => (÷)

4. Multiplication  =>  (x)  

Here we have

In 2017 the library was able to record 4907 borrowed books  

By December of the same year, the library has 6 times its January record.  

[ Here we use Multiplication to find the December record ]

The December record = 6 times of January record

⇒ 6 × January record

⇒ 6 × 4907    

⇒ 29442

Therefore,

The library’s December record is 29442

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The vectors having length of 10 units are,

-6 + 8i , 10 ,  10i , -10 , -10i , 3 + 9i , -3 + 9i

We have to find the seven complex numbers that have the length of 10 units.

So, the vectors having length of 10 units are,

1) -6 + 8i

2) 10

3) 10i

4) -10

5) -10i

6) 3 + 9i

7) -3 + 9i

Hence, the vectors having length of 10 units are,

-6 + 8i , 10 ,  10i , -10 , -10i , 3 + 9i , -3 + 9i

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Among the equations and inequality the true expression is 1 / 3 × 9 = 3.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Therefore, let's check the inequality that is true.

Hence,

1 / 4 × 28  > 8

28 / 4 > 8

7 > 8 (false)

1 / 6 × 48 < 5

48 / 6 < 5

8 < 5 (False)

1 / 3 × 9 = 3

9 / 3 = 3

3 = 3(True)

1 / 5 × 25 = 125

25 / 5 = 125

5 ≠ 125(False)

1 / 6 × 24 > 9

24 / 6 > 9

4 > 9 (False)

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The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

In the question,

it is given that ,

the sum of speed of two trains = 723.5 miles per hour

let the speed of the first train = x miles per hour

let the speed of the second train = y miles per hour ,

also given that , the speed of the first train is 4.5 mph faster than that of the second train , which means

x = y + 4.5 .

the sum is 723.5 ,

so , the equation is

x + y = 723.5

y + 4.5 + y = 723.5

2y + 4.5 = 723.5

2y = 719

y = 719/2

y = 359.5

So , x = 359.5 + 4.5 = 364 .

Therefore , The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

The given question is incomplete , the complete question is

The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each train ?

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