1-8 Homework Exercises Course 2 Mathematics Common Core

Answer:

[tex]21x^4+3y-35x^2+41[/tex] must be subtracted

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

Step-by-step explanation:

We have the following polynomial

[tex]21x^4+3y-6x^2+34[/tex]

And need to find a polynomial to subtract from it to get

[tex]29x^2-7[/tex]

This means that if we subtract these two polynomials, we will get our desired polynomial

[tex]21x^4+3y-6x^2+34-(29x^2-7)\\\\21x^4+3y-6x^2+34-29x^2+7\\\\21x^4+3y-35x^2+41[/tex]

Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found

[tex]21x^4+3y-6x^2+34-(21x^4+3y-35x^2+41)\\\\21x^4+3y-6x^2+34-21x^4-3y+35x^2-41\\\\-6x^2+34+35x^2-41\\\\29x^2-7[/tex]

As we got the desired result, we know that this answer is correct.

And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?

Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.

This means that our desired polynomial needs to only have some amount of x's and constants.

We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2

[tex]21x^4+3y-6x^2+34-(x-2)\\\\21x^4+3y-6x^2+34-x+2\\\\21x^4+3y-6x^2-x+36[/tex]

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

Answer:

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x^2 + 3x - 1[/tex]

Required

Determine g(x), if f(x) is reflected across the y axis

When a function (x,y) is reflected across the y axis, the new function becomes (−x,y).

In other words,

[tex]g(x) = f(-x)[/tex]

Calculating f(-x)

[tex]f(-x) = 2(-x)^2 + 3(-x) - 1[/tex]

[tex]f(-x) = 2x^2 - 3x - 1[/tex]

Substitute g(x) for f(-x)

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Hence;

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Answer:

[tex]x[/tex]  = -6

[tex]x[/tex] = 3

Step-by-step explain

[tex]x^{2}[/tex] = 3[tex]x[/tex] - 18 =0

[tex]x^{2}[/tex] =6[tex]x[/tex]  - 3[tex]x[/tex]  - 18 = 0

[tex]x[/tex] x ([tex]x[/tex] + 6) -3[tex]x[/tex]  - 18 = 0

[tex]x[/tex] x ([tex]x[/tex] + 6) - 3([tex]x[/tex]  = 6)=0

([tex]x[/tex]  = 6) x ([tex]x[/tex] 3) = 0

[tex]x[/tex] +6 = 0

[tex]x[/tex] - 3 = 0

[tex]x[/tex]  = -6

[tex]x[/tex] = 3

Answer:

ED and EC

Step-by-step explanation:

If the two rays which extend in the opposite direction having same endpoint is said to be opposite rays.

From the picture attached,

Rays having same endpoint E but not in the opposite directions are ED and EC.

This pair of rays meet at point E having different directions.

Similarly EA and EB is the other pair of rays having same end point (at E) but not in opposite directions.  

Answer:

0.31 - 0.39

Step-by-step explanation:

3/10 = 0.3

2/5 = 0.4

All the values between 0.3 and 0.4 excluding 0.3 and 0.4 (can't be 0.3 or 0.4)

The decimal number that is greater than 3/10 and less than 2/5 will be;

⇒ 0.35

A decimal number is a number that consists of a whole and a fractional part.

Given that;

A decimal number is greater than 3/10 and less than 2/5.

Now,

Let a decimal number = x

So, We get;

⇒ 3/10 < x < 2/5

Since, We have;

⇒ 3/10 = 0.3

⇒ 2/5 = 0.4

Thus, The decimal number that is greater than 3/10 and less than 2/5 is 0.35.

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Answer:

27

Step-by-step explanation:

20=v-7

v=20+7

v=27

Hence, v equals to 27

[tex]\huge\mathbb\purple{EXPLAIN}[/tex]

[tex]20 = v - 7[/tex]

[tex]v = 20 + 7 = 27[/tex]

Answer:

number of girls = 90

Number of boys = 125

Number of adults = 20

Step-by-step explanation:

Total people at the summer camp= 235

Let

number of girls=x

Number of boys = x + 35

Number of adults = x - 70

Total people at the summer camp= number of girls + Number of boys + Number of adults

235 = x + (x+35) + (x - 70)

235 = x + x + 35 + x - 70

235 = 3x - 35

Add 35 to both sides

235 + 35 = 3x

270 = 3x

Divide both sides by 3

x= 270/3

= 90

x = 90

number of girls= x = 90

Number of boys = x + 35

= 90 + 35

= 125

Number of adults = x - 70

= 90 - 70

= 20

Total = 90 + 125 + 20

= 235

Answer:

There are 90 girls, 125 boys, and 20 adults.

Step-by-step explanation:

Let x be the number of girls. How many boys were there?

x + 35

How many adults were there?

x - 70

We know that 235 people are at RSM summer camp. Use this to make an equation.

x + (x + 35) + (x - 70) = 235

x + x + 35 + x - 70 = 235

3x - 35 = 235

3x - 35 + 35 = 235 + 35

3x = 270

3x ÷ 3 = 270 ÷ 3

x = 90

x, x + 35, x - 70

90, 125, 20

Answer: function

Step-by-step explanation: To determine whether the relation shown here

is a function, remember that a relation is a function if each x term

corresponds to exactly one y term.

In the data set show, each x term, -2, 9, 1, 3, and 10 appears only once.

This means that each x term corresponds to exactly one y term.

So yes, the relation is a function.

Answer:

$5400 USD

Step-by-step explanation:

Investment=3,000

Interest=8% = .08

Time=10 years

([3000 x .08 x 10] + 3,000

[240 x 10] + 3,000

2,400 + 3,000= 5,400

Answer:

Largest possible number of sweets in each tray[tex]=4[/tex]

Step-by-step explanation:

Given:

Number of orange-flavored sweets = 36

Number of grape-flavored sweets = 44

To find: largest possible number of sweets in each tray

Solution:

HCF(highest common factor) of two or more numbers refers to the greatest number which can divide the given numbers

To find largest possible number of sweets in each tray, find the HCF(highest common factor) of 36 and 44.

[tex]36=2^{2}\times 3^{2}\\44=2^{2}\times 11[/tex]

So,

[tex]HCF(36,44)=2^{2}=4[/tex]

So,

Largest possible number of sweets in each tray[tex]=4[/tex]

The largest possible number of sweets in each tray is 4.

In order to determine the largest possible sweets in each tray, the highest common factor of the number of sweets have to determined. The highest common factor is the highest factor that is common to two or more numbers.

Factors of 36 =  1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 44 = 1, 2, 4, 11, 22, 44.

Common factors = 1, 2, 4

Highest common factor - 4  

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90

Plug in 7 for x and solve.

[tex]{y}^{2} + 5y + 6[/tex]

[tex]{(7)}^{2} + 5(7) + 6[/tex]

[tex]49 + 35 + 6[/tex]

[tex]90[/tex]

Answer:

63 sandwiches

Step-by-step explanation:

Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter

They brought 7 loaves of bread

Each loaves have 18 slices

They used 2 slices each to make the sandwich

The first step is to calculate the total number of slices

Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows

= 7 ×18

= 126 slices

Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows

= 126/2

= 63

Hence 63 sandwiches were made for the shelter

Answer:

Step-by-step explanation:

y - 2 = 3(x - 1)

y - 2 = 3x - 3

y = 3x - 1

Step-by-step explanation:

Write 0.1 as

0.1

1

Multiply both numerator and denominator by 10 for every number after the decimal point

0.1 × 10

1 × 10

=

1

10

Reducing the fraction gives

1

10

In fraction form the number 0.1 can be written as 1/10.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.

The given number is: 0.1

Since the given number is a decimal  number,

And it has only in digit after decimal.

Therefore,

Divide and multiply by 10 with this number,

[tex]0.1 \times \dfrac{10}{10} = \dfrac{1}{10}[/tex]

Hence,

The fraction from of  the number 0.1 is 1/10

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Answer:

The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Step-by-step explanation:

Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.

Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.

Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm

So the perimeter of the triangle is P = a + b + c

substituting the values of a, b and c, we have

P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm

opening the brackets and collecting like terms, we have

P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm

P = (9.1p + 2.4q - 4.1) centimetres

So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Answer:

Negative

Step-by-step explanation:

If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3

whats the answer 5(x-y+2)

Answer :

5x - 5y + 10

Step-by-step explanation:

5(x - y + 2)

5(x) + 5( - y) + 5(2)

5x - 5y + 10

[tex]\boxed{\boxed{\bold{THANKS}}} [/tex]

Answer:

a

Step-by-step explanation:

Answer:

There are 76 oatmeal raisen cookies altogether.

Step-by-step explanation:

4 + 11 = 15

285/15 = 19

19 * 4 = 76

Answer:

Their place values

Step-by-step explanation:

On eight is in thousands while the other is in hundreds

Answer:

"8" on the left is ten times the value of the "8" on the right

Step-by-step explanation:

I am going to assume that the comma " , " denotes divisions of "thousands" and not the European system where the comma represents a decimal point.

(refer to attached for definitions of place values)

we can see that for the number 8,809 :

1) the 8 on the left is in the thousands place and hence represents 8000.

2) the 8 on the right is in the hundreds place and hence represents 800.

in order to find the relative order of difference between the two digits, we simply we divide the value of the two digits:

8000 ÷ 800 = 10

Hence the "8" on the left is ten times the value of the "8" on the right

Answer

Median

Step-by-step explanation:

It should be noted that medians are resistant to outliers.

Outliers simply means the data records which are different from every other record. It escapes normality. The outlier affects mean, inter-quartile range, mode and the range.

It should be noted that the median isn't affected by outliers. The reason for this is that the median depends on the arrangement and the order of the data. For example, when one changes the lowest score in a given set of numbers, the order won't be affected.

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Answer:

Race and Ethnicity are considered to be social constructs that enable humans to be grouped or categorized. They are sometimes used interchangeably but most argue that they are different and give them different definitions.

Race is generally used to refer to people that have the same physical characteristics such as skin color or the same texture of hair for instance Black and White/Caucasian.

Ethnicity on the other hand relates to people sharing a common culture, language, nation, and/ or tribal heritage for instance, the English, the Irish and the Igbo.

Answer:

The terms race and ethnicity are often used interchangeably throughout society. However, there is a distinct difference between the two. Race refers to a classification system based on inherited physical or biological traits, such as eye, hair, or skin color. In contrast, ethnicity refers to a group of people that can be linked together by common characteristics such as shared experiences, history, culture, or beliefs. Examples of ethnic groups include Native Americans, French Canadians, and Kongos.

Step-by-step explanation:

(edg2020)

Answer:

1. 54

2.?

Step-by-step explanation:

:) Have a nice day

Answer:

y=2/5x + 7

Step-by-step explanation:

First, you have to rewrite 2x-5y=15 to slop intercept form.

To do that you have to first subtract 2x from both side to cancel it out.

2x- 2x-5y= 15 -2x.    

-5y= -2x+15

Next, you divide 5 on both side to leave the y by itself.

y= -2x/-5 + 15/-5

Simplify

y= 2/5x + (-3)                     2/5 is our slope

Now that we found the slope, we need to the y-intercept of line b

y=2/5x + b

To find the y-intercept, we substitue x and y with the coordinates (-10,3)

3= 2/5(-10) +b

Now we just solve for b

3= -4 +b

3-(-4) = b

7=b

Now we have identified that 7 is the y intercept

The full equation is y= 2/5x +7

I hope this helped :)

See the attached sketch. Let [tex]\beta[/tex] denote angle ABC and [tex]\beta'[/tex] denote angle CBD. Then [tex]\beta'=2\beta[/tex].

From the sketch, we see that

[tex]\tan\beta=\dfrac15[/tex]

[tex]\tan(\beta+\beta')=\tan(3\beta)=\dfrac{AD}5[/tex]

Write [tex]\tan(3\beta)[/tex] in terms of [tex]\tan\beta[/tex]. Recall the angle sum identity for tangent:

[tex]\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}[/tex]

This gives us

[tex]\tan(3\beta)=\dfrac{\tan\beta+\frac{2\tan\beta}{1-\tan^2\beta}}{1-\tan\beta\cdot\frac{2\tan\beta}{1-\tan^2\beta}}=\dfrac{\tan\beta(\tan^2\beta-3)}{3\tan^2\beta-1}[/tex]

and plugging in [tex]\tan\beta=\frac15[/tex] leaves us with

[tex]\tan(3\beta)=\dfrac{37}{55}[/tex]

and so AD = 5 * 37/55 = 37/11.

Answer:

Step-by-step explanation: