Classify the following polynomials. Combine any
like terms first.
x^2+3x + 2x - 2x^2
X^3+ 4x - 4x - 4x^2
X^3+2x - X^3- 2x^2+ 3

Answer:

is that the full question?

Answer:

Solution:-

Given,

ab =perpendicular (p)= 6cm

ac =hypotenuse (h)= 12cm

cd =base (b)= ?

using , Pythagoras theorem we have ,

b²=√h²-p²

or,cd²=√ac²-ab²

= √12²-6²

= √144-36

=√108

=√10.8²

=10.8cm

the length of cd is 10.8 cm

hope it is helpful to you

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{3^3 \times 5^4}[/tex]

[tex]\mathsf{3^3}[/tex]

[tex]\mathsf{= 3\times3\times3}[/tex]

[tex]\mathsf{= 9\times3}[/tex]

[tex]\mathsf{= \bf 27}[/tex]

[tex]\mathsf{5^4}[/tex]

[tex]\mathsf{= 5\times 5\times5\times 5}[/tex]

[tex]\mathsf{= 25\times25}[/tex]

[tex]\mathsf{= \bf 625}[/tex]

[tex]\mathsf{27 \times625}[/tex]

[tex]\mathsf{= \bf 16,875}[/tex]

[tex]\mathsf{2\times5^3\times11}[/tex]

[tex]\mathsf{5^3}[/tex]

[tex]\mathsf{= 5\times 5\times5}[/tex]

[tex]\mathsf{= 25\times 5}[/tex]

[tex]\mathsf{\bf = 125}[/tex]

[tex]\mathsf{2\times125\times11}[/tex]

[tex]\mathsf{= 250\times11}[/tex]

[tex]\mathsf{\bf = 2,750}[/tex]

[tex]\large\textsf{Find the Greatest Common Factor (GCF) of 16,875 \& 2,750}[/tex]

[tex]\large\textsf{16,875: 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 625, 675, 1,125,}\\\\\large\textsf{1,875, 3,375, 5,625, \& 16,875}[/tex]

[tex]\large\textsf{2,750: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 125, 250, 275, 550, 1,375, \& 2,750}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: the GCF is \bf 125 }}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 18 {x}^{2} - 69x - 55}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] = (9x + 5) - ( - 2 x+ 10)(9x + 5) - ( - 2x + 10)[/tex]

[tex] = (9x + 5) + 2x (9x + 5) - 10(9x + 5) - ( - 2x + 10)[/tex]

[tex] = 9x + 5 + 18 {x}^{2} + 10 x- 90x - 50 + 2x - 10[/tex]

Collect the like terms.

[tex] = 18 {x}^{2} + (9x + 10x- 90x + 2x) + (5 - 50 - 10)[/tex]

[tex] = 18 {x}^{2} + (21x - 90x) +(5 - 60)[/tex]

[tex] = 18 {x}^{2} - 69x - 55[/tex]

[tex]\sf\pink{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Answer:

0.534375

45328

36763

-6

-78

The values of x and y that satisfy the graphs are:

(-1, 0), and (-5, 0).

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

We can start by simplifying the quadratic equation:

y = (x + 3)² – 4

y = x² + 6x + 9 - 4

y = x² + 6x + 5

Now, we can use various methods to find values of x and y that satisfy this equation. Here are five possible values:

If we substitute x = -1, we get:

y = (-1)² + 6(-1) + 5

y = 0

So, one solution is (-1, 0).

If we substitute x = 0, we get:

y = 0² + 6(0) + 5

y = 5

So, another solution is (0, 5).

If we substitute x = -5, we get:

y = (-5)² + 6(-5) + 5

y = 0

So, another solution is (-5, 0).

To find rational solutions, we can factor in the quadratic expression:

y = x² + 6x + 5

y = (x + 1)(x + 5)

So, the solutions are x = -1 and x = -5. Substituting these values into the equation, we get:

For x = -1, y = (-1)² + 6(-1) + 5 = 0

For x = -5, y = (-5)² + 6(-5) + 5 = 0

So, the solutions are (-1, 0) and (-5, 0).

To learn more about the quadratic equation;

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Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer:

Part 1)

10,000 different numbers.

Part 2)

A) 1 in 10,000.

Step-by-step explanation:

Part 1)

Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:

[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]

Thus, 10,000 different numbers are possible.

Part 2)

Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.

This is equivalent to 0.0001 or a 0.01% chance of winning.

Answer:

x = ±i√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra II

Imaginary root i

Step-by-step explanation:

Step 1: Define

Identify

5x² - 2 = -12

Step 2: Solve for x

Answer:

In Picture

Step-by-step explanation:

Brainliest please~

Answer:

The  percentage of adults in the USA have stage 2 high blood pressure=98.679%

Step-by-step explanation:

We are given that

Mean, [tex]\mu=120[/tex]

Standard deviation, [tex]\sigma=18[/tex]

We have to find percentage of adults in the USA have stage 2 high blood pressure.

[tex]P(x\geq 160)=P(Z\geq \frac{160-120}{18})[/tex]

[tex]P(x\geq 160)=P(Z\geq \frac{40}{18})[/tex]

[tex]P(x\geq 160)=P(Z\geq 2.22)[/tex]

[tex]P(x\geq 160)=1-P(Z\leq 2.22[/tex]

[tex]P(x\geq 160)=0.98679[/tex]

[tex]P(x\geq 160)=98.679[/tex]%

Hence,  the  percentage of adults in the USA have stage 2 high blood pressure=98.679%

Answer:

3x+4

Step-by-step explanation:

When you factor 9x^2+24x+16, it factors to (3x+4)^2

Factoring 9x^2 - 16 factors to (3x+4)(3x-4)

Therefore the common factor is 3x+4

I hope this helps!

Answer:

(-2,3,10,8)

Step-by-step explanation:

eg

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

Answer:

y=2x+7

Step-by-step explanation:

y=2x-8

2 is the gradient.

-4 is x

-1 is y

-1=2(-4)+c

-1=-8+c

-1+8=c

c=7

therefore,

y=2x+7

Answer:

(a) 74553

(b) 172120

(c) 234802

Step-by-step explanation:

Given

[tex]y = \frac{340110}{1 + 377e^{-0.259t}}[/tex]

Solving (a): 1998

Year 1998 means that:

[tex]t =1998 - 1980[/tex]

[tex]t =18[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*18}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-4.662}}[/tex]

[tex]y = \frac{340110}{1 + 3.562}[/tex]

[tex]y = \frac{340110}{4.562}[/tex]

[tex]y = 74553[/tex] --- approximated

Solving (b): 2003

Year 2003 means that:

[tex]t = 2003 - 1980[/tex]

[tex]t =23[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*23}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-5.957}}[/tex]

[tex]y = \frac{340110}{1 + 0.976}[/tex]

[tex]y = \frac{340110}{1.976}[/tex]

[tex]y = 172120[/tex] --- approximated

Solving (c): 2006

Year 2006 means that:

[tex]t = 2006 - 1980[/tex]

[tex]t =26[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*26}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-6.734}}[/tex]

[tex]y = \frac{340110}{1 + 0.4485}[/tex]

[tex]y = \frac{340110}{1.4485}[/tex]

[tex]y = 234802[/tex] --- approximated

Answer:

See explanation

Step-by-step explanation:

Given

[tex]M \to[/tex] randomly selecting a male

[tex]B \to[/tex] randomly selecting someone with blue eyes

Solving (a): Interpret P(M|B)

The above implies conditional probability

The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected

Solving (b): is (a) the same as P(B|M)

No, they are not the same.

The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

Use formula:

[tex]\sf{V = \pi(\frac{d}{2})^2h}[/tex]

Solving for diameter:

[tex]\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}[/tex]

[tex]\sf\huge\underline\red{FINAL \: ANSWER}[/tex]

[tex]\large\boxed{\sf{\green{d=0.17}}}[/tex]

[tex]_____________________________________[/tex]

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ

Answer:

[tex]PQ=6\frac{1}{2} =\frac{13}{2}[/tex]

[tex]|Q-P|=\frac{13}{2}[/tex]

[tex]|Q+4|=\frac{13}{2}[/tex]

[tex]Q+4=+-\frac{13}{2}[/tex]

[tex]Q=-4[/tex] ± [tex]\frac{13}{2}[/tex]

[tex]Q=\frac{21}{2} \times2\frac{1}{2}[/tex]

[tex]Answer: C)~2\frac{1}{2}[/tex]

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

Each shirt = $12.25

so, x = shirts = 12.25 x

cost including shipping= 77.49

So,

12.25 x + 3.99=77.49

Answer: D)

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

hope it helps...

have a great day!!

Step-by-step explanation:

x=-6 y= 0

x0 y= -1

y=mx+b

b= -1

0= -6m -1

-6m= 1

m= -1/6

parallel lines have the same slope

slope = -1/6

Answer:

0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

The manager of a donut store believes that 35% of the customers are first-time customers.

This means that [tex]p = 0.35[/tex]

Sample of 150 customers

This means that [tex]n = 150[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.35[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.35*0.65}{150}} = 0.0389[/tex]

What is the probability that the sample proportion will be between 0.2 and 0.4?

p-value of Z when X = 0.4 subtracted by the p-value of Z when X = 0.2.

X = 0.4

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.4 - 0.35}{0.0389}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.35}{0.0389}[/tex]

[tex]Z = -3.85[/tex]

[tex]Z = -3.85[/tex] has a p-value of 0.0001

0.8997 - 0.0001 = 0.8996

0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4

Answer:

Step-by-step explanation:

You already have this set up to answer your question. This quadratic is in work form, aka vertex form, where the vertex is (3.5, 15). The first coordinate of the vertex is the time it takes to reach its max height, which is the second coordinate of the vertex. So it takes 3.5 seconds to reach a max height of 15 meters.

Answer:

8/22: this fraction will NOT terminate

189/270: this fraction WILL terminate

Step-by-step explanation:

I saw in the question that it says to solve the question by demonstrating the method discussed in class. I don't know what's the method you were taught, but I'll explain how I solved it.

When a fraction is in its simplest form, write out the prime factors of the denominator. If the denominator has 2s and/or 5s, the fraction WILL terminate in their decimal form.

8/22 in its simplest form is 4/11:

The only prime factors of the denominator, 11, are 1 and 11. There are no 2s and/or 5s present, so this fraction will NOT terminate.

189/270 in its simplest form is 7/10.

The prime factors of 10 are 2 and 5, meaning that this fraction WILL terminate.

Hope it helps (●'◡'●)

Answer:

5 sandwiches he made in bread

Answer:

Sine Theta is a negative number, Tan Theta is a greater number then zero.

Step-by-step explanation:

If Sine Theta is less then zero, she is a negative number. So 0 - y = -y.

So if Tan Theta is a greater number than zero, her number is not negative. So 0 + y = y

I hope this helped! I didn’t really understand the question though.

Hey there!

(4 + 21) - (1 - 71)

4 + 21 = 25

= 25 - (1 - 71)

1 - 71 = -70

= 25 - (-70)

= 25 + 70

= 95

Answer: 95

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Q1 = 32.5

Q3 = 50

D2 = 29

D8 = 52

67th percentile = 46.5

Step-by-step explanation:

Given the ordered data:

13, 13, 13, 20, 26, 29, 32, 33, 34, 34, 35, 35, 36, 37, 38, 41, 41, 41, 45, 46, 47, 47, 48, 52, 54, 55, 56, 62, 67, 82

The first quartile :

Q1 = 1/4(n+1)th term

n = sample size = 30

Q1 = 1/4(31) = 7.75 = (7th + 8th) / 2 = (32+33) / 2 = 32.5

Q3 = 3/4(n+1)th term

n = sample size = 30

Q3 = 3/4(31) = 23.25 = (23rd + 24th) / 2 = (48+52) / 2 = 50

D2 = 2nd decile

2 * 10% = 20%

20% * n

0.2 * 30 = 6th = 29

D8 = 8th decile

8 * 10% = 80%

80% * 30 = 24th = 52

67th percentile :

0.67 * 30 = 20.1 th

(20th + 21th) / 2

(46 + 47) / 2

= 46.5

Answer:

32 in^2

Step-by-step explanation:

8-2=6, 6-2=4. 4 inches wide

10-2=8. 8 Inches tall.

4*8=32

Answer:

F) Convenience Sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

A statistics student interviews the last fifteen attendees to arrive.

Conveniently available, so convenience, and the correct answer is given by option F.

Answer:

ok so we have to find 2% or 252 so

252*0.02=5.04

So they completed 5 cases this year

Hope This Helps!!!

Answer:

68

Step-by-step explanation:

I did it on my test

The missing value in the table is 68. The correct answer would be option (B).

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The table shows the relationship between the number of faculty members and the number of students at a local school.

Faculty     Students

1                     17

2                   34

3                   51

4                    ?

The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.

Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.

Thus, the missing value in the table is B. 68.

Learn about the linear relationship here :

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Answer:

44 seats in each row

Problem:

A rectangular auditorium seats 1144 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.

Step-by-step explanation:

Let n be the number of rows.

If the number of seats exceed the number of rows by 18, then the number ot seats can be represented by n+18.

So we have a n by n+18 rectangle whose number of seats in all is 1144.

So we need to solve n(n+18)=1144

Distribute: n^2+18n=1144

Subtract 1144 on both sides" n^2+18n-1144=0

What two numbers multiply to be -1144 but also add to be 18?

Hmmm.. let's break -1144 down a little into smaller factors.

-1144=2(-572)=4(-286)=8(-143)=-8(13)(11)=-26(44)

We found a pair of factors that will work? -26 and 44.

So the factorization of our quadratic equation is (n-26)(n+44)=0.

This implies either n-26=0 or n+44=0 .

n=26 by adding 26 on both sides for first equation.

n=-44 by subtracting 44 on both sides for second equation.

n=26 is the only one that works.

This means there are 26 rows and 26+18 seats in each row.

26 rows

44 seats in each row

That product does equal 1144 seats in all.

Answer:

Answer is in the picture. have a look