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[tex](14)\\\\x^2 + 14x +45\\\\=x^2 +5x +9x +45\\\\=x(x+5) +9(x+5)\\\\=(x+9)(x+5)\\\\(15)\\\\x^2 +18x +45\\\\=x^2 +15x +3x +45\\\\= x(x+15) +3(x+15)\\\\=(x+3)(x+15)\\\\\\(16)\\\\x^2+46x+45\\\\=x^2 +45x +x +45\\\\=x(x+45) +(x+45)\\\\=(x+45)(x+1)[/tex]

Answer:

yes

Step-by-step explanation:

we know that every integer is a rational number and Zero can be represented as the ratio of two integers.

Answer:

-320; 303

Step-by-step explanation:

Well... you could really just use a calculator to do this, I mean?

124 - 444 = -320

345 - (-7)*(-6) = 345 - 42 = 303

Answer:

1) 320

2) 303

Step-by-step explanation:

1) simple Subtraction

2) first multiply -7 & -6 = 42

then 345-42 = 303

Answer:

Parallel: a and c

Perpendicular: a and b, c and b

Step-by-step explanation:

Basically you would want to isolate for y.

Line a:

4y - 12x = 20

4y = 12x  + 20

y = 12x/4 + 20/4

y = 3x + 5

Line b:

3y = -x+2

y = -x/3 + 2/3

Line c:

y=3x - 1

Now look at each line and compare their slopes.

-Lines a and c have same slope., thus they are parallel.

-lines a and b are perpendicular because the slopes are negative reciprocals each other

-lines b and c are also perpendicular

Answer:

Exactly One Solution

Step-by-step explanation:

4x + 2 = x + 8

3x = 6                Simplify.

x = 2                  Divide by 2.

Answer:

One solution, x = 2

Step-by-step explanation:

4x + 2 = x + 8 (Given)

4x = x + 6

(The 2 is subtracted from the right side, therefore the left side is also subtracted. 8 becomes 6.)

3x = 6

(The x is subtracted from the right side to the left side. Thus turning the 4x into 3x)

x = 2

(The 3 is divided out to get x alone. So, the 6 has to be divided by 3 as well, turning it into 2)

Answer:

x= 48

Step-by-step explanation:

x+90+42=180

x= 48

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Answer:

70

Step-by-step explanation:

Given -

the least common denominator of 10 and 14 is - *70*

Prime factor of 14 are 2 and 7

14 = 2 * 7

Prime factor of 10 are 2 * 5

10 = 2 * 5

Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10

LCM (10,14) = 2 * 5 * 7

LCM (10,14) = 70

Answer:

Tan 70 = opp/adj

Tan 70 = x/6

multiply by 6 on both sides

16.5 = x

Answer:

I think you forgot to attach the table

Answer is in the attached file...

Answer:

92

Step-by-step explanation:

- ( 2 - 6 )

= - ( - 4 )

= 4

- ( 2 - 6 ) ( 23 )

= 4 x 23

= 92

The evaluation of  - (2- 6) ( 23) is 92

In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.

From the given information:

= - ( 2 - 6) (23)

= - ( -4) (23)

= 4 × 23

= 92

Learn more about how to evaluate in mathematics here:

https://brainly.com/question/10426112

Answer:

22

Step-by-step explanation:

-10/-2 is 5

5+17 is 22

Answer:

10.23% to the nearest hundredth.

Step-by-step explanation:

This is a Binomial Probability Distribution.

If exactly 25 are left handed then exactly 5 are right handed.

So (probability that exactly 25 are left handed)

= 30C5*(0.1)^5(0.9)^25

= 0.1023047706

= 10.23%.

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).

The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.

The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.

We want to find the probability that exactly 25 students out of 30 are left-handed.

This can be calculated using the binomial probability formula:

[tex]P(X = k) = ^nC_ kp^k (1 - p)^{n-k}[/tex]

where:

n = 30 (the number of trials)

k = 25 (the number of successes we want)

p = 0.9 (the probability of success in each trial)

Plugging in the values, we get:

[tex]P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5[/tex]

Using a calculator or statistical software, we can find that:

P(X = 25) ≈ 0.2031

Therefore,

The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.

Learn more about probability here:

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Answer:

Step-by-step explanation:

5a.) It starts with two at time one and increases by one each time

5b.) x+1

6.) Formula: (2/3)(x-1)+1, the fifth term would be (2/3)*(5-1)+1= 11/3

7a.) I will leave you to make the table. n+2 is wrong because it's increasing by 2 blocks each time

7b.) 2n+1

8a.) x²

8b.) just draw a 6x6

8c.) 12²=144

Answer:

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Prime Factorization of 80: 80 = 24 × 5.

Step-by-step explanation:

Answer:

This is true

Step-by-step explanation:

This is true because of the communitive property that makes the numbers you multiply the same product in different orders

Answer:

slope = 1

Step-by-step explanation:

1) expand those brackets on the left side my multiplying

x - 5 = 3y + 12 - 2y + 1

2) simplify by collecting like terms

x - 5 = y + 13

3) bring -5 to the right side by adding 5

x = y + 18

4) let's rearrange this equation in the form y = mx + c where m is the gradient (slope) and c is the y intercept. by subtracting 18 on both sides

y = (1)x - 18 (there is a 1 in front of the x, but we don't write it like that. m is 1)

y = x - 18

the slope is the gradient, which is 1

Answer:

Step-by-step explanation:

50 of 100

= 50%

120 of 1

= 1.2%

Answer:

This is because he rides 37.5 k/m every week. Multiply that by four and you get 150

Answer:

Sanjay will need to ride his bike to work for 4 weeks in order to ride 150 kilometers.

Answer:

The equivalent expressions are;

1. 8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expressions are;

1. 8 (y - 7)

2. - 2 (x + 7)

3. 3/5x + 2/5 + 3/5x

Now,

Solve all the expression as;

1. 8 (y - 7) = 8 × y - 8 × 7

              = 8y - 56

Thus,  8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2 × x - 2 × 7

                  = - 2x - 14

Thus, - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = 3/5x + 3/5x + 2/5

                              = (3x + 3x)/ 5 + 2/5

                              = 6x / 5 + 2/ 5

                              = (6x + 2) / 5

Thus, 3/5x + 2/5 + 3/5x = (6x + 2) / 5

Therefore, The equivalent expressions are;

1. 8 (y - 7) = 8y - 56

2. - 2 (x + 7) = - 2x - 14

3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5

Learn more about the expression visit:

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Answer:

1

Step-by-step explanation:

Using the cofunction identity

sec(90 - x) = cosecx , then

sec(90 - 58)° = cosec32° , so

[tex]\frac{cosec32}{sec58}[/tex]

= [tex]\frac{cosec32}{cosec32}[/tex]

= 1

The value of x is 96/y where y is not equal to zero.

Given the expression that relates x and y as xy = 96

We are told that x and y are positive numbers. To get the value of x, we will divide both sides by y as shown:

[tex]xy = 96\\\frac{xy}{y} =\frac{96}{y} \\x = \frac{96}{y} \\[/tex]

From the result, we can conclude that the value of x is 96/y where y is not equal to zero.

Learn more on functions here: https://brainly.com/question/17431959

Using the binomial distribution, it is found that there is a [tex]\mathbf{\frac{1}{16}}[/tex] probability you will win the big prize.

For each ball, there are only two possible outcomes, either it is hit or it is not. The probability of hitting a ball is independent of any other ball, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

You win the big prize if you hit 4 balls, hence, the probability is P(X = 4).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{4,4}.\left(\frac{1}{2}\right)^{4}.\left(\frac{1}{2}\right)^{0} = \frac{1}{16}[/tex]

[tex]\mathbf{\frac{1}{16}}[/tex] probability you will win the big prize.

A similar problem is given at https://brainly.com/question/24863377

Answer:

1/16

Step-by-step explanation:

yurr

Answer:

The slope is undefined.

Step-by-step explanation:

You can use slope formula (y - y)/(x - x) and you will get a zero on the bottom (never allowed) OR notice that the x's are the same so sketch a graph, the line is vertical...that means that slope is undefined.

Answer: she would have saved 120$$

Step-by-step explanation:

Answer:

$7.50+m > $19

The inequality to be used for determining the maximum number of milkshakes she can buy will be in the form of:

[tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]

  The inequality in the position or the relationship between two variables in order to make the total either greater than, less than, or greater than equal to, or less than equal to the total amount.  

The inequality can be between numbers or algebraic expressions.  

In the given case,

To determine the inequality for the number of milkshakes the inequality will be formed as follows:  

The total cost of ice cream cones will be added with the total cost of milkshakes (where m is the number of milkshakes) and the sign used will be greater than or equal to the given amount to be spent.  

Therefore, the inequality will be  [tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]

  To know more about inequality, refer to the link:

https://brainly.com/question/11897796    

Answer:

(2^102•5^102)

Step-by-step explanation:

(10)^102 = (2•5)^102 = 2^102 • 5^102

Answer:

16/3

Step-by-step explanation:

(3x + 14)x = 5

3x² + 14x = 5

3x² + 14x - 5 = 0

3x² + 15x - x - 5 = 0

3x(x + 5) - 1(x + 5) = 0

(3x - 1)(x + 5) = 0

x = 1/3 & -5

Here,

r = 1/3

s = -5

r - s

1/3 - (-5)

1/3 + 5

1 + 15/3

16/3

the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]

Answer:

Solution given:

(3x+14)x=5

opening bracket

3x²+14x=5

3x²+14x-5=0

Doing middle term factorisation

3x²+(15-1)x-5=0

3x²+15x-x-5=0

3x(x+5)-1(x+5)=0

(3x-1)(x+5)=0

either

x=-5

or

3x-1=0

3x=1

x=⅓

According to question value of x is r>s

so

⅓>-5

so

r=⅓

and

s=-5

Now

r-s=⅓-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]

Answer:

y=x+1

Step-by-step explanation:

1) Find the slope

m=-3-4/-4-3

m=-7/-7

m=1

2) Use y=mx+c

by using the point (3,4)

4=1(3)+c

4=3+c

c=1

3) The answer

y=x+1

Step-by-step explanation:

m = y2-y1/x2-x1

m = 16 - 2/ 14 - 11

m = 14/3

m = 14 / 3

Hope it helps.