What I Have Learned?
Part 1
Direction. Determine whether each system of linear equations is consistent and
dependent, consistent and independent, or inconsistent. Answer on the
separate sheet
(2x+y = 3
12x + y = 6
3.
(6x-27=
2y 8
ly=3x – 4
1.
4.
3x + y = 10
4x + y - 7
(3x + 5y = 15
14x - 7y = 10
2.
1 ​

Answer:

Step-by-step explanation.

This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.

Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3 } \times \sqrt{2 \times {5}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2 \times 5 \sqrt{5 \times 3 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 10 \sqrt{30} [/tex]

Answer:

Seconds and Minutes

Step-by-step explanation:

Randomly pick 55 students to run a lap around the track and measure their time.

This is the only option that avoids any type of bias.

(a) Larry took ( 1/3 ) of the sweets in the box.

(b) There were a total of 72 sweets in the box.

(c) The fraction of sweets taken by Keith and Joe are ( 288/9) and ( 144/9 ) respectively.

Keith, Larry, and Joe shared a box of sweets.

Let the total number of sweets be y.

Now, Joe took ( 2/9) of the sweets.

Therefore, the number of sweets Joe took = ( 2/9 )y

Now, Keith took twice as many sweets as Joe.

Therefore, the number of sweets Keith took = 2 × ( 2/9 )y = (4/9) y

Then, the number of sweets Larry too k will be:

= y - ( 2/9 )y - (4/9) y

(a) Then the fraction of sweets Larry took is:

= y - ( 2/9 )y - (4/9) y

= y - [ ( 2 + 4) / 9 ] y

= y - ( 6 / 9 )y

= y - ( 2/3)y

= [ ( 3 - 2 )/3 ]y

= ( 1/3 )y

(b) If Larry took 24 sweets less than the total number of sweets taken by Joe and Keith.

Then,

the number of sweets Keith took + the number of sweets Joe took - 24 = ( 1/3 )y

( 4/9 )y + ( 2/9)y - 24 = ( 1/3 )y

( 6/9 )y - 24 = ( 1/3 )y

( 6/9)y - ( 1/3 )y = 24

[ ( 6 - 3) / 9 ]y = 24

( 3/9 )y = 24

( 1/3)y = 24

y = 24 × 3

y = 72

There were 72 sweets in the box.

(c) The number of sweets Keith took

= (4/9) y

= ( 4/9 ) × 72

= ( 288/9 )

The number of sweets taken by Joe is:

= ( 2/9 )y

= ( 2/9) × 72

= ( 144/9 )

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The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.

From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:

585.43 + x - 302.05 ≥ 300

Collect like terms

x ≥ 300 - 585.43 + 302.05

x ≥ $16.62

She's needs to deposit at least $16.62.

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The combined number of widgets and gadgets that the packaging department can handle is 2300 per day that is x + y =2300

A manufacturer makes widgets and gadgets. At least 500 widgets(x) and 700 gadgets (y) are

[tex]x\geq 500\\\\y\geq 700[/tex]

The machinery can produce no more than 1200 widgets(x) and 1400 gadgets(y) per day

[tex]x\leq 1200\\\\y\leq 1400[/tex]

The combined number of widgets and gadgets that the packaging department can handle is 2300 per day

x+ y =2300

then the possible values of x and y are

( 1000, 1300)

(1100, 1200)

( 1200,1100) etc.

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Answer:

11: Area as sum: 7d + 28

Area as product 7(d+4)

12: Area as sum: 2y + 3y   (could also be y^2 + 3y)

Area as product: y(y+3)

Step-by-step explanation:

For area as sum it's just distributing to each box, and then adding.

For area as product you just undistribute it and put it into parenthesis.

Answer:

27%

Step-by-step explanation:

3000 + 3500 + 4000 + 4200 = 14700

4000 / 14700 ≈ 0.27

0.27 = 27%

The statistical measures for the 10-day vacation are given as follows:

a) Mean: $2470.

b) Standard deviation: $189.74.

c) Variance: $²36,001.

To find the mean for n days, we take the mean amount for the distribution in a single day and multiply by n.

Hence, considering that the mean for a single day is of $247:

247 x 10 = $2470.

To find the standard deviation for n days, we take the standard deviation for a single day and multiply by the square root n.

Hence, considering that the standard deviation for a single day is of $60, we have that:

60 x sqrt(10) = $189.74.

For any distribution, the variance is the square of the standard deviation, hence:

($189.74)² = $²36,001.

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Step-by-step explanation:

(B) 12 Inches is the answer because perimeter (P) =4l =4×3=12

The points does he need to score in the last game to have an average of 25 PPG is 33 points

Given that

To find

So, according to the question

We have,

        ∵ [tex]average = \frac{sum\;of\;terms}{number\;of\;terms}[/tex]

        ∴ Total points gained by Larry in 4 games

                         = (average points in 4 games) × 4

                         =  23 × 4

                         =  92 points.

Let's assume Larry scored x points in the 5th match to have an average of 25 PPG.

So, we can say that

        Larry's average in 5 games = [tex]\frac{total\;points\; in\; 5\;games}{5}[/tex]

                                                 25 = [tex]\frac{92+x}{5}[/tex]

                                           25 × 5 = 92 + x

                                                125 = 92 + x

                                                    x = 125 - 92

                                                    x = 33.

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Multiply 5 by 25 to find the total points Larry needs to score in 5 games, 5 × 25 = 125. Then find the total points Larry scored in the frist 4 games, 4 × 23 = 92. Subtract to find the number of points Larry needs to score

took the quiz

The total earning of Whitney in may including her salary and commission is $70,400.

A sales commission is money given to an employee for completing a task, typically selling a specific amount of products or services.

Now, as per the given question;

The monthly salary of Whitney is $60000.

The sales he did in the month of the may is $13000.

He got 8% commission on his total sales.

8% of $13000 = 10,400.

Thus, the total earning of the may will be-

Total earning = Salary + commission

Total earning = $60000 + 10,400

Total earning = $70,400

Therefore, the total earning done by Whitney in the May is $70,400.

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Answer:

q = [tex]\frac{7}{5}[/tex]p + 7

Step-by-step explanation:

7p -5q = -35  Subtract 7p from both sides of the equation

-5q = -7p - 35  /Dive all the way through by -5

q = [tex]\frac{7}{5}[/tex]p + 7

The prime factors in ascending order are 2,7.

Given that, 56 is a number that is needed to be expressed as the product of prime numbers that is prime factors.

prime number is defined as , if a number is divided by only one and itself then it is named as a prime number.

prime factor is defined as , if a number can be represented in terms of multiplication  of the prime numbers is known as the prime factor.

prime numbers are 2,3,5,7,11,13,17,1923,29,31,37..etc.

expressing 56 in terms of prime factors.

As 56 is an even number, you can just express this in smallest prime number that is 2 .

firstly you can express 56 in product of 23 and 2.

you can not divide  again 23 as it was prime number.

so , you can express 56 as 23*2 or you may access this as 2*2*2*7

Prime factors in ascending order are , 2,7 or 2,23.

As we choose least prime factors we prefer 56 = 2*2*2*7.

Therefore ascending order of prime factors will be 2,7.

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Answer:(1/2, 7) as decimal = (0.5, 7)

Step-by-step explanation:

===================================================

Explanation:

The x coordinates are 3 and -2

The x coordinate of the midpoint is 0.5

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

The steps are the same idea for the y coordinates

The y coordinate of the midpoint is 7

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

Overall, the midpoint is located at (0.5, 7)

You can confirm this by letting

A = (3,8)

B = (0.5, 7)

C = (-2,6)

Then use the distance formula to see that AB = BC

The solution set for the inequality expression is (-∞, -6)

Inequality are expressions that does not involve an equality sign.

Given the following parameters

-3x + 3 > -21

Subtract 3 from both sides

-3x + 3 - 3 > 21 - 3

-3x > 18

Divide both sides by -3

-3x/-3 < 18/-3

x < -6

Hence the solution set for the inequality expression is (-∞, -6)

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Using the monthly payment formula, it is found that the best plan is given by:

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For the simple interest payment method, the parameters are given as follows:

r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]

A = 334.64.

For the credit card payment method, the parameters are given as follows:

r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.

Hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]

A = 238.37.

The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.

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The unit rate of the watermelons would tell us the cost of 1 of the watermelon. The last option is correct.

The question tells us that the melons are sold for 5 for $20.

Hence the price of 1 would be at: 20/5

= 4 dollars per watermelon.

The weight of one of the melons is 8 pounds and the unit rate for 1 is 4 dollars. The unit rate is the price per one of the fruits or the cost of the fruit.

Hence we can say that The unit rate of the watermelons would tell us the cost of 1 of the watermelon.

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Answer:

It depends on the steepness of the climb

Step-by-step explanation:

The last digit of the product of numbers from 0 to 99 is 0.

Multiplication is a method of finding the product of two or more numbers.

We have,

1, 2, 3, .............till 99.

We know that any number multiplied by 10 will give us 0 as the last digit.

And there are 10, 20, 30, 40, 50, 60, 70, 80, and 90.

We also know that 5, 15, 25, 35, 45, 65, 75, 85, 95 if multiplied with an even number the last digit is zero.

So if all the numbers from 1 to 99 are multiplied together, the last digit of the product will be a zero.

Thus the last digit of the product of numbers from 0 to 99 is 0.

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Answer:

Plug in the numbers to the variables

Step-by-step explanation:

Im not giving ya'll the straight answer because I use it all the time in almost all of my math.

Because you have the value of the variables, all you need to do is plug those variables in and the solve like you usually would (PEMDAS)

Hope this helps and ya'll got this! ;)

We can reduce the rate of refusals in telephone surveys by doing face to face surveys.

A phone study can keep going extremely lengthy, which brings about getting legitimate reactions and knowledge of the respondent's perspective which helps

social event a lot of information. Time limits are a disadvantage of telephone interview studies. Frequently, when you contact individuals at home, they are engaged with different exercises, like having supper or sitting in front of the TV. A few potential interviewees may be hesitant to partake in a meeting because of how much time they dread it will take. Examination can be assembled rapidly in light of the fact that telephone interviews are prompt and gifted questioners can finish a great deal of overviews in a day of work. A great many people have phones, so you have an adequate crowd for get-together a delegate test to finish the study.

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The solution set to the inequality is m>2.The correct ray to represent the solution is o---> placed at 2.

Inequality is a statement of order,greater than, less than, greater than or equal to or less than or equal to between two algebraic expression. Inorder to solve an inequality we change the sides of the unknown variable and the constants. We always have to keep in mind the change of sign, if we change sign then we have to change the relation between the two expressions too. Here we have been given an inequality which is

m-7>-2(m+0.5)

In this inequality m is the unknown variable and we have to solve for m,

m-7>-2(m+0.5)

⇒m-7>-2m-1

⇒2m+m>7-1

⇒3m>6

⇒m>2

The solution set to the given inequality is m>2, so the correct ray to represent the solution is o---> placed at 2 on the number line.

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Answer:

x = -3

Hope this helps

Step-by-step explanation:

( (2x*3) + (18*3) ) = 36

(6x + 54) = 36

6x + 54 = 36

6x + 54 - 54 = 36 - 54

6x = -18

6x / 6 = -18 / 6

x = -3

The equation representing the minimum and maximum scores |x-87| = 1.8

Given that the average score on a lab report is 87 points. All students score within 1.8 points of the average.

Let 'x' be the score of student. The maximum and minimum score of a student lies within 1.8 points of the average.

Then, maximum score of a student, x = 87+1.8

and minimum score of a student, x = 87-1.8

Combining these two equations, we get, x = 87 ±1.8

Or, more conveniently, |x-87| = 1.8 represents the minimum and maximum scores obtained by a student.

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The distance of the boat from its destination depends on

So with these factors, the distance of the boat from its distance can be calculated.

The distance of the boat from the destination currently is 63 miles

Speed of the boat is 10 miles / hr

Let c be the speed of the river current and

h be the number of hours to reach a particular destination

So, the formula to find the distance of the boat from destination is given by

D = 63 - h(10 - c)

We need to find the formula for boat's distance from its destination after 3 hours

Thus h = 3 hrs

Let us substitute h in above equation, Then

D = 63 - 3(10 - c)

D = 63 - 30 - 3c

D = 33 - 3c

which is the formula for the boat's distance from its destination after 3 hours.

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