MATHEMATICS HIGH SCHOOL

Match the terms to their definition. 1. consistent equations the determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system 2. equivalent equations the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system 3. inconsistent equations equations having a common solution in a system 4. linear inequality equations having no common solutions in a system 5. substitute replace a quantity with its equal 6. system determinant equations having all common solutions 7. x-determinant an open sentence of the form Ax By C < 0 or Ax By C > 0 8. y-determinant the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system

Answers

Answer 1

Answer:

Answer:

1-----3

2-----6

3------4

4------7

5-------5

6-------8

7--------1

8--------2

step-by-step explanation:

consistent equation: equations having a common solution in a system.

Equivalent equation: equations having all common solutions.

Inconsistent equations: equations having no common solutions in a system

Linear inequality: an open sentence of the form Ax+By+C < 0 or Ax+By+C > 0.

substitute: replace a quantity with its equal.

system determinant: the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system.

x-determinant: the determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system.

y-determinant: the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system.

Answer 2

Answer:

Final answer:

The terms are matched with their respective definitions, providing clarity about equations, linear inequality, substitution, and determinants in the context of a system of linear equations.

Explanation:

Let's go ahead and match these terms to their correct definitions:

Consistent equations are equations having a common solution in a system.
Equivalent equations refer to equations having all common solutions.
Inconsistent equations are equations having no common solutions in a system.
Linear inequality is an open sentence of the form Ax + By < C or Ax + By > C.
To Substitute means to replace a quantity with its equal.
System determinant for this instance, since specific definition is not provided, could be considered as a determinant that serves as a pivotal element in the solution of system of linear equations.
X-determinant is the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system.
Y-determinant is the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system.

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Which of these is the algebraic expression for the verbal expression "ten times the difference of a number and twelve?"10(x − 12)
x − 12 ⋅ 10
12(x − 10)
10 ⋅ x − 12

Answers

Hello,

Answer A

10*(x-12)
first x-12 (parenthesis) : difference of some number and 12
second 10* the result before==> the product of 10 by the diffrence of x and 12.

Answer:

Step-by-step explanation:

10(x − 12)

x − 12 ⋅ 10

12(x − 10)

10 ⋅ x − 12

Find the balance in the account. $2,500 principal earning 4%, compounded quarterly, after 4 yearsA. $40,000.00

B. $41,600.00

C. $2,924.65

D. $2,931.45

Answers

Answer:

The balance in the account is $2931.45 .

Option (D) is correct.

Step-by-step explanation:

Formula

$Amount = P(1 +(r)/(4))^(4t)$

Where P is the principle , r s the rate of interest in the decimal form and t is the time in years .

As given

The account. $2,500 principal earning 4%, compounded quarterly, after 4 years.

P = $2500

4% is written in the decimal form

$= (4)/(100)$

= 0.04

r = 0.04

t = 4 yeas

Put all the values in the formula

$Amount = 2500(1 +(0.04)/(4))^(4* 4)$

$Amount = 2500(1 +(0.04)/(4))^(16)$

$Amount = 2500(1 +0.01)^(16)$

$Amount = 2500(1.01)^(16)$

$Amount = 2500* 1.17258$

Amount = $2931.45

Therefore the balance in the account is $2931.45 .

Option (D) is correct.

Hello there,

A(4) = 2500(1.01)^16
----
A(4) = 2500*1.1726
----
A(4) = $2931.45

Hope this helps!

I’ve been trying to work this out for a while…
Please give the answer with explanation

Answers

a) Yes, The average speed of the train could have been greater than 145 km/h,

b) the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.

a) To determine if the average speed of the train could have been greater than 145 km/h, we need to calculate the maximum possible average speed given the track length rounded to the nearest 10 km.

The track length is 290 km, rounded to the nearest 10 km. This means the actual track length could be anywhere between 285 km (290 km - 5 km) and 295 km (290 km + 5 km).

To find the maximum average speed, we'll assume the train took the minimum possible time (120 minutes) to cover the maximum possible track length (295 km):

Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)

Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)

Since 2.4583 km/minute is greater than 145 km/h (which is approximately 2.4167 km/minute), the answer is:

Yes, the average speed of the train could have been greater than 145 km/h.

b) Now that we know the track was measured to the nearest 5 km, we'll calculate the new maximum average speed in km per minute based on the maximum possible track length (295 km) and the minimum possible time (120 minutes):

Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)

Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)

So, the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.

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If C is between A and B, then AC = CB.

Answers

Yes, assuming Point C bisects line AB

This only works if C is the midpoint of the line AB

There are ten bird baths in a park. On the first day of spring, the bird baths are filled. Several weeks later, the overall change in the water level is found. The results are shown in the table. What is the range of the data?2.2, 0.3, -1.5, 2.6, 1.9, 0.4, 0.6, -1.6, 2.5, -0.6

Answers

The range of the data is 4.2

what is range of the data?

The range in statistics for a given data set is the difference between the highest and lowest values.

Given:

2.2, 0.3, -1.5, 2.6, 1.9, 0.4, 0.6, -1.6, 2.5, -0.6

Arranging the data in some order

-1.6 , -1.5, -0.6, 0.3, 0.4, 0.6, 1.9, 2.2, 2.5, 2.6

So, range

=highest data - lowest data

=2.6 - (-1.6)

=2.6+1.6

=4.2

Hence, the range is 4.2.

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Answer:

The range is -4.2

Step-by-step explanation:

Least to Greatest:

-1.6

-1.5

-0.6

0.3

0.4

0.6

1.9

2.2

2.5

2.6

Subtract Least Number from Greatest Number

-1.6 - 2.6

=-4.2

the coordinates of a point on a coordinate grid are (−1, 5). the point is reflected across the x-axis to obtain a new point. the coordinates of the reflected point are (1, −5) (−1, 5) (1, 5) (−1, −5)

Answers

Hello,

Answer D (-1,-5)
==============

Answer:

D 1,5 is the answer

Step-by-step explanation:

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