Here are some functions. For each function, describe, in words, the outputs for very

If 4a - 13 = 6b + 35 = 8c -17 = d, find the smallest possible value of a + b + c + d.

Afina-wow [57]

Answer:

The smallest possible value of a+b+c+d is: 4

Step-by-step explanation:

since we are given that:

4a - 13 = 6b + 35 = 8c -17 = d

on taking the first two equality i.e. 4a-13=6b+35

we get $b=\dfrac{2}{3}a-8$

on using the first and third equality we have:

4a-13=8c-17

$c=\dfrac{1}{2}a+\dfrac{1}{2}$

also from the first and last equality we have:

d=4a-13

Hence,

$a+b+c+d=a+\dfrac{2}{3}a-8+\dfrac{1}{2}a+\dfrac{1}{2}+4a-13\\\\a+b+c+d=\dfrac{37a}{6}-\dfrac{41}{2}$

$a+b+c+d=\dfrac{37a-123}{6}$

the smallest possible value such that the expression a+b+c+d is positive will be claculated as:

a+b+c+d>0

that means $\dfrac{37a-123}{6}>0$

$a>3.324$

But as a is an integer, hence the smallest such value is 4.

4 0

3 years ago

Select all the statements that are true for the following systems of equations

Aleks [24]

Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

System A

2x - 3y = 4 .....equation 1

4x - y = 18 .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8 ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

$y = \frac {10}{5}$

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

$x = \frac {10}{2}$

x = 5

Solutions (x, y) = (5, 2)

System B

3x - 4y = 5 ..... equation 1

y = 5x + 3 ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

$x = \frac {-17}{17}$

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

Solutions (x, y) = (-1, -2)

System C

2x - 3y = 4 ..... equation 1

12x - 3y = 54 ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

$x = \frac {50}{10}$

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

$y = \frac {6}{3}$

y = 2

Solutions (x, y) = (5, 2)

5 0

2 years ago

Plsss help It due tmr plsss

geniusboy [140]

Answer: 50

Step-by-step explanation:

exterior angles are supplement of interior angle therefore the 110 thing must be 70, also youre given 60 so 70+60=130

50 is missing from 180

6 0

3 years ago

The slope of a line is 5/9 and the slope of another line is -975. The two lines are

Bond [772]

Answer:

the third option - they are perpendicular to each other.

Step-by-step explanation:

for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.

and that is exactly what happened here.

3 0

3 years ago

Two lines, C and D, are represented by the following equations:

guapka [62]

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

The meaning of "solution to the system of equations" is that both lines intersect at the solution point. That is, they both pass through that point.

8 0

3 years ago

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