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3 years ago

Determine whether the system of equations has one solution, no solution, or infinitely many solutions. 4x=10+4y and 2x-2y=15

Mathematics

1 answer:

galben [10]3 years ago

6 0

Answer:

infinitely many solutions

Step-by-step explanation:

Given the simultaneous equation

4x=10+4y... 1

2x-2y=15 .... 2

_____________

4x-4y = 10 * 1

2x-2y = 15 * 2

__________--

4x-4y = 10

4x-4y = 30

Add both equation

8x - 8y = 10+30

8x-8y = 40

Divide though by 8

x-y = 5

x = 5 + y

Since the result gave 1 equation and 2 unknowns, then we will let x =k

k = 5 + y

y = k -5

k can be any integer

(x,y) = (k, k-5)

This show that the equation has infinitely many solutions

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Quadratic Equation

Natasha_Volkova [10]

Step-by-step explanation:

The sum of ages of two friends is 13 years.

The product of their ages is 42.

Let the age of 1st friend and 2nd friend is x, y respectively.

1 st condition= The sum of ages of two friends is 13 yrs.

i.e x+y = 13........ (I)

2nd condition= The product of their ages is 42.

i.e X*y = 42........(ii)

From equation (I)

X+y = 13

or, X = 13-y........ (iii)

Putting the equation (iii) in equation (ii).

X*y= 42

(13-y) * y = 42

13y - y^2 = 42

${y}^{2} - 13y + 42 = 0$

${y}^{2} - (7 + 6)y + 42= 0$

${y}^{2} - 7y - 6y + 42 = 0$

$y(y - 7) - 6(y - 7) = 0$

$(y - 6) (y - 7) = 0$

Either; y-6 = 0

y = 6

Or;

y-7=0

y = 7

Keeping the value of y as "7" in equation (ii)

x*y = 42

7x = 42

X = 42/7

Therefore, the value of X is 6.

Therefore, either 1st friend is 6 years and 2nd is 7 years.

Hope it helps...

7 0

3 years ago

A number cube was rolled as part of an experiment. The results are displayed in the table below. What is the best explanation of

Mars2501 [29]

Answer:

The outcome table was not given. But find below how to find the experimental probability

Step-by-step explanation:

Experimental Probability = number of times you rolled a three / the number of times you rolled the die itself.

4 0

3 years ago

Read 2 more answers

In a calculus class, Jack Hartig scored 4 on a quiz for which the class mean and standard deviation were 2.9 and 2.1, respecti

nataly862011 [7]

Answer: Norm Alpina did better with z-score 0.79

Step-by-step explanation:

Z score formula = (raw score - mean) / standard deviation

For Jack Hartig,

score = 4; mean = 2.9; standard deviation = 2.1

Hence, Z score = (4 - 2.9) /2.1

= 1.1/2.1

= 0.52

For Norm Alpina,

score = 8; mean = 6.5; standard deviation = 1.9

Hence, Z score = (8 - 6.5) /1.9

= 1.5/1.9

= 0.79

Relatively, Norm Alpina did better for having Z score 0.79

6 0

3 years ago

-3 (C - 10) + -4 = 2 C =

DENIUS [597]

-3(c-10) + -4= 2
-3c+ 30+ -4= 2
-3c + 26= 2
-3c= -24
C= 8

7 0

3 years ago

Read 2 more answers

The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis

andreyandreev [35.5K]

Answer:

a. Let the variable be $x$ for the fundraising activities and $M$ as the revenue for foundation.

b. $M =0.60x$

c. $43.2

d. $1416.67

Step-by-step explanation:

Given that:

The World Issues club donates 60% of the total of their fundraising activities.

Answer a.

Let us choose the variable $x$ to represent the money earned during fundraising activities and $M$ for the revenue generated for foundation.

Answer b.

Foundation will receive 60% of the total of the fundraising activities.

Equation to determine the money that will be received by foundation:

$M = 60\%\ of\ x\\OR\\M = 0.6x$

Answer c.

Given that x = $72, M = ?

Putting the value of x in the equation above:

$M = 0.6 \times 72\\\Rightarrow \$43.2$

Answer d.

Given that M = $850, x = ?

Putting the value of M in the equation above to find x:

$850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67$

So, the answers are:

a. Let the variable be $x$ for the fundraising activities and $M$ as the revenue for foundation.

b. $M =0.60x$

c. $43.2

d. $1416.67

5 0

3 years ago