All categories

3 years ago

Solve the system using substitution. Check your answer.

Mathematics

1 answer:

KonstantinChe [14]3 years ago

4 0

Step-by-step explanation:

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

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

sub 2 in 1

4x - (x -1) = 1

4x - x + 1 = 1

3x = 1 - 1

3x = 0

divide by 3 on both side

x = 0

sub the value of x in 2

3y = 0 - 1

3y = -1

divide by 3 on both sides

y = - 1/3

(x;y)

(0;-1/3)

You might be interested in

Paula leaned a 10 ft ladder against a building as shown below. if Paula wants the top of the ladder to reac

amm1812

The distance between the building and the base of the ladder is 5√3 feet.

Step-by-step explanation:

Consider a right angle triangle,

Hypotenuse = Paula leaned a 10 ft ladder against a building.
Height = the top of the ladder is exactly 5 feet up in the building.
Base = 'x' ft, distance between the building and the base of the ladder.

From the Pythagorean theorem,

Base, x = $\sqrt{hypotenuse^{2}-height^{2} }$

⇒ x = $\sqrt{10^{2} -5^{2} }$

⇒ x = $\sqrt{100-25}$

⇒ x = $\sqrt{75}$

⇒ x = 5√3

The distance between the building and the base of the ladder is 5√3 feet.

7 0

3 years ago

What is area of the larger triangle

slavikrds [6]

The area of the larger ttaingle is 12 cm squared

8 0

4 years ago

Read 2 more answers

: Find the slope between the two points given. Then, use the slope and point ONE to write the equation of the line in Point-Slop

Ierofanga [76]

Answer:

slope: $\bold{m=3}$

equation: $\bold{y-2=3(x-1)}$

Step-by-step explanation:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\(1,\,2)\ \implies\ x_1=1\,,\ y_1=2\\(0,\,-1)\ \implies\ x_2=0\,,\ y_2=-1\\\\m=\dfrac{-1-2}{0-1}=\dfrac{-3}{-1}=3$

$y-y_1=m(x-x_1)$ - point-slope form of Equation of the Line

$x_1=1\,,\ y_1=2\,,\ m=3\\\\equation:\\{}\qquad\qquad y-2=3(x-1)$

8 0

3 years ago

A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts. Estimate the true proportion

Andreas93 [3]

Answer: (0.5496, 0.5754)

Step-by-step explanation:

The confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where $\hat{p}$ = Sample proportion , n= sample size , z*= Critical z-value.

Let p be the proportion of all college students who are in favor of banning Hawaiian shirt.

Given, A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts.

i.e. n=4000

$\hat{p}=\dfrac{2250}{4000}=0.5625$

z-value for 90% confidence level is 1.645

Now , 90% confidence interval for p would be :

$0.5625\pm (1.645)(\sqrt{\dfrac{0.5625(1-0.5625)}{4000}})$

$=0.5625\pm (1.645)(\sqrt{0.0000615234375})\\\\=0.5625\pm (1.645)(0.00784368774876)\\\\\approx0.5625\pm0.0129\\\\=(0.5625-0.0129, \ 0.5625+0.0129)\\\\=(0.5496,\ 0.5754)$

Hence, the required 90% interval = (0.5496, 0.5754)

6 0

4 years ago

Determine the value of x in the diagram 112° xº 68° 112° What IS x ?

Zina [86]

Step-by-step explanation:

112+68+112+x = 360⁰

292⁰+x = 360⁰

x = 360⁰- 292⁰

x= 68⁰

7 0

3 years ago