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3 years ago

Find the area of a triangle whose vertices have the coordinates (-1,1) (-1,5) (4,1)

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

7 0

The triangle that forms is a right-angled triangle. To work out the area, you just do the base × height, all divided by 2.

Therefore, you do 5 (the base) × 4 (the height) and you get 20.

Then you divide by 2 to finish the equation and you should find that the total area of the triangle is 10 units² (20 ÷ 2 = 10).

Hope that helps :)

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Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Col

natali 33 [55]

Answer:

$\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]$

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

$\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]$

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

$A^{-1}$ = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = $\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]$

$A^{-1}$ = $\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]$ = $\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]$

4 0

2 years ago

Line p represents the rule x and y are equal

MArishka [77]

Ok so then line p is the equation y=x

is that all you needed?

4 0

3 years ago

Please help asap, its due in 20min

mojhsa [17]

Answer:

The scalar factor is 4/3

Step-by-step explanation:

The bottom of triangle B is 16 units, the bottom of triangle A is 12 units. So to find the scalar factor you have to divide B by A:

6/12=4/3

8 0

2 years ago

How many liter of 15% weed killer mixture must be added to 5 liters of 10% weedkiller mixture to make 12% weed killer mixture?

finlep [7]

Answer: 3 1/3 liter

Brainliest? <3

let x equal the number of liters of 15% weedkiller.

your equation is .15 * x + .10 * 5 = .12 * (x + 5)

simplify to get .15 * x + .10 * 5 = .12 * x + .12 * 5

simplify further to get .15 * x + .5 = .12 * x + .6

subtract .12 * x from both sides and subtract .5 from both sides and simplify to get .03 * x = .1

divide both sides by .03 to get x = .1 / .03 = 3.333333333 rounded to 9 decimal digits.

you would need 3.333333333 liters of 15% solution to be added to 5 liters of 10% solution to get 8.333333333 liters of 12% solution.

.15 * 3.333333333 = .5

.10 * 5 = .5

.5 + .5 = 1

5 + 3.333333333 = 8.333333333

1 divided by 8.333333333 = .12 which is equal to 12%.

4 0

2 years ago

For a standard normal distribution find the approximate value of p(z<0.42)

Kruka [31]

Answer:

p(z<0.42) = 0.6628

Step-by-step explanation:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. That is to say:

μ = 0

σ² = 1

Using a calculator, we find that:

p(z<0.42) = 0.6628 (See picture attached)

8 0

3 years ago

Read 2 more answers