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3 years ago

Beyonce is solving a system of equations: 2x – 3y = -2

Mathematics

1 answer:

nlexa [21]3 years ago

7 0

Answer:

Step-by-step explanation:

A system of equations has no solutions if you end up with a contradiction. For example, the system of two equations

y = 2x + 4

y = 2x

If you subtract the second equation from the first, you get

0 = 4

an obvious contradiction. If you were to graph the equations, you would see that the lines are parallel. They never intersect, so there is no point that satisfies both equations.

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Three equal-sized cardboard boxes are stacked on top of each other. Each box is 56.4 cm in height.

blsea [12.9K]

Since the boxes are identical we can say that the total height is 3 times that of a single box:

Total = 3 * 56.4cm
Total = 169.2cm

5 0

3 years ago

Read 2 more answers

The mean plus or minus one standard deviation defines the ________ percent probability range of a normal distribution. 82 68 95

zzz [600]

This is the "empirical rule." Approx. 68% of a data set lie within one standard deviation of the mean.

7 0

4 years ago

Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))

Softa [21]

Answer:

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Step-by-step explanation:

tan(sin⁻¹x + cos⁻¹y)

Use angle sum formula:

[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]

To evaluate these expressions, I suggest drawing right triangles.

For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1. Therefore:

sin θ = x/1

θ = sin⁻¹x

Using Pythagorean theorem, the adjacent side is √(1−x²). Therefore:

tan θ = x / √(1−x²)

tan(sin⁻¹x) = x / √(1−x²)

Draw a new triangle. This time we'll make y the adjacent side to angle θ.

cos θ = y/1

θ = cos⁻¹y

Using Pythagorean theorem, the opposite side is √(1−y²). Therefore:

tan θ = √(1−y²) / y

tan(cos⁻¹y) = √(1−y²) / y

Substituting:

[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]

Multiply top and bottom by √(1−x²).

[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]

Multiply top and bottom by y.

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

3 0

3 years ago

Please help me thanks sooo much

natima [27]

Answer:

P = 21x + 4

Step-by-step explanation:

The perimeter is the length of all the sides added up.

(3x) + (4x + 1) + (2x - 2) + (2x - 2) + (3x + 1) + (4x + 5) + (3x + 1)

3x + 4x + 1 + 2x - 2 + 2x - 2 + 3x + 1 + 4x + 5 + 3x + 1

21x + 1 - 2 - 2 + 1 + 5 + 1

21x + 4

The equation for the perimeter is

P = 21x + 4

6 0

3 years ago

What is the equation of the circle with center (1, −1) that passes through the point (5, 7)?

kykrilka [37]

Answer:

Option C $(x-1)^2+(y+1)^2=80$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from the center of the circle to any point on the circumference of the circle is equal to the radius of the circle

we have

(1,-1) and (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$d=\sqrt{(7+1)^{2}+(5-1)^{2}}$

$d=\sqrt{(8)^{2}+(4)^{2}}$

$d=\sqrt{80}\ units$

step 2

Find the equation of the circle in center radius form

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

substitute

$(x-1)^2+(y+1)^2=(\sqrt{80})^2$

$(x-1)^2+(y+1)^2=80$

3 0

3 years ago