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2 years ago

Triangle LMN, with vertices L(-9,5), M(-4,2), and N(-6,9), is drawn inside a rectangle, as shown below.

Mathematics

2 answers:

Natalija [7]2 years ago

6 0

Answer:

20.38

Step-by-step explanation:

wlad13 [49]2 years ago

5 0

Answer:

l(yj)

Step-by-step explanation:

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Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the

maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

$y=ax^2+bx+c$

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

$x_v=-\frac{b}{2a}$

In this problem, we have:

$y=-x^2-6x-13$

Then:

a = -1

b = -6

We write now:

$x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3$

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

$-x^2-6x-13=0$

To solve this, we can use the quadratic formula:

$x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}$

And solve:

$x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}$ $x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}$

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

$y=-0^2-6\cdot0-13=-13$

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

$x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20$ $x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8$

The two points are:

(1, -20)

(-1, -8)

Part 6:

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

$y=-(-3)^2-6(-3)-13=-9+18-13=-4$

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

8 0

8 months ago

12 stamps increased by 125% what is the new amount

GREYUIT [131]

12 x 1.25 = 15

15 is the new amount

4 0

2 years ago

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$

3 0

2 years ago

(b-c)3 +(c-d) raise to3 3+(d-b)3

Juliette [100K]

Answer:3 b − 2 c− d , t o 3 , 3 + 3d − 3 b

Step-by-step explanation:

( b − c ) ⋅ 3 + ( c -d ) raise t o 3 3 + ( d − b ) ⋅ 3

Write the problem as a mathematical expression.

( b − c ) ⋅ 3 +( c − d ) raise t o3 3+ ( d − b) ⋅ 3

Remove parentheses.

( b − c) ⋅ 3 + c − d , t o 3 , 3 + ( d − b ) ⋅ 3

Simplify each term.

Apply the distributive property.

b ⋅ 3 − c ⋅ 3 + c− d

Move 3 to the left of b . 3 ⋅ b − c ⋅ 3 + c − d

Multiply 3 by − 1 ⋅ 3 b − 3 c + c − d

Add − 3 c and c. 3 b − 2 c − d , t o 3 , 3 + ( d − b ) ⋅ 3

Simplify each term.

Apply the distributive property.

3 + d ⋅ 3 − b ⋅ 3

Move 3 to the left of d . 3 + 3 ⋅ d − b ⋅ 3

Multiply 3 by − 1 . 3 + 3 d − 3 b

4 0

2 years ago

Can the expression be used to solve 29x14? yes or no for each expression a(9x4)+(20x4)+(9x1)+(20x1) yes No

Alekssandra [29.7K]

no because

29×14 is 406

9×4

20×4

9×1

49×10 490

490 and 406 aren't equal

7 0

3 years ago