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3 years ago

7.

Mathematics

2 answers:

harina [27]3 years ago

5 0

Answer: C) [-1,-3,-7,-19]

Step-by-step explanation:

Range = {-2(-2) - 5, -2(-1) - 5, -2(1) - 5, -2(2) - 5} = {4 - 5, 2 - 5, -2 - 5, -4 - 5} = (-1, -3, -7, -9}

Serga [27]3 years ago

3 0

Answer:

-2(-2)-5= -1 -2(-1)-5=-3 -2(1)-5=-7 -2(2)-5=-9... A. {-1, -3, 7, 9}

Step-by-step explanation:

By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain

The given function is :

f(x) = -2x - 5

For x = -2 , f(x) is:

f(-2) = (-2*-2) - 5 = 4 - 5 = -1

For x = -1, f(x) is :

f(-1) = (-2*-1) - 5 = 2 - 5 = -3

For x = 1 , f(x) is

f(1) = (-2*1) - 5 = -2 -5 = -7

For x = 2, f(x) is

f(2) = (-2*2) - 5 = -4 -5 = -9

The range is -1 , -3 , -7 , -9

Hope this helps ..!!

Thank you :)

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almond37 [142]

Answer:

x + 6y = -3

Step-by-step explanation:

Explained in the paper.

8 0

3 years ago

Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!

Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0

3 years ago

4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.

tamaranim1 [39]

9514 1404 393

Answer:

a) see attachment

b) base: 4, height: 4√3

c) area: 16√3

Step-by-step explanation:

a) The figure is drawn in the attachment

b) The side lengths of a 30-60-90 right triangle have the ratio ...

1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

c) The area is the product of base and height:

A = bh

A = 4(4√3) = 16√3 . . . . square units