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WITCHER [35]
2 years ago
8

Step 1: d+3 < 1 Step 2: b+6< 9

Mathematics
1 answer:
In-s [12.5K]2 years ago
3 0

Answer:

1) d < -2

2) b < 3

Step-by-step explanation:

1) d+3< 1

subtract both sides by 3

d+3 -3 < 1-3

d<-2

2) b+6< 9

subtract both sides by 6

b+6 -6 < 9 -6

b< 3

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Fundraising The robotics team needs new uniforms. The students plan to sell plush toy lions ​(the school​ mascot) for​ $5 each.
nataly862011 [7]

Answer:

Company C!

Step-by-step explanation:

In order to see which company has the best buy  we have to see the amount each company sells for one stuffed mascot. In order to do this we have to divide .

Company A:

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Company B:

Company B sells 18 lions for $50.22 this is the same as 1 stuffed lion for  $2.79.

Company C:

Company C sells 12 lions for $32.88 this is the same as 1 stuffed lion for $2.74

Thus as you can see the company with the best buy is company C.

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3 years ago
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diamong [38]

Answer:

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Step-by-step explanation:

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7 0
3 years ago
Item 7
Mariulka [41]

Answer:

A = 74.7^\circ

B = 42.5^\circ

C = 62.8^\circ

Step-by-step explanation:

Given

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2

For AB

A = (-1,2) \to (x_1,y_1)

B = (2,8) \to (x_2,y_2)

d = \sqrt{(-1 - 2)^2 + (2 - 8)^2

d = \sqrt{(-3)^2 + (-6)^2

d = \sqrt{45

So:

AB = \sqrt{45

For BC

B = (2,8) \to (x_2,y_2)

C = (4,1) \to (x_3,y_3)

BC = \sqrt{(2 - 4)^2 + (8 - 1)^2

BC = \sqrt{(-2)^2 + (7)^2

BC = \sqrt{53

For AC

A = (-1,2) \to (x_1,y_1)

C = (4,1) \to (x_3,y_3)

AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2

AC = \sqrt{(-5)^2 + (1)^2

AC = \sqrt{26

So, we have:

AB = \sqrt{45

BC = \sqrt{53

AC = \sqrt{26

By representation

AB \to c

BC \to a

AC \to b

So, we have:

a = \sqrt{53

b = \sqrt{26

c = \sqrt{45

By cosine laws, the angles are calculated using:

a^2 = b^2 + c^2 -2bc \cos A

b^2 = a^2 + c^2 -2ac \cos B

c^2 = a^2 + b^2 -2ab\ cos C

a^2 = b^2 + c^2 -2bc \cos A

(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A

53 = 26 +45 - 2 * 34.21 * \cos A

53 = 26 +45 - 68.42 * \cos A

Collect like terms

53 - 26 -45 = - 68.42 * \cos A

-18 = - 68.42 * \cos A

Solve for \cos A

\cos A =\frac{-18}{-68.42}

\cos A =0.2631

Take arc cos of both sides

A =\cos^{-1}(0.2631)

A = 74.7^\circ

b^2 = a^2 + c^2 -2ac \cos B

(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B

26 = 53 +45 -97.67 * \cos B

Collect like terms

26 - 53 -45= -97.67 * \cos B

-72= -97.67 * \cos B

Solve for \cos B

\cos B = \frac{-72}{-97.67}

\cos B = 0.7372

Take arc cos of both sides

B = \cos^{-1}(0.7372)

B = 42.5^\circ

For the third angle, we use:

A + B + C = 180 --- angles in a triangle

Make C the subject

C = 180 - A -B

C = 180 - 74.7 -42.5

C = 62.8^\circ

8 0
2 years ago
suppose a weather app says that the probability of rain today is 30%. What is the complement of the event ""rain today"" what is
ValentinkaMS [17]

Answer:

The complement event would be: "No rain today"

Its probability would be 70%

Step-by-step explanation:

Given the event:

A= rain today

The probability of rain today is 30%

P(A)=30%=0.3

The complement event has all the values that are not included in the event.

The complement event would be:

A'= No rain today

The probability of a event is the subtraction between 1 and the complement event:

P(A')=1-P(A)

Then, the probability of the event "No rain today" will be:

P(A')=1-0.3=0.7=70%

4 0
3 years ago
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