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3 years ago

10 POINTS Solve the combined inequality: 6 -2x < 12 or 7 + 2x < -11

1 answer:

8 0

The first thing we must do in this case is to solve both inequations.
We have then:
Inequality 1:
6 -2x <12
6-12 <2x
-6 <2x
-6/2 <x
-3 <x
Inequality 2:
7 + 2x <-11
2x <-11-7
2x <-18
x <-18/2
x <-9
Answer:
(-inf, -9) U (-3, inf)

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If AB=x and x=4, then the transitive property states

Anarel [89]

Answer:

4. AB=4

Step-by-step explanation:

Transitive property is like substitution, or that's how I like to think of it. Since we have 2 common variables and 2 equations, we can "link them together". Replacing x with 4, you get AB=4.

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3 years ago

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3 years ago

5. Find the lateral surface area of the net of the cube. 1.8 cm

igor_vitrenko [27]

Given:

Given that the side length of the cube is 1.8 cm

We need to determine the lateral surface area of the cube.

Lateral surface area of the cube:

The lateral surface area of the cube can be determined using the formula,

$LSA=4a^2$

where a is the side length.

Substituting a = 1.8 in the above formula, we get;

$LSA=4(1.8)^2$

Squaring the term, we get;

$LSA=4(3.24)$

Multiplying, we get;

$LSA=12.96$

Thus, the lateral surface area of the cube is 12.96 cm²

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3 years ago

Which describes the relationship between 15,700 and 157,000? A 15,700 is 1/10 of 157,000 B 157,000 is 1/10 of 15,700 C 15,700 is

viva [34]

Answer: 15,700 is 1/10 of 157,000 (A)

Step-by-step explanation:

The relationship between 15,700 and 157,000 is that 15,700 is 1/10 of 157,000

1/10 × 157,000 = 15,700

A 15,700 is 1/10 of 157,000

= 1/10 × 157,000

= 15700 (Correct)

15700 equals 15700

B 157,000 is 1/10 of 15,700

= 1/10 × 15700 = 1570 (Wrong)

1570 is not equal to 157000

C 15,700 is 1/100 of 157,000

= 1/100 × 157,000 = 1570 (Wrong)

1570 is not equal to 15700

D 157,000 is 1/100 of 15,700

1/100 × 15700 = 157 (Wrong)

157 is not equal to 157000

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3 years ago

In the diagram, TC represents a vertical building. The points, A and B, are on the same level as the foot C of the building such

Alenkinab [10]

Answer:

(a) The height of the building is 60.06 m

(b) The distance AB is 139.43 m

Step-by-step explanation:

The given parameters are

Given that segment BT = segment AT + 29

By trigonometric ratios, we have;

cos∠ATC = CT/AT

cos∠BTC = CT/BT

Therefore, we have;

cos(40°) = CT/AT.................................(1)

cos(56°) = CT/BT = CT/(AT + 29).....(2)

cos(56°) = CT/(AT + 29)......................(3)

From equation (1)

CT = AT×cos(40°)

From equation (3)

AT×cos(56°) + 29 × cos(56°) = CT

Therefore;

AT×cos(40°) = AT×cos(56°) + 29 × cos(56°)

AT×cos(40°) - AT×cos(56°) = 29 × cos(56°)

AT×(cos(40°) - cos(56°)) = 29 × cos(56°)

AT = 29 × cos(56°)/(cos(40°) - cos(56°)) = 78.4 m

TC = CT = AT×cos(40°) = 78.4×cos(40°) = 60.06 m

The height of the building = 60.06 m

(b) BT = AT + 29 = 78.4 m + 29 m= 107.4 m

AB = AT×sin(∠ATC ) + BT×sin(∠BTC) = 78.4×sin(40°) + 107.4×sin(56°) = 139.43 m

The distance AB = 139.43 m.

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3 years ago