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3 years ago

In the figure to the right, can you conclude that triangle GHI is congruent to triangle KJI? Justify your reasoning.

Mathematics

1 answer:

inessss [21]3 years ago

7 0

Answer:

Step-by-step explanation:

You cannot conclude that ΔGHI is congruent to ΔKJI, because although you can see/interpret that there all the angles are congruent with one another, like with vertical angles (∠GIH and ∠KIJ) and alternate interior angles (∠H and ∠J, ∠G and ∠K), we don't know the side lengths.

All the angles could be congruent, but the sides might be different. For example, ΔGHI might be a bigger triangle than ΔKJI, which could make them similar to one another, but not congruent.

For something to be congruent to another, everything must be exactly the same.

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Can someone please help me with this

JulsSmile [24]

Answer:

x=155

Step-by-step explanation:

(2x-120)+10=180

or,2x-130=180

or,2x=180+130

or,2x=310

or,x=310÷2

x=155

6 0

2 years ago

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per uni

aleksandrvk [35]

Answer:

a. x1 = No. of units to purchase from Iowa

x2 = No. of units to purchase from Illinois

b. Min 6x1 + 5.5x2

c. x1 + x2 ≥ 12000

x1 ≤ 8000

x2 ≥ 6000

Step-by-step explanation:

a. We can consider the variables x1 and x2 as:

x1 = No. of units to purchase from Iowa

x2 = No. of units to purchase from Illinois

b. Price per unit of Iowa corn = $6

Price per unit of Illinois corn = $5.5

Objective function that would minimize the total cost can be written as:

Min 6x1 + 5.5x2

c. The manufacturer needs at least 12000 units of corn which means that the combined number of units from Iowa and Illinois must be greater than or equal to 12000. So, we can write:

x1 + x2 ≥ 12000

The Iowa cooperative can supply up to 8000 units which means that the value of x1 must not be greater than 8000. So, we can write:

x1 ≤ 8000

Similarly, the Illinois cooperative can supply at least 6000 units which means that the value of x2 must not be less than 6000. So, we can write:

x2 ≥ 6000.

The constraints for these conditions are:

x1 + x2 ≥ 12000

x1 ≤ 8000

x2 ≥ 6000

6 0

2 years ago

Find the length of the arc shown in red. Leave your answer in terms of .

docker41 [41]

Answer:

red segment = 25.12 ft

Step-by-step explanation:

circumference of full circle = (3.14)(24) = 75.36 ft

semi circle = 75.36/2 = 37.68 ft

60° segment = (60/360)(75.36) = 12.56 ft

red segment = 37.68 - 12.56 = 25.12 ft

8 0

3 years ago

A cylindrical grain bin has a radius of 7 feet and a height of 25 feet. How many cubic feet of grain can the bin hold

dimaraw [331]

Answer:

1225π

Step-by-step explanation:

The question concerns the volume of the cylinder.

The formula of the volume is:

$V=\pi r^{2} h$ , where r is the radius and h is the height.

Plugging the given numbers into the formula, we find that:

$V=\pi * 49 * 25=1225\pi$

The result - 1225π shows that the cylinder can be filled fully with that given amount.

5 0

3 years ago

I really need help. Any help is appreciated.

finlep [7]

The equation is:
$f ( x ) = 4 * 5 ^{2x}$
f ( - 1 ) = 4 * 1/25 = 4/25 ( false )
f ( 0 ) = 4 * 1 = 4 ( false )
f ( 1 ) = 4 * 25 = 100 ( false )
f ( 2 ) = 4 * 5 ^4 = 4 * 625 = 2500 ( correct )
Answer:
D ) ( 2, 2500 )

4 0

2 years ago