What extra step must be done to solve for x once a polynomial has been factored?

The scale on a map shows that 1 cm equals 10km if the distance between 2 cities on the map is 4.5 cm how far is the actual dista

ikadub [295]

Answer:

45 km

Step-by-step explanation:

Let's review the scale factor of this problem.

1 cm = 10 km

This means that for every 1 cm of distance on the map, 10 km is represented in the real world. Because of this, we know that dividing the actual distance by 10 will give us the distance on the map.

Ex. 40 km in real world = 4 cm on map

So, we will use d to represent the actual distance.

d=distance in real world

Then, we will divide d by 10 and set it equal to 4.5, because that's the distance on the map.

d/10 = 4.5

Now to solve this equation, we just have to multiply both sides by 10.

d=45

This is your answer.

4 0

3 years ago

Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at lea

lbvjy [14]

Answer:

(0, 33) : Yes

(4.8, 30.5) : Yes

Step-by-step explanation:

height of at least 24 ft : y >= 24

horizontal distance of no more than 10 ft. : 0 <= x <= 10

The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.:

y >= 3x and y <= 33

So Constraints:

24 <= y <= 33

y >= 3x

0 <= x <= 10

Now check to see if those coordinate points meet all the constraints

(0, 33) : Yes

(4.8, 30.5) : Yes

(9, 26) : No (because 26 is less than (3 * 9) = 27)

(4, 36) : No (because 36 > 33, must be 24 <= y <= 33)

(2, 22): No (because 22 <24, must be 24 <= y <= 33)

5 0

3 years ago

The owner of Sack of Suds paid his cashier $60 when he was actually owed only $42. What was the

OLga [1]

Answer: 42.9%

Step-by-step explanation:

Percent error is the difference between the measured and known value, which is divided by the known value, and then multiplied by 100%.

Percent error = (Estimated number- Actual number)/Actual Number × 100.

= (60 - 42)/42 × 100

= 18/42 × 100

= 0.429 × 100

= 42.9%

5 0

3 years ago

There is 1000cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is this enough alum

stealth61 [152]

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

Step-by-step explanation:

The given is,

Volume of aluminium available is 1000 cubic centimeters

Shape of trophy is right square pyramid

Trophy has a base edge of 10 cm and slant height of 13 cm

Step:1

Formula for volume of right square pyramid,

$Volume, V = a^{2}\frac{h}{3}$ .....................................(1)

Where, a - Base edge value

h - Height of pyramid

From given,

a = 10 cm

h = 13 cm

Equation (1) becomes,

$= 10^{2}(\frac{13}{3} )$

$= (100)(4.333)$

$= 433.33 cm^{3}$

Volume of trophy = 433.33 cubic centimeters

Compare with the volume of available aluminium and volume of right square pyramid,

$Volume of available aluminium > Volume of right square pyramid$

$1000 cm^{3} > 433.33 cm^{3}$

So, the given volume of aluminium is enough to make right square pyramid shaped trophy.

Result:

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

6 0

3 years ago

Read 2 more answers

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.75. Wi

Dafna1 [17]

Answer:

0.2915

Step-by-step explanation:

Let W represent water and D represent Dying probability

W = water

D = die

->If with water, it will die with probability 0.4

P(W & D) = 0.82 x 0.4 = 0.328

->Without water the plant will die with probability 0.75

P(W ' & D) = 0.18 x 0.75 = 0.135

Taking sum of the above values with water and without water.

P(D) = P(W & D) + P(W ' & D) = 0.4643

P(W ' | D) = P(W ' & D) / P(D)

= 0.135 /0.463

= 0.2915 ≈ 29.15%

Thus, the probability the neighbor forgot to water is 0.2915

4 0

3 years ago