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Vladimir [108]
3 years ago
9

Doors for the small cabinets are 11.5 inches long. Doors for the large cabinets are 2.3 times as long as the doors for the small

cabinets. How many large doors can be cut from a board that is 10 1/2 feet long?
Mathematics
1 answer:
tiny-mole [99]3 years ago
7 0
The size of the large cabinets door = 2.3 * 11.5 = 26.45 inches
the board size in inches = 10 1/2 * 12 = 126 inches
number of doors = 126 / 26.45 = 4.76
so the number of doors = 4 doors
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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
To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. Let
Rudiy27
The function that models exponential growth is:

P(t) = P0*(1 + r)^t, where

P0 = P(0) is the initial value of P

r is the growth rate as a decimal

In our case we have:

P(0) = 2800

r = 0.035 or 3.5%

P(t) = 2800*(1 + 0.035)^t

P(t) = 2800*(1.035)^t

The same exponential function written using y and t is:

y = 2800*1.035^t.

Explanation: https://softmath.com/algebra-word-problems/to-begin-a-bacteria-study-a-petri-dish-had-2800-bacteria
7 0
2 years ago
GEOMETRY HELP ME
Aleksandr [31]

Answer:

x= 110°

Step-by-step explanation:

if you continue drawing the top purple line you will have a triangle with three angles

70° ; is given

180-140= 40°; is the same angle as the supplement angle of 140° (complementary angles are congruent)

180-70-40 = 70°; because sum of angles in a triangle is 180°

So angle x= 180 -70 = 110 because are a linear pair

6 0
2 years ago
Read 2 more answers
*In ∆ABC, on the extension of the side BC , draw a line segment CD ≅ CA . Draw the segment AD . The line segment CE is the angle
Leya [2.2K]

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Step-by-step explanation:

In ∆ABC

  • On the extension of the side BC , draw a line segment CD ≅ CA
  • Draw the segment AD
  • The line segment CE is the angle bisector of ∠ACB
  • The line segment CF is the median towards AD in ∆ ACD

We want to prove that CF ⊥ CE

Look to the attached figure

In Δ ABC

∵ CE is the bisector of angle ACB

∴ ∠ACE ≅ ∠BCE

In Δ ACD

∵ CA = CD

∴ Δ ACD is an isosceles triangle

∵ AD is the median towards AD

- In any isosceles triangle the median from a vertex to its opposite

  side bisects this vertex

∴ AD bisects ∠ACD

∴ ∠ACF ≅ ∠DCF

∵ BCD is a straight segment

∵ CE , CA , CF are drawn from point C

∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°

∵ m∠ACE ≅ m∠BCE

∵ m∠ACF ≅ m∠DCF

- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF

∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°

∴ 2 m∠ACE + 2 m∠ACF = 180°

- Divide all terms by 2

∴ m∠ACE + m∠ACF = 90°

∴ EC ⊥ CF

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Learn more:

You can learn more about perpendicular lines in brainly.com/question/11223427

#LearnwithBrainly

7 0
3 years ago
Evaluate the following expression. Round to the nearest hundredth when necessary.<br><br> 6³ - 18
SSSSS [86.1K]

Answer:

198

Step-by-step explanation:

Because 6 to the power of three is 6 x 6 x 6 = 216 - 18 = 198

8 0
3 years ago
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