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3 years ago

HURRY!!!!!

Mathematics

2 answers:

olga nikolaevna [1]3 years ago

6 0

Answer:

$x = 11$

Step-by-step explanation:

The bases of a trapezoid are parallel

The angles,

$(9x) \degree$

and

$(7x + 4) \degree$

are same side interior angles. These two angles are supplementary.

$(7x + 4) + 9x = 180 \degree$

$7x + 9x = 180 - 4$

$16x = 176$

Divide both sides by 16.

$x = \frac{176}{16}$

$x = 11$

lubasha [3.4K]3 years ago

6 0

Answer:

$x=11$

Step-by-step explanation:

We have been given that a carpenter cuts the corners of a rectangle to make the trapezoid. We are asked to find the value of x.

Since trapezoid is made of rectangle, so both bases will be parallel to each other.

We know that two consecutive interior angle of parallel lines are supplementary. We can set an equation to solve for x as:

$9x+7x+4=180$

$16x+4=180$

$16x+4-4=180-4$

$16x=176$

$\frac{16x}{16}=\frac{176}{16}$

$x=11$

Therefore, the value of x is 11.

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A car is traveling at a speed of 25 meters per second what is the cars speed in kilometers per hour how many kilometers will the

Likurg_2 [28]

Answer:

90 km/h
180 km

Step-by-step explanation:

There are 1000 m in 1 km, and 3600 s in 1 h, so the speed conversion is ...

$\dfrac{25\,m}{s}\cdot\dfrac{1\,km}{1000\,m}\cdot\dfrac{3600\,s}{1\,h}=\dfrac{90\,km}{h}$

The car's speed is 90 km/h.

In 2 hours, the car will travel ...

distance = speed · time = (90 km/h)(2 h) = 180 km

7 0

3 years ago

A number is picked randomly in the range [0,7]. What is the probability that the number picked is between 3 and 5? What is the p

emmasim [6.3K]

Answer:

(1) 0.125

(2) 0.125

Step-by-step explanation:

The total number of possible outcomes is:

N = 8

(1)

Compute the probability that the number picked is between 3 and 5 as follows:

Number of Favorable outcomes = 1

The probability is:

P (Number picked is between 3 and 5) = 1/8 = 0.125

Thus, the probability that the number picked is between 3 and 5 is 0.125.

(2)

The number usually picked appears to be in in the range [3,5], i.e. the numbers could be, {3, 4 or 5}.

Number of Favorable outcomes = n (Number < 4 and within [3, 5]) = 1

P (less than 4 ∩ within [3, 5]) = 1/8 = 0.125

Thus, the probability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5] is 0.125.

4 0

3 years ago

Find the lateral area of the regular pyramid<br><br> L.A. =

Arisa [49]

Answer:

FOR REGULAR PYRAMID with those dimension.

L.A = 96

FOR HEXAGONAL PYRAMID with those dimension

L.A = 171.71

Step-by-step explanation:

Please the question asked for L.A of a REGULAR PYRAMID, but the figure is a HEXAGON PYRAMID.

Hence I solved for both:

FOR REGULAR PYRAMID

Lateral Area (L.A) = 1/2* p * l

Where p = Perimeter of base

P = 4s

P = 4 * 6

P = 24cm

l = slanted height

l = 8cm

L.A = 1/2 * 24 * 8

L.A = 1/2 ( 192)

L.A = 96cm ^ 2

FOR AN HEXAGONAL PYRAMID

Lateral Area = 3a √ h^2 + (3a^2) / 4

Where:

a = Base Edge = 6

h = Height = 8

L.A = 3*6 √ 8^2 + ( 3*6^2) / 4

L.A = 18 √ 64 + ( 3 * 36) / 4

L.A = 18 √ 64 + 108/4

L.A = 18 √ 64+27

L.A = 18 √ 91

L.A = 18 * 9.539

L.A = 171.71

8 0

3 years ago

PLEASE HELP ME! THIS IS THE MOST URGENT! I WOULD HIGHLY APPRECIATE IT! PLEASE PLEASE PLEASE.

sergeinik [125]

Answer:

see attached

Step-by-step explanation:

The infinite series with a common ratio greater than 1 will not have a finite sum.

8 0

3 years ago

Read 2 more answers

A welder drops a piece of red-hot steel on the floor. The initial temperature of the steel is 2,500 degrees Fahrenheit. The ambi

sergey [27]

Answer: After 18.05 minutes, the temperature of steel becomes 100 degrees.

Step-by-step explanation:

Since we have given that

Initial temperature = 2500

At t = 0,

we get that

$f(t)=Ce^{-kt}+80\\\\2500=C+80\\\\2500-80=C\\\\2420=C$

After 2 minutes, the temperature of the steel is 1500 degrees.

so, it becomes,

$1500=2420e^{-2k}+80\\\\1500-80=2420e^{-2k}\\\\\dfrac{1420}{2420}=e^{-2k}\\\\0.587=e^{-2k}\\\\\ln 0.587=-2k\\\\-0.533=-2k\\\\k=\dfrac{0.533}{2}\\\\k=0.266$

So, We need to find the number of minutes when the temperature of steel would be 100 degrees.

So, it becomes,

$100=2420e^{-0.266t}+80\\\\100-80=2420e^{-0.266t}\\\\20=2420e^{-0.266t}\\\\\dfrac{20}{2420}=e^{-0.266t}\\\\\ln \dfrac{20}{2420}=-0.266t\\\\-4.8=-0.266t\\\\t=\dfrac{4.8}{0.266}\\\\t=18.05$

Hence, after 18.05 minutes, the temperature of steel becomes 100 degrees.

7 0

3 years ago