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3 years ago

Three times the sum of three consecutive integers is 72. What are the integers? a. 4, 5, 6 c. 9, 10, 11 b. 7, 8, 9 d. 6, 7, 8

Mathematics

2 answers:

loris [4]3 years ago

5 0

Answer:

Step-by-step explanation:

7+ 8+ 9= 24

24 x 3= 72

Lady bird [3.3K]3 years ago

4 0

Answer:

The three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9

Step-by-step explanation:

Let x, y, and z be the three consecutive integers

The sum of x, y, and z will be: x+y+z

The three times the sum of three consecutive integers is 72.

so the equation becomes:

3(x+y+z)=72

Now, putting x = 7, y=8 and z=9 in the L.H.S equation to check

3(x+y+z)

⇒ 3(7+8+9)

⇒ 3(24)

⇒ 72

Therefore, it is clear that the three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9

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3 years ago

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Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

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3 years ago

Jenny drives from Paris to Rochefort, a distance of 483 km. her average speed on the journey is 84 km/h, she leaves at 9:50. Wha

Mrrafil [7]

The correct answer is 3: 35

Explanation:

To calculate at what time Jenny will arrive in Rochefort, the first step is to calculate the approximate time of the trip. Now, to calculate this consider the time of a movement (t) equals to the distance (d) divided by the speed (s), the process is shown below:

t = 483 km / 84 km/h

t = 5.75 hours

In this number 5 refers to the hours and 0.75 represents 45 minutes considering 0.75 x 60 minutes in one hour = 45 minutes. Therefore, the total time from Paris to Rochefort is 5 hours and 45 minutes. Now, to calculate the time of arrival add this result to the time of departure.

Add the hours: 5 hours + 9 hours: 14 hours

Add the minutes: 50 minutes + 45 minutes =95 minutes

95 minutes are equivalent to 1 hour (60) minutes and 35 minutes

Calculate the total

Hours: 14 hours + 1 hour = 15 hours or 3 in the 12 hour system (15 hours - 12 hours = 3 p.m.)

Minutes: 35 minutes

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3 years ago

Abigail has 16 apples she eats 2 apples per day.let y be the apples remaining as a function of the number of week,x

Greeley [361]

Answer:

Let X be the number of weeks.

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we add 16 on both sides.

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4 years ago

Please please help me!! i don’t know how to figure this out

MissTica

Answer:

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Step-by-step explanation:

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x = r * pi (3.1415926535)

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