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adell [148]
3 years ago
11

Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the

number?
(the three numbers is the same number)
Mathematics
1 answer:
ss7ja [257]3 years ago
3 0

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

<u><em>The correct question is </em></u>

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

x+2(x+1)+3(x+2)=-76

solve for x

apply distributive property

x+2x+2+3x+6=-76

Combine like terms

6x+8=-76

subtract 8 both sides

6x=-76-8

6x=-84

Divide by 6 both sides

x=-14

so

x+1=-14+1=-13

x+2=-14+2=-12

therefore

The numbers are -14,-13 and -12

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Step-by-step explanation:

7 0
3 years ago
Answer both with STEPS
Amanda [17]

Answer:

7 )

x =  \frac{3\sqrt{2} }{2}

y= 3

8 )

x=6\sqrt{6}

y= 9\sqrt{2}

Step-by-step explanation:

7  )                                 8)

In Δ ABC                                      In Δ XYZ            

∠ C = 45°                                          ∠ X = 60°

∠ A = 90°                                           ∠ Y = 90°

AC= \frac{3\sqrt{2} }{2}             XY= 3\sqrt{6}

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45°  ......Angle sum property of a triangle i.e 180°

∴  Δ ABC is an Isosceles Triangle

∴ AC = AB = x =  \frac{3\sqrt{2} }{2}

Now appplying Trignometry identity we get

\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2}  }{2}\\\\y= 3

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30°  . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}

\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\  y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}

Now,

\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}

8 0
3 years ago
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
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Answer:

Step-by-step explanation:

Triangle IJK is a right angle triangle.

From the given right angle triangle

JK represents the hypotenuse of the right angle triangle.

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Cos θ = adjacent side/hypotenuse. Therefore,

Cos K = 36/85

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4 0
3 years ago
How many megabytes of data can a 4.7 gigabyte dvd store?
dedylja [7]
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yan [13]
Hey there!

When we multiply fractions and whole numbers, we simply take that whole number and put it over them, and just multiply across. That gives us:

\frac{1}{2}x*8 = \frac{8}{2} = 4

Notice how it's four, because when we have a fraction, we divide. 8 divided by 2 equals four. Next:

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\frac{1}{3}*6 = \frac{6}{3} = 2

That's because 6/3 = 2.

Hope this helps!

7 0
3 years ago
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