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3 years ago

Find four consecutive even integers such that seven times the first exceeds their sum by 18.

Mathematics

1 answer:

Ganezh [65]3 years ago

8 0

Answer:

10, 12, 14, 16

Step-by-step explanation:

Given: Four consecutive even integers such that seven times the first exceeds their sum by 18.

Lets assume the first number be "x".

As it is even integers

∴ Second consecutive number will be $(x+2)$

Third consecutive number will be $(x+4)$

Fourth consecutive number will be $(x+6)$

Now, as given seven times the first exceeds their sum by 18.

∴ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

solving the equation to find the number.

⇒ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

Opening parenthesis

$x+x+2+x+4+x+6+18 = 7x$

⇒ $4x+30= 7x$

subtracting both side by 4x

⇒ $30= 3x$

Dividing both side by 3

∴ x= 10.

Hence, subtituting the value x to find four consecutive even integers.

First number is 10

Second consecutive number will be $(10+2)$ = 12

Third consecutive number will be $(10+4)$ = 14

Fourth consecutive number will be $(10+6)$ = 16

∴ Four consecutive even integers are 10,12,14,16.

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IgorC [24]

Answer:

la respuesta que buscas es bastante simple pero no lo sé

Step-by-step explanation:

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3 years ago

At the beach, 11% of people have white towels and 53% have blue towels. If

telo118 [61]

Answer:

36 percent.

Step-by-step explanation:

We have been given that 11 percent of people of the peach have white towels, and 53 percent have blue towels.

With this information, we can find the remaining percentage of people that have red towels.

Recall that the total percentage is always 100 percent.

lets make r for the percentage of people that have red towels.

You can solve it by changing it to fraction, decimal, or just keep it at percent.

I will show you all of the possible ways.

Percent:

11 percent plus 53 percent plus r =100 percent

combine the like terms, or add 11 plus 53 to simplify the equation.

You have 64 percent plus r =100 percent Our goal is to isolate r, so subtract both sides by 64 percent.

100-64 is 36 percent.

r=36 percent of people who have red towels.

With fractions.

Write it as 11/100 plus 53/100 plus r/100= 100/100.

Combine the fractions.

64/100 plus r/100=100/100.

Subtract both sides by 64/100.

You are left with r=36/100, 9/25, or 36 percent.

With decimals.

11 percent as a decimal is 0.11. Just move the decimal spot 2 times. In 11, since you can write it as 11.0, you move it to the right twice.

53 percent is 0.53.

r is r.

100 percent is 1.

0.11 plus 0.53 plus r=100

Combine or add 0.53 and 0.11. That is 0.64.

Subtract both sides by 0.64.

You get r to be 0.36 or 36 percent.

I hope this helps, and I hope you have a good day!

8 0

3 years ago

Read 2 more answers

A quadratic equation is shown below:

sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

$3x^{2}-11x+10=0$ has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

$\frac{d}{dx}(3x^{2}-11x+10)=6x-11$

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

$x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}$

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

$x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}$

6 0

3 years ago

Can someone help me with 1-142 all the way to 1-144??

mezya [45]

CL.1.142):

A):

x5 ==> 4 boxes = 3ft <==== x5

20 boxes = ? ft

20 boxes is 15 ft. high

B): x3 ===> 4 boxes = 3ft. <==== x3

? boxes = 9ft.

12 boxes will fit in one stack.

c): CL.143

Perimeter = 15 + 29 + 9 + 11 + 6 + 18 =====> 88m

A1 = b * h

(18)(15)

270m^2

A2 = b * h

(11)(9)

Total Area ======> 270 + 99 ======> 369m^2

CL.1-144

1/4 + 1/4 + 1/5 = 5/20 + 5/20 + 4/20 ====> 14/20

1/4 * 5/5 =====> 5/20

1/5 * 4/4 =====> 4/20

14/20 + ?/20 = 20/20

? = 6 Missing Section

6/20 ======> 3/10

CL-1.145

A): 40/100 = 4/10 ====> 2/5

0.4 ========> 40%

B): 1/6 ======> .00000

0.16 (Repeating 6) ======> 16.6%

C): 37.5/100 = 375/1000 =======> 3/8

0.375 =========> 37.5%

CL-1.146

ADD: 1/6 + 1/2 show all steps:

1/6 + 1/2

1/6 + 3/6

1 + 3 / 6

4/6 =======> 2/3 =======> Decimal: =======> 0.666667

Hope that helps!!!! : )

5 0

3 years ago

Find the thirteenth term of an arithmetic sequence if the first term is 3 and the common difference is 3

lesya692 [45]

Answer:

Step-by-step explanation:

Formula for the nth term (an) = a1 + d(n - 1) where a1 = the first term and d = common difference.

So here the 13th term = 3 + 3(13 - 1)

= 3 + 3*12

= 39 (answer).

8 0

3 years ago