What is the height of the trapezoid?

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

Ganezh [65]

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.

8 0

2 years ago

In the model below what is x and how do I solve it

tiny-mole [99]

Answer:so that’s a interior triangle so the mean your 2 points in the inside and the equation on the outside.

X=6

Step-by-step explanation:

(8x-4)+(3x+17)=(17x-23)

Combined our alike terms on the left side of the equation. So 8x+3x and -4+17.

11x+13=17x-23

Now this is what the equation should look like after combining ur alike terms.

11x+13=17x-23

-11x. -11x.

now u take the lowest x which is 11x and mince that from 17x but u only mince if it’s a positive but is it’s a negative u add it.

13=6x-23 so if u moved the x on the right side u move non variable number to the left but if u moved the x to the left u move the non variable number to the right so in this case the non variable number would be -23 so now u add 23 on both sides.

36=6x and now u just divide the 36 by 6 and remember to always divide by the x

Now the answer is x=6

7 0

3 years ago

AXY Z with vertices X(1,1),Y (3,5), and Z(5, 1) will be rotated 180°about the origin. What will be the coordinates of

Lana71 [14]

Answer:

(-3,-5)

Step-by-step explanation:

When rotating 180˚ degrees about the origin just switch the value of the number from positive to negative or negative to positive

6 0

3 years ago

Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d^2y/dx

nikdorinn [45]

Answer:

Differentiation will give you the gradient for the tangent at any point, and you use the product rule whenever a function can be thought of as two functions multiplied together.

If

f

(

x

)

=

g

(

x

)

×

h

(

x

)

then

f

'

(

x

)

=

g

'

(

x

)

h

(

x

)

+

g

(

x

)

h

'

(

x

)

so if

y

=

x

×

sin

x

then

d

y

d

x

=

1

×

sin

x

+

x

×

cos

x

=

sin

x

+

x

cos

x

We know that

x

=

π

2

, so the gradient is

m

=

sin

(

π

2

)

+

π

2

cos

(

π

2

)

=

1

+

π

2

×

0

=

1

Therefore, we can say that

y

=

m

x

+

c

y

=

(

1

)

x

+

c

y

=

x

+

c

So all we really need to find now is the value for

c

, the

y

intercept. We do this by working out a point

(

x

,

y

)

on the graph. We are already given that

x

=

π

2

, so

y

=

x

sin

x

=

π

2

sin

(

π

2

)

=

π

2

×

1

=

π

2

∴

(

x

,

y

)

=

(

π

2

,

π

2

)

Now we substitute this into the equation we already have for the tangent,

y

=

x

+

c

,

(

x

,

y

)

=

(

π

2

,

π

2

)

π

2

=

π

2

+

c

=

π

2

−

π

2

=

0

∴

y

=

x

+

c

=

x

+

(

0

)

=

x

which means the tangent to the curve

y

=

x

sin

x

at

(

π

2

,

π

2

)

is simply

y

=

x

.

3 0

2 years ago

Help me guyssss pleaseee

matrenka [14]

Answer:

a

Step-by-step explanation:

trust me i used to this all the time

3 0

2 years ago

What is the height of the trapezoid?​

What is the height of the trapezoid?