I need this someone answer this please.

How would I solve this?

givi [52]

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

$(7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360$

solve for x

Combine like terms

$10x^{2}-70x+180=360$

$10x^{2}-70x-180=0$

Divide by 10 both sides

$x^{2}-7x-18=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$x^{2}-7x-18=0$

so

$a=1\\b=-7\\c=-18$

substitute in the formula

$x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}$

$x=\frac{7(+/-)\sqrt{121}} {2}$

$x=\frac{7(+/-)11} {2}$

$x=\frac{7(+)11} {2}=9$

$x=\frac{7(-)11} {2}=-2$

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral is

$24-46x$

substitute the value of x

$24-46(9)=-390\°$

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

$(7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°$

therefore

The valid value of x is x=-2

7 0

3 years ago

What transformations are represented by the following coordinate graphing? (geometry)

Minchanka [31]

Answer:

(a,b) → (a,-b) : Reflection about x axis.

(a,b) → (a, b+5) : Translation of the point by 5 units up.

(a,b) → (b,-a) : Rotation by 90 degree clockwise.

Step-by-step explanation:

Given:

The transformation of points are given as:

(a,b) → (a,-b)

(a,b) → (a, b+5)

(a,b) → (b,-a)

Now, let us consider each transformation one by one.

(1) (a,b) → (a,-b)

Here, the order of the coordinates has not changed. But, the y coordinate of the point has changed. The y coordinate was 'b' and it has changed only its sign but not value. So, it is a transformation related to reflection.

In reflection, only the sign changes. Since, the 'y' coordinate sing is reversed, so, it is a reflection about x axis.

(2) (a,b) → (a, b+5)

Here, the 'y' coordinate of the point has changed. The change is from 'b' to 'b+5'. So, 5 is added to the y coordinate. As per transformation rules, if a positive number 'C' is added to the y coordinate, then the point shifts vertically up by 'C' units. Hence, there is a translation of 5 units up here.

(3) (a,b) → (b,-a)

Here, the 'x' and 'y' coordinates interchange their values and also the new y coordinate has its sign reversed. This happens in rotation.

We know that, (x, y) → (y, –x) is true when there is rotation by 90 degree clockwise.

So, the point (a,b) → (b,-a) is rotated by 90 degree clockwise.

5 0

3 years ago

I need help with this please hurry it's timed

rodikova [14]

Answer:

I think B 82.3%

Step-by-step explanation:

4 0

2 years ago

Please help! Thank you

Contact [7]

Answer:

A. 3.85 units

Step-by-step explanation:

Diameter = 2 × radius

radius = 7.7 /2

= 3.85 units

3 0

3 years ago

Sarah invested $1000 in an account paying 5.5% interest compounded semi-annually. How long will it take for the account balance

NISA [10]

Answer: it will take 43.25 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $1000

A = $10450

r = 5.5% = 5.5/100 = 0.055

n = 2 because it was compounded 2 times in a year.

Therefore,.

10450 = 1000(1 + 0.055/2)^2 × t

10450/1000 = (1 + 0.0275)^2t

10.45 = (1.0275)^2t

Taking log of both sides, it becomes

Log 10.45 = 2t log 1.0275

1.019 = 2t × 0.01178 = 0.02356t

t = 1.019/0.02356

t = 43.25 years

4 0

3 years ago