How to find volume of a rectangular prism ith surface area, width and length but no height

Does y=x^5 represent y as a function of x?

Sindrei [870]

Yes, definitelyl, y = x^5 represents a function of x. x^5 is a polynomial, and all poly. are functions.

5 0

3 years ago

Which ordered pair is a solution of the system of equation y=x-4

enyata [817]

There are many solutions, probably too many to list

7 0

2 years ago

Reduce the fraction to lowest terms.

mel-nik [20]

This reduced fraction would be c. x+y/8.

You can apply the Difference of Two Squares Formula (x^2+y^2)=(x+y)(x-y). Then, you can factor out the common term 8 and cancel out the common factor x-y. Hope this helps! :)

5 0

3 years ago

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use

Naddik [55]

Question has missing figure, the figure is in the attachment.

Answer:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

Step-by-step explanation:

Given,

We have an isosceles triangle which we can named it as ΔABC.

In which Length of AB is equal to length of BC.

And also m∠B is equal to m∠C.

ext.m∠C= 115°(Here ext. stands for exterior)

We have to find the measure of angles angles 1 through 5.

Solution,

For ∠1.

∠1 and ext.∠C makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle1+ext.\angle C=180\°$

On putting the values, we get;

$\angle 1+115\°=180\°\\\\\angle1=180\[tex]\therefore m\angle2=65\°$ -115\°=65\°[/tex]

Thus the measure of ∠1 is 65°.

For ∠2.

Since the given triangle is an isosceles triangle.

So, $m\angle1=m\angle2$

Thus the measure of ∠2 is 65°.

For ∠3.

Here ∠1, ∠2 and ∠3 are the three angles of the triangle.

So we use the angle sum property of triangle, which states that;

"The sum of all the angles of a triangle is equal to 180°".

$\therefore \angle1+\angle2+\angle3=180\°$

Now we put the values and get;

$65\°+65\°+\angle3=180\°\\\\130\°+\angle3=180\°\\\\\angle3=180\°-130\°=50\°$

Thus the measure of ∠3 is 50°.

For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle2 +\angle 4 =180\°$

Substituting the values of of angle 2 to find angle 4 we get;

$65\°+ \angle 4 = 180\°\\\\ \angle 4 = 180\°-65\°\\\\\angle 4= 115\°$

Thus the measure of ∠4 is 115°.

For ∠5.

∠4 and ∠5 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle4 +\angle 5 =180\°$

Substituting the values of of angle 4 to find angle 5 we get;

$115\°+ \angle 5 = 180\°\\\\ \angle 5 = 180\°-115\°\\\\\angle 5= 65\°$

Thus the measure of ∠5 is 65°.

Hence:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

6 0

2 years ago

the polynomial ky^3+3y^2-3 and 2y^3-5y+k when divided by (y-5) leave the same remainder in each case. Find the value of k.

marshall27 [118]

Answer:

$k=\frac{153}{124}$

Step-by-step explanation:

According to the Remainder Theorem; when P(y) is divided by y-a, the remainder is p(a).

The first polynomial is :

$p(y)=ky^3+3y^2-3$

When p(y) is divided by y-5, the remainder is

$p(5)=k(5)^3+3(5)^2-3$

$p(5)=125k+75-3$

$p(5)=125k+72$

When the second polynomial:

$m(y)= 2y^3-5y+k$ is divided by y-5.

The remainder is;

$m(5)= 2(5)^3-5(5)+k$

$m(5)= 225+k$

The two remainders are equal;

$\implies 125k+72=225+k$

$\implies 125k-k=225-72$

$\implies 124k=153$

$k=\frac{153}{124}$

3 0

3 years ago