Heron’s formula: Area = Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.

A polynomial identity is the identity whose left terms gives exactly right side terms.

In order to check if which of those have left side equals right side, we need to expand both side to the simplest step.

A. (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)

We could foil left side (a^2+b^2)(c^2+d^2)

It gives a^2c^2+a^2d^2+b^2c^2+b^2d^2.

Let us expand right side (ac-bd)^2+(ad+bc)

We get (ac-bd)^2 = a^2c^2+b^2d^2-2acbd

(ac-bd)^2+(ad+bc) = a^2c^2+b^2d^2-2acbd +ad+bc

Left side a^2c^2+a^2d^2+b^2c^2+b^2d^2 is not equal to right side a^2c^2+b^2d^2-2acbd +ad+bc.

Therefore, A. (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc) is not a polynomial identity.

B. (a+b)^2=a^2+2ab+b^2

Let us expand left side of the identity, we get

(a+b)^2 = a^2 +2ab + b^2.

We got left side a^2 +2ab + b^2 equals right side a^2+2ab+b^2.

Therefore, B. (a+b)^2=a^2+2ab+b^2 is a polynomial identity.

C. a^3-b^3=(a-b)(a^2+ab+b^2)

Let us expand right side of the identity, we get

(a-b)(a^2+ab+b^2) = a^3+a^2b+ab^2-a^2b-ab^2-b^3 = a^3-b^2.

We got left side a^3-b^3 equals right side a^3-b^2.

Therefore, C. a^3-b^3=(a-b)(a^2+ab+b^2) is a polynomial identity.

D. a^2(b+c)=a^3(b/a +c)

Expanding left side

a^2(b+c) = a^2b + a^2c

Expanding right side

a^3(b/a +c) = a^3*b/a + a^3c = a^2b +a^3c.

Left side a^2b + a^2c is not equal to right side a^2b +a^3c.

Therefore, D. a^2(b+c)=a^3(b/a +c) is not a polynomial identity.

The correct answer is D. [tex]\(a^2(b+c)=a^3(b/a+c)\)[/tex] is not a polynomial identity.

To determine which option is not a polynomial identity, let's examine each one:

A. [tex]\( (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2 \)[/tex]

 This is a polynomial identity known as the Brahmagupta–Fibonacci identity. It can be verified by expanding the right-hand side and simplifying:

[tex]\( (ac-bd)^2+(ad+bc)^2 = a^2c^2 - 2abcd + b^2d^2 + a^2d^2 + 2abcd + b^2c^2 \)[/tex]

[tex]\( = a^2c^2 + b^2d^2 + a^2d^2 + b^2c^2 \)[/tex]

[tex]\( = a^2(c^2+d^2) + b^2(c^2+d^2) \)[/tex]

[tex]\( = (a^2+b^2)(c^2+d^2) \)[/tex]

B. [tex]\( (a+b)^2=a^2+2ab+b^2 \)[/tex]

This is the well-known square of a binomial, which is a basic algebraic identity.

C.[tex]\( a^3-b^3=(a-b)(a^2+ab+b^2) \)[/tex]

This is the difference of cubes factorization, which is a standard polynomial identity. It can be verified by expanding the right-hand side:

[tex]\( (a-b)(a^2+ab+b^2) = a^3 - a^2b + ab^2 - b^3 \)[/tex]

[tex]\( = a^3 - b^3 \)[/tex]

D.[tex]\( a^2(b+c)=a^3(b/a+c) \)[/tex]

This is not a polynomial identity because when we simplify the right-hand side, we get:

[tex]\( a^3(b/a+c) = a^3(b/a) + a^3c \)[/tex]

[tex]\( = aba^2 + a^3c \)[/tex]

[tex]\( = a^3b + a^3c \)[/tex]

This is not equivalent to the left-hand side, [tex]\( a^2b + a^2c \)[/tex], unless [tex]\( a = 0 \) or \( a^2 = a^3 \)[/tex], which is not true for all values of [tex]\( a \)[/tex]. Therefore, the expression is not a polynomial identity.

Answer:

The length of CC' is, [tex]\sqrt{29}[/tex]units

Step-by-step explanation:

Using distance(D) formula for any two points is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

As per the statement:

From the graph:

The coordinates of C and C' are:

C = (2, 2) and C' = (7, 4)

Apply the distance formula to find length CC', we have;

[tex]CC'= \sqrt{(7-2)^2+(4-2)^2}[/tex]

⇒[tex]CC'= \sqrt{(5)^2+(2)^2}[/tex]

⇒[tex]CC'= \sqrt{25+4}[/tex]

Simplify:

[tex]CC'= \sqrt{29}[/tex]

therefore, the length of CC' is, [tex]\sqrt{29}[/tex] units

Answer:

32 pounds

Step-by-step explanation:

Answer:  The correct option is

(B) (4, -2).

Step-by-step explanation:  Given that the triangle DEF is translated  units down.

We are to find the co-ordinates of point E' in the image.

From the graph, we note that

the co-ordinates of the vertices of triangle DEF are D(1, 2), E(4, 3) and F(3, 1).

We know that

if a point (x, y) is translated 5 units down, then its co-ordinates becomes

(x, y)  →  (x, y-5).

Therefore, after translation, the co-ordinates of the vertex E' in the image are

E(4, 3)  →   E'(4, 3-5) = E'(4, -2).

Thus, (B) is the correct option.

Answer:

(4 ,-2)

Step-by-step explanation:

Answer:

The given equation [tex]3x^2+4x+2=0[/tex] has exactly 2 solutions.

Step-by-step explanation:

Given :  Equation [tex]3x^2+4x+2=0[/tex]

We have to find the number of solutions of the given equation [tex]3x^2+4x+2=0[/tex]

Consider the given equation [tex]3x^2+4x+2=0[/tex]

Since, The highest degree of the given polynomial is 2.

For a polynomial, the highest degree gives the number of solution of that polynomial.

So, [tex]3x^2+4x+2=0[/tex] has 2 solutions.

The given equation [tex]3x^2+4x+2=0[/tex] has exactly 2 solutions.

Answer:

A IS THE ANSWER

Step-by-step explanation:

A.birch Street is horizontal. A perpendicular street would have to be vertical. Elm Street is not vertical. Birch Street has 0 slope. Elm Street would have to have undefined slope to be perpendicular to Birch Street

The value of x is -3.5 and y is 6.5 for the given equations.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The equations will be solved as:-

−3x + y = 4

−9x + 5y = −1

Multiply the first equation by 3 and subtract the second equation.

−15x + 5y = 20

9x - 5y = -1

--------------------

-6x =   21

  x = -3.5

Put x = -3.5 into first equation.

(-3x3.5) + y = 4

y = 6.5

Hence, the values are -3.5 and 6.5.

To know more about equations follow

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The equations are simplified in the standard form will be x - 2y - 20 = 0 and 7x - 9y + 63 = 0.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The standard form is Ax + By + C = 0

The equations are given below.

y = (1/2)x - 10

y - 3 = (7/9)(x + 4)

Convert the equation y = (1/2)x - 10 into a standard form. Then we have

y = (1/2)x - 10

y = (x - 20) / 2

2y = x - 20

x - 2y - 20 = 0

Convert the equation y - 3 = (7/9)(x + 4) into a standard form. Then we have

y - 3 = (7/9)(x + 4)

y - 3 = (7x + 36) / 9

9y - 27 = 7x + 36

7x - 9y + 63 = 0

The equations are simplified in the standard form will be x - 2y - 20 = 0 and 7x - 9y + 63 = 0.

More about the linear equation link is given below.

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Answer:

(f•g)(10)= 606

Step-by-step explanation:

We have been given that

[tex]f(x)=x^2+1\\\\g(x)=x-4[/tex]

We have to find the value of (f•g)(10)

We can write (f•g)(10) = f(10)•g(10)

Let us find the value of the functions at x = 10

[tex]f(10)=10^2+1\\\\f(10)=100+1\\\\f(10)=101[/tex]

And the value of g(10) is

[tex]g(10)=10-4\\\\g(10)=6[/tex]

Hence,

(f•g)(10)

= f(10)•g(10)

= 101×6

= 606

Therefore, (f•g)(10)= 606

Hello there!

We have the slope and a point.

We can use the point-slope formula:

y-y1=m(x-x1)

Plug the point and the slope:

y-8=7(x-1)

y-8=7x-7

y=7x-7+8

y=7x+1

So the answer is Option A

Hope this helps

~Just a gloomy gal

#CarryOnLearning

[tex]SilentNature[/tex]

Why is sodium chloride (NaCl) put on icy roads and sidewalks in the winter?

          Your answer would be   

  a) It is ionic and lowers the freezing point of water.

Explanation:

to lower the freezing point so people don't slip

Hope this helps.

Answer:  a) It is  ionic and lowers the freezing point of water.

Freezing point depression is the process of the decrease in the freezing point of a solvent by addition of a non-volatile solute such as salt. The salt is added to the icy roads so as to lower down the freezing point of water and preventing the formation of the ice on the road this phenomena is called as freezing point depression. The ionic components of the salt split apart like Na⁺ and Cl⁻ and interacts with the water molecules which combines to form the solid state ice. Thereby, ions of salt interrupting in the formation of the solid structure that is ice.

Answer:

xy = 1 for all points.

Step-by-step explanation:

To solve this problem yo need to have the "x", the "y", and the radius. To find the radius since it is not given we use the formula.

sq rt(-3^2+1^2)

sq rt(9+1)

sq rt(10) would be the length of the radius in this case.

Then we use the sine cosine and tangent fractions

sin:y/r

cos:x/r

tan:y/x

With the values plugged in the equations are

SIN:1/sqrt(10) Since there can´t be a sq rt in hte denominator we change it to 1(sq rt(10))/10

COS:-3/sqrt(10) Since there can´t be a sq rt in the denominator we change it to -3(sq rt(10))/10

TAN:1/-3 This one can stay the same.

This would be the measures of SIN, COS, and TAN.

Answer:

Sin

Tan

Csc

Cot

Step-by-step explanation:

I just did it on edg

The odds in favor of picking a white marble from a bag of 4 green and 5 white marbles are 5 to 4.

To find the odds in favor of picking a white marble from a bag that contains 4 green marbles and 5 white marbles, first understand that 'odds in favor' are defined as the ratio of the number of ways the desired outcome can occur to the number of ways the desired outcome cannot occur. In this scenario, the desired outcome is drawing a white marble, and there are 5 white marbles. The number of ways the desired outcome can not occur is the number of non-white marbles, which is 4 green ones. Therefore, the odds in favor of drawing a white marble are 5 white marbles to 4 non-white marbles, or 5 to 4.