Find the area of the parallelogram with vertices a(1,2,3), b(1,3,6), c(3,8,6), and d(3,7,3,)

Answer:

I think it is the first one

Step-by-step explanation:

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The forces are equal and opposite, the book remains at rest, representing a state of balanced forces.

Balanced forces occur when the net force acting on an object is zero, meaning that the forces are equal in magnitude and opposite in direction. As a result, the object remains in a state of equilibrium and does not accelerate.

One example that best represents balanced forces is:

A book resting on a table.

When a book is placed on a table, it doesn't move because the force of gravity pulling it down (its weight) is balanced by the normal force exerted by the table, pushing the book upward.

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Answer:

19.3 square units .

Step-by-step explanation:

∠D=∠F=52°

Opposite sides of equal angles are equal .

So, DE=EF =6.3

Now sum of all angles of triangle is 180°

So, ∠D+∠F+∠E = 180°

52°+52°+∠E =180°

104°+∠E =180°

∠E =180°-104°

∠E =76°

Now to find the length of DF we will use law of cosines

[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]

[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]

[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]

[tex]DF^2=79.38+79.38 (0.2419)[/tex]

[tex]DF^2=98.582[/tex]

[tex]DF=\sqrt{98.582}[/tex]

[tex]DF=9.9[/tex]

Now we are supposed to find the area of triangle

To calculate the area of given triangle we will use the heron's formula :

[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

a,b,c are the side lengths of triangle  

Now substitute the values :

[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]

[tex]s =11.25[/tex]

[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]

[tex]Area = 19.2907[/tex]

Hence the area of the triangle is 19.2907 ≈19.3 square units .

Answer:

Step-by-step explanation:

The quadratic equation [tex]ax^2+bx+c=0[/tex]

The roots of quadratic equation is defined as that value when we substitute in the quadratic equation then we get zero.

Solution of quadratic equation is defined as that value of roots which substitute in the equation then we get zero.

x-intercept of the quadratic equation is defined as that  real  value of x on the x- axis  when we substitute in the equation then the value of equation becomes zero.

From the above definitions we can see that roots of quadratic equation can be imaginary or real but x- intercept value of equation is always a real value.

Solution is also called the value of roots but x- intercept is equal to roots when the value of roots is real.

Now, we can says that roots and solutions of quadratic equation are same when values of roots are real. But when the roots are imaginary then we can not find x- intercept in cartesian   coordinate plane .

Answer:

n = 5

Step-by-step explanation:

This problem follows the theorem "If two chords intersect each other inside a circle, the products of their segments are equal."

To follow this theorem, you must multiply both segments of the chord with each other.

Do it to both chords.

The two chords are equal to each other. It should look like:

18*(n+1) = 9*(n+7)

[distributive property]

18n + 18 = 9n + 63

9n = 45

n = 5

Answer: The answer is (a) The scale factor is 1.25.

Step-by-step explanation:  We are given two figures in the question, where the second one is dilated from the first one. We are to find the scale factor here.

One side of the dilated figure is of length 10 inch and the original figure has a side of length 8 units.

Therefore, the scale factor is given by

[tex]S.F.=\dfrac{10}{8}=1.25.[/tex]

Therefore, the scale factor is 1.25 and (B) is the correct option.

The inequality to represent the amount of electricity generated by the catfish, which can generate up to 350 volts, is:  [tex]\[ 0 \leq E \leq 350 \][/tex] where [tex]\( E[/tex]  represents the amount of electricity in volts.

This inequality indicates that the electricity generated by the catfish is at least 0 volts and at most 350 volts. The lower bound of 0 volts is included because the catfish cannot generate negative voltage, and the upper bound of 350 volts is the maximum it can generate.

Answer:

The answer is the option B

[tex]23\°[/tex]

Step-by-step explanation:

we know that

In a parallelogram consecutive angles are supplementary

so

In this problem

[tex]5y\°+65\°=180\°[/tex]

Solve for y

[tex]5y\°=180\°-65\°[/tex]

[tex]y=115\°/5=23\°[/tex]

Answer:

23

Step-by-step explanation:

just took the test

The answer explains how to divide 4 stickers into 3 piles, resulting in 1 sticker each.

To find out how many stickers are in each pile:

Serena bought two equally priced game at a price of $44.99 each and the total money spent in buying all three games is $284.97.

Given information:

The price Serena paid for buying the first game is $194.99

The overall price Serena paid for buying three games is $284.97

Let, the price of one of the two equally priced game is [tex]\bold{P}[/tex]

As, the price of second and third game is equal, we can consider the combined price of second and third game.

Thus , the equation formed according to the information given in the question is:

[tex]\bold{194.99+2P=284.97}[/tex]

Solve, the above equation in order to find the price of one game.

[tex]2P=284.97-194.99\\\2P=89.98}\\{P=44.99}[/tex]

Hence, the price of one game in two equally priced game is $44.99

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Slope of the line = -4/3

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

The slope of line is the measure of steepness or the direction of line the coordinate plane.

m = Δy/Δx

where, m is the slope

Given,

A = (-9,4)

B = (3, -12)

Slope of line AB = (y - y')/(x-x')

                           = -12-4/3 - -9

                           = -16/12

Slope of line AB = -4/3

Hence, -4/3 is the slope of the line.

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Answer:

Step-by-step explanation:

2.8, 5.6, 5.6

Answer:

Step-by-step explanation:

They are saying the player gets points if the PRODUCT of the two numbers rolled is odd not the SUM  So the answer should be

(1,3) (1,5) (3,1) (3,3) (3,5) (5,1)(5,3)(5,5)  which is 9 out of 36 which would be 1/4 or 0.25

Final answer:

In this activity, the student needs to calculate the number of outcomes in the sample space, list and count the outcomes for event E, and find the probability of getting an odd number.

P(E) = 9/36 = 1/4 = 0.25.

Explanation:

To find the number of outcomes in the sample space (n(S)) of the trial, we need to consider all the possible combinations of rolling two six-sided dice. Since each die has six sides, the total number of outcomes for each die is 6. To find the total outcomes in the sample space, we multiply the outcomes for each die: n(S) = 6 * 6 = 36.

In this game, we are interested in the outcomes where the product of the two numbers rolled is odd. To list and count these outcomes, we need to consider the combinations where one or both of the numbers rolled is odd. By listing all the possible outcomes, we have: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5). There are 9 outcomes for event E.

To find the probability of getting an odd number, we need to divide the number of outcomes for event E by the total number of outcomes in the sample space. P(E) = 9/36 = 1/4 = 0.25.