Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B. x=2, x=-3

Step-by-step explanation:

Hello,

We are given this system of equations:

y=4-x²

x-y=2

And we want to solve it for x.

There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.

But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.

In x-y=2, subtract x from both sides.

-y=-x+2

Multiply both sides by -1.

y=x-2

Substitute y as x-2 in y=4-x².

x-2=4-x²

Add x² to both sides.

x²+x-2=4

Subtract 4 from both sides.

x²+x-6=0

Now factor using FOIL.

1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.

Two numbers that add up to 1 but multiply to get -6 are -2 and 3.

So now factor:

(x-2)(x+3)=0

Split and solve:

x-2=0

x=2

x+3=0

x=-3

The solutions for x are x=2 and x=-3, which means the answer is B.

Hope this helps!

Using Pythagorean Theorem

[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]

[tex]\\ \sf\longmapsto H^2=8^2+15^2[/tex]

[tex]\\ \sf\longmapsto H^2=64+225[/tex]

[tex]\\ \sf\longmapsto H^2=289[/tex]

[tex]\\ \sf\longmapsto H=\sqrt{289}[/tex]

[tex]\\ \sf\longmapsto H=17[/tex]

By definition of bisector, the angle bisector of any angle of a triangle divides that angle in two equal parts.

But first you must know the definition of the bisector of a triangle.  The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle.

In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.

Each interior angle of the triangle corresponds to a bisector, so since each triangle has three interior angles, it has three bisectors.  The three bisectors of a triangle meet at a point called the incenter and it is always an interior point of the triangle.

In summary, the bisector of any angle of a triangle is a segment that divides the angle into two equal parts.

Learn more about angle bisector of a angle of a triangle:

Answer: m∠ATC = 54°

Step-by-step explanation:

Ok, we know that:

m∠ATB = 20° and  m∠BTD = 72°

then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:

m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°

Now, we also know that m∠CTD = 38°

And the angle:

m∠ATC  will be equal to the angle between A and D, minus the angle between C and D, or:

m∠ATC = m∠ATD - m∠CTD = 92° - 38° = 54°

Answer:

-4, -1/7,0.09,π/2,√3 ,√225,17

Step-by-step explanation:

π/2, is approx 1.5

-4,

0.09,

17,

√3 is approx 1.7

,-1/7, is approx -.143

√225 = 15

From most negative to greatest

-4, -1/7,0.09,π/2,√3 ,√225,17

Answer:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Step-by-step explanation:

So we have the numbers:

[tex]\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}[/tex]

(And without using a calculator) approximate each of the values.

π is around 3.14, so π/2 is around 1.57.

17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.

-1/7 can be divided to be about -0.1429...

And the square root of 225 is 15.

Now, use the approximations to place the numbers:

[tex]\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15[/tex]

The smallest is -4.

Next is -1/7 or about -0.14

Followed by the first positive, 0.09.

And then with π/2 or 1.57

And then a bit bigger with the square root of 3 or 1.7.

And then with the square root of 225 or 15.

And finally the largest number 17.

Thus, the correct order is:

[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]

Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

The decimal number is 0.9

Answer:

2

Step-by-step explanation:

a1= 1

r= a2/a1

r= (1/2)/1

r=0.5

s= a1/1-r

s= 1/1-0.5

s=2

Answer:

1. x = 7

2. 270x+274

Explanation:

see attached filed for step by step reasoning

Answer:

∠PQR =  67.36° (Approx)

Step-by-step explanation:

Given:

PRQ is a right triangle

∠R = 90°

PQ = 13 cm

QR = 5 cm

PR = 12 cm

Find:

∠PQR = ?

Computation:

Using trigonometry application.

SinФ = 12 / 13

SinФ = 0.92

Sin 67.36° = 0.92

So,

∠PQR =  67.36° (Approx)

9514 1404 393

Answer:

  c = a - b

Step-by-step explanation:

Subtract b from both sides of the equation.

  a = b + c

  a - b = b + c - b . . . . . show the subtraction

  a - b = c . . . . . . . . . . simplify

  c = a - b . . . . . . write with c on the left

The guidance director is conducting a sample poll in this experimental design.

Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.

We are required to fill the blank with appropriate term among the options.

The correct option is sample poll because the guidance director collects data in his school only.

Census collects the whole population of the country.

Sample poll means collecting data from small population.

Random sample means collecting data from a part of popultion without identifying any variable.

Hence we found that he was doing sample poll.

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Answer:

Collinear occurs when the two points has the same gradient,

So, for this question any line that forms by any three points would be collinear.

Hence, EBF,DGC,MGN,BGA are all collinears

Step-by-step explanation:

Answer:

[tex]\boxed{6.875 \text{\: grams}}[/tex]

Step-by-step explanation:

Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by [tex]2^{x}[/tex], where x  is equal to the amount of half-lives.

In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.

[tex]\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}[/tex]

Work Shown:

T = average Celsius temperature two Sundays ago

8% = 8/100 = 0.08

8% of T = 0.08T

L = average Celsius temperature last sunday

L = 8% higher than T

L = T + (8% of T)

L = T + 0.08T

L = 1.00T + 0.08T

L = (1.00 + 0.08)T

L = 1.08T

The 1.08 refers to the idea that L is 108% of T

Answer:

b and d

Step-by-step explanation:

khan

Answer:

[tex]\large \boxed{\mathrm{-3w + 5(2w + 1)}}[/tex]

Step-by-step explanation:

-2w + 3 + 5w - 2

Combine like terms.

3w + 1

-3w + 5(2w + 1)

Expand brackets.

-3w + 10w + 5

Combine like terms.

7w + 5

Answer:

The answer is C.

-3w +5(2w +1)

Step-by-step explanation:

Answer:

.15

Step-by-step explanation:

Answer:

Does the answer help you?

that's what I got, you can confirm if it's correct or not... I'm not sure

have a nice dayʘ‿ʘ

Answer:

There is not enough information to the problem.

The things we know are:

Zhi wants to draw a king of clubs or an ace of clubs.

There is a 52 card deck, but we do not know which cards are in play.

Now, the probability of drawing two specific cards out of a deck of 52 cards is equal to:

P = 2/52 = 0.038.

Now, suppose that there are X cards in game, and Zhi knows the cards (and he can see that the king of clubs and the ace of clubs are not in the table, so the must be on the card pile), now the probability is bigger, because now we want to draw two specific cards out of 52 - X cards, so the probability now is:

p = 2/(52 - X)

and 52 - X is smaller than 52, so the denominator is smaller, which means that the probability is actually larger.

Answer:

31%

Step-by-step explanation:

Since the two events, drawing a face card and drawing an ace card, are non-overlapping, we can use the following formula:

P left parenthesis A c e space o r space F a c e right parenthesis equals P left parenthesis A c e right parenthesis plus P left parenthesis F a c e right parenthesis equals 4 over 52 plus 12 over 52 equals 16 over 52 equals 4 over 13 equals space 0.308 space o r space 31 percent sign

The width of the gym will be W=60 feet for the area of 6,960 square feet.

Area is defines as the space covered by a surface in the two dimensional plane.

It is given that

Area of the gym =6960 square feet

Width of the gym = ?

Length of the gym=116 feet

The width of the gym will be calculated as

[tex]A=\L\times W\\\\\\6960=116\times W\\\\\\w=\dfrac{6960}{116}=60\ \ Feet[/tex]

hence the width of the gym will be W=60 feet for the area of 6,960 square feet.

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Answer:

15/8

Step-by-step explanation:

one big rectangle is 1 or 8/8 and the other is 7 out of 8, therefore we have 8/8+7/8 = 15/8.

Answer:

$522.49

Step-by-step explanation: 549.99*.05=27.50 (discount)

549.99-27.50=$522.49

Answer:

$522.49

Step-by-step explanation:

First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"

5% = 0.05

549.99 ⋅ 0.05 = 27.4995

That means the discount amount is $27.50

Subtract the discount amount from the original price

$549.99 - $27.50 = $522.49

Answer:

Correct options are 2, 5 and 7.

Step-by-step explanation:

Consider the given vertices of triangle are A(-3,-3), B(-3,2) and C(1,2).

Distance formula:

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

Using distance formula, we get

[tex]AB=\sqrt{(-3-(-3))^2+(2-(-3))^2}[/tex]

[tex]AB=\sqrt{(0)^2+(5)^2}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5[/tex]

Similarly,

[tex]BC=\sqrt{(1-(-3))^2+(2-2)^2}=4[/tex]

[tex]AC=\sqrt{(1-(-3))^2+(2-(-3))^2}=\sqrt{16+25}=\sqrt{41}[/tex]

From the above calculation it is clear that AC>AB and AC>BC.

According to Pythagoras theorem, in a right angle triangle, the square of largest side is equal to the sum of squares of two small sides.

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

[tex]AC^2=(\sqrt{41})^2=41[/tex]

[tex]AB^2+BC^2=(5)^2+4^2=24+16=41=AC^2[/tex]

So, given triangle is a right angle triangle and AC is its hypotenuse.

Therefore, the correct options are 2, 5 and 7.

Answer:

21

[tex] \frac{1}{3} s = 7 \\ s = 7 \times 3 \\ s = 21[/tex]

The 2 triangles are congruent

Answer:

Divide the diameter by 2.

Step-by-step explanation:

The radius of any circle is always the end to the center.

The diameter is a point of the circle to the opposite side.

This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.

Hope this helped!

Answer:

Divide the diameter by 2. d/2=r

Step-by-step explanation:

If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.

If the diameter was 10, the radius would 10/2=5.

Answer:

5⁻³ = 1/5³ = 1/125

Answer: 1/125

Step-by-step explanation:

Answer: Its everthing except irrational

Step-by-step explanation: