Look at the figure below

Answer:

306. If you multiply 30 and 9 you will get 270, and if you add 4 * 9, which is 36, you will get 306.

Step-by-step explanation:

I hope that helped you out! :)

The Multiplication of 7 and 2 results to 14.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

We have to multiply 9 x 34.

So, we can split the number 34 as (30 + 4) then

First, 9 x 30 = 270

and, 9 x 4 = 36

Now, add the values

9 x 34

= 270 + 36

= 306

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Answer:

a) The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle PQR is [tex]5\sqrt{2}[/tex].

Step-by-step explanation:

The statement is incomplete. The complete question will be presented below:

Consider the points below: P(2, 0, 2),  Q(−2, 1, 3),  R(4, 2, 4)

(a) Find a nonzero vector orthogonal to the plane through the points

P, Q,  and R. (b) Find the area of the triangle PQR.

a) Let [tex]P(x,y,z) = (2,0,2)[/tex], [tex]Q(x,y,z) = (-2,1,3)[/tex] and [tex]R(x,y,z) = (4,2,4)[/tex]. First, we construct vectors PQ and PR by using the following formulas:

[tex]\overrightarrow{PQ} = Q(x,y,z) -P(x,y,z)[/tex] (1)

[tex]\overrightarrow{PQ} = (-2,1,3)-(2,0,2)[/tex]

[tex]\overrightarrow{PQ} = (-4,1,1)[/tex]

[tex]\overrightarrow{PR} = R(x,y,z) -P(x,y,z)[/tex] (2)

[tex]\overrightarrow{PR} = (4,2,4)-(2,0,2)[/tex]

[tex]\overrightarrow{PR} = (2,2,2)[/tex]

Then, we can find the nonzero vector orthogonal to the plane by means of the following cross product:

[tex]\vec S = \overrightarrow{PQ}\,\times\,\overrightarrow{PR}[/tex]

Which can be solved by the following determinant (Law of Sarrus):

[tex]\vec S = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4&1&1\\2&2&2\end{array} \right |[/tex]

[tex]\vec S = (2-2,2+8, -8-2)[/tex]

[tex]\vec S = (0, 10,-10)[/tex]

The nonzero vector orthogonal to the plane through the points P, Q and R is (0, 10, -10).

b) The area of the triangle is determined by the following formula:

[tex]A = \frac{1}{2}\cdot \|\overrightarrow{PQ}\,\times\,\overrightarrow{PR} \|[/tex]

[tex]A = \frac{1}{2}\cdot \|\vec S\|[/tex] (3)

[tex]A = \frac{1}{2}\cdot \sqrt{0^{2}+10^{2}+(-10)^{2}}[/tex]

[tex]A = 5\sqrt{2}[/tex]

The area of the triangle PQR is [tex]5\sqrt{2}[/tex].

Answer:

q =90

Step-by-step explanation:

q/18=5

Multiply each side by 18

q/18  * 18=5* 18

q =90

Answer:

q = 90

Step-by-step explanation:

Multiply each side by 18:

q = 90

Answer:

25% increase

Step-by-step explanation:

[tex]\frac{(v_{2}- v_{1}) }{|v_{1}| }x100[/tex]

[tex]\frac{25-20}{|20|}x100[/tex]

=[tex]\frac{5}{20}x100[/tex]

=0.25×100

=25% change

=25% increase

Answer:

a) yes

The point ( 1,-3) lie on the given line y = 5x-8

b) No

 The point ( -2,-7) does not lie on the given line y = -3 x +1        

Step-by-step explanation:

Step(i):-

a)   Given line  y = 5 x - 8 ...(i)

   Point ( 1, -3 )

 substitute  ( 1,-3 ) in equation (i)

           -3 = 5(1) - 8

         -3 = 5 -8

         -3 = -3

∴ The point ( 1,-3) lie on the given line y = 5x-8

b)

Given line  y = -3 x +1 ...(i)

   Point ( -2, -7 )

 substitute  (-2, -7 ) in equation (i)

           -7 = -3(-2) +1

         -7 ≠ 7

 The point ( -2,-7) does not lie on the given line y = -3 x +1        

Answer:

I just got this right...hopefully this helps :)

Step-by-step explanation:

Answer:

as a decimal = 0.45

Fraction= 9/20

Step-by-step explanation:

Answer:

The length of the rectangle is of 9 units.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

Area of a rectangle:

A rectangle has width [tex]w[/tex] and length [tex]l[/tex]. The area is the multiplication of these measures, that is:

[tex]A = wl[/tex]

The length of a rectangle is the sum of the width and one.

This means that [tex]l = w+1[/tex], or [tex]w = l - 1[/tex]

The area direct angle 72 units. What’s the length, in units, of the rectangle

We want to find the length. So

[tex]wl = 72[/tex]

[tex](l-1)l = 72[/tex]

[tex]l^2 - l - 72 = 0[/tex]

Quadratic equation with [tex]a = 1, b = -1, c = -72[/tex]. So

[tex]\bigtriangleup = (-1)^{2} - 4(1)(-72) = 289[/tex]

[tex]l_{1} = \frac{-(-1) + \sqrt{289}}{2*(1)} = 9[/tex]

[tex]l_{2} = \frac{-(-1) - \sqrt{289}}{2*(1)} = -8[/tex]

Since the length is a positive measure, the length of the rectangle is of 9 units.

In the given triangle the measure of ∠Q is (B) 73.5°.

So, let's use the Sine rule in the calculation as follows:

Therefore, in the given triangle the measure of ∠Q is (B) 73.5°.

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Answer:

32x^25

Step-by-step explanation:

4x^14*8x^11

Answer:-20=41

Step-by-step explanation:

3(-2-21)-7=41

Answer:

A: 2x^3 + 3x - 5

Step-by-step explanation:

All of the others have fractions in places where they aren't allowed to.

Answer:

A: 2x^3 + 3x - 5

Step-by-step explanation:

Answer:

Proved

[tex]A^2 - B^2 = 20, 40,60,80...[/tex]

Step-by-step explanation:

Given

[tex]A = N + 1[/tex]

[tex]B = N - 1[/tex]

Required

Prove that [tex]A\² - B\²[/tex] is a multiple of 20

First, we need to evaluate [tex]A\² - B\²[/tex]

Start by applying difference of two squares

[tex]A\² - B\² = (A + B)(A - B)[/tex]

Substitute values for A and B

[tex]A\² - B\²= (N + 1 + N - 1)(N + 1 -(N-1))[/tex]

[tex]A\² - B\² = (N + 1 + N - 1)(N + 1 - N + 1)[/tex]

Collect Like Terms

[tex]A\² - B\² = (N + N+ 1 - 1)(N - N + 1+ 1)[/tex]

[tex]A\² - B\² = (2N)(2)[/tex]

[tex]A\² - B\² = 2N*2[/tex]

[tex]A\² - B\² = 4N[/tex]

Since, N is a multiple of 5, then the possible values of N are:

[tex]N = 5, 10, 15, 20...[/tex]

For each of these values, the possible values of [tex]A^2 - B^2[/tex] are

[tex]A^2 - B^2 = 4N: 4 * 5, 4*10,4*15,4*20...[/tex]

[tex]A^2 - B^2 = 20, 40,60,80...[/tex]

The above shows that [tex]A^2 - B^2[/tex] is a multiple of 20

Answer:17

Step-by-step explanation:

5w + 2

5(3) + 2

15 + 2

17

Answer:

5. 40% of Sam's collection of 64 cars is new. How many cars are new?

Known: Number of cars.

Unknown: How many cars are new.

Equation: 64*0.4=x x=24.

6. 90 out of 20 students liked pizza. What percent of students did

not like pizza?

Known: number of students

Unknown: percent of students did not like pizza.

Equation: 90*20/20 = 90.

90>20 so 0% did not like pizza.

Answer:

2,057.18

Step-by-step explanation:

Answer:

0 (b)

Step-by-step explanation:

So we're estimating in this one.

we can round -49/100 to -50/100 and 10/21 to 10/20

Then we can get a common denominator

10/20 will become 50/100

so

-50/100 + 50/100 = 0

So your answer is b.

Answer:

B. 0

Step-by-step explanation:

-49/100 + 10/21

They are both about half

Therefore, since one is negative and the other is a positive they would equal about .02 which the closest number out of the 4 answers would be B. 0

Answer:

the answer is B

Step-by-step explanation:

different sides are marked

Answer:

c.

Step-by-step explanation:

even though that the 2 cides are not congruent to each other, it must be asking for the perimeter of the triangle. we don't know if it is congruent because we do not know the  length of the last side.

Answer:

dont really know this one sorry:)

Step-by-step explanation:

Answer:

50 gallons

Step-by-step explanation:

400/8 = 50

Answer:

50 gallons were poured per hour

Step-by-step explanation:

hope this helps

Hey there!

the slope of the line is [tex]3[/tex]

Slope is [tex]\frac{rise}{run}[/tex], meaning that the slope is [tex]\frac{3}{1}[/tex] or [tex]3[/tex]

Hope it helps and have a great day!

Answer = b. 7

THANK YOU FOR LISTENING TO MY TED TALK

Answer: He drove 42 miles per gallon and remainder 4.

Step-by-step explanation:

Answer:

[tex]a = 9in[/tex]

Step-by-step explanation:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]

[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]

[tex]a = \sqrt{ {10.6}^{2} - {5.6}^{2} } [/tex]

[tex]a = \sqrt{112.36 - 31.36} [/tex]

[tex]a = \sqrt{81} [/tex]

[tex]a = 9in[/tex]

Answer:

tito

Joshua

Caleb

Arthur

Answer:

go and watch a movie together

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees.

Let the third angle be x.

Add all the quantities and subtract the answer from 180.

So: 180= 40+60+x

      180-100=x

      80=x

Answer:

the third one

List 3

Step-by-step explanation:

1*100=100

2*50=100

4*25=100

5*20=100

10*10=100