Given the vectors ⃗⃗ = 〈2, 3, 5〉, ⃗ = 〈−2, 5, 0〉, ⃗⃗ = 〈−3, 2, 7〉 calculate:
a) ⃗⃗ + ⃗ + ⃗⃗

Answer:

Step-by-step explanation:

Pythagorean Theorem Formula: a² + b² = hypotenuse²

x² + 5² = 13²

x² + 25 = 169

x² + 25 - 25 = 169 - 25 (subtract 25 in both sides)

x² = 169 - 25

√x² = √144

x = 12

Answer:

208 ft^3

Step-by-step explanation:

Let the plane through the 4 ft X 4ft square at the top of the figure break the figure into 2 boxes, one has dimensions (8-7) by 3 by 4 = 1ft X 3ft X 4ft, and the other has dimensions 7 by 7 by 4 = 7ft X 7ft X 4ft.

They have volumes of (1)(3)(4) = 12 ft^3, and (7)(7)(4) = 196 ft^3, respectively, so the total volume = 12 + 196 = 208 ft^3, the answer.

Answer:

6/5

Step-by-step explanation:

4/5 divided by 2/3 in simplest form is 6/5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

4/5 divided by 2/3

Now,

=(4/5)/(2/3)

=12/10

=6/5

Therefore, by algebra answer in simplest form will be 6/5.

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Answer: 1/3

Step-by-step explanation:

1/3

Answer:

A. 8

The missing side is 8

Answer:

Construction of 60° exactly

Trigonometric ratios are useful in calculating the side lengths of a triangle.

(a) Length, z

First we calculate (h) using the following sine ratio

[tex]\mathbf{sin(75) = \frac{h}{40}}[/tex]

Make h the subject

[tex]\mathbf{h = 40sin(75)}[/tex]

Next, we calculate (z) using the following sine ratio

[tex]\mathbf{sin(10)= \frac{h}{z}}[/tex]

Make z the subject

[tex]\mathbf{z= \frac{h}{sin(10)}}[/tex]

Substitute [tex]\mathbf{h = 40sin(75)}[/tex]

[tex]\mathbf{z= \frac{40sin(75)}{sin(10)}}[/tex]

[tex]\mathbf{z= 222.5 ft}[/tex]

Hence, the length of the zip line is 222.5 ft

(b) The height, h

In (a), we have

[tex]\mathbf{h = 40sin(75)}[/tex]

Evaluate

[tex]\mathbf{h = 38.6}[/tex]

Hence, the height where the ladder rests against the tree is 38.6 ft

(c) The distance, b

To do this, we make use of the following sine ratio

[tex]\mathbf{sin(15) = \frac{b}{40}}[/tex]

Make b the subject

[tex]\mathbf{b = 40sin(15)}[/tex]

[tex]\mathbf{b = 10.4}[/tex]

Hence, the distance between the base of the ladder and that of the tree is 10.4 ft

(d) Distance, B

To do this, we make use of the following sine ratio

[tex]\mathbf{sin(80) = \frac{B}{z}}[/tex]

Make B the subject

[tex]\mathbf{B = z\ sin(80)}[/tex]

Substitute [tex]\mathbf{z= 222.5 ft}[/tex]

[tex]\mathbf{B = 222.5\ sin(80)}[/tex]

[tex]\mathbf{B = 219.1}[/tex]

Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft

Read more about trigonometry ratios at:

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[tex]\large\underline{\sf{Solution-}}[/tex]

Given that:

[tex]\sf p(y) = 2y^3+my^2+11y+m+3 [/tex]

We are also given that, p(y) is divisible by 2y - 1.

So, 2y - 1 is a factor of p(y).

[tex]\sf\longmapsto 2y-1=0[/tex]

[tex]\sf\longmapsto y=\dfrac{1}{2}[/tex]

So, 1/2 is a zero of p(y).

[tex]\sf\longmapsto p(1/2) =0 [/tex]

[tex]\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 [/tex]

[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 [/tex]

So,

[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 [/tex]

[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 [/tex]

[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} [/tex]

[tex]\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} [/tex]

[tex]\sf\longmapsto 0 =\dfrac{5m+35}{4}[/tex]

[tex]\sf\longmapsto 5(m+7)=4\times0[/tex]

[tex]\sf\longmapsto 5(m+7)=0[/tex]

[tex]\sf\longmapsto m+7=0[/tex]

[tex]\longmapsto\bf m=-7[/tex]

Therefore, the value of m is -7.

Answer:

12x15=100

Step-by-step explanation:

Its times because I know it

Answer:

X = 5/3

Step-by-step explanation:

-14 + 6x = 1 - 3x

-14 + 9x = 1

9x = 15

x = 5/3

Hope this helps! Pls give brainliest!

Answer:

Step-by-step explanation:

Value of x

-14 + 6x = 1 - 3x

=> 6x + 3x = 1 + 14

=> 9x = 15

[tex] = > x = \frac{15}{9} [/tex]

[tex] = > x = \frac{5}{3} [/tex]

[tex] = > x = 1 \frac{2}{3} (ans)[/tex]

Answer:

7452

Step-by-step explanation:

Answer:

Sample Response: First, write 828 as a sum of 800 + 20 + 8. Next, multiply each number by 9. Add the products to get 7,452.

Step-by-step explanation: edge 2021

Answer:

[tex]x=4\frac{1}{8}[/tex]

Step-by-step explanation:

Step 1: Multiply (2x+5) by [tex]-\frac{3}{4}[/tex].

[tex]-\frac{3}{4}(2x+5)=-\frac{3}{4}*2x-\frac{3}{4}*5=-\frac{3}{2}x-\frac{15}{4}[/tex]

The equation becomes [tex]2\frac{1}{2}x-\frac{3}{2}x-\frac{15}{4}=\frac{3}{8}[/tex]

Step 2: Combine all terms that have a variable.

[tex]2\frac{1}{2}x-\frac{3}{2}x=\frac{5}{2}x-\frac{3}{2}x=\frac{2}{2}x=x[/tex]

The equation becomes [tex]x-\frac{15}{4}=\frac{3}{8}[/tex]

Step 3: Add [tex]\frac{15}{4}[/tex] to both sides of the equation.

[tex]x-\frac{15}{4}+\frac{15}{4}=\frac{3}{8}+\frac{15}{4}[/tex]

[tex]x=\frac{3}{8}+\frac{15}{4}=\frac{3}{8}+\frac{30}{8}=\frac{33}{8}=4\frac{1}{8}[/tex]

[tex]x=4\frac{1}{8}[/tex]

Rs. 250000 was the price of the refrigerator.

Let x represent the price of the refrigerator.

Since she made a Rs. 40,000 down payment. On delivery paid another Rs. 80,000 and owed 60% of the purchased price. Hence:

Total Money paid = 100% - 60% = 40% of purchased price

40000 + 60000 = 40% of x

100000 = 0.4x

x = Rs. 250000

Hence, Rs. 250000 was the price of the refrigerator.

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14÷0.50

=28

Hope this helped you- have a good day bro cya)

Answer:

they are already matched

Step-by-step explanation:

Answer: (x^7)/(x^4) = x^3, x^(-3) = 1/(x^3), x^0 = 1, (x^4)/(x^3) = x

Step-by-step explanation:

Dividing two exponents with the same base can be simplified by subtracting the exponents. Thus (x^7)/(x^4) is the same as x^(7-4), or x^3.

A negative exponent is the same as the reciprocal of the positive exponent. x^-3 is the same as 1/(x^3).

Anything with an exponent of 0 is equal to 1.

Again, when dividing two exponents, if they have the same base, you can just subtract the exponents. (x^4)/(x^3) = x^(4-3) = x^1 = x.

Answer:

x = 32

(The answer should be 32 if we are solving for x)

Answer:

[tex]for \: \: dmain \: of \: {f}^{ - } \: \: is \: equal \: f \: range \\ y = \sqrt{x } - 5 \\y \: range \: is \: y \geqslant - 5\\ y + 5 = \sqrt{x} \\ x = {(y + 5)}^{2} \\ {f}^{ - 1} = {(x + 5)}^{2} \\ \\ dmain \: of \: \: {f}^{ - 1} \: x \geqslant - 5[/tex]

Answer:

B

Step-by-step explanation:

the line pass through the point (2.52) and (14.78)

So k= 78-52 =26 =

4-2 =2

Answer:

A well-defined collection of elements is a set.

Hi there! :)

4x=-36

Divide both sides by 4 in order to isolate x:

x=-9

Hope this helps you and have a nice day!

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

70.5%

Step-by-step explanation:

[tex] \frac{1 + \frac{41}{100} }{2} = \frac{x}{100} [/tex]

I wish I could help

No need to type in the percent symbol as that's already taken care of.

==============================================================

Explanation:

The square on the left is fully shaded in to represent 100% so far.

The square on the left is partially shaded in to represent an additional percentage on top of that 100%.

Note that we have 10 rows and 4 columns of white squares, so 10*4 = 40 white squares. Plus the additional white square to the right to get 41 white. That means there are 100-41 = 59 blue squares shaded in. This means that 59% of the second square is shaded blue.

That leads us to 100% + 59% = 159%

Answer:

hii

Step-by-step explanation:

plzz see attachment

hope it helps u

plz mark as brainliest

Answer: A  F D G

Step-by-step explanation:

Answer:

$2.50 × 4 = $10

so $10 is equal to 4 pairs of socks.

The average distance traveled by Steven in 1 month is 1,005 miles.

So, average miles traveled in 1 month:

So, the average distance traveled in 1 month is:

Therefore, the average distance traveled by Steven in 1 month is 1,005 miles.

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Answer:

The average distance traveled by Steven in 1 month is 1,005 miles.

Step-by-step explanation:

Answer:

a. Find y if w = -4 --- y = 14

b. Find y if w = 10 --- y = -14

Step-by-step explanation:

This is all about substitution!! For question a, we need to substitute "w" with "-4" ...

2 (-4) + y = 6

We know that a positive time a negative equals a negative...so 2 · -4 is -8.

-8 + y = 6

Now let's add 8 on both sides to isolate the variable...which equals to

y = 14

Onto question b...We substitute w with 10.

2 (10) + y = 6

 = 20 + y = 6

Subtract 20 from both sides to isolate "y"

y = -14

Hope this helpsss :D

Answer:

there is no line parallel to y = -3x + 8 that goes through (5, -7). this point falls on this line

Step-by-step explanation:

[tex]y = - 3x + 8[/tex]

[tex] - 7 = - 3(5) + b \\ - 7 = - 15 + b \\ b = 8[/tex]

The answer is

[tex]y = - 3x + 8[/tex]