Given the figure below, find the values of x and z. z° 68° +14x84°

4. If v = -2i - 7j, then its magnitude is

||v|| = √((-2)² + (-7)²) = √53

and the unit vector in the direction of v is

[tex]\dfrac{v}{\|v\|} = \boxed{-\dfrac2{\sqrt{53}} \, \vec\imath - \dfrac7{\sqrt{53}} \, \vec\jmath}[/tex]

5. Given u = i + 2j and v = -i + 5j, we have

u • v = (i + 2j) • (-i + 5j) = -(i • i) - 2 (j • i) + 5 (i • j) + 10 (j • j)

Since i and j are orthogonal unit vectors, we have i • i = j • j = 1 and i • j = 0, so the product reduces to

u • v = -1 - 0 + 0 + 10 = 9

The surface area of the square based pyramid is 61.25 centimetre square

surface area of the pyramid = A + 1 /2 ps

where

A = area of the base

p = perimeter of the base

s = slant height

Therefore,

A = 3.5² = 12.25 cm²

p = 4(3.5) = 14 cm

s = 7 cm

Therefore,

surface area of the pyramid = 12.25 + 1 /2 × 14 × 7

surface area of the pyramid = 61.25 cm²

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Answer:

32

Step-by-step explanation:

7×18+2×18=32

x=14

y=18

Have a great day!

Answer:

[tex]4649 \div 39 = 119.205128295[/tex]

Step-by-step explanation:

I hope it's help u

Answer:

119 R 8

Step-by-step explanation:

convert 4649 to tens place, write 1

46 - 39 = 7

drop the 4 in the tens place, write 1

74 - 39 = 35

drop the 9 in the ones place, write 9

359 - 351 = 8

• For each time we got 39 or another number, we wrote the multiple of that number we used to get the result.

• We got the remainder by the general subtraction.

Hey there!

x^2 – y

= 4^2 – 2

= 4 * 4 - 2

= 16 - 2

= 14

Therefore, the answer should be: 14

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Hey there!

[tex] \displaystyle \blue{\boxed{\green{\bold{v = 8}}}} [/tex]

[tex] \\ [/tex]

-5v + 6 = -12v + 62

[tex] \\ [/tex]

▪️Subtract 6 from both sides :

-5v + 6 - 6 = -12v + 62 - 6

-5v = -12v + 56

▪️Add 12v to each side :

-5v + 12v = -12v + 56 + 12v

7v = 56

▪️ Divide both sides by 7 :

7v / 7 = 56 / 7

v = 8

[tex] \\ [/tex]

Therefore, our answer is v = 8.

[tex] \\ [/tex]

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Answer:

v = 8

Step-by-step explanation:

Hello!

We can solve the equation by moving all terms of V to one side, and all integer values to the other.

The value of v is 8.

We can plug back 8 into the original to check our answer:

Since both sides match, the solution of v = 8 is correct.

Answer:

#9 is 6 #10 is 1 #11 is 7 #12 is 6

Step-by-step explanation:

Equation to show the proportional relationship between the regular price, r, of an item and its sale price, s is 10s -7r=0.

A sale price is the discounted price at which goods or services are being sold. This price is usually offered for a limited period of time, typically to spur sales during a slow period or to sell off excess inventory.

Let the regular price be r and sale price be 's'

Since price of every item reduced by 30%.

So, sale price will be

[tex]s= r- 30% of r[/tex]% of r

[tex]s= r- \frac{30}{100} *r[/tex]

s= r - 0.3 r

s= 0.7 r

s-0.7r=0

or, 10s -7r=0

Thus, equation shows the proportional relationship between the regular price, r, of an item and its sale price, s :10s -7r=0

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Answer:

$00.245

Step-by-step explanation:

.98/4=00.245

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Step-by-step explanation: answer: 108

270

[tex]270 \times \frac{60}{100} [/tex]

[tex]27 \times 6 = 162[/tex]

270=60%

60% =162

40% = not going

270 students - 60% 162= 108

→108 students are not going

Answer:

270 students - 60% 162= 108

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Just do it backwards.

94 - 12 = 82.

82 + 6 = 88.

88 - 18 = 70.

Answer:

65º

Step-by-step explanation:

Angles in a triangle add to 180º so:

180- 44 - 71 = 180 - 115 = 65º

Answer:

408.40704

Step-by-step explanation:

Answer:

38400/=

Step-by-step explanation:

8(p-1500)=8p-12000

2(p+1000)= 2p+2000

8p-12000+2p+2000=53000

10p-10000=53000

10p=53000+10000

10p=63000

p=6300/=

8 books=8(6300-1500)

=38400/=

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

[tex]3x+2=14\\\\3x+2-2=14-2\\\\3x=12\\\\\displaystyle \frac{3x}{3}=\frac{12}{3}\\ \\ x=4[/tex]

Answer:

  313°

Step-by-step explanation:

The reference angle (α) can be found using the tangent relation:

  Tan = Opposite/Adjacent

__

In this problem, that means ...

  tan(α) = 78/83

  α = arctan(78/83) ≈ 43° . . . . . . angle from -x axis

The bearing angle will be this value added to 270°, since bearing angles are measured clockwise from north.

  bearing = 270° +43° = 313°

Answer:

D. 293

Step-by-step explanation:

He delivers 38 papers each day of the week except sunday, so six days a week

38 x 6 = 228

228 + the 65 he delivers on sunday = 293 papers a week

Answer:

2,48,000

Step-by-step explanation:

Answer:

1st choice : 706.5 square inches

Step-by-step explanation:

circumference is pi times diameter

divide 94.2 by pi to get diameter = 29.9847912785

diameter 29.9847912785 divided by 2 is

14.9923956393 which is the radius

area is pi times radius times radius again

pi times 14.9923956393 times 14.9923956393 =

706.141834613

Answer:

A =281 ft^2

Step-by-step explanation:

A=2πrh+2πr^2

A = 2 (3.14) (4)(5) + 2 (3.14) (5)^2

A =281 ft^2

Answer: 33 integers

Step-by-step explanation:

The numbers with a factor of 3 must be a multiple of 3. Therefore, since 99 is the greatest multiple of 3 that is less than 100, we can divide 99 by 3 to get 33 integers (for every 3 consecutive integers, there is one multiple of 3). We can also divide 100 by 3 to get 33 1/3, which rounds to 33 integers.

I hope this helps!

Answer:

.0022

Step-by-step explanation:

Answer:

600 inches or 50 feet

Step-by-step explanation:

Scale factor = model car : actual car = 1 : 300

We have a 2 inch model car.

Answer:

Area = 3430

Step-by-step explanation:

Graphing y = 28x - x^2 with it's limit interval (0<x<28). They ask for four sub-interval of LRAM.

Divide the base of 28 into 4 equal rectangles.

Area = (Base * Height) + (Base * Height) + (Base * Height) + (Base * Height)

Area = (0 * 7) + (147 * 7) + (196 * 7) + (147 * 7)

Area = 3430

The values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively

The function is given as:

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

When x = 1, we have:

y = (1 +3)(1 - 2)

y = -4

When x = 2, we have:

y = (2 +3)(2 - 2)

y = 0

Hence, the values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively

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Answer:

a) 20

Step-by-step explanation:

90 - 46 = 44

44 - 4 = 40

40/2 = 20

If there is 15% off and the sales tax rate is 8.25%. Then the price of the car will be $ 8,189.11.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%.

The cost after 15% off will be

→ 0.85 × $8,900

→ $ 7,565

Then the final cost after the sale tax of 8.25% will be

Cost = $ 7,565 × 1.0825

Cost = $ 8,189.11

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Once he passes his friends, The miles Josiah has left to run would be 10.95 miles.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

Josiah is running a marathon which is 26 1/5 miles long.

At four 1/4 miles from the start, he meets his wife, who is cheering him on.

7 1/2 miles further down the marathon course.

26 1/5 = 131/ 5

7 1/2 = 15/2

The marathon run by Josiah

= 1/4 + 15/2

= 15.25

The miles Josiah has left to run

= 131/ 5 - 15.25

= 10.95

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Hey there!

EQUATION:

6ac^2

ASSUMING:

= 6(2)(3)^2

SOLVING:

= 6(2)(3^2)

= 12(3^2)

= 12(3 * 3)

= 12(9)

= 108

Therefore, the answer should be: 108

Good luck on assignment & enjoy your day!

~Amphitrite1040:)