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It is proved that ca⇀ and cb⇀ are orthogonal .

Let AO = - u vector , OB = u vector and OC = α vector .

According to question ,

u * u = v * v = r ^ 2 and

AC vector = AO vector + OC vector = u + v

BC vector = BO vector + OC vector v - u ,

Applying dot - product ,

( AC vector ) . ( BC vector ) = ( v + u ) . ( v - u )

                                            = ( v . v ) - ( u . u )

                                          = ( r ^ 2 ) - ( r ^ 2 )

                                           = 0

Hence , AC and BC are orthogonal .

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Answer: 5 m³

Step-by-step explanation:

    We will break the figure into two different parts.

    Volume of a rectangular prism can be found with V = L * W * H

V = L * W * H

V = (2 m) * (1.5 m) * (1.5 m)

V = 4.5 m³

-

V = L * W * H

V = (2 m) * (2 m - 1.5 m) * (0.5 m)

V = 0.5 m³

    Now, we will add them together.

4.5 m³ + 0.5 m³ = 5 m³

Answer:

5m³

Step-by-step explanation:

Hello!

You can picture this rectangular prism as a whole prism with a part removed.

The dimensions of the whole prism are 1.5m, 2m, and 2m.

The part cut out is 1m, 0.5m, and 2m.

We can find the volume of the whole rectangular prism and subtract the volume of the removed part.

Since the units of length are meters, the volume should be represented as meters³. The volume is 5m³.

The angle for shooting laser gun should be 89.98°.

The vertical height where a tiny but horrible alien is standing is given as 443443443 meters. The horizontal distance of a men in black agent from building is given in the question as 181818 meters. So, let us assume the angle formed to be theta (θ).

Writing the formula for tan theta, that relates the given height and distance

Now, tan θ = vertical height ÷ horizontal distance

Keep the values in above mentioned equation of theta to find the angle.

tan θ = [tex]\frac{443443443}{181818}[/tex]

Performing division to find the tan theta and subsequently calculate the angle

tan θ = 2438.94

θ = tan⁻¹ 2438.94

Calculating tan inverse to find the value of theta

θ = 89.98°

Therefore, the  angle for shooting laser gun by a men in black agent  should be 89.98°.

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The amount that James left has left after paying his friend 10% is; $80.325

We are told that James and his friend both earn $8.5 per hour. Thus;

Amount earned by James per hour = $8.5

Amount earned by the friend per hour = $8.5

Total time James works in his first week = 10 ¹/₂ hours

Now, James agreed to pay his friend 1/10 of his salary

Thus, amount that James earned is;

10.5 * 8.5 = $89.25

Thus, amount he has left after paying his friend 10% is;

(100% - 10%) * $89.25 = $80.325

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Answer:

Step-by-step explanation:

1+(-2/3)-(-9/2)\

1-2/3+9/2

29/6

This warm-up serves two purposes. It refreshes the concept of distance, rate, and time of travel from grade 6, preparing students to use scale drawings to solve speed-related problems.

It also allows students to estimate decimal calculations.

Students are likely to approach the question in a few different ways. As students work, notice students using each strategy.

By finding or estimating the speed of the train in miles per hour and comparing this to the speed of the car

By finding the distance the car travels in 4 hours and comparing it to the distance the train travels in 4 hours

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Answer:

c

Step-by-step explanation:

The number of solutions of the equation [tex]5x^2+7x-4=0[/tex] is 2. Option (c) is correct.

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

The polynomial function has n roots or zeroes.

Given:

The equation is [tex]f(x)=5x^2-7x-4=0[/tex]

According to the Fundamental Theorem of Algebra the function has 2 roots

Solve the above equation to obtain the zeros.

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-7\pm \sqrt{7^2-4\cdot \:5\left(-4\right)}}{2\cdot \:5}[/tex]

[tex]\sqrt{7^2-4\cdot \:5\left(-4\right)}[/tex]

[tex]=\sqrt{129}[/tex]

[tex]x_1=\frac{-7+\sqrt{129}}{2\cdot \:5},\:x_2=\frac{-7-\sqrt{129}}{2\cdot \:5}[/tex]

so, x has 2 solutions

Answer:

options c

Step-by-step explanation:

I hope it's helpful for you to

Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75

number line - A line on which numbers are marked at intervals and used to illustrate simple numerical operations.

absolute value - absolute value of real number is its distance from the zero.

The absolute value of 2.75 is 2.75 and the absolute value of -2.75 is 2.75

Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75

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The population is the ads selected.

A population is a distinct group of individuals, animals, or objects that can be distinguished from one another for the purposes of data gathering and analysis in statistics and other branches of mathematics.

Now,

In the given number of sales from 100 randomly selected L'oreal Makeup ads,

Hence, the population is the ads selected.

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Answer:

1.66...

Step-by-step explanation:

5/3=

5 * 1/3=

5 * 0.33...=1.66...   ==> with bar on top of the 6

Answer:

-2/45

Step-by-step explanation:

Answer:

x + 4

For the equation to be true, you have to input the x value and it should give you the y value that corresponds. For example, we will input -2. Hopefully we get -7

-2 + 4

2

this means that x + 4 is not correct.

What about -3x? lets see

-3(-2)

-6

nope!

2x - 3

2(-2) - 3

-4 - 3

-7!!

2x - 3 is the answer!!

Step-by-step explanation:

Answer:

50mm

Step-by-step explanation:

From the smaller to the larger:

Let s + the scale factor

3s = 10  Divide both sides by 3

s = [tex]\frac{10}{3}[/tex]

15[tex](\frac{10}{3})[/tex] = [tex]\frac{150}{3}[/tex] = 50

Answer:

should be -1,4

Step-by-step explanation:

Answer:

the answer is blank, don't type anything in just f a I l

Answer:

[tex]2 \sqrt{3} [/tex]

Answer:

23.5kg

Step-by-step explanation:

the total mass of the things he bought is what we are asked to find.

13kg of onions+3.5kg of potatoes+7kg of cabbage is the total mass he carried home.

=23.5kg

The perimeter of the triangle is 40 feet .

Kat is painting the edge of a triangular stage prop with reflective orange paint. the lengths of the edges of the triangle are (3x – 4) feet, (x2 – 1) feet, and (2x2 – 15) and x = 4

Now , According to the question:

Let the sides of triangle be a , b , c

a = 3x -4

b = x^2 -1

c = 2x^2 - 15

x = 4

Substitute the value of x in a, b , c

a = 3 × 4 -4 = 8 feet

b = 4 × 4 -1 = 15 feet

c = 2× 4× 4 - 15 = 17 feet

The perimeter of the triangle is sum of all sides

then, a + b + c

= 17 + 15 + 8 = 40 feet

Hence, The perimeter of the triangle is 40 feet .

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At least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

What is Division by Sharing?

let the number of gummy bears bag = x

9x/8 = 5

9x = 40

x = 4.4

Thus, at least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

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The height h will be equal to 13 cm for the parallelogram.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.

Given that a right-angled triangle and a parallelogram are shown b

13 cm and 6 cm. The area of the parallelogram is 4 times the area of the right angle.

The height h will be calculated as,

A= 1/2 x6 x 13 = 3 x 13 =39 square

Area of the parallelogram is,

39=156cm square

156 divided by 12

h=13 cm

Therefore, the height h will be equal to 13 cm for the parallelogram.

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The probability of  getting 2 on the first roll and not getting 4 on the second roll is 5/36.

The two events mentioned are independent.

Given, first event getting 2 on the first roll and second event getting 4 in second roll.

So, the first roll of the die is independent of the second roll.Therefore, the probabilities can be directly multiplied.

P (getting first 2) = 1/6

P (no second 4) = 5/6

Therefore P (getting first 2 and no second 4) = 1/6 x 5/6  = 5/36

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Answer: B

Step-by-step explanation:

Answer:

I don't know it like off

Answer:

Step-by-step explanation:

$52.00

In a linear equation value of x and y  (x, y) = ( -2 , 6) when the graph of y=-3x and x=-2 intercept .

What in mathematics is a linear equation?

y= - 3x

Put x = -2 put in the equation

y = -3  * -2

y = 6

So, value of x and y  (x,y) = ( -2 , 6)

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If (-7,2) is a point on a circle centered at (0,2), the equation represents the circle is [tex]x^{2} +(y-2)^{2}=49[/tex]

Given,

Center of the circle = (0,2)

One point on the circle = (-7,2)

First we have to find the distance between the center and the given point

that is the radius of the circle.

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} } \\d=\sqrt{(0+7)^{2}+(2-2)^{2} } \\d=\sqrt{49}[/tex]

d= 7  units

The standard equation of  the circle

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Substitute the values in the equation

[tex](x-0)^{2}+(y-2)^{2}=7^{2} \\x^{2} +(y-2)^{2}=49[/tex]

Hence, If (-7,2) is a point on a circle centered at (0,2), the equation represents the circle is [tex]x^{2} +(y-2)^{2}=49[/tex]

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Answer:

Step-by-step explanation:

Answer: $1.05

Step-by-step explanation:

March has 31 days

Hence,

[tex]\displaystyle\\32.55:31=\\\\32\frac{55}{100}*\frac{1}{31} =\\\\32\frac{11}{20} *\frac{1}{31} =\\\\\frac{(32)(20)+11}{(20)(31)} =\\\\\frac{640+11}{620} =\\\\\frac{651}{620}=[/tex]

$1.05

Reason:

There are two mountain peaks, which show the two modes (at 0.27 and 0.31). Therefore, this data set is bimodal.

The data set is also symmetric because of the mirror line at 0.29; stuff to the left of 0.29 can be reflected over the mirror line to get the stuff on the right side.

We can rule out choice A since the curve doesn't represent a normal distribution. A normal distribution has exactly one mode only.

Choice C is ruled out because a skewed distribution isn't symmetric, and vice versa.

The data set isn't uniform since all stacks of points aren't the same height. This rules out choice E.

Answer:

m=-5/13

Step-by-step explanation:

(-4,3) and (9,-2)

y2-y1/x2-x1

-2-3/9+4

-5/13

Hope this helps!

Please mark as brainliest if correct!

the answer of all the 5 expressions is given as : 0, 14, 49, -49, -14 respectively.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here the given expression are :

1)  |-7| - 7 :

now, here considering the modulus value of -7 as 7 that is positive only :

 |-7| - 7 = 7-7 = 0

2) 2|-7| = 2x 7

   2|-7| = 14

3) (-7)² = -7 x -7 = 49

4) -7² = -(7 x 7) = -49

5) -7 -|-7| = -7 - 7 = -14

it should be noted that we have considered only positive value of modulus function only.

Therefore, the answer of all the 5 expressions is given above.

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