Find the side lengths in the following triangle.

In this question, the client will buy one item, which is composed by a boot, a pair of skis and a hat. Since the items are independent, the fundamental counting principle can be used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

60 boots, 30 pairs of skis, 40 hats. So

60*30*40 = 72,000

The customer can purchase an item in 72,000 ways from the store.

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Answer:

the log function is the "inverse" function of an exponential function

by definition  [tex]log_{a} b = c[/tex]  then [tex]a^{c} = b[/tex]

in this problem you have [tex]log_{10} 100[/tex]

thus what x solves this ?  [tex]10^{x} = 100[/tex]  the answer is [tex]10^{2}[/tex]

thus (100,2)

B) the x intercept is when y = 0

   [tex]10^{0} = 1[/tex]

   x intercept at (1,0)

C) at 100, the curve will hit y = 5000

Step-by-step explanation:

Answer:

Mother is presently 34

Scott is 11

Step-by-step explanation:

Let the mother's age = x

Let the son's age = y

First Equation

x + y = 45

Second equation

3*(x + 5) - 9 =  y+5                Add 9 to both sides

3(x + 5) = y + 5 + 9

3(x + 5) = y + 14                    Remove the brackets

3x + 15 = y + 14                    Subtract 14 from both sides

3x + 15 - 14 = y

3x + 1 = y

Put the first equation into the second equation

x + y = 45                             Subtract y from both sides

y = 45 - x

Put this value for y into the second equation's results.

3x + 1 = 45 - x                       Add x to both sides

3x + x + 1 = 45                    

4x + 1 = 45                            Subtract 1 from both sides

4x = 45 - 1

4x = 44                                Divide by 4

x = 44/4

x = 11

x + y = 45

11 + y = 45

y = 34

Answer:

37.5%

Step-by-step explanation:

150/450 = .375 = 37.5%

The percentage is 150 grams out of 400 grams will be 37.5%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

It is given that the difference between the initial and final value is 15 grams and the initial value is 400 grams.

Then the percentage is 150 grams out of 400 grams will be

P = (150 / 400) x 100

P = 0.375 x 100

P = 37.5%

Thus, the percentage is 150 grams out of 400 grams will be 37.5%.

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Answer:

(8,7)

Step-by-step explanation:

Because our x-value for this ordered pair is 1, and it says to move to the right 7 units, 1+7 = 8. Therefore, our x-value for the ordered pair would be 8.

Because our y-value for this ordered pair is 6, and it says to move up 1 unit, 6+1=7. Therefore, our y-value for the ordered pair would be 7.

Once we have our x- and y-value, we can set up the ordered pair:

(8,7)

Answer:

(7, 8)

Step-by-step explanation:

In the picture below, when the point is moved up, it only changes the y part of the point, and the x part is kept the same. When the point is moved right by 7 units, the x part is changed while the y part is kept the same.

Hope this helps.

Answer:

4w = -5-19

4w=-24

w=-6

hope that answers your question

good luck

Answer:

7-4*(-1)

7-4*(-1)7+4

7-4*(-1)7+411

Step-by-step explanation:

hope it will help u

Answer:

A(- 1) = 11

Step-by-step explanation:

Substitute x = - 1 into A(x) , that is

A(- 1) = 7 - 4(- 1) = 7 + 4 = 11

Answer:

Krishna is at the 7th floor

Step-by-step explanation:

Given

[tex]Start = 12[/tex]

[tex]Up = 3[/tex]

[tex]Down = 8[/tex]

Required

The current floor

This is calculated as:

[tex]Floor = Start + Up - Down[/tex]

[tex]Floor = 12 + 3 - 8[/tex]

[tex]Floor = 7[/tex]

Answer:

a is the perimeter which is given as 820 mm.

Step-by-step explanation:

Perimeter, P = 820 mm

Length is 100 m less than twice of width

let the length is x and the width is y.

So,

x = 2 y - 100

P = 2 (x + y)

820 = 2 (2y - 100 + y)

410 = 3 y - 100

3 y = 510

y = 170 mm

x = 2 x 170 - 100 = 240 mm

The equation is

2 x = 2 y = a

where, a is the perimeter which is given as 820 mm.

Answer:

[tex]U = x[/tex]

[tex]V=10[/tex]

Step-by-step explanation:

Given

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Required

Find U and V

We have:

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Expand

[tex]x^2 + 6x + 9 + 14x + 42 + 49 = (U + V)^2[/tex]

Collect like terms

[tex]x^2 + 6x + 14x + 9 + 42 + 49 = (U + V)^2[/tex]

[tex]x^2 + 20x + 100 = (U + V)^2[/tex]

Expand

[tex]x^2 + 10x + 10x + 100 = (U + V)^2[/tex]

Group

[tex][x^2 + 10x] + [10x + 100] = (U + V)^2[/tex]

Factorize each group

[tex]x[x + 10] + 10[x + 10] = (U + V)^2[/tex]

Factor out x + 10

[tex][x + 10][x + 10] = (U + V)^2[/tex]

So, we have:

[tex][x + 10]^2 = (U + V)^2[/tex]

By comparison

[tex]U = x[/tex]

[tex]V=10[/tex]

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

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

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer:

-26 sqrt(3)

Step-by-step explanation:

-12 sqrt(12) - 2 sqrt(3)

Rewriting

-12 sqrt(4*3) - 2 sqrt(3)

We know sqrt(ab) = sqrt(a)sqrt(b)

-12 sqrt(4)sqrt(3) - 2 sqrt(3)

-12 (2) sqrt(3) - 2 sqrt(3)

-24 sqrt(3) - 2 sqrt(3)

-26 sqrt(3)

Answer:

(x + 74) - 318 = 200

x + 74 = 200 + 318

x +74 = 518

x = 518 - 74

x = 444

Answer:

y= -6

x = 2

(2,-6)

Step-by-step explanation:

Indepedent variable = x = 2

Plug 2 in for x

f(2) = -5(2) + 4

-10 + 4 = -6

y = -6

Answer:

(a,a)

Step-by-step explanation:

Keep in mind that the vertical line represents the y axis and the horizontal line represents the x axis

We want to find the coordinates of C

We can do this by looking at the given coordinates and the axis..

We are given that B is at (0,a) and we are given that D is at (a,0)

Now looking at C, we can tell that C shares the same y value as B and the same x value as D

If B has a y value of a and D has an x value of a then C would have an x and y value of a

Hence C would be at (a,a)

Answer:

the red marble was kept out so you can not draw it again

Answer:

Yes; you may not get a red marble again.

Step-by-step explanation:

there is a chance to get a red marble but it is not high

Answer:

Corresponding angles postulate

Step-by-step explanation:

<3 and <7 are corresponding angles and if corresponding angles are equal, the lines are parallel.

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

[tex]\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

[tex]\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta[/tex]

Simplify. The denominator uses the difference of two squares pattern:

[tex]\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

[tex]\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Split into two separate fractions:

[tex]\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta[/tex]

Rewrite the two fractions:

[tex]\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta[/tex]

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

[tex]\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta[/tex]

Hence verified.

Answer:

w+5/w - w+1/2w

w+9/2w

Step-by-step explanation:

Answer:

A&D are corect

Step-by-step explanation:

combine like terms

9514 1404 393

Answer:

  can't be done. x = 6, not 36

Step-by-step explanation:

Without the diagram we must speculate that the 150 cm length is the hypotenuse. Then we have ...

  150² = (7x)² +(24x)² = (49 +576)x² = 625x² . . . . Pythagorean relation

  150²/625 = x² = 36 . . . . . divide by 625

  x = √36 . . . . . . . . . . . take the square root

  x = 6

Answer:

find the indicated functional value for the floor function: f(-3/2)

B. 0

Step-by-step explanation:

hope it helped.

° ° °

The indicated functional value for the floor function is option (C) -1 is the correct answer.

The floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted floor(x) or f(x). It gives the largest nearest integer of the specified value.

For the givens situation,

The floor function is f(-3/2).

The indicated functional value for the floor function is

⇒ [tex]f(-3/2)= f(-1.5)[/tex]

Here x = -1.5, the indicated functional value should be a greatest integer less than or equal to x.

Thus the indicated functional value of [tex]f(-1.5)[/tex] is [tex]-1[/tex].

Hence we can conclude that the indicated functional value for the floor function is option (C) -1 is the correct answer.

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Answer:

I think it would be 100%

Step-by-step explanation: because it is certain that means its going to happen

Answer:

Fraction of profit from other departments = 17/28

Step-by-step explanation:

Total profit of R. White and Co = 6/7 million dollars

Profit from the spinning department = 1/4 of million dollars

Fraction of profit from other departments = Total profit of R. White and Co - Profit from the spinning department

= 6/7 million dollars - 1/4 of million dollars

= 6/7 - 1/4

Lowest common multiple (LCM) of 7 and 4 is 28

= (24-7) / 28

= 17/28

Fraction of profit from other departments = 17/28

Answer:

x = 2 ±sqrt( 97)

Step-by-step explanation:

log10(x^2 -4x+7) =2

Raise each side to the base 10

10 ^ log10(x^2 -4x+7) =10^2

x^2 -4x +7 = 100

Subtract 7 from each side

x^2 -4x+7-7 = 100-7

x^2 -4x = 93

Complete the square

-4/2 = -2  (-2)^2 = 4

Add 4 to each side

x^2 -4x+4 = 93+4

(x-2)^2 = 97

Take the square root of each side

sqrt((x-2)^2 )=±sqrt( 97)

x-2 = ±sqrt( 97)

Add 2 to each side

x = 2 ±sqrt( 97)

Answer:

3

Step-by-step explanation:

The value of x is 3 if the volume of the triangular prism is 54 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that  volume of the triangular prism is 54 cubic units.

We have to find the value of x

The volume of the prism with triangular base is 54 unit³.

The base is a triangle with,

base = 4 units

height = x units

height of the prism = 3x

V= 6x²

54= 6x²

Divide both sides by 6

x² = 9

x=3

Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.

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Step-by-step explanation:

The slope of the line is - 5, the equation will be y=-5x-1.

y+5x=-1

The missing equations are;

a + 2b + 3c = 12

3a + 2b + 5c = 22

2a + 4b + 4c = 18

Answer:

a = 2

b = 0.5

c = 3

Step-by-step explanation:

We are told that;

a represent the price per pound of apples

b represent the price per pound of bananas

c represent the price per pound of oranges

The equations system is;

a + 2b + 3c = 12 - - - (eq 1)

3a + 2b + 5c = 22 - - - (eq 2)

2a + 4b + 4c = 18 - - - (eq 3)

Divide through equation 3 by 2 to get

a + 2b + 2c = 9 - - - (eq 4)

Subtract eq 4 from eq 1 to get;

3c - 2c = 12 - 9

c = 3

Put 3 for c in eq(2) and eq 4;

3a + 2b + 5c = 22

3a + 2b + 5(3) = 22

3a + 2b + 15 = 22

3a + 2b = 7 - - - (5)

a + 2b + 2(3) = 9

a + 2b + 6 = 9

a + 2b = 3 - - - (eq 6)

Subtract eq 6 from eq 5 to get;

2a = 7 - 3

2a = 4

a = 2

Put 2 for a in eq 6;

2 + 2b = 3

2b = 3 - 2

2b = 1

b = 1/2

b = 0.5

Answer:

It's A

Step-by-step explanation:

edge 2021

Answer:

No

Step-by-step explanation:

irrational numbers have nonrepeating and non terminating decimals

This decimal stops at one digit so this is a rational number

Answer:

I would say no

Step-by-step explanation:

An irrational number can't be written as a simple fraction.  

Answer:

Mohamad payed 8% of sales tax.

Step-by-step explanation:

First, we need to find the additional amount he paid to find the tax percentage.

70.20 - 65.00 = $5.20

Now, we divided that answer by the original price to find the actual percentage.

5.20/65.00 = 0.08 = 8%

Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.