Three forces, (15i+j) N, 5qi – pj) N and (-3pi - gj) N, where p and q are
constants, act on a particle.
Given that the particle is in equilibrium, find the value of p and the value of q.

Answer:

4.33

Step-by-step explanation:

Answer:

What option are you talking about for, is it for your quiz or for your classwork

Answer:

0.7

Step-by-step explanation:

Since 7 is above 5, you round 0.676 to 0.7

Answer: 0.7

Step-by-step explanation:

The nearest tenth is one decimal space after the dot. ex: 0.1234

Therefore, rounding 0.676, the 7 is ≥ 5, therefore we round the 6 up one number. This means the 0.6 becomes 0.7.

Answer:

x=12 y=2

Step-by-step explanation:

Due to fractions have screen shorted the steps in the image above

Answer:

[tex]f(x) = x(x - 1)[/tex]

Step-by-step explanation:

The inverse of a quadratic function is not a function.

Answer:

$9.33

Step-by-step explanation:

Interest = Principal × Rate × Time by 100

Therefore, I = 200×8×7/12 by 100

=16×7/12

=9.33

Answer:

more because it is 9 pitchers and 4/7 of energy drink in each

Answer:   x^2+4

Work Shown:

x = -2i

x^2 = (-2i)^2

x^2 = 4i^2

x^2 = 4(-1)

x^2 = -4

x^2+4 = 0

Side note: Since -2i is one root, this means 2i is the other conjugate root.

[tex]\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0[/tex]

The sum of the first 10 terms of the given geometric series 300 +360+432 +518.4+..... is 7787.60.

Let's suppose its initial term is  a , the multiplication factor is  r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

For the given geometric series, the common ratio is,

r = (360/300) = 1.2

Also, the first term of the series is 300. Therefore, the sum of the first ten terms of the series are:

Sum = a(rⁿ-1)/(r-1) = 300(1.2¹⁰-1)/(1.2-1) = 300(5.1917)/0.2 = 7787.60

Hence, the sum of the first 10 terms of the given geometric series is 7787.60.

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Answer:

You didnt give us a question to answer, just a statement.

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\bf\:19}[/tex]

Step-by-step explanation:

Given,

Now, the expression is: [tex]20 - (3y - 4x)[/tex].

To solve this question we just need to substitute the values of x & y in the given expression. Then,

[tex]20 - (3y - 4x)\\= 20 - (3(7) - 4(5))\\= 20 - (21 - 20)\\= 20 - 1\\= \boxed{\bf\:19}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

48

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

We know one angle measures 42°.

Another angle is a right angle, so it measures 90°.

Only the angle labeled x is unknown.

42 + 90 + x = 180

132 + x = 180

x = 48

Answer: 48

The amount of pizza left over in the fraction form will be 1/4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the swim team is sharing 6 pizzas. There are 36 players on the team. If each member has 1 slice, and each pizza has 8 slices.

Total slices = 8 x 6 = 48

Total players = 36

Left slices = 48 - 36 = 12

The portion in fraction left is,

L = 12 / 48

L = 1 / 4

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Answer:

3 ounces

Step-by-step explanation:

1 pound = 16 ounces

2(16) + 2(16) = 16 = 80 ounces of train mix - 5 from sister = 75 remaining

75 ounces of trail mix / 25 snack bags = 3 ounces of mix in each bag

Answer:

x = 87

Step-by-step explanation:

37 + 56 = 93

triangles always equal to 180

180 - 93 = 87

Answer:

17, 18, 19, 20

Explanation:

Let the numbers be x, x + 1, x + 2, x + 3

Their sum is equals to 74

x + x + 1 + x + 2 + x + 3 = 74     (group the variables)

x + x + x + x + 1 + 2 + 3 = 74    (simplify)

4(x) + 6 = 74                             (subtract both sides by 6)

4x = 68                                     (divide both sides by 4)

x = 17

Other numbers:

x + 1 = 17 + 1 = 18

x + 2 = 17 + 2 = 19

x + 3 = 17 + 3 = 20

Answer:

17, 18, 19, 20

Step-by-step explanation:

Answer:

24

Step-by-step explanation: 5 dozens = 60  so  3 +2=5 . 60 / 5 = 12 12 x 2 = 24

Answer: F(x) = 4x - 16

Step-by-step explanation: G(x) = 4x

if F(x) is the graph G(x) shifted over to the right by 4 then

F(x) = G(x-4) = 4(x-4) = 4x - 16

The general equation is f(x - amount_shifted)

The equation of the graph of the function F(x) is F(x) = (x - 3)⁴.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given a function F(x) and G(x).

Given that,

F(x) has the same shape as the graph of G(x) = x⁴.

The difference is that F(x) is shifted to the right 3 units.

A function G(x) when shifted right to k units becomes G(x - k).

So the function F(x) is,

F(x) = G(x - 3)

      = (x - 3)⁴

Hence the correct option is B.

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Answer:

x = -5/3

Step-by-step explanation:

-4 = [tex] \dfrac{20}{3}x[/tex]

-4×3 = 20 x

-12 = 20 x

[tex]x = \dfrac{-5}{3}[/tex]

Answer:

f(g(x)) = -1

Step-by-step explanation:

[tex]f(x) = \frac{1}{x} \\ \\ g(x) = x - 2 \\ \\ \implies \: f(g(x)) = \frac{1}{x - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{1 - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{ - 1} \\ \\ \implies \: f(g(1)) = - 1[/tex]

Answer:

[tex]4*\frac{1}{6}[/tex]

Step-by-step explanation:

The number lines end points are 0 and 1 so the whole number line has a value of 1.

The number line is also broken up into 6 sections.

Then we have the pink rectangles that cover up each section. There are 4 of them and each cover 1/6 of the number line

So the expression that would represent the model would be 4 x 1/6

Answer:

4 * 1/6

Step-by-step explanation:

So to begin, I would find out what all the answers are equal to.

4 * 1/8 = 4/8 = 1/2

4 * 1/4 = 4/4 = 1

4 * 1/6 = 4/6 = 2/3

4 * 1/3 = 4/3

Next I would rule out all the answers bigger or equal to one, so 4 * 1/4 and 4 * 1/3.

Last, this fraction splits one into six parts, and 4 parts are highlighted. 4/6 is equal to 4/6. Your answer is 4 * 1/6

Answer:

  p = 2

Step-by-step explanation:

A rational function has a vertical asymptote where the denominator is zero.

__

Your function will have a denominator that is zero when ...

  x -p = 0   ⇒   x = p

We are told there is a vertical asymptote at x = 2. That means ...

  p = 2

Answer:

Graph B

Step-by-step explanation:

Replace y with x and vice versa.

y=1/2x+2 becomes x=1/2y+2

Then solve for y. Subtract 2 from both sides, then multiply by 2 which results in:

y=2x-4

Graph B is the one that has a y-intercept at -4 and a rise/run of 2.

A transformation's preimage is the shape before the change. The image that is a pre-image is A'B'C', which is in blue colour.

We have a term for the shape before the transformation and another one for the shape after the transformation. The shape after a transformation is the image of the transformation. A transformation's preimage is the shape before the change.

In maths, the pre-image is the original figure. Therefore, the image that is a pre-image is ABC, which is in red colour.

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Answer:

A. 1.725 L

B. 0.0775 L or 775 mL

Step-by-step explanation:

Part A

↓ Determine the liters of juice Rachel used ↓

750 + 650 +325 = 1,725

Rachel used 1,725 mL of juice. Convert the given mililiters to liters.

[tex]1725 \: ml \: \times \frac{1liter}{1000 \: ml} = 1.725 \: liters[/tex]

→ Rachel used 1.725 L of juice

Part B.

Determine the amount of sparkling water added to the punch bowl.

2.5 - 1.725 = 0.775 L

0.775 L was added tot he punch bowl. Convert liters to milliliters. ↓

[tex]0.775 \: \times \frac{1000 \: ml}{1 \: liters} = 775 \: ml[/tex]

Therefore, the answer is:

1.725 L & 775 mL