F(x) = 3* + 10xand g(x) = 5x - 3, find (f - g) (x)

Answer:

Step-by-step explanation:

hello :

1)

the equation is : f(x)= a(x+1)(x-2)  because : x- ints of -1 and 2  means :

f(-1)=0 and f(2)=0

calculate : a   given f(4)=10

so :  a(4+1)(4-2)=10

10a =10   so : a = 1

the equation is : f(x)= (x+1)(x-2)

2) and 3) same method but   * y int of -3* meanes : f(0)= - 3

The force is 1.6N and the distance between them is 1.3 meters

An inverse variation from force to the square of distance is represented s:

k = Fd^2

Where k represents the variation constant

When F = 10, d = 2.

So, we have:

k = 10 * 2^2

k = 40

Substitute k = 40 in k = Fd^2

Fd^2 = 40

When d = 5, we have:

F * 5^2 = 40

This gives

25F = 40

Divide by 25

F = 1.6

Hence, the force is 1.6N

In (a), we have:

Fd^2 = 40

When F = 25, we have:

25 * d^2 = 40

This gives

25d^2 = 40

Divide by 25

d^2 = 1.6

Take the square root of both sides

d = 1.3

Hence, the distance between them is 1.3 meters

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For the square with side length n, the diagonal measures:

[tex]d = \sqrt{2} *n[/tex]

The sidelength of the square is n, and we want to get the length of the diagonal d.

Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.

Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;

[tex]d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n[/tex]

That is the length of the diagonal.

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It takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

A ratio can sometimes be regarded as fraction. While rate has something to do with time.

Given that Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes. Kay and Elle take 35 minutes to do the same job. When Jay and Elle work together, the job takes 42 minutes.

Let

The interpretation of the question go thus;

1/J + 1/K = 1/30 ........ (1)

1/K + 1/E = 1/35 .........(2)

1/J + 1/E = 1/42 .........(3)

Make 1/J and 1/E the subject of formula in equation 1 and 2 respectively and substitute them in equation 3

1/J = 1/30 - 1/K  ........ (4)

1/E = 1/35 - 1/K  .........(5)

1/30 - 1/K + 1/35 - 1/K = 1/42

Collect the like terms

- 1/K - 1/K = 1/42 - 1/30 - 1/35

-2/K = (35 - 49 - 42)/1470

-2/K = -56/1470

1/K = 28/1470

Reciprocate both sides

K = 1470/28

K = 52.5 minutes.

Substitute K in both equation 4 and 5

1/J = 1/30 - 28/1470

1/J = (49 - 28)/1470

1/J = 21/1470

Reciprocate both sides

J = 1470/21

J = 70 minutes

1/E = 1/35 - 28/1470

1/E = (42 - 28)/1470

1/E = 14/1470

Reciprocate both sides

E = 1470/14

E = 105 minutes

Therefore, it takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

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Answer:

see explanation

Step-by-step explanation:

- 3 | 5x + 6 | + 1 ≥ 6

First step : subtract 1 from both sides

- 3 | 5x + 6 | ≥ 5

Answer:

14n^2.

Step-by-step explanation:

This is Arithmetic with first term a =  14 and common difference d =  28.

Sum of n terms = n/2[2a + (n-1)d]

= n/2(28 +( n -1)28]

= n/2(28 + 28n - 28)

= 14n^2

Answer:

14n²

Step-by-step explanation:

14 = 14 *1

42 = 14 *3

70 = 14 *5

28n -14 = 14*2n - 14 = 14*(2n -1)

14 + 42 + 70 + ........+(28n -14) = 14*1  + 14*3  + 14*5 + ....... + 14*(2n - 1)

                                               = 14 * (1 + 3 + 5 + ......+ (2n-1) )

                                               = 14 * n²

                                               = 14n²

1 + 3 + 5 + .... +(2n -1)  ->  sum of first 'n' odd numbers.

Formula for finding sum of first 'n' odd numbers  = n²

The correct option regarding whether the equation x² = y² is a function is:

No, since if you solve the equation for x, then [tex]x = \pm y[/tex]

In a function, each value of x can be associated with only one value of y.

In this problem, the equation is:

[tex]x^2 = y^2[/tex]

Then:

[tex]x = \pm \sqrt{y^2}[/tex]

[tex]x = \pm \sqrt{y}[/tex]

x is associated with two values, [tex]-\sqrt{y}[/tex] and [tex]\sqrt{y}[/tex], hence it is not a function.

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Answer:

In total she got $555 so we have to divide that to see how much she got per hour.

Step-by-step explanation:

y/x=?

$555/15= $37

Now how much money multiplied by how many hours

$37 X 15 = $555

I hope this helps, if you need any more information just comment!

Have an Amazing Day!!!

The best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.

There are four main categories of transformations:

A stiff transformation known as an isometry maintains perimeter and area while also preserving length and angle measurements. In other words, there is congruence between the preimage and the image. Translations, reflections, and rotations are therefore isometric, but dilations are not since the image and preimage are comparable, rather than congruent figures.

The transformation in the question will be isometric when the preimage of the rectangle before 360° rotation, will be congruent to the image after the rotation.

The congruency is best described by the option "The rectangle did not change shape or size", as that is the basis of congruency.

Thus, the best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.

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The provided question is incomplete. For the complete question, refer to the attachment.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming the equation is:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\huge\textbf{If so, let's start simplifying it:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (12.3\times 12.3) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (151.29) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= 151.29 - 0.246 \div3}[/tex]

[tex]\mathsf{= 151.29 - 0.082}[/tex]

[tex]\mathsf{= 151.208}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\large\boxed{\mathsf{Exactly \rightarrow} \frak{\ 151.208\ } \& \textsf{ Corrected to two significant figures}\rightarrow \frak{150 \ or \ 151}}\large\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Due to its subject-specific classification, ink color in pens is a qualitative variable.

Consequently, option (C) is the appropriate choice.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (f + g)(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(x) + g(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]

This is considered as decision making under risk.

Decision Making Under Risk

A circumstance in which the implications of the chosen course of action and the likelihood that it will occur are understood is referred to as decision-making under risk . For instance, the lottery selection tasks are frequently employed to examine the nature of decision-making in risky situations.

We make the assumption that there are two or more choices and that each alternative's characteristics are explicitly specified. For each attribute, the CV (coefficient of variation) is configured in case of such decision under risks. And, since in the given question, decision maker is supposed to consider several possible outcomes for each alternative, each with a given probability of occurrence. Thus the decision made will be decision under risk.

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The five-number summary are as follows:

The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.

Therefore,

Given:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

Therefore,

Minimum = 58

Lower quartile(Q₁) = 67

Median = 79 + 79 / 2 = 79

Upper quartile(Q₃) = 82

Maximum = 87

Interquartile range = Q₃ - Q₁ = 82 - 67 = 15

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The  sum of the links of the two parallel sides is 5cm

The formula for calculating the area of a trapezoid is expressed as:

A = 0.5(a+b)h

where

h is the height of the trapezoid

a+b is the sum of the sides

Substitute

20 = 0.5(a+b)8

40 = 8(a+b)

a+b = 40/8

a+b = 5cm

Hence the  sum of the links of the two parallel sides is 5cm

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[tex]a(n) = 3 + 5n[/tex]

[tex]b(n) = - 2 + 6n[/tex]

[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]

[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]

Answer:

bvjh

Step-by-step explanation:

bn

Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

Answer:

300 dollars

Step-by-step explanation:

Note that:

{Peter's revenue on Monday: 150 dollars

Peter's revenue on Tuesday: 100 dollars

Peter's revenue on Wednesday: 50 dollars}

---------------------------------------------------------------

In this problem, we need to find how much is Peter's revenue so far (total).

We need to use addition to determine how much Peter's revenue is in total.

So, add 150, 100, and 50.

We get 150 + 100 + 50 = 300

Finally, Peter's revenue in total is 300 dollars.

Answer:

$300

Step-by-step explanation:

add 150+100+50

=300

Answer:

72.

Step-by-step explanation:

Number of strings with exactly 2 1's

= 9C2

= 9*8/2*1

= 36.

Same for  2 0s

= 36.

Answer:

[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]

Step-by-step explanation:

[tex]2\pi 8(\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{80}{360} )[/tex]

[tex]=16\pi (\frac{2}{9})[/tex]

[tex]=\frac{32\pi }{9}[/tex]

Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In this problem, the parameters are:

a = 800, b = 900, C = 70º.

Hence the distance across the lake is c, found as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

c² = 800² + 900² - 2(800)(900)cos(70º)

c² = 957491

[tex]c = \sqrt{957491}[/tex]

c = 978.5.

The distance across the lake is of 978.5 feet.

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Answer:

33.

Step-by-step explanation:

8x + 4y = 44

4(2x + y) = 44

2x + y =  44/4 = 11.

6x + 3y

= 3(2x + y)

= 3 * 11

= 33.

Answer:

X-19

Step-by-step explanation:

First you need to distribute the three into the numbers in the parenthesis,

(3 * x) + (3  * -5) - (2x + 4)

That then turns into,

3x - 15 - (2x + 4)

but we aren't done distributing yet, because the second set of parenthesis has a negative sign in front of it we also have to distribute that. (this is because the negative sign is really just -1)

3x - 15 + (-1 * 2x) + (-1 * 4)

that turns into,

3x - 15 - 2x -4

from here all we have to do is add like terms,

(3x - 2x) + (-15 + -4)

and that leaves us with: 1x -19 or x-19

Hope that helped :))  

By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.

In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 120

Reference angle = 60°.

For the coordinates, we have:

sin(-120) = -sin(60) = -1/2.

cos(-120) = -cos(60) = -√3/2.

By applying Pythagorean theorem, we have:

z² = x² + y²

z = √((-1/2)² + (-√3/2)²)

z = √(1/4 + 3/4)

z = √1

z = 1.

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Step-by-step explanation:

I don't see any numbers, so I just give you an example :

11

every position in a number is worth 10 times the value of the position to its very right.

so, in e.g. 11

the left 1 is worth 10 times the value of the right 1.

Answer:

Vertex - (2, -1)

Axis of Symmetry - x = 2

X intercept - (3,0) (1, 0)

Y intercept (0, 3)

Domain - (negative infinity, positive infinity)

Range - [-1, infinity)

Step-by-step explanation:

I graphed with desmos and found it.