Write the point slope of the equation of the line described show work.


through: (3,-2), parallel to y= -3/2x - 1

The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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Answer:

Step-by-step explanation:

How to find the mean of the probability distribution: Steps

Step 1: Convert all the percentages to decimal probabilities. For example: ...

Step 2: Construct a probability distribution table. ...

Step 3: Multiply the values in each column. ...

Step 4: Add the results from step 3 together.

The composite function ( f. g(x)) is x² + 4x + 3

A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.

The variables are known as;

From the information given, we have the functions as;

To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;

( f. g(x)) = (x + 2)² - 1

Now, let's expand the square

( f. g(x)) = (x + 2) ( x+ 2) - 1

Expand the bracket

( f. g(x)) = x² + 2x + 2x + 4 - 1

Now, let's collect like terms, we get

( f. g(x)) = x² + 4x + 3

Thus, the function is x² + 4x + 3

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The complete question:

Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2

Answer:

y=10

Step-by-step explanation:

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

Answer:

\(x=\frac{\pm\sqrt{29} +1}{4}\)

Step-by-step explanation:

Quadratic Formula: \(x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}\)

Step 1: Write quadratic equation

4x² - 2x = 7

Step 2: Solve for x

Answer:

because "five less of a number (n)" could be any number. Five less of a number is any number subtracted by 5. n - 5 ----> 17 - 5 = 12 (12 is NOT less than 5). "a number less than five" any number that is smaller than five.

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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First , Transform 10^-7 in 1/(10^7)

then divide

5.871/ (10^7)

Result is 0.0000005871

Answer: 11.59 months

Step-by-step explanation:

You need to divide 339.12 by 29.26. Then you should check your answer by multiplying 11.59 by 29.26. Which should get you 339.1234. When you sound that you get 339.12. Hope this helps!!

Applying the right triangle altitude theorem, the value of x in the given right triangle is: x = 4.

According to the right triangle altitude theorem, we have the following from the theorem as:

h = √(xy), where h is the altitude of the triangle and x and y are the segments divided on the hypotenuse.

Therefore, we have:

2√6 = √(x*3)

(2√6)² = x*3

12 = 3x

x = 12/3

x = 4

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Answer:

X = 10.588

Y = 28.2

Z = 21.176

Step-by-step explanation:

Consider Nova savings as X

Helga is Y

Maurice is Z

As per first ratio we conclude 8X=3Y

Second ratio we conclude 3Y = 4Z

We deduce 8X = 4Z

Last sentence => X+Y+Z=60 multiple it by 3

=> 3X + 3Y + 3Z= 180 but 8X = 4Y

=> 3X + 8X + 3Z =180 => 11X + 3Z=180 multiple the equation by 4/3

44/3 X + 4Z = 240 but 4Z = 8X

=> 44/3 X + 8 X = 240

=> 68/3 X = 240

=> 68X = 720

=> X =10.588

And Y=8/3 X =28.2

And Z=3/4 Y = 21.176

Answer:

you first calculate time in hours by changing 20 mins to hours

20/60

a third hour

speed is given by distance over time

we have 200 km divided by a third

200 divide by a third

answer is 600km per hour

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Denis's and Dasha's methods use different operations to simplify the expressions in different orders.

Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.

Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.

Denis's Assignment

2* 6+2w-54

12+2w = 54

12-12+2w= 54-12

2w=42

w= 21  

Dasha's Assignment

54-2* 6

54-12= 42

The two widths add to 42 cm

42/ 2-21

We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.

She subtracts the product of 2 and 6 from 54.

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The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer: infinite solutions

Step-by-step explanation:

Answer:

  116

Step-by-step explanation:

Given the ratio 1.2 : 29, you want x in the equivalent ratio 4.8 : x.

Equivalent ratios can be written as a proportion:

  1.2/29 = 4.8/x

Multiplying by 29x, we have ...

  1.2x = 29(4.8)

Dividing by 1.2 gives ...

  x = 29(4.8/1.2) = 29(4) = 116

The ratio is the same as 4.8 to 116.

__

Additional comment

A proportion like this can be written 4 ways. The solution takes only one step if the unknown is in the numerator.

  \(\dfrac{1.2}{29}=\dfrac{4.8}{x},\quad\dfrac{29}{1.2}=\dfrac{x}{4.8},\quad\dfrac{1.2}{4.8}=\dfrac{29}{x},\quad\dfrac{4.8}{1.2}=\dfrac{x}{29}\)

The expected value of the number of upgrades selected is 1.04.

The given probability mass function provides the probabilities for the number of upgrades purchased per customer. We are asked to find the expected value, which is a measure of central tendency in probability theory. To do this, we need to multiply each possible value of upgrades by its probability and then sum them up.

First, we need to figure out the value of f(3). We know that the sum of all probabilities in a probability mass function is 1. Therefore, we can use the given probabilities to calculate f(3) as follows:

1 = f(0) + f(1) + f(2) + f(3)

1 = 0.50 + 0.20 + 0.06 + f(3)

f(3) = 1 - (0.50 + 0.20 + 0.06)

f(3) = 0.24

Now that we know the value of f(3), we can calculate the expected value as follows:

E(X) = (0 x 0.50) + (1 x 0.20) + (2 x 0.06) + (3 x 0.24)

E(X) = 0 + 0.20 + 0.12 + 0.72

E(X) = 1.04

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are called composite numbers.

A prime number cannot be divided by any other numbers without leaving a remainder. An example of a prime number is 13. |  15 is not an example of a prime number because it can be divided by 5 and 3 as well as by itself and 1.

To work out if a number is prime, you can try to divide the number by all numbers that are smaller than it. If it can only be evenly divided by 1 and the number itself, then it is a prime number.

Answer:

2 groups

Step-by-step explanation:

3 photos (per group)

8 drawings (per group)

Hope this helps :)

Hiii :))

Answer is in the attachment.

Identity used :-

1) cosec² α = 1 + cot² α

Trigonometric Ratio :-

1) cot 30° = √3

_____

Reddam is an expensive school, right?

RainbowSalt2222 ☔

Answer:

hello :-D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Basically the number above the 10 means how many 0's to add to the number.

For 9 x \(10^7\), you add 7 0's, so you'd get:

90,000,000

For 2 x \(10^5\), you add 5 0's, so you'd get:

200,000

To find how many times more it is, you can just divide.

90,000,000 / 200,000

= 450

Answer:

D)  450

Step-by-step explanation:

The distance from the Earth to the Sun is approximately 9 × 10⁷ miles.

The distance from the Earth to the moon is approximately 2 × 10⁵ miles.

To find out how many times the distance from the Earth to the Moon is the distance from the Earth to the Sun, we can divide the distance to the Sun by the distance to the Moon:

\(\dfrac{9 \times 10^7}{2 \times 10^5}\)

To simplify this using exponent rules, apply the rule for dividing numbers with the same base:

\(\boxed{\dfrac{a^m}{a^n} = a^{m - n}}\)

In this case, the base is 10, and the exponents are 7 and 5. Therefore:

\(\begin{aligned}\dfrac{9 \times 10^7}{2 \times 10^5}&=\dfrac{9}{2} \times \dfrac{10^7}{10^5}\\\\&=\dfrac{9}{2} \times 10^{7-5}\\\\&=\dfrac{9}{2} \times 10^2\\\\&=\dfrac{9}{2} \times 100\\\\&=4.5 \times 100\\\\&=450\end{aligned}\)

Therefore, the distance from the Earth to the Sun is approximately 450 times the distance from the Earth to the Moon.

Answer:

Yes

Step-by-step explanation:

If F(x)= log base 5 of x, then yes, it is increasing.

Answer: True

Step-by-step explanation: Got it correct on a-p-e-x