What’s the rate of change of y=5.75x-2.5(x-2)

The correct option is: z = -23 and the pair of vertical angles has measures (2z + 43)° and (−10z + 25)°.

We need to find the value of z.

Let's recall the property of vertical angles:

Vertical angles are formed by the intersection of two lines. These angles are opposite to each other and are equal in measure.

It means, if two lines AB and CD intersect at point P, and form four angles, ∠APC = ∠BPD and ∠BPC = ∠APD.

Now we have given, (2z + 43)° = −(−10z + 25)°(2z + 43)° = (10z - 25)°2z + 43 = 10z - 25

Solving for z2z - 10z = -25 - 433z = -68z = -68/3z = -22.6666.....

But, we need an integer value of z.

Therefore, the correct option is: z = -23.

To know more about angles visit:

https://brainly.com/question/31818999

#SPJ11

Answer:

y - 11/8

Explanation:

The first step in simplifying the expression is to expand it.

A bit of rearranging gives

Now,

and

therefore,

Hence, our answer is

which can be written as

the equation of the plane passing through the points P₀(-5, 2, -3), Q₀(2, 3, 3), and R₀(1, 2, 0) is -18x + 18y - 6z - 144 = 0.

PQ = Q₀ - P₀ = (2 - (-5), 3 - 2, 3 - (-3)) = (7, 1, 6)

PR = R₀ - P₀ = (1 - (-5), 2 - 2, 0 - (-3)) = (6, 0, 3)

Taking the cross product of PQ and PR, we get the normal vector N:

N = PQ x PR = (1(0) - 6(3), 6(3) - 7(0), 7(0) - 1(6)) = (-18, 18, -6)

The equation of the plane can be written as:

-18(x - x₀) + 18(y - y₀) - 6(z - z₀) = 0

Substituting the values of P₀(-5, 2, -3) into the equation, we have:

-18(x + 5) + 18(y - 2) - 6(z + 3) = 0

Simplifying the equation gives:

-18x - 90 + 18y - 36 - 6z - 18 = 0

Combining like terms, the equation of the plane becomes:

-18x + 18y - 6z - 144 = 0

Learn more about equation here : brainly.com/question/29657988

#SPJ11

Step-by-step explanation:

Given

6 people = 180g flour

1 person = 180/6 = 30g flour

3 people = 3 x 30 = 90g flour

Answer:

You would have to distribute each one or use the box method whinch gives you :

12x^4 − 34x^3 + 20x^2

In order for the function to be continuous at x = -7, the limits from either side as x approaches -7 must be equal:

\(\displaystyle \lim_{x\to-7^-} f(x) = \lim_{x\to-7}(x^2-12x+16) = 149\)

\(\displaystyle \lim_{x\to-7^+} f(x) = \lim_{x\to-7}(kx+268) = -7k+268\)

Solve for k :

149 = -7k + 268

7k = 119

k = 17

The function f(x) is continuous at x = -7 if and only if k = 41. This is because for continuity to hold at x = -7, the value of k must be such that the left-hand limit, right-hand limit, and the actual value of the function at x = -7 are equal. In this case, the value of k that satisfies this condition is k = 41.

For a function to be continuous at a specific point, the following conditions must be satisfied:1. The function must be defined at that point (i.e., the function should have a value at x = -7).

2. The limit of the function as x approaches -7 from the left must be equal to the limit of the function as x approaches -7 from the right.

3. The value of the function at x = -7 must be equal to the limits mentioned in condition 2.

Let's go through each of these conditions step by step for the given function:

Given function:

f(x) = { \(x^2 - 12x + 16\), for x <= -7

        kx + 268, for x > -7

1. The function must be defined at x = -7:The function is defined at x = -7 for the first part of the piecewise definition: x^2 - 12x + 16. So, this condition is satisfied.

2. The limit from the left must be equal to the limit from the right as x approaches -7:We need to calculate the limits as x approaches -7 from the left (LHL) and from the right (RHL) for the second part of the piecewise definition: kx + 268.

LHL as x approaches -7: lim (x->-7-) [kx + 268] = -7k + 268.

RHL as x approaches -7: lim (x->-7+) [kx + 268] = -7k + 268.

Since both the left-hand limit and the right-hand limit are equal (-7k + 268), this condition is satisfied.

3. The value of the function at x = -7 must be equal to the limits: \(f(-7) = -7^2 + 12 * 7 + 16 = 49 - 84 + 16 = -19.\)

The limits from conditions 2 are -7k + 268.

To have continuity, the value of the function at x = -7 must be equal to the limits: -19 = -7k + 268.

Solving for k: -7k = -19 - 268

-7k = -287

k = 41.

So, for the function f to be continuous at x = -7, the value of k must be 41.

To know more about continuous:

https://brainly.com/question/31523914

#SPJ3

Answer:

68, 17, $17

Step-by-step explanation:

filling in the first blank using the chart. Money made for 4 sweatshirts is $68

68/4=17, this is the unit price, meaning the amount it would cost for one sweatshirt. Thats where we get the next blank's answer. 17/1 and since we found the unit price, we already answered the last question, $17 per sweatshirt.

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$30000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (30000)(0.05)(5) \implies I = 7500\)

The notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

What is end behavior of polynomial?

The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.

From the graph we know that the vertex of this parabola is V(0, 8).

This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.

Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.

In a mathematical language this is:

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

Hence, the notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

To know more about end behavior of polynomial, click on the link

https://brainly.com/question/10639050

#SPJ4

Steps to solve:

x + 5 = 34

~Subtract 5 to both sides

x = 29

Best of Luck!

Answer:

It is an Arithmetic sequence

Common difference = 3/4

Step-by-step explanation:

Determine whether the given sequence could be geometric, arithmetic, or neither. If possible identify the common ratio or common difference 1/2,5/4, 2, 11/4..

We are given the sequence:

1/2, 5/4, 2, 11/4.

We are to determine if this is an Arithmetic or Geometric sequence

Hence:

To determine if this is an Arithmetic sequence, we find the Common difference

Common difference = Second term - First term

= 5/4 - 1/2

Lowest Common Denominator = 4

= 5 - 2/4 = 3/4

or Third term - Second term

2 - 5/4

Lowest Common Denominator = 4

2/1 - 5/4

8 - 5/4

= 3/4

We have the same common difference.

To determine if this is an Geometric sequence, we find the Common ratio

Common ratio = Second term / First term

= 5/4 ÷ 1/2

5/4 × 2/1

= 5/2 = 2 1/2

or Third term /Second term

2 ÷ 5/4

2 × 4/5

= 6/5

= 1 1/5

It is not a geometric sequence

Therefore , the above sequence in the Question is an Arithmetic sequence.

The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

Learn more about exhaustive here:

https://brainly.com/question/30239943

#SPJ11

Answer:

5x + 8 = 18

5x = 18 - 8

5x = 10 (divide both sides by 5 to get x)

5x/5 = 10/5

x = 2

Step-by-step explanation:

also can i get brainliest

Answer:

12 pennies

4 dimes

3 nickels

2 quarters

Step-by-step explanation:

Let p = pennies

d = dimes

q = quarters

n - nickels

d + n + p + q = 21

p = 4n

d = n + 1

q = n - 1

Now just subsitute them in and add the terms

(n + 1) + n + (4n) + (n - 1) = 21

7n = 21

Divide both sides by 7

7n/7 = 21/7

n = 3

Now use the new n to plug in the rest of the equations

p = 4(3) = 12

d = 3 + 1 = 4

q = 3 - 1 = 2

Chad has a coin collection he has a total of 21 coins which include 12 number of pennies, 3 number of nickels, 4 number of dimes, 2 number of quarters.

Let's break down the information given in the problem step by step:

Chad has a total of 21 coins.

He has 4 times as many pennies as nickels.

He has 1 more dime than the number of nickels.

He has 1 less quarter than the number of nickels.

Let's use variables to represent the number of each type of coin:

Let P be the number of pennies.

Let N be the number of nickels.

Let D be the number of dimes.

Let Q be the number of quarters.

Now we can create a system of equations based on the information given:

P + N + D + Q = 21 (total number of coins)

P = 4N (four times as many pennies as nickels)

D = N + 1 (one more dime than the number of nickels)

Q = N - 1 (one less quarter than the number of nickels)

Now we can substitute the expressions for P, D, and Q from equations 2, 3, and 4 into equation 1:

4N + N + (N + 1) + (N - 1) = 21

Combine like terms:

7N = 21

Divide both sides by 7:

N = 3

Now that we know the number of nickels (N = 3), we can use this information to find the number of each type of coin:

Pennies (P) = 4N = 4 * 3 = 12

Dimes (D) = N + 1 = 3 + 1 = 4

Quarters (Q) = N - 1 = 3 - 1 = 2

So, Chad has:

12 pennies

3 nickels

4 dimes

2 quarters

To know more about number of nickels click here :

https://brainly.com/question/30605010

#SPJ3

The correct answer of the operation is option B: 4x^2 - 9.

To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:

First: Multiply the first terms of each binomial.

(2x)(2x) = 4x^2

Outer: Multiply the outer terms of each binomial.

(2x)(3) = 6x

Inner: Multiply the inner terms of each binomial.

(-3)(2x) = -6x

Last: Multiply the last terms of each binomial.

(-3)(3) = -9

A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.  

Now, let's combine the like terms:

4x^2 + 6x - 6x - 9

Notice that the terms 6x and -6x cancel each other out.

Simplifying further, we have:

4x^2 - 9

The correct answer is option B: 4x^2 - 9.

for such more question on operation

https://brainly.com/question/4721701

#SPJ8

The value of x in the ratio 5x : 9 = 7 : 3 is x = 21/5

From the question, the ratio is given as

5x : 9 = 7 : 3

Express the ratio, as a fraction

So, we have the following representation

5x / 9 = 7 / 3

Cross multiply the following expression

So, we have the following representation

3 * 5x = 9 * 7

Evaluate the products

15x = 63

Divide both sides by 15

So, we have

x = 63/15

Simplify the fraction

x = 21/5

Hence, the solution to the ratio is x = 21/5

Read more about ratio at

https://brainly.com/question/1781657

#SPJ1

For similar triangle is:

For similar triangle:

and

So

both triangle then :

LE=11 , LD=9 , LM=90, LN=110

For similar triangle ratio of ED and MN is 9/10

Answer:

Step-by-step explanation:

You take the 15 he had and subtract 9.52 from that which would look like this

15 - 9.52 = 5.48

Now with our new value 5.48 we divide it by two.

5.48 / 2 = 2.74

So he saved $2.74

Answer:

value of n is 3,150 .... .

Answer:

n = 3150 is the answer

Step-by-step explanation:

63 x 50 = 3150/5000

Answer:

12/-24 Simplified is 1/-2

Step-by-step explanation:

4-(-8)

-11-13

If ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1), the measure of x will be 29°.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),

Complementary angles are those where the sum of the two angles is 90 degrees. In other words, two angles are considered complementary if they combine to form a right angle. The two angles are said to complement one another in this context.

Since ∠EFH and ∠HFI are complementary angles,

∠EFH + ∠HFI = 90

(2x + 2)+ (x+1) =90

3x+3=90

x+1=30

x=29°

Thus, if ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),the measure of x will be 29°.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ1

Answer:

Step-by-step explanation:

To make a valid prediction about the mean of the population based on the sample means provided, we can examine the given data.

Looking at the sample means:

208

235

245

207

205

210

The highest sample mean is 245, so we can conclude that the mean of the population is unlikely to be greater than 245.

Therefore, a valid prediction about the mean of the population would be: The predicted mean of the population will be less than 245.

The other options, stating that the predicted mean will be less than 200, more than 275, or more than 250, are not supported by the given data.

Answer:

6.06

Percentage Calculator: 20 is what percent of 330? = 6.06.

The correct option is A) No, because the center of a distribution and the spread are not related

The standard deviation is a measure of the spread or dispersion of a set of data. It is not directly related to the mean or average of the data.

The standard deviation is calculated based on the deviations of each data point from the mean, taking into account how many data points there are.

The mean does not affect the calculation of the standard deviation, as the formula for standard deviation is based solely on the data itself and not on any summary statistics like the mean.

The value of the standard deviation can remain the same even if the mean changes, and conversely, the mean can change without affecting the standard deviation.

Thus, option A) No, because the center of a distribution and the spread are not related is correct.

To know more about standard deviation Visit:

brainly.com/question/23907081

#SPJ4

Answer:

4x + 4y - 8

Step-by-step explanation:

4(x - 2 +y) = 4*x -4*2 + 4*y by the distributive property

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

To know more about dividend, here

brainly.com/question/3161471

#SPJ11