Can y’all help me with thjs

For the system of the equation given we have proven that b = -1.

Given that,
a - 2b = 8
4a + 3b = 21
To prove b= -1

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
a - 2b = 8  - - - - - - - (1)
4a + 3b= 21 - - - -- - - (2)
From equation 1
a = 8 + 2b
put a in equation 2
4 (8 + 2b) + 3b = 21
32 + 8b + 3b = 21
11b = 21 - 32
11b = -11
b = -1
Hence proved.

Thus, for the system of the equation given, we have proven that b = -1.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

Based on the information, the integer used will be (10 - 4). The difference is 6.

On a number line, there'll be 6 units between the numbers

To find the difference between two integers by adding the additive inverse, we can follow these steps:

Subtract the smaller integer from the larger one: (larger integer) - (smaller integer).

Take the absolute value of the result to get the distance between the two integers on a number line.

The distance between two integers is the absolute value of the difference, so we do not include the sign in our answer. The answer will always be a non-negative number.

By plotting the two integers on a number line and counting the units between them, we can visualize the distance between them.

Learn more about integer on:

https://brainly.com/question/929808

#SPJ1

The area of the region bounded between the graphs of\(y = -x^2 + 8x\) and \(y = x^2 + 2x\) is 9 square units.

To find the area of the region bounded between the graphs of\(y = -x^2 + 8x\)and\(y = x^2 + 2x\), we need to find the points of intersection of the two curves and then integrate the difference of the curves between these points.

First, we find the points of intersection by setting the two curves equal to each other:

\(-x^2 + 8x = x^2 + 2x\)

Simplifying and rearranging, we get:

\(2x^2 - 6x = 0\)

Factoring out 2x, we get:

\(2x(x - 3) = 0\)

So, \(x = 0 or x = 3.\)

Substituting these values of x in either of the two equations, we get the corresponding y values:

For\(x = 0, y = 0^2 + 2(0) = 0.\)

For\(x = 3, y = 3^2 + 2(3) = 15.\)

So, the points of intersection are (0, 0) and (3, 15).

Now, we can integrate the difference of the curves between these points to find the area.

\(A = ∫[0, 3] [(x^2 + 2x) - (-x^2 + 8x)] dx\)

Simplifying the integrand, we get:

\(A = ∫[0, 3] (2x^2 - 6x) dx\)

Integrating this expression, we get:

\(A = [(2/3) x^3 - 3x^2] [0, 3]\\A = [(2/3) (3)^3 - 3(3)^2] - [(2/3) (0)^3 - 3(0)^2]\\A = (18 - 27) - (0 - 0)\\A = -9\)

Therefore, the area of the region bounded between the graphs of\(y = -x^2 + 8x\) and\(y = x^2 + 2x\) is 9 square units.

Note that the area is a positive quantity even though the integrand was negative because the area is defined as the absolute value of the integral.

Learn more about area of a region

brainly.com/question/9485980

#SPJ11

One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

For more such questions on milliliters: brainly.com/question/29502712

#SPJ4

The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(10,-4) and (6,-16)

We have

\(m = \frac{ - 16 - - 4}{6 - 10} = \frac{ - 16 + 4}{ - 4} = \frac{12}{4} = 3 \\ \)

We have the final answer as

Hope this helps you

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

To find an explicit formula for the sequence, we first need to solve the recurrence relation. We can do this by finding the roots of the characteristic equation r^2 - 4r + 3 = 0, which are r = 1 and r = 3. Therefore, the general solution to the recurrence relation is ak = A(1)^k + B(3)^k, where A and B are constants determined by the initial conditions. Plugging in a0 = 1 and a1 = 2, we get the system of equations A + B = 1 and A + 3B = 2. Solving for A and B, we get A = 1/2 and B = 1/2. Therefore, the explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

To know more about equations visit:

https://brainly.com/question/22688504

#SPJ11

Function aligns value from one set to another. The function will have a removable discontinuity at x = -3.

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us,

\(F(x) = \dfrac{(x^2+12x+27)}{(x^2+4x+3)}\)

Now, factorizing the numerator and the denominator,

\(F(x)=\dfrac{(x+3)(x+9)}{(x+3)(x+1)}\)

Now, in order to find the point at which the function will be discontinued, we will equate the denominator with 0.

\((x+3)(x+1)=0\\\\\\(x+3)=0\\x =-3\\\\\\(x+1)=0\\x=-1\)

Now, As (x+3) is the factor of the numerator and the denominator, therefore, you will have a removable discontinuity, which appears as a hole in the graph.

Hence, the function will have a removable discontinuity at x = -3.

Learn more about Function:

https://brainly.com/question/5245372

Answer:

first one is (-3,-3)

second one is B (x=-1)

Step-by-step explanation:

Answer:

\((x+1)(-3x-6)\)

Step-by-step explanation:

Polynomial Form Steps:

\((1+x)(x*2-5x-6)\\=(x+1)(-3x-6)\)

Answer: y = 14.50x + 2.99

Step-by-step explanation:

The equation is y = mx + b

y is the total cost and x is the number of shirt

We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope

The 2.99 shipping fee is the y-intercept

So our equation is

y = 14.50x + 2.99

To define a default field value in a form or a database, you can use the attribute "default". When you add the "default" attribute to a field, it will automatically assign the specified value to that field if no other value is provided by the user or system.

This can be particularly useful when designing forms or databases that require certain fields to have a value even when the user does not provide one.
For example, in a web form, you might have a "Country" field that requires users to select their country from a dropdown list. By setting a default value for this field, such as "United States," the system ensures that there is always a value associated with that field even if the user does not make a selection.
Similarly, in a database schema, you might have a "DateCreated" field that automatically assigns the current date and time as the default value. This ensures that the date and time are always recorded for each new entry, even if the user does not manually input a value.
In both cases, the "default" attribute allows you to streamline the data collection process and ensure that your forms and databases maintain consistent and complete data. Using default values can also improve the user experience by reducing the amount of input required, making it easier for users to complete forms and submit their data.

To learn more about the database, refer:-

https://brainly.com/question/30634903

#SPJ11

ok

Hose 1 = H = 5g/2 m

Hose 2 = M = 10g/8 m = 5g/4m

Hose 1 + Hose 2 = Total

5g/2 m + 5g/4 m = Total

10g/4m + 5g/4m = Total

15 gallons/4 min = total

15 gallons ---------------------------- 4 min

750 gallons -------------------------- x

x = (750 x 4) / 15

x = 3000 / 15

x = 200 min

Result. It will take 200 min to fill the pool

Answer:

Step-by-step explanation:

Sum = -14

Product = - 32

So, the factors = -16 , 2

When we add -16 +2 = -12 and when we multiply it is -32

w⁴ - 14w² - 32 =  w⁴ - 16w² + 2w² - 16 * 2

                      = w²(w² - 16) + 2(w² - 16)

                      = (w² - 16)(w² + 2)

                      = (w² - 4²)(w² + 2)

                      = (w + 4)(w - 4)(w² + 2)

Step-by-step explanation:

Replace w^2 with any other variable for eg: w^2=a

so that will make the equation:

a^2-14a-32

now factorize this equation and u can find the value of a

a^2-16a+2a-32

a(a-16)+2(a-16)

so factors= (a+2) (a-16)

since a was w^2 so replace them with w^2 and u got factors of the equation

you can also directly factorize the whole equation through middle term breaking

w^4-16w^2+2w^2-32

w^2(w^2-16)+2(w^2-16)

(w^2+2)(w^2-16)

you get the same answer

Answer:

Step-by-step explanation:

Incomplete question, but if my guess is correct, you're trying to determine which is a better deal between the two. I will go with the second one. The $650/month rent.

I choose so because, $800/month totals to $9600 at the end of the year. While $650/month totals to $7800 per year. Again, with the $650/month, if you try to leave before the end of the year, say 11 months even, you pay a penalty of $1300, which still leaves you on the profit side. And the whole idea of choosing is to find which is more beneficial and cost effective.

We use the Taylor series expansion of e⁽⁻ˣ²⁾and evaluate the infinite series up to a point where the next term is smaller than 0.001.

To approximate the definite integral i = 0.5 x^2e⁽⁻ˣ²⁾ dx within the indicated accuracy of |error| < 0.001, we need to use a series approximation.

To do this, we can use the Taylor series expansion of e⁽⁻ˣ²⁾, which is given by:

e⁻ˣ² = 1 - x₂ + (x⁴)/2 - (x⁶)/6 + …

Substituting this into the integral expression, we get:

i = 0.5 ∫ x²(1 - x² + (x⁴)/2 - (x⁶)/6 + …) dx

We can then integrate each term separately:

∫ x² dx - ∫ x⁴ dx/2 + ∫ x⁶ dx/6 - …

= (x³)/3 - (x⁵)/10 + (x⁷)/42 - …

Evaluating this from 0 to infinity, we get:

i = lim(x→∞) [(x³)/3 - (x⁵)/10 + (x⁷)/42 - …] - [(0³)/3 - (0⁵)/10 + (0⁷)/42 - …]

The series converges rapidly, so we can stop after a few terms. To ensure that the error is less than 0.001, we can compute the next term and check that it is smaller than 0.001. If it is, then we can stop and use the computed sum as our approximation.

Therefore, to approximate the definite integral i to within the indicated accuracy, we use the Taylor series expansion of e⁽⁻ˣ²⁾ and evaluate the infinite series up to a point where the next term is smaller than 0.001.

To learn more about Taylor series expansion here:

brainly.com/question/16462992#

#SPJ1

Answer:

x = 2, y = 3

Step-by-step explanation:

x - 3y = - 7 → (1)

x = 5 - y → (2)

Substitute x = 5 - y into (1)

5 - y - 3y = - 7

5 - 4y = - 7 ( subtract 5 from both sides )

- 4y = - 12 ( divide both sides by - 4 )

y = 3

Substitute y = 3 into (2)

x = 5 - 3 = 2

solution is (2, 3 )

From unitary method calculations, we have found that the large jar is the best value for money because a penny buys more honey.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We need to determine which has the best value for money using the quantity a pound can purchase.  

So, first for the large jar.

£4.10 will be purchase 540g of honey then,

£1.00 will be purchase xg

Then cross multiplying for x will be;

x = 1.00 (540g )/4.10

x = 131.7g

Hence for the large jar a penny will buy 131.7g of honey.

Now second for the small jar

£2.81 will be purchase 360g of honey then,

£1.00 will purchase xg

Now cross multiplying

x = 1.00 (360g )/ 2.81

x = 128.1g  

Hence for the small jar a penny will buy 128.1g of honey.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ1

Answer:

Step-by-step explanation:

In a one-tail hypothesis test where you reject only in the upper tail, 1.753 is the critical value of the t-test statistic with degrees of freedom at the level of significance.

The upper critical value in a one-tail hypothesis test where you only reject in the upper tail corresponds to the t-test statistic with degrees of freedom at the level of significance. The difference between the region where the null hypothesis is accepted and the region where it is rejected is indicated by this value.

One must utilise the subsequent step-by-step procedure to determine the upper critical value of the t-test statistic with degrees of freedom at the level of significance:

Determine the degrees of freedom and the significance level (df).

Find up the t-test statistic's critical value from a t-table together with the relevant degrees of freedom at the level of significance.

The value shown in the t-table is the highest critical value of the t-test statistic with the matching degrees of freedom at the level of significance.

The upper critical value of the t-test statistic with the appropriate degrees of freedom at the level of significance, for instance, is 1.753 if the level of significance is 0.05 and the degrees of freedom are 15.

To learn more about hypothesis visit:

https://brainly.com/question/15980493

#SPJ4

Answer:

a. 48

b. You need 6 packs of cups and 8 packs of plates

c. 72 is another one she would need 9 packs of cups and 12 packs of plates to get this one

hope im right

Answer: 24 plates and 24 cups

3 packs of Cups

4 packs of plates

Two others:

6 packs of Cups

8 packs of plates

9 packs of Cups

12 packs of plates

Step-by-step explanation:

The goal of the first problem, is to find the smallest number that is a multiple of 8 and 6.

The answer is 24.

24/8=3

24/6=4

24 is the smallest number that is divisible by 8 and 6

The goal of the second problem is to find the factors of the smallest multiple of 8 and 6

24/8=3

24/6=4

3*8 and 6*4 are the equations that get you that number.

The goal of the third problem, is to find two other multiples of both 8 and

6

The probability that both will be married before the age of 18 is 0.0036. The probability that both will be married by the age of 25 is 0.25. Finally, the probability that both will be married by the age of 30 is 0.5476.

According to the brief report by NCHS, approximately 6% of women in the United States married for the first time before their 18th birthday, and 50% of women married by their 25th birthday. 74% of women married by their 30th birthday.The probability of a family with two daughters marrying at different ages is asked in the question. The probability that both daughters will be married by the ages of 18, 25, and 30 will be determined

The question requires finding the probability that both daughters of a family will be married by the ages of 18, 25, and 30 respectively. Since each daughter's wedding is a separate event, the individual probability of a daughter marrying at a given age will be determined separately and then multiplied together to get the probability of both daughters being married at the given age. So, let's find the probabilities of each daughter marrying at a given age:

Probability of one daughter getting married by 18 years:

As per the brief report, 6% of women in the United States married before the age of 18.

Therefore, the probability of one daughter getting married before the age of 18 is 0.06

Probability of one daughter getting married by 25 years:

As per the brief report, 50% of women in the United States get married by the age of 25. Therefore, the probability of one daughter getting married by 25 years is 0.5.

Probability of one daughter getting married by 30 years:

As per the brief report, 74% of women in the United States get married by the age of 30. Therefore, the probability of one daughter getting married by 30 years is 0.74.

The probability of both daughters getting married at the same age is the product of each daughter's probability of getting married at that age.

The probability that both daughters will get married before the age of 18 is:

P(both daughters married at 18 years) = P(daughter1 married at 18) × P(daughter2 married at 18)= 0.06 × 0.06= 0.0036

The probability that both daughters will get married by the age of 25 is:

P(both daughters married at 25 years) = P(daughter1 married at 25) × P(daughter2 married at 25)= 0.5 × 0.5= 0.25

The probability that both daughters will get married by the age of 30 is:

P(both daughters married at 30 years) = P(daughter1 married at 30) × P(daughter2 married at 30)= 0.74 × 0.74= 0.5476

The probability that in a family with two daughters, both will be married before the age of 18 is 0.0036. The probability that both daughters will be married by the age of 25 is 0.25. Finally, the probability that both daughters will be married by the age of 30 is 0.5476.

To know more about probability visit:

brainly.com/question/31828911

#SPJ11

Answer:

complementary angles

Step-by-step explanation:

The two angles add to 90 degrees, which means they are complementary angles

Answer:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Step-by-step explanation:

This is the fibonacci sequence with each term times x.

Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.

That is:

1x+1x=2x

1x+2x=3x

2x+3x=5x

3x+5x=8x

So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.

f(1)=1x since first term of f is 1x

f(2)=1x since second term of f is 1x

Yes, I'm naming the sequence f.

So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...

Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.

So in general f(n)=f(n-1)+f(n-2).

So the full recursive definition is:

f(n)=f(n-1)+f(n-2)

f(1)=1x

f(2)=1x

Answer:

666

Step-by-step explanation:

666

4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

Given that,

A cyclist travels at a speed of 24 miles per hour on average.

We have to find what is the required riding time (in hours) if she wants to cycle 180 km.

We know that,

The velocity is a vector quantity (has magnitude and direction) that is calculated by dividing the distance by the amount of time needed to travel the distance in question.

So, the distance is 180 km, and the speed is 24 miles per hour.

To calculate the amount of time needed to travel the distance, we divide the distance by the speed.

The distance is first converted to miles as 1 mile is equal to 1.6098 kilometers,

180 kilometers are equal to 111.84681 Miles.

111.84681 miles traveled in 24 hours

111.84681/24

4.66 hours.

Therefore, 4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

To learn more about average visit: https://brainly.com/question/27193544

#SPJ4

Answer:

-5

Step-by-step explanation:

F(x) = y

When y= -2

x= -5

The total number of possible ways of giving 5 awards in a group of 20 people are 1860480.

A permutation is the number of ways a set can be arranged or the number of ways things can be arranged. Mathematically, permutation can be expressed as -

P[n, r] = n!/(n - r)!

Given is race of 20 people such that the top 5 in the race will win a prize.

Now, from a group of 20 people only 5 will be awarded with the prize. The total number of possible ways of giving 5 awards in a group of 20 people can be calculated as -

P[20, 5] = (20!/(20 - 5)!)

P[20, 5] = (20 x 19 x 18 x 17 x 16 x 15!)/15!

P[20, 5] = 20 x 19 x 18 x 17 x 16

P[20, 5] = 1860480

Therefore, the total number of possible ways of giving 5 awards in a group of 20 people are 1860480.

To solve more questions on permutations, visit the link below-

https://brainly.com/question/112112

#SPJ1

Answer:

I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.

Step-by-step explanation:

We can calculate P(11≤X≤17) by finding P(X≤17) - P(X≤10).9. P(1111.7) = 0.20281083, P(11≤X≤17) = 0.96154525, and P(11)

The value of probablities P(X=12) = 0.09034815;  P(X=11) = 0.20281083; P(X≤12) = 0.95539708;  P(X<26) = 1; P(X≥12) = 0.04460292;  P(X=11.7) = 0;  P(X>11.7) = 0.20281083;  P(11≤X≤17) = 0.96154525;  P(1111.7) = 0.20281083:

This can be calculated using the CDF of the binomial distribution again. In software, we can find this by using the pbinom() function, which gives us the probability of getting at least a certain number of successes.

Therefore, we can calculate P(X>11.7) by finding 1 - P(X≤11).8. P(11≤X≤17) = 0.96154525: This can be calculated using the CDF of the binomial distribution again.  In software, we can find this by using the pbinom() function, which gives us the probability of getting between a certain number of successes.

Therefore, we can calculate P(11≤X≤17) by finding P(X≤17) - P(X≤10).9. P(1111.7) = 0.20281083, P(11≤X≤17) = 0.96154525, and P(11).

To know more about  binomial  visit:

brainly.com/question/29137961

#SPJ11