Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d. Justify your answer.2x + 4y = f
cx + dy = g."
Not quite sure what is meant by the question "what can you say." My only thought so far is that If the system is consistent, that means x and y have the same value for both equations:
x(2 + c) + y(4 + d) = f + g, which, if c = f+g, fits into the form ax + by = c. But that's about it.

Answer:

3% increase

Step-by-step explanation:

Answer:

36.

Step-by-step explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.

Answer:

Center = (-3, -3)

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]

[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]

In  linear equation, 2 miles per hour is the rate in miles per hour .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Divide the distance by the time.

(1/5 miles) / (1/10 hour)

= 10(1/5) miles per hour

= 2 miles per hour

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Answer:

1/5

Step-by-step explanation:

Answer:

The solution is 1/5 or 0,2

Step-by-step explanation:

[tex] \displaystyle \sf\lim_{x \to 3} \frac{ {x}^{2} - 5x + 6 }{2 {x}^{2} - 7x + 3} \: \: \: \: \: \: \: \: \: \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)(x - 3)}{(2x - 1)(x - 3)} \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)\cancel{(x - 3)}}{(2x - 1)\cancel{(x - 3)}} \\\\ = \displaystyle \sf \lim_{x \to 3} \frac{(x - 2)}{(2x - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf = \frac{(3 - 2)}{(2(3) - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ = \boxed{\sf \frac{1}{5} \: or \: 0.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Reason:

The standard deviation is the square root of the variance.

[tex]\text{Standard deviation} = \sqrt{\text{variance}}\\\\\text{Standard deviation} = \sqrt{1.56}\\\\\text{Standard deviation} \approx 1.24899959967968\\\\\text{Standard deviation} \approx 1.25\\\\[/tex]

Round the answer however you need to, or however your teacher instructs. I rounded to two decimal places since 1.56 is to two decimal places.

The standard deviation of the discrete random variable if the variance is 1.56 is 1.25

Given that, a discrete random variable has a variance of 1.56, we need to find its standard deviation

We know that,

The standard deviation is the square root of the variance.

Standard deviation = √ variance

Standard deviation = √1.56

Standard deviation = 1.24899959967968

Standard deviation = 1.25

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The probability of getting two twos is 0.003

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

probability = sample space/total outcome

probability of getting two = 1/6

probability of getting two twos = 1/36

getting two two can only 10times = 1/36 ÷ 10

= 10/36 = 0.003 (nearest thousandth)

therefore the probability of getting two twos in 20 rolls is 0.003( nearest thousandth)

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a) The distribution of the mean weight of 10 apples picked at random is normally distributed.

b) The mean, μ, is 45 oz.

What is normal distribution and mean?

normal distribution: The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean.

Mean: In mathematics, a mean is the average of a data set, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

a) The distribution of the mean weight of 10 apples picked at random is approximately normally distributed. This is because, according to the Central Limit Theorem, when the sample size is sufficiently large, the distribution of the sample mean becomes normal regardless of the underlying population distribution.

Here, we have a sample size of 10, which is considered large enough to apply the Central Limit Theorem. Also, we know that the underlying population distribution of the weight of a single apple is normal.

b) The mean weight of 10 apples picked at random is simply the mean of the individual weights of those 10 apples. Since the individual weights of the apples are normally distributed with a mean of 45 oz and a standard deviation of 3 oz, the mean weight of 10 apples will also be normally distributed with a mean equal to the mean of the individual weights, which is 45 oz.

Therefore, the mean, μ, is 45 oz.

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Answer:

-30

Step-by-step explanation:

so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]

now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90

[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3

The two events are mutually exclusive

"Information available from the question"

Stacy rolls a pair of six-sided fair dice.

Now, According to the question:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favorable outcomes  of either a multiple of 3 or an even number are:-

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

Probability = Number of fav. outcomes/ Total no. of outcomes

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.

In our case this will be;

24/36 = 2/3

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The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7.5/2

Constant of proportionality, k = $3.75.

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The store with the best deal is given as follows:

Store D.

The store with the best deal is obtained applying the proportions in the context of the problem.

The best deal is the store with the lowest cost per hour, and the cost per hour is obtained dividing the total cost by the number of hours.

Hence the hourly cost for each store is obtained as follows:

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Answer:

Step-by-step explanation:

К счастью, другое маленькое дерево поблизости заметило растущее дерево и дало несколько интересных советов о том, как удерживать его распускающиеся листья новыми и интересными способами. Было забавно испытать на других маленьких деревьях множество различных способов расположения листьев. Другие маленькие деревья вскоре заметили это и начали поворачивать свои немногочисленные листья под углом. Другие маленькие деревья могли лишь слегка приподнять свои листья.

Растущее дерево решило, что будет немного приподнимать листья на радость другим деревьям. Но, в конце концов, все маленькие деревья начали отращивать больше листьев на ветвях, которые тянулись еще дальше. С каждым сезоном многие листья невозможно было приподнять. Некоторые из растущих деревьев продолжали шептаться, в то время как некоторые научились громко смеяться, некоторым, казалось, нравилось плакать и падать духом, а некоторые росли вдали от группы из-за того, как многие времена года влияли на них и на другие деревья и животных вокруг них.

За прошедшие годы родительские деревья время от времени мельком смотрели вниз, чтобы увидеть, как растут их семена, и они поднимали свои ветви к небу, чтобы пропустить солнечный свет через полог. Все растущие деревья заметят это и поднимут головы, чтобы насладиться солнечным светом. Те, кто не обращал внимания на поведение своего родительского дерева, обычно подражали другим растущим деревьям и умудрялись собирать немного солнечного света. Иногда растущее дерево переставало расти, потому что не могло достичь солнечного света. Его листья не будут такими обильными, а его ветви будут тянуться дальше, чтобы быть ближе к солнечному свету других растущих деревьев. По прошествии многих сезонов растущие деревья становились все выше и теперь можно было видеть, что их место среди кроны деревьев было довольно тесным.

Answer:

The correct answer is D. y = 3.35x + 73.96.

Step-by-step explanation:

D. y = 3.35x + 73.96

a. The number of pizzas the pizzeria must sell today for employees to receive the bonus will be 78 pizza.

b. The percent decrease in the number of pizzas sold today compared to yesterday is 7.69%.

a) To determine the number of pizzas the pizzeria must sell today for employees to receive the bonus, we need to calculate 20% of the 65 pizzas sold yesterday. 20% of 65 pizzas is 0.20 * 65 = 13. So, the pizzeria must sell 65 + 13 = 78 pizzas today for employees to receive the bonus.

b) To calculate the percent increase or decrease in the number of pizzas sold today compared to yesterday, we need to divide the difference between the two days' sales by the number of pizzas sold yesterday and multiply by 100.

((60 - 65) / 65) * 100

= (-5 / 65) * 100

= -7.69%

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According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.

The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.

Rate of change for Pennsylvania  [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]

Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]

As a result, Nevada's property prices have grown more rapidly.

b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]

c) Pennsylvania[tex]= 42400 + 1092x[/tex]

Nevada[tex]= 53700 + 1816x[/tex]

[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]

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The degree of the polynomial is; 6.

The leading coefficient of the polynomial is; 1.

The maximum number of real zeroes is; 6.

As evident in the task content; the given polynomial is;

f (x) = 2x⁵ - x³ + x⁶ - 4.

By observation, the term with the highest power of x is; x⁶.

Therefore, the degree is; 6.

The leading coefficient is the coefficient of x⁶ which is; 1.

The maximum number of real zeroes possible is dependent on the degree of the polynomial and is; 6.

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The value of x is 12. The solution has been obtained by using trigonometry.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.

We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.

Using trigonometry,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 11/x

Here, θ = 24°

So,

⇒cos 24° = 11/x

⇒x = 11/cos 24°

⇒x ≈ 12.04

⇒x ≈ 12

Hence, the  value of x is 12.

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Step-by-step explanation:

22x + 2y = -14

2y = -22x - 14

y = -11x - 7

Answer:

60% i mean it sounds right

Step-by-step explanation:

Answer:

1. 18 + 35

2. 6 * 50

3. b - 25

4. x / 4

5. t + 11

6. 100 - k

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = l x w

A = 105.1m x 67.1m

A = 7052.21m

Convert to yds.

7052.21 / 0.9144  =  7712.4

To the nearest whole, the area is 7712 yds2.

Answer:

Step-by-step explanation:

Calculate the total hours used: We add up the hours used each year to find the total hours used:

2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500

Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:

$219,000 - $19,500 = $199,500

Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:

$199,500 / 6 = $33,250

Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:

$33,250 / 12,500 = $2.66

So the depreciation expense per hour is $2.66.

Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:

Year 1: 2,800 * $2.66 = $7,448

Year 2: 1,400 * $2.66 = $3,724

Year 3: 1,500 * $2.66 = $3,990

Year 4: 2,500 * $2.66 = $6,650

Year 5: 2,300 * $2.66 = $6,118

Year 6: 2,000 * $2.66 = $5,320

So the depreciation expense for each year is:

Year 1: $7,448

Year 2: $3,724

Year 3: $3,990

Year 4: $6,650

Year 5: $6,118

Year 6: $5,320

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

y = f(x) represents a function with output value as y and x as an input in the function.

Therefore, f(2) represents value of function (y) at x = 2

so the correct choice here would be : " the output (y - value) when x = 2 "

The echelon form of the given augmented matrix with 1's on the diagonal is:

1 -1 0 1000

0 1 0 1100

0 0 1 300

To find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:

Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:

1 -1 2 400

0 1 -2 500

0 -2 5 -700

Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:

1 -1 2 400

0 1 -2 500

0 0 1 300

Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:

1 -1 0 1000

0 1 0 1100

0 0 1 300

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Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

The perimeter of the trapezoid is 49.4.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

From the graph,

Height = 12 units

Parallel sides = 9 units and 15 units

Now,

Another side = x

Using Pythagorean theorem.

x² = 6² + 12²

x² = 36 + 144

x² = 180

x = √180

x = 13.42

Now,

The perimeter of the trapezoid.

= 12 + 13.42 + 9 + 15

= 49.42

= 49.4

Thus,

49.4 is the perimeter of the trapezoid.

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now, we're making the assumption we're simply doing an identity proof, so

[tex]sec(\theta )-tan(\theta )sin(\theta )=\cfrac{1}{sec(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE 1st step} }{\cfrac{1}{cos(\theta )}-\cfrac{sin(\theta )}{cos(\theta )}\cdot sin(\theta )}\implies \cfrac{1}{cos(\theta )}-\cfrac{sin^2(\theta )}{cos(\theta )}\implies \cfrac{1-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )} \\\\\\ cos(\theta )\implies \cfrac{1}{sec(\theta )}[/tex]