What is the solution to -5y - 6y = -22

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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If the population grows at the same rate 't' , then the population in next 20 years will be approximately 896 people.

The general formula can be used to calculate the exponential growth, which is:

P(t) = P0 e^(rt)

In the above equation,

P(t) is the population at time t

P0 is the population present initially

r is the rate of growth

e is the mathematical constant, whose value is approximately equal to 2.71828...

Since the population is growing at a rate proportional to the population present at time t, we know that: r = kP(t) (k is the proportionality constant)

P(t) = P0 e^(kP(t) t)

Since we are provided with the value of initial population P0 is which is 500, and that the population increases by 20% in 10 years. This infersthat:

P(10) = 500 + 0.2(500) = 600

The information above can be used to find the value of k. We plug in t=10 and P(10) = 600 into the equation above and solve for k:

600 = 500 e^(10k)

1.2 = e^(10k)

ln(1.2) = 10k

k = ln(1.2)/10

Now we can use this value of k can be utilized in order to calculate P(20), the population after 20 years:

P(20) = 500 e^(20k)

P(20) = 500 e^(20 ln(1.2)/10)

P(20) = 896 (approx.)

Hence, in can be said that the population in 20 years will be approximately 896 people.

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One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

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Answer: 32604

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

Hope it helps!

Answer:

D

Step-by-step explanation:

Complete question:

The amount of garbage, G produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f

Answer:

The information of town Tola can be represented in function as 6 = f(45)

Step-by-step explanation:

Given;

population of Tola, p = 45,000

amount of garbage produced in tons per week, G = 6 tons = 6,000 kg

The function is given by;

G = f(p)

where;

G is the amount of garbage produced in tons per week

p is the population of Tola

Substitute in the given values into the function

6000 = f(45,000)

6 = f(45)

Therefore, the information of town Tola can be represented in function as 6 = f(45)

Answer:

WHat is it :(

Step-by-step explanation:

Answer:

Easy Question: I/pt=r

Step-by-step explanation:

You take the equation i=prt and you solve it out.

You divide the half "prt" by pt like this: prt/pt

You also do that to the other side "I"

You are left with I/pt=r and there it is!!

There are 10,000 different telephone numbers possible in city A.

Since the first three digits of the telephone number are fixed to be 719, we only need to consider the possible combinations for the last four digits.

Each of the last four digits can be any of the ten digits 0 through 9, so there are 10 choices for each of the four digits. Therefore, the total number of possible telephone numbers is:

10 × 10 × 10 × 10 = 10,000

Therefore, there are 10,000 different telephone numbers possible in city A.

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Answer:

# of broken crayons    # of boces

           1-5                            1

          6-10                          4

          11-15                          5

          16-20                        3

          21-25                         1

Step-by-step explanation:

1-5: 4 (1 number)

6-10: 6, 6, 8, 9 (4 numbers)

11-15: 12, 13, 14, 14, 15 (5 numbers)

16-20: 17, 17, 19 (3 numbers)

21-25: 24 (1 number)

Answer:

Number of broken crayons Number of boxes

1-5 = 4

6-10 = 9

11-15 = 14

16-20 =19

21-25 =24

Step-by-step explanation:

To find the number of boxes compared to the number of broken crayons you have to find 5 consecutive (hence there being five boxes to fill in) numbers with a constant rate of change. Start with the largest number possible that you can pick and then find the second largest so 24 and 19 the rate of change is 5. Compared to 17 and 19 the rate of change is 2 so it doesn’t have the same rate of change but if you try 19-5 you get 14 which is an option if you subtract 14-5 you get 9 which is another option 9-5 is 4 the lowest number you could possibly pick and they all have a constant rate of change of 5 so the answer is correct.

Answer:

A is the cheapest deal.

Step-by-step explanation:

find unit rate; cost / quantity

20.20 / 10 = $2.02 per gallon

26.04 / 12 = $2.17 per gallon

28.24 / 24 = $2.01 per gallon

30.45 / 25 = $2.03 per gallon

Answer:

this one has to be answer 1

Step-by-step explanation:

4x - y = -5

x + 2y =1

8x - 2y = -10

x + 2y = 1

9x = -9

Answer:

K-273=C

Step-by-step explanation:

K=C+273

Subtract 273 from each side

K-273=C+273-273

K-273=C

Answer:

12/3=4

Y= Time and X=The number of shoelaces

Answer: y = 4x (y = shoelaces & x = minutes)

Step-by-step explanation: We know that 12 shoelaces are produced in 3 minutes and that the ratio of shoelaces produced to minutes spent is proportional. We can figure out, therefore, that if you multiply the number of minutes by 4, you will get the number of shoelaces. As an equation, this would be y = 4x (y = shoelaces & x = minutes).

Good Luck!

Answer:

1. Multiply the area by 2 and divide the result by the central angle in radians.

2. Find the square root of this division.

3. Multiply this root by the central angle again to get the arc length.

Step-by-step explanation:

Answer:

\(C=4\)

Step-by-step explanation:

\(7(c-18)=-98\\7c \frac{-126}{+126}=\frac{-98}{+126} \\\frac{7c}{7}=\frac{28}{7}\\c=4\)

⊰_________________________________________________________⊱

Answer:

Step-by-step explanation:

\(\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}\)

\(\pmb{\tt{done \ !!}}\)

⊱_________________________________________________________⊰

Based on the stress-strain curves shown, the most likely statement is that Material A is likely a ceramic material because it shows brittle behavior.

Brittle behavior is characterized by low ductility and little plastic deformation before failure, which is evident in the stress-strain curve for Material A. The curve for Material B shows some plastic deformation before fracture, which indicates a higher level of ductility than Material A. The stress-strain curve for Material C shows a high level of ductility, with a long plastic deformation region before fracture. This behavior is typical of polymeric materials, so Material C is most likely a polymeric material.

It is not possible to determine the specific type of material based solely on stress-strain curves, as many materials can exhibit similar behaviors. Additionally, it is not accurate to say that Material B or Material C are likely ceramic materials based on their stress-strain curves, as both exhibit significant plastic deformation before failure, which is not typical of brittle ceramics.

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Step-by-step explanation:

\(9 {( - \frac{8}{3}) }^{} {}^{2} + 48( - \frac{8}{3} ) + 64 \\ \\ 9( - \frac{64}{9} ) - \frac{48}{3} + 64 \\ \\ - 64 - 16 + 64 = - 16\)

Answer:

D

Step-by-step explanation:

Answer:   x^2+4

Work Shown:

x = -2i

x^2 = (-2i)^2

x^2 = 4i^2

x^2 = 4(-1)

x^2 = -4

x^2+4 = 0

Side note: Since -2i is one root, this means 2i is the other conjugate root.

\(\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0\)

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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Answer:

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 5.9pounds/square inch

Given mean of the sample = 6.0pounds/square inch

Given that variance of the Population = 0.36

The standard deviation of the Population = √0.36 =0.6

critical value (Z₀.₀₅)= 1.96

Step(ii):-

Null Hypothesis:H₀: x⁻ = μ

Alternative Hypothesis:H₁:  x⁻ ≠ μ

Test statistic

              \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

               \(Z = \frac{6.0-5.9 }{\frac{0.6}{\sqrt{160} } }\)

              Z  =  2.1097

Final answer:-

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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An algebraic expression to show representatives r, the students will have in any year is r=(a+b+c+d+e)/50.

An expression is combination of variables, numbers and operators.

Given, that school district can send a representative to the state spelling bee for every 50 students in the school district that year.

There are 5 schools woth a b c d e students respectively.

We need to find the algebraic expression to show how many representatives r, the students will have in any year.

r=(a+b+c+d+e)/50

THe above expression is used to represent the representives.

Hence, (a+b+c+d+e)/50 is an algebraic expression to show representatives r, the students will have in any year

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The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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