Use the given equation to determine if the points in the brackets are on the graph
of the line determine by the equation 4x- 3y=-6

{(0,2),(1,3),(4,7),(6,10)}

Answer:

(- 2, - 4 )

Step-by-step explanation:

The x- coordinate of the vertex is calculated as

x = - \(\frac{b}{2a}\)

g(x) = x² + 4x

with a = 1, b = 4 , then

x = - \(\frac{4}{2}\) = - 2

Substitute x = - 2 into g(x) for corresponding y- coordinate

g(- 2) = (- 2)² + 4(- 2) = 4 - 8 = - 4

vertex = (- 2, - 4 )

The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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The completed blanks in the statement are underlined as follows

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

A mathematical expression

The mathematical expression is given as

2x⁴ + 53x⁵ - 2 + x⁶

The standard form

To do this, we rearrange the expression from the highest power to the least

So, we have the following representation

x⁶ + 53x⁵ + 2x⁴  - 2

The degree

This is the highest power in the expression

So, the degree is 6

The leading coefficient

This is the coefficient of the term that has highest power of x

So, the leading coefficient is 1

The name of the expression

The expression has 4 terms

So, the name is a polynomial

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Answer:

--------------------------

Given x-values in the table.

Use the equation of the function to find the corresponding y-values:

When x = - 27:

When x = 0:

When x = 27:

So the missing numbers are: - 3, 0 and 3.

The matching choice is B.

Your answer for A is correct.

For B, I would keep the base of the logarithm as simple as possible.

\(y = 100 \cdot 3.24^x \implies \dfrac y{100} = 3.24^x \implies \log_{3.24}\left(\dfrac y{100}\right) = \log_{3.24}(3.24)^x \\\\ \implies x = \log_{3.24} \left(\dfrac y{100}\right)\)

In part A, the function told us the number of students with cell phones (dependent variable) after some number of years post-2000 (independent variable). Our new function turns this around and tells us the time in years after 2000 (dependent) based on how many student have cell phones (independent).

For C, if we set \(y=7200\) students, then we can estimate the time it takes for the all students to acquire cell phones by solving for \(x\).

\(x = \log_{3.24}\left(\dfrac{7200}{100}\right) = \log_{3.24}(72) \approx 3.63794\)

If you're using a typical calculator, it probably won't have buttons for logarithms of any base other than 10 or the natural base \(e\). To work around that, use the change-of-base identity

\(\log_{3.24}(72) = \dfrac{\log_{10}(72)}{\log_{10}(3.24)} = \dfrac{\ln(72)}{\ln(3.24)}\)

At any rate, it would take about 3.64 years for all students to get a cell phone, according to this model.

The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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Answer:

2688

Step-by-step explanation:

3mt

m = 56

t = 16

(3)(56)(16) = 2688

Hopefully this helps you :)

pls mark brainlest ;)

The equation in the form y = f(x) is: y = 3 - 4x^2. To write the equation in the form y = f(x), we need to isolate y on one side of the equation.

We can do this by subtracting 16x^2 from both sides of the equation:

16x^2 + 4y = 12

4y = 12 - 16x^2

Now divide both sides of the equation by 4 to get y by itself:

y = (12 - 16x^2)/4

Simplifying the right-hand side of the equation, we get:

y = 3 - 4x^2

Therefore, the equation in the form y = f(x) is: y = 3 - 4x^2.

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Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

The area of the triangle ABC, obtained using the formula for a triangle where two sides and the included angles are known is the option C

C. 81.1 cm²

The formula for the area of a triangle, where the lengths of two sides and the included angle are known, can be presented as follows;

Area, A = (1/2) × a × b × sin(C)

Where a and b are the lengths of the two sides and the included angle C is the measure of the included angle between the two sides, therefore;

The diagram indicates that we get;

Where;

a = 11 cm and b = 18 cm and the measure of the included angle C = 55°, we get;

A = (1/2) × 11 × 18 × sin(55°) ≈ 81.1

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The success rates of the three treatments in preventing cardiac events are approximately 90.91% for the stress management program, 79.41% for the exercise program, and 70% for usual heart care.

a. Two-way table:
| Treatment | Cardiac Events | No Cardiac Events |
|-----------|-----------------|----------------------|
| Stress Management | 3 | 30 |
| Exercise | 7 | 27 |
| Usual Care | 12 | 28 |
b. The success rates of the three treatments in preventing cardiac events can be calculated as the percentage of people in each group who did not experience a cardiac event.
- Stress management: 90.9% success rate (30/33)
- Exercise: 79.4% success rate (27/34)
- Usual care: 70% success rate (28/40)
Therefore, the stress management program had the highest success rate in preventing cardiac events, followed by the exercise program and then usual care.

Stress management and its impact on reducing heart attacks. Let's analyze the study results and create a two-way table, as well as calculate the success rates of the three treatments in preventing cardiac events.
a. Two-way table:
| Treatment          | Cardiac Events | No Cardiac Events | Total |
|--------------------|----------------|-------------------|-------|
| Stress Management  | 3              | 30                | 33    |
| Exercise Program   | 7              | 27                | 34    |
| Usual Heart Care   | 12             | 28                | 40    |
| Total              | 22             | 85                | 107   |
b. Success rates of the three treatments in preventing cardiac events:
1. Stress Management:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (30 / 33) * 100
Success rate ≈ 90.91%
2. Exercise Program:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (27 / 34) * 100
Success rate ≈ 79.41%
3. Usual Heart Care:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (28 / 40) * 100
Success rate = 70%

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Answer:2 1 4 then 3

Step-by-step explanation:

The option (3) 0.03, 0.3, 0.35 represents the order from least to greatest. Option (3) is correct.

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56, 0.3 etc. are the numbers.

We have decimal number:

0.35, 0.3, 0.03

Here, the smallest number is 0.03

And the greatest number is 0.35

So,

The order from least to greatest:

0.03 > 0.3 > 0.35

Thus, the option (3) 0.03, 0.3, 0.35 represents the order from least to greatest. Option (3) is correct.

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The probability that a yellow disk will be selected is 1/5.

It is one fifth that a yellow disk will randomly selected from the bag

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability that a yellow disk will be selected is:

= 5 / 25

= 1/5.

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Answer:

2.  3.913 kg (3 dp)

3.  light cream

4.  240 CoffeeStops

5.  7 CoffeeStops per square mile

6.  2,861 cups of coffee each day

Step-by-step explanation:

Given:

Question 2

\(\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}\)

Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)

---------------------------------------------------------------------------------------------

Question 3

Given:

\(\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}\)

Therefore, the container holds light cream.

---------------------------------------------------------------------------------------------

Question 4

Given:

\(\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}\)

Therefore, there are 240 CoffeeStops.

---------------------------------------------------------------------------------------------

Question 5

Given

\(\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}\)

Therefore, the density of CoffeeStops is 7 per square mile.

---------------------------------------------------------------------------------------------

Question 6

Given:

\(\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}\)

\(\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}\)

Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.

Answer:

23

Step-by-step explanation: hope this helps

Answer:

greater than

hope this helps! <3

Answer:

first Q . mirror

Second Q. sight and touch

Answer:    Smoothest surface: mirror

senses being used: sight and touch

hope this helps!

Step-by-step explanation:

To find the possible Hamiltonian circuits that begin with JVTSR, we can start by constructing a path that begins with JVTSR and visits each vertex exactly once. Such a path must be of the form JVTSRX, where X is the remaining vertex.

Case 1: JVTSRQX

To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to Q are S and R. Thus, we must have X = S or X = R, and the circuits are JVTSRQS and JVTSRQR.

Case 2: JVTSRXQ

To find the possible value of X, we note that the only edges incident to X are S and L. Thus, we must have X = L, and the circuit is JVTSRLQ.

Case 3: JVTSRLX

To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to L are T and R. Thus, we must have X = R, and the circuit is JVTSRLR.

Case 4: JVTSRXL

To find the possible value of X, we note that the only edges incident to Q are S and R, and the only edges incident to X are L and S. Thus, we must have X = L, and the circuit is JVTSRQL.

Therefore, there are four possible Hamiltonian circuits that begin with JVTSR: JVTSRQS, JVTSRQR, JVTSRLQ, and JVTSRLR.

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The equations of the tangents are:y = -3/2 + sqrt(37)/2(x - 10) (smaller slope)y = -3/2 - sqrt(37)/2(x - 10) (larger slope):y=-\frac{3}{2}+\frac{\sqrt{37}}{2}(x-10) (smaller slope)y=-\frac{3}{2}-\frac{\sqrt{37}}{2}(x-10) (larger slope).

Curve isx = 6t^2 + 4, y = 4t^3 + 4the slope of tangent of this curve dy/dx is dy/dx=12t/(3t^2+2)Then, equation of tangent with slope m and passing through (x1, y1) is given by(y - y1) = m(x - x1) ............(1)Here, point is (10,8)Therefore, equation of tangent passing through (10, 8) will be of the form(y - 8) = m(x - 10)Let this tangent intersect the curve at point P. Then, the coordinates of point P are given byx = 6t^2 + 4y = 4t^3 + 4.

Equating this with equation (1), we get:4t^3 + 4 - 8 = m(6t^2 - 6)4t^3 = 6m(t^2 - 1)2t^3 = 3m(t^2 - 1)2t^3 + 3mt - 3m = 0t = -m/2 ± sqrt(m^2/4 + 3m)Therefore, the two tangents are given by:y - 8 = m1(x - 10), where m1 = -3/2 + sqrt(37)/2y - 8 = m2(x - 10), where m2 = -3/2 - sqrt(37)/2Hence, the equations of the tangents are:y = -3/2 + sqrt(37)/2(x - 10) (smaller slope)y = -3/2 - sqrt(37)/2(x - 10) (larger slope):y=-\frac{3}{2}+\frac{\sqrt{37}}{2}(x-10) (smaller slope)y=-\frac{3}{2}-\frac{\sqrt{37}}{2}(x-10) (larger slope).

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Note that the rule that describes the translation that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction.

Translation in geometry refers to shifting a form into a different place without affecting it in any manner. Shape translation is presented to Year 5 students by providing them shapes on squared paper that must be moved a specified number of squares up, down, left, or right.

Hence, the  translation rule

that was aplied to the trapezoid D.O.G.S to create D'.O'. G'. S' is (x,y) → (x-3, y-7).

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

Each of the three sisters owes $75 to cover the cost of hiring the karaoke deejay for Taylor's graduation party.

To determine how much each sister owes, we need to first calculate the total cost of the party and then divide that cost by three, since there are three sisters splitting the cost.

1. Tent rental: $45
2. Microphone system: $60
3. Deejay cost: $30/hour × 4 hours = $120

Now, we'll add these costs together to find the total cost:
Total cost = $45 (tent) + $60 (microphone) + $120 (deejay) = $225

Finally, we'll divide the total cost by the number of sisters (3) to find out how much each sister owes:
Amount owed per sister = $225 (total cost) ÷ 3 (sisters) = $75

So, each sister owes $75 for the karaoke deejay at Taylor's graduation party.

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Answer:

\(1 \div {3}^{( 30)} \)

Step-by-step explanation:

There are exponent rules I posted above that are being used here.

We have (3^-6)^-5

Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.

So, we're left with 3^-30.

If you look at the photo, there's a rule for negative exponents.

Take the inverse of the base number, so 3 in this case:

1 / 3

and then make the exponent positive after taking the inverse.

So, we should get 1 / 3^30

Hope this helps!

Answer:

Step-by-step explanation:

(x / -5) + 7 ≥ 1

To convert steps to miles, use the average stride length to calculate the distance covered by the steps.The average stride length for a person is approximately 2.5 feet, and there are approximately 5,280 feet in a mile.

Unit conversion is the process of changing a quantity from one unit of measurement to another, while maintaining its value. This is often done to compare measurements in different systems of units or to express a measurement in a unit that is more appropriate for a particular situation.

For example, converting between metric units (such as grams or meters) and imperial units (such as ounces or feet) is a common type of unit conversion. The process of unit conversion involves using a conversion factor, which is a ratio that relates the units being converted.  

To convert steps to miles, simply multiply the number of steps taken by the average stride length, and then divide the result by 5,280.

For example, if you take 10,000 steps, the distance covered would be approximately 4.47 miles (10,000 x 2.5 / 5,280).

Keep in mind that the average stride length can vary based on factors such as height, age, and fitness level, so it is important to measure your own stride length for the most accurate results.

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Answer:

1.5 seconds

Step-by-step explanation:

plug 0 in for y

0=-16t^2+36

then slove for t

-36=-16t^2

-36 / -16 = 9/4

9/4=t^2

square root of 9/4 is 3/2 or 1.5

t=1.5

The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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Answer:

y=1 x=9

Step-by-step explanation:

-4(9y) + y = -35

-36y+y=-35

-35y= -35

y=1

To check-

-4(9) + 1 = -35

-36 + 1 =-35

3x-9x²

Factor out 3x from the expression

Answer: 3x^ x(1-3x)