standard to slope intercept form

The kinematics equation s = 1/2at² can be used to determine the acceleration in the Second Law Experiment, where acceleration is calculated by measuring the time taken for the cart to move from the start point to the end point.

Let's derive how the equation is used to find the acceleration from this experiment:

Drivation of kinematics equation:

The kinematics equation is derived by integrating the acceleration function twice with respect to time (t).

Acceleration, a = d²s/dt², where s is displacement, and d²s is the second derivative of displacement with respect to time.

taking integral w.r.t time twice:

∫ a dt = ∫ d²s/dt² dt integrating once gives, v = at + C₁ (where C₁ is a constant of integration)

integrating twice gives, s = 1/2at² + C₁t + C₂ (where C₂ is a constant of integration)

Thus, the kinematics equation for an object moving with constant acceleration can be represented by

s = 1/2at² + vit + s₀,

where s is the displacement, a is the acceleration, t is time, vi is initial velocity, and s₀ is initial displacement.

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Answer:

12 pi

Step-by-step explanation:

volume of sphere = 4/3 pi r2

4/3 pi 3 x 3

12 pi unit square

Answer:

Step-by-step explanation:

50 an hour for 2 hours. 50(2) is 100

plus the 99 consultation fee.

Assuming there's no taxes because you're one of the lucky ones that doesn't have to pay, the total charge would be $199 dollars

Answer:

.04

because 4% of 100 is 4

The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9

A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.

The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.

Complete Question:

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

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In parallelogram lonm, om is 34.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

First we have OQ =QM,

So 2x+3=3x-4,

x =7.

Hence OM =2(17)=34.

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Answer: D) 34

Step-by-step explanation:

edge 2023

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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Answer:

its A!

Step-by-step explanation:

Answer:

2.5(2-(-6))

Step-by-step explanation:

first of all,

the difference between 2 and -6 is

2-(-6)

then product of 2.5 with this difference is

2.5× (2-(-6)=

2.5(2-(-6))

Answer:

8

Step-by-step explanation:

To find the median, look at the line in the box. it lines up with 8 on the number line. Therefore, 8 is the median.

A. The linear relationship can be expressed by the equation, 3y = 5x + 10

B. For  25 kg, the height is 45 cm

   For  52 kg, the height is 90 cm

C. For 60 cm, the mass is 34

    For 80 cm, the mass is 46

The equation of a straight line is a relationship between x and y coordinates, The two point form of the equation of a straight line is,

y-y₁ =  (y₂-y₁)/(x₂-x₁)*(x-x₁)

Given that,

The scatter plot,

which shows the linear relationship,

And passes through the points,

(10, 20), (40, 70)

the equation of line can be written as,

y - 20 =  (70-20)/(40-10)*(x-10)

y - 20 = 50/30*(x-10)

y - 20 = 5/3*(x-10)

3y - 60 = 5x - 50

3y = 5x + 10

A. The linear relationship,
3y = 5x + 10

B.    If x = 25, we can substitute this value into the equation to find the corresponding value of y:

3y = 5 x 25 + 10

3y = 125 + 10

3y = 135

Dividing both sides of the equation by 3:

y = 45

So, if x = 25, then y = 45.

similarly,  the value of y for x = 25 is, 90

In the same manner,

when,

For y = 60 x will be 34

And for y = 80 x will be 46

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Answer:

\(Q_n=(2000)-(20)P_n\)

Step-by-step explanation:

From the question we are told that:

Initial Quantity demanded Q_1= 200 units

Initial demand price \(P_1=\$90\)

Final Quantity demanded \(Q_2= 1200 units\)

Final demand price \(P_2=\$40\)

Generally the  Demand Equation is mathematically given by

 \(Q_n=a-bP_n\)

Where

a=Other factors affecting price

b=Slope of the demand curve

Therefore

 \(Q_1=a-bP_1\)

 \(200=a-b(90)\)

 \(Q_2=a-bP_2\)

 \(1200=a-b(40)\)

Comparing both above equations

  \(a=2000\)

  \(b=20\)

Therefore the  Demand Equation is mathematically given by

  \(Q_n=(2000)-(20)P_n\)

Answer:

Area of the figure = 171 in²

Step-by-step explanation:

Composite figure given in the picture comprises of three figures, two right triangles and one rectangle.

Area of the composite figure = Area of two right triangles + Area of the rectangle at the center

Area of one right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                           = \(\frac{1}{2}(12)(9)\)

                                           = 54 in²

Area of the rectangle = Length × Width

                                    = 7 × 9

                                    = 63 in²

Area of the composite figure = 2(54) + 63

                                                  = 108 + 63

                                                  = 171 in²

Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.

1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:

\(\rm I = P \times r \times t\)

Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.

2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:

\(\rm a^2 + b^2 = c^2\)

Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.

3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)

Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.

4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:

BMI = (weight in kilοgrams) / (height in meters)²

A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.

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Complete question:

Describe some common or unique mathematical formulas that you use in your life.

Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

To calculate the size of the container Camillo should buy, we need to find a container size that can accommodate the required 2,400 oz of peanut butter.

By comparing the given container sizes, we can see that the 40-oz container is the largest one available. As Camillo needs 2,400 oz of peanut butter, he would need to purchase multiple containers.

To find out how many of those containers Camillo will need, we can divide the total amount of peanut butter needed (2,400 oz) by the size of each container (40 oz). This gives us:

Number of containers = Total amount needed / Size of each container

Number of containers = 2,400 oz / 40 oz

Number of containers = 60 containers

So Camillo would need to buy 60 of the 40-oz containers to meet his requirement.

To calculate the total cost of those containers, we need to multiply the number of containers (60) by the price of each container. The price for each 40-oz container is $12.40. Therefore:

Total cost = Number of containers * Price per container

Total cost = 60 containers * $12.40

Total cost = $744.00

Hence, the total cost of the 60 containers would be $744.00.

In summary, Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

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Complete Question

Camillo needs 2,400 oz of peanut butter.

What size container should Camillo buy?

How many of those containers will he need?

What will be the total cost of those containers?

Container Size    Price          Unit Price

12-oz                   $2.52           $0.21/oz

16-oz                   $4.00           $0.25/oz

32-oz                  $5.12             $0.16/oz

40-oz                  $12.40           $0.31/oz

Let's take a look at the graph of the polynomial:

Now, notice that those three turning points tell us that the function changes from decreasing to increasing, or viceversa, right at that point.

This way, the decreasing intervals are:

And the increasing intervals are:

Answer:

a I think

Step-by-step explanation:

I dont know how to explain if its not im sorry

Therefore, √128 lies between 11 and 12 on a number line.

To determine the two numbers between which √128 lies on a number line, we can calculate the square roots of consecutive perfect squares that surround 128.

By calculating the square roots, we can find the two nearest whole numbers that √128 lies between.

Calculating the square roots of perfect squares near 128:

√121 = 11

√144 = 12

Since 128 is greater than 121 and less than 144, √128 lies between √121 and √144 on the number line.

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Answer:

-2/2 or -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The lines are neither parallel nor perpendicular.

Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if the product of their slopes is -1.

To find the slope of a line given in the form of Ax + By = C, we can rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.

The first line, 6x - 12y = 24, can be rearranged into slope-intercept form as follows:

12y = -6x + 24

y = -0.5x + 2

The slope of the first line is -0.5.

The second line, 4x + 2y = 8, can be rearranged into slope-intercept form as follows:

2y = -4x + 8

y = -2x + 4

The slope of the second line is -2.

Since the product of the slopes is not -1, the lines are not perpendicular. And since the slopes are not the same, the lines are not parallel. So, the lines are neither parallel nor perpendicular.

Answer:

Step-by-step explanation:

Define Variables:

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangos cost $8, then:

2p+3m=8

Write System of Equations:

5p+6m=17.75

2p+3m=8

System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangoes cost $8, then:

2p+3m=8

System of Equations:

5p+6m=17.75

2p+3m=8

Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

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the graph of f(x) = x^3 - 3x^2 - 9x + 5 is concave down on the interval (-∞, 1), concave up on the interval (1, +∞), and has a point of inflection at x = 1.

To determine the intervals on which the graph of a function is concave up or concave down, we need to analyze the second derivative of the function. The concavity of a function can change at points where the second derivative changes sign.

Here's the step-by-step process to find the intervals of concavity and points of inflection:

Find the first derivative of the function, f'(x).

Find the second derivative of the function, f''(x).

Set f''(x) equal to zero and solve for x. The solutions give you the potential points of inflection.

Determine the intervals between the points found in step 3 and evaluate the sign of f''(x) in each interval. If f''(x) > 0, the graph is concave up; if f''(x) < 0, the graph is concave down.

Check the concavity at the points of inflection found in step 3 by evaluating the sign of f''(x) on either side of each point.

Let's go through an example to illustrate this process:

Example: Consider the function f(x) = x^3 - 3x^2 - 9x + 5.

Find the first derivative, f'(x):

f'(x) = 3x^2 - 6x - 9.

Find the second derivative, f''(x):

f''(x) = 6x - 6.

Set f''(x) equal to zero and solve for x:

6x - 6 = 0.

Solving for x, we get x = 1.

Therefore, the potential point of inflection is x = 1.

Determine the intervals and signs of f''(x):

Choose test points in each interval and evaluate f''(x).

Interval 1: (-∞, 1)

Choose x = 0 (test point):

f''(0) = 6(0) - 6 = -6.

Since f''(0) < 0, the graph is concave down in this interval.

Interval 2: (1, +∞)

Choose x = 2 (test point):

f''(2) = 6(2) - 6 = 6.

Since f''(2) > 0, the graph is concave up in this interval.

Check the concavity at the point of inflection:

Evaluate f''(x) on either side of x = 1.

Choose x = 0 (left side of x = 1):

f''(0) = -6.

Since f''(0) < 0, the graph is concave down on the left side of x = 1.

Choose x = 2 (right side of x = 1):

f''(2) = 6.

Since f''(2) > 0, the graph is concave up on the right side of x = 1.

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Answer:

14

because 6(5)=30 and -2(8)=-16

30-16=14

Answer:

14

Step-by-step explanation:

All we need to do to get the value of 6a-2b is to plug in 5 for the variable "a" (replace a with 5) and plug in 8 for variable "b" (replace b with 8).

Because the variables are right next to the number, that indicates multplication, so the equation is basically saying 6*a-2*b

So let's plug in the numbers for the variables and solve:

6*5-2*8

6*5=30

2*8=16

30-16=14

So our final answer is 14

Answer:

x = 47/4

Step-by-step explanation:

The acute angles of a right triangle are complementary, i.e. their sum is 90

So, 5x + 3x - 4 = 90

       8x = 94

         x = 94/8 = 47/4

Answer: The value of X is 47/4

Step-by-step explanation:

Only 95% of the HF is recovered.  So, there is no change in the amounts of ore and H2SO4 needed to produce 100 kg of HF.

In the reaction: CaF2(s) + H2SO4(aq) → 2HF(g) + CaSO4(s)To calculate the quantity of fluorite ore and 90% H2SO4 solution needed to produce 100 kg of aqueous hydrofluoric acid, we proceed as follows:

Atomic masses: Ca = 40, F = 19, H = 1, S = 32, O = 16Molecular mass of CaF2 = 40 + (2 × 19) = 78 g/molMolecular mass of H2SO4 = 2(1 + 32 + 4 × 16) = 98 g/molWe have a feed that is 96% CaF2. Therefore the amount of feed required to produce 100 kg of HF is:78 kg of CaF2 is required.

Mass of 90% H2SO4 required = [1000/(90/1000)] × [(100/98) × (78/100)] = 907.75 kg

Total mass of slurry = 100 kg of 60% HF = 60/100 × 100 kg = 60 kg of HF + 40 kg of water + other impurities added in the process.

We have calculated the weight of fluorite ore and 90% H2SO4 solution to produce 100 kg of HF, so this side reaction has nothing to do with these amounts.

The amount of the produced HF that is consumed in an undesirable side reaction is given to us to be 5%, therefore only 95% of the HF is recovered.

We don’t need to change the amounts of ore and H2SO4 that we calculated. So, there is no change in the amounts of ore and H2SO4 needed to produce 100 kg of HF.

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Answer:

8p²

Step-by-step explanation:

9p²-3p²+2p²

Combine like terms.

9p²-3p²+2p² = 8p²

Hope this helps!

Please mark as brainliest if correct!

Answer:

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

Corresponding angles are congruent:

Answer:

If the triangles are similar:

If the triangles are right triangles:

Step-by-step explanation:

Note: As the question does not state if the triangles are similar triangles or right triangles, I have provided the answer for both options.

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

In similar triangles, corresponding interior angles are congruent.

Therefore, y = 43.

In similar triangles, corresponding sides are always in the same ratio.

\(\implies \sf 21:14=x:12\)

\(\implies \sf \dfrac{21}{14}=\dfrac{x}{12}\)

\(\implies \sf x=\dfrac{21 \cdot 12}{14}\)

\(\implies \sf x=18\)

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

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

Note: Assuming the triangles are right triangles.

Triangle x

Given:

Substitute the given values into the tan trigonometric ratio and solve for x:

\(\implies \tan(43^{\circ})=\dfrac{x}{21}\)

\(\implies x=21\tan(43^{\circ})\)

\(\implies x=19.5828168...\)

\(\implies x=19.6 \sf \; \;(nearest\;tenth)\)

Triangle y

Given:

Substitute the given values into the tan trigonometric ratio and solve for y:

\(\implies \tan(y^{\circ})=\dfrac{12}{14}\)

\(\implies y^{\circ}=\tan^{-1}\left(\dfrac{12}{14}\right)\)

\(\implies y^{\circ}=40.6012946...^{\circ}\)

\(\implies y=40.6\;\; \sf (nearest\;tenth)\)

Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 68° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

 From right angle triangle

     x = 16 × cos 68°

    x = 16 × 0.4067

    x = 6.5077

  x = 6.5 ft

The length of the ladder = 6.5 ft

Answer: -1, 1.5, 3 1/12

Step-by-step explanation: I was tested on these type of questions

Answer:

B

Step-by-step explanation:

Answer:

Just took the test the answer is 85%