Angle c and angle d are vertical angles with m angle c = -3x + 58 and m angle d = x - 2

The equation of the line perpendicular to y = 6x -2 and passes through (6, -2) is y = - 1 / 6 x - 1

The equation of a linear graph can be represented in slope intercept form.

Therefore,

y = mx + b

where

Therefore,  the equation of the line is perpendicular to y = 6x -2 and passes through (6, -2).

Perpendicular lines follows the rule below:

m₁ m₂ = -1

6m₂ = -1

m₂ = - 1 / 6

Therefore, let's find the y-intercept using (6, -2)

y = - 1 / 6 x + b

-2  = - 1 / 6 (6) + b

- 2 + 1 = b

b = -1

Therefore, the equation of the line is y = - 1 / 6 x - 1

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Answer: Just get closer

Step-by-step explanation:

Walk next to someone to hear them left foot right foot towards them.

The value of x is 1/2y+3/2

Answer:

y = 2x - 3

Step-by-step explanation:

8 + 2y - 5x + y = x - 1

3y = 6x - 9

y = 2x - 3

slope is 2, y-intercept is -3

Answer:

So what is the question trying to find out because it seems like an incomplete question.

the correct answer is 4.05

Answer:

See picture below.

Explanation

I took the test and got a 100% on it, so this should be right for any future students.

Answer:

Refer to the attachment!~

a) it takes 9.61 seconds for the automobile to overtake the truck. b) The automobile was initially 165.34 meters behind the truck. c) During the overtaking, the speed of the truck is 21.142 m/s, and the speed of the automobile is 33.635 m/s.

To solve this problem, we can use the equations of motion to calculate the time it takes for the automobile to overtake the truck, the initial distance between them, and their speeds during the overtaking.

Let's denote the time it takes for the automobile to overtake the truck as t.

(a) For the truck:

Using the equation of motion s = ut + (1/2)a\(t^{2}\), where s is the distance covered, u is the initial velocity (0 in this case), a is the acceleration (2.2 m/s^2), and t is the time, we can find the distance covered by the truck when the automobile overtakes it.

s_truck = (1/2) * 2.2 * \(t^{2}\)

s_truck = 1.1 *  \(t^{2}\)

For the automobile:

s_automobile = (1/2) * 3.5 * \(t^{2}\)

s_automobile = 1.75 *  \(t^{2}\)

Given that the truck has moved 60 m when the automobile overtakes it, we can set up the equation:

s_truck = s_automobile + 60

1.1 *  \(t^{2}\)  = 1.75 *  \(t^{2}\)  + 60

Simplifying the equation:

0.65 *  \(t^{2}\)  = 60

\(t^{2}\)  = 60 / 0.65

\(t^{2}\)  ≈ 92.3077

t ≈ √92.3077

t ≈ 9.61 seconds

Therefore, it takes approximately 9.61 seconds for the automobile to overtake the truck.

(b) To find the initial distance between the automobile and the truck, we can substitute the value of t into either of the equations:

s_automobile = (1/2) * 3.5 *  \(t^{2}\)

s_automobile = (1/2) * 3.5 * \((9.61)^{2}\)

s_automobile ≈ 165.34 meters

Therefore, the automobile was initially approximately 165.34 meters behind the truck.

(c) To find the speeds of the automobile and the truck during overtaking, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.

For the truck:

v_truck = 0 + 2.2 * 9.61

v_truck ≈ 21.142 m/s

For the automobile:

v_automobile = 0 + 3.5 * 9.61

v_automobile ≈ 33.635 m/s

Therefore, during the overtaking, the speed of the truck is approximately 21.142 m/s, and the speed of the automobile is approximately 33.635 m/s.

Correct Question :

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a constant acceleration of 2.2 m/s2 and the automobile has an acceleration of 3.5 m/s 2. The automobile overtakes the truck when it (truck) has moved 60 m.

(a) How much time does it take to automobile to overtake the truck?

(b) How far was the automobile behind the truck initially?

(c) What is the speed of each during overtaking?

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Answer:

is this 9th grade math????

Step-by-step explanation:

1

Answer:

D) 2x² + x - 10

Step-by-step explanation:

First, distribute the negative sign to all terms within the second parenthesis:

- (4x - x² + 6) = -4x + x² - 6

Next, combine like terms:

5x + x² - 4 - 4x + x² - 6

(x² + x²) + (5x - 4x) + (-4 - 6)

2x² + x - 10

2x² + x - 10 , or D) is your answer.

Answer:

2x^2+x-10 (the pink/red one)

Step-by-step explanation:

(5x+x^2-4)-(4x-x^2+6)

5x+x^2-4-4x+x^2-6

2x^2+x-10

Answer:

1 X 88=88

2 X 88=176

3X88=264

4X88=352

Step-by-step explanation:

a) the calculated t-value (2.344) is greater than the critical t-value (1.984), we reject the null hypothesis. b) The p-value associated with a t-value of 2.344 is approximately 0.010 (two-tailed test).

(a) To determine if the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, we can conduct a two-sample t-test.

Let's define our null hypothesis (H0) as "there is no significant difference in average yearly reading growth between Program A and Program B" and the alternative hypothesis (H1) as "Program A leads to higher average yearly reading growth than Program B."

We have the following information:

For Program A:

Sample size (na) = 64

Sample mean (xA) = 1.2

Sample standard deviation (sA) = 0.26

For Program B:

Sample size (nb) = 100

Sample mean (xB) = 1.0

Sample standard deviation (sB) = 0.28

To calculate the test statistic, we use the formula:

t = (xA - xB) / sqrt((sA^2 / na) + (sB^2 / nb))

Substituting the values, we have:

t = (1.2 - 1.0) / sqrt((0.26^2 / 64) + (0.28^2 / 100))

t ≈ 2.344

Next, we determine the critical t-value corresponding to a 5% significance level and degrees of freedom (df) equal to the smaller sample size minus 1 (df = min(na-1, nb-1)). Using a t-table or statistical software, we find the critical t-value for a two-tailed test to be approximately ±1.984.

(b) To calculate the p-value, we compare the calculated t-value to the t-distribution. The p-value is the probability of observing a t-value as extreme as the one calculated, assuming the null hypothesis is true.

From the t-distribution with df = min(na-1, nb-1), we find the probability corresponding to a t-value of 2.344. This probability corresponds to the p-value.

(c) Based on the results of the hypothesis test, where we rejected the null hypothesis, we can conclude that there is evidence to suggest that Program A leads to higher average yearly reading growth compared to Program B.

(d) To calculate the probability of a Type II error (β), we need additional information such as the significance level (α) and the effect size. The effect size is defined as the difference in means divided by the standard deviation. In this case, the effect size is (xA - xB) / sqrt((sA^2 + sB^2) / 2).

Let's assume α = 0.05 and the effect size (xA - xB) / sqrt((sA^2 + sB^2) / 2) = 0.1. Using statistical software or a power calculator, we can calculate the probability of a Type II error (β) given these values.

Without the specific values of α and the effect size, we cannot provide an exact calculation for the probability of a Type II error. However, by increasing the sample size, we can generally reduce the probability of a Type II error.

In summary, the differences in average yearly reading growth between Program A and Program B are significant at a 5% level, suggesting that Program A leads to higher average yearly reading growth. The p-value of the test results is approximately 0.010. Based on these findings, it may be recommended to adopt Program A over Program B. The probability of a Type II error (β) cannot be calculated without specific values of α and the effect size.

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It will take 2.2 hours for the two trains to meet.

We can find the time taken by the two trains to meet by using the formula,

large Time=Distance/Speed

Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.

Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.

Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.

The distance covered by the second train in time "t"=105t.

So, the total distance covered by both the trains in time "t" is,

Distance covered = 85t+105t=190t.

But we know the distance between the two trains is 418 miles.

Therefore,190t = 418

Now, solve for "t"t = 418/190t = 2.2 hours

Therefore, the two trains will meet in 2.2 hours.

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Answer:

60$

Step-by-step explanation:

The formula for simple interest is:

I = P x r x t

where I is the interest earned, P is the principal amount (initial investment), r is the annual interest rate, and t is the time in years.

In this case, P = $500, r = 3% = 0.03 (since the annual interest rate is expressed as a decimal), and t = 4 years. Plugging these values into the formula, we get:

I = $500 x 0.03 x 4

I = $60

Therefore, the interest earned after 4 years is $60.

By using the concept of compound interest, rate of interest is 3.1 %

What is compound interest?

If the interest on a certain principal at a certain rate over a certain time increase exponentially rather than linearly, the interest earned is called Compound interest.

If the principal is P, rate is r and time is t, then amount is

\(A = P(1 + \frac{r}{100})^n\)

Let the principal be $P and the rate be r% per annum

After 5 years there is $673.40 in the account.

\(673.40 = P(1 + \frac{r}{100})^5\\\)............. (1)

After 8 years there is $737.99 in the account.

\(737.99 = P(1 + \frac{r}{100})^8\) ................. (2)

Dividing (2) by (1),

\((1 +\frac{r}{100})^3 = 1.096\\\\1 + \frac{r}{100} = (1.096)^{\frac{1}{3}}\\\\1 + \frac{r}{100} = 1.031\\\\\frac{r}{100} = 1.031 -1\\\\\frac{r}{100} =0.031\\\\r = 0.031 \times 100\\\)

r = 3.1 %

Rate is 3.1 %

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Answer:

3/10

Step-by-step explanation:

If homeroom 101 has 1/2 of the bulletin board, and 3/5 of their side is used.

To calculate the area that is using we multiply both values,

1/2 x 3/5 = 3/10

Which is our answer!

The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

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

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

\(h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80\)

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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Answer:

B is the answer

plug any number in for y and work though each option

Answer: deku joking answer is B

Step-by-step explanation:

Answer: The answer is 3/8.

Learn how to add and subtract fractions

Khan Academy Video: Adding and subtracting fractions

The value of expression in fraction form is,

⇒ 3/8

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ 7/8 - 1/2

Now, We can simplify as;

⇒ 7/8 - 1/2

⇒ (7 - 4) / 8

⇒ 3 / 8

Thus, The value of expression in fraction form is,

⇒ 3/8

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Answer: Slope = -8/9 using the slope formula

Step-by-step explanation:

Answer: 30%

Step-by-step explanation: Solution for 6300 is what percent of 21000: 6300:21000*100 = (6300*100):21000 = 630000:21000 = 30. Now we have: 6300 is what percent of 21000 = 30.

if we take 21000(origin amount) to be the 100%, what's 6300 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 21000 & 100\\ 6300& x \end{array} \implies \cfrac{21000}{6300}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{10}{3} ~~=~~ \cfrac{100}{x}\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30\)

Answer:

c = 0.85 ; $1.7 ; c = 0.79p

Step-by-step explanation:

Given :

Cost per pound of supply shipped = $0.85

Total cost, c to ship p pounds of horse supply

Total cost = cost per pound * pound of supply

c = 0.85 * p

c = 0.85p

Cost of shipping 2 pounds :

c = 0.85 * 2

c = $1. 7

B.)

Reduction in shipping cost :

Reduced cost = $0.85 - $0.06 = $0.79

Total cost = cost per pound * pound of supply

c = 0.79 * p

c = 0.79p

Answer:

√9 = ±3

Step-by-step explanation:

... Because 3 × 3 = 9 and (-3) × (-3) = 9

However, it is agreed universally that we take the so-called “positive square root”. That is, we accept that the only answer is 3. In contrast, when we have (x^2) =9, where x is a variable, we don't know whether x is positive or negative so we cannot rule out the possibility that x is negative.

Square root means a number that produces a specified quantity when multiplied by itself.

Answer:

± 3

Step-by-step explanation:

\(\sqrt{9}\) = ± 3

That is + 3 or - 3

Since 3 × 3 = 9 and - 3 × - 3 = 9

The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

4x - 2y = 8  

Adding 2y on both sides of the equation , we get

2y + 8 = 4x

Subtracting 8 on both sides of the equation , we get

2y = 4x - 8   be equation (1)

Now , let the second equation be represented as B

Now , the value of B is

y = ( 3/2 )x - 2

On simplifying the equation , we get

2y = 3x - 4   be equation (2)

Now , subtracting equation (2) from equation (1) , we get

4x - 8 - ( 3x - 4 ) = 0

4x - 8 - 3x + 4 = 0

x - 4 = 0

Adding 4 on both sides of the equation , we get

x = 4

Substitute the value of x = 4 in equation ( 1 ) , we get

2y = 8

y = 4

So , the value of x = 4 and y = 4

The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )

Hence , the equations are solved

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The first difference is linear with time and pop. growth. The second difference is constant

The data presented shows the growth of the Javanese gibbon population on three different islands over time.

Analyze data to determine growth function by plotting and observing curve shape. Since the table only has data, analyze trends by comparing consecutive terms.

To do this, we can calculate the first difference and the second difference in the population data.

The first difference:

- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10

Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15

- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20

The second difference:

- Batanta: 10 - 10 = 0, 10 - 10 = 0

- Example: 15 - 10 = 5, 15 - 15 = 0

- Salavati: 20 - 20 = 0, 20 - 20 = 0

The first difference is linear with time and pop. growth. The second difference is constant. The population growth model is a linear function:

M(x) = mx + b

where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).

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The Complete Question

Scientists are studying the population of a rare species of primates, known as a Javan gibbons, on the Raja Ampat Islands in Indonesia. They are studying the gibbons on three different islands, Batanta, Misool, and Salawati. The scientists studied the population growth and recorded the data in the table.

Years (x)

Batana

B(x)

Misool

M(x)

Salawati

S(x)

0

2

20

38

1

6

120

81

2

18

420

124

3

54

920

167

4

162

1620

210

5

486

2520

253

What type of function is B(x), linear, quadratic or exponential? Justify your answer and show calculations to support your conclusion.

What type of function is M(x)? Justify your answer and show calculations to support your conclusion.

What type of function is S(x)? Justify your answer and show calculations to support your conclusion.

A white-handed gibbon population, represented by W(x), was recorded at a fourth location, starting in year three.

Of the functions B(x), M(x), and S(x), which function is the same type as W(x)? Justify your answer and show calculations to support your conclusion.

Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

The vector OB can be expressed as OB = b since b is a unit vector and O is the origin.

The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.

The angle between a and b is 60°, so we have:

|a| |b| cos 60° = a · b

2|b| · 1/2 = a · b

|b| = a · b

We can now express the vector [OB + (1 - O)A] as:

[OB + (1 - O)A] = b + (1 - O)2b

= (2 - O) b

The cross product of a and [OB + (1 - O)A] is:

a × [OB + (1 - O)A] = a × [(2 - O) b]

= (2 - O) (a × b)

The magnitude of the cross product is:

|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|

= |2 - O| |a| |b| sin 60°

= √3 |2 - O| |b| |a| / 2

= √3 |2 - O| |b|^2 |b| / 2

= √3 |2 - O| |b|^3 / 2

Substituting |b| = a · b, we get:

|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2

Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:

√k = √3 |2 - O| (a · b)^3 / 2

Squaring both sides, we get:

k = 3 (2 - O)^2 (a · b)^6 / 4

Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To estimate the required sample size for estimating the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36, we need to use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96)

p = estimated proportion (since we have no prior information, we can use p = 0.5, which gives the maximum sample size required)

E = margin of error

Substituting the values into the formula:

n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.36^2

n = (3.8416 * 0.25) / 0.1296

n ≈ 9.6042 / 0.1296

n ≈ 74.0842

Rounding up to the nearest whole number, the required sample size is approximately 75. Therefore, you would need to survey at least 75 randomly selected Americans to estimate the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36.

To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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