HURRY ITS TIMED !!
Look at the table shown below:
х у
0 0
2 3
4 6
6 9
8 12

Determine the slope of the line that passes through the points.

ANSWER CHOICES

A. 1/2
B. 2/3
C. 2
D. 3/2

The tortoise ran distance for approximately 1.0625 hours, which is equivalent to 1 hour and 3 minutes.

Let's denote the time the tortoise ran as T (in hours) and the distance they both ran as D (in miles).

We know that the tortoise ran at a speed of 2 ½ mph, which can be expressed as 2.5 miles per hour. Therefore, the distance D is given by:

D = 2.5T

Similarly, the hare ran at a speed of 8 ½ mph, which can be expressed as 8.5 miles per hour. The hare reached the finish line 45 minutes (3/4 of an hour) before the tortoise, which means the hare ran for T - 3/4 hours. Therefore, the distance D is also given by:

D = 8.5 × (T - 3/4)

Since the distances are equal, we can set up an equation:

2.5T = 8.5 × (T - 3/4)

Now, let's solve this equation to find the value of T, which represents the time the tortoise ran:

2.5T = 8.5T - 6.375

6.375 = 8.5T - 2.5T

6.375 = 6T

T = 6.375 / 6

T ≈ 1.0625

Therefore, the tortoise ran for approximately 1.0625 hours, which is equivalent to 1 hour and 3 minutes (since there are 60 minutes in an hour).

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Answer:

Not only that, some of them have even had hair, eyes, and hands! The average mouth produces over 25,000 quarts of saliva, which helps protect your mouth from germs, over a lifetime – enough to fill two swimming pools!

Step-by-step explanation:

Answer:

two hundred pools worth of saliva

Step-by-step explanation:

I need the size of each pool, so this is the answer you are asking for based off of what u said

Answer:

cos θ = 4/5.

tan θ = 3/4.

Step-by-step explanation:

Given sin θ = 3/5, we can find the value for the other side of the right triangle.

Using the Pythagorean formula, we can derive the value of this other leg.

5² = 3² + x²

x = 4.

Since sin θ is O/H, the Hypoteneus is 5 and the Opposite side is 3. The Adjacent side is 4, which will be used when finding cos θ and tan θ.

cos θ= A/H --> cos θ = 4/5.

tan θ= O/A --> tan θ = 3/4.

Answer:

see explanation

Step-by-step explanation:

Equation 1

y = kx² → B

Equation 2

y = \(\frac{k}{x^2}\) → D

Equation 3

y = \(\frac{k}{x}\) → C

Equation 4

y = kx → A

Answer:

80 cm

Step-by-step explanation:

The perimeter of parallelogram LMNO

Is calculated using the formula

Perimeter = 2(a + b)

a = 18 cm

b = 22cm

Perimeter = 2(18 + 22)

= 2(40 cm)

= 80 cm

The perimeter of the parallelogram = 80 cm

Answer:

D. 80 cm

Step-by-step explanation:

Just took the quiz on Edg (2021)!!

To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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Step-by-step explanation:

Not true....is they are perpendicular  the slopes have the relation

  m   and    - 1/m    where m is the slope

slope 2 has a perpendicular slope = - 1/2

the answer is in the above image

Answer:

5x+9 =  109

3x+11 =71

Step-by-step explanation:

A linear pair adds to 180

5x+9  + 3x+11 =180

Combine like terms

8x + 20 =180

Subtract 20 from each side

8x +20-20 = 180-20

8x = 160

Divide each side by 8

8x/8 = 160/8

x=20

5x+9 = 5*20+9 = 100+9 = 109

3x+11 = 3*20+11 = 60+11=71

The statement is true for all positive integers n greater than or equal to 2 by mathematical induction. Using mathematical induction, it can be proved that 1. 3n ≤ n! if n is an integer greater than 6, and 2. n³ > n² + 3 for all n ≥ 2.

Using Mathematical Induction to prove 3n ≤ n! if n is an integer greater than 6:

Step 1: Basis Step

Let n = 7, then 3n = 3(7) = 21 and 7! = 5040. Therefore, 3n ≤ n! is true for n = 7.

Step 2: Inductive Step

Assume that the statement 3n ≤ n! is true for an arbitrary positive integer k ≥ 7, that is, 3k ≤ k!

Multiplying both sides of the inequality by (k + 1) yields:
3k (k + 1) ≤ k! (k + 1)

Now, since k ≥ 7, we have k + 1 > 8. Therefore, we can write:
3k+1 ≤ (k + 1) k! < (k + 1)!

This shows that the statement 3n ≤ n! is true for k + 1 whenever it is true for k. Hence, the statement is true for all positive integers n greater than or equal to 7 by mathematical induction.

Using Mathematical Induction to prove n³ > n² + 3 for all n ≥ 2:

Step 1: Basis Step
Let n = 2, then n³ = 8 and n² + 3 = 7. Therefore, n³ > n² + 3 is true for n = 2.

Step 2: Inductive Step
Assume that the statement n³ > n² + 3 is true for an arbitrary positive integer k ≥ 2. Multiplying both sides of the inequality by (k + 1) yields:

(k + 1)³ > (k + 1)² + 3

(k + 1)(k + 1)³ > (k + 1)² + 3(k + 1)

(k + 1)⁴ > k² + 5k + 4

Now, since k ≥ 2, we have k² + 5k + 4 > k² + 4k + 4 = (k + 2)². Therefore, we can write:

(k + 1)⁴ > (k + 2)²

This shows that the statement n³ > n² + 3 is true for k + 1 whenever it is true for k. Hence, the statement is true for all positive integers n greater than or equal to 2 by mathematical induction.

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Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box.

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box. In general, more metal is required for larger, thicker boxes. One must first calculate the box's volume in order to determine how much metal is required. The box's length, width, and height can be multiplied together to get this. The thickness of the metal must next be determined. The total amount of metal required can be estimated by multiplying the volume of the box by the thickness of the metal once the volume and thickness of the metal have been established. For instance, consider a box with dimensions of 6 inches long, 6 inches wide, and 6 inches high and a metal thickness.

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Answer:

x-2y=-8

Step-by-step explanation:

it is what it is

The equation of the linear function having an x-intercept of -8 and a y-intercept of 4 is y = (1/2)x + 4.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A linear function has an x-intercept of -8 and a y-intercept of 4.

So, The two points on the line are (- 8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 + 8).

slope(m) = 4/8.

slope(m) = 1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Therefore, The linear function is y = (1/2)x + 4.

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Answer:

(2/5)

Step-by-step explanation:

(-2/5) = -(2/5)

|-(2/5)| = (2/5)

Answer:

4v^2 + 6v + 3

Step-by-step explanation:

|z| = 0.669 < 1.96, we fail to reject the null hypothesis at any significance level up to α = 0.05.

In other words, we do not have enough evidence to conclude that the true proportion of executives who would agree with the statement is different from one-half.

The null hypothesis that the true proportion of all such executives.

Agree with this statement is one-half, we can use a two-sample z-test for proportions.

Let p be the true proportion of executives who would agree with the statement and let. \(\^p\) be the sample proportion.

Under the null hypothesis, the test statistic z is given by:

\(z = (\^p - 0.5) / \sqrt(0.5 \times 0.5 / n),\)

n is the sample size (104 in this case).

This test statistic follows a standard normal distribution under the null hypothesis.

To reject the null hypothesis at a significance level α, we need to find the critical values.\(z\alpha/2\) and \(-z\alpha/2\) such that \(P(Z > z\alpha/2) = \alpha/2\) and\(P(Z < -z\alpha/2) = \alpha/2\), where Z is a standard normal random variable.

The lowest level of significance at which the null hypothesis can be rejected against a two-sided alternative.

The smallest α such that \(|z| > z\alpha/2.\)

The two-sided alternative implies that we are interested in deviations from the null value of 0.5 in either direction.

Using the given information, we have:

\(\^p = 50/104 = 0.4808,\)

n = 104.

Substituting these values into the formula for z, we get:

\(z = (0.4808 - 0.5) / \sqrt(0.5 \times 0.5 / 104) = -0.669.\)

The critical value \(z\alpha/2\), we look up the corresponding value in the standard normal distribution table.

\(z\alpha/2\) such that \(P(Z > z\alpha/2) = \alpha/2\), or equivalently, \(P(Z < -z\alpha/2) = \alpha/2\). Since the standard normal distribution is symmetric, we can look up the value of zα/2 that satisfies. \(P(Z > z\alpha/2) = \alpha/2\), and then take its absolute value to find. \(-z\alpha/2.\)

Using a standard normal distribution table, we find that z0.025 = 1.96 (rounded to two decimal places).

The critical values for rejecting the null hypothesis at a significance level α are:

\(z\alpha/2\) = ±1.96.

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The researchers who examined 18th century medical records in Sweden found that the size of a person's family was/were the strongest factor in determining adult longevity.

Longevity is the amount of time a living organism or object remains functional. It is frequently utilized to refer to human life expectancy. Longevity can be impacted by a variety of factors, including genetics, lifestyle, and environmental factors.

Researchers analyzed the medical records of 14,000 people born in Skelleftea, Sweden, between 1720 and 1829, from birth and baptism records to death certificates and wills. The researchers discovered that individuals from larger families were more likely to live to be 60 years old or more, despite the fact that many of these households were not wealthy.

According to a study published in the journal Evolution, Medicine, and Public Health, this pattern persisted even after researchers adjusted for wealth, social class, and other factors.

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The solution is all values of x greater than -9.

The correct graph for the given inequality "Negative 3x - 7 < 20" is:

From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.

To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:

Negative 3x - 7 + 7 < 20 + 7

Negative 3x < 27

Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:

Negative 3x/-3 > 27/-3

x > -9

Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.

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At the same temperature and pressure, balloons of equal volume will always contain the same amount of air molecules due to the constant collisions of the molecules with each other and the walls of the container.

At the same temperature and pressure, balloons of equal volume will always contain the same amount of air molecules. This is because air molecules take up a certain amount of space, and the same amount of air molecules will take up the same amount of space regardless of the container. The molecules are constantly colliding with each other and the walls of the container, pushing against the walls and applying a pressure to the walls of the container. Since the pressure is the same, the amount of air molecules will remain the same and thus the volume of air in the container will remain the same. In this case, since the balloons are of equal volume, they will both contain the same amount of air molecules.

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Using the expression M = B, the number of magazines the Smith family receive is 2.

The Smith family received 19 pieces of mail on November 29th.

Let the ads be A, the bills be B, the magazines be M, and the letters be L.

They received five more letters than Ads.

L = 5 + A

There are three more ads than bills.

A = B + 3

There are the same number of magazines as bills.

M = B

Now, the total number of mails received are 19.

L + A + M + B = 19

L + A + 2B = 19

5 + A + A + 2B = 19

5 + 2A + 2B = 19

5 + 2(B + 3) + 2B = 19

5 + 2B + 6 + 2B = 19

11 + 4B = 19

4B = 8

B = 2

Therefore, using the expression M = B the number of magazines they receive is 2.

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Answer:

57.5

Step-by-step explanation:

8 km = 5 m

97/8 = 11.5

5 * 11.5 = 57.5

Answer:B

Step-by-step explanation

Answer:

B

Step-by-step explanation:

Answer:

5% times 3=15%

4% times 3=12%

15-12=3

1300 times 0.03= $39

39 dollars.

Step-by-step explanation:

Since bx can be defined for all real numbers r, the domain of an exponential function is all real numbers. The range of bx is all real numbers greater than 0. ... If b > 1, then f is an increasing function. I.e. f(x) increases in value as x increases.

If the Euro (USD/EUR) goes down from 1.04 to 1.02 in the next 15 days, the speculation profit would be $11,052.74.

The calculation for speculation profit if the Euro (USD/EUR) goes down from 1.04 to 1.02 in the next 15 days is given below.

Borrowing amount = $10 million

Spot rate = 1.04

Expectation = 1.02

Borrowing rate for EUR = 7%

Borrowing rate for USD = 5%

Lending rate for EUR = 6%

Lending rate for USD = 4%

Conversion rate = 1/1.04

Interest on the USD amount borrowed = $10 million × 5% × (15/360) = $20,833.33

Interest on the EUR amount borrowed = ($10 million × 1/1.04) × 7% × (15/360) = €45,673.08

Interest earned on the USD amount deposited = ($10 million × 4% × (15/360)) = $16,666.67

Interest earned on the EUR amount deposited = (($10 million × 1/1.02) × 6% × (15/360)) = €40,441.18

Profit = (Interest earned on the EUR amount deposited + Interest earned on the USD amount deposited) - (Interest on the EUR amount borrowed + Interest on the USD amount borrowed) = €40,441.18 + $16,666.67 - €45,673.08 - $20,833.33 = $11,052.74

Therefore, the speculation profit would be $11,052.74.

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Given:

There are given the complex equation:

Explanation:

To find the value, we need to put the standard value of z into the above-given complex function:

Then,

Then,

So,

Then,

Final answer:

Hence, the value of the given complex function is shown below:;

A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.

A ray is named using its endpoint first, and then any other point on the ray

Properties of ray:

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Hey there!

First, we are given:

\(\frac{1\frac{1}{4}}{1\frac{3}{8}}\)

To make this easier, I am going to change the fractions in to decimals.

\(\frac{1.25}{0.375}\)

To get the unit rate, we can use proportions:

\(\frac{1.25}{0.375} = \frac{x}{1}\)

Using cross products, we know that...

\(1.25 * 1 = 0.375 * x\)

Now, we solve for \(x\):

\(1.25 * 1 = 0.375 * x\\ 1.25 = 0.375x\\ 3 \frac{1}{3} = x\)

Therefore, the unit rate is \(\frac{3\frac{1}{3} }{1}\)

Now, do the same with the other problem, and the unit rate is \(\frac{1\frac{4}{5} }{1}\)

Have a terrificly amazing day!!!

The solutions of provide logarithmic equations are present in below :

1) x = 9 ; 2) x = 0 ; 3)p = 7/9 ; 4) k= 2 ; 5) a= -1 ; 6) r = -1/2 ; 7) n = 2 ; 8) x = 1/35 ; 9) m = -2 ; 10) x = 84 ; 11) v = -6, -6 ; 12) x = -4, -7

The logarithmic number is associated with exponent and power, such that if xⁿ = m, then it is equal to logₓ m = n. That is exponential value are inverse of logarithm values. Some basic properties of logarithmic numbers:

Now, we solve each logarithm equation one by one. Assume that 'log' is the base-10 logarithm where absence of base.

1) log (5x) = log (2x + 9)

Exponentiate both sides

=> 5x = 2x + 9

=> 3x = 9

=> x = 9

2) log (10 − 4x) = log (10 − 3x)

Exponentiate both sides,

=> 10 - 4x = 10 - 3x

simplify, => x = 0

3) log (4p − 2) = log (−5p + 5)

Exponentiate both sides,

=> 4p - 2 = - 5p + 5

simplify, => 9p = 7

=> p = 7/9

4) log (4k − 5) = log (2k − 1)

Exponentiate both sides,

=> 4k - 5 = 2k - 1

simplify, => 2k = 4

=> k = 2

5) log (−2a + 9) = log (7 − 4a)

Exponentiate both sides,

=> - 2a + 9 = 7 - 4a

simplify, => 2a = -2

=> a = -1

6) 2log₇( −2r) = 0

=> log₇( −2r) = 0

using the property, log꜀a = n <=> cⁿ = a

=> ( 7⁰) = - 2r

=> -2 × r = 1 ( since a⁰ = 1 )

=> r = -1/2

7) −10 + log₃(n + 3) = −10

=> log₃(n + 3) = −10 + 10 = 0

using the property, log꜀a = n <=> cⁿ = a

=> 3⁰ = n + 3

=> 1 = n + 3

=> n = 2

8) −2log₅ ( 7x ) = 2

=> log₅ 7x = -1

=> 5⁻¹ = 7x

=> x = 1/35

9) log( −m) + 2 = 4

=> log( −m) = 2

Exponentiate both sides,

=> -m = 2

=> m = -2

10) −6log₃ (x − 3) = −24

simplify, log₃ (x − 3) = 4

=> (x - 3) = 3⁴ ( since log꜀a = n <=> cⁿ = a )

=> x - 3 = 81

=> x = 84

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

=> log₁₂ (v²+ 35) - log₁₂ (−12v − 1) = 0

Using the quotient property of logarithm,

\(log_{12}( \frac{v²+ 35}{-12v-1}) = 0 \)

\(\frac{v²+ 35}{-12v - 1} = {12}^{0} = 1 \)

\(v²+ 35 = −12v − 1\)

\(v²+ 35 + 12v + 1 = 0\)

\(v²+12v + 36 = 0\)

which is a quadratic equation, and solve it by middle term splitting method,

\(v²+ 6v + 6v + 36= 0\)

\(v(v + 6) + 6(v + 6)= 0\)

\((v + 6) (6 + v)= 0\)

so, v = -6, -6

12) log₉(−11x + 2) = log₉ (x²+ 30)

=> log₉ (x²+ 30) - log₉(−11x + 2) = 0

Using the quotient property of logarithm,

\(log₉(\frac{x²+ 30 }{−11x + 2}) = 0\)

\( \frac{x²+ 30}{-11x + 2} ={9}^{0} = 1 \)

=> x² + 30 = - 11x + 2

=> x² + 11x + 30 -2 = 0

=> x² + 11x + 28 = 0

Factorize using middle term splitting,

=> x² + 7x + 4x + 28 = 0

=> x( x + 7) + 4( x + 7) = 0

=> ( x + 4) (x+7) = 0

=> either x = -4 or x = -7

Hence, required solution is x = -4, -7.

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Complete question:

kuta software infinite algebra 2 logarithmic equationsSolve each equation.

1) log 5x = log (2x + 9)

2) log (10 − 4x) = log (10 − 3x)

3) log (4 − 2) = log (−5 p + 5)

4) log (4k − 5) = log (2k − 1)

5) log (−2a + 9) = log (7 − 4a)

6) 2log₇ −2r = 0

7) −10 + log₃(n + 3) = −10

8) −2log₅ 7x = 2

9) log −m + 2 = 4

10) −6log₃ (x − 3) = −24

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

12) log₉(−11x + 2) = log₉ (x²+ 30)