Find the slope of the line that contains the following pair of points (1,6) and (9,-4)

Complete Question:

Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters.  This year he wants to make the garden three times as long and two times as wide.  

Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.  

How many more meters of fencing is needed for this year’s garden than last year’s?

Answer:

26 meters of fencing needed

Step-by-step explanation:

Given

Last Year:

\(Width = 5m\)

\(Area = 20m^2\)

This Year:

\(Length = 3\ times\ longer\)

\(Width = 2\ times\ wider\)

Required

Determine how many more meters is needed

Represent last year's length of Fence with L and last year's width with W

First, we need to calculate L

\(Area = L * W\)

Where

\(Area = 20m^2\)

\(W = 5m\)

\(20m^2 = L * 5m\)

Divide both sides by 5m

\(\frac{20m^2}{5m} = \frac{L * 5m}{5m}\)

\(\frac{20m^2}{5m} = L\)

\(L = \frac{20m^2}{5m}\)

\(L = 4m\)

So, we have that:

For Last Year

\(Length = 4m\) and \(Width = 5m\)

For this year:

\(Length = 3\ times\ longer\)

\(Length = 3 * 4m\)

\(Length = 12m\)

\(Width = 2\ times\ wider\)

\(Width = 2 * 5m\)

\(Width = 10m\)

So, for this year, we have:

\(Length = 12m\) and \(Width = 10m\)

Next, we calculate perimeter of fencing in both years.

\(Perimeter = 2 * (Length + Width)\)

Last Year:

\(Perimeter = 2 * (4m + 5m)\)

\(Perimeter = 2 * 9m\)

\(Perimeter = 18m\)

This Year:

\(Perimeter = 2 * (12m + 10m)\)

\(Perimeter = 2 * 22m\)

\(Perimeter = 44m\)

To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.

\(Difference = 44m - 18m\)

\(Difference = 26m\)

Hence, there are 26 meters of fencing needed

The correct interpretation of the p-value of the hypothesis is given as follows:

If 15% of teenagers get 8 to 10 hours of sleep each school night, there is a 35% probability that the sample proportion would be 0.19 or more different by chance alone.

At the null hypothesis, it is tested if the proportion is of 15%, that is:

H0: p = 0.15.

At the alternative hypothesis, it is tested if the proportion is different of 15%, that is:

H1: p ≠ 0.15.

We have a two-tailed test, as we are testing if the proportion is different of a value, meaning that the p-value gives the probability of the sample proportion differing by 0.15 at least by the proportion that it differed.

The p-value of this test is given as follows:

0.35.

Hence the first option is correct.

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

#SPJ1

Answer:

bhj

Step-by-step explanation:

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

For more such questions on line segment

https://brainly.com/question/30756145

#SPJ8

Answer:<-26, 26>

Step-by-step explanation: <4(-5), 4(2)> and

<3(-2), 3(6)>

<-20, 8> and <-6, 18>

Now add <(-20+(-6)), (8+18)>

<-26, 26>

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

For such more question on equation

https://brainly.com/question/29174899

#SPJ8

Answer:

the answer to your eqauation is 531,441

Step-by-step explanation:

3^5 x 3^7

243 x 2,187

=531,441

Hope this helped!! :)

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

To learn more about arithmetic operations visit,

brainly.com/question/4721701

#SPJ1

Answer:

5.50

Step-by-step explanation:

They save 5.50

Answer:

$5.50

Step-by-step explanation:

Hello! This is an easy one. If we are trying to find how much she is saving all we would need to do is multiply.

$22.00 * 25% = $5.50

If we are trying to find out the total with the discount all we would need to do is subtract.

22 - 5.5 = $16.50

Hope this helps!!

Answer:

1. What is the true density of water?

The true density of water is 1 g/cm³. (Actually, the exact density if water is not really 1 g/cm³, but a bit less (very, very little less), at 0.9998395 g/mol at 40 degree Celsius)

2. What variables change the density of water?

Temperature and purity can change the density of water.

3. How does water go against the concept of "Thermal Expansion"?

When water is a liquid, the water molecules are packed relatively close together but can slide past each other and move around freely(as stated earlier, that makes it a liquid). As the temperature increases or decreases from 4 degree Celsius, the density of water decreases.

Answer:

im not sure but i do have a tip when you go to goo gle i want you to simplify your question (not what you asked on here) then copy your question as it is simple then search it on here because its slightly  for others to understand

Step-by-step explanation:

.

Answer:

-7

32

Step-by-step explanation:

a)9-16=-7

b)4-10=-6

2∆-6

36-4

32

The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

For similar question on cheapest price.

https://brainly.com/question/1153322  

#SPJ8

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

To know more about triangle:

https://brainly.com/question/28835566

#SPJ1

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

Find out more on the coupon rate at https://brainly.com/question/28528712

#SPJ1

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

Learn more about Proposition here:

https://brainly.com/question/30695879

#SPJ1

Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

Answer:

The percent of change in Anna's working hours is 22%, indicating an increase.

Step-by-step explanation:

Step 1: Calculate the difference:

Difference = 36 hours - 28 hours

Difference = 8 hours

Step 2: Calculate the percent change:

Percent Change = (Difference / Original Value) * 100

Percent Change = (8 hours / 36 hours) * 100

Percent Change ≈ 22.22%

Therefore, the percent change in Anna's working hours is approximately 22.22%, representing an increase.

Answer:

A' (12, 8), B'(4, 8), C'(12, -4), D'(4, -4)

Step-by-step explanation:

Since the dilation is in the center, we just need to multiply everything by our scale factor, 2.

A (6,4) → (12, 8)

B (2,4) → (4, 8)

C (6, -2)  → (12, -4)

D (2, -2) → (4, -4)

Hope this helps!

Answer:

The answer is last option

As we know 1 + tan^2 = sec^2

Answer:

secФ = ±\(\sqrt{1+tan^{2} }\)

Step-by-step explanation:

We can use the identity sec²Ф = 1 + tan²Ф to solve for secФ

Answer:

the answer is -5

Step-by-step explanation:

simply put the slope is going down one unit so that would me that for every one year equals 5lb so the would make the ratio 5/1 and when we simply that we get -5 for the first year or range they want us to answer.(And its negative because the slope is going down for the range they give us)

\(44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}\)

Answer:

C

Step-by-step explanation:

Answer:

I am not certain but I think it's no solution but how the number of X's their is and won't have it's value, it's by themselves

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

\($P(x=a) = P(a-1/2 \leq x \leq a+1/2)$\)

∴ \($P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$\)

                   \($=P(27.5 \leq x \leq 28.5)$\)

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5

Answer:

Step-by-step explanation:

Domain:  since x begins to the right of x = -2 and ends at x =2, the domain is  (-2, 2]

Range:  The smallest y value shown is y = -5 and the largest is y = 4.  Thus, the range is [-5, 4].

Answer:

C. 2 and 3 opens down

Step-by-step explanation:

see graph

Answer:

9/10

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by that fraction's reciprocal (basically the fraction flipped).

\(\frac{3}{5}\) ÷ \(\frac{2}{3}\) = \(\frac{3}{5} *\frac{3}{2} =\frac{3*3}{5*2} =\frac{9}{10}\)

Answer: The normal answer is 0.9! Hope this helps!