What is the slope, in its most simplified form, of the line that contains (1, 3) and (5, 9)

y - 1/z = 1   ==>   y = 1 + 1/z

z - 1/x = 1   ==>   z = 1 + 1/x

==>   y = 1 + 1/(1 + 1/x) = 1 + x/(x + 1) = (2x + 1)/(x + 1)

x - 1/y = x - (x + 1)/(2x + 1) = (2x ² - 1)/(2x + 1) = 1

==>   2x ² - 1 = 2x + 1

==>   2x ² - 2x - 2 = 0

==>   x ² - x - 1 = 0

==>   x = (1 ± √5)/2

If you start solving for z, then for x, then for y, you would get the same equation as above (with y in place of x), and the same thing happens if you solve for x, then y, then z. So it turns out that x = y = z.

y = -2x-3

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope  , then a line perpendicular to this has slope . That means the slope of our perpendicular line is

The equation of the line that is perpendicular to 8x - 2y = 4 and passes through the point (4, 3) is y = (-1/4)x + 4.

To find the equation of a line that is perpendicular to the line 8x - 2y = 4 and passes through the point (4, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope:

8x - 2y = 4

-2y = -8x + 4

Divide both sides by -2:

y = 4x - 2

The slope of the given line is 4.

The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.

Now, we have the slope (-1/4) and a point (4, 3). We can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Substituting the values, we have:

y - 3 = (-1/4)(x - 4)

Expanding and simplifying, we get:

y - 3 = (-1/4)x + 1

Adding 3 to both sides, we have:

y = (-1/4)x + 4

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Doing this, we get that the smallest number of coins is: 6

89 cents:

Thus, the smallest amount of coins needed is 1 + 1 + 1 + 1 + 2 = 6.

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Answer:

mocha madness = 30 pounds

Step-by-step explanation:

Let

x =  Mocha Madness

y = Sumatra Sweetness

two equations can be derived from the question

x + y = 40 equation 1

12x + 20y = 14 x 40 equation 2

Multiply equation 1 by 12

12x + 12y = 480 eqn 3

subtract eqn 2 from 3

8y = 80

y = 10

substitute for y in equation 1

x + 10 = 40

x = 40 - 10

x = 30

8y = 180

y = 10 pounds

x = 30 pounds

2

3x. + 63x + 9x + 189

Step-by-step explanation:

Use distributive law, in other words multiply the first bracket terms by the second bracket terms

Answer:

54

Step-by-step explanation:

The perimeter is the sum of the outside

P = 8+4+5+10+( 4+10) +(8+5)

P = 54

Answer:

[tex]\sqrt{136}[/tex]

Step-by-step explanation:

Formula for Pythagorean theorem: [tex]a^{2} +b^{2} = c^{2}[/tex]

Plug in:

[tex]6^{2}+10^2=x^2[/tex]

Solve:

36 + 100 = [tex]x^{2}[/tex]

136 = [tex]x^{2}[/tex]

[tex]\sqrt{136}[/tex] = x

The answer is [tex]\sqrt{136}[/tex].

Hope this helped.

Answer:

28.284

Step-by-step explanation:

Complete question is;

Alejandra correctly wrote the equation y – 3 = (1/5) (x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

Answer:

y – 3 = 2(x – 10)

Step-by-step explanation:

Since the original line is;

y – 3 = (1/5) (x – 10)

This means the slope is 1/5 and the x and y coordinates are (10, 3) respectively.

Now, if she changes the slope to 2 and it still passed through the same point, then it means it's x and y points are still (10, 3). Thus, the equation will now be;

y – 3 = 2(x – 10)

Solution :

Maximize, S = xy

subject to 2x + 2y = 996

So,

2x + 2y = 996

2(x + y) = 996

x + y = 498

y = 498 - x

Therefore,

S = x (498 - x)

S = 498x - [tex]x^2[/tex]

S = [tex]-x^2 + 498x[/tex]

[tex]$S = -(x^2-498x + 249^2) + 300^2$[/tex]

[tex]$S= -(x-249)^2 + 249^2$[/tex]

S = x (498 - x)

S = 498x - [tex]x^2[/tex]

[tex]$\frac{dS}{dx}= 498 - 2x$[/tex]

[tex]$\frac{dS}{dx}= 0$[/tex]

498 - 2x = 0

2x = 498

x = 249

∴ y = 498 - x

  y = 498 - 249

     = 249

Answer:

A = 249 x 249 = 62001 square meter.

Side is L = 249 m

Step-by-step explanation:

Total length of the fence is 996 m.

Let the length is L and the width is W.

Perimeter = 2 (L + W)

996 = 2 (L + W)

498 = L + W

L = 498 - W ...... (1)

Let the area is

A = L W

A = (498 - W) W

A = 498 W - W^2

Differentiate with respect to W.

dA/dW = 498 - 2 W

Put it equal to zero.

498 - 2 W = 0

W = 249 m

Now, L = 498 - 249 = 249 m

Differentiate with respect to W again

[tex]\frac{d^2A}{dW^2} = - 2[/tex]

As it is negative so the area is maximum.  

The maximum area is

A = 249 x 249 = 62001 square meter.

Side is L = 249 m

Answer:

Area of triangle =1/2b×h

1/2×10×8.7

=44 square inches

Answer:

44

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

where b is the base and h is the height

A = 1/2 (10) (8.7)

A= 43.5

Rounding to the nearest whole number

A = 44

Answer:

I HOPE IT WILL HELP

EXPLANATION IS IN THE PHOTO .

Let

We know

[tex]\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}[/tex]

[tex]\\ \sf\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)[/tex]

[tex]\\ \sf\longmapsto n(A\cap B)=60+65-100[/tex]

[tex]\\ \sf\longmapsto n(A\cap B)=125-100[/tex]

[tex]\\ \sf\longmapsto n(A\cap B)=25[/tex]

Sin74 = Cos16

cause 16 + 74 = 90

Whenever the sum of two angles is equal with 90, the Sin of one is equal with the Cos of the other like :

Sin(30) = Cos(60)

and also

Tan(30) = Cot(60)

Answer:

16

Step-by-step explanation:

sin(74) = cos(x)

sin(x)=cos(90-x)

sin (74) = cos(90-74)

sin 74 = cos( 16)

Answer:

y - 7 = -4 (x + 2)

Step-by-step explanation:

y - 7 = -4 (x + 2)

Answer:

all except the first

Step-by-step explanation:

do u really want an explanation

Answer:

The value of 3^-2 is 1/9

Step-by-step explanation:

This is because negative exponent such as [tex]2^{-1}[/tex] transfer to 1/2. Therefore, you might notice a pattern of negative exponent -> fraction. 3^-2 -> 1/(3^2)-> 1/9

PLEASE MARK BRAINIEST IF THIS HELPED!!!

Answer:

Step-by-step explanation:

Concept:

Here, we need to know the idea of exponents.

The exponent of a number says how many times to use the number in a multiplication.

Any number to the 0th power, it is equal to 1.

Solve:

Question 1. What is the value of 3⁻²?

Question 2. What is the value of 3⁰?

Question 3. What is the value of 3¹?

Question 4. What is the value of 3³?

Hope this helps!! :)

Please let me know if you have any questions

Answer:

24.83 hours

Step-by-step explanation:

Given that :

Let time taken by pumps be :

Pump A = 60 hours

Pump B = 80 hours

Pump C = 90 hours

Recall :

Rate = 1 / time taken

The rates of the pumps are :

Pump A rate = 1 / 60

Pump B rate = 1/80

Pump C rate = 1/90

Combined rate : 1/60 + 1/80 + 1/90

Combined rate = (12 + 9 + 8) / 720 = 29/720

Combined rate = 29/720

The time taken together will be :

1 / combined rate = 1/(29/720) = 720 / 29 = 24.827 hours

Answer:

x=8

Step-by-step explanation:

x^2+15^2=17^2, x=sqrt(64)=8

============================================================

Explanation:

Each x represents a data point location.

So, for example, having an x over 60 means 60 is part of the set.

The set of values we're working with is

{59,60,61,63,63,64,66,68,70,71,71,73}

The repeated values are due to the fact we have a stack of two 'x' markers, and they occur at 63 and 71.

To find the IQR (interquartile range), we'll first need to find the median of this set. That's the middle most value.

Count out the number of values to find that there are n = 12 values.

The list splits into two halves that are n/2 = 12/2 = 6 items each

Between slots 6 and 7 is where the median is located.

The value in slot 6 is 64 and the value in slot 7 is 66. Average those two items to get (64+66)/2 = 65

The median is 65

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

Next, we'll form two groups L and U such that

L = set of items lower than the median

U = set of items larger than the median

Because n is even, we simply just break the original set into two equal groups (6 items each)

L = {59,60,61,63,63,64}

U = {66,68,70,71,71,73}

The values of Q1 and Q3 represent the medians of L and U in that order.

The median of set L is (61+63)/2 = 62, so Q1 = 62

The median of set U is (70+71)/2 = 70.5, which is Q3

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

To summarize everything so far, we have found

Subtract those items to get the IQR

IQR = Q3 - Q1

IQR = 70.5 - 62

IQR = 8.5 which points us to choice C as the final answer.

Answer:

The question is incomplete, but after a small search I've found that the complete question is something like:

To celebrate something, a teacher will make pizzas for the class.

There are 30 students in his class and each pizza serves 8

Julio will bring the pizza sauce. Which point should Julio use to determine the amount of pizza sauce he needs to bring?

In a graph, the vertical axis is represented with the variable y, which is defined as the dependent variable, while the horizontal axis represents the variable x, which is the independent variable.

The notation for a point in that graph is (x, y)

Here, we know that the x-axis represents the number of pizzas, and the y-axis represents the number of cups of pizza sauce needed for the x pizzas.

So, for example, the point (3, 2) means that:

for x = 3 pizzas, you need y = 2 cups of pizza sauce.

So, now let's find the number of pizzas that will feed the whole class.

There are 30 students, Each pizza serves for 8.

Then the number of pizzas needed is:

30/8 = 3.75 pizzas.

But we can round it to 4 pizzas because making a 0.75 of a pizza does not make a lot of sense.

Then we could use point B, which is (4, 2.6)

This means that, for 4 pizzas, they need 2.6 cups of pizza sauce.

So Julio should bring 2.6 cups of pizza sauce.

Which point should Julio use to determine the amount of pizza sauce he needs to bring?

(B 4,26)

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

let,

x=ky

y=39 when x=7 so,

7=39k

or, k=7/39

now, when x=22

22=7y/39

or, y=39×22/7

or, y=858/7

or, y=122.57 (rounded to the nearest hundredth)

Step-by-step explanation:

म नजन्मिदै विधवा भएकी हिमाल

खै! किन हो मेरा यी हेर्ने नयनले उनलाइ

अझै पनि दिन र रातमा

सेतै लुगा पहिरिएकी देख्छ

अचम्म लाग्छ मलाइ पहिरिएकी सेतो लुगा माथि

मुनालले पाइला टेके पनि विष्ठा गरे पनि कहिल्यै

मैलो हुदैन सेतो लुगाको वास्तविक रङ

उत्तिकै सेतो देख्छु म

निर्जीव वस्तु भएनी हिमाललाइ

सजीव मनुस्यको जस्तै चोटको कल्पना गरेको छु मैले

किनकी चोटै चोटले ग्रसित भएकी उनी आजभोली

अपाङ्गको सिकार बनिसकेकी छिन

उनलाइ अन्धो भन्छु म किनकी उनी आँखा देख्दैनन

आँखा नदेखे पनि अरु कसैलाइ सुम्सुम्याउन समेत सक्दैनन

तर पनि कस्तुरी, डाफे,मुनाल,घोरल,चितुवा आदि जनावरहरुको

सहारा दिने आश्रय स्थल भएर उभिएकी छिन, के कम छिन र?

जमिन भित्र उनको खुट्टा गाडिएर होला

खुट्टाको दृश्य मैले अझै पनि देख्न पाएको छैन

कस्तो होला है! हिमालको खुट्टा ? सोचिरहन्छु म

सायद खुट्टा नै छैन र पो कहिल्यै पनि हिड्डुल गर्न सक्दैनन कि?

जब कुनै समयमा चुचुरोमा हावा बहन थाल्यो

एकदिन सेतो कपाल धरतीमा हाम फालेर

नदिहरु बढ्न थाले तर उहीँ बहेको हावाले

हिमालको श्रवण गर्ने कानको जाली

नै फुटाइदिएछ त्यही भएर म भन्छु

हिमाललाइ बहिरो पनि हुनुहुन्छ तपाईं

सधै टोलाएर बसेकी देख्छु म

रोजगारी भन्ने कुरा त उहीँ हो हिमाललाइ

बिहानीपख देखि सन्ध्या काल सम्म

प्रकृतिले बसिबसी ऐना टल्काउने

पदभार ग्रहण गराइदिएको छ जब घाम

झुल्किन्छ उनी अस्ताउन्जेल सम्म ऐना टल्काइरहन्छिन्

त्यसैले म भन्छु हिमाललाइ बिधवा भएर के भो त

खान लाउनको लागि रोजगारी मिलेकै छ क्यारे !

Last Option

Rita will spend $25

5(8-3)

Answered by Gauthmath must click thanks and mark brainliest

Answer:  The correct answer is D.

Step-by-step explanation:

Since 3 of Rita's 8 friends don't want to play laser tag, Rita only has to pay for 5 of her friends to go.

So, the expression would be:

5 (8 - 3)

= 5 (5)

= $25

Hope this helps! :)

9514 1404 393

Answer:

  A, C

Step-by-step explanation:

Any table with no repeated x-values is a relation that is a function.

Answer:

[tex](6a-7)5a=30a^2-35a[/tex]

Step-by-step explanation:

Message if you want a detailed explanation.

Answer:

The test statistic will be "-2.33". A further explanation is provided below.

Step-by-step explanation:

According to the question,

[tex]H_0: \mu = 2.05[/tex]

[tex]H_0: \mu < 2.05[/tex]

Given:

[tex]\bar x = 1.98[/tex]

[tex]s = 0.3[/tex]

[tex]n = 100[/tex]

The test statistics will be:

⇒ [tex]t_0 = \frac{\bar x - \mu_0}{\frac{s}{\sqrt{n} } }[/tex]

       [tex]=\frac{1.98-2.05}{\frac{0.3}{\sqrt{100} } }[/tex]

       [tex]=-2.33[/tex]

and the P-value will be:

= [tex]0.011< \alpha[/tex]

They could complete the job together in 2.4 days

The known parameters are;

The number of days it would take Michelle to complete the landscaping job = 6 days

The number of days it would take Danielle to complete the landscaping job = 4 days

The unknown parameter;

The number of days can the job be completed if they work together

The process of finding the solution;

The rate at which Michelle works = 1/6 of the landscaping work per day

The rate at which Danielle works = 1/4 of the landscaping work per day

Method;

Find their combined work rate, from which the time would take them to complete the job together can be found

Let, C, represent their combined work rate

Therefore, we have;

C = (1/6 + 1/4) = 5/12 of the landscaping (work) job/(per) day

The number of days they could complete the, 1, job = 1 job(work)/(5/12 (work)job/day) = 12/5 days = 2.4 days

∴ The number of days they could complete the job together = 2.4 days.

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