two angles are supplementary if the sum of their measures is 180°. If one of two supplementary angles measures 85°, what is the measure of the other angle?

a=2

b=6

c=-6

You can use the substitution method to solve.

Final answer:

The probability that neither of them suffer from myopia can be calculated by finding the probability that one individual does not suffer from myopia and then multiplying that probability by the probability that the second individual also does not suffer from myopia.

Explanation:

The probability that neither of them suffer from myopia can be calculated by finding the probability that one individual does not suffer from myopia and then multiplying that probability by the probability that the second individual also does not suffer from myopia.

The probability that one individual does not suffer from myopia is 1 - 0.381 = 0.619. Since the two individuals are chosen randomly and independently, the probability that the second individual does not suffer from myopia is also 0.619.

Therefore, the probability that neither of them suffer from myopia is 0.619 * 0.619 = 0.382161.

Answer:

500

Step-by-step explanation:

Assume camel stays at the market after complete delivery.

Idea is to drop off some bananas between the plantation and the market.  Refrigeration is required to avoid bananas going bad!

Status (planatation, 250 mile point, 500 mile point, market)

First trip with 1000 bananas, stop at 250 miles, drop off 500 bananas, and come back to plantation.  (status:  2000, 500, 0, 0) camel ate 500 bananas.

Second trip with 1000 bananas, stop at 250 miles, pick up 250 (to make 1000), drop off 250 at 500 mile point, come back to plantation.  (Status: 1000, 250,250,0) Camel ate 1500 bananas.

Last trip with 1000 bananas, stop at 250 miles, fill-up 250 (total 1000), stop at 500 miles, fill-up to make total 1000.  Travel all the way to market with 500 left.

(Status: 0,0,0,500) Camel ate 500+1000+1000.

Net delivery: 500 bananas to market.

Using the camel to transport bananas across the desert, George loses all bananas to the camel's consumption before reaching the market, resulting in 0 bananas delivered.

The question asks how many bananas can George, the plantation owner, transport to the market across a 1000 mile stretch of desert using a camel that can carry 1000 bananas and eats one per mile. George has 3000 bananas to start with.

To maximize the number of bananas delivered, George must use a strategy that conserves bananas while accounting for the camel's consumption. For the first trip, George loads the camel with 1000 bananas, travels 333 miles (eating one banana per mile), deposits 667 bananas, and returns with 0. He repeats this until all bananas are 333 miles into the desert. This requires three round trips for the first third of the journey, resulting in the loss of 2000 bananas and leaving 1000 bananas 333 miles into the desert.

Next, he takes 1000 bananas, goes another 500 miles (leaving 500 bananas), and returns for the last batch of 500. This leaves him with 500 bananas 500 miles into the desert. Finally, he carries the last 500 bananas the remaining distance of 500 miles to the market, arriving with 0 bananas. Therefore, the greatest number of bananas George can deliver to the market is 0. This proves that it is impossible to deliver any bananas to the market under the given conditions.

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what is the expression

52 feet.

13 x 4 because its all the same length.

The equation for this is x2-x1/y2-y1 and so you plug in the numbers and get -5/7, and that is your slope.

Answer:

Answer 3 (-6x-2y=12)

Step-by-step explanation: Turn to slope form to check

First- Add the 6x from both sides

-2y=6x+12

Second- Divide by two on both sides

y= -3x-6

Answer:

C.[tex]-6x-2y=12[/tex]

Step-by-step explanation:

We are given that  a graph.

We have to find the equation of given graph.

The line passes through the point (-2,0) and (0,-6).

Slope:m[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]

By using the formula

[tex]m=\frac{-6-0}{0+2}=-3[/tex]

Slope-intercept form:[tex]y=mx+C[/tex]

Where m=Slope of line

C=y-intercept

y-intercept: It is that value of y for which x=0

We have y- intercept=-6

Using the formula

Equation of line

[tex]y=-3x-6[/tex]

[tex]3x+y=-6[/tex]

Multiply by -2 on both sides then we get

[tex]-6x-2y=12[/tex]

Well, the opposite of an exponent is a square root. However, in this case, it is to the power of 3. So in order to find p, you must do the cube root on both sides in order to get your answer:

[tex]p^3=3[/tex]

[tex]\sqrt[3]{p^3} =\sqrt[3]{8}[/tex]

[tex]p=2[/tex]

The length of each side of a square with an area of 29 square inches, estimated to the nearest whole number, is approximately 5 inches.

The area of a square is calculated by squaring the length of one side. So, if the area of a square is 29 square inches, you need to find the square root of 29 to determine the length of each side. The square root of 29 is approximately 5.385. However, you're asked to estimate to the nearest whole number, so the answer would be 5 inches as the closest whole number.

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m + 3 = 7

m = 4

m + 3 = -7

m = -10

m = 4, -10

The given equation is |m + 3|= 7. The values of m are 4 and -10.

An equation represents the equality of two or more mathematical expressions.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The given equation is |m + 3|= 7.

m + 3 = 7

m = 4

m + 3 = -7

m = -10

Hence, m = 4, -10

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[tex]\dfrac{4}{9}-\left|\dfrac{5}{18}\right|=\dfrac{4}{9}-\dfrac{5}{18}=\dfrac{8}{18}-\dfrac{5}{18}=\dfrac{3}{18}=\dfrac{1}{6}[/tex]

The colors on the image should match the correct blank spots on the proof. Please let me know if you disagree or is confused by my choices.

Answer:

120:300 is in the same ratio as 2:5. Can you add the pound sign? My keyboard does not have it.

Step-by-step explanation:

Add the two parts of the ratio together

2 + 5 = 7

Find 5:7

5:7 = x:420  

5/7 = x/420              Cross multiply

7x = 5 * 420             Combine the right

7x = 2100                  Divide by 7

x = 2100/7

x = 300                      

Find the second number

420 - 300 = 120

120 : 300 is the answer

Divide top and bottom by 60

120/60 = 2

300 / 60 = 5

The answer you are looking for is 2/3.

When adding or subtracting fractions, they must have the same denominator. To make 1/6 and 1/2 have the same denominator, you must multiply 1/2 by 3/3 straight across. This gives you 3/6 which you can now add 1/6 to to get 4/6. 4/6 can be simplified down to 2/3 by dividing by 2/2. Thus making 2/3 the answer.

I hope this helps!

To add one sixth and one half, convert them to have the same denominator, resulting in 1/6 plus 3/6 (or 4/6), which simplifies to two thirds.

When adding fractions such as one sixth and one half, it's essential to have a common denominator. To find a common denominator for 1/6 and 1/2, we need to think about the multiples of both 6 and 2. The smallest common multiple is 6, so we convert 1/2 into a fraction that has 6 as the denominator. The fraction 1/2 is equivalent to 3/6 since 2 multiplied by 3 equals 6. Now we can add the fractions:

Therefore, one sixth plus one half is equal to two thirds.

First open the bracket by multiplying with -2

-2x - 26 +9x = 4

Solving like terms

7x - 26 = 4

Adding 26 to both sides

7x - 26 +26 = 4+26

7x = 30

X = 30/7

[tex]-2(x+13)+9x=4\\\\-2x-26+9x=4\\\\7x=30\\\\x=\dfrac{30}{7}[/tex]

Let cost of Emma's phone = x

Given that cost of Sophie's phone = 640

Then ratio of their phones cost will be x:640 or x/640

Given that ratio of their phones cost is 7:8 or 7/8

So both ratios will be equal.

[tex]\frac{x}{640}=\frac{7}{8}[/tex]

[tex]x=\frac{7}{8}*640[/tex]

x=560

So the new ratio of the cost of their phones will be 560:640

Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.

So let that decreased amount is k then we will get equation :

[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]

11(560-k)=9(640-k)

6160-11k=5760-9k

6160-5760=11k-9k

400=2k

200=k

Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.

Answer : b) 13/16

Given : t varies as v

So t = k v  where k is the constant of proportionality.

t = 2 4/7 when v =13/14. Using these values we find out k

[tex]t = 2\frac{4}{7} =\frac{18}{7}[/tex]

[tex]v =\frac{13}{14}[/tex]

t = k * v

[tex]\frac{18}{7}= k *\frac{13}{14}[/tex]

Multiply by 14/13 on both sides

[tex]\frac{18}{7} *\frac{14}{13} = k *\frac{13}{14}*\frac{14}{13}[/tex]

So  [tex]k =\frac{36}{13}[/tex]

We got the value of k. Now we find v when t = 2 1/4

[tex]t = 2\frac{1}{4} =\frac{9}{4}[/tex]

t = k * v

We know the value of t and k

[tex]\frac{9}{4}= \frac{36}{13}* v[/tex]

Multiply by 13/36 on both sides

[tex]\frac{9}{4} *\frac{13}{36} =\frac{36}{13}*\frac{13}{36}* v[/tex]

So  [tex] \frac{13}{16}= v[/tex]

Option B is correct

69 divided by 3 is 23

so it would be 21, 23, 25

The first integer (x) is equal to the consecutive even integers, x+2, x+4.

x = (x+2) + (x+4)

x = 2x + 6

x - 6 = 2x

x = -6 (First integer)

+2

-4 (Second integer)

+4

-2 (Third integer)

Integers: -6, -4, -2

Equation: x = (x+2) + (x+4)

Answer:

2x+2=x+4

Step-by-step explanation:

In f(x) = 2.20x + 50 the dependent function is the total cost of flooring the carpet.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A flooring company sells stain-resistant carpets for $2.20 per square foot and will install the carpet for an additional fee of $50 which is represented by f(x) = 2.20x + 50.

Here dependent variable is f(x) which is the cost of the complete project depending on the square foot.

learn more about functions here :

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Matthew traveled a total of 43 blocks.

To calculate the total blocks traveled by Matthew, we need to add up the distances he walked and the distances he rode on the bus. He walked 7 city blocks, rode 13 blocks on the bus, and then walked 1 and a half blocks to the store. To return home, he traveled the same route, so we can double the distance. Adding all these distances together, Matthew traveled a total of 7 + 13 + 1.5 + 7 + 13 + 1.5 = 43 blocks.

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If the speed in still air is s, and the wind speed is w,

580/(s+w) = 5

580/(s-w) = 10

s=87

w=29

Final answer:

To determine the speed of the plane in still air and the speed of the wind, we use the distances and times provided to create two equations. Solving this system reveals that the speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.

Explanation:

To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations based on the given information. We'll let p represent the speed of the plane in still air and w represent the speed of the wind.

When the plane travels with the wind, its effective speed is p + w, and the time taken for the trip is 5 hours, covering 580 miles. So, our first equation is:

1) (p + w) * 5 = 580

When the plane returns against the wind, its effective speed is p - w, and the time taken for this trip is 10 hours, again covering 580 miles. Thus, our second equation is:

2) (p - w) * 10 = 580

Solving this system of equations, we'll start by simplifying both:

p + w = 116 (By dividing the first equation by 5)

p - w = 58 (By dividing the second equation by 10)

Now we can add both equations to eliminate w:

2p = 174

Divide by 2 to get the speed of the plane in still air:

p = 87 mph

To find the speed of the wind, substitute the value of p in one of the equations:

87 + w = 116

So, the speed of the wind is:

w = 116 - 87

w = 29 mph

The speed of the plane in still air is 87 mph, and the speed of the wind is 29 mph.

Answer: 18≤n≤38 is absolute value inequality for the problem.

Step-by-step explanation:

Given situation:- Half of a number n is at most 5 units from 14

that means the difference between 14 and half times n is less than 5

[tex]\Rightarrow |14-\frac{1}{2} \times n|\leq 5\\\Rightarrow|2( 14-\frac{1}{2} \times n)|\leq2(5)\\\Rightarrow|2(14)-2(\frac{1}{2} \times n)|\leq2(5)\ \text{(Multiplying 5 on the both sides)}\\\Rightarrow|\ 28-n|\leq10\\\Rightarrow\ 28-n\leq10\ or\ -(28-n)\leq10\\\Rightarrow\ n=28-10=18\ or\ n=28+10=38\\(i.e.)\ 18\leq\ n\leq \ 38[/tex]

⇒18≤n≤38 is absolute value inequality for the problem.

Answer: ⇒ =x-2

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Step-by-step explanation:

Compute [tex]\frac{x^3-3x^2+3x-2}{x-2}[/tex] to get the rest of the equation.

[tex]\frac{(x-2)(x^2-x+1)}{x^2-x+1}[/tex]

Then you had to cancel by the common factor of [tex]x^2-x+1[/tex]

[tex]=x-2[/tex]

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This is an exponential decay because it decreases by 1/2 each time

Answer:

The answer is exponential decay.

Step-by-step explanation:

At a chess tournament the number of competitors in each round is 50% of the number of competitors in the previous round.

So, the relationship that most appropriately models this situation is exponential decay.

Exponential decay is the process of reducing any given amount by a fixed or gradual percentage rate over a period of time.

It can be written like [tex]y= a(1-b)^{x}[/tex]

Where, y is the final amount

a is the original amount

b is the decay factor

x is the amount of time that has passed.

Hey there!!

Given :

Sum of two integers = -5 and the product is -36.

Hence,

... x + y = -5

... xy = -36

x + y = -5

... y = -x - 5

xy = -36

...x ( -x - 5 ) = -36

... -x² - 5x = -36

... x² + 5x - 36 = 0

This can't be factored so solve using quadratic equation

x = [-b ±√(b2-4ac)]/2a      a=1, b=5, c = -36

x = [-5±√(52-4(-36))]/2

x = [-5 ±√169]/2

x = (-5 ± 13)/2

x = (-5+13)/2= 8/2 = 4  OR

x = (-5-13)/2 = -18/2 = -9

x = 4, -9

Note here that since x+y=-5

For x=4, y=-9

for x = -9, y = 4

The two numbers are 4, -9

Hope my answer helps!!

The two integers are 4 and -9.

To find the two integers, let's assume that one integer is x and the other integer is y. Since the sum of the two integers is -5, we can write the equation x + y = -5. Similarly, the product of the two integers is -36, so we can write the equation xy = -36.

Now, we can solve these equations simultaneously to find the values of x and y.

From the first equation, we can express x in terms of y as x = -5 - y. Substituting this value into the second equation, we get (-5 - y)y = -36.

Simplifying this equation gives us y^2 + 5y - 36 = 0. Factoring or using the quadratic formula, we find that y = -9 and y = 4.

Substituting these values back into the equation x = -5 - y, we find that x = 4 and x = -9.

Therefore, the two integers are 4 and -9.

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Let the speed of the boat in still water = X

The current is 3 mph, so the speed of the boat going upstream would be x-3

Speed of the boat going down stream would be x +3

The trip upstream is 26 / x-3

The trip downstream is 38 / x+3

Set them to equal and solve for x:

26/x-3 = 38/x+3

Multiply both sides by (x+3)(x-3):

38(x-3) = 26(x+3)

Simplify:

38x - 114 = 26x+78

Subtract 26x from each side:

12x -114 = 78

Add 114 to each side:

12x = 192

Divide both sides by 12:

x = 192 / 12

x = 16

The speed is 16 miles per hour.

To determine the boat's speed in still water, an equation is set up that relates the upstream and downstream times, given that the current influences the boat's effective speed by 3 mph. Solving this equation yields a speed of 16 mph for the boat in still water.

To find the speed of the boat in still water, we need to account for the effect of the current on the boat's speed when going up and down the river. Let the speed of the boat in still water be v mph.

When the boat is going upstream (against the current), its effective speed is (v - 3) mph because the current slows the boat down by 3 mph. When the boat is going downstream (with the current), its effective speed is (v + 3) mph because the current speeds the boat up by 3 mph.

Since the boat covers 26 miles upstream and 38 miles downstream in the same time, we can set the time equal for both scenarios:

Time = Distance / Speed

By equating the two times, we get:

26 / (v - 3) = 38 / (v + 3)

To solve for v, cross-multiply and simplify:

26(v + 3) = 38(v - 3)

26v + 78 = 38v - 114

12v = 192

v = 192 / 12

v = 16 mph

Therefore, the speed of the boat in still water is 16 mph.

A. 2(4.1)+3=11.2

B.16-5(2.3)=4.5

c.(4.1)+(2.3)=6.4

12/4=x/20

x=60

60 people are needed

4x3=12 right. Then 20x3=60.