Graph the following on the axes below:
* 6x+5y=-10

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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Answer:

E=(-1,3)  F= (3,3) G=(-2,-1) H=(4,-1)

the shape is a trapizode

Check the picture below.

now, notice the triangles made, 3 right triangles with legs of 5 and 4 each.

looking at quadrilateral (1), from the leg 5 units long, we have a line with a run of -1 and a rise of 3, from the leg 4 units long, we have a line with a run of 4 and a rise of -1.

Now, quadrilaterals (2) and (4) display the same lengths and rise and runs, which means they're all congruent, quadrilateral (3) has no equal.

so 1 ≅ 2 and 1 ≅ 4.

Answer:

\(\dfrac{a^6}{144b^8}\)

Step-by-step explanation:

a) They did not use the exponent rule: \((a \cdot b)^n=a^nb^n\) correctly.

They added the exponents rather than multiplied them.

b) Correct solution:

\((12a^{-3}b^4)^{-2}\)

Apply exponent rule:  \(a^{-b}=\dfrac{1}{a^b}\)

\(\implies \dfrac{1}{(12a^{-3}b^4)^2}\)

Apply exponent rule: \((a \cdot b)^n=a^nb^n\)

\(\implies \dfrac{1}{12^2a^{(-3\times2)}b^{(4 \times2)}}\)

\(\implies \dfrac{1}{144a^{-6}b^8}\)

Apply exponent rule:  \(\dfrac{1}{a^{-b}}=a^b\)

\(\implies \dfrac{a^6}{144b^8}\)

Answer:

3

Step-by-step explanation:

Degree of the polynomial is the highest degree of the polynomial. Here highest degree is 3.

The probability that the sum exceeds 5 is P ( A ) = 0.6111

Given data ,

To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.

The outcomes where the sum exceeds 5 are:

(2, 4), (2, 5), (2, 6)

(3, 3), (3, 4), (3, 5), (3, 6)

(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.

So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:

P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %

Hence , the probability is P ( A ) = 0.6111

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The complete question is attached below :

A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5

a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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The likelihood that one or more of the dice will land on an even number is 1296.

The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.

Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.

For 2 of the same: 5×5×642) =900

For 3 of the same: 5×643) =120

For 4 of the same: 644) =6

Combined: 900+120+6=1026

Total possibilities: 64=1296

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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.

The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:

(1/2) × (1/2) × (1/2) × (1/2) = 1/16

Therefore, the probability that at least one of the dice lands on an even number is:

1 - 1/16 = 15/16

So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.

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Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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The reconciliation for Bane can be summarized as,

Adjusted bank balance = $1380.

A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.

Given that,

Beginning checkbook balance is $1400.

Service charge = $20

Adjusted balance = $1400 - $20 = $1380

Also, given that,

Ending balance on the statement = $1480

Deposit in transit = $200

Checks outstanding = $300

Adjusted balance = $1480 + 200 - 300

                              = $1380

Hence the adjusted balance is $1380.

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Answer:

Step-by-step explanation:

Start by observing that ln(1) = 0

So ln 1^4 = 0 as well.

My calculator says that 4 ln(1) + ln (3) - ln1

is ln(3).

I'm not sure it's right.  Is that a bug or is it actually what the answer is? I will accept it is ln3 but I have my doubts -- especially when when there is a zero involved. If you get a different responder to this and something different is said, I would accept that answer.

Very interesting question.

Answer:

-4, -9/4, 0.5, 2.2 (the last one) , 3.7

Step-by-step explanation:

I hope you have a great day and LEAVE ME ALONE! <3

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the normal distribution are

Mean value of the set of data = 88.2

Standard deviation value of the set of data = 1.3

The actual data value = 88.2

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (88.2 - 87.9)/1.3

Evaluate the difference of 88.2 and 87.9

z = 0.3/1.3

Evaluate the quotient of 0.3 and 1.1

z = 0.23

The probability that the mean fill is more than 88.2 ounces is then calculated as:

P(x > 88.2) = P(z > 0.23)

From the z table of probabilities, we have;

P(x > 88.2) = 0.5910

Hence, the probability that the mean fill is more than 84.8 ounces is 0.5910

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Answer:

I wanna say 18 but I'm not to sure

Answer:

x + 3y = 30

Step-by-step explanation:

We are given that a line contains the points (12,6) and (-3,11)​.

We want to write the equation of this line in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.

Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

So first, let's find the slope of the line.
The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points.

Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.

\(x_1=12\\y_1=6\\x_2=-3\\y_2=11\)

Now substitute these values into the formula.

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{11-6}{-3-12}\)

Subtract

m=\(\frac{5}{-15}\)

Simplify

m=\(-\frac{1}{3}\)

The slope is -1/3

Here is the equation of the line so far in slope-intercept form:

\(y=-\frac{1}{3} x + b\)

We need to solve for b.

As the equation passes through (12,6) and (-3,11)​, we can use either one to help solve for b.

Taking (12, 6) for example:

\(6=-\frac{1}{3}(12) + b\)

Multiply

\(6=-\frac{12}{3} + b\)

Divide

6 = -4 + b

Add 4 to both sides.

10 = b

Substitute 10 as b in the equation.

\(y = -\frac{1}{3} x + 10\)

Here is the equation in slope-intercept form, but remember, we want it in standard form.

In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.

\(\frac{1}{3} x + y = 10\)

Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.

So, let's multiply both sides by 3 to clear the fraction.

\(3(\frac{1}{3} x + y) = 3(10)\)
Multiply.

x + 3y = 30

Topic: finding the equation of the line (standard form)

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Answer:

Step-by-step explanation:

1) 40 +5b =  1240

2) 40 + 5b = 1240 {Subtract 40 from both sides}

          5b = 1240 - 40

          5b = 1200     {Divide both sides by 4}

           b = 1200/4

          b = $ 300

Answer:

If they are divisible by the numbers in the original shape, then try and see if the others sides of the scaled copy are scaled by the same factor. If they are, then they are a scaled copy.

Step-by-step explanation:

If x changes from 1.6 to 1.8 is Δx = 0.2,  the corresponding change in f(x) with respect to x is 2.5 at Δx = 0.2 and the value of f(1.8) = 3.66.

As per the question given,  

Suppose we have a linear function f(x) that changes with respect to X at a constant rate of 2.5. If you know that f(1.6) equals 2.6, you can use this information to answer interesting questions.

First, if x changes from 1.6 to 1.8, how much has x changed? The answer is Δx = 0.2 because 1.8 minus 1.6 equals 0.2.

Second, what is the corresponding change in f(x)? The rate of change of f(x) with respect to x is 2.5, so at Δx = 0.2, f(x) changes by Δf(x) = 2.5 times 0.2, which equals 0.5.

Finally, what is the value of f(1.8)? You can use the linear function equation to find this value. Using the fact that f(1,6) equals 2.6 and the rate of change of f(x) with respect to x is 2.5, we can derive the equation f(x) = 2.5x - 1.14. replacing x = 1.8 to this equation you get f(1.8) = 3.66.

Then you have it! By knowing the rate of change of a linear function and learning basic algebra, you can answer these questions and better understand how the function behaves for different values ​​of x.

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The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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\(6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}\)

Answer: 10/5 or 2

Step-by-step explanation: Using the equation y2-y1/x2-x1 you would substitute the numbers in, having it be 3-(-7)/3-(-2). Once you have that you just subtract/add the numbers and whatever fraction you get is your slope.

Answer:

y=2x-3

Step-by-step explanation:

gradient = y2-y1/x2-x1

-7-3/-2-3

-10/-5=2

y=-3

so the equation is y=2x-3

Answer: 10x^2 - 4x

Step-by-step explanation:

To expand, you are not simplifying, so multiplying out is the answer here. To do this, use the distributive property. The distributive property in this case means that if you are multiplying one number by a whole expression inside parenthesis, multiply the one number by each term in the expression:

2x(5x - 2)

= 2x(5x) + 2x(-2)

= 10x^2 - 4x

The product of the expression is equivalent to -

10x² - 4x.

Given is the expression as follows -

2x(5x - 2)

The given expression is -

2x(5x - 2)

10x² - 4x

Therefore, the product of the expression is equivalent to -

10x² - 4x.

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Answer:

\(y=-5x+7\)

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer: $773.18

Step-by-step explanation:

Revenue=Cost 1−Gross Margin

Revenue=5,670.001−0.1200

Revenue=6,443.18

Gross Profit=Revenue×Gross Margin

Gross Profit=6,443.18×0.1200

Gross Profit=773.18

Mark Up=Gross ProfitCost×100

Mark Up=773.185,670.00×100

Mark Up=13.64%

Ann made money from illegal gambling in 2019 in $2,197,890

As per the details provided in the above question are as follow,

Consider the income obtained from Extortion is x.

While the income obtained from the illegal gusting is y

Now in 2019

x + y = $3956202

\(y=x+\frac{x \times 25}{100}\\y=\frac{5}{4} x\)

Substitute the value of  \($x=\frac{4}{5} y$\) in above equation we get,

\(\frac{4}{5} y+y & =3,956,202 \\\\\frac{9}{5} y & =3956202 \\\\y & =\frac{5}{9} \times 3956202\)

y = $2197890

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