common demominator of 1/3 and 3/4

Answer:

y = -3x - 3

Step-by-step explanation:

By equation of a straight line, this could mean:

Slope intercept form: \(y=mx+b\)

Point slope form: \(y-y1=m(x-x1)\)

Because we do not have the y intercept, it would be much easier to write it in point slope form where y1 and x1 are points and m is the slope.

First, we need to find the slope. We can do this by using the slope formula \(\frac{y2-y1}{x2-x1}\) where y2, y1, x2, and x1 are points.

\(\frac{-3-0}{2-1}\)

Evaluate

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

Now that we have the slope, lets use the ordered pair (1,0) and write the equation of the line in point slope form.

\(y-0=-3(x-1)\)

Simplify

\(y=-3x-3\)

Would you look at that, we get the equation of the line in slope intercept form!

The value of x is 10 centimeters

The complete question is in the image

The value of x is calculated using the following Pythagoras theorem

x^2 = 6^2 + 8^2

Evaluate the sum of exponents

x^2 = 100

Take the square roots

x = 10

Hence, the value of x is 10 centimeters

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Answer:

1. 2,772

2.1,071

3.4,641

4. 36,610

5. 4,096

6. 36,270

7. 2,403

8. 3,320

Answer:

28÷4=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Hello there! Grace is here to help you! :)

28:4=7

Hope it helps!

______

Additional Comment

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Answer:

Undefined

Step-by-step explanation:

Answer:

Y=4x

Step-by-step explanation:

Answer:

1/4 per hour

Step-by-step explanation:

1 bracelet in 4 hours

1 divided by 4 = 1/4

1/4 bracelets per hour

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

A. $1 less

Step-by-step explanation:

24 divided by 8 (unit rate) = $3

28 divided by 7 = $4

4-3=1

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

The measure of side KL from triangle KLM is 22 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle HIJ is similar to triangle KLM.

From the similar triangles,

JH/MK =HI/KL

31/13.9 =49/KL

31KL=49×13.9

31KL=681.1

KL=681.1/31

KL=21.97

KL≈22

Therefore, the measure of side KL is 22 units.

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Answer:

Step-by-step explanation:

The answer is, no!

Step-by-step explanation:

The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.

So, here is the given information on what we need to classify a shape as a parallelogram:-

1) Parallel Sides

2)Opposite Sides are equal.

3) Adjacent sides are not equal.

4) Opposite angles are equal.

5)Adjacent angles are not equal.

Based on this, we can classify a shape as a parallelogram.

Hope, this answer helps!

Answer:

  D 1/4

Step-by-step explanation:

Your question is a problem in reading comprehension. It tells you its own answer.

  x is always 1/4

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

The value of k is given as follows:

k = 24.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

From the table, we have that when x = 6, y = k, hence the value of k is found replacing each of the three instances of x by 6, as follows:

k = (6 - 3)(6 - 5)(6 + 2)

k = 3 x 1 x 8

k = 24.

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Answer:

Solving the equation \(4+5(m-1)=34\\\) we get m=7

Step-by-step explanation:

We need to solve the equation \(4+5(m-1)=34\\\) and find value of m

Solving using transpose method which states that if one term is added one one side, it gets subtracted on other side of equality

\(4+5(m-1)=34\\Multiply \ 5 \ with \ terms \ inside \ the \ brackets\\4+5m-5=34\\5m+4-5=34\\5m-1=34\\Adding \ 1 \ on \ both \ sides\\5m-1+1=34+1\\5m=35\\Divide \ by \ 5\\\frac{5m}{5} =\frac{35}{5}\\m=7\)

So, solving the equation \(4+5(m-1)=34\\\) we get m=7

(a) One ball is drawn at random from the urn and it is red, so the posterior distribution of X can be found using Bayes' theorem:

P(X = x | red) = P(red | X = x) * P(X = x) / P(red)

where P(X = x) is the prior probability of X being x, P(red | X = x) is the probability of getting a red ball given that X is x, and P(red) is the total probability of getting a red ball.

Since all possible values of X from 0 to 9 are equally likely, the prior probability of X being x is P(X = x) = 1/10 for x = 0, 1, 2, ..., 9.

The probability of getting a red ball given that X is x can be calculated using the hypergeometric distribution:

P(red | X = x) = (x choose 1) * (9-x choose 8-x) / (9 choose 1)

where (x choose k) is the number of combinations of x items taken k at a time.

The total probability of getting a red ball is:

P(red) = sum(P(red | X = x) * P(X = x)) for x = 0, 1, 2, ..., 9

Using these formulas, we can find the posterior distribution of X and the mean of X:

Posterior distribution of X:

P(X = x | red) = P(red | X = x) * P(X = x) / P(red)

Mean of X:

E(X | red) = sum(x * P(X = x | red)) for x = 0, 1, 2, ..., 9

(b) Now suppose that a second ball is drawn from the urn, without replacing the first, and it is green, so the posterior distribution of X can be found using Bayes' theorem again:

P(X = x | red, green) = P(green | X = x) * P(X = x | red) / P(green)

where P(X = x | red) is the posterior distribution of X from part (a), P(green | X = x) is the probability of getting a green ball given that X is x, and P(green) is the total probability of getting a green ball.

The probability of getting a green ball given that X is x can be calculated using the hypergeometric distribution:

P(green | X = x) = (9-x choose 1) * (x choose 8-x) / (9 choose 1)

The total probability of getting a green ball is:

P(green) = sum(P(green | X = x) * P(X = x | red)) for x = 0, 1, 2, ..., 9

Using these formulas, we can find the posterior distribution of X and the mean of X:

Posterior distribution of X:

P(X = x | red, green) = P(green | X = x) * P(X = x | red) / P(green)

Mean of X:

E(X | red, green) = sum(x * P(X = x | red, green)) for x = 0, 1, 2, ..., 9

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The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer:

Total time taken by walking, running and cycling = 22 minutes.

Step-by-step explanation:

Let the speed of walking = x

As given,

The distance of walking = 1

Now,

As \(Time = \frac{Distance }{Speed}\)

⇒ Time traveled by walking = \(\frac{1}{x}\)

Now,

Given that - He runs twice as fast as he walks

⇒Speed of running = 2x

Also given distance traveled by running = 1

Time traveled by running = \(\frac{1}{2x}\)

Now,

Given that - he cycles one and a half times as  fast as he runs.

⇒Speed of cycling =  \(\frac{3}{2}\) (2x) = 3x

Also given distance traveled by cycling = 1

Time traveled by cycling = \(\frac{1}{3x}\)

Now,

Total time traveled = Time traveled by walking + running + cycling

                                = \(\frac{1}{x}\) +  \(\frac{1}{2x}\) + \(\frac{1}{3x}\)

                                = \(\frac{6+3+2}{6x} = \frac{11}{6x}\)

If he cycled the three mile , then total time taken = \(\frac{1}{3x}\) + \(\frac{1}{3x}\) + \(\frac{1}{3x}\) = x

Given,

He takes ten minutes longer than he would do if he cycled the three miles

⇒x + 10 = \(\frac{11}{6} x\)

⇒\(x - \frac{11}{6} x = -10\)

⇒\(-\frac{5}{6}x = -10\)

⇒x = \(\frac{60}{5}\) = 12

⇒x = 12

∴ we get

Total time traveled by walking + running + cycling = \(\frac{11}{6} x = \frac{11}{6} (12) = 11 (2) = 22\) min

The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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Answer:

9

Step-by-step explanation:

One did 10,one did 9, and 1 did 8 and 9 is the median number of those 3 numbers.

Answer:

Abdu, Tonya, Gao, Lily, Mike, Rishab

Step-by-step explanation:

Answer:

I'm pretty sure the answer is 42. You just subtract 180 and 138 because the KD line would be 180.

Answer:

D is not a function--an x-value cannot correspond to more than one y-value.

Answer:

$541.41

Step-by-step explanation:

the tax is $42.41

so if you add that to $499 you get

499+42.41= 541.41

It should be noted that to write a system of equations in standard form, you need to express each equation in the form Ax + By = C, where A, B, and C are constants and x and y are variables. The steps are given below.

Here are the steps to follow:

Rewrite each equation in standard form by moving all the variables to one side and all the constants to the other side.

Make sure that the coefficients of x and y are integers and, if possible, that they have a greatest common factor of 1. If the coefficients have a common factor, divide both sides of the equation by that factor to simplify the equation.

Arrange the equations in standard form in a matrix form. You can write the matrix form by lining up the coefficients of x, y, and the constants in a matrix.

Finally, you can also represent the system of equations in standard form using variables and constants.

This is the standard form of a system of linear equations.

Note that an overview was given since your information is incomplete.

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Answer:

\( {x}^{2} + {8}^{2} = {y}^{2} ...(1) \\ {x}^{2} + {23}^{2} = {z}^{2} ...(2) \\ {y}^{2} + {z}^{2} = {(23 + 8)}^{2} \\ {y}^{2} + {z}^{2} = {(31)}^{2} ...(3) \)

You should be able to solve this simultaneously...to find x,y and z.

Answer: -2

Step-by-step explanation:

-7w + 1 = 8

Subtract 1 from both sides

-7w + = 7

Divide -7 from both sides

w = -1

then

8(-1) = -8

-8 + 6 = -2

The total number of animals are 112 if the ratio of kangaroos to emus is 9:7 and the number of emus are 49.

A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3).

A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values.

Given,

The ratio of kangaroos to emus is 9:7

And also given that the number of emus=49

Since, the ratio is 9:7

The number of kangaroos=63

63:49

9:7

Total number of animals=63+49

=112

Therefore, the total number of animals are 112 if the ratio of kangaroos to emus is 9:7 and the number of emus are 49.

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Answer:

\(\lim_{x\to -\infty} f(x)=\infty,\\\lim_{x\to \infty} f(x)=2,\)

Step-by-step explanation:

The end behaviors of a function simply denote where the function is headed at x approaches negative and positive infinity. In \(f(x)=\left(\frac{1}{3}\right)^x+2\), as \(x\) gets approaches \(-\infty\), the function will approach \(y=\infty\). As \(x\) approaches \(\infty\), the function will approach \(y=2\).

We can write this in the following format to denote these end behaviors:

\(\lim_{x\to -\infty} f(x)=\infty,\\\lim_{x\to \infty} f(x)=2,\)