The variables are higher or lower

Answer:

5x-8

Step-by-step explanation:

7x-14-2x+6

-14+6=-8

7x-2x=5x

Answer:

13.27 cm

Step-by-step explanation:

The hypotenuse is always the longest side so:

a^2 + 20^2 = 24^2

a^2 + 400 = 576

a^2 = 176

a = 13.27

Answer:

The answer is 2.

Step-by-step explanation:

2 appears three times while the others appear only twice

To find the number of ways to draw three balls at random from an urn containing 5 red balls and 4 blue balls, we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of balls in the urn, r is the number of balls we want to draw, and the exclamation mark denotes factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1).

In this case, we have:

n = 5 + 4 = 9 (total number of balls in the urn)

r = 3 (number of balls to draw)

So the number of ways to draw three balls is:

9C3 = 9! / 3!(9-3)! = (9 x 8 x 7) / (3 x 2 x 1) = 84

Therefore, there are 84 ways to draw three balls at random from an urn containing 5 red balls and 4 blue balls.

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Answer:

carton = 12

12x17=204

miranda needs 204 more eggs to fill 17 egg cartons

To find the height of the new rectangular box, we first need to determine the volume of the original can. The can has a height of 6 inches and a diameter of 4 inches, which means it has a radius of 2 inches. The volume of a cylinder (can) is calculated using the formula V = πr²h.

In this case, V = π(2²)(6) = 24π cubic inches.

Now, we need to find the height of the new rectangular box that has a width of 4 inches and a depth of 2 inches. To maintain the same volume, the formula for the volume of a rectangular prism (box) is V = lwh.

Since we know the volume (24π cubic inches), width (4 inches), and depth (2 inches), we can solve for the height (h):

24π = (4)(2)(h)
24π = 8h

Now, divide both sides by 8:

h = 3π inches

So, the height of the new rectangular box would be 3π inches to maintain the same volume as the original can.

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Answer:

I think it should be correct

Good Luck!

Answer:

1/4

Step-by-step explanation:

You are being asked to find 1/3 of 3/4. To find a fraction of a number, you multiply them:

1/3 * 3/4

(cross multiply)

3/12

(simplify (divide top and bottom by three))

1/4

Answer:

Hmmm I think it would 108 I think I’m sorry if it wrong ;^;

Step-by-step explanation:

The proofing that Triangle CAD equals triangle CBD is given below.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to a 180 degree angle.

Given,

AC is the common hypotenuse. ∠B=∠D=90°.

To prove,

∠CAD=∠CBD

Since, ∠ABC and ∠ADC are 90°, these angles are in the semi-circle.  lThus, both the triangles are lying in the semi-circle and AC is the diameter of the circle.

⇒ Points A,B,C and D are concyclic.

Thus, CD is the chord.

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Complete question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD=∠CBD.

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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No, f(x, y) = 3x - 3y^2 is not a harmonic function.

A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
                                                                            ∂²f/∂x² + ∂²f/∂y² = 0.

Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0

Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.

As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.

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Given:

The angle 140 degree.

The co-terminal angles is defined as an angle, where two angle are drawn in the standard position.

It is determine by adding or subtraction 360 degree to each angle.

Answer: Positive co-terminal angle of 140 degree is 500 degree.

Option A is correct.

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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Answer:

\(\displaystyle \frac{14}{3}\sqrt{5}\)

Step-by-step explanation:

Simplify:

\(\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}\)

We must express the mixed fraction into an improper fraction:

\(2\frac{2}{9}=2+\frac{2}{9}=\frac{20}{9}\)

\(\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{80} + \sqrt{\frac{20}{9}}\)

Since 80 = 16*5 and 20=4*5

\(\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{16*5} + \sqrt{\frac{4*5}{9}}\)

\(\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle 4\sqrt{5} + \frac{2}{3}\sqrt{5}\)

Adding the fractions:

\(\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle (4 + \frac{2}{3})\sqrt{5}\)

\(\mathbf{\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \frac{14}{3}\sqrt{5}}\)

Answer:

y = 2x + 2

Explanation:

We can use the following equation to write an equation in slope-intercept form.

Where (x1, y1) is a point in the line and m is the slope. Additionally, the slope can be calculated as:

Where (x2, y2) is another point in the line.

So, replacing (x1, y1) by (0, 2) and (x2, y2) by (3, 8), we get that the slope is equal to:

Finally, replacing m by 2 and (x1, y1) by (0, 2), we get:

Therefore, the equation in slope-intercept form is:

y = 2x + 2

When a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1, synthetic division is used. Any polynomial equation, regardless of degree, can, for instance, be divided by x + 1, but not by x2+1.

Additionally, the binomial must be of degree 1; synthetic division cannot be used to divide by a binomial such as x2 + 1. Here are the steps for performing synthetic division on a polynomial by a binomial.

To get the quotient and the remainder, write down the coefficients and divide them by the linear factor's zero. Q(x) + (R/(x - a)) = (P(x)/(x - a)).

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Answer:

(4m - 1) × (2n + n)

Step-by-step explanation:

8m - 2 + 4mn - n

2(4m - 1) + 4mn - n

2(4m - 1) + n × (4m - 1)

= (4m - 1) × (2n + n)

The answer is (4m - 1) × (2n + n)

The simplest way of factorizing is:

Factorise: 8m-2+4mn-n

⇒ 8m - 2 + 4mn - n

⇒ 2(4m - 1) + 4mn - n

⇒ 2(4m - 1) + n × (4m - 1)

⇒ (4m - 1) × (2n + n)

Factorising is a way of writing an expression as a product of its factors using brackets.

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Answer:

1 ounce of toppings

Step-by-step explanation:

Mr. X sold 20.5 donuts and 5.5 bagels. X is selling donuts and bagels for a school fundraising event. But the prices changed to battle against inflation.

Let x be the number of donuts sold, and y be the number of bagels sold. Then we can set up a system of linear equations to represent the given information:

x + y = 26 (the total number of donuts and bagels sold is 26)

3x + 4.5y = 94.5 (the total money raised is $94.50)

To solve for x and y, we can use elimination or substitution method. Here, we will use substitution method:

x + y = 26 (multiply both sides by 3 to eliminate x's coefficient)

3x + 4.5y = 94.5

3x + 3y = 78

3y = 16.5

y = 5.5

Substitute y = 5.5 into either equation to solve for x:

x + 5.5 = 26

x = 20.5

Therefore, Mr. X sold 20.5 donuts and 5.5 bagels. However, since he cannot sell half a donut or half a bagel, we can round the values to the nearest whole number. Thus, he sold 21 donuts and 6 bagels.

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Answer:

15

Step-by-step explanation:

The formula for distance when given vertices is

√(x2 - x1)² + (y2- y1)²

Where we have points (x1,y1) and (x2,y2)

So, (-2,7) and (3, -3)

Distance = √(3 -(-2))² + (-3 -7)²

= √5² + (-10)²

= √25 + 100

= √125

= 15

Therefore, the distance between (-2,7) and (3, -3) is 15

2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

A. 2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. 4x:2y=2:4 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 2:4.

C. 4x:2y=4:8 is correct because it states that for every 4 units of x, there are 2 units of y, so the ratio of x to y is 4:8.

F. 2x:3y=4:8 is correct because it states that for every 2 units of x, there are 3 units of y, so the ratio of x to y is 4:8.

the complete question is :

Kiesha and her classmates wrote proportions for the reduction of a triangle. Which proportions are set up correctly? select three options.

A. 1/2:2/3:3/4

B. 3/2:2/3:1/4

C. 1/2:2/4:3/6

D. 1/4:2/3:4/5

E. 2/3:3/4:4/5

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2x:4y=4:8

B. 4x:2y=2:4

C. 4x:2y=4:8

D. 2x:4y=2:4

E. 3x:2y=2:4

F. 2x:3y=4:8

B, C, F

B. The formula 4x:2y=2:4 is accurate because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 2:4.

C. 4x:2y=4:8 is true because it says that there are 2 units of y for every 4 units of x, making the x:y ratio 4:8.

F. 2x:3y=4:8 is true because it says that there are 3 units of y for every 2 units of x, making the x to y ratio 4:8.

The total percentage of athletes who enjoy cycling is given by:

74.5%.

A percentage is the division of an amount by a total amount, which is then multiplied by 100%.

In this problem, the percentages are already given for the entire population.

The percentage of athletes who enjoy cycling is divided into two nodes, as follows:

The percentages associated from each node are given on the text as follows:

Hence the proportion of athletes who enjoy cycling is given as follows:

0.45 x 0.80 + 0.55 x 0.70 = 0.745.

Then the percentage is of:

0.745 x 100% = 74.5%.

Which means that the last option is correct.

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The distance Chyna ran is 7 1 / 2 kilometres.

Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5

kilometres

Therefore, the distance Chyna ran in kilometres can be calculated as follows:

Therefore,

Distance Ronaldo ran = 6 3 / 5  = 33 / 5 kilometres

Hence,

Distance Chyna ran = 33 / 5 + 9 / 10

Distance Chyna ran = 66 + 9 / 10

Distance Chyna ran = 75 / 10

Therefore,

Distance Chyna ran = 7 5 / 10

Distance Chyna ran = 7 1 / 2 kilometres

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Answer:

(16√75)/(5√12) = 8

Step-by-step explanation:

Answer:

16√75÷5√12

= 8

Step-by-step explanation:

Hope it is helpful.....

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

\( [\frac{7}{12} + ( - \frac{5}{12} )] -[ \frac{5}{9} + ( - \frac{2}{9} )] \\ \\ = [ \frac{7}{12} - \frac{5}{12} ] - [ \frac{5}{9} - \frac{2}{9} ] \\ \\ = [ \frac{7 - 5}{12} ] - [ \frac{5 - 2}{9} ] \\ \\ = \frac{2}{12} - \frac{3}{9} \\ \\ = \cancel \frac{2}{12} - \cancel \frac{3}{9} \\ \\ = \frac{1}{6} - \frac{1}{3} \\ \\ = \frac{1 - 2}{6} \\ \\ = - \frac{1}{6} \)

Answer:

         \(\frac{-1}{6}\)

Step-by-step explanation:

\(Sum \ of \ \ \frac{5}{9} \ and \ \frac{-2}{9} =\frac{5}{9} + \frac{-2}{9} = \frac{5-2}{9} = \frac {3}{9} = \frac{1}{3}\)

\(Sum \ of \ \frac{7}{12} \ and \ \frac{-5}{12} = \frac{7}{12} \ + \ \frac{-5}{12} = \frac{7-5}{12} = \frac{2}{12} = \frac{1}{6}\)

\(subtract \ first \ from \ second = \frac{1}{6} - \frac{1}{3} = \frac{1 -2}{6} = \frac{-1}{6}\)

Answer:

2, 5

Step-by-step explanation:

hope this helps

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