ABCD is a rhombus.

The coordinates of A are (5,11)
The equation of the diagonal DB is y = [tex]\frac{1}{3}[/tex] x + 5
The equation of the diagonal AC can be written in the form y = mx + c where m and c are integers.

Work out the value of m and the value of c.

Square root of 15.625 is 3.906

What in mathematics is a square root?

A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.

How is the square root calculated?

The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."

Find the nearest perfect square, in this case 16 .

Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906

Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.

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Answer:

-35.4

Step-by-step explanation:

Using PEMDAS divide 63 first by 5 and u will get:

Now we have 12.6-48. If we subtract them together we will get:

Hence, the answer is -35.4

The answer can't be determined by the amount of data given in the question for ellipse.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

The standard equation for an ellipse is (x-h)²/a²+(y-k)²/b² = 1

a, b = semi-major and semi-minor axes respectively.

The center of the ellipse is at (0,0).

here, h=0, k=0.

One focus is at (12, 0)

Therefore

c = 12,

We can't find out the directrix with the given data.

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The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

Given,

The constant rate at which helium is pumped into the spherical balloon, r = 5 ft.³/s

We have to find the rate at which the radius of the balloon is increasing after 2 minutes.

Here,

dV/dt = (dV/dr) × (dr/dt)

Then,

dr/dt = (dV/dt) / (dV/dr)

The volume of balloon after 2 minutes (120 seconds) V₁₂₀ ;

V₁₂₀  = 120 s × 5 ft.³/s = 600 ft.³

The radius of balloon after 2 minutes ;

V = 4/3 π r³

dV/dr = 4 π r²

r = [tex]\sqrt[2]{\frac{2}{4.\pi } V}[/tex]

Then,

r₁₂₀ = [tex]\sqrt[2]{\frac{2}{4.\pi } 600}[/tex] ≈ 9.77

dr/dt = (dV/dt) / (dV/dr) = 5 / 4π r²

At t = 2 minutes (120 seconds), r ≈ 9.77 feet

dr/dt ≈  5 / 4π 9.77² ≈ 4.16 × 10⁻³

That is,

The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

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If the triangle is equiangular, then the triangle is an equilateral triangle.

What is equiangular triangle?

A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60

What is equilateral triangle?

an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°.

As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.

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The value of x₃  , starting with  x₁ = 8 is 4.578

Given in the question ,

The iterative formula for the sequence is

=> xₙ₊₁ = 5 - 2 / xₙ

Also , x₁ = 8

Putting n = 2 in iterative formula

x₂ = 5 - 2 / x₁

Substituting the value of x₁

=> x₂ = 5 - 2 / 8

=> x₂ = 5 - 1 / 4

=> x₂ = (20 - 1)/4

=> x₂ = 19/4

=> x₂ = 4.75

Now , putting n = 3

x₃ = 5 - 2 / x₂

Substituting the value of x₂

=> x₃ = 5 - 2 / x₂

=> x₃ = 5 - 2 / 4.75

=> x₃ = 5 - 0.421

=> x₃ = 4.578

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The true statements about the three quadrilateral is

The measurements of quadrilateral D  = 3 units and 1 units

The measurements of quadrilateral F = 3 units and 1 units

The measurements of quadrilateral E = 2 units and 6 units

The similar figure defined as the figures that have the same shape but not same size

The congruent is defined as the figures that have the same shape and size

Here D and F are congruent but they are not similar because they have same size

D and E are similar but not congruent because of same shape and different size.

Hence, true statements about the three quadrilateral is

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Answer:

x > 2.8

Step-by-step explanation:

x < -x + 7(x - 2)

Expand using the Distributive Property

x < -x + 7x - 14

x < 6x - 14

Subtract x from both sides

0 < 6x - 14 - x

0 < 5x - 14

Add 14 for both sides

5x > 14

x > 14/5

x > 2.8

The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.

we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.

Here, the margin of error is E=2 and the level of significance is α=0.05

The critical value is Zα/2=Z₀.₀₂₅

or the critical value is 1.96

Now, we will find the sample size

n=((Zα/2)×σ/E)²

n=(1.96×8.4/2)²

n=67.76

n≈68

Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

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Answer:

(3, 1/64)

(−1, 4)

Step-by-step explanation:

took the test

Answer:

(3, 1/64)

(−1, 4)

Step-by-step explanation: toom the test :)

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:

p-value = 0.09 is the probability of obtaining a value for the test statistic.

We are going step by step

Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample

Step 2) Here the Confidence level is equal to 0.95

So the level of significance is equal to 0.05

p-value = 0.09

Since the p-value is higher than the level of significance that we do not reject the null hypothesis.

Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.

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Answer:

$25.00

Step-by-step explanation:

Total amount of bill is $25.

Given information:

The amount of tip = $4.50

The percentage given = 18%

4.50 of 18% is $25

A stem club has 30 members and to find out how many ways are there to choose 4 members of the club to serve on an executive committee is as follows:

Given the stem club has 30 members.

The number of ways to choose 4 members of the club to serve on an executive committee is to be considered as 30c4

we know that the formula is

     [tex]n{cr}[/tex] = [tex]\frac{n!}{(n-r)!r!}[/tex]

there n = 30 and r = 4

that is., [tex]30_{c4}[/tex] = [tex]\frac{30!}{(30-4)!4!}[/tex]

                  = [tex]\frac{30!}{26!4!}[/tex]

                  = 29x15x7x9  = 27,405

Hence, the number of ways to choose 4 members of the club to serve on an executive committee is equal to 27,405.

Hence the number of ways to choose an executive member = 27,405

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The length of each of the other two pieces = 0.

Jessica cuts a ribbon with a length of 12 inches into three pieces.

The length of one piece is [tex]3\frac{1}{2}[/tex]

The lengths of the other two are the same

To find out the length of each of the other two pieces:

Based on the given conditions, we write formula as

(3-3)÷2

The sum of two opposites equals O: [tex]\frac{3-3}{2}[/tex]

Apply Zero property of Multiplication: 0

So we get the result = 0

Hence the answer if the length of each of the other two pieces = 0.

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Answer: 7.6 meters.

Step-by-step explanation:

1.2(2) + 2.6(2)

2.4 + 5.2

7.6

Remember, perimeter is L(2) + W(2).

Roy's younger brother's age is 11 years.

According to the question,

We have the following information:

If Roy is 4 years older than his brother and the product of their ages is 165.

Now, let's take the age of Roy's younger brother to be x years.

Age of Roy = 4+x

So, we have the following expression:

x(4+x) = 165

[tex]x^{2} +4x-165=0[/tex]

Now, we will factorize this equation by splitting the middle term:

[tex]x^{2}[/tex]+15x-11x-165 = 0

Now, taking x as a common factor from the first two terms and -11 as a common factor from the last two terms:

x(x+15)-11(x+15) = 0

Taking (x+15) as a common factor:

(x+15) (x-11) = 0

x+15 = 0 and x-11 = 0

x = -15 and x = 11

Now, we know that age can not be negative.

Hence, Roy's younger brother is 11 years old.  

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The number of small boxes sent is 6 and the number of large boxes sent is 3.

Given:

Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books.

Let x be the number of small boxes and y be the number of large boxes.

20x + 35y = 225

x = 2y

20(2y) + 35y = 225

40y + 35y = 225

75y = 225

divide by 75 on both sides

75y/75 = 225/75

y = 225/75

y = 3 large boxes.

x = 2y

= 2*3

x= 6 small boxes.

Therefore the number of small boxes sent is 6 and the number of large boxes sent is 3.

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The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.

A square is a four sided polygon with 4 equal angles and length.

The fourth corner = 90° - 36°

= 54°

Recall,

Alternate angles are equal

So,

(4x + 4)° = 36°

substract 4 from both sides

4x = 36 - 4

4x = 32

divide both sides by 4

x = 32/4

x = 8

(4y + 10)° = 54°

substract 10 from both sides

4y = 54 - 10

4y = 44

divide both sides by 4

y = 44/4

y = 11

In conclusion, the value of the following given equations are:

(4x + 4)° = 36°

4(8) + 4 = 36

32 + 4 = 36

36° = 36°

(4y + 10)° = 54°

4(11) + 10 = 54

44 + 10 = 54

54 ^= 54°

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The pressure applied on a cubic object with side 4inches with 50N force is 50N/m

Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area. The basic formula for pressure is F/A (Force per unit area). Unit of pressure is Pascals (Pa).

1 inch= 0.025m

4inches= 0.025×4= 0.1m

Pressure = Force/area

area= 0.1×0.1= 0.01m^2

therefore Pressure= 50/0.01

= 5000N/m^2

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Answer: a is the correct answer

Step-by-step explanation:

Answer:

The prices of apples this week is $1.40.

Step-by-step explanation:

First, convert the 20% into 0.20, then on a calculator, type this equation into it:

0.20 x 1.75 = 0.35

0.35 isn't the answer, but we use 0.35 to subtract it from 1.75:

1.75 - 0.35 = $1.40

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Answer:

f(x) = –2x + 3

Step-by-step explanation:

The sales of phones and accessories should be 6 and 12 each, correspondingly.

The data stated in question-

Let 'P' be the number of the phones sold.

Then, the accessory sold be '2P'.

The equation will form for the total cost will be;

11P  +  3(2P) = 102

11P  +  6P = 102

17P = 102

P = 102 / 17 =

P = 6  (number of sold phones)

Accessories sold = 2P = 2 x 6 = 12

Thus, the sales of phones and accessories should be 6 and 12 each, correspondingly.

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Answer:

the rd one

Step-by-step explanation:

its the -21/2

if u need help tell me

The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

In the question ,

seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.

we have to find statement which are true .

Option (a)

Thickness of the slide is dx for disk method and

dy for the shell method while rotating about x - axis ,

So , statement of option(a) is false .

Option(b)

In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,

thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,

So , statement of option (b) is false .

Option(c)

In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,

Thus , slices are cut perpendicular to the x axis .

statement of option (c) is True .

Option (d)

As in 2D , the  bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .

So , statement of option(d) is True .

Option(e)

When using shell method, we cut region into small slices perpendicular  to the x-axis .

So , statement of option(e) is False .

Option(f)

There can be both the kinds of cases , like in some cases disk method is easier than shell method and

in other cases shell method can be easier than disk method .

So , statement of option(f) is False .

Option(g)

When using disk method, we cut region into small slices perpendicular to x-axis .

So , statement of option (g) is False .

Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

The given question is incomplete , the complete question is

Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:

(a) The thickness of the slices will be dx for both methods.

(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.

(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.

(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using the shell method, we cut the region into small slices parallel to the x-axis.

(f) The shell method will always result in a less complicated integral.

(g) When using the disk method, we cut the region into small slices parallel to the z-axis.

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Answer:

450 bacteria

Step-by-step explanation:

90 percent of 100 is 90 90x5 is 450

No drew is incorrect and the right answer to this question is - 9/14 which can be calculated by using BODMAS rule.

What is BODMAS rule?

It stands for Bracket Of Division Multiplication Addition Subtraction which is a simple rule for solving calculation. It means first we solve brackets of a statement and so on.

Main Body:

Given :

⇒3/7÷ 2/3

This can be solved by changing the division to multiplication and taking reciprocal of the  term behind it.

⇒3/7×-3/2

⇒-9/14

Hence the correct answer to the statement is -9/14.

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The distance from the headquarters to a point on the ground directly below the balloon (to the nearest foot) is 1221 feet

The distance is calculated using tangent of the angle using the formula

tan x = opposite / adjacent

From the question it can be deduced that

x = 55°11'

opposite = the required distance

adjacent = 849 feet

solving for the opposite

tan x = opposite / adjacent

tan 55°11' = opposite / 849

opposite = 849 * tan 55°11'

opposite = 1220.793

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