consider the difference 11; 5; -1; -7;....​

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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Answer:

100

Step-by-step explanation:

10 times 10=100

Answer: 100

Step-by-step explanation: The 2 in this problem means that we are going to multiply 10 twice in order to find the answer.

When we multiply a number by itself, it's called squaring.

So any number squared is that number times itself.

So 10² is just 10 · 10 or 100.

9514 1404 393

Answer:

  (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Step-by-step explanation:

The area of the hexagon is given by the formula ...

  A = (3/2)√3·s^2 . . . . for side length s

The area of the hexagonal face of this solid is ...

  A = (3/2)√3·(2 ft)^2 = 6√3 ft^2

__

The area of the circular hole in the hexagonal face is ...

  A = πr^2

The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.

  A = π(1 ft)^2 = π ft^2

Then the area of the "solid" part of the face of the figure is ...

  A = (6√3 -π) ft^2

__

The volume is ...

  V = Bh . . . . . where B is the area of the base of the prism, and h is its height

  V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Answer:

h = 6\(\sqrt{3}\)

Step-by-step explanation:

The given is the special right triangle with angle measures : 90-60-30

and the side lengths for the given angles are represented by :

2a-a\(\sqrt{3}\)-a

the side length that sees 60 degrees is represented by a\(\sqrt{3}\) (h in this case)

the area of a triangle is calculated by multiplying height and base and that is divided by 2

a\(\sqrt{3}\)*a/2 = 18\(\sqrt{3}\) multiply both sides by 2

a^2\(\sqrt{3}\) = 36\(\sqrt{3}\) divide both sides by \(\sqrt{3}\)

a^2 = 36 find the roots for both sides

a = 6

since h sees angle measure 60 and is represented by a\(\sqrt{3}\)

h = 6\(\sqrt{3}\)

Answer:

3.27*10^22

Step-by-step explanation:

Given the expression 9.6x10^85/3x10^63, we are to write it on scientific notation as shown:

9.6x10^85/3x10^63

= (9.8/3) * (10^85/10^63)

= (9.8/3)  * 10^{85-63}

= (9.8/3) *10^22

= 3.27 *10^22

Hence the expression in scientific notation is  3.27*10^22

Answer:

\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)

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

And replacing we got:

\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)

And for this case we can use the first point to find the intercept like this:

\( 6 = -\frac{2}{5}(3) +b\)

And solving we got:

\( b = 6 +\frac{6}{5}= \frac{36}{5}\)

And then the line equation would be given by:

\( y = -\frac{2}{5}x +\frac{36}{5}\)

Step-by-step explanation:

For this case we have the following two points given:

\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)

And for this case we want an equation for a line with the two points given by:

\( y = mx+b\)

Wher m is the slope and b the y intercept. We can find the slope with this formula:

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

And replacing we got:

\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)

And for this case we can use the first point to find the intercept like this:

\( 6 = -\frac{2}{5}(3) +b\)

And solving we got:

\( b = 6 +\frac{6}{5}= \frac{36}{5}\)

And then the line equation would be given by:

\( y = -\frac{2}{5}x +\frac{36}{5}\)

Answer:

Yes that is true. People just like to judge on what we look like on the outside. I Don't Know why tho.

Answer:

7 × 8

Step-by-step explanation:

7 number of students × 8 books each student has 7 × 8 = 56

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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Answer:

a:h=square root of 0.6

Step-by-step explanation:

thank you for your time today

Answer:

none of the above

Step-by-step explanation:

KHAN

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

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Answer:

$3.05

Step-by-step explanation:

Each box is $0.05

The shades boxes represent the value of coin in each pocket :

Number of shaded boxes on the left = 24

Value of coins in left pocket = 24 * $0.05 = $1.2

Number of shaded boxes on the right = 37

Value of coins in right pocket = 37 * $0.05 = $1.85

Tital value if coins :

$1.85 + $1.2

= $3.05

Answer:

Step-by-step explanation:

Given the data:

Year___Actual sale (At) ___forecast(Ft)

2005__450_____________410

2006__495____________ 422

2007__518____________ 443.9

2008_ 563____________ 466.1

2009_584____________ 495.2

2010__

Using the formula :

Ft = Ft-1 + alpha(At-1 - Ft-1)

Ft-1 = previous year forecast

At-1 = previous year actual

Alpha = 0.3

Forecast:

2006:

410 + 0.3(450 - 410) = 422.0

2007:

422 + 0.3(495 - 422) = 443.9

2008:

443.9 + 0.3(518 - 443.9) = 466.1

2009:

466.1 + 0.3(563 - 466.1) = 495.2

2010:

495.2 + 0.3(584 - 495.2) = 521.8

Forecasted value for 2010 = 521.8

Answer:

Cannot be determined.

Step-by-step explanation:

The equation 5x + (-2y) = 8 is not directly giving us information about the discount. However, we can use some algebraic manipulation to solve for y and then use that information to determine the discount.

Starting with the equation 5x + (-2y) = 8, we can add 2y to both sides to get:

5x = 2y + 8

Then, we can divide both sides by 2 to isolate y:

y = (5/2)x - 4

Now we can see that y is a linear function of x with a slope of 5/2 and a y-intercept of -4. This means that for every additional frame purchased, the amount spent increases by 5/2 units.

To determine the discount, we need to know the original price of the frames and the amount saved when the discount is applied. Without that information, [we cannot determine the value of the discount from this equation alone.]

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is  y = -7/5(x) -53/5

Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)

The slope-intercept form of a straight line is:

y = mx + c

where m is the slope and c is the y-intercept

For perpendicular case:

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₁ x m₂ = -1

-7/5 x m₂ = -1

m₂= 5/7

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = 5/7 (-4) + c

-5 = -20/7 + c

c = -15/7

Thus, the equation of the line is y = 5/7(x) -15/7

For parallel case:

When the two lines are parallel, they have equal slope i.e. m₁ = m₂

Line1(given):

7x+5y = 4  => y = (-7/5)x + 4/5

Thus,  m₁ = -7/5

m₂= -7/5

Line 2(unknown) with the point (−4,-5):

y = mx + c

-5 = -7/5(-4) + c

-5 = 28/5 + c

c = -53/5

Thus, equation of the line is y = -7/5(x) -53/5

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

two solutions work: x = 5 + \(\sqrt{19}\) and x = 5 - \(\sqrt{19}\)

Step-by-step explanation:

x + 6 ( 1/x ) = 10

x^2 + 6 = 10x

x^2 - 10x + 6 = 0

x = 5 + \(\sqrt{19}\), 5 - \(\sqrt{19}\)

The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

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Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

The missing numbers are a = 25 and b = 92.

Let's start by finding the mean of the given numbers. The mean is calculated by summing all the numbers and dividing the sum by the total count. In this case, we have:

(a + 31 + 42 + 65 + b) / 5 = 51

Now, we can simplify the equation:

a + 31 + 42 + 65 + b = 51 x 5

a + 138 + b = 255

Next, we know that the greatest number is 67 more than the least number:

b = a + 67

Now we can substitute this value into the previous equation:

a + 138 + (a + 67) = 255

Combining like terms:

2a + 205 = 255

Subtracting 205 from both sides:

2a = 50

Dividing both sides by 2:

a = 25

Substituting this value back into the equation b = a + 67:

b = 25 + 67

b = 92

Therefore, the missing numbers are a = 25 and b = 92.

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Reorder from least to greatest.

4, 4, 6, 6, 6, 8, 10, 15, 15

                /\

                 |

Median is the middle number.

This would be 6.

---

hope it helps

Answer:

7.07 in^2 is what i got

Given the information, we know that the groth is linear, and also we have two points: (2,4) and (5,5.5). Then we can find the equation in the following way:

If h are the inches and n the weeks, then the equation is:

Now, if we want to know how tall will be the plant in 10 weeks, we just make n=10 and find the value of h:

therefore, after 10 weeks, the plant will be 8 inches.

Finally, to find out how many weeks will it take the plant to grow 20 inches, we make h=20 and solve for n:

therefore, the plant will be 20 inches tall in 34 weeks

Answer:

H0 : The variables are independent

H1 : The variables are not independent

Step-by-step explanation:

In a Chisquare test ; The null hypothesis is used to lay claim that the variables are independent, that is no relationship exists between the categorical variables in the population while the alternative hypothesis negates the null thus claiming that the variables aren't independent.

The null hypothesis, H0 : The variables are independent, A = B = C

The alternative hypothesis ; H1 : The variables are not independent, A ≠ B ≠ C

Answer:Gn

Step-by-step explanation: bbbbhh

Answer:

B

Step-by-step explanation:

B . x+3 and -2x2 - 4x +47-6

B . x+3 and -2x2 - 4x +47-6

The divisor and the dividend for the given synthetic division problem are : \(x+3\) and \(2x^3+4x^2-4x+6\)

"It is a way of dividing one polynomial by another polynomial of first degree."

"The value that is divided by another value to get the result. "

"The value that divides another number either completely or with a remainder."

For given question,

We have been given a synthetic division problem.

- 3/ 2 4 -4 6

We need to represent the divisor and the dividend for the given synthetic division problem.

We know that, to perform synthetic division, here are the steps:

- The leading coefficient of the divisor should also be 1.

- Express the dividend in standard form.

- Write the leading coefficient in the dividend.

- Place the product of the number you brought down and the number in the division box in the preceding column.

- Write the result at the bottom of the row.

So, the divisor of the given synthetic division form would be,

x - (-3) = x + 3

And the dividend of the given synthetic division form would be,

There are four leading coefficient.

This means the dividend polynomial must be of degree 3.

From the leading coefficients 2 4 -4 6

\(2x^3+4x^2-4x+6\)

Therefore, the divisor and the dividend for the given synthetic division problem are : \(x+3\) and \(2x^3+4x^2-4x+6\)

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Answer:

approx 26%

Step-by-step explanation:

you try find the multiplier

200000 * 1. ???? ^3= 400000

rearrange equation

\(\sqrt[3]{\frac{400000}{200000} }\)       =   multiplier

1.25992105

subract one

0.25992105

multiply by 100 to get percentage

25.9%

rounded to whole number = 26%

The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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