In the isosceles trapezium , = 5,
= , and the length is 5cm less than
. If the perimeter is 38cm. Find the area.

Point slope form of the line is y−9=−1/4(x+2) y-9 = -1/4 (x+2)

What do you mean by point slope form of the line?

The equation is useful when we know :

One point on the line: (x1, y1)

the slope  sof the line: m,

and want to find other points on the line.

The "point-slope" form of the equation of a straight line is:

y - \(y_{1}\) = m(x - \(x_{1}\))

Given passing point, (\(x_{1},x_{2}\)) = (-2,9)

Slope of the line, m = -1/4

Point slope form of the line ⇒ y - \(y_{1}\) = m(x - \(x_{1}\))

⇒ y - 9 = -1/4 (x - (-2))

⇒ y - 9 = -1/4(x + 2)

⇒ y - 9 = -x/4 - 1/2

⇒ y = -x/4 - 1/2 + 9

⇒ y = -x/4 + (-1/2 + 9)

⇒ y = -x/4 + 17/2

⇒ y = \(\frac{-x+34}{4}\)

⇒ 4y = -x+34

⇒ 4y + x = 34

It can also be written as y - 9 = -1/4(x + 2)

Therefore, point slope form of the line is y - 9 = -x/4 - 1/2 = -1/4(x + 2)

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Step-by-step explanation:

calculate the tax on an item, we need to multiply the price by the tax rate as a decimal.

For the sneakers:

Tax on sneakers = 0.08 * $129.99 = $10.40

For the boots:

Tax on boots = 0.08 * $89.99 = $7.20

The difference between the tax on the sneakers and the tax on the boots is:

$10.40 - $7.20 = $3.20

Therefore, the correct answer is (A) The tax on the sneakers is $3.20 more than the tax on the boots

Answer: A. The tax on the sneakers is $3.20 more than the tax on the boots.

There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).

Synthetic division

The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

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a) -3x + 7y = 28 -4x + 3y = 12

7y - 28 = 3x

x = (7y - 28)/3

Substitution

-4(7y - 28)/3 + 3y = 12

-4(7y - 28)/3 = 12 - 3y

-4(7y - 28) = 3(12 - 3y)

-28y + 112 = 36 - 9y

112 - 36 = 28y - 9y

76 = 19y

y = 76/19

y = 4

x = [(7*4) - 28)]/3

x = [28 - 28]/3

x = 0/3

x = 0 Result x = 0, y = 4

b) x + 3y = -7 -7x - 4y = -19

x = -7 - 3y

Substitution

-7(-7 - 3y) - 4y = -19

49 + 21y - 4y = -19

17y = -19 - 49

17y = -68

y = -68/17

y = -4

x = -7 - 3(-4)

x = -7 + 12

x = 4 Result x = 4, y = -4

c) 3x + 2y = 4 6x - 3y = -27

x = (4 - 2y)/3

Substitution

6(4 - 2y)/3 - 3y = -27

6(4 - 2y)/3 = -27 + 3y

6(4 - 2y) = 3(-27 + 3y)

24 - 12y = -81 + 9y

-12y - 9y = -81 - 24

-21y = -105

y = -105/-21

y = 5

x = (4 - 2(5))/3

x = (4 - 10)/3

x = -6/3

x = -2 Result x = -2, y = 5

d) It is not complete

e) -x + 4y = -5 x - 6y = 7

x = 7 + 6y

-(7 + 6y) + 4y = -5

-7 - 6y + 4y = -5

-6y + 4y = -5 + 7

-2y = 2

y = 2/-2

y = -1

x = 7 + 6(-1)

x = 7 - 6

x = 1 Result x = 1, y = -1

Answer:

2V3 and V3

Step-by-step explanation:

a) 2V3-V3=V3 (irational)

b) 2V3*V3=2*3=6 (rational)

c) 2V3/V3=2 (rational)

the parabola is upward or downward depending on the position=

a) So this one is upward

and the vertex is the minimum value of y, (in upward parabola)

so the vertex here, we can see from the graph is: x=2 and y=2

b) (2,2)

the axis of symmetry is the x value of the vertex, so:

c) x=2

the parabola never crosses the x-axis, so

d) x-intercept= none

and the y-intercept is when the line cross over the y axis, so:

y-intercept= 6

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

A. R180 degree rotation

Step-by-step explanation:

if you think about a graph, it has four quadrants, so imagine each of the quadtrants, being an add on of 90 degrees from the one you started on, so if you started in the double negative quatrant in the bottom left, it would take two quadrants to go in a circle to get to the full positive quadrant, making this, a 180 degree rotation

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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The residual value for x = 1 is 0. To find the residual value for x = 1, we need to plug in x = 1 into the equation for the least squares regression line (lsrl) that we have been given. The equation for the lsrl is ŷ = 5.5x + 18.5.

So, when x = 1, we have:
ŷ = 5.5(1) + 18.5
ŷ = 24
This means that the predicted value of y for x = 1 is 24.
To find the residual value, we need to subtract the predicted value of y from the actual value of y for x = 1.
The actual value of y for x = 1 is 24 (according to the data given).
So, the residual value for x = 1 is:
residual = actual value of y - predicted value of y
residual = 24 - 24
residual = 0
Therefore, the residual value for x = 1 is 0.

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Answer:

45

Step-by-step explanation:

1

Using the factors of 18, it is found that he can hang the pictures in the wall in the following ways:

The factors of 18 are the numbers by which 18 is divisible by, which are: {1, 2, 3, 6, 9, 18}, since:

\(\frac{18}{1} = 18, \frac{18}{2} = 9, \frac{18}{3} = 6, \frac{18}{6} = 3, \frac{18}{9} = 2, \frac{18}{18}\)

Considering the factors, the ways to organize the pictures are:

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The proof for <2 is congruent to <3 is given below.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given are,

<1 and <2 form linear pair

m<1 + <3 = 180°

We have, <1 and <2 form linear pair.

We know that, sum of the measures of angles of linear pair is supplementary.

So, <1 + <2 = 180°

⇒ <2 = 180° -  <1

Also we have,

<1 + <3 = 180°

⇒ <3 = 180° - <1

So measures of both angles <2 and <3 are equal.

So they are congruent.

Hence the angles <2 is congruent to <3.

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The top 10% of professors spend above $125.94 each week on entertainment. To find the z-score for the top 10% of professors, we need to find the z-value that corresponds to the 90th percentile.

To find out the amount of money spent by the top 10% of professors on entertainment each week, we need to use the z-score formula and the standard normal distribution table.

The z-score formula is:

z = (x - μ) / σ

where:

x = the amount spent on entertainment

μ = the mean amount spent on entertainment

σ = the standard deviation

To find the z-score for the top 10% of professors, we need to find the z-value that corresponds to the 90th percentile. The 90th percentile can be calculated as follows:

90th percentile = mean + z-score * standard deviation

From the standard normal distribution table, we can find that the z-score corresponding to the 90th percentile is 1.28.

So,

90th percentile = 95.25 + 1.28 * 27.32 = 125.94

Therefore, the top 10% of professors spend above $125.94 each week on entertainment.

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Answer:

A. (4,2)

Step-by-step explanation:

In coordinates, the x-value appears first then the y-value. This means coordinates are set up like, (x,y). So, to solve find the coordinates whose values match one pair of values on the table. Option A has x=4 and y=2. In the last row of the table, you can see the same values with x=4 and y=2. Therefore, A is correct.

Answer:

25+3(a−5)+7a.

25+3a-15+7a

7a+3a+25-15

10a+10

10(a+1)

Note that where you see the word "Pie" you should replace it with its symbol

First find the area of the circle

Area of circle = Pie × Radius²

Area of circle = Pie × 5²

Area of circle = Pie × 25

Area of circle = 78.54ft²

Now multiply the area by the height to find the volume

78.54 × 11 = 863.94ft³

We can approximate this answer to 864ft³

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

There are 56 different sequences of coin toss results that Kathy could have gotten, given that she got 3 heads and 5 tails in 8 tosses.

To find the total number of different sequences of coin toss results that Kathy could have gotten, we can use the formula for permutations:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, the total number of coin tosses) and r is the number of objects selected (in this case, the number of heads or tails that Kathy got).

Since Kathy got 3 heads and 5 tails, there are 8 choose 3 (or 8 choose 5) ways to arrange the sequence of heads and tails. This is equivalent to the number of ways to select 3 objects out of 8, or 5 objects out of 8:

8C3 = 8! / (3! x (8 - 3)!) = 56

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The number of child tickets sold that day was 81.

To solve the problem, let's use algebra. Let x be the number of child tickets sold and 3x be the number of adult tickets sold. The total sales can then be expressed as:

6.40x + 9.60(3x) = 950.40

Simplifying this equation:

6.40x + 28.80x = 950.40

35.20x = 950.40

x = 27

This means that 27 child tickets were sold. However, the problem asks for the number of child tickets sold on Friday, when three times as many adult tickets were sold.

So the number of child tickets sold on Friday is:

3x = 3(27) = 81

Therefore, 81 adult tickets and 27 child tickets were sold on Friday, and the revenue was $950.40.

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The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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IM NOT QUIT SO SURE BUT IF MY CALCULATIONS ARE CORRECT ITS C

Answer:

i got u, its A

Step-by-step explanation:

Answer:

c = 13

Step-by-step explanation:

1. Pythagorean theorem states that c^2 = a^2 + b^2

2. In this case, a = 5, b = 12. Therefore, the equation is:

c^2 = 5^2 + 12^2

3. c^2 = 25+144 = 169

4. square root both sides

5. c = 13, c = -13

6. c = 13 since a length cannot be negative.

7. Final answer: C = 13

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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The result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

To subtract the expression 7x - 9 from 2x² - 11, we need to distribute the negative sign to every term within the expression 7x - 9, and then combine like terms.

First, let's distribute the negative sign:

2x² - 11 - (7x - 9)

Now, distribute the negative sign to each term within the parentheses:

2x² - 11 - 7x + 9

Next, let's combine like terms:

2x² - 7x - 2

Therefore, the result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

In this expression, the highest power of x is 2, which means it is a quadratic expression. The coefficient of x² is 2, and the coefficient of x is -7. The constant term is -2.

This quadratic expression can be further simplified or factored if needed, but the subtraction process is complete with the result 2x² - 7x - 2.

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Answer:

33

Step-by-step explanation:

23+23+28+28+33=135

$135/5tickets=$27avg

The cost of the fifth ticket is $33.

Stacy bought two tickets at $23 each, so the total cost for the first two tickets is 2×23.

She bought two tickets at $28 each, so the total cost for the second two tickets is 2×28.

Adding these costs together, we have:

2×23+2×28+x=46+56+x=102+x.

The average price Stacy paid for the five tickets was given as $27. We can set up an equation using the average:

46+56+x/5 = 27

Now, we can solve for x:

102+x=5×27,

x=135−102

x=33.

So, the cost of the fifth ticket is $33.

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