Find the area of the triangle below.
Be sure to include the correct unit in your answer.
10yd
4yd
7yd

The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.

In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.

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The complete question is:

A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: 8/3is equivalent fraction to three

Answer:

9/24

Step-by-step explanation:

The total amount that will be paid for the products with a sales tax of 7.5% will be $1290.

Your information isn't complete as the table denoting the appropriate values aren't given.

Let's assume that the price of a product A is given as $800 ane product B is $400. If the sales tax is 7.5%, the total amount that will be paid will be:

= ($800 + $400) + (7.5% × $1200)

= $1200 + $90

= $1290

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Answer:

B) y - 2 = (-1/4)(x - 2)

Step-by-step explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.

Answer:

7 + 2 + 4 = 13 km
13 km x 0.62 = 8.06
The answer is about 8.06 miles

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

c

Step-by-step explanation:

Solution:

Consider the number a. The multiplicative inverse of a is 1/a. Then, if a=-1.1, its multiplicative inverse would be:

so that, we can conclude that the correct answer is:

Answer: C ( square root of 1.5 x 3.6)

Step-by-step explanation:

The price for the variance is 3.6 times 1.5. Standard deviation is the square root of variance, so the answer is the square root of 1.5 x 3.6.

The standard deviation expression of the distribution P is √(1.50 × 3.6)

Given the Parameters :

The price for the variance of the distribution can be written as :

The standard deviation of the distribution D is related to the variance by the formular :

Therefore, the standard deviation in $ of P will be √(1.50 × 3.6)

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Step-by-step explanation:

138 I guess I think. this is the answer.

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer:

Answer:

5:6 --> 10:12

Step-by-step explanation:

A good way to think of this is to provide a perspective: there are 5 boys every time there is 6 girls. So if there is 10 boys, that means there would be 12 girls (because 5 *2 = 10 and 6*2 = 12).

tl:dr: 5 *2 = 10 so 6*2 = 12

Let's suppose you have a population of 1000 people.

If the incidence rate of the disease is 0.9%, it means that 1000(0.009) = 9 people will have the disease

It means that 991 people will not have the disease.

Of the 9 people who have the disease, 4% of them will test negative, then 9(0.04) = 0.36 people will test negative, so the remaining 8.64 people will test positive.

Of the 991 people who don't have the disease, 991(0.02) = 19.82 people will test postive.

Then, the probability will be:

The probability is 0.30358 or 30.358%

The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.

Let d represent the amount of cash in dollars and p represent the amount of prizes.

Since the  grand prize winner is guaranteed to win at least $500,

So, p + d ≥ 500

Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

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We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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Answer:

on what

Step-by-step explanation:

??????

Answer:

What do you need help with?

Step-by-step explanation:

Upload a picture

Explanation

Answer: -126

Answer:

angle B = 71 degrees

Step-by-step explanation:

If angle A and angle B are complementary, and angle A = 19°, what is the measure of angle B?

complementary angles summed together equal 90 degrees so:

angle B = 90 - 19

angle B = 71 degrees

Answer:

P ( x < 5050.5 ) ≈ 0.16104

Step-by-step explanation:

Total number of voters ( n ) = 10000

Before election : 5050 people preferred Candidate D ( k ) ≈ 50.1 %

Candidate D eventually wins with 51% of the votes

winning ( p ) = 0.51

Applying continuity correction formula

P ( x < 5050.5 ) ≈ 0.16104

attached below is the remaining part of the solution

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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Answer:

A. 55°

Step-by-step explanation:

Complementary angles are angles that add up to give us 90°.

Since <A and <B are complementary angles, it implies that:

m<A + m<B = 90°

If m<A = 35°, therefore:

35° + m<B = 90°

Subtract 35° from each side

m<B = 90° - 35°

m<B = 55°

The translated vertices of the rhombus are: K(-1,-3), L(3,-1), M(1,-5) and N(-3,-7)

The rhombus is a parallelogram which has all sides equal. the diagonals of a rhombus bisect at right angles. the difference between a rhombus and a square is that none of the angles of a rhombus are 90°.

To translate a figure with given co-ordinates into another figure with a particular translation we simply add or subtract the given values from the coordinates of the available points.

Given co-ordinates of Rhombus are K(-3, 2),L(1, 4),M(-1 ,0)and N(-5, -2).

The translation is given as (x,y) → (x+2, y-5)

So we calculate the coordinates as:

The translated co-ordinate  K(-3, 2)→ K'(-1,-3)

The translated co-ordinate  L(1, 4)→  L'(3,-1)

The translated co-ordinate  M(-1 ,0)→ M'(1,-5)

The translated co-ordinate N(-5, -2)→ N'(-3,-7)

Hence the co-ordinates of rhombus translated by  (x,y) → (x+2, y-5) are  K(-1,-3), L(3,-1), M(1,-5) and N(-3,-7).

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Given:

The sides of the triangular shape are 10 feet, 7 feet, and 9 feet.

Aim:

We need to find the area of the triangle.

Explanation:

let a = 10 feet, b =7 feet and c =9 feet.

Consider the formula to find the area of the triangle.

where s is the semi perimeter of the triangle.

The formula to find the semi perimeter.

Substitute a =10 feet, b =7 feet, and c = 9 feet.

Substitute s =13, a =10 feet, b =7 feet, and c = 9 feet.

Final answer:

Answer:

Step-by-step explanation:

That will be a square with a diagonal of 20

side length of 20sin45

and area of (20sin45)² = 200 units²

prove it you say?

Area of a rectangle is base times height

A = bh

With a radius of 10, the diagonals of any rectangle inscribed will be 20 units

20² = b² + h²

h = \(\sqrt{400 - b^2}\)

A = bh

A = b\(\sqrt{400 - b^2}\)

Area will be maximized when the derivative is set to zero

           dA/db = \(\sqrt{400 - b^2}\) - b²/ \(\sqrt{400 - b^2}\)

                   0 = \(\sqrt{400 - b^2}\) - b²/ \(\sqrt{400 - b^2}\)

b²/\(\sqrt{400 - b^2}\) =  \(\sqrt{400 - b^2}\)

                  b² = 400 - b²

                2b² = 400

                  b² = 200

                  b = \(\sqrt{200}\)

h = \(\sqrt{400 - b^2}\)

h = \(\sqrt{400 - \sqrt{200}^2 }\)

h = \(\sqrt{200}\)

A = bh

A =  \(\sqrt{200}\)•\(\sqrt{200}\)

A = 200 units²