What will be the area of triangle if its length and breadth is 14cm and 7cm?

Answer: 10

Step-by-step explanation:

If [tex]-5 < x < 5[/tex], then [tex]|x-5|=5-x[/tex] and [tex]|x+5|=x+5[/tex].

So, the expression is equal to 10.

In quadrant IV, [tex]\sin(A)[/tex] is negative. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]

Answer:

C

Step-by-step explanation:

using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

note that [tex]\frac{7\pi }{12}[/tex] = [tex]\frac{\pi }{3}[/tex] + [tex]\frac{\pi }{4}[/tex] , then

sin [tex]\frac{7\pi }{12}[/tex]

= sin([tex]\frac{\pi }{3}[/tex] + [tex]\frac{\pi }{4}[/tex] )

= sin[tex]\frac{\pi }{3}[/tex]cos[tex]\frac{\pi }{4}[/tex] + cos[tex]\frac{\pi }{3}[/tex]sin[tex]\frac{\pi }{4}[/tex]

= ( [tex]\frac{\sqrt{3} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] ) + ([tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{2}+\sqrt{6} }{4}[/tex]

The median number of computers owned by the 17 students is 2.

A dataset's median represents the midpoint; half of the data points are smaller and half are greater than the median.

Identifying the median: The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd.

The total number of students are 17.

The data can be arranged in the following table

number of students        number of computers

             6                                         1

             3                                         2

             3                                         3

             2                                         4

             3                                         5

Arrange the given frequencies in the increasing order-

1 1 1 1 1 1 2 2 2 3 3 3 4 4 5 5 5

The middle term of the arrange frequencies is 17/2 = 8.5

Median = (8 term + 9 term)/2

            = (2 + 2)/2

            = 2

Therefore, the median number of computers owned by the 17 students is 2.

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The correct question is -

Of the 17 students in a programming class, 6 own 1 computer, 3 own 2 computers, 3 own 3 computers, 2 own 4

computers, and 3 own 5 computers. What is the median number of computers owned by the 17 students?

Mark and Don have 18  and 92 marbles respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

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Answer: The answer is D

Step-by-step explanation:

Let the missing number x

So, ATQ

[tex] \frac{3}{14} \times x = 6[/tex]

[tex] \frac{14}{3} \times \frac{3}{14} x = 6 \times \frac{14}{3} [/tex]

[tex] \frac{1}{3} \times 3x = \frac{14}{3} \times 6[/tex]

[tex]x = \frac{14}{3} \times 6[/tex]

[tex]x = 14 \times 2[/tex]

[tex]x = 28[/tex]

Therefore, 3/14 of 28 is 6...

Answer:

28

Step-by-step explanation:

Let the number we are looking for = [tex]x[/tex]

∴ [tex]\frac{3}{14}[/tex] of [tex]x[/tex] is 6

⇒  [tex]\frac{3}{14}[/tex]   ×  [tex]x = 6[/tex]

• Divide both sides of equation by  [tex]\frac{3}{14}[/tex] :

⇒  [tex]x = 6 \div \frac{3}{14}[/tex]

⇒ [tex]x = 28[/tex]

∴ The missing part is 28.

Answer: a

Step-by-step explanation:

The slope is the rate at which a line goes up or down (i.e., how steep it is). It is measured by the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where (x1, y1) and (x2, y2) are two points on the line.

Below, (x1, y1) are (c, d) and (x2, y2) are (a, b).

When all variables are plugged in, the slope is

[tex]\frac{b-d}{a-c}[/tex]

Answer:

Federal tax

Step-by-step explanation:

It is used for tax returns, given out by federal govt

Answer:

C. federal Tax.

Step-by-step explanation:

/     \

/      \

One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.

In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

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Answer:

yes

no

yes

Step-by-step explanation:

sin C = opp/hyp = 9/15 yes

tan B = opp/adj = 12/9 no

tan B = 12/9; B = tan^-1 12/9 = 53.13°

The probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

The true proportion, p for the population is given to 0.12.

Thus, the mean, μ, for the sample = np = 27*0.12 = 3.24.

The sample size, n, given to us is 27.

Thus, the standard deviation, s, for the sample can be calculated using the formula, s = √{p(1 - p)}/n.

s = √{0.12(1 - 0.12)}/27 = √0.003911 = 0.0625389.

We are asked to calculate the probability that the number of tested rafts that develop cracks is no more than 3, that is, we need to calculate P(X ≤3).

P(X ≤ 3)

= P(Z ≤ {(3 - 3.24)/0.0625389) {Using the formula z = (x - μ)/s}

= P(Z ≤ -3.8376114706)

= .00006 {From table}.

Thus, the probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

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The solutions to the given system of equations are x = 6 and y = -5

From the question, we are to solve the given system of equations

The given system of equation is

4x+5y=-1

-5x-8y=10

Multiply the first equation by 5 and the second equation by 4

5× (4x+5y=-1)

4× (-5x-8y=10)

20x + 25y = -5

-20x - 32y = 40

------------------------

0x + (-7y) = 35

-7y = 35

y = 35/-7

y = -5

Substitute the value of y into the first equation to find x

4x + 5y = -1

4x + 5(-5) = -1

4x -25 = -1

4x = -1 +25

4x = 24

x = 24/4

x = 6

Hence, the solutions to the given system of equations are x = 6 and y = -5

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Step-by-step explanation:

pythogoras theorem = Q²=P²+R²

P=P

Q= 57.6

R=33.8 =

(57.8)²=(P)²+(33.8)²

=3,340.84=(P)²+1142.44

=3340.84-1142.44=P²

=2,198.4=P²

[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]

A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution

x1 = x2 = .... = xk =0. Then the set  {v1,v2,...,vk} is linearly dependent otherwise.

So putting in the formula we get

x1u1 + x2u2 + x3u3 = 0

x1u1 + x2u2 = -x3u3

au1 + bu2 = u3               ∵ (-x1/x3 = a & -x2/x3 = b)

On putting in the values

a(3,-1) + b(4,5) = (-4,7)

(3a+4b,-a+5b) = (-4,7)

On comparing we get

3a + 4b = -4 -(1)

-a + 5b = 7  -(2)

on solving these equations we get

b = 17/19 and a= -48/19

which is non trivial.

Thus the following form linearly dependent sets of vectors.

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Answer:

The measure of the acute angle = 90 - a

Leg 1 = a cos(a)

Leg 2 = a sin(a)

Step-by-step explanation:

In a right triangle ,the two acute angles are complementary

We are given that the measure of one of the acute angles is ‘a’

Then

The measure of the other one is ‘90 - a’

Now, we use the law of sine to determine the length of the legs :

Let x and y be respectively the length of the two legs.

[tex]\frac{x}{\sin \left( 90-a\right) } =\frac{a}{\sin \left( 90\right) }[/tex]

[tex]\Longleftrightarrow \frac{x}{\sin \left( 90-a\right) } =a[/tex]

[tex]\Longleftrightarrow x = a \times\sin \left( 90-a\right)[/tex]

[tex]\Longleftrightarrow x = a \times\cos \left( a\right)[/tex]

On the other hand,

[tex]\frac{y}{\sin \left( a\right) } =\frac{a}{\sin \left( 90\right) }=a[/tex]

Then

[tex]y = a \times \sin(a)[/tex]

Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

Answer:

218,048. skeins

Step-by-step explanation:

This question is built to throw you off by not telling you about the information in order.

First, the polypay sheep produces 9.9 pounds of wool.

Then, each pound produces 10.95 miles of yarn.

And finally, the yarn is packaged into skeins that are 175 yards each.

Each polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.

BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).

So, our equation will look like this:

(#of sheep) [tex]\times[/tex] (9.9 pounds per sheep) [tex]\times[/tex] (10.95 miles per yarn) [tex]\times[/tex] (1760 yards per mile) [tex]\div[/tex] (175 skeins per yard)

The number of sheep Bill has is 200.

So, we plug that into the number model we made.

[tex]200\times9.9\times10.95\times1760\div175[/tex]

We end up with:

218,048.914

The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.

Since, that remainder is not a complete skein, we must ignore its existence.

So the number of skeins expected is:

218,048

The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a polypay sheep produces an average 9.9 pounds of wool annually.

Farmer Bill has a flock of 200 polypay sheeps

So, total weight of wool is 9.9×200

= 1980 pounds

One pound of wool makes 10.95 miles of yarn.

So, the number of yarns = 1980/10.95

= 180.82 miles of yarn

We know that, 1 mile =1760 yards

Then, 180.82 miles

= 318243.2 yards

This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.

Number of skeins = 318243.2/175

= 1819

Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.

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Due to length restrictions, we cannot summarize the results of the three parts about the quadratic equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.

In this question we have several exercises with quadratic equations of the form x² + b · x + c = 0 and, to be more exactly, quadratic equations with the following characteristics:

x² - (r₁ + r₂) · x + r₁ · r₂ = 0      (1)

Please notice that the first grade coefficient is equal to the inverse of the sum of the two roots and the zero grade coefficient is the product of the two coefficients.

Now we proceed to resolve all the points:

Part I

a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1

b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4

c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1

d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2

Part II

a) x² - 12 · x + 27

b) (x + 4) · (x + 8)

c) (x - 5) · (x - 7)

d) (x - 4) · (x - 5)

Part III

a) (x - 18) · (x + 3) = x² - 15 · x - 54

b) (x + 18) · (x + 3) = x² + 21 · x + 54

c) (x + 18) · (x - 3) = x² + 15 · x - 54

d) (x - 18) · (x - 3) = x² - 21 · x + 54

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Answer:

x = 753.6 ft

Step-by-step explanation:

One leg is x.

The other leg is given.

The trig function that relates the two legs of a right triangle is the tangent.

tan A = opp/adj

tan 37° = x/1000ft

x = 1000 ft × tan 37°

x = 753.6 ft

Answer: 753.6 feet

Step-by-step explanation:

The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.

Hence,

tan 37 = x/1,000

x = tan 37 * 1000

x is approximately 753.6, rounded to the nearest tenth.

Nani could purchase her pineapple from stores A, D, and E.

Given Information

It is given that Nani needs to purchase  8 cups of pineapple.

The unit prices of pineapple at each store is as follows,

Store A : 0.49

Store B : 0.51

Store C : 0.55

Store D : 0.48

Store E : 0.45

Amount that Nani has = $4

Reason Behind Purchasing From Either A, D, or E

Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,

Store A : 0.49(8) = $3.92

Store B : 0.51(8) = $4.08

Store C : 0.55(8) = $4.40

Store D : 0.48(8) = $3.84

Store E : 0.45(8) = $3.60

As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.

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Answer:

Let the number be a.

==: a + (5x³-2x²+3x+7) = (7x³+7x-5)

==: a = (7x³+7x-5) - (5x³-2x²+3x+7)

==: a = 7x³ + 7x - 5 - 5x³+ 2x² - 3x - 7

==: a = 2x³ + 2x² + 4x - 12

i guess this is the process if you don't understand i can explain more

Answer:

4, 4√3

Step-by-step explanation:

In a 30-60-90 triangle:

The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4

The longer leg is √3 times the shorter leg: 4*√3 = 4√3

Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64

Answer:

[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometry ratios:

       [tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]

                   [tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]

The total amount of money Levi spent on renting movie and buying candy is $5.75

Total = Amount Levi rented movie + A package of candy

= $3.20 + $2.55

= $5.75

Therefore, the total money spent by Levi is $5.75

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Answer:160ft^3

Step-by-step explanation:

Volume=(bh/2)h

V=(5ftx8ft/2)8ft

V=20x8=160

Volume=160ft^3

HOPE YOU GET IT RIGHT:)!

The area of the circle is 78.5 unit square.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

The formula for area of circle is;

Area = [tex]\pi[/tex](radius)²

The distance between the two points are calculated by distance formula.

[tex]\begin{aligned}&d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \\&d=\text { distance } \\&\left(x_{1}, y_{1}\right)=\text { coordinates of the first point } \\&\left(x_{2}, y_{2}\right)=\text { coordinates of the second point }\end{aligned}[/tex]

Calculation for the area of the circle;

As, the radius of the circle is xy.

The distance between x and y points will be calculated by the distance formula.

x=(0,3)  y=(-3,-1)

[tex]\begin{aligned}&d=\sqrt{\left(-3-0\right)^{2}+\left(-1-3\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{\left(-3\right)^{2}+\left(-4\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{25} \\\end{aligned}[/tex]

[tex]d=5[/tex]

As, distance between x and y point is 5 units which is the radius of the circle.

Area of circle = [tex]\pi[/tex](radius)²

                      = 3.14×(5)²

                      = 78.5

Therefore, the area of the circle is 78.5 unit square.

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