Triangle XYZ with vertices X(-8, 3), Y(-6, 5), and Z(-5, -2): x = -4​

Hello, in this question we will use the "Sinus Theorem".

The general formula of the Sine Theorem is as follows;

We are given the length of the two sides and the sine value of the angle of the unknown side. We also know the area of the triangle. Let's substitute the required values in this formula to get the result.

In the last step, we are left with a quadratic equation with one unknown. To solve this equation, we need to calculate the discriminant value.

There are only two roots of a quadratic equation with one unknown.

Thus our x values;

We cannot accept the first root [tex]x_1[/tex]. Because length cannot be a negative value.

Ans = [tex]x_{2}=\frac{-1+\sqrt{177} }{4}=3.076[/tex]

The corresponding element in the range when 6 is an element in the domain is f(6) = -4.

Given function f(x) = 8–2x.

6 is an element in the domain of this function.

To find the corresponding element in the range of the function,

Substitute x = 6 in the given function f(x).

So,

f(6) = 8 - 2(6)

f(6) = 8 -12

f(6) = -4

Hence, the corresponding element in the range when 6 is an element in the domain is -4.

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In every triangle the addition of all internal angles is always 180 degrees.

So this means we can build this equation

5x + 35 + 60 = 180

now separate x values and numerical values

5x = 180 - 60 - 35

x= (180 - 60 - 35)/ 5 = 85/5 = 17

Probability that the man wins money from at least one of the sources, a lottery and a card game, is equal to  17/50.

Probability that he wins from first source = 1/100

Probability that he doesn’t wins from first source = 99/100

Probability that he wins from second source = 1/3

Probability that he doesn’t wins from second source  = 2/3

Probability that the man wins money from at least one of the sources = 1-(probability that the man wins no money from any of the sources)

[tex]=1-[(\frac{99}{100} )(\frac{2}{3} )] =1-(\frac{33}{50} )=\frac{17}{50}[/tex]

So, the required probability of winning the money by the man from at least one of the sources is 17/50.

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Answer:

C = 62.8

Step-by-step explanation:

C = 2πr

π = 3.14

diameter = 20 ft

r = 10 ft

Get r or the radius by taking half of the diameter which is 20 ft and get 10 ft.

Plug this information in the formula and multiply to get C or the circumference.

C = 2(3.14)(10)

C = 62.8

Let

number of children admitted = x

number of adult admitted = y

Total number admitted = 335

number of children = 160

number of adult = 175

The price per share after 5 hours is $28.32

The price per share after 23 hours is $-2.1

Given,

A​ company's stock began the day at ​$ 36.77per share.

and, price drops be $1.69 each hour.

To find the what is the price per share after 5hours

and, also find what will be after 23 hours rate continues?

Now, According to the question:

The price of the company's stock is initially at $36.77 per share. Each hour the price drops by $1.69. This condition can be modeled by the function:

P(t) = 36.77 - 1.69t

Where t is the time in hours.

The sign means the function is decreasing as time passes.

When t=5 hours, the price will be:

P(5) = 36.77 - 1.69 × 5 = 28.32

The price per share after 5 hours is $28.32

Now find the price when t=23 hours

P(23) = 36.77 - 1.69 × 23 = - 2.1

The price per share after 23 hours is $-2.1

Hence, The price per share after 5 hours is $28.32

The price per share after 23 hours is $-2.1

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Answer:

(2, 3)

Step-by-step explanation:

the work is all in the pic go check it out I am so sorry if it's incorrect also have a nice day:)

The dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.

For the given question,

The perimeter of the triangle is 50 units.

The three sides of the triangle is given as;

The formula for finding the perimeter is;

Perimeter =  sum of all sides.

Let 'P' be the perimeter of the triangle. Then,

P = x-1 + 2x-3 + 3x - 6

Simplifying.

P = x + 2x + 3x - 1 - 3 - 6

50 = 6x - 10

6x = 60

x = 10

For the measure of the side length, put x = 10 in the sides.

Thus, the dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.

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To determine  probability with replacement, It uses sampling with replacement. In other words, you want to determine the likelihood of an event in which you choose a ball, card, or other object from a set of options and then swap it out after each choice.

Example:

Consider a scenario in which you wished to sample two people from a population of seven.

Those people are:

John, Jack ,Qiu, Tina, Hatty, Jacques, Des

Their names could be placed in a hat. If you sample with replacement, you would pick one name, put it back in the hat, and then pick a different name. Your two-name sample has the following potential outcomes:

John, John

John, Jack

John, Qui

Jack, Qui

Jack Tina

…and so on.

The two products you sample with replacement are independent. In other words, the outcome of one has no bearing on the other. The odds of picking the first name are 1/7, and the odds of picking the second name are 1/7.

P(John, John) = (1/7) * (1/7) = .02.

P(John, Jack) = (1/7) * (1/7) = .02.

P(John, Qui) = (1/7) * (1/7) = .02.

P(Jack, Qui) = (1/7) * (1/7) = .02.

P(Jack Tina) = (1/7) * (1/7) = .02.

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Answer: 3/5 cm

Step-by-step explanation:

Let the length of the base be x. Then, using the formula for the area of a triangle,

[tex]\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}[/tex]

ANSWER

The percent error is 10.9 %

EXPLANATION

The percent error is:

In this problem, the approximate value is 16 and the exact value is 14.25:

Answer:

10.9%

Step-by-step explanation:

14.25/16 = 0.890625

0.890625 * 100 = 89.0625

1 - 89.0625 = 10.9375%

No, Hannah is incorrect.

We are given the expression 42*19.

Hannah got the solution by multiplying 40*10 and 2*9 and then adding the values.

This can be done by using distributive property, which is given by:-

(a + b)(c + d) = ac + ad + bc + bd

We can write,

42*19 = (40 + 2)(10 + 9) = 40*10 + 40*9 + 2*10 + 2*9

Hence, the answer is not just 40*10 + 2*9 but 40*10 + 40*9 + 2*10 + 2*9.

Hannah did not add the remaining 40*9 + 2*10 to calculate the answer.

That is why Hannah was incorrect.

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Answer:

a) £960

b) £576

Step-by-step explanation:

Hi!

Ok so since the store has a 20% sale we multiply 0.2 to the original amount it would have costed without the sale:

a) [tex]1200*0.2 = 240[/tex]

Then we subtract the number we got from the price:

1200 - 240 = 960

Now we do the same thing but this time add since we are trying to find the price of the table before the sale:

b) [tex]480*0.2 = 96[/tex]

480 + 96 = 576

Please ask me if you have any more questions!

and Have a great day! :)

Question 7:

The y-axis on a graph is the vertical line on a graph, it represents the dependent variable.

Any point on the y-axis of a graph, has an x-value of zero.

Therefore, from the list given, any coordinate with an x-value of zero is on the y-axis.

Apply the point form: (x, y)

The following coordinates represent a point y-axis:

(x, y) ==> (0, -4)

(x, y) ==> (0, 3)

ANSWER:

(0, -4)

(0, 3)

The greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

In the question ;

it is given that

number of card that Bride's family has = 154

number of cards that Groom's family has = 140 cards.

So , to find the greatest number of cards that April can place in a row we need to find the GCF(154,140) ,

to find the GCF (154,140)

prime factorization of 154 = 2*7*11

prime factorization of 140 = 2*2*5*7

common factors = 2*7

Hence the GCF(154,140) = 14

Therefore , the greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

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Answer:

-1/2; take both points which equals to -1/2

Step-by-step explanation:

AnswerAnswerAnswer:

mutiply 14 by 6704

Step-by-step explanation:

The multiplication expression for the area covered is 3 x 8 and the number of grids will be 24.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given decimal grid,

The number of colored raw = 8

The number of colored columns = 3

Total grids = 8 x 3 = 24

Hence "The multiplication expression for the area covered is 3 x 8 and the number of grids will be 24".

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Step1:

You are to subtract g(x) from f(x)

Step2:

Simplify and collect like terms

therefore,

Option D is the correct answer

Answer: [tex]m=\frac{360^{\circ}}{n}[/tex]

Step-by-step explanation:

This is a standard result.

The second option is the segment addition postulate.

The third option is the sum of the angles of a polygon with n sides.

The fourth option is the measure of each interior angle of a regular polygon with n sides.

The fifth option is the angle addition postulate.

Answer:

y=(5/2)x-4

Step-by-step explanation:

1) You would have to find the slope by using the slope equations

(x1-x2)/(y1-y2)

(6-1)/(4-2)

Slope =5/2

2) the next is to find the y-axis

the line land on the x=0 at -4

y-axis=-4

3) plug into slope intercept form

y=mx+b

m=slope

b=y-axis

y=(5/2)x+(-4)

y=(5/2)x-4

Answer:

[tex]y=\frac{5}{2}x-4[/tex]

Step-by-step explanation:

1. we pick 2 points from a graph...one is (0,-4) and the other is (1,2)

2. we find the gradient between the two points using this equation m=[tex]\frac{y2-y1}{x2-x1}[/tex]

3. we plug the value in the equation

4. m = 5/2

5. equation of a straight line is y = mx +c

-where c is the intercept of the graph and m is the gradient

-4=5/2(0)+c

c =-4

therefore [tex]y=\frac{5}{2}x -4[/tex]

The square root of a number can also be negative number so x could also be -9

Square root of a number is the number such that if it is multiplied by itself we get the square. The opposite of squaring an integer is finding its square root. As we know multiplication of two negative numbers produce a positive number. this is the reason why square of both positive and negative numbers are both positive. therefore, square root of a number can also be positive or neegative both. That is why we can't take square root of negative numbers.

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Answer:

Your answer is 93.3.

Step-by-step explanation:

[tex]53-[/tex][tex](-40) = 93.3[/tex]

Answer:

(A) Nuclear fission takes place in the nucleus of atoms

Step-by-step explanation:

I took the test!

Firstly, let's draw a picture of the distribution:

Graphically, we want to calculate the blue area. To put it differently, we want to calculate

To do this, we need to find the z-score associated with 6. We can calculate it by

Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.

The probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.

Step-by-step explanation:

Solve for y: -2 = y + 5/6

-2 = y + 5/6 subtract 5/6 from both sides:

-2 - 5/6 = y + 5/6 - 5/6

-2 - 5/6 = y

combine left side:

-17/6 = y

so:

y = -17/6

OR:

[tex]y = -2\frac{5}{6}[/tex]

Answer:

$2,000

Step-by-step explanation:

Amount invested in Fund A = 6000

Profit rate of return = 5%

Amount of profit = 6000 x 5% = 6000 x 0.05 = $300

Let amount invested in Fund B be $x

Profit amount = 0.01x

Total amount invested is 6000 + x

Total profit in $ = 300 + 0.01x

Total profit in percentage = Total Profit/Total investment x 100

= 4 %

So Total Profit/Total investment = 4/ 100 = 0.04

= (300 + 0.01x) / (6000 + x)  = 0.04

Multiply both sides by (6000 + x)

=> 300 + 0.01x = 0.04(6000 + x)

=> 300 + 0.01x = 240 + 0.04x

==> 300 - 240 = 0.04x - 0.01x

=> 60 = 0.03x

x = 60/0.03

x = $2,000

Amount invested in Fund B = $2,000

Step-by-step explanation:

Fund A

$6000 returned a 5% profit. that means it had at the end 105% of the original investment

the formally correct way

100% = 6000

1% = 100%/100 = 6000/100 = $60

5% = 1%×5 = 60×5 = $300

in short, if we knew what we are doing, we could have simply calculated 6000 × 0.05 = $300.

and by the way, 6000 × 1.05 = $6300. which is the current balance of the account (investment plus the returned profit). but we don't need this here. this is just FYI.

Fund B

x returned 1% profit.

Fund A + Fund B

6000 + x returned 4% profit.

so, we have

6000×0.05 + x×0.01 = (6000 + x)×0.04

300 + 0.01x = 240 + 0.04x

60 + 0.01x = 0.04x

60 = 0.03x

x = 60/0.03 = $2000

so, he invested $2000 into fund B.

The unknown angles are as follows:

The value of ST in the line segment is 22 units.

An angle bisector is a bisector that bisect an angles into two equal parts.

Therefore, EF is the angle bisector of ∠EFG.

The bisector divides the ∠EFG equally into ∠EFH and ∠HFG.

Hence,

∠EFH  = ∠HFG

m∠HFG = 80°

m∠EFH  = 80°

m∠EFG = 80 + 80

m∠EFG = 160°

12.

Let's find ST in the line segment.

PT = 40

QS = 12

PQ = QR = RS = x

QR + RS = QS

2x = 12

x = 12 / 2

x = 6

Therefore,

PQ = QR = RS = 6 units

PS = PQ + QR + RS

PS = 6 + 6 + 6

PS = 18 units

Hence,

ST = PT - PS

ST = 40 - 18

ST = 22 units

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Applying the law of indeces for the fraction with radicals, the value of A=3, b=14 and c=-5

In mathematics, the term radical expressions such that contain a square root. In this question, we have fractions at both sides of the equation with radicals.

To solve this question, let's see some laws below that will help us:

[tex] \sqrt[x]{a} = {a}^{ \frac{1}{x} } [/tex]

[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]

[tex] \frac{1}{ {a}^{x} } = {a}^{ - x} [/tex]

From the given equation; the left hand side will be simplified as follows;

[3^(1/7)]÷[3^(1/2)]=[3^[(2-7)/14]=3^(-5/14)

And the right hand side will be simplified as follows;

1÷[A^(c/b)]=A^-(c/b)

Hence, by comparing both sides of the equation after simplifying the fractional radicals, the value of A is 3, b is 14 and c is -5.

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We can use the given points to find the slope

It means that every year, there are 1.4 million MORE households with personal computers