In the diagram, rectangle ABCD is split in half by AC . What is the value of tan x?​

Answer:

y = -6

Step-by-step explanation:

Answer:

Step-by-step explanation:

3. Use Cosine law to find the  length of the unknown side (PR)

q² = p² +  r² - 2prCos Q

q is the opposite side of ∠Q;  

p is the opposite side of ∠P; p = 33

r is the opposite sides of ∠R ; r = 67

q² = 33² + 67² -  2* 33*67 Cos 19°

    = 1089 + 4489 - 4422 * 0.95

     = 1089 + 4489 - 4200.9

    = 1377.1

q = √1377.1

q = 37.1

PR = 37.1

To find the angle use law of sin

[tex]\sf \dfrac{q}{Sin \ Q} =\dfrac{p}{Sin \ P}\\\\\\\dfrac{37.1}{Sin \ 19}=\dfrac{33}{Sin \ P} \\\\\\\dfrac{37.1}{0.33}=\dfrac{33}{Sin \ P}\\\\\\37.1* Sin \ P = 33 *0.33\\\\Sin \ P =\dfrac{33*0.33}{37.1}[/tex]

Sin P = 0.3

[tex]P = Sin^{-1} 0.3\\[/tex]

P = 17.5°

∠R = 180 - (19 + 17.5)

    = 143.5°

Answer: Calculate Total Amount Accrued (Principal + Interest), solve for A. A = P(1 + rt)

Calculate Principal Amount, solve for P. P = A / (1 + rt)

Calculate rate of interest in decimal, solve for r. r = (1/t)(A/P - 1)

Calculate rate of interest in percent. ...

Calculate time, solve for t

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final Answer: 19.5%

The total percentage 19.5% increase in the investor's stock account

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5900 and his stock in Company B was worth $1850.

The total worth is $5900 + $1850 = $7750

The stock in Company A has increased 20% since last year.

So,

20% of 5900,

= 20 x 5900 /100

= $1180

And the stock in Company B has increased 18%.

So,

18% of 1850,

= 18 x 1850/100

= $333

The total increased amount,

= $333 + $1180

= $1513

The increased percentage,

1513 = n x 7750/100

n = 1513 x 100/7750

n = 19.522

n = 19.5% to the nearest tenth.

Therefore, 19.5% is the required percentage.

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Answer:

y=90(0.5)^x

The y-intercept is (0,90), so when x=0, y should be 90.

By replacing x=0 in all equations you get;

1)

y=90(2)^0 =90 accepted

2)

y=2(90)^0 =2 rejected

3)

y=0.5(90)^0 =0.5 rejected

4)

y=90(0.5)^0 =90 accepted

Since this is an exponential decrease,

y=90(2)^x is rejected.

Step-by-step explanation:

Perimeter=2(l+b)

=2(152+120)

=544 cm

Your salary in x years is modeled an the exponential growth

The equation that determines your salary in x years is y = 45000(1.05)^x

The model of the exponential growth is given as:

y = a(1 + r)^x

From the question, we have:

Initial salary, a = 45000

Raise, r = 5%

So, the equation becomes

y = 45000(1 + 5%)^x

Evaluate the sum

y = 45000(1.05)^x

Hence, the equation that determines your salary in x years is y = 45000(1.05)^x

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Volume of the cone = 1/3 x base area x height

so

V = 1/3 x pi x r² x h = 1/3 x pi x 2² x 6 = 8 x pi

Answer:

1/9

Step-by-step explanation:

Probability is defined as the number of cases fitting a constraint divided by the number of total cases.

We will calculate the number of total cases first (bc its easier xD):

3 numbers for the first spin times 2 cases for the flip times 3 numbers for the first spin = 18 total cases.

Now, we will calculate the number of cases fitting the constraint:
For the first constraint, there are two possible ways of spinning an odd number, landing on 1 or 3.
For the second constraint there is only 1 way, which is spinning a head.
For the 3rd constraint, there is only 1 way to spin yellow.

2 * 1 * 1 = 2

Number of cases over total cases:

2/18 = 1/9

Step-by-step explanation:

we seek the probability of a combination of independent events.

since they are independent, we can simply multiply the 3 individual probabilities.

1. spin an odd number (in our case that means 1 or 3) out of the possible 3. that probabilty is therefore 2/3.

2. flipping head with a coin. so, 1 out of possible 2. that probabilty is therefore 1/2

3. spin yellow. that is 1 out of possible 3. that probabilty is therefore 1/3.

again, none of the single events is influencing the outcome of any of the other 2 events, so, the total probabilty of the combination is the product of the single probabilities :

2/3 × 1/2 × 1/3 = 2/18 = 1/9

FYI : the first single probabilty is actually the result of an "or" relationship of 2 possible results of one event :

the probabilty to get an odd number is the same as the probabilty to get 1 or to get 3. both are non-overlapping possible outcomes of one event, so we can add the individual probabilities for the result.

each possible outcome has the probabilty of 1/3, so the "or" relation has a probabilty of 1/3 + 1/3 = 2/3.

Answer:

Step-by-step explanation:

Answer:

1.5625

Step-by-step explanation:

rround to 2

Answer:

5 538 163

Step-by-step explanation:

convert 5547 g to mg

5547×1000=5547000mg

5547000mg-8837mg= 5 538 163mg

Answer:

5538.2

Step-by-step explanation:

convert 8837mg to g

8.8

minus that from 5538=

5538.2

Answer:
x = 20

Step-by-step explanation:

to make 3x + 5 = 65, first you can subtract 5 from 65, then divide. 60/3, which equals 20, so x = 20

Answer:

8:00 PM

Note that any blue dots represent a new day.

Answer:

I've attached an image showing the intersection and the angle.

Answer:

C: They are complementary

Step-by-step explanation:

We can see from the image that angle 1, angle 2 and 90° are on a straight line. We know that sum of angles on a straight line is 180°. Thus;

∠1 + ∠2 + 90° = 180°

Rearranging, we have;

∠1 + ∠2 = 180° - 90°

Thus;

∠1 + ∠2 = 90°

Now, from angle proofs in trigonometry, it states that If the non-common sides of two adjacent angles add up to 90°, then it means that the angles are complementary.

In our problem here, sum of ∠1 and ∠2 equals 90°. Also, they are the non-common sides of 2 adjacent angles. Thus, we can say that they are complementary.

Step-by-step explanation:

Answer:

Athletes swim 3/20 kilometer for every kilometer they run.

Step-by-step explanation:

3/20 = .15

multiply 10 by 3/20

10 * .15 = 1.5

Answer:

3/20 kilometers for every kilometer ran

Step-by-step explanation:

divide

[tex]-6n < -12\\\\\implies 6n > 12\\\\\implies n > \dfrac{12}6\\\\\implies n > 2[/tex]

Answer:

90

Step-by-step explanation:

37 and 41 is only in the 25% percentile.  

360 X .25 = 90

Plus, I took the K12 test and got it right.

The number of employees took a break that lasted between 37 and 41 minutes is 60.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We know that;

There are 360 employees in total and that they are evenly distributed along this plot. Therefore, we can divide 360 by the width of this plot to find how many employees are represented by one unit on this plot. The width of this plot is 58 - 34 = 24 units.

So, 360 / 24 = 15

This means that for every unit on this plot, there are 15 employees who took a break with that duration.

Now we can multiply this number by the width of the box to find how many employees took a break between 37 and 41 minutes. The width of the box is 41 - 37 = 4 units. So,

15 * 4 = 60

This means that there are 60 employees who took a break that lasted between 37 and 41 minutes.

Therefore, by the unitary method the answer will be 60 employees

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The inequality for this situation is given as b + n ≥ 16 and 6b + 9n > 108

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let b represent the number of bracelets she sells, and let n represent the number of necklaces she sells.

Hence:

b + n ≥ 16  (1)

and:

6b + 9n > 108   (2)

The inequality for this situation is given as b + n ≥ 16 and 6b + 9n > 108

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Step-by-step explanation:

a = 18

n = 10 th term

difference (d) = 72-10 = 62

an ( n th term ) = a + (n-1)d

a10 ( 10 th term = 18 + (10-1)62

= 18 + 9×62

= 18 + 558

10 the term = 576

AnswerAnswerAnswerAnswer:

the answer is  D h(x) = 1/4 x

Step-by-step explanation:

Have a great day!

A brainliest would help!

Around 57%

17 / 30 = .56666666...

Move two decimal places to the left;

56.66666...

Estimate: 57%

Answer:

43.33%

Step-by-step explanation:

30 - 17 = $13

% discount = 13*100 / 30

= 43.33%

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

To convert from polar to Cartesian coordinates, recall that [tex](x,y)=(r\:cos\theta,r\:sin\theta)[/tex], thus, [tex](x,y)=(6\:cos\frac{5\pi}{6},6sin\frac{5\pi}{6})=(6(-\frac{\sqrt{3}}{2}),6(\frac{1}{2}))=(-3\sqrt{3},3)[/tex]

Therefore, C is the correct answer

Problem 2

Convert from polar to Cartesian coordinates:

[tex](x,y)=(-5\:cos\frac{2\pi}{3},-5\:sin\frac{2\pi}{3})=(-5(-\frac{1}{2}),-5(\frac{\sqrt{3}}{2}))=(\frac{5}{2},\frac{-5\sqrt{3}}{2})[/tex]

Therefore, U is the correct answer

Problem 3

Since [tex]r=\sqrt{x^2+y^2}[/tex], then [tex]r^2=x^2+y^2[/tex]. Don't also forget to use the substitution [tex]x=r\:cos\theta[/tex]:

[tex]x^2+y^2-7x=0\\\\r^2-7rcos\theta=0\\\\r(r-7cos\theta)=0\\\\r-7cos\theta=0\\\\r=7cos\theta[/tex]

Therefore, B is the correct answer

Problem 4

[tex]r=(tan\theta)(sec\theta)\\\\r=(\frac{sin\theta}{cos\theta})(\frac{1}{cos\theta})\\ \\\frac{r^2}{r}=(\frac{rsin\theta}{rcos\theta})(\frac{r}{rcos\theta})\\ \\\frac{x^2+y^2}{\sqrt{x^2+y^2}}=(\frac{y}{x})(\frac{\sqrt{x^2+y^2}}{x})\\ \\x^2+y^2=\frac{y(x^2+y^2)}{x^2}\\ \\1=\frac{y}{x^2}\\\\x^2=y[/tex]

Therefore, A is the correct answer

Answer:

5/7

Step-by-step explanation:

Umm because the denominator 7 is less than 10 and 7 is the nearest number to 1/2

I hope it helps

Answer:

C, D, E,

Step-by-step explanation:

All of these will round to 187.55

Answer:

Given function:

t(s) = 3s + 20

where:

Given function:

s(d) = 20d

where:

To determine the composite function that represents how many palm trees Carlos can expect to grow over a certain number of days, simply substitute s = 20d into t(s) = 3s + 20:

⇒ t(d) = 3(20d) + 20

⇒ t(d) = 60d + 20

The unit of measurement is how many palm trees Carlos can expect to grow over a certain number of days:

[tex]\sf \dfrac{palm \ trees}{days}[/tex]

Answer:

$9400

Step-by-step explanation:

You start with $1000 and get 7% more every month.

7% of 1000 is 70 so that means $70 is added to the credit union each month.

So you add $70 dollar to $1000 for every month there is which would be 12 months timers the ten years:

1000 + (70 x 12 x 10) = 9400

Answer:

Median: 5

Mean: 6

Step-by-step explanation:

4,4,4,5,7,9,9

(4x3)+5+7+(9x2)

12+5+7+18

17+25=42

42÷7=6