If ABCD is a parallelogram. BC=13 and AB=5, what is the perimeter of the parallelogram?

Answer:

The values of x and angle ABC are;

Explanation:

From the instruction above;

Line BX bisects angle ABC.

So;

Given;

Substituting this values, we have;

Then we can solve for x; collecting the like terms

Then we can now solve for angle ABC;

Since line BX bisect angle ABC, Angle ABC equal 2 times angle ABX;

Therefore, the values of x and angle ABC are;

Answer:

C.

Step-by-step explanation:

Answer:Compare this experimental probability to the population probability that fall is the favorite season. a. Out of 300 people, 4 people would say that fall is their favorite season.

Step-by-step explanation:

The missing value in the logarithm are as follows:

Using logarithm rule,

logₐ b - logₐ c = logₐ (b / c)

logₐ b + logₐ c = logₐ (b × c)

Therefore,

log₃ 7 - log₃ 2 = log₃ (7 / 2)

log₉ 7 + log₉ 4 = log₉ (7 × 4) =  log₉ 28

log₆ 1 / 81 = log₆ 81⁻¹ = log₆ 3⁻⁴ =  - 4 log₆ 3

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Answer:

B-6 1/4

Step-by-step explanation:

You take 1,250 and divided by 50 because that you base you should get 25. You then Take 1/4 and turn it into a decimal .25, then you times .25 by 25 and get 6.25. All you do after that is make it a fraction of 6 1/4 and you have your answer.

Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

Answer:

x=−3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Let one fish weigh xlbs and other 11xlbs

\(\\ \sf\longmapsto x+11x=132\)

\(\\ \sf\longmapsto 12x=132\)

\(\\ \sf\longmapsto x=\dfrac{132}{12}\)

\(\\ \sf\longmapsto x=11lbs\)

\(\\ \sf\longmapsto 11x=121lbs\)

Answer:

Step-by-step explanation:

.

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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The rate at which the distance between the cars is increasing 2 hours later is 0 mi/h, by using the Pythagorean theorem.

To find the rate at which the distance between the cars is increasing, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Let's assume that after 2 hours, the distance traveled by the southbound car is d_south and the distance traveled by the westbound car is d_west.

Since the southbound car travels at a speed of 50 mi/h for 2 hours, we have d_south = 50 mi/h \(\times\) 2 h = 100 mi.

Similarly, the westbound car travels at a speed of 20 mi/h for 2 hours, so d_west = 20 mi/h \(\times\) 2 h = 40 mi.

Now, we can use the Pythagorean theorem to find the distance between the two cars:

\(distance^2 = d_south^2 + d_west^2distance^2 = 100^2 + 40^2distance^2 = 10000 + 1600distance^2 = 11600\)

distance ≈ sqrt(11600) ≈ 107.68 mi

To find the rate at which the distance between the cars is increasing, we differentiate the equation with respect to time:

2 \(\times\) distance \(\times\) \(\(\frac{{d(\text{{distance}})}}{{dt}}\)\) = 2 \(\times\) d_south \(\times\) \(\(\frac{{d(d_{\text{{south}}})}}{{dt}}\)\) + 2 \(\times\) d_west \(\times\) (d(d_west)/dt)

Since d_south and d_west are constant (no mention of their rates of change), we can simplify the equation to:

2 \(\times\) distance \(\times\) \(\(\frac{{d(\text{{distance}})}}{{dt}}\)\) = 0

Therefore, the rate at which the distance between the cars is increasing 2 hours later is 0 mi/h.

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\(6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}\)

There are 60 professors and 168 lecturers according to the given information.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main BODY:

Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:

X + Y = 228

Then, as there are 5 professors for every 14 lecturers:

5 X = 14 Y or X = (14/5) Y

Replacing this last value of X on the first equation:

(14/5) Y + Y = 228

(14/5) Y + (5/5) Y = 228

(19/5) Y = 228

Y = 228 * (5/19)

Y = (228*5)/19

Y = 1140 / 19

Y = 60

Then we can find X:

X = (14/5) Y = (14/5) * 60 = 168

X = 168

Hence thre are 60 professors and 168 lecturers.

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Answer:

1232    =>      1

2464    =>     2

6160    =>      5

9856   =>      8

Step-by-step explanation:

The 3 interior angles in every triangle add up to 180 degrees, and in isosceles triangles the two base angles are the same, so:

180=80+2x

180-80=2x

100=2x

x=100/2=50 degrees

The measures of the base angles are 50 degrees

Our starting value: $89.50.

Deposits means putting money in the account, so money will increase.

Withdrawal means that you are depleting the account, so money will decrease.

1. 11/4 - Deposited $17.25

So you will add $89.50 + $17.25 = $106.75

2. 11/4 = Withdrawal $35.90

So you will subtract $106.75 - $35.90 = $70.85

3.  11/7 - Deposit $10.77

So you will add $10.77 + $70.85 = $81.62

4. 11/11 - Withdrawal of $3.02

So you will now subtract $81.62- $3.02 = $78.60

$78.60 is our final balance! I hope this helps!

Answer:84.7

Step-by-step explanation: you add up all the side lengths

area = 255 \(m^{2}\)

perimeter = 20+6.7+8+8+15+26 = 83.7m

Step-by-step explanation:

top left triangle - base is 3 because (20-8-9).  so 1/2 bh = 1/2 (3) (6) = 9

left rectangle = l x w = 20 x 6 = 120

middle square = l x w = 8 x 9 = 72

lower right triangle = height is 12 because (26-8-6), so 1/2 bh =1/2 (9)(12) = 54

9+120+72+54 = 255

The intercept of a line is the y-coordinate of the point where the line crosses the y-axis, in this case, we can see from the graph that the line goes through the origin, then the intercept of the line b is 0

Answer:

a)  P (COO)  = 0,135

b) P ( SISI) = 0,00015

Step-by-step explanation:

a) the probability of an ion channel in open position is 50 %   0,5

   the probability of an ion channel in close position is 50 %   0,5

probability for the following sequence of states COO

to be closed   0,5    (C)

from (C) to pass to open  0,3  (O)

and to stay O  is 0,9

Then the probability of the sequence of states COO is

P (COO)  = 0,5 * 0,3 * 0,9  

P (COO)  = 0,135

b) If people are either infected or susceptible, then

Probability of an individual infected is  0,5

Probability of an individual susceptible  is 0,5

to pass from susceptible to infected is 0,05

to pass from infected to susceptible is 0,12

then

P ( SISI) = 0,5 * 0,05*0,12*0,05

P ( SISI) = 0,00015

probability for the following sequence of states COO

Answer:

Given: A = 72°, a = 34, b = 21

Calculated: B = 35.97°, C = 72.03°, c = 34.00

Step-by-step explanation:

\( \dfrac{\sin A}{a} = \dfrac{\sin B}{b} \)

\( \dfrac{\sin 72^\circ}{34} = \dfrac{\sin B}{21} \)

\( \sin B = \dfrac{21\sin 72^\circ}{34} \)

\( \sin B = 0.5874 \)

\( B = \sin^{-1} 0.5874 \)

\( B = 35.97^\circ \)

C = 180° - 72° - 35.97°

C = 72.03°

\( \dfrac{\sin A}{a} = \dfrac{\sin C}{c} \)

\( \dfrac{\sin 72^\circ}{34} = \dfrac{\sin 72.03^\circ}{c} \)

\(c = \dfrac{\sin 72.03^\circ \times 34}{\sin 72^\circ}\)

\( c = 34.00 \)

Given: A = 72°, a = 34, b = 21

Calculated: B = 35.97°, C = 72.03°, c = 34.00

Answer:

\(B\approx35.97^\circ\\C\approx72.03^\circ\\c\approx34\)

Step-by-step explanation:

Law of Sines

\(\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\)

Given information

\(A=72^\circ\\a=34\\b=21\)

Check if solutions exist

As \(A=72^\circ < 90^\circ\) and that \(a > b\rightarrow 34 > 21\), then there exists only one possible triangle by the Ambiguous Case

Solve the triangle

\(\frac{sin(72^\circ)}{34}=\frac{sin(B)}{21}\\ \\ 21sin(72^\circ)=34sin(B)\\\\\frac{21sin(72^\circ)}{34}=sin(B)\\ \\B=sin^{-1}(\frac{21sin(72^\circ)}{34})\\ \\B=35.97394255^\circ\approx35.97^\circ\)

\(A+B+C=180^\circ\\\\72^\circ+35.97394255^\circ+C=180^\circ\\\\107.97394255^\circ+C=180^\circ\\\\C=72.02605745^\circ\approx72.03^\circ\)

\(\frac{sin(72^\circ)}{34}=\frac{sin(72.02605745^\circ)}{c}\\\\c*sin(72^\circ)=34sin(72.02605745^\circ)\\\\c=\frac{34sin(72.02605745^\circ)}{sin(72^\circ)}\\ \\c=34.00502065\approx34\)

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

x:y I think this answer is correct

Step-by-step explanation:

The value of f(g(x)) is 4x² – 8x+ 2 .

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(x) = x² – 2x – 1

g(x) = 2x - 1

So, f(g(x))

=f(2x - 1)

=(2x-1)² – 2(2x-1) – 1

=4x² – 4x + 1 -4x + 2 -1

=4x² – 8x+ 2

hence, the value of f.g(x) is  4x² – 8x+ 2 .

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Answer:

Answer:

550

Step-by-step explanation:

Rewrite in exponential form:

10^3=2x-100

Solve for x:

1000= 2x-100

2x=1100

x=550

The solution to this equation is x =550

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Given

Rewrite in exponential form:

10³=2x-100

Solve for x:

1000= 2x-100

2x=1100

x=550

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Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Answer:

The pooled variance for the two samples is 90

Step-by-step explanation:

Here in this question, we are interested in computing the pooled variance for the two given samples.

From the question;

n1 = 9

ss1 = 710

n2 = 6

ss2 = 460

The pooled variance can be calculated using a mathematical formula as shown below;

S^2 =( ss1 + ss2)/(n1 + n2 -2)

where S^2 refers to the pooled variance of both samples.

Plugging the values into the equation, we have ;

S^2 = (710 + 460)/9 + 6 -2 = 1170/13 = 90

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.

The coordinates are given as:

First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).

Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)

Calculate the distance AB and A'B' using:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ AB = √ (-4 + 3)² + (9 - 7)²

⇒ AB = √1 + 4

⇒ AB = √5

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ A'B' = √ (3 - 3)² + (6 + 4)²

⇒ A'B' = 10

This gives, Divide A'B' by AB to determine the scale factor (k)

k = 10 / √5

k = 2√5

Hence, this transformation is a by a factor of 2√5

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Answer:

Reflection and 2

Step-by-step explanation:

for plato