Given: Parallelogram PORS, QT is perpendicular to PS, SU is perpendicular to QR

Prove: PT congruent to RU

Perimeter of the rectangle is: 6x + 6 cm

Area of the rectangle is: 18x - 18 cm²

Area = (length)(width)

Perimeter = 2(length + width).

Given the following:

Length of rectangle = 3x - 3

Width = 6

Area = (3x - 3)(6)

Area = 18x - 18 cm²

Perimeter = 2(3x - 3 + 6) = 2(3x + 3)

Perimeter = 6x + 6 cm

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Answer:

Step-by-step explanation:

The domain is the set of x values.

The range is the set of y values.

The equation of the axis of the curve is determined by (c) c

The equation is given as:

y= a sin[k(x - d)] + c

In the above equation, the midline is

y = c

This represents the equation of the curve axis

Hence, the equation of the axis of the curve is determined by (c) c

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Answer:

C. 3(x+1)(x-1)-4x

Step-by-step explanation:

3(x+1)(x-1)-4x

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

3(x^2-1)-4x

3x^2-4x-3

To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201

The given parameters are:

This means that

df = 11 and t = 1.910

To calculate the t value,

We check the row where the heading of the degree of freedom is 11

i.e. df = 11

On this row, the t value 1.910 would be between 1.796 and 2.201

This is because 1.910 is greater than 1.796 and it is less than 2.201

Hence, the complete statement is

To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201

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Using it's concept, there is a 0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The company has 6 + 2 + 8 = 16 employees, out of which 2 + 8 = 10 have a bachelor's or a master's degree, hence the probability is:

p = 10/16 = 0.625.

0.625 = 62.5% probability that he or she has a bachelor's or a master's degree.

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Answer:

5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c

= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)

= 16a²b + 4ab²

Answer:

D. Avialable

Step-by-step explanation:

the correct spelling is available :)

The answer is D.

The correct spelling of the word in the given option is : Available

Instead, here the places of a and i have been interchanged, causing it to be misspelt.

The number of bacteria present after 15 hours is 18928

An exponential equation is represented as;

y = ab^x

Where

a = y, when x = 0

From the table, we have:

y = 1796 when x = 0

So, we have:

y = 1796b^x

Also, we have the point (1, 2097)

This gives

2097 = 1796b^1

Divide by 1796

b = 1.17

Substitute b = 1.17 in y = 1796b^x

y = 1796(1.17)^x

This means that the exponential equation is y = 1796(1.17)^x

After 15 hours, we have:

y = 1796(1.17)^15

Evaluate

y = 18928

Hence, the number of bacteria present after 15 hours is 18928

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Answer:

1 - 100 primes numbers

Step-by-step explanation:

2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797

Answer:

[tex]\huge\boxed{\sf x =6,\ y = 42}[/tex]

Step-by-step explanation:

Let the numbers be x and y

x + y = 48 --------(1)

y = 7x -------------(2)

Put Eq. (2) in (1)

x + 7x = 48

8x = 48

Divide 8 to both sides

x = 48/8

Put x = 6 in Eq. (2)

y = 7 (6)

[tex]\rule[225]{225}{2}[/tex]

Assume a is the 1st number and b is the 2nd number, a + b = 48

b = 7a (the second number is seven times the first number​)

a = a

So, equation: a + 7a = 48

a + 7a = 48

8a = 48

a = 6

To find b = 7 (6) = 42

Hope it helps!

Answer:

English (Ingles):
10 Women come to the party.

Spanish (Espanol):

10 Las mujeres vienen a la fiesta.

Step-by-step explanation:

English (Ingles):

We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.

So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.

This means 25% of 16 is 4.

This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.

It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.

As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.

Spanish (Espanol):

Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.

Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.

Esto significa que el 25% de 16 es 4.

Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.

Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al ​​25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.

Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.

The number whose sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed is 32

the number can be expressed as 10x + y

x + y = 5

(10x+y) - 9

= 10y+x

x + y = 5

9x - 9y = 9

x + y = 5

x - y = 1

Add the equations

2x = 6

x = 6/2

x = 3

substitute into

x + y = 5

3 + y = 5

y = 5 - 3

y = 2

Therefore, the unknown number is 32.

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Answer:

= 5x-39-18-12x

=5x-12x-39-18

=-7x-57

The total cost to laminate the tabletop is $96.

The first step is to determine the area of the trapezoid.

Area of the trapezoid = 0.5 (sum of parallel sides) x height

0.5 x (6 + 10) x 3 = 24 feet²

The total cost of laminating = cost per square feet x area

$4 x 24 = $96

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The equation of the directrix is y = -5

The equation is given as:

(x -1)^2 = 12(y + 2)

Express 12 as a product of 4 and 3

(x -1)^2 = 4 * 3(y + 2)

The parabola is represented as:

(x -h)^2 = 4p(y - k)

Where the directrix is

y = k - p

By comparison, we have:

k = -2 and p = 3

So, we have:

y = -2 - 3

Evaluate

y = -5

Hence, the equation of the directrix is y = -5

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Answer:

1.5 is the slope and 2 is the intercept

Step-by-step explanation:

I am assuming that the equation is y = 1.5x + 2.

Answer:

5.9512

Step-by-step explanation:

1. Convert the percentage to decimal

8% = 8/100 = 0.08

2. Multiply the decimal by the quantity to be extracted

(0.08)(74.39) = 5.9512

Hope this helps

Answer:

you need to upload a pic so we can see what you're talking about

Answer:

a^-27

Step-by-step explanation:

(a^3)^-3)^3)

(a^-9)^3)

a^-27

When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷

The following data were obtained from the question:

We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:

((a³)⁻³)³

Recall

(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)

Thus,

((a³)⁻³)³ = (a⁻⁹)³

= a⁻²⁷

Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷

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a) The probability of a head exists at 0.7.

b) He could improve his experiment by doing more coin flips.

Probability signifies possibility. It exists a branch of mathematics that values the event of a random event. The value exists represented from zero to one.

Given: Coin flipped 10 times.

The Head comes T times and the tail comes 7 times.

To estimate the probability of head in the outcome.

The total number of outcomes is 10 and the head comes 7 times.

a) Probability(head) = 7/10 = 0.7

The probability of a head exists at 0.7.

b) He could improve his experiment by doing more coin flips

Therefore, the correct answer is option c) doing more coin flips.

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Answer:

429/7 kg or 61 2/7 kg

Step-by-step explanation:

I'll answer according to how I understand this problem, but I'm not sure this is correct.

"39 kg of rice is taken out of bag of rice. If 8/22 of the rice is left, what was the original weight of the rice in the bag?"

8/22 is a strange number to work with because it could have been given as 4/11. This is another reason I'm not too sure about this problem.

8/22 = 4/11

If 4/11 is left, then since 11/11 - 4/11 = 7/11, 7/11 of the rice remains.

7/11 x = 39

x = 39 × 11/7

x = 429/7

x = 61 2/7

The correct responses found using trigonometric ratios are as follows;

1. The depth of the water = 15 × tan(4°) = 1.049 m

The height of Brooke's boot = 1 m

Therefore;

2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°

Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;

3. Height reached by the plane = 9 × tan(21°) = 3.455

Therefore;

4. Height of the chimney at the factory = 50 × tan(51°) = 61.745

The minimum chimney height = 65 m.

Therefore;

6. Length of the bridge = 72 × tan(55°) ≈ 102.83

Therefore;

7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7

Therefore;

8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8

Therefore;

9. Height reached by plane = 26 × tan(9°) ≈ 4.12

The plane flies under the cloud therefore;

10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83

Therefore;

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The hypothesis illustrates that the males in the group don't follow a same distribution as all the males that are in the United States.

Based on the information given, it should be noted that the degree of freedom given in this case will be:

= 4 - 1

= 3

By using the Excel function, the p-value is given as 0.0002. In this case, we've to reject the null hypothesis if the p value is less than 0.1.

Therefore, we will reject the null hypothesis in this case. In inferential statistics, the null hypothesis is that two possibilities are the same. It is observed difference is due to chance alone. Using statistical tests, it is possible to calculate the likelihood that the null hypothesis is true

Therefore, the hypothesis illustrates that the males in the group don't follow the same distribution as all the males that are in the United States.

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Answer: 100

Step-by-step explanation:

2|48,64,72,96,108

2|24,32,36,48,54

2|12,16,18,24,27

2|6,8,9,12,27

2|3,4,9,6,27

2|3,2,9,3,27

3|3,1,9,3,27

3|1,1,3,1,9

3|1,1,1,1,3

LCM

Answer:

Vertex: (0,0)

Left 2 points: (-1,1) , (-2,4)

Right 2 points: (1,1) , (2,4)

Step-by-step explanation:

Using the given linear equation, we conclude that you can invite a maximum number of 21 guests.

Here the function is:

C(p) = 325 + 15*p

Where p is the number of guests minus 10, now we know that your budget is $600, then the maximum value of guests allowed is such that:

C(p) = 600 = 325 + 15*p

Now we can solve this equation for p:

600 - 325 = 15*p

275 = 15*p

175/15 = p = 11.67

Then the maximum whole number that p can take is p = 11

This means that the maximum number of guest that you can have is:

Guests = 10 + p = 10 + 11 = 21.

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Answer: (1,3)

Step-by-step explanation:

Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.

Let's multiply the whole first equation by -2 to achieve this:

[tex]-2(x+2y=7)[/tex] now becomes [tex]-2x-4y=-14[/tex]

Now let's add both equations

[tex]-2x-4y=-14[/tex]

[tex]2x-y=-1[/tex]

[tex]-5y= -15[/tex]

Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.

[tex]\frac{-5y}{-5} = \frac{-15}{-5}[/tex]

[tex]y=3[/tex]

Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.

[tex]2x-3=-1[/tex]

We can now solve for x.

[tex]2x=2[/tex] [Adding 3 to both sides]

[tex]x=1[/tex] [Dividing by 2 on both sides]

We now have both x and y, so we can put it in an ordered pair to answer the question.

[tex](1,3)[/tex]

Answer:

Step-by-step explanation:

hello :

(4a) × (3b)​ =12ab