What is the area of a triangle with vertices at (–2, –1), (4, –1), (6, 5)?

6 square units

9 square units

18 square units

36 square units

[tex]\bf \begin{array}{ccll} tons&weeks\\ \cline{1-2}\\ \frac{3}{4}&1\frac{1}{2}\\\\ 2&x \end{array}\implies \cfrac{~~\frac{3}{4}~~}{2}=\cfrac{~~1\frac{1}{2}~~}{x}\implies \cfrac{~~\frac{3}{4}~~}{2}=\cfrac{~~\frac{3}{2}~~}{x}\implies \cfrac{~~\frac{3}{4}~~}{\frac{2}{1}}=\cfrac{~~\frac{3}{2}~~}{\frac{x}{1}} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{2}=\cfrac{3}{2}\cdot \cfrac{1}{x}\implies \cfrac{3}{8}=\cfrac{3}{2x}\implies 6x=24\implies x=\cfrac{24}{6}\implies x=4[/tex]

Answer:

50.29 in^2

Step-by-step explanation:

From the circumference we need to find the radius.

Since C = 2*pi*r, r = C / (2*pi).

Here, with C = 25  1/7 in, r = (25  1/7 in) / [ 2(22/7) ], or r = 4 in

The area of the cake is A = pi*r^2, or (here)  A = (22/7)(4 in)^2 = 50.29 in^2

Answer:

Padma pays $11 dollars a month for the sports channel. I do not see the question for the magazine:(

Step-by-step explanation:

ANSWER

The correct choices are:

[tex] {8a}^{15} - 27[/tex]

and

[tex]216 {a}^{6} - 27 {y}^{3} [/tex]

EXPLANATION

A difference of perfect cube is of the form:

[tex] {(m)}^{3} - {(n)}^{3} [/tex]

We can rewrite

[tex]216 {a}^{6} - 27 {y}^{3} [/tex]

Try rewriting the terms as powers to an exponent of 3.

[tex]216 {a}^{6} - 27 {y}^{3} = {6}^{3}( {a}^{2})^{3} - {3}^{3} {y}^{3} [/tex]

This implies that:

[tex]216 {a}^{6} - 27 {y}^{3} = ( 6 {a}^{2})^{3} - {(3y)}^{3} [/tex]

Hence this is a difference of perfect cube.

Also, we can rewrite

[tex] {8a}^{15} - 27[/tex]

as

[tex]{8a}^{15} - 27 = {2}^{3} ( {a}^{5})^{3} - {3}^{3} [/tex]

[tex]{8a}^{15} - 27= {(2{a}^{5})}^{3} - {3}^{3} [/tex]

The answer is:

The correct option is:

B)  [tex]5^{12}\div5^{4}=5^{8}[/tex]

To solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

[tex]\frac{a^{m} }{a^{n} }=a^{m-n}[/tex]

If we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

So, we are given the expression:

[tex]5^{12}\div5^{4}[/tex]

Which is equal to write:

[tex]\frac{5^{12} }{5^{4}}[/tex]

Then, calculating we have:

[tex]\frac{5^{12} }{5^{4}}=5^{12-4}=5^{8}[/tex]

Hence, the answer is:

B)  [tex]\frac{5^{12} }{5^{4}}=5^{8}[/tex]

or

 [tex]5^{12}\div5^{4}=5^{8}[/tex]

Have a nice day!

Answer:

The correct answer is option B. 5^8

Step-by-step explanation:

Points to remember

Identities

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

x⁻ᵃ = 1/xᵃ

To find the correct option

It is given an expression, 5^12 ÷ 5^4  

⇒ 5¹²/5⁴

By using identities we can write,

5¹²/5⁴ = 5⁽¹² ⁻ ⁴⁾

 = 5⁸

Therefore the correct answer is option B. 5^8

Answer:

46 craft sticks per student

Step-by-step explanation:

The simplest situation would be that in which the available 644 craft sticks are evenly divisible by the number of students receiving them.  If that's the case, all we have to do is to divide:

644 craft sticks

----------------------- = 46 craft sticks per student

     14 students

Answer:

tanx-(\sqrt(11))/(5)cosx>0

Step-by-step explanation:

Because to do this kind of trig you first have to know how to do basic trg

The median is 12.

The arithmetic mean is 12.7

The geometric mean is 11.3

Answer:

30th percentile:109

90th percentile: 188

Step-by-step explanation:

The given data set is:

129, 113, 200, 100, 105, 132, 100, 176, 146, 152

We arrange the data set in ascending order to obtain;

Array= [tex]100,100,105,113,129,132,146,176,200[/tex]

The 30th percentile is located at

[tex](\frac{30}{100}\times 10 )}[/tex] -th position, where n=10 is the number of items in the data set

This implies that the 30th percentile is at the 3rd position.

Since 3 is an integer, the 30th percentile is the average of the 3rd and 4th occurrence in the array;

This implies that the 30th percentile = [tex]\frac{105+113}{2}=\frac{218}{2}=109[/tex]

The 90th percentile is located at

[tex](\frac{90}{100}\times 10 )}[/tex] -th position, where n=10 is the number of items in the data set

This implies that the 90th percentile is at the 9th position.

Since 9 is an integer, the 90th percentile is the average of the 9th and 10th occurrence in the array;

This implies that the 90th percentile = [tex]\frac{176+200}{2}=\frac{376}{2}=188[/tex]

Answer:

D. f(2) = 0

Step-by-step explanation:

If x-2 is a factor of a function, then f(2) must be zero

f(x) = p(x) * (x-2) since (x-2) is a factor of f(x)

Substitute in x=2

f(2) = p(2) (2-2)

f(2) = p(2) *(0)

Anything times 0 = 0

f(2) = 0

For this case we must find the product of the following expression:[tex]3 (x + 4) (x-5)[/tex]

We must apply distributive property to the terms of the first parenthesis:

[tex](3x + 12) (x-5) =[/tex]

Again we apply the distributive property:

[tex]3x ^ 2-15x + 12x-60 =\\3x ^ 2-3x-60[/tex]

ANswer:

[tex]3x ^ 2-3x-60[/tex]

Step 1: Distribute the 3 to x and 4

(3x + 12)(x - 5)

Step 2: FOIL (First, Outside, Inside, Last)

Multiply the first of the values in the parentheses together

(3x + 12) (x - 5)

[tex]3x^{2}[/tex]

Multiply the outside values in the parentheses together

(3x + 12)(x - 5)

-15x

Multiply the inside values of the parentheses together

(3x + 12)(x - 5)

12x

Multiply the last values of the parentheses together

(3x + 12)(x - 5)

-60

Step 3: Add all the FOIL values together

3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)

Step 4: Combine like terms

3[tex]x^{2}[/tex] + (-15x) + 12x + (-60)

3[tex]x^{2}[/tex] - 3x - 60

Hope this helped!

Answer:

A) Sample bias

Step-by-step explanation:

If a sample of 100 participants includes 20 men and 80 women, then the sample is biased. Women account for;

(80/100)*100 = 80% of the total participants while men only for 20%.

The sample does not represent the entire population in fair proportions hence the sample is biased

Answer:

D

Step-by-step explanation:

Use the formula for the SA of a hemisphere.

[tex]SA=2\pi r^2[/tex]

Now we can find the radius of the hemisphere, which is 15.

Then, we can square that and multiply it by 2 to get 450.

Now, let's use the formula for the Volume of a hemisphere.

[tex]V=\frac{2\pi r^3}{3}[/tex]

Now we can cube 15 and multiply it by 2 to get 6750.

Then we can divide this number by 3.

2250.

So the answer is D.

Answer:

0.5 hour

Step-by-step explanation:

Given

Speed of Dina = 10 km/h

Distance = 20 km

So the time Dina taken to complete the track is:

[tex]Speed=\frac{distance}{time}\\10=\frac{20}{time}\\time=\frac{20}{10}\\ time=2\ hours[/tex]

The time taken by Dina is 2 hours. As masha started with dina but she was 4 km of the path left to cycle,

her distance covered in 2 hours was:

[tex]Distance\ covered\ by\ Masha\ in\ 2\ hours=20-4\\=16 km[/tex]

So we know the time and distance:

Now,

[tex]Speed\ of\ Masha=\frac{distance}{time}\\ =\frac{16}{2}\\ =8\ kilometer\ per\ hour[/tex]

We have to calculate the time that will be needed by MAsha to complete the track:

As we know the speed and remaining distance

[tex]Speed=\frac{distance}{time}\\8=\frac{4}{time}\\ time=\frac{4}{8}\\time=0.5\ hours[/tex]

Masha needs 0.5 hour to complete the track ..

Answer:

30 minutes

Step-by-step explanation:

Answer:

A) 6

Step-by-step explanation:

This would be your best answer.

Answer:

1.) 5

2.) -6

3.) -3

4.) -15

5.) 5

Final answer:

To determine the number of dimes Jared has, we set up an equation based on the total value of dimes and quarters equaling $5.50. After solving the equation, we find that Jared has 10 dimes.

Explanation:

The student's question asks how many dimes Jared has if he has a total of $5.50 consisting of quarters and dimes, with 8 more quarters than dimes. Let 'd' represent the number of dimes. Since a dime is worth $0.10, the total value of the dimes is 0.10d dollars. Jared has 8 more quarters than dimes, so he has 'd+8' quarters. A quarter is worth $0.25, so the total value of the quarters is 0.25(d+8). The sum of the values of the dimes and quarters is $5.50, so we can set up the equation 0.10d + 0.25(d+8) = 5.50.

Now, solving for d:

0.10d + 0.25(d+8) = 5.50

0.10d + 0.25d + 2 = 5.50

0.35d + 2 = 5.50

0.35d = 5.50 - 2

0.35d = 3.50

d = 3.50 / 0.35

d = 10

Jared has 10 dimes.

The Riemann sum for f(x) = 2x on [2,4] is evaluated as n approaches infinity to give the integral from 2 to 4 of 2x dx, resulting in an area of 12 square units under the curve.

To find the Riemann sum for the function f(x) = 2x over the interval [2, 4], we start by dividing the interval into n equal subintervals, with each subinterval of width ∆x = (b - a) / n. For the right-hand endpoint, the kth point c at which f(x) is evaluated is given by c_k = a + k*∆x. Therefore, the Riemann sum is:

∑_{k=1}^{n}f(c_k)*∆x = ∑_{k=1}^{n}2(a + k*∆x)*∆x.

As n → ∞, the Riemann sum approaches the definite integral of the function. For the given function, the integral can be calculated directly, and the limit of the Riemann sum as n approaches infinity gives us the area under the curve, which in this case is equivalent to the area of a right triangle with base 2 and height 4.

Thus, we find that the area under the curve on the interval [2, 4] for f(x) = 2x is simply integral from 2 to 4 of 2x dx, which evaluates to 4^2 - 2^2, or 12 square units.

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The question is asking to solve a problem that'll "add up", or in other words, makes sense; through the use of Trigonometric functions. The leaning ladder is the hypotenuse of 17ft, adjacent to that is a wall that measures 16.5ft above the ground. The angle both sides make must be <=70°. The function here is Opposite over Hypotenuse i.e 16.5/17 . We use the inverse operation of Sin which is Sin^(-1) to find if the angle is < or = to 70°. Using a calculator, we find the angle to be 76.06°, which is > more than, 70°.

Thus, the ladder will not be safe for its height and therefore won't make sense.

Step-by-step explanation:

The letters of the word troposphere can be sorted to be:

ee h oo pp rr s t

with 7 distinct letters of which 4 are in pairs for a total of 11 letters.

The number of words that can be formed from n distinct letters

= n!/(1!1!1!....1!)   [n times in the denominator]

The number of words that can be formed from n letters of which 2 are duplicated and the rest distinct is

= n!/(2!1!1!....1!)     [n-1 times 1!]

Similarly, the number of words that can be formed from 11 letters, of which there are 4 pairs of duplicated letters is

N=11! / (2!2!2!2!1!1!1!)

= 39916800 / (2*2*2*2*1*1*1)

= 2494800

Answer:  The point is (-2, 7)

Step-by-step explanation:

If we have a function f(x) and we apply the transformation

[tex]y = f (x + h)[/tex] then ::

If [tex]h <0[/tex] the graph of f(x) moves horizontally h units to the right

If [tex]h> 0[/tex] the grace of f(x) moves horizontally h units to the left

In this case we have the function f(x) and the point (0,7) and the transformation [tex]y = f (x + 2)[/tex]

Then [tex]h = 2> 0[/tex]. Therefore the graph of f(x) moves 2 units towards the left.

Therefore the point (0,7) moves 2 units to the left and we have the point (-2, 7) in the transformed function

Answer: r=16tan theta sec theta

Step-by-step explanation:

I have this question on my test but all the answers are different except that one

The polar form of the parametric equation is option (A), r = 16 tan theta sec theta is the correct answer.

Polar form of a complex number is represented by a line whose length is the amplitude and by the phase angle. A polar form of a vector is denoted by  ( , ) , where represents the distance from the origin and represents the angle measured from the -axis.

Given the parametric equations x=4t and y=t².

Consider x= 4t

⇒ t = x/4

Now substitute  t in y equation,

[tex]y= (\frac{x}{4} )^2[/tex]

[tex]y=\frac{x^2}{16}[/tex]

We know that in polar form,

x= r cosθ and y= r sinθ

Now y becomes

r sinθ= [tex]\frac{r^2\cos^2\theta}{16}[/tex]

16 r sin θ = r² cos²θ

r = 16 sinθ/cos²θ

⇒r =16 tanθ secθ

Hence we can conclude that the polar form of the parametric equation is option (A), r = 16 tan theta sec theta is the correct answer.

Learn more about the polar form here:

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Answer:

C = 26.5g - 2

Step-by-step explanation:

We can plug in our given numbers for g and see if the C corresponds.

g = 7, C = 16.55

A) C = 2.65*7 --> C = 18.55

We know that C ≠ 18.55, so it should be B (I think you typed that one wrong, it is C = 2.65g - 2)

The equation C=2.65g could be used to determine the cost for purchasing g gallons of gasoline with the discount.

To determine the cost for purchasing g gallons of gasoline with the discount, we need to examine the given options. Option A states that the cost, C, equals 2.65g, which means the cost is directly proportional to the number of gallons. This could be a valid equation for determining the cost with the discount. However, option B states that the cost, C, equals 2.65g-12. This equation subtracts a constant value of 12, which is not mentioned in the problem, so it is not a valid way to determine the cost with the discount. Therefore, option A could be used to determine the cost for purchasing g gallons of gasoline with the discount.

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The ball hits the ground at 2.5sec

The answers aren’t all showing but neither of the top two showing are correct. Pick the answer that fits with the ball being in the air for 2.5sec.

Answer:

Required logarithmic function is :

[tex]f\left(x\right)=\log_3\left(x\right)[/tex]

Step-by-step explanation:

We have been fiven that table for the logarithmic function is:

x f(x)

9 2

27 3

81 4

which can be rewritten as:

x f(x)

3^2 2

3^3 3

3^4 4

Which are basically powers of 3

So we can use logarithmic function as

[tex]\log_3\left(9\right)=\log_3\left(3^2\right)=2\log_3\left(3\right)=2(1)=2[/tex]

Hence required logarithmic function is :

[tex]f\left(x\right)=\log_3\left(x\right)[/tex]

Answer:

$0.84

Step-by-step explanation:

The expected value of target A = 12% of $7

12% = [tex]\frac{12}{100}[/tex] = 0.12

expected value of A  = 0.12 × $7 = $0.84

Given that Peter contributes 20% of the total money and his part is $4.00, it is deduced that the total combined amount the five brothers have is $20.00.

To solve this, we can set up a simple proportion where 20% (or 0.20 in decimal form) of the total amount is equal to $4.00.

Step-by-Step Solution:

Let x represent the total combined amount of money that Peter and his brothers have.

Since Peter contributes 20% of the total, we can express this as 0.20 imes x = $4.00.

To find x, we divide both sides of the equation by 0.20, giving us x = $4.00 / 0.20.

By performing the division, we find that x = $20.00.

Therefore, the total combined amount Peter and his brothers have is $20.00.

This is an example of exponential growth. The population of this village triples every hundred years. Given the village was founded 400 years ago by 20 people, the current population would be 1620 people.

The given situation is an example of exponential growth, which can be found in various scenarios such as population growth. From the information provided, the population of the village triples every hundred years. Since the village was founded four hundred years ago and initially had 20 people, we can calculate the population today using the following steps:

So, the population of the village today would be 1620 people.

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The population of the village today is 720 people.

To find the population of the village today, we need to calculate the number of population doublings that have occurred over the four hundred year period.

Since the population triples every one hundred years, it doubles twice in that time frame.

Doubling a number is the same as multiplying it by 2.

So, the population at the start was 20, then it doubled to 40 after one hundred years, and doubled again to 80 after two hundred years.

Finally, it tripled to 240 after three hundred years, and tripled again to 720 after four hundred years.

Therefore, the population of the village today is 720 people.

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To work this out, you find out how many triangles can fit into the shape.

To do this, you take the number of sides and subtract it by 2.

So in a polygon with 11 sides, there are:

9 triangles          (11 - 2 = 9)

Remember, the total number of angles in one triangle is 180 degrees.

So to work out the total number of angles in a polygon, you multiply the number of triangles in it by 180.

So the total sum of interior angles in a polygon with 11 sides is:

180 x 9  = 1620 degrees          (180 degrees times number of triangles)

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

Answer:

1620 degrees

Answer:

85%

Step-by-step explanation:

If the sporting goods store received a lot of 80 baseball caps... and 12 of them were green that means that 68 (80-12) were NOT green.

Thus, the probably to randomly pick up a cap that is NOT green is 68 out of 80...

68/80 = 17/20 = 85%