Which inequality is true?
O A. 1 2 > 2
OB. 8 - T > 5
O C. 1071 > 30
O D. 1+4<7

The measures of the angles between the peaks are;

m∠BSC = 22.5°

m∠ASB = 67.5°

The reason for arriving at the above angles is as follows:

The known values are;

The location of the surveyor = Point S

The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC

The measure of angle m∠ASC = A right angle = 90°

Required:

To find m∠ASB and m∠BSC

From the given diagram, we have;

m∠ASC = 90°

m∠ASC = m∠ASB + m∠BSC (angle addition postulate)

m∠ASB = 3 × m∠BSC

∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC

m∠ASC = 4 × m∠BSC = 90°

m∠BSC = 90°/4 = 22.5°

m∠BSC = 22.5°

m∠ASB = 3 × m∠BSC

∴ m∠ASB = 3 × 22.5° = 67.5°

m∠ASB = 67.5°

Learn more about angle addition postulate here:

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Answer:

Graph C.

*See attachment below

Step-by-step explanation:

A graph that shows a set of ordered pairs representing a function would have each x-value being plotted against only one y-value. That is, every x-value must have exactly one y-value. Every x-value must not have more than 1 y-value being plotted against it.

The graph that shows this is the graph in option as shown in the attachment below.

Answer:

a) The rocket travels 200 meters horizontally.

b) The height of the rocket mid-flight is of 1000 meters.

Step-by-step explanation:

Height of the rocket:

The height of the rocket, in meters, after an horizontal distance of x, is given by:

[tex]y = 0.1x(200 - x)[/tex]

a) How far does the rocket travel horizontally?

This is x when [tex]y = 0[/tex]. So

[tex]0.1x(200 - x) = 0[/tex]

Then

[tex]0.1x = 0[/tex]

[tex]x = 0[/tex]

And

[tex]200 - x = 0[/tex]

[tex]x = 200[/tex]

So

The rocket travels 200 meters horizontally.

b How high does the rocket reach mid-flight?

This it the height y when x = 0, so:

[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]

The height of the rocket mid-flight is of 1000 meters.

the answer will be 0.092 as a decimal

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1[/tex]

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

[tex]\displaystyle y - y_1 = m( x - x_1)[/tex]

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

[tex]\displaystyle y - (4.8) = 0.1(x - 10)[/tex]

Simplify:

[tex]\displaystyle y = 0.1(x-10) + 4.8[/tex]

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

The initial volume is when t = 0. Evaluate:

[tex]\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8[/tex]

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

[tex]60 = 0.1(t - 10) + 4.8[/tex]

Subtract:

[tex]55.2 = 0.1(t - 10)[/tex]

Divide:

[tex]552 = t - 10[/tex]

Add. Therefore:

[tex]t = 562\text{ minutes}[/tex]

It will take 562 minutes for the tank to be completely filled.

Answer:

[tex]i)14 + 4 \sqrt{6} [/tex]

[tex]ii) \sqrt{10} + 28[/tex]

[tex]iii) 243[/tex]

Step-by-step explanation:

[tex]i)(2 \sqrt{3} + \sqrt{2} {)}^{2} [/tex]

➡️ [tex]12 + 4 \sqrt{6} + 2[/tex]

➡️ [tex]14 + 4 \sqrt{6} [/tex] ✅

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

[tex]ii)(3 \sqrt{5} - \sqrt{2} ) \times ( \sqrt{2} + 2 \sqrt{5} )[/tex]

➡️ [tex]3 \sqrt{10} + 30 - 2 - 2 \sqrt{10} [/tex]

➡️ [tex] \sqrt{10} + 28[/tex] ✅

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

[tex]iii)3 \sqrt{81} \times 3 \sqrt{9} [/tex]

➡️ [tex]3 \times 9 \times 3 \times 3[/tex]

➡️ [tex]243[/tex] ✅

Answer:

B: 30 and 60

Step-by-step explanation:

First, let's set up an equation. Since the two angles are complementary, we can write the equation like this:

2p + p = 90

Now, let's solve it!

2p + p = 90

Combine like terms:

3p = 90

Divide each side by 3 to isolate p:

3p/3 = 90/3

p = 30

Now that we know how many degrees one of our angles is, we can subtract that from 90 to get both of the complementary angles.

90 - 30 = 60

Therefore, the two angles that are complementary in this case are 30 and 60 degrees.

Answer:

proper fraction

Step-by-step explanation:

a proper fraction has smaller numerator than its denominatot.

Answer: Proper Fraction

Step-by-step explanation:

The denominator is equal or bigger than the numerator.

Must click thanks and mark brainliest

Answer:

3m = -3

Step-by-step explanation:

2m−6=8m

Subtract 2m from each side

2m−6-2m=8m-2m

-6 = 6m

Divide by 6

-6/6 = 6m/6

-1 = m

3m = 3(-1) = -3

2m - 6 = 8m

2m - 8m = 6

-6m = 6

m = -6/6

m = -1

Answer:

Hence the correct option is option c has a Binomial distribution with n=21 and p=50%.

Step-by-step explanation:

1)  

A coin is tossed 19 times,  

P(Head)=0.5  

P(Tail)=0.5  

We have to find the probability of a total number of heads in all the coin tosses equals 9.  

This can be solved using the binomial distribution. For binomial distribution,  

P(X=x)=C(n,x)px(1-p)n-x  

where n is the number of trials, x is the number of successes, p is the probability of success, C(n,x) is a number of ways of choosing x from n.  

P(X=9)=C(19,9)(0.5)9(0.5)10  

P(X=9)=0.1762  

2)  

A fair die is rolled twice.  

Total number of outcomes=36  

Possibilities of getting sum as 9  

S9={(3,6),(4,5)(5,4),(6,3)}  

The total number of spots showing in all the die rolls equals 9 =4/36=0.1111  

3)  

The event of getting a good number of spots on a die roll is actually no different from the event of heads on a coin toss since the probability of a good number of spots is 3/6 = 1/2, which is additionally the probability of heads. the entire number of heads altogether the tosses of the coin plus the entire number of times the die lands with a good number of spots has an equivalent distribution because the total number of heads in 19+2= 21 tosses of the coin. The distribution is binomial with n=21 and p=50%.

1m

2m

3m

4m

5m

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Answer:5

Step-by-step explanation:

On the first day he ate 5. Second day he ate 7. Then 9, 11, and finally 13. That all equals to 45. I don't know for sure though...

Answer:

Step-by-step explanation:

Each number increases by 3. Therefore, n+3.

the models aren't given..

Answer: no models given

Step-by-step explanation:

This requires finding the number of small sweaters the company made last week

Number of small sweaters the company produced last week is 372

Total sweaters made = 1,612

Let

Small sweaters = 3x

Medium sweaters = x

Large sweaters = 3(3x) = 9x

Total = small + medium + large

1,612 = 3x + x + 9x

1612 = 13x

Divide by 13

x = 1612/13

Medium sweaters = x = 124

Small sweaters = 3x

= 3(124)

= 372

Read more:

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Answer:

[tex]x ^{m - 3} \div x^{m - 4} \\ \frac{ {x}^{m - 3} }{ {x}^{m - 4} } \\ \frac{ {x}^{m - 3 - m + 4} }{x} \\ \frac{ {x}^{1} }{x} \\ x \: and \: x \: will \: cancel \: each \: other \: hence \: answer \: will \: be \: 1[/tex]

Answer:

It's a decimal, so it's around 6.771cm

Step-by-step explanation:

First, divide 144cm² by pi, or 3.14. Then find the square root of the answer, giving you the radius. The formula for the area of a circle is pi x radius squared, so to find out the radius you just use this formula in reverse.

If I messed up or didn't make my explanation clear, please comment.

Answer:

radius is [tex]\frac{12}{\sqrt{\pi } }[/tex] = 6.77 cm

Step-by-step explanation:

we know,

[tex]\pi[/tex] × r² = Area

⇒ [tex]\pi[/tex] × r² = 144

⇒ r² =[tex]\frac{144}{\pi}[/tex]

⇒ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

∴ r= [tex]\frac{12}{\sqrt{\pi } }[/tex]

pls mark this as the braniliest

9514 1404 393

Answer:

  is a polynomial

Step-by-step explanation:

The expression is a sum of products.

Each product involves a numerical value and a product of variables to positive integer powers.

These meet the requirements for an expression to be a polynomial, so ...

  the given expression is a polynomial

Answer:

Option C. √280

Step-by-step explanation:

From the question given above, the following data were obtained

MN = 19

ML = 9

LN =?

We can obtain the value of LN by using the pythagoras theory as illustrated:

M ² = ML² + LN²

19² = 9² + LN²

361 = 81 + LN²

Collect like terms

361 – 81 = LN²

280 = LN²

Take the square root of both side

LN = √280

Therefore, the length of LN is √280

Answer:

A: The distribution is skewed to the left.

Step-by-step explanation:

Skewness:

If the distribution has a long left tail, it is skewed to the left.

If it has a long right tail, it is skewed to the right.

Otherwise, it is approximately symmetrical.

In this question:

Lots of values on the start(left), few on the end(right), so it is skewed to the left, and the correct answer is given by option a.

Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.

Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(a - b) • (a - c) = 0

or

(a - b) • (b - c) = 0

or

(a - c) • (b - c) = 0

We have

a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)

a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)

b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)

Case 1: If (a - b) • (a - c) = 0, then

(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0   ==>   x = -6

which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (a - b) • (b - c) = 0, then

(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0   ==>   x = -2

which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (a - c) • (b - c) = 0, then

(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0

but the solutions to x here are non-real, so we throw out this case.

So there are two possible values of x that make a right triangle, x = -6 and x = -2.

Answer:

Reflection

Step-by-step explanation:

It is the opposite of the first,...

That's a question about quadratic function.

Any quadratic function can be represented by the following form:

[tex]\boxed{f(x)=ax^2+bx+c}[/tex]

Example:

[tex]f(x)= -3x^2-9x+57[/tex] is a function where [tex]a=-3[/tex], [tex]b=-9[/tex] and [tex]c=57[/tex].

Okay, in our problem, we need to find the value of x when [tex]f(x)=0[/tex]. That's mean that the result of our function is equal to zero. Therefore, we have the quadratic equation below:

[tex]x^2+4x-5=0[/tex]

To solve a quadratic equation, we use the Bhaskara's formula. Do you remember the value of a, b and c? They going to be important right now. This is the Bhaskara's formula:

[tex]\boxed{x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]

So, let's see the values of a, b and c in our equation and apply them in the Bhaskara's formula:

In [tex]x^2+4x-5=0[/tex] equation, [tex]a=1[/tex], [tex]b=4[/tex] and [tex]c=-5[/tex]. Let's replace those values:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-4\pm \sqrt{4^2-4\times1\times(-5)} }{2\cdot1}[/tex]

[tex]x=\frac{-4\pm \sqrt{16-(-20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{16 + 20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{36} }{2}[/tex]

[tex]x=\frac{-4\pm 6 }{2}[/tex]

From now, we have two possibilities:

To add:

[tex]x_1 = \frac{-4+6}{2} \\x_1=\frac{2}{2} \\x_1=1[/tex]

To subtract:

[tex]x_2=\frac{-4-6}{2} \\x_2=\frac{-10}{2} \\x_2=-5[/tex]

Therefore, the result of our problem is: [tex]x_1 = 1[/tex] and [tex]x_2=-5[/tex].

I hope I've helped. ^^

Enjoy your studies.  \o/

Answer:

Slope = 5

Step-by-step explanation:

To find the slope of a line perpendicular to a given line, take the opposite reciprocal of the given line's slope.

Ex. -1/5 ⇒ 5

Opposite = opposite sign (- ⇒ +)

Reciprocal = numerator and denominator flipped (1/5 ⇒ 5/1 = 5)

Answer:

Not very sure what you mean,

But in the provided set, 8 is the greatest number, and 1 is the smallest.

Hope this helps!!

Answer:

Quadratic

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

for every one unit increase in x, there is a 3 unit increase in y

The slope of the plot line would be 3

The y intercept of the plot line would be -1

y = 3x - 1

13x - 4[x + (3 - x)] =

= 13x - 4(x + 3 - x) =

= 13x - 4 · 3 = 13x - 12

C.

Answer:

13x -12

Step-by-step explanation:

13 x - 4[ x + (3 - x )].

Combine like terms inside the brackets

13 x - 4[ 3 -0x]

13x - 4[3]

Multiply

13x -12

use x^2 when x=0 because the restriction for it is "use x if x is less than or equal to 1"

when x = 0, (0)^2 will make f(x) = 0

the graph of f(x) will just be a dot at 0