Which ordered pair solves this linear system?
Y= -x
Y= 2x

You found the correct slope for Line 1, but Line 2 has a slope of (3 - 2)/(6-3) = 1/3.

If 2 lines are parallel, their slopes are the same; perpendicular and their slopes are opposite reciprocals (change the sign of the first slope, then divide 1 by it and you get the perpendicular line's slope). 1/3 is NOT the opposite reciprocal of 3 (because they have the same sign) and 1/3 is NOT equal to 3, so that makes the answer neither.

The slope for Line 3 is (3 - 1)/(1 - (-1)) = 2/2 = 1

The slope of Line 4 is (1 - (-1))/(4 - 2) = 2/2 = 1

1 = 1, so these lines are parallel

Answer:

(4+7)/2 = 5.5 - median

6- mean

9- range

2,4,7,11 assending order

11,7,4,2 decending order

Step-by-step explanation:

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Answer: 3.65 M

Step-by-step explanation:

14.6/4 = 3.65

Answer: Answer is 27.

Step-by-step explanation: -5 squared is 25 plus 2 is 27.

Answer:

27

Step-by-step explanation:

-x^2+2

Substitute the x for a 5

-5^2+2

-5^2=25

25+2=27

The answer is 27

Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

Answer:

0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

Step-by-step explanation:

For each 3-pointer shot, there are only two possible outcomes. Either the player makes it, or the player does not. The same is valid for free throws. This means that both the number of 3-pointers and free throws made are given by binomial distributions.

Since 3-pointers and free throws are independent, first we find the probability of making exactly 3 3-pointers out of 10, then the probability of making exactly 5 free throws out of 10, and then the probability that the player will make exactly 3 3-pointers and 5-free throws is the multiplication of these probabilities.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Probability of making 3 3-pointers out of 10:

The chances of a basketball player hitting a 3-pointer shot is 0.4, which means that \(p = 0.4\). So this is \(P(X = 3)\) when \(n = 10\).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.21499\)

Probability of making 5 free throws out of 10:

The probability of hitting a free-throw is 0.65, which means that \(p = 0.65\). The probability is \(P(X = 5)\) when \(n = 10\).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{10,5}.(0.65)^{5}.(0.35)^{5} = 0.15357\)

Calculate the probability that the player will make exactly 3 3-pointers and 5-free throws.

0.21499*0.15537 = 0.0334

0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

Answer:

1st Question is ice

2nd Question is plant and animal remains

Step-by-step explanation:

Edg. 2020

Answer:

What natural element is one of the best preservers of prehistoric life?  

✔ ice

What clues in fossils help scientists identify different ice ages?  

✔ plant and animal remains

Step-by-step explanation:

edge

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

(x+1/2)^2=289/4

Step-by-step explanation:

Got it right on khan

Answer:

The answer is below

Step-by-step explanation:

1) A triangle is a polygon with three sides and three angles. There are different types of triangles such as obtuse, scalene, right angle, equilateral and isosceles triangle.

Given that triangle ABC is right angled and AC = 25 cm = hypotenuse and BC = 15 cm. Using Pythagoras:

AC² = BC² + AB²

25² = AB² + 15²

AB² = 25² - 15²

AB² = 400

AB = √400

AB = 20 cm

Using sine rule:

\(\frac{sin(B)}{AC}=\frac{sin(A)}{BC}=\frac{sin(C)}{AB}\\\\But\ \angle B= 90^o(right\ angle)\ hence:\\\\ \frac{sin(B)}{AC}=\frac{sin(A)}{BC}\\\\\frac{sin(90)}{25}=\frac{sin(A)}{15}\\\\sin(A)=\frac{sin(90)}{25}*15\\\\sin(A)=0.6\\\\A=sin^{-1}(0.6)\\\\A=36.87^o\)

2)

Using Pythagoras:

hypotenuse² = 8² + 6²

hypotenuse² = 100

hypotenuse = √100

hypotenuse = 10

Using sine rule:

\(\frac{sin(x)}{8}=\frac{sin(90)}{10}\\\\sin(x)=\frac{sin(90)}{10}*8\\\\sin(x)=0.8\\\\x=sin^{-1}(0.8)\\\\x=53.13 ^o\)

Answer:

Step-by-step explanation:

We can say that 28 is 1/1
or to make the denominator same we can say its 7 / 7

So, 4/7 of 28 is 16
4 x 28 = 16
7

We can add 16 to 28 to find out the answer
Thus, 28 + 16 = 44

Therefore, 4/7 of 44 is 28

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

Answer:

7/11

Step-by-step explanation:

Total students (14+8) = 22

Boys = 14

Probability for boys,

= 14/22

= 7/11

I'm not sure. Hope, this is correct.

Answer:

\(\frac{13}{33}\)

Step-by-step explanation:

14 + 8 = 22

14/22

22 - 1 = 21

14 - 1 = 13

The next time there are 21 students and 13 boys.

13/21

14/22 × 13/21

13/33

angle 98 and angle 9b - 8 are supplementary angles, therefore:

98 + (9b-8) = 180

Solving for b:

98 + 9b - 8 = 180

90

The area of the region bounded by the curve \(r = {e}^{x} \) and the specified sector is 1/4 \((e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )\).

What is area?

Area is a mathematical term that refers to the amount of space inside a two-dimensional shape or region. It is a measure of the extent or size of a surface or a planar region. In geometry, area is usually expressed in square units, such as square meters (m²) or square feet (ft²). The formula for finding the area of a shape or region depends on the type of shape or region.

The given curve is \(r = e^x\), which is a polar equation for an exponential curve in the polar coordinate system.

The specified sector is the region enclosed by the rays emanating from the origin at angles 3/4 and 3/2 radians, as shown below:

To find the area of this region, we need to integrate the area element dA over the given sector,\(dA = \frac{1}{2} r^2 dθ\) where θ varies from 3/4 to 3/2, and \(r = e^x\)

.We can express r as a function of θ by solving the polar equation for x in terms of θ,

\(r = e^x \\ x = ln(r) \\ r = e^{(ln(r))} \\ r = r\)

Therefore,

\(r = e^{ln(r)} = e^{(θ)}\)

Substituting this into the area element,

\(dA = \frac{1}{2} (e^{(2θ)}) dθ\)

Integrating this from θ = 3/4 to θ = 3/2, we get,

\(A = \int( \frac{3}{2} )( \frac{3}{4} ) \frac{1}{2} (e^{(2θ)}) dθ \\ =[ \frac{1}{4} (e^{(2θ)}]( \frac{3}{4} )^{( \frac{3}{4} )} \\ = \frac{1}{4} (e^{ \frac{3}{2} } - e^{ \frac{3}{4} }\)

Therefore, the area of the region bounded by the curve \(r = e^x\) and the specified sector is 1/4 \((e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )\).

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Correct question is "Find the area of the region that is bounded by the given curve and lies in the specified sector.

r = e^x, 3/4 ≤ x ≤ 3/2."

Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

What is Sine rule of triangle?

By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Where, a, b, c are sides of a triangle.

Given that;

Measure of ∠A = 27°

Measure of ∠B = 76°

Since, Sum of all angles of triangle = 180°

Hence,

∠A +  ∠B +  ∠C = 180°

27° + 76° + ∠C = 180°

∠C = 180° - 103°

∠C = 77°

So, Measure of ∠C = 77°

Since, By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Since, sin A = sin 27° = 0.95

sin B = sin 76° = 0.566

sin C = sin 77° = 0.99

Hence,

0.95 / a = 0.566 / b = 0.99 / c = 1 / k

Taking terms as;

0.95 / a = 1 / k

a = 0.95 k

And, 0.566 / b = 1 / k

b = 0.566 k

And, 0.99 / c = 1 / k

c = 0.99 k

Hence, Sides of triangles are;

a : b : c = 0.95 k : 0.566 k : 0.99 k

a : b : c = 0.95 : 0.566 : 0.99

Thus, Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

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14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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The length of the hypotenuse of the triangle is b = x√2 units

Given data ,

Let the triangle be represented as ΔABC

And , the triangle is a 45 - 45 - 90 triangle

So , the two legs are congruent to one another and the non-right angles are both equal to 45 degrees

And , the sides are in the proportion x : x : x√2

Now , the length of the sides of the triangle are

The measure of base BC = a units = x

The measure of height AB = c units = x

So , the measure of the hypotenuse of the triangle is = x√2 units

Hence , the triangle is solved and hypotenuse AC = x√2 units

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Ratios

Note A has a frequency of

fa=1,760 Hz

Note D has a period of 1,175 hertz

(the previous data should be frequency, not period)

We are required to find the ratio of A to D. Let's call it r:

Dividing: r = 1.4978. Rounding to two decimal places:

r = 1.50

Now to express the answer in integer ratio form, we need to simplify the fraction.

First, we divide by 5 up and down:

There are no more common divisors for both numbers, thus the integer ratio form is r = 352/235

Answer:

Your answer is correct

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

To raise a power to another power, multiply the exponents.

Multiply 6 by 2.

The correct option is the third.

Answer:

210m

Step-by-step explanation:

60+60+45+45

120+90

210m

Answer:

n=10

a10= - 3 (2)^(10-1)= -3(2)^9

= -1536

Answer:

Step-by-step explanation:

1) Find the Mean of all the numbers.

3+4+5+7+10+12+15=56

56/7=8 mean is 8

Now We Calculate Standard Deviation:

S=\(\sqrt{(3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2}\)

You take each number from the problem i.e 3,4,5...

and then you subtract the mean from it and then square it.

S=\(\sqrt{(-5)^2+(-4)^2+(-3)^2+(-1)^2+(2)^2+(4)^2+(7)^2}\)

S=\(\sqrt{25+16+9+1+4+16+49}\)

S=\(\sqrt{120}\)

S=\(\sqrt{120}/7\)

7 is the amount of data units given in the problem.

120/7=17.1428571429

\(\sqrt{17.1428571429}\) =4.1403933560541

Nearest hundredth=4.14

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer: - 40

Explanation:

The first step is to determine if there is a common difference between the terms. We would subtract the first term from the second,the second from the third and compare the difference

- 12 - - 5 = - 12 + 5 = - 7

- 19 - - 12 = - 19 + 12 = - 7

Thus, there is a common difference of - 7

Thus, the term after - 33 is

- 33 + - 7

= - 33 - 7