suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is pi/3. what is the length of the third side of the triangle

Answers

Answer 1

Apply cosine rule:

c²=b²+a²-2ba cosC

C= pi/3 = 180/3 = 60 degrees
cosine 60 deg = 0.5
c²=2²+3²-[2×2×3×0.5]
c²=7
c=√7
c=2.645 ;length of third side of angle

Answer 2

The length of the third side of the triangle will be 2.65 units.

What is law of cosine?

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:

a² + b² – 2ab cos(C) = c²

A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.

Then the length of the third side of the triangle will be

c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)

c² = 4 + 9 – 12 x (1/2)

c² = 13 – 6

c² = 7

c = √7

c = 2.65 units

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Related Questions

D^2+d-30/d^2+3d-40 + d^2+14d+48/d^2-2d-48
A. D^2+14d+16/(d+8)(d-8)
B. 2d^2+14d+16/(d+8)(d-8)
C.2d^2+15d+18/2d^2+d-88
D.2d^2+15d+18/(d+8)(d-8)

Answers

I think D.2d^2+15d+18/(d+8)(d-8)

Answer: option B.

   2d^2 + 14d + 16
----------------------------
        (d+8)(d-8)

Explanation:

The question is:

[tex] \frac{d^2+d-30}{d^2+3d-40} + \frac{d^2+14d+48}{d^2-2d-48} [/tex]

1) Start factoring all the polynomials to rewrite the fractions.

2) d^2 + d - 30 = (d + 6)(d - 6)

3) d^2 + 3d - 40 = (d + 8)(d - 5)

4) d^2 + 14d + 48 = (d + 6) (d + 8)

5) d^2 - 2d - 48 = (d - 8)(d + 6)

6) rewrite the fractions:

(d+6)(d-5)         (d+8)(d+6)
----------------- + -----------------
(d+8)(d-5)          (d-8)(d+6)

7) simplify the fractions cancelling the factors that are equal in the numerator and the denominator:

d+6     d+8
-------- + -------
d+8       d-8

8) take least common denominatior: (d+8)(d-8), and sum the fractions:

   (d-8)(d+6) + (d+8)^2
--------------------------------
        (d+8)(d-8)

9) expand the parenthesis in the numerator and combine like terms:

d^2 - 2d - 48 + d^2 + 16d + 64
------------------------------------------- =
               (d+8)(d-8)

        2d^2 + 14d + 16
=   ----------------------------
            (d+8)(d-8)

And that is the option B.

how to do midpoint and distance formula

Answers

The Distance Formula= you have to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) and use the formula d (x2 x1) 2 (y2 y1) The Midpoint Formula= you have to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) and use the formula , . y1 , y2 2 x1 , x2 2
hopes this helped

Final answer:

The midpoint formula calculates the center point between two points on a coordinate plane, while the distance formula calculates the distance between two points using the Pythagorean theorem.

Explanation:

Understanding the Midpoint and Distance Formulas

The midpoint formula is used to find the exact center point between two defined points on a coordinate plane. To find the midpoint (M) between two points, (X1, Y1) and (X2, Y2), you use the formula:

M = ((X1 + X2) / 2, (Y1 + Y2) / 2)

For example, to find the midpoint between the points (2, 3) and (4, 8), you would calculate:

M = ((2 + 4) / 2, (3 + 8) / 2) = (3, 5.5)

The midpoint between these points is at coordinates (3, 5.5).

The distance formula, on the other hand, is used to determine the distance between two points on a coordinate plane.

The formula is derived from the Pythagorean theorem and is written as:

D = $√((X2 - X1)^2 + (Y2 - Y1)^2)$

Using the above points, the distance (D) would be:

D = $√((4 - 2)^2 + (8 - 3)^2)√ = \(√(4+25) = \(√29$√

The distance between the two points is the square root of 29.

Practicing these formulas enhances your problem-solving skills and helps in many areas of mathematics, including geometry and algebra.

Can someone help quickly plz

Answers

we have that

using a graph tool
see the attached figure

the answer is the first option
y<=3x
y>-2x-1

ava pours 3 gallons of paint equally into 5 cans

Answers

Ok what is the question

Each can will have 3/5 gallon of paint.

The accountant at patton company has determined that income before income taxes amounted to $11,000 using the fifo costing assumption. if the income tax rate is 30% and the amount of income taxes paid would be $600 greater if the lifo assumption were used, what would be the amount of income before taxes under the lifo assumption? $11,600 $13,000 $9,000 $10,400

Answers

Given:
Income before income taxes under fifo costing : $11,000
Income tax rate: 30%
Income tax paid under lifo costing: $600

Amount of income before taxes under lifo method is $13,000

600 / 30% = 2,000
2000 + 11,000 = 13,000

FIFO means first-in; first-out. LIFO means Last-in,First-out. These methods are used in accounting for inventories. It affects the amount that reflects on the cost of goods sold portion of the income statement. FIFO costing is used to maximize income values in Financial statements while LIFO costing is used for tax accounting purposes to minimize tax obligations.

in a sentence,describe the relevant angle relationship in the diagram. that is,descr

Answers

5x+3x=90+30
8x=120
(1/8) (8x) = (1/8) (120)
x=15

m<JAH= 3(15)=45
m<HAG= 5(15)=75

and the first one is
<KAE and <EAF are adjacent angles whose measurements are equal to
<KAF; <KAF and <JAG are vertical angles and are of equal measurement.

A football stadium holds 52,000 fans. A college student is doing research and determines that on any given game day, the home team has five times as many fans as the visiting team. In order to help the student in his research, he represents the number of home team tickets as H and the visiting team’s tickets as V.

Answers

You probably are interested in setting up system of equations to find the number of fans for Home Team and Visiting Team.

Based on this data, we can find the number of number of fans of each team.

Following data has been provided:

1) Total number of fans stadium can hold = 52000
So on a given day if stadium is full,
H + V = 52000

2) Home team has 5 times as many fans as the visiting team.
So,
H = 5V

Using the value of H in first equation, we get:

5V + V = 52000
6V = 52000
V = 8667 fans

H + V = 52000
⇒
H = 52000 - V = 52000 - 8667 = 43333 fans

So,
there will be 43,333 fans of home team and 8667 fans of visiting team.

Plzz plzzzzz help !!

Answers

The answer is (B&C) hope it helps and have a great day!

In a normal distribution, most numbers in the data set fall within one standard deviation of the mean. True or False

Answers

Answer:

True

Step-by-step explanation:

A hypothesis test has a significance level of 10%. Explain what this significance level represents.

Answers

1.)A significance level of 10% means that there is a 10% probability of rejecting the null hypothesis incorrectly.
2.) the significance level determines the critical region of the hypothesis test

Answer:

A significance level of 10% i.e.0.10 represents the chance of rejecting the null hypothesis

Step-by-step explanation:

Given :A hypothesis test has a significance level of 10%.

To Find :Explain what this significance level represents.

Solution :

Definition : The significance level is the probability of rejecting the null hypothesis when it is true.

So, significance level = 10%.

This means there is a 0.10 chance of rejecting the null hypothesis

Hence a significance level of 10% i.e.0.10 represents the chance of rejecting the null hypothesis

Point T' has coordinates (-3, 4). If it was translated up 3 units, what were the coordinates of its pre-image?

(0, 4)
(-3, 7)
(-3, 1)
(-6, 4)

Answers

Translation refers to a rigid motion or transformation where you move an object from one location to another.
Translations are base on the rule (x,y) -- (x+a, y+b) where the words right and left represent the change in the x-axis, and the words up and down the change in the y-axis.

In this exercise it is asked you to find the coordinates of the preimage of point T', which has the coordinates (-3,4) and is the effect of a translation of 3 units up. As previous said, the words up and down represent a change on the y-axis, meaning that the y-coordinate is the one that should be changed.

If the translation from the preimage to the image was 3 units up, then the preimage can be found by subtracting three units.
Pre-image: (-3,4-3)= (-3,1)

The point that represents the coordinates of the pre-image is (-3,1).

Answer: the answer is (-3, 1)

yes I know I am late :)

What rigid transformation would map ABC to EDC?

Answers

I believe it would be a rotation around line c, the last option

Answer: D is the answer

Step-by-step explanation:

A rectangular window is 1 meter high and 2 meters wide. What is the perimeter of the window in meters? What is it in centimeters?

Answers

The perimeter is the total length of all sides of the shape.

It is 1 meter + 1 meter + 2 meter + 2 meter = 6 meters

1 meter = 100 centimeter

6(100) = 600 centimeter

Hope this helps! :)

A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 89 feet from a building and 115 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.

Answers

The distance to the top of the building above the range finder can be found from the Pythagorean theorem.
.. d = √(115² -89²) ≈ 72.8 . . . . feet

Adding the height of the range finder, we find the height of the building to be
.. h = d+3 = 75.8 ft

Solve the inequalities by graphing. Select the correct graph. y > x y < -x

Answers

my answer is x y because as the simulation show here y>x y <-× and because we are taking a way the x in this problem here I am assuming that the yas well have to be taking out as well for for the fact that is one we are subtracting from the x so we stay with x y it show you in the example y> / yx /<-x

The solution to the system of inequalities y > x and y < -x is a V-shaped region in the second and fourth quadrants of the coordinate plane.

Graph attached.

To solve the system of inequalities graphically, you need to shade the regions on the coordinate plane that satisfy both inequalities.

The first inequality is y > x. This means that all points above the line y = x satisfy this inequality.

The second inequality is y < -x. This means that all points below the line y = -x satisfy this inequality.

Now, let's graph both lines and shade the regions that satisfy both inequalities:

Graph the line y = x. This is a straight line with a slope of 1 that passes through the origin (0,0) and goes up and to the right.

Graph the line y = -x. This is also a straight line with a slope of -1 that passes through the origin (0,0) and goes down and to the right.

Graph attached.

The shaded region that satisfies both inequalities is the area between these two lines, below y = -x, and above y = x.

It forms a V-shaped region in the second and fourth quadrants of the coordinate plane.

Therefore, the correct graph should show the shaded V-shaped region that represents the solution to the system of inequalities.

Graph attached.

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How do you write 5.82 × 10^3 in standard form?

Answers

5.82 × 10^3

Because of the 10 to the power of 3, you are able to move the decimal point to get to standard form.

If the exponent is positive, move the decimal point to the right. If it's negative, move it the left.

Here, the 3 is positive, so we'll be moving the decimal in 5.82 three times to the right.

One space to the right would change it to be 58.2 * 10^2.
Two spaces would be 582 * 10.
Three spaces would be 5820.

The standard form of 5.82 × 10^3 is 5820.

What is the least common denominator of the equation 2/9x+2/3x=7

Answers

You are not asked to solve it.
9x = 3 * 3 * x
3x = 3 * x

The common denominator has two 3s and one x
Least common denominator = 3*3* x = 9x <<<< answer.

the least common denominator is 9

△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) . Which reflection results in the transformation of △ABC to △A′B′C′ ?

Answers

the vertices of the preimage and final image are as follows
A(−7, 1) ---> A′(−7, −1)
B(−5, −3) ---> B′(−5, 3)
C(−3, 2) ---> C′(−3, −2)
it can be noted that whilst the x coordinates remain the same in the final image, y coordinate values, the sign changes.
eg: A (x = -7) and A' (x = -7)
therefore x coordinates haven't changed the value nor sign
A (y = 1) and A' (y = -1)
y coordinates have been multiplied by -1 hence changing the sign.
the reflection goes as (x,y) = (x,-y)
this is a reflection over the x axis.

what is 9/10 take away 6 tenths

Answers

Hello!

If you were taking 6 away from [tex] \frac{9}{10} [/tex], you would get [tex] \frac{3}{10} [/tex]. Different from tenths, only in decimals.

Enjoy.
~Isabella

the answer is 3/10 because since they are both tenths its like doing 9 - 6

How long will it take for 2 g of a sample of iodine-131, which has a half-life of about 8 days, to decay to 0.04 g?

Answers

we know that

This problem can be represented through the following equation

A = A₀(1/2)^t/h
where
A-----------> is the amount of substance left after time t
A₀ ----------> is the original amount---------> 2 g
h-------------> is the half-life-----------> 8 days

for A=0.04 g
t=?
0.04 = 2(1/2)^t/8
0.02 = (1/2)^t/8
Take ln on both sides:
ln(0.02) = ln [(1/2)^t/8]
ln(0.02) = (t/8)(ln 1/2)
t = 8*ln(0.02)/ln(1/2)
t = 45.15 days

the answer is 45.15 days

I have created a triangular garden such that the largest side is 8m less than twice the smallest and the medium side is 12m larger than the smallest side. If the total perimeter of the garden is 104m, what are the lengths of the three sides?

Answers

The smallest side is 25 m, the medium side is 37 m, and the largest side is 42 m.

pete's pools installs rectangular pools that are all 10 feet wide. the length can vary from 10 feet to 30 feet. the company installed a pool with a perimeter of 76 feet. what was the length of the pool ?

Answers

the length is 28 because 76 -10x2 is 56 divided by 2 is 28

The length of pool is 28 feet.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Given rectangular pool

width of pool is 10 feet,

and length is between 10 to 30 feet

perimeter of pool = 76 feet

perimeter = p = 2(l + b)

where l = length and b = breadth/width

76 = 2(l + 10)

l + 10 = 38

l = 38 - 10

l = 28 feet

Hence length of pool is 28 feet.

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a magazine contains fourteen pages. You open to a random page, the page number is three or seven..... where do i start i need to show work

Answers

This is a question of randomness so there really is no answer. I would guess 7 since that is the center page and you're more likely to open it up in or near the middle

The possibility to open to page seven is 75% percent. The possibility of opening to page 3 is about 25%
Our human body will order us to open to the middle page without us realizing unless we are looking and know which random page we want.
Due to the lack of information of the questions there is not much be said or to answer in any case.

Eric and his work crew have 50 trees to plant. In 8 hours today, they planted 40 trees. If they work at the same rate tomorrow, how long will it take to finish planting the trees? 2 hours

Answers

Answer: 2 hours

Explanation:

1) Determine how many trees they will have to plant tomorrow.

That is: 50 - 40 = 10 trees.

2) Determine the rate of planting:

40 trees / 8 hours

3) Set the ratio for the 10 trees:

10 trees / x

4) Set the proportion:

10 trees / x = 40 trees / 8 hours

5) Solve for x:

x = 10 tress * 8 hours / 40 trees = 2 hours

Answer:

a.) 2 hours to finish planting trees

Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (100, 120, 1206). the positive x-axis points east and the positive y-axis points north. (a) if you walk due south, will you start to ascend or descend?

Answers

Answer: You start to ascend

Explanation:

Since you are walking due south and the positive y-axis points north, the y-coordinate decreases.

Let

[tex]y'[/tex] = y-coordinate after walking due south
[tex]z'[/tex] = z-coordinate (or the height) after walking due south

So, the point where you stand after walking due south has a coordinate of [tex](100, y', z')[/tex]. Moreover,

[tex]z' = 1,400 - 0.05(100)^2 - 0.01(y')^2 \\ \boxed{z' = 1350 - 0.01(y')^2}[/tex]

Since the y-coordinate decreases after walking due south and [tex]z' = 1350 - 0.01(y')^2[/tex],

[tex] y' \leq 120\\ \Rightarrow (y')^2 \leq 120^2 = 14,400\\ \Rightarrow -0.01(y')^2 \geq -0.01(14,400) = -144\\ \Rightarrow z' = 1,350 - 0.01(y')^2 \geq 1,350 - 0.01(14,400) = 1,206\\ \Rightarrow \boxed{z' \geq 1,206}[/tex]

So, the height after walking due south exceeds 1,206 meters, which is the previous height before walking due south. Therefore, if you walk due south from point with coordinates (100, 120, 1206), you are ascending.

If walking due south from the point (100, 120, 1206) will cause you to descend, as the slope of the hill in the southward direction is negative.

To determine whether you will ascend or descend when walking due south from the point (100, 120, 1206), we need to consider the slope of the hill in the southward direction, which corresponds to the negative y-direction.

Given the equation of the hill's shape: [tex]\[ z = 1400 - 0.005x^2 - 0.01y^2 \][/tex]

We can find the slope in the y-direction (southward) by taking the partial derivative of z with respect to y:

[tex]\[ \frac{\partial z}{\partial y} = -2 \cdot 0.01 \cdot y \][/tex]

Evaluating this derivative at the point (100, 120, 1206) gives us the slope in the y-direction at that point:

[tex]\[ \frac{\partial z}{\partial y}\Bigg|_{(100, 120, 1206)} = -2 \cdot 0.01 \cdot 120 = -2.4 \][/tex]

Since the slope is negative, this means that as you move in the positive y-direction (northward), the height z decreases. Conversely, moving in the negative y-direction (southward) will also result in a decrease in height z, because the slope is linear and does not change direction.

Therefore, walking due south from the point (100, 120, 1206) will cause you to descend, as the slope of the hill in the southward direction is negative.

Econometrics answers using the ols estimates shown in the table below, compare the estimated effects of a 13 % increase in average district income on test scores in california and massachusetts.

Answers

Please Send Lions, Monkeys, Cats And Zebras Into Lovely Hot Countries
Signed General Penguin
P - potassium
S - sodium
L - lithium
M - magnesium
C - calcium
A - aluminium
Z - zinc
I - iron
L - lead
H - hydrogen
C - copper
S - silver
G - gold
P - platinum

Graph each quadrilateral ABCD. Then determine the most precise name for it.
A(3, -2). B(5,4). C(3,6). D(1,4).

Answers

This quadrilateral is 'deltoid'. All the details are in the picture.

if the height of a rectangular prism is doubled then the surface area of the prism is and I need work to PLEASE HELP ME

Answers

The surface area of a rectangular prism (S) is given in terms of length L, width W, and height H by
.. S = 2(LW +H(L +W))

If you double the height, now you have new surface area S'
.. S' = 2(LW +2H(L +W)) = 2(LW +H(L +W)) +2H(L +W)
.. = S +2H(L +W)

This is larger than the original surface area S, but is not as much as 2S.

Selection C is appropriate.

True: If it is a function
False: If it is not a function

{(2, 3), (4, 5), (4, 3), (3, 4)}

Answers

Answer: false.

Explanation:

The given relation does not fit the definition of function.

A function is a relationship that states unambigously the image (output) of the input (independent) variable.

In the set of ordered pairs it is true form the input-values 2, and 3, because their images are 3 and 4, respectively.

But, could you tell the image of 4?. It may be 5 or 3. That is an ambiguity. That is why the given relationship is not a function.

A function is defined as a set of ordered pairs no two of which have the same first values or first component.

This means if more than one ordered pairs will have the same first component, the relation will not be a function.

In the given relation, the first component of 2nd and 3rd ordered pair is the same, so the relation {(2, 3), (4, 5), (4, 3), (3, 4)} is not a function.

So the Answer is False.

thank youuuuuuuuuuuuuu

Answers

the perimeter, as you already know, is the sum of all the sides.

14)

[tex]\bf (x+3)+(2x+4)+(y)=\stackrel{perimeter}{6x}\implies 3x+7+y=6x \\\\\\ 7+y=3x\implies y=3x-1[/tex]

15)

a rectangle has twin widths and twin lengths, therefore

[tex]\bf \stackrel{width}{(3x-3)}+\stackrel{width}{(3x-3)}+\stackrel{length}{(y)}+\stackrel{length}{(y)}=\stackrel{perimeter}{10x+6} \\\\\\ 6x-6+2y=10x+6\implies -6+2y=4x+6\implies 2y=4x+12 \\\\\\ y=\cfrac{4x+12}{2}\implies y=\cfrac{4x}{2}+\cfrac{12}{2}\implies y=2x+6[/tex]

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