Hunter wants to draw an obtuse equilateral triangle, but hes's having trouble drawing it. Is sush a triangle possible to draw? Explain your reasoning.

Statement/Reason is a method of presenting your logical thought process as you go from the "givens" in a problem statement to the desired conclusion. Each statement expresses the next step in the solution process. It is accompanied by the reason why it is true or applicable.

For example, if you have an equation that says ...

... x + 3 = 5

Your next "statement" might be

... x + 3 - 3 = 5 - 3

The "reason" you can make that statement is that the addition property of equality allows you to add the same quantity to both sides of an equation without violating the truth of the equality. You know this because you have studied the properties of equality and how they relate to the solution of equations.

In geometry (where you're more likely to encounter statement/reason questions), you know the statements you're allowed to make because you have studied the appropriate postulates and theorems. The "reason" is generally just the name of the applicable postulate or theorem. The "statement" is the result of applying it to your particular problem.

For example, if you have ∠ABC and ∠CBD, you might want to say (as part of some problem solution) ...

... m∠ABC + m∠CBD = m∠ABD

The reason you can say this is the angle addition postulate, which you have studied. It will tell you that the measures of non-overlapping angles with a common side and vertex can be added to give the measure of the angle that includes them both. (Many such postulates seem obvious, as this one does.)

_____

Side comment on geometric proofs

As you go along in geometry, you study and develop more and more theorems that you can use to find solutions to problems. Sometimes, you're required to use a restricted subset of the ones you know in order to prove others.

As an example, in some problems, you may be able to use the fact that the midline of a triangle is parallel to the base; in other problems, you may be required to prove that fact.

I sometimes found it difficult to tell which theorems I was allowed to use for any given problem. It may help to keep a list that you can refer to from time to time. Your list would tell you the name of the theorem, axiom, or postulate, and what the meaning of it is, and where it might be applied.

_____

Which reason fits which statement?

The "reason" is telling how you know you can make the statement you made. It is anwering the question, "what allows you to make that statement?"

How do I form true statements?

The sequence of statements you want to make comes from your understanding of the problem-solving process and the strategy for solution you develop when you analyze the problem.

Your selection of statements is informed by your knowedge of the properties of numbers, order of operations, equality, inequality, powers/roots, functions, and geometric relationships. You study these things in order to become familiar with the applicable rules and properties and relationships.

A "true" statement will be one that a) gets you closer to a solution, and b) is informed by and respects the appropriate properties of algebraic and geometric relations.

In short, you're expected to remember and be able to use all of what you have studied in math—from the earliest grades to the present. Sometimes, this can be aided by remembering a general rule that can be applied different ways in specific cases. (For me, in Algebra, such a rule is "Keep the equal sign sacred. Whatever you do to one side of an equation, you must also do to the other side.")

Answer:

a. $0.07

Step-by-step explanation:

Profit = Charge -Cost

We want to make a profit of 25 and the cost is 10

25 = Charge -10

Add 10 to each side

25+10 = Charge -10+10

35 = Charge

We need to charge 35 per jar.

Each jar contains 500 marbles

The cost per marble is Cost/ number of marbles

cost per marbles = $35 / 500

                             = $.07

Answer:

Option A : $0.07

Step-by-step explanation:

Given :

A school purchases jars of marbles.

Each jar contains 500 pieces of marbles.

Each jar costs $10.

To Find : How much does the school have to charge for each piece of marbles to make a profit of $25 per  jar?

Solution :

Cost of one jar is $10

Now, school wants to make profit of $25 on each jar .

using formula : Profit = Charge - cost

⇒$25 = charge - $10

⇒$35 = charge

Thus school should charge one jar of marbles of $35.

Since each jar contains 500 marbles.

So,to calculate cost of each marble when charge of jar is $35.

Cost of 500 marbles is $35

Cost of 1 marble = 35/500 = $0.07

cost of each marble when charge of jar is $35 is $0.07

Hence , the school have to charge $0.07 for each piece of marble to make a profit of $25 per  jar.

Option A is correct

Answer:

5√2 cm or 7.1 cm

Step-by-step explanation:

We can use Pythagoras' Theorem:

The square on the diagonal is equal to the sum of the squares of the other two sides.

d² = 5² + 5²

d² = 25 + 25

d² = 50

d = √50

d  = √(25×2)

d = 5√2

d≈ 7.1 cm

Answer:

C) 70%

Step-by-step explanation:

To find his percentage we take part over total

14/20

We want it over 100, so multiply the top and bottom by 5

14*5

---------

20*5

70/100

Percent means out of 100

so we have 70 percent

70 %

Answer:

c 70%

Step-by-step explanation:

20 into 14 = 70%

y +3 = (1/4)(x +3)

The two-point form of the equation for a line is good for this.

... y -y1 = (y2-y1)/(x2-x1)(x -x1)

Substituting your values, we have ...

... y -(-3) = (-1-(-3))/(5-(-3))(x -(-3))

... y +3 = 2/8(x +3)

Since you ask for "an equation," we can leave it in this form.

... y +3 = (1/4)(x +3)

_____

Or we can rearrange it to slope-intercept form:

... y = (1/4)x -(2 1/4)

or put it in standard form:

... x -4y = 9

Answer:

6ft 3in

Step-by-step explanation:

The height of a tree that is 75 inches tall is approximately 6 feet 3 inches when converted.

In this question, we are required to convert the height of a tree from inches to feet and inches. One foot equals twelve inches. Therefore, to convert 75 inches into feet, we divide 75 by 12. This results in a quotient approximately equal to 6.25 ft. However, we want to also express the height in the remaining inches, so we take the decimal portion (0.25) and multiply it by 12 to convert it back to inches, giving us 3 inches. Hence, a tree that is 75 inches tall corresponds to 6 feet 3 inches tall when converted.

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Answer:

<2 = 37.5 degrees

Step-by-step explanation:

Complementary angles add together to equal 90 degrees.

Let < 1 = x  and < 2 = y

x + y= 90

x = y+15

Substitute the second equation into the first equation.

(y + 15) + y = 90

Combine like terms

2 y + 15 = 90

Subtract 15 from each side.

2y+15-15 = 90-15

2y =75

Divide each side by 2

2y/2 = 75/2

y = 37.5

<2 = 37.5 degrees

Answer:

It is D. Perpendicular lines intersect at a 90 degree angle.

Step-by-step explanation:

Answer:

The answer is the option D

[tex]73.7\°[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC of the figure

[tex]sin(B)=\frac{AC}{BC}[/tex]

in this problem

[tex]AC=24\ units[/tex] ------> opposite side angle B

[tex]BC=25\ units[/tex] ------> the hypotenuse of the right triangle

substitute the values

[tex]sin(B)=\frac{24}{25}[/tex]

[tex]B=arcsin(\frac{24}{25})=73.7\°[/tex]

Answer:

61.56/6

10.26

Step-by-step explanation:

For this case we must indicate how much each of the 6 people should pay knowing that the bill is $ 61.56.

For this, we divide:

Let "x" be the amount of money each person must pay, then:

[tex]x = \frac {61.56} {6}\\x = $ 10.26[/tex]

Thus, each one must pay $ 10.26.

Answer:

$ 10.26.

Answer:

2/(7a) < x < 7

Step-by-step explanation:

The product of roots of ax² +bx +c is c/a. In this case, that means the second root of the equation is ...

... 2/(7a)

Since a < 0, the parabola opens downward and 2/(7a) < 0. The quadratic function will be positive between the two roots, on the interval ...

... 2/(7a) < x < 7

Answer:

Without an actual drawing to show which side is 74 inches, then the answer could either be the square root of 6052 inches OR 70 inches.  

Step-by-step explanation:

All right triangles follow the rule of the pythagorean theorem, which states that a^2 + b^2 = c^2, where 'a' and 'b' represent the legs of a triangle and 'c' represents the hypotenuse.  The legs of a right triangle are the two sides that come together to form the 90 degree angle and the hypotenuse is the angled line across from the 90 degree angle.  In this case, the height would have to represent one of the legs, while the other 'side' would need to represent either a leg or the hypotenuse (depending on the actual diagram presented which is not shown in the problem posted).  So, if you substitute the values given into our legs, or 'a' and 'b', you would end up with the value of 'c' as the square root of 6052.  However, if the given side is actually the hypotenuse, you would solve by subtracting the c^2 from a^2 to get 'b'=70 inches.  

The height of the right angle triangle is 70 inches

Using Pythagoras's theorem for right angle triangle

c²  = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

c = 74 inches

a = 24 inches

74² = 24² + b²

5476  = 576 + b²

5476 - 576 = b²

b² = 4900

square root both sides

b = √4900

b = 70 inches

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Answer:

r= 3b

Step-by-step explanation:

We can find the slope of the line by using

m= (y2-y1) /(x2-x1)

   = (12-9)/ (4-3)

   = 3/1

The slope is 3

We can use the point slope form for the equation of a line

y-y1 = m(x-x1)

y-12 = 3(x-4)

Distribute the 3

y-12 = 3x-12

Add 12 to each side

y -12+12 = 3x-12+12

y= 3x

let r =y

and x=b

r = 3b

Answer: Correct Answer is 4th option , 28

Step-by-step explanation:

We can find the measure of the angle using the tangent.

We know, tangent of an angle = Perpendicular/Base, corresponding to that angle.

So, Tan of angle T = RG / RT

or, Tan of angle T = 8/15

or, angle T = tan inverese of 8/15

or, angle T = 28.07

So, angle T rounded to nearest degree = 28

Hope this helps.

Thank you.

You can see that the graph of [tex] g(x) [/tex] is the graph of [tex] f(x) [/tex] translated one unit to the left.

Horizontal translations are given by the transformation

[tex] f(x) \mapsto f(x+k) [/tex]

If [tex] k>0 [/tex] the function is translated k units to the left, else if [tex] k<0 [/tex] the function is translated k units to the right.

So, in your case, [tex] k=1 [/tex]

And thus you have

[tex] g(x) = f(x+1) = 2^{x+1} [/tex]

Answer:

2^x+1

Step-by-step explanation:

Answer:

The correct answer is D) The rate in which he burns calories

Step-by-step explanation:

We can tell this because the slope is always the change in y value over the change in x value. Since the y value is calories and the x value is minutes, we get the following.

Calories/minute

Which can also be written as calories per minute, which is a rate.

The graph says about the rate of calorie burned.

A plane created by the intersection of two perpendicular coordinate axes is referred to as a cartesian plane. The x-axis is the horizontal axis, while the y-axis is the vertical axis. These axes cross at the origin, whose location is specified as (0, 0). Any location on the cartesian plane is shown as (x, y).

Given the graph between calories burned and time in minutes,

X axis shows the time and Y axis shows the calorie burned,

The ratio of the change in y value to the change in x value is the slope. We obtain the following because the y value is calories and the x value is minutes.

Calories/minute

This is a rate and can also be represented as calories per minute.

Hence Option D is best suitable for condition.

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Answer:

(a) 13

(b) LIFO: $19.60; FIFO: $37.50; Avg: $28.26

Step-by-step explanation:

(a) The starting inventory was 12 sets. Added to that were 4, 6, 6, 10, to make a total of 38 paint sets. 25 were sold, so 13 remained at the end of the year.

(b)

LIFO

Sets purchased at the end of the year are sold first (last-in, first-out). So the sets remaining in inventory are the ones purchased at the beginning of the year. Those 13 sets cost 12@1.50 +1@1.60 = $19.60.

FIFO

Sets purchased first are sold first, so the sets remaining in inventory are the ones purchased last. Those 13 sets cost 10@3.00 +3@2.50 = $37.50.

Avg

The total cost of all inventory purchases was ...

... 12@1.50 +4@1.60 +6@2.20 +6@2.50 +10@3.00

... = 18.00 +6.40 +13.20 +15.00 +30.00 = $82.60

Then the value of the remaining 13 of the 38 items bought is ...

... (13/38)·$82.60 = $28.26.

_____

I find it convenient to let a spreadsheet do the arithmetic.

Q. P

12. 1.5. 18.00

4. 1.6. 6.40

6. 2.2. 13.20

6. 2.5. 15

10. 3. 30

__ __. ___

38. 10.8. 82.6

Sales. 25

Ending inventory 25-38=13. Answer a

B) ending inventory under LIFO

12×1.5=18

1×1.6=1.6

___

19.6 Answer

Ending inventory under FIFO

10×3=30

3×2.5=7.5

___

37.5. Answer

Ending inventory under weighted average

82.6÷38=2.17

2.17× 13=28.21 ...Answer

Hope it helps!

A solution to a pair of equations is the set of points where their graphs intersect. Points in that set will satisfy both equations, which is what "solution" means.

Here, the graphs of p(x) and f(x) each intersect the graph of g(x) in one place. Hence f(x) = g(x) has one solution, as does p(x) = g(x).

Finding the solution is a matter of reading the coordinates of the point of intersection from the graph.

A. The graphs interesect at x=1, y=-1.

B. Any point on the red line is a solution. We already know one of them from part A. Another is the x-intercept, where y=0. That point is (2, 0).

C. g(x) intersects f(x) at their mutual y-intercept: y = 3. x = 0 at that point.

$16,307.64

The table value for n=8 quarters (2 years) and 2.00% (8% annual rate divided by 4) is 8.58297. Multiply this by the dollar amount Carlene deposits to get the balance at the end of the period.

... $1900 × 8.58297 ≈ $16,307.64

Answer:

81

Step-by-step explanation:

width x length = area of a square

in a square width = length

9 x 9 = area

81 = area

Answer:

81 ft²

Step-by-step explanation:

To solve for Square area, note the equation:

Area = side x side

Note that for the rule of square, all sides are congruent, which means they have the same measurements. Therefore, if one side is 9, all the other are 9.

Multiply the base with the height: 9 x 9 = 81

81 ft² is your answer

~

Answer:

x=9     and x=1

Step-by-step explanation:

If 6 is added to the square of an integer, the result is 3 less than 10 times that integer.

x^2 +6 = 10x-3

Subtract 10x from each side.

x^2 -10x +6 = 10x-10x-3

x^2 -10x +6 = -3

Now add 3 to each side.

x^2 -10x +6+3 = -3+3

x^2 -10x +9 = 0

Now we can factor the left side of the equation.

What numbers multiply together to give positive 9 and add together to give -10?

-9* -1 = 9      -9+-1 = -10

(x-9)  * (x-1) = 0

Using the zero product property

x-9 = 0 and x-1 = 0

x-9+9 = 0+9     x-1+1 = 0+1

x=9     and x=1

Answer:

The function r(x) represents a constant rate per unit change in x.

Step-by-step explanation:

This is because when you increase in 2, it goes from 37 to 25, a decrease in 12, then when the x goes from 2 to 3, then it has to drop down by 6, or else it won't be linear. It does. 25-6 is 19. Then it goes from 3 to 5, meaning it has an increase of 2 in x, meaning it has to drop down in 12 to be linear, It does. 19-12 is 7. So it is linear, meaning it has a constant rate per unit change in x.

Answer:

y = 3x-2

Step-by-step explanation:

We can find the slope using the formula

m = (y2-y1)/(x2-x1)

  = (16-4)/(6-2)

  =12/4

 =3

We then use the point slope form of a line

y-y1= m(x-x1)

y-4 = 3(x-2)

Distribute the 3

y-4= 3x-6

Add 4 to each side

y-4+4 = 3x-6+4

y = 3x-2

This is in slope intercept form

Answer:

Option b. 30.5

Step-by-step explanation:

Given in the picture is a triangle ABC with sides AB = 22.3 and side BC=24.1

The included angle B = 82 degrees

We have to find the third unknown side AC = b

REcollect the cosine formula for triangles.

[tex]b^{2} =a^{2} +c^{2} -2ac cos B[/tex]

substitute for a and c

We get

[tex]b^2 = 22.3^2+24.1^2-2(22.3)(24.1) cos 82\\=928.587[/tex]

b = square root of 928.587

b =30.47=30.5

Thus we get b = 30.5

Answer:

(4,0)

Step-by-step explanation:

insert 0 where the y is located and solve for x

6x – 3y = 24

6x – 3(0) = 24?

6x = 24

6x / 6 = 24 / 6

x = 4

x-intercept = (4, 0)

The x-intercept of the line 6x - 3y = 24 is (4, 0).

The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept of the line 6x - 3y = 24, we need to set y = 0 and solve for x.

Substituting y = 0 into the equation, we get 6x - 3(0) = 24. Simplifying this equation gives us 6x = 24, and dividing both sides by 6 gives x = 4.

Therefore, the x-intercept of the line 6x - 3y = 24 is (4, 0).

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In degrees: -270°, 90°, 450°.

In radians: -3π/2, π/2, 5π/2.

The cosine is always zero where the sine is 1. The sine is 1 at an angle of 90°, and every integer number of 360° added (or subtracted) to that. The corresponding point on the unit circle is (0, 1), labeled A in the diagram.

The angle from the x-axis to the positive y-axis can be called any of ...

... 90°

... -270°

... 450°

... 810°

... π/2 radians

... -3π/2 radians

... 5π/2 radians

... 9π/2 radians

You are asked to pick three of these (or some others you may choose) so that you have 3 different names for the angle to this point.

_____

Comment on the second figure

The graphing calculator easily shows places where function values are zero. To show where sin(x) = 1, we rewrite it as sin(x) -1 = 0. Then, the zeros are highlighted. In degrees, the ones shown are -270°, 90°, 450°, 810°. You can see that cos(x) is zero at those same angles.

x ≈ {-3.082, 1.082}

I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.

___

From vertex form

The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...

... y = (x +1)² -13/3

This has x-intercepts easily found.

... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0

... (x +1)² = 13/3 . . . . . . . add 13/3

... x +1 = ±√(13/3) . . . . . take the square root

... x = -1 ±√(13/3) . . . . . subtract 1

... x ≈ {-3.0816660, 1.0816660}

_____

Using the quadratic formula

This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.

... x = (-b±√(b²-4ac))/(2a)

... x = (-6 ±√(6² -4(3)(-10)))/(2(3))

... x = (-6 ±√156)/6 = -1 ±√(13/3) . . .  or . . . -1 ±(√39)/3

Answer:

Replace 5 and 4 with 6s. Replace 2 and 3 with 1s. Then there will be 3 faces with 6 and 3 faces with 1.

Step-by-step explanation:

In order for the mean to remain unchanged, the sum of opposite faces must remain the same: 7. In order to have the standard deviation as large as possible, the largest and smallest possible numbers need to be used: 6 and 1.

Replacing 4 and 5 with 6s, and replacing 2 and 3 with 1s will accomplish your goal.

check the picture below.

so, we know the radius of this circle is 5 then, namely, the distance from (0,0) to (5,0) is 5.

now, if (√(21) , 2) indeed lies on that circle curve, then the distance from (0,0) to (√(21) , 2) will also be the same radius of 5 units.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{origin}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{\sqrt{21}}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(\sqrt{21}-0)^2+(2-0)^2}\implies r=\sqrt{(\sqrt{21})^2+2^2} \\\\\\ r=\sqrt{21+4}\implies r=\sqrt{25}\implies r=5~~~~\checkmark[/tex]

Answer:

It does. "Proof" below.

Step-by-step explanation:

In order for the given points to lie on the circle, they must both be the same distance from the origin. The Pythagorean theorem is used to make a "distance formula" for computing the distance between two points.

For a point (x, y), its distance (d) to the origin will be ...

... d = √(x² +y²)

For the reference point that we know is on the circle, this distance (the circle's radius) is ...

... d = √(5² +0²) = √25 = 5

For the point in question, the distance to the origin is ...

... d = √((√21)² +2²) = √(21 +4) = √25 = 5

Both points have the same distance to the origin, 5 units, so a circle (of radius 5) centered there will contain both points.

_____

A graph is not proof, but it can confirm the result.