Mathematics High School

In spherical geometry, which indicates the possible number of right angles a triangle may have?
1
2
3
All of the above

Answers

Answer 1
In planar geometry, we know that the sum of all angles of a triangle is exactly 180°, However, in spherical geometry, different rules apply. When three arcs drawn on the surface of the sphere are connected together through vertices, that is called a spherical triangle. In that case, the sum of all three angles of a spherical triangle is between 180° and 540°.

So, if a triangle has one 90° angle, there are still excess angles to make up for a maximum of 540°. The same is true for two 90° angles. You would exceed 180° but that is just the lower limit so that is still acceptable. If you have three 90° angles, you form a spherical triangle with a total of 270°, which is within the given range. Thus, the answer is all of the above.

Related Questions

Factor completely 36x2 − 49.


A (3x + 7)(12x − 7) B (3x − 7)(12x + 7) C (6x − 7)(6x − 7) D (6x + 7)(6x − 7)

A B C D ?

Answers

The answer is D.

6x * 6x = 36x^2
6x * -7 = -42x
6x * 7 = 42x
-7 * 7 = -49

The -42x and 42x cancel each other out, resulting in 36x^2 - 49.

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is

[tex]36x^2-49[/tex]

It can be written as

[tex](6x)^2-(7)^2[/tex]

Using the formula

[tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex](6x)^2-(7)^2=(6x+7)(6x-7)[/tex]

Therefore the complete factor form of given expression is (6x+7)(6x-7). The correct option is D.

What is the peremeter of this polygon? (With picture)

Answers

check the picture below.

so.. simply, use the distance formula, to get their length an add them up, and that's the perimeter of the polygon.


[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 2}})\quad % (c,d) &({{ 2}}\quad ,&{{ 4}})\\ &({{ 2}}\quad ,&{{ 4}})\quad % (c,d) &({{ 3}}\quad ,&{{ -2}})\\ &({{ 3}}\quad ,&{{ -2}})\quad % (c,d) &({{ -2}}\quad ,&{{ -3}})\\ &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ -1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]

[tex]\bf -------------------------------\\\\ d=\sqrt{[2-(-1)]^2+(4-2)^2}\implies d=\sqrt{(2+1)^2+(2)^2} \\\\\\ d=\sqrt{3^2+2^2}\implies \boxed{d=\sqrt{13}}\\\\ -------------------------------\\\\ d=\sqrt{(3-2)^2+(-2-4)^2}\implies d=\sqrt{1^2+(-6)^2}\implies \boxed{d=\sqrt{37}}\\\\ -------------------------------\\\\ d=\sqrt{(-2-3)^2+[-3-(-2)]^2}\implies d=\sqrt{(-5)^2+(-3+2)^2} \\\\\\ d=\sqrt{(-5)^2+(-1)^2}\implies \boxed{d=\sqrt{26}}[/tex]

[tex]\\\\ -------------------------------\\\\ d=\sqrt{[-1-(-2)]^2+[2-(-3)]^2}\implies d=\sqrt{(-1+2)^2+(2+3)^2} \\\\\\ d=\sqrt{(1)^2+(5)^2}\implies \boxed{d=\sqrt{26}}[/tex]

so, those are their lengths, sum them all up, that's the polygon's perimeter.

Consider the trinomial x2 – 9x + 18. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?

Answers

x^2 - 9x + 18
AC = 18
Factors of AC: 1 * 18, 2 * 9, 3 * 6, -1 * -18, -2 * -9, -3 * -6
Sum to -9: 19, 11, 9, -19, -11, -9

(x - 3)(x - 6)

The required pair of number are -3 and -6

The factored form of the trinomial is (x-3) and (x-6)

The standard form of a quadratic equation is expressed as:

[tex]ax^2+bx+c=0[/tex]

Given the expression [tex]x^2 - 9x + 18.[/tex]

[tex]a=1\\b=-9\\c=18[/tex]

We are to get two values that we must add to get b, and that we will multiply that will give c.

The given values are -6 and -3

Check:

[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]

Factorize the trinomial

[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]

Hence the factored form of the trinomial is (x-3) and (x-6).

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Which graph shows a triangle and its reflection image over the x-axis?
A. first picture
B. 2nd picture
C. picture 3
D. picture 4

A. is wrong

Answers

Assuming the choices are A,B,C,D in that order from left to right (according to your attachments), then it would be the fourth one. 

To make sure we're on the same page, I'm attaching your fourth drawing below. It's the result of taking a triangle and reflecting it over the horizontal x axis. Think of it like mirroring an image.

Answer-

In picture 4, the triangle is reflected over x axis.

Solution-

While reflecting a point over x axis, (x, y) → (x, -y) rule is followed.

Only the sign of y-coordinate is changed, keeping x-coordinate intact.

In the first picture, though the image is reflected, but it is reflected over y axis.

In the second picture, the image is first reflected over y axis, then it is translated 1 unit down.

We rotating a point 90° clockwise, (x, y) → (y. -x) rule is followed.

In the third picture, the triangle is rotated 90° clockwise and then translated 1 unit to right.

But, in case of the fourth picture, the figure is reflected over x axis. Only the y coordinates sign are changed, all the x coordinates are same as before.


Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.

Answers

Each transformation will give these following coordinates

Translation 7 units right gives E(4, 4), F(8, 3), G(10, 6), and H(8, 6) as shown in brown in the diagram below

Reflection on the y-axis gives E(3, 4), F(-1, 3), G(-3, 6) and H(-1, 6) as shown in green in the diagram below

Reflection on the x-axis gives E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) as shown in red in the diagram below

Translation 5 units down gives E(-3, -1), F(1, -2, G(3, 1) and H(1, 1) as shown in purple in the diagram below 

Answer:

Answers a little bit more simplified, all credit to the expert :)

E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right

E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis

E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis

E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down

Step-by-step explanation:

A recipe for pastry has flour, butter and water mixed in the ratio 24 : 8 : 3 if fiona follows the recipe and uses 3 cups of flour, how many cups of butter should she use?

Answers

To determine the amount of butter in cups that is required to prepare the recipe given the amount of the flour supplied, we calculate first for the ratio of the flour by the amount of butter.

Ratio = amount of flour / amount of butter
Ratio = 24 / 3 = 8

This means that there is 8 cups of flour in every cup of butter.

Amount of butter = (3 cups of flour) x (1 cup of butter / 8 cups of flour)
Amount of butter = 3/8 cups of butter

Hence, the amount of butter needed is 3/8 cups. 

The same can be done in order to determine the amount of water needed to be mixed for the recipe. 
Final answer:

Fiona should use 1 cup of butter when using 3 cups of flour, according to the recipe's ratio of 24:8:3 for flour to butter to water.

Explanation:

The question asks how much butter Fiona should use if she's using 3 cups of flour and the recipe calls for flour, butter, and water in the ratio of 24:8:3. To solve this, we take the ratio for butter (which is 8) and divide it by the flour ratio (which is 24), then multiply by the number of cups of flour Fiona is using (which is 3 cups).

Step-by-step Solution:

Write down the original ratio: 24 parts flour : 8 parts butter : 3 parts water.Calculate the ratio of butter to flour, which is 8/24. This simplifies to 1/3.Since Fiona is using 3 cups of flour, multiply the simplified butter ratio by the amount of flour: (1/3) * 3 cups = 1 cup. Thus, she would need 1 cup of butter.

PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?

3y − x = −6
4y − x = 44

3y + x = −6
4y + x = 44

3y − 3x = −6
4y − 4x = 44

3y + 3x = −6
4y + 4x = 44

Answers

1/3x - 2 = 1/4x + 11....it looks to me like one y was subbed in for another...

ur 2 equations are :
y = 1/3x - 2 and y = 1/4x + 11...but we need them in standard form...

y = 1/3x - 2
-1/3x + y = -2 ..multiply by 3
-x + 3y = -6.....or 3y - x = -6 <==

y = 1/4x + 11
-1/4x + y = 11 ...multiply by 4
-x + 4y = 44 or 4y - x = 44 <==

The system of equations are 3y − x = −6 and 4y − x = 4

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

One third x − 2 = one fourth x + 11

1/3x - 2 = 1/4x + 11

Now let us take y as 1/3x - 2

y= 1/3x - 2

3y=x-6

Subtract x on both sides

3y-x=-6

and Let us consider the right side equation

y=1/4x + 11

4y=x+44

Subtract x on both sides

4y-x=44

Hence, the system of equations are 3y − x = −6 and 4y − x = 44

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WILL GIVE A BRAINLIEST IF UR RIGHT!!

Evaluate f(–2) in the given function below.

f(x)= 3x-3 if -5 ≤ x < 3 x+4 if 3 ≤ x ≤ 12


A.
–6
B.
–3
C.
2
D.
–9

Answers

F(x)=3x-3

f(-2)=3(-2)-3

f(-2)=-6-3=-9

so D is correct

Which expression is equivalent to (5^-2) (5^-1)

-1/125
-1/5
1/125
1/5

Answers

5^(-2)=1/25
5^(-1)=1/5
1/25*1/5=1/125

what is the average rate of change for this quadratic function please help

Answers

Answer: Choice A) 2

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

Explanation:

When x = 0, the value of y is y = -6. You can see this as you draw a vertical line through x = 0. This vertical line is the y axis. The parabola crosses the y axis at -6. This point is the y intercept.

When x = 3, the value of y is y = 0. This is one of the two x intercepts. An x intercept is a location where the graph crosses the x axis.

So we have the two points (0,-6) and (3,0). Let's find the slope of the line through these two points

(x1,y1) = (0,-6)
(x2,y2) = (3,0)

Slope:
m = (y2-y1)/(x2-x1)
m = (0-(-6))/(3-0)
m = (0+6)/(3-0)
m = 6/3
m = 2

The slope of the line through those two point is m = 2. 

Can someone please answer this for me I'm begging

Answers

if the length of JK is 16.4 miles, it will be diameter of this circle, the radius will be JK/2 = 8.2 miles

As we know the length of circle is 2π*r  in this case r = 8.2

The arc JM is 1/4 length of the whole circle so arc JM = (2π*8.2)*(1/4) = 2π*8.2/4 = π*8.2/2 = π*4.1

if we assume that π=3.14 the answer will be 3.14 * 4.1 = 12.874.... And as the answer needs to be rounded to the nearest tenth it will be 12.874≈12.9

So the answer will be 12.9

How many years will it take $1,000 invested at 7% interest to earn $280?

Answers

7% of 1,000 is 70.
280/70 = 4
It will take 4 years.

Solve for x.

The length of a rectangle is equal to 2 times the width plus 3 feet. If the area of the rectangle is 20 square feet, what are the dimension of the rectangle?

Answers

l*w=20, so l=20/w
l=2w+3

20/w=2w+3
20=2w^2+3w
2w^2+3w-20=0

Slip and slide
w^2+3w-40
(w+8)(w-5)
(w+8/2)(w-5/2)
(w+4)(2w-5)

w= -4 or 5/2, but since width must be positive, it is 5/2

(5/2)*l=20
l=8

Final answer: Length= 8, Width= 5/2
let width be x feet 
then the length = 2x + 3 feet

then the area  = x(2x + 3) = 20

2x^2 + 3x - 20 = 0

(2x - 5)(x + 4) = 0

x = 2.5 or -4 ( ignore the negative value)

so the deimnasions are width = 2.5 feet and length = 2(2.5) + 3 =  8 feet

For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?

e ≥ 50 or e ≤ 100
e > 50 or e < 100
50 < e < 100
50 ≤ e ≤ 100

Answers

d is the answer
50 ≤ e ≤ 100

Answer:

The answer is D.

Step-by-step explanation:

We know this because it is an "and" problem because it is numbers in between, not outside.

We also know it is "no less" or "no more" than 50 or 100. so we use a less than and equal too. Not just a less than sign.

Really hoped this helped, kind of in a test right now so just giving a brief way of how to figure this stuff out.

Continue and have fun learning!

what is the length of a circle that has a central angle of 98 degrees and 6 cm rounded to the nearest 100th. using 3.14

Answers

Arc length = 2[tex] \pi [/tex]r * Θ/360 = [tex] \pi [/tex]d * Θ/360
so...
If we take pi to be 3.14,
Arc length = 2(3.14)(6) * 98/360
= 37.68 * 98/360 = 10.26 cm

a scale model of a school building is 5 inches tall. If the building is 100 feet tall, find the scale of the model

Answers

It's 20 feet to one inch or 10 feet to half an inch.

Answer with Step-by-step explanation:

A scale model of a school building is 5 inches tall.

Actual size of the school building is 100 feet.

1 feet=12 inches

100 feet=12×100 inches

             = 1200 inches

5 inch is representing 1200 inches

1 inch represents  1200/5 inches

1 inch represents  240 inches

or  1 inch represents  12×20 inch

or 1 inch represents 20 feet

Scale of the model is:

1 inch represents  240 inches

1 inch represents 20 feet

what is the algebraic expression for the product of 9 and a number t

Answers

Algebraic expressions are expressions like:

[tex]3x^5+8x^2y^3+xy+8[/tex], [tex]x^2+2xy+y^3[/tex], [tex]a^3b+a^b+2ab-4[/tex], 

so they are expressions made from integers, integers multiplying variables of different degrees, and algebraic operations like addition, subtraction etc...

thus, the algebraic expression for the product of 9 and a number t is 9t.

Answer: 9t


A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6 find the toal area of the pyramid

Answers

now, if you check the picture below, the top-side has the base alone, the hexagon, notice, if you divide a circle the 360° of a circle in 6 even angles, like the hexagon does, you end up with 6 angles of 60° each, and 6 equilateral triangles made by them, now, if you run an angle bisector, like we did on the bottom side of the hexagon, you end up splitting the angle in equal halves.

so.. then we end up with the a 30, 60, 90 angles triangle, and thus we apply the 30-60-90 rule, to get the apothem.

now the area of a regular polygon is just (1/2) (apothem)(perimeter).

now, we know the apothem, the perimeter of the hexagon is just 4+4+4+4+4+4.  So, just get those values, plug them in to get the area of the hexagonal base.

if you look at the picture bottom-side, the slant-height of the pyramid, is just the altitude/height of the triangular face.  So, you really have 6 triangles whose base is 4 and height is 6, and you know how to get the area of a triangle.

so, just get the area of the base, plus the area of the triangular faces, sum them up, and that's the total area of the hexagonal pyramid.

Find the missing value. Show your work
(GEOMETRY, PLEASE HELP!!)

Answers

sin51=y/12

y=12sin51 units

y≈9.33 units (to nearest hundredth of a unit)

...

tanα=12/5

α=arctan2.4°

α≈67.38°  (to nearest hundredth of a degree)

...

tan13=x/24

x=24tan13 units

x≈5.54 units (to nearest hundredth of a unit)

...

sin20=10/x

x=10/sin20 units

x≈29.24 units (to nearest hundredth of a unit)

Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3, b = 5, c = 5 B. a = 3, b = −5, c = 5 C. a = 5, b = −5, c = 0 D. a = −3, b = 5, c = −5

Answers

3x2− 5x + 5 = 0.
a=3 b=-5 c=5

A. a = 3, b = 5, c = 5
B. a = 3, b = −5, c = 5
C. a = 5, b = −5, c = 0
D. a = −3, b = 5, c = −5

answer is B


A cell phone company orders 500 new phones from a manufacturer. If the probability of a phone being defective is 2.6%, predict how many of the phones are likely to be defective. Round to the nearest whole number.
A.)16 phones
B.)11 phones
C.)13 phones
D.)130 phones

Answers

2.6% of 500 =
0.026(500) = 13 <==

Can someone please help me

Answers

V = Volume of cylinder
B = area of base
h = height of cylinder

It turns out that
V = B*h
In a similar way to that of a cube

If we know that V = 84pi and h = 7, then we can plug those values into the formula above, and solve for B

V = B*h
84pi = B*7
84pi/7 = B*7/7 ... divide both sides by 7
12pi = B
B = 12pi

Therefore the base is 12pi square units

Which of the following is a solution of x2 + 5x = −2?

5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.

Answers

x^2 + 5x = -2
x^2 + 5x + 2 = 0

x = -b (+-) sqrt (b^2 - 4ac) / 2a
a = 1, b = 5, and c = 2

x = -5 (+-) sqrt (5^2 - 4(1)(2)) / 2(1)
x = -5 (+-) sqrt (25 - 8) / 2
x = -5 (+-) sqrt (17) / 2

answer is : negative 5 plus or minus the square root of 17 divided by 2

Answer:

negative 5 plus or minus the square root of 17 divided by two: [tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].

Step-by-step explanation:

We have the equation

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

[tex]x^2+5x+2=0[/tex].

To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.

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

where a is the coefficient of [tex]x^2[/tex], in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.

[tex]x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}[/tex]

[tex]x=\frac{-5\pm\sqrt{25-8}}{2}[/tex]

[tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].

How can ΔABC be mapped to ΔXYZ?



First, translate .

Next, rotate ΔABC about B to align the sides and angles.

Answers

Final answer:

To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.

Explanation:

In order to map ΔABC to ΔXYZ, you can follow these steps:

First, translate ΔABC by moving it horizontally and vertically to a new position.Next, rotate ΔABC about point B to align the sides and angles with ΔXYZ.

By performing these steps, you can map one triangle to another.

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What is a quartic function with only the two real zeros given?

x = -4 and x = -1




A.
y = x4 + 5x3 + 5x2 + 5x + 4


B.
y = x4 - 5x3 - 5x2 - 5x - 4


C.
y = -x4 + 5x3 + 5x2 + 5x + 4


D.
y = x4 + 5x3 + 5x2 + 5x - 5

Answers

Given that the two real solutions are x = -1 and x = -4 you now that (x+1) and (x+4) are factors of the quartic function.

So, you need to factor the polynomials given or divide them by (x+1)(x+4).

(x+1)(x+4) = x^2 + 5x + 4

Using the first function you get:

(x^4 + 5x^3 + 5x^2 + 5x + 4) / ( x^2 + 5x + 4) = x^2 + 1

And you know that x^2 + 1  does not have a real solution, so the function

x^4 + 5x^3 + x^2 + x + 4 has the two real solutions given, x = -1 and x = -4, and two not real solutions.

Now you know that the answer is the first option.

If you want to check the other functions you just must divide and analyze the quotient obtained.

Answer: option A. x^4 + 5x^3 + 5x^2 + 5x + 4. 




Question text
Which volume formula or formulas show(s) a joint variation?

I V=8^3

II V=πr^2h

III V=Bh

Select one:
a. III only
b. I only
c. II and III only
d. I, II, and III

Answers

1. V = s3 
2. V = pr2h 
3. V = Bh 

Joint variation means that V will be dependent on at least two different variables. Looking at the three choices, only 2 and 3 show this. 

In 2, V varies jointly as r2 and h (assuming p is the constant of proportionality). And in 3, V varies jointly as B and h, with the proportionality constant being 1.

The correct answer is: c. II and III only

To determine which volume formula(s) exhibit joint variation, we need to consider if the volume (V) varies directly with two or more variables. In joint variation, V is directly proportional to the product of two or more variables.

Let's analyze each formula:

I. V = 8^3 → This is not a joint variation as V is solely dependent on the constant 8.

II. V = πr^2h → This shows joint variation as V varies directly with both r and h.

III. V = Bh → This also exhibits joint variation since V varies directly with both B (base area) and h (height).

What would you do to isolate the variable in the equation below, using only one step? x + 5 = -12 Select one: a. Add 5 to both sides of the equation. b. Subtract 5 from both sides of the equation. c. Add 12 to both sides of the equation. d. Subtract 12 from both sides of the equation.

Answers

subtract 5 from both sides then it would look like x=-17   
Final answer:

To isolate the variable in x + 5 = -12, subtract 5 from both sides of the equation. This leads to the equation x = -12 - 5.

Explanation:

In order to isolate the variable x in the equation x + 5 = -12, you should subtract 5 from both sides of the equation. This gives us the equation in a simplified form that allows us to determine the value of x. The idea here is to cancel out the +5 on the left side by subtracting 5 from both sides, resulting in x = -12 - 5. Hence, the answer is option b.

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Describe the relationship between the segments made when secant lines intersect outside a circle. Use the following image as reference.

Answers

Let the extensions of secants AD and BC meet at point P.

Let the measure of ar DC be 2a, then m(DAC)=m(DBC)=a, since angles DAC and DBC are both inscribed angles intercepting arc DC.

m(P)=b.

Then triangles APC and BPD are similar, because they have 2 pairs of common angles.

from the similarity of APC and BPD, we can write the ratios:

[tex] \frac{AP}{BP} = \frac{PC}{PD} = \frac{AC}{BD} [/tex]

a game spinner has regions that are numbered 1 through 8. if the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7?

Answers

Each number on the spinner has an equally likely chance of being selected, 1/8. For this type of problem you multiply the probabilities.
P(3) = 1/8
P(7) = 1/8
(1/8) * (1/8) = 1/64

The probability that the first number is a 3 and the second is a 7 is 1/64

What is probability?

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

spinner had region numbered from 1 to 8

So, the probability on the spinner has an equally likely chance of being selected= 1/8.

P(3) = 1/8

P(7) = 1/8

Thus, probability that the first number is a 3 and the second is a 7

=(1/8) * (1/8)

= 1/64

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Identify all the sets to which 0.41567 belongs. Choose from rational,irrational,whole,and integer

Answers

0.41567 is:
 
... rational because it can be expressed as a fraction (e.g., 41567/100000)
... not irrational for the same reason
... not whole (obviously)
... not integer (obviously)

Answer:

1.) D

2.) C

3.) C

4.) B

5.) A

6.) D

7.) A

8.) D

9.) A

10.) D

Step-by-step explanation:

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