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Given the measures a = 10, b = 40, and
A = 30°, how many triangles can possibly be formed?

Given the measures b = 10, c = 8.9, and
B = 63°, how many triangles can possibly be formed?

Answer:

  C.  population; students

Step-by-step explanation:

Since every member of the population is asked, the survey is not a sample. If opinions are given equal weight, there are more students than staff, so we expect students to have more influence on results.

Answer:

C population, students

Step-by-step explanation:

Since everyone is asked the question, a population is used  (sample only uses part).  There are more students than staff, so students will have a bigger influence on the results

Answer:

The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

* Lets solve the problem

- ABC is a triangle, where A = (1 , -1) , B = (0 , 2) , C = (2 , 1)

- The Δ ABC reflected over the line y = x to form ΔA'B'C'

∵ The image of the point (x , y) after reflected across the line y = x

   is (y , x)

∴ We will switch the coordinates of each point in Δ ABC to find the

  coordinates of Δ A'B'C'

# Vertex A

∵ A = (1 , -1) ⇒ x = 1 , y = -1

∴ The x-coordinate of the image is -1

∴ The y-coordinate of the image is 1

∴ A' = (-1 , 1)

# Vertex B

∵ B = (0 , 2) ⇒ x = 0 , y = 2

∴ The x-coordinate of the image is 2

∴ The y-coordinate of the image is 0

∴ B' = (2 , 0)

# vertex C

∵ C = (2 , 1) ⇒ x = 2 , y = 1

∴ The x-coordinate of the image is 1

∴ The y-coordinate of the image is 2

∴ C' = (1 , 2)

* The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)

i dont quite get the question but...

i guess this is how it is.

Take the mirror image of∆ABC Through the a line through the point y=3.

The new ∆ABC would have point C=(4,2)

B=(3,-6) A=(1,-3)

Now shifting the ∆ABC one unit (i.e. 2 acc. to the graph as scale is 1 unit =2) towards right ( or adding 2 to the x coordinates of ∆ABC)

We get the Coordinates of triangle ABC as A=(3,-3) B=(5,-6) C=(6,2).

This coordinate is the same coordinates of ∆A"B"C".

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The answer is 420 lunch specials

Step-by-step explanation:

10×7=70 70×6=420

Answer:

the total different lunches is 420

Step-by-step explanation:

Given that:

As we know that, a customer can choose 3 of the above items in their lunch and it is a combination problem.

So we have:

So the total different lunches is:

P(A) *P(E)*P(D)

= 7*10*6

= 420

Hope it will find you well.

Answer:

  see below

Step-by-step explanation:

A regular tessellation is created by repeating a regular polygon. The first and third diagrams show multiple regular polygons of different sizes and shapes. The second diagram has no regular polygons in it.

The last diagram shows a regular tessellation.

Answer:

  B.  49:9

Step-by-step explanation:

The ratio of surface areas is the square of the ratio of edge lengths:

  7² : 3² = 49 : 9

Answer:

  b.  10

Step-by-step explanation:

For the most part, these are problems in addition. The measures of the different angles add up according to the relationships given in the problem statement.

From the picture, you can tell that ∠JKN is the sum of ∠1 and ∠2, which are said to be equal (congruent). That is, ∠1 has a measure that is half of that of ∠JKN.

Since ∠JKN is a right angle, 90°, and the measure of ∠1 is half that, m∠1 is 45°.

So, to find t, we equate the given expression for m∠1 to 45 and solve.

  4t +5 = 45

  4t = 40 . . . . . subtract 5

  t = 10 . . . . . . . divide by 4 . . . . . matches answer choice B

Answer:

b

Step-by-step explanation:

(625x¹²y⁸)^¼

(5⁴x¹²y⁸)^½

5×x³×y²

5x³y²

5|x³|y²

For it to be positive,

x³ should be positive because 5 and y² already are positive.

First you must know that the sides 2x and x + 8 are equal to each other and sides x and 3x - 16 are equal to each other.

This means you can make a formula like so:

2x = x + 8

and

x = 3x - 16

Now you may solve for x for both of them (you should get the same answer for both x's)

2x - x = (x - x) + 8

x = 8

and

x - 3x = (3x - 3x) - 16

-2x = -16

-2x/-2 = -16/-2

x = 8

To find the length of each side just replace x with 8!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

Let c represent the number of liters of champagne Lauren uses. Then (15-c) will be the number of liters of orange juice. The total cost of the mix will be ...

  12c +1.50(15-c) = 5.00(15)

  10.5c = 52.50 . . . . . subtract 22.50, simplify

  52.50/10.5 = c = 5 . . . . divide by the coefficient of c

Then the amount of orange juice is ...

  15 -c = 15 -5 = 10 . . . . liters

Lauren should use 5 liters of champagne and 10 liters of orange juice.

Answer:

  [tex]\dfrac{r_s}{r_r}\approx 6.3346[/tex]

Step-by-step explanation:

The ratio of the radii is the square root of the ratio of the areas:

  [tex]\dfrac{r_s}{r_r}=\sqrt{\dfrac{22680}{565.2}}\approx 6.3346[/tex]

The radius of sphere s is about 6.3346 times as large as the radius of sphere r.

To determine the ratio of the sizes of the radii of the two spheres based on their surface areas, you can use the ratios of the square roots of the surface areas. Using this method, the radius of Sphere S is found to be roughly 8 times larger than Sphere R

The subject topic of this question is related to geometry, specifically looking at the relationship between the surface areas of two spheres and their respective radii. Given that the surface area (SA) of a sphere is given by the formula SA=4πr², you can set up a ratio for the radii.

The square roots of the ratios of the surface areas of the spheres will give us the ratio of the radii. In other words, sqrt(SA of sphere S/ SA of sphere R) = ratio of the radii. Substituting the given values, we get sqrt(22680/565.2) which approximately equals to 8.

Therefore, the radius of Sphere S is approximately 8 times larger than Sphere R.

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Answer:

219.9  feet to the nearest tenth.

Step-by-step explanation:

Use trigonometry:

tan 35 = opposite / adjacent side

= 154/x

x =  154 / tan35

= 219.93

Answer:

219.9 ft

Step-by-step explanation:

After looking at pic, cross multiply to get x tan(35)=154

then divide both sides by tan(35) giving x=154/tan(35)

x is approximately 219.9 ft

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{3m-6}{4m+12} \cdot \frac{m^2+5m+6}{m^2-4}[/tex]

We factor to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+2)(m+3)}{(m-2)(m+2)}[/tex]

Cancel out the common factors to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+3)}{(m-2)}[/tex]

We cancel further to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot\frac{(m+3)}{(m-2)}=\frac{3}{4}[/tex]

The correct chice is B.

Answer: Lena eats 1/4 of the whole bar

Step-by-step explanation:

Half of the bar is 50. A full bar would be 100%. If Phillip has half, amd Lena eats half of that half, she eats 0.25 out of 0.5. 0.5 is half of the whole bar, so 0.5×0.5 is 1, and if lena ate 0.25 of 1, that is 1/4.

If you translate circle 1 with the vector (6,-4), the center will become

[tex](-4,5)+(6,-4) = (-4+6,5-4)=(2,1)[/tex]

So, circles 1 and 2 are now concentric. The radii are, respectively, 2 and 6. This means that, if we dilate circle 1 with a scale factor of 3, its radius will become 6 as well.

After this two transformations, both circles will have center (2,1) and radius 6.

The transformation rule is (x+6, y-4).

We dilate by a factor of 3.

A circle is a perfectly round shape meaning any point around its curve is the same distance from its central point called the center

Firstly we need to shift the center.

Again we need to dilate the circle.

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Answer:

  20 dimes

Step-by-step explanation:

We can group the coins into groups that are ...

  4 quarters + 2 dimes + 1 nickel

Then each group satisfies the ratio requirements, and the total value of a group is $1.25.

Since the total value in the register is $12.50, there must be 10 such groups, hence 20 dimes.

Answer:

  y = 45,121,040×1.027^t

Step-by-step explanation:

An exponential growth equation is generally of the form ...

  value at time t = (initial value)(growth factor)^t

where the growth factor is the multiplier for a period equal to one time unit.

Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...

  y = 45,121,040×1.027^t . . . . where t = years after 2014

Looks like [tex]f(x,y)=x^2+y^2-x^2y+7[/tex].

[tex]f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1[/tex]

[tex]f_y=2y-x^2=0\implies2y=x^2[/tex]

The latter two critical points occur outside of [tex]D[/tex] since [tex]|\pm\sqrt2|>1[/tex] so we ignore those points.

The Hessian matrix for this function is

[tex]H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}[/tex]

The value of its determinant at (0, 0) is [tex]\det H(0,0)=4>0[/tex], which means a minimum occurs at the point, and we have [tex]f(0,0)=7[/tex].

Now consider each boundary:

[tex]f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4[/tex]

which has 3 extreme values over the interval [tex]-1\le y\le1[/tex] of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

[tex]f(-1,y)=8-y+y^2[/tex]

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

[tex]f(x,1)=8[/tex]

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

[tex]f(x,-1)=2x^2+8[/tex]

which has 3 extreme values, but the previous cases already include them.

Hence [tex]f(x,y)[/tex] has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

The function must first have its partial derivatives set to zero to find its critical points. Also, considering the given domain's boundaries with Lagrange multipliers can establish the function's maximum and minimum points.

This function is a multivariable function and to find its extreme values within a specified domain you would use multivariable calculus methods. For the given function f(x, y) = x2 + y2 − x2y + 7, we first find its critical points by setting its partial derivatives equal to zero and then solve for x and y. Additionally, we need to consider the boundaries of the set {|x| ≤ 1, |y| ≤ 1} by using the method of Lagrange multipliers. The extreme values are obtained at the critical points within the domain, including the boundary.

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Answer:

  B)  36x^13*y^7

Step-by-step explanation:

The two rules of exponents that apply are ...

Expanding the second factor gives ...

  (4x^3*y^5)(3^2*x^(5*2)*y^2)

  = 36*x^(3+10)*y^(5+2)

  = 36x^13*y^7 . . . . . . matches selection B

Answer: second option.

Step-by-step explanation:

Given the transformation [tex]T:(x,y)[/tex]→[tex](x-5,y+3)[/tex]

 You must substitute the x-coordinate of the point A (which is [tex]x=2[/tex]) and the y-coordinate of the point A (which is [tex]y=-1[/tex]) into [tex](x-5,y+3)[/tex] to find the x-coordinate and the y-coordinate of the image of the point A.

Therefore, you get that the image of A(2,-1) is the following:

[tex](x-5,y+3)=(2-5,-1+3)=(-3,2)[/tex]

You can observe that this matches with the second option.

The answer is in the attachment below!

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I don’t understand. Explain mate

Answer:

(- 1, 4)

Step-by-step explanation:

The line x = 1 is a vertical line.

The point P(3, 4) is 2 units to the right of x = 1 ( 3 - 1 = 2 )

Hence the reflection will be 2 units to the left of x = 1, that is  (1 - 2)

P'(- 1, 4)

The reflection of point P(3, 4) about the vertical line x = 1 is P'(-2, 4).

Reflection is a transformation that flips a figure over a line or a plane. It is a type of symmetry transformation that maintains the same shape and size of the object but changes its orientation with respect to the line or plane of reflection.

Given: Point P(3, 4).

The line x = 1 is a vertical line.

Now, let's find the reflection of point P(3, 4) about the vertical line x = 1:

To reflect a point about a vertical line, we reverse the sign of the x-coordinate while keeping the y-coordinate the same.

So, the reflection of P(3, 4) will be (-2, 4).

Hence, the reflection of point P(3, 4) is P'(-2, 4).

Learn more about Reflection here:

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Answer:

The correct answer option is c. the net deposit amount.

Step-by-step explanation:

We know that Michael is making a deposit with a check and wants some cash back.

According to The Federal Reserve System and The Federal Deposit Insurance Corporation, the deposit slip must have the name his name, his account number, date, amount of the check, amount of cash that he want, his signature and the net deposit amount.

Answer:

C

Step-by-step explanation:

Answer:

  d.  (3, 7, -3)

Step-by-step explanation:

The reduced row-echelon form of the augmented matrix has 1s on the diagonal and zeros off-diagonal, except for the answer in the last column. It can be convenient to start by writing the augmented matrix using the second equation first:

[tex]\left[\begin{array}{ccc|c}-1&2&-3&20\\9&-4&1&-4\\4&4&-1&43\end{array}\right] \\\\\text{Add 9 times the first row to the second, and 4 times the first row to the third}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&14&-26&176\\0&12&-13&123\end{array}\right][/tex]

[tex]\text{Subtract 2 times the third row from the second}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&-10&0&-70\\0&12&-13&123\end{array}\right] \\\\\text{Divide the second row by -10}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&1&0&7\\0&12&-13&123\end{array}\right][/tex]

[tex]\text{Subtract 2 times the second row from the first, and}\\\text{subtract 12 times the second row from the third}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&-13&39\end{array}\right] \\\\\text{Divide the third row by -13}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]

[tex]\text{Add 3 times the third row to the first, then multiply the result by -1}\\\\\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]

The method may not be strictly according to some algorithm, but it avoids fractions and gives the correct result: (x, y, z) = (3, 7, -3).

Answer:

The answer is d. (3, 7, -3)

Step-by-step explanation:

100% sure I got a 100 on review exam

Answer:

Step-by-step explanation:

121b^4 - 49 is a "difference of squares."

Formula for factoring a "difference of squares:"

 a² - b² =  (a - b)(a + b)

So:  rewrite your 121b4 - 49 as 11²b^4 - 7² = (11b²)² - 7²

                                                                  = (11b² - 7)(11b² + 7)

This answer matches the last of the four given answer choices.

Answer:

r = 15.2

Step-by-step explanation:

Where AB meets the circle creates a right angle.  This is a right triangle problem involving missing sides.  This means that we will use Pythagorean's theorem to find the length of the radius.  Pythagorean's theorem applies this way:

[tex]10^2+r^2=(r+3)^2[/tex]

Foiling the right side gives us the equation:

[tex]100 + r^2=r^2+6r+9[/tex]

When we combine like terms, we find the squared terms cancel each other out, leaving us with

100 = 6r + 9 and

91 = 6r so

r = 15.2

In the context of mathematical geometry, if 'A⊥Y and X || Y', it means that A is perpendicular to Y and X is parallel to Y. In such a scenario, A would also be perpendicular to X.

In mathematical terms, the symbols used in this question represent geometric relationships. Here, 'A⊥Y' means that A is perpendicular to Y, meaning A intersects with Y at a right angle (90 degrees). 'X || Y' signifies that X and Y are parallel, meaning they are in the same plane never intersect or meet, regardless of how far extended.

When it is given 'A⊥Y and X || Y', this suggests a specific geometric condition. In such a case, the vector A (or line/segment) is perpendicular to the vector Y. Also, the Vector X is parallel to Y. From these conditions, if one line is perpendicular to a second line, and a third line is parallel to the second line, then the first and third lines are also perpendicular to each other. Therefore, the conclusion in this case would be 'A is perpendicular to X' or 'A⊥X'.

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Explanation:

There is nothing to "solve." This equation is a trig identity.

Often, it works well to express all trig functions in terms of sine and cosine. When you're trying to prove an identity, you usually pick one side to rearrange, and leave the other side alone. Here, we will rearrange the right side.

[tex]\csc\theta=\dfrac{\cot\theta+1}{\cos\theta+\sin\theta}\\\\\csc\theta=\dfrac{\dfrac{\cos\theta}{\sin\theta}+1}{\cos\theta+\sin\theta}=\dfrac{\left(\dfrac{\cos\theta+\sin\theta}{\sin\theta}\right)}{\cos\theta+\sin\theta}=\dfrac{1}{\sin\theta}\\\\\csc\theta=\csc\theta[/tex]

Answer:

x={-2,2}

Step-by-step explanation:

Graph them when intersecting.

Algebraically:

x^2 + 1 = -x^2 + 9

Add x^2 on both sides and subtract 1 on both sides.

2x^2 = 8

Divide 2 on both sides

x^2 = 4

Square root on both sides

|x| = 2

Remove abs value by putting + or - on the other side

x = {-2,2}

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2,2

B in edge

I am taking the test

XV is 1/2 a circle , which is equal to 180 degrees ( a full circle is 360).

ZW = WY, so ZV = VY = 43.

XY = XV-43 = 180 - 43 = 137

The answer is B. 137