Geometry: write a two column proof

Answer:

Option B  7sqrt2

Step-by-step explanation:

I assume that in the right triangle y and 7 are the legs and x is the hypotenuse

so

we know that

In the right triangle

cos(45)=7/x ----> the cosine of angle of 45 degrees is equal to divide the adjacent side to angle of 45 degrees by the hypotenuse

In this problem y=7 because is a 45-90-45 triangle

Remember that

cos(45)=√2/2

equate the equations

√2/2=7/x

x=14/√2

x=14/√2*(√2/√2)=14√2/2=7√2 units

Answer:

30 ft

Step-by-step explanation:

This is a classic right triangle problem, where the length of the ladder represents the hypotenuse, where the ladder is lengthwise from the building is the base of the triangle, and what we are looking for is the height of the triangle.  Pythagorean's Theorem will help us find this length.

[tex]32^2-10^2=y^2[/tex] so

1024 - 100 = y^2 and

y = 30.4 so 30 feet

Final answer:

Using the Pythagorean theorem, it is determined that the ladder reaches approximately 30 feet up the building when one end is placed 10 feet from the wall.

Explanation:

To determine how far up the building the ladder will reach, we can use the Pythagorean theorem, which applies to right-angled triangles. The ladder forms the hypotenuse, the distance from the wall to the base of the ladder forms one leg, and the height the ladder reaches up the wall forms the other leg of the triangle.

Using the given lengths:

Ladder (hypotenuse) = 32 feet

Distance from the wall (adjacent) = 10 feet

Let height up the wall (opposite) be represented by y.

The Pythagorean theorem states that:

a^2 + b^2 = c^2

Where a and b are the legs of the triangle and c is the hypotenuse. Plugging in the values:

10^2 + y^2 = 32^2

100 + y^2 = 1024

y^2 = 1024 - 100

y^2 = 924

y = √924

y ≈ 30.4 feet

To the nearest foot, the ladder reaches approximately 30 feet up the wall.

Answer:

10 in

Step-by-step explanation:

So we want to consider the surface area of this sphere.

The formula for surface area of a sphere is [tex]A=4 \pi r^2[/tex].

So we have that the surface area is [tex]100 \pi[/tex].

So I'm going to replace [tex]A[/tex] in [tex]A=4 \pi r^2[/tex] with  [tex]100 \pi[/tex].

[tex]100\pi=4\pi r^2[/tex]

Now our main objective here is to solve for [tex]r[/tex]:

Divide both sides by [tex]4 \pi[/tex]:

[tex]\frac{100\pi}{4 \pi}=\frac{4\pi r^2}{4 \pi}[/tex]

This gets us [tex]r^2[/tex] by itself:

[tex]25=r^2[/tex]

What number squared gives you 25? If you don't know, just take the square root of both sides giving you:

[tex]\sqrt{25}=r[/tex]

Now you can just put [tex]\sqrt{25}[/tex] in your calculator.  You should get 5.

5 is the radius

The diameter is twice the radius.

So 2(5) is 10, so the diameter is 10 in.

Answer:

C) 10.0 in.

Step-by-step explanation:

If Hasan is painting a spherical model of a human cell for his science class and uses 100π square inches of paint (in one coat) to evenly cover the outside of the cell, the diameter of Hasan’s cell model is 10.0 inches.

Radius = 5

Diameter = Radius x 2

Therefore 5 x 2 = 10

The diameter is 10 in.

Answer:

The given statement is true.

Step-by-step explanation:

Quadrilaterals are similar if their corresponding sides are proportional.

This statement is true.

Quadrilaterals are similar when

a) corresponding angles are equal

b) the corresponding sides are proportional i,e the ratios of corresponding sides are equal

So, the given statement is true.

Answer:

  FALSE

Step-by-step explanation:

Corresponding angles must also be congruent for the figures to be similar. Proportional sides is not a sufficient condition.

Answer:

Step-by-step explanation:

It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...

  x + y = 85

The total of charges is the sum of the products of charge per minute and minutes used:

  7/20x + 2/5y = 31.00

We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.

  -7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)

  -7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses

  y = 25 . . . . . . . . simplify

Then the value of x is

  x = 85 -y = 85 -25

  x = 60

Answer:

The second, fourth and B option are correct.

Step-by-step explanation:

In order to solve this problem, we are going to define the following variables :

[tex]X:[/tex] ''Minutes she used her pay-as-you-go phone for a call''

[tex]Y:[/tex] ''Minutes of data she used''

Then, we are going to make a linear system of equations to find the values of [tex]X[/tex] and [tex]Y[/tex].

''This month, she used a total of 85 minutes'' ⇒

[tex]X+Y=85[/tex]  (I)

(I) is the first equation of the system.

''The bill was $31'' ⇒

[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II)

(II) is the second equation of the system.

The system of equations will be :

[tex]\left \{ {{X+Y=85} \atop {(\frac{7}{20})X+(\frac{2}{5})Y=31}} \right.[/tex]

The second option ''The system of equations is [tex]X+Y=85[/tex] and [tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] .'' is correct

Now, to solve the system, we can eliminate the x-variable from the equations by multiplying the equation with the fractions by 20 and multiplying the other equation by -7. Then, we can sum them to obtain the value of [tex]Y[/tex] :

[tex]X+Y=85[/tex] (I)

[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II) ⇒

[tex](-7)X+(-7)Y=-595[/tex] (I)'

[tex]7X+8Y=620[/tex] (II)'

If we sum (I)' and (II)' ⇒

[tex](-7)X+(-7)Y+7X+8Y=-595+620[/tex] ⇒ [tex]Y=25[/tex]

If we replace this value of [tex]Y[/tex] in (I) ⇒

[tex]X+Y=85\\X+25=85\\X=60[/tex]

The fourth option ''To eliminate the x-varible from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7'' is correct.

With the solution of the system :

[tex]\left \{ {{X=60} \atop {Y=25}} \right.[/tex]

We answer that the option ''B-She used 60 minutes for calling and 25 minutes for data'' is correct.

[tex]|\Omega|=3\cdot3=9\\|A|=1\cdot2=2\\\\P(A)=\dfrac{2}{9}\approx22\%[/tex]

Answer:

4.97485 (approximately)

Step-by-step explanation:

You have the information SAS given.

This is a case for law of cosines.

[tex]b^2=a^2+c^2-2ac*cos(B)[/tex]

[tex]b^2=12^2+10^2-2(12)(10)*cos(24)[/tex]

[tex]b^2=144+100-240cos(24)[/tex]

[tex]b^2=244-240cos(24)[/tex]

Take the square root

[tex]b=\sqrt{244-240cos(24)}[/tex]

I was saving rounding to the end that is why I didn't put 240*cos(24) in my calculator.

So now I'm going to put sqrt(244-240*cos(24)) in my calculator. Make sure your calculator says deg (for degrees).

4.97485 (approximately)

Answer:

  (-2, -2)

Step-by-step explanation:

Compare the two functions ...

  f(x) = -|x +2| -2

  f(x) = a·g(x -h) +k

where f(x) is a translation and scaling of function g(x). Here, you have ...

  g(x) = |x|

The scale factor is a = -1.

The horizontal shift is h = -2.

The vertical shift is k = -2.

_____

The original vertex at (0, 0) has been shifted by (h, k) to ...

  (0, 0) + (h, k) = (0, 0) + (-2, -2) = (-2, -2).

Answer:

(-2,-2)

Step-by-step explanation:

I took a test and got it right

Answer:

Initial height or what the ball was originally bounced from a height of 9 feet

Step-by-step explanation:

9 represents the height that the ball was originally bounced from.

If you plug in 0 for [tex]n[/tex] into [tex]f(n)=9(0.7)^n[/tex], you get:

[tex]f(0)=9(0.7)^0=9(1)=9[/tex].

9 feet is the initial height since that is what happens at time zero.

Answer:

Initial height or what the ball was originally bounced from a height of 9 feet

Step-by-step explanation:

9 represents the height that the ball was originally bounced from.

If you plug in 0 for  into , you get:

.

9 feet is the initial height since that is what happens at time zero.

Answer:

  center: (2, -4); radius: 5

Step-by-step explanation:

Group x-terms and y-terms. Add the squares of half the coefficient of the linear term in each group. It can be convenient to subtract the constant, too.

  (x^2 -4x) +(y^2 +8y) = 5

  (x^2 -4x +4) +(y^2 +8x +16) = 5 + 4 + 16

  (x -2)^2 +(y +4)^2 = 5^2

Comparing this to the form of a circle centered at (h, k) with radius r, we can find the center and radius.

  (x -h)^2 +(y -k)^2 = r^2

  (h, k) = (2, -4) . . . . . the circle center

  r = 5 . . . . . . . . . . . . the radius

Answer:

Circumference = 25m

Area = 50 m2

Step-by-step explanation:

formula for circumference of a circle is π(d)

when radius is 4m, diameter is 8m

3.14(8)= 25.13

nearest tenth = 25m

formula for area of circle is 2πr or π(r)(r)

when radius is 4m

3.14(4)(4)=50.27 m2

nearest tenth =50m

Answer: circumference of the circle is 25.12 m  and the area of the circle is 50.2 m²

Step-by-step explanation:

To find the circumference of the circle of radius  4 meters, we simply use the formula;

area of a circumference = 2πr

                      π is given to be 3.14 and radius r=4 meter, we will substitute this variable into the formula

area of a circumference = 2πr

                                          = 2 × 3.14 × 4

                                          =25.12

                                           ≈25.1  to the nearest tenth

Therefore, the circumference of the circle is is 25.1 meters

To find the area of the circle, we simply use the formula:

area of circle = π[tex]r^{2}[/tex]

                     =  3.14 × (4)²

                      =3.14 × 16

                        =50.24

                        ≈50.2   to the nearest tenth

Therefore, the area of the circle is 50.2 m²

Answer:

  (4, -2)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h)

for a line with slope m through point (h, k).

Comparing this to the equation you're given, you can see that the point that was used is (h, k) = (4, -2).

_____

You can find other points on the line, but this one is the easiest to find, since it can be read directly from the equation.

Answer:

-1

Step-by-step explanation:

They already did the opposite reciprocal for you.

They have it in the form [tex]y=\frac{1}{4}x+b[/tex] now.

To find b you just enter (x,y)=(8,1).

Let's do that.

[tex]1=\frac{1}{4}(8)+b[/tex]

[tex]1=2+b[/tex]

Subtract 2 on both sides:

[tex]-1=b[/tex]

b=-1

Hey there! :)

Perp. to y = -4x + 3 ; intersects (8, 1)

Slope-intercept form is : y=mx+b where m = slope, b = y-intercept

So, our slope of the given equation is -4. However, our new slope is 1/4 because it is the negative reciprocal of -4. We have to use the negative reciprocal because our new line is perpendicular to our given one.

Now, using (8, 1) and our new slope (1/4), simply plug everything in to the point-slope form.

Point-slope : y-y1 = m(x - x1)

y - 1 = 1/4(x - 8)

Simplify.

y - 1 = 1/4x - 2

Add 1 to both sides.

y = 1/4x - 1 ⇒ our new equation.

Therefore, the number that fits in the question mark is -1.

~Hope I helped!~

Answer:

Step-by-step explanation:

The trig identities are helpful for this.

  sin² θ = 1 - cos² θ = 1 -(1/6)² = 35/36

  sin θ = (√35)/6 . . . . . . take the square root

__

  tan² θ = sec² θ -1 = (1/cos² θ) -1 = 6² -1 = 35

  tan θ = √35 . . . . . . . . . take the square root

The answer of this question is c) 14

MN=NO

4x-5=2x+1

2x=6

x=3

Again

MO=MN+NO

MO=4×3-5+2×3+1

MO=7+7

MO=14

Answer:

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

-4  |  3     -10       7

Step-by-step explanation:

Take the coefficients of the numerator inside the division bar

Take the opposite of the number in the denominator

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

-4  |  3     -10       7

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

[tex]\frac{3x^2-10x+7}{x+4}[/tex]

Here the numerator is

[tex]3x^2-10x+7[/tex]

So, the coefficients of numerator are 3, -10 and 7.

If the denominator of an expression is (x+c), then in synthetic division form -c is written on outside and coefficients of numerator are written under the sign of division(descending order of degree of terms).

The denominator of the expression is (x+4), so -4 is written outside the sign of division.

[tex]-4\overline{|3\quad -10\quad 7}[/tex]

Therefore the correct option is B.

Answer:

  84%

Step-by-step explanation:

The empirical rule tells you that 68% of the standard normal distribution is within 1 standard deviation of the mean. The distribution is symmetrical, so the amount in the lower tail is (1 -68%)/2 = 16%.

Since the number you're interested in, 240, is one standard deviation above the mean (200 +40), the percentage of interest is the sum of the area of the central part of the distribution along with the lower tail:

  68% + 16% = 84%.

Answer:

Part 1) [tex]-1.25[/tex] -------> [tex]2.75/(-2.2)[/tex]

Part 2) [tex]-4\frac{1}{3}[/tex] --------> [tex](-2\frac{3}{5}) / (\frac{3}{5})[/tex]

Part 3) [tex]\frac{2}{3}[/tex] ------> [tex](-\frac{10}{17}) / (-\frac{15}{17})[/tex]

Part 4) [tex]3[/tex] ------> [tex](2\frac{1}{4}) / (\frac{3}{4})[/tex]

Step-by-step explanation:

Part 1) we have

[tex]2.75/(-2.2)[/tex]

To calculate the division problem convert the decimal number to fraction number

[tex]2.75=275/100\\ -2.2=-22/10[/tex]      

so

[tex](275/100)/(-22/10)[/tex]

Remember that

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](275/100)/(-22/10)=(275/100)*(-10/22)=-(275*10)/(22*100)=-(275)/(220)[/tex]

Simplify

Divide by 22 both numerator and denominator

[tex]-(275)/(220)=-125/100=-1.25[/tex]

Part 2) we have

[tex](-2\frac{3}{5}) / (\frac{3}{5})[/tex]

To calculate the division problem convert the mixed number to an improper fraction  

[tex](-2\frac{3}{5})=-\frac{2*5+3}{5}=-\frac{13}{5}[/tex]

so

[tex](-\frac{13}{5}) / (\frac{3}{5})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](-\frac{13}{5}) / (\frac{3}{5})=(-\frac{13}{5})*(\frac{5}{3})=-\frac{13*5}{5*3}=-\frac{13}{3}[/tex]

Convert to mixed number

[tex]-\frac{13}{3}=-(\frac{12}{3}+\frac{1}{3})=-4\frac{1}{3}[/tex]

Part 3) we have

[tex](-\frac{10}{17}) / (-\frac{15}{17})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](-\frac{10}{17}) / (-\frac{15}{17})=(-\frac{10}{17})*(-\frac{17}{15})=\frac{10*17}{17*15}=\frac{10}{15}[/tex]

Simplify

Divide by 5 both numerator and denominator

[tex]\frac{10}{15}=\frac{2}{3}[/tex]

Part 4) we have

[tex](2\frac{1}{4}) / (\frac{3}{4})[/tex]

To calculate the division problem convert the mixed number to an improper fraction  

[tex](2\frac{1}{4})=\frac{2*4+1}{4}=\frac{9}{4}[/tex]

so

[tex](\frac{9}{4}) / (\frac{3}{4})[/tex]

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

[tex](\frac{9}{4}) / (\frac{3}{4})=(\frac{9}{4})*(\frac{4}{3})=\frac{9*4}{4*3}=\frac{9}{3}=3[/tex]

To match each division problem to its quotient, you'll need to perform each division and then see which of the given quotients corresponds to the result of each division. Let's go through the steps for each division problem you might have:
1. Start with the first division problem. For example, if it's `45 / 5`, you'd perform the division by determining how many times 5 goes into 45.
2. To solve `45 / 5`, you can count by fives until you reach 45, or recognize that 5 times 9 is 45. Hence, the quotient for `45 / 5` is 9.
3. Look at the potential quotients given to you and match the result. If one of the choices is 9, match `45 / 5` with that quotient.
4. Repeat the process for the next division problem, say `30 / 6`. Divide 30 by 6 to get the quotient. Since 6 times 5 is 30, the quotient here is 5.
5. Again, look at your potential quotients. If there is a 5 among them, this is incorrect since 5 is not a choice in our example set of potential quotients. Instead, you would expect to see a 6, as that is the typical mistake that such a setup might be aiming to identify.
6. Move on to the next division problem, for instance, `18 / 3`. To find the quotient, you divide 18 by 3, which gives you 6 because 3 times 6 is 18.
7. Match `18 / 3` with the correct quotient from your list of choices, which in this case would be 6.
Remember, these are hypothetical examples. In your actual matching exercise, you would perform the division for each problem you've been given and then find the corresponding quotient from the choices available to you. The key is to perform each division accurately and then pair it with the right answer. If you perform all the divisions and none of the quotients match the results you have obtained, there might be an error in the given quotients or the division problems.

Answer:

Let Frank spends x amount in purchasing the magazines and newspapers.(though this is not used here)

MU is marginal utility where a customer can decide a particular way to allocate his income.

This allocation is done in a way, that the last dollar spent on purchasing a product will yield the same amount of extra marginal utility.

MU from the final magazine is 10 units while his MU from the final newspaper is also 10 units.

MU per dollar spent on magazines = [tex]\frac{10}{5}=2[/tex]

MU per dollar spent on newspapers = [tex]\frac{10}{2.5}=4[/tex]

We can see the MU per dollar spent on magazine is less than newspapers.

Therefore, according to the utility-maximizing rule, Frank should re-allocate spending from magazines to newspapers.

Answer:

He should investing more money on newspaper

Step-by-step explanation:

Given:

His MU from the final magazine and final newspaper is 10 utils, so we have:

magazine = $5 / 10 utils = $0.50 per util

newspaper = $2.50 / 10 utils = $0.25 per util

He should investing more money on newspaper  because twice the amount obtained from each dollar spent on newspapers than magazines as we can see above,

Hope it will find you well.

Answer:

[tex](x+\frac{b}{2a})^2+(\frac{4ac}{4a^2}-\frac{b^2}{4a^2})=0[/tex]

[tex](x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]

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

Step-by-step explanation:

[tex]x^2+\frac{b}{a}x+\frac{c}{a}=0[/tex]

They wanted to complete the square so they took the thing in front of x and divided by 2 then squared.  Whatever you add in, you must take out.

[tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2+\frac{c}{a}-(\frac{b}{2a})^2=0[/tex]

Now we are read to write that one part (the first three terms together) as a square:

[tex](x+\frac{b}{2a})^2+\frac{c}{a}-(\frac{b}{2a})^2=0[/tex]

I don't see this but what happens if we find a common denominator for those 2 terms after the square.  (b/2a)^2=b^2/4a^2 so we need to multiply that one fraction by 4a/4a.

[tex](x+\frac{b}{2a})^2+\frac{4ac}{4a^2}-\frac{b^2}{4a^2}=0[/tex]

They put it in ( )

[tex](x+\frac{b}{2a})^2+(\frac{4ac}{4a^2}-\frac{b^2}{4a^2})=0[/tex]

I'm going to go ahead and combine those fractions now:

[tex](x+\frac{b}{2a})^2+(\frac{-b^2+4ac}{4a^2})=0[/tex]

I'm going to factor out a -1 in the second term ( the one in the second ( ) ):

[tex](x+\frac{b}{2a})^2-(\frac{b^2-4ac}{4a^2})=0[/tex]

Now I'm going to add (b^2-4ac)/(4a^2) on both sides:

[tex](x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]

I'm going to square root both sides to rid of the square on the x+b/(2a) part:

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

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

Now subtract b/(2a) on both sides:

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

Combine the fractions (they have the same denominator):

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

Answer:

  x = 6

Step-by-step explanation:

An angle bisector divides the segments on either side of it so they are proportional. That is ...

  x/12 = 5/10

  x = 12(5/10) = 6 . . . . . multiply by 12

Answer:

a_{n}=20+4(n-1)

Step-by-step explanation:

It is given that the number of corn stalks in rows of the field can be modeled by an arithmetic sequence.

The 5th row has 36 corn stalks. This means 5th term of the sequence is 36. i.e.

[tex]a_{5}=36[/tex]

The 12th row has 64 stalks. So,

[tex]a_{12}=64[/tex]

In order to write the explicit rule we need to find the first term(a1) and common difference(d) of the sequence.

The explicit rule for the arithmetic sequence is of the form:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

Writing the 5th and 12th term in this way, we get:

[tex]a_{5}=a_{1}+4d[/tex]

[tex]a_{1}+4d=36[/tex]                                                     Equation 1

Similarly for 12th term, we can write:

[tex]a_{1}+11d=64[/tex]                                                     Equation 2

Subtracting Equation 1 from Equation 2, we get:

7d = 28

d = 4

Using the value of d in Equation 1, we get:

[tex]a_{1}+4(4)=36\\\\ a_{1}=20[/tex]

Thus, for the given sequence first term is 20 and common difference is 4. Using these values in the general explicit rule, we get:

[tex]a_{n}=20+4(n-1)[/tex]

Answer:

48

Step-by-step explanation:

Answer:

There are 1,679,616 possibles outcomes

Step-by-step explanation:

This can be calculated using a rule of multiplication as:

     6    *      6   *      6    *    6       *      6    *      6     *      6     *      6     =  1,679,616

1st Roll      2nd       3rd       4th          5th        6th       7th          8th

Because the die is rolled 8 times and every roll has 6 possibilities.

Then, if the order matter, there are 1,679,616 possible outcomes.

Answer:

y = 4.8

Step-by-step explanation:

Since AM is an angle bisector then the following ratios are equal

[tex]\frac{AC}{AB}[/tex] = [tex]\frac{CM}{MB}[/tex], that is

[tex]\frac{9.6}{8}[/tex] = [tex]\frac{y}{4}[/tex] ( cross-  multiply )

8y = 38.4 ( divide both sides by 8 )

y = 4.8

Answer:

  see below

Step-by-step explanation:

Each reflection is along a line through the other focus of the conic. The two foci of the parabola are the one shown and the one at infinity (the source of light rays).

The light ray in the telescope will be reflected by each conic surface in a specific manner: converging at the parabolic mirror, diverging at the hyperbolic mirror, and converging again at the elliptical mirror.

The diagram shows a telescope fitted with different types of mirror surfaces, including parabolic, hyperbolic, and elliptical mirrors. When a ray of light parallel to the parabolic axis enters the telescope, it will be reflected by each conic surface in a certain way.

The light ray will be reflected by the parabolic mirror surface and converge to a single point called the focus. This is due to the property of the parabola that all incoming parallel rays are reflected to a common focal point.

The reflected ray will then strike the hyperbolic mirror surface, where it will be reflected in such a way that it diverges outwards. Hyperbolic mirrors have a property that makes them reflect incoming parallel rays into diverging rays.

Finally, the diverging ray from the hyperbolic mirror will enter the elliptical mirror surface. The elliptical mirror will reflect the ray in such a way that it converges to a point located at the eyepiece of the telescope. Elliptical mirrors have a property that makes them reflect incoming parallel rays to a focal point.

In summary, the light ray will be reflected by the parabolic mirror surface, then the hyperbolic mirror surface, and finally, the elliptical mirror surface, converging and diverging in different ways along the way.

https://brainly.com/question/32184600

#SPJ11

Answer: False

Step-by-step explanation: I believe it would be false. Using the law of sines with the side lengths of 113.29 feet and 125 feet, and the corresponding angels of 25 and 65 degrees, the angle of the light is about 58.29. I believe this would make it false as the angle is incorrect.

Answer:

Exact Form:

11/  5

Decimal Form:

2.2

Mixed Number Form:

2  1/ 5

Step-by-step explanation:

For the decimal, divide 11 by 5.

To get the Mixed number form, find out how many times 5 goes into 11, then then what is left over. Put the number left over the number that was dividing. 5 goes into 11 2 times, then 1 is left over, put the 1 over 5.

Answer:

21.77 After the donation

Step-by-step explanation:

3.99 Multiplied by 6 is 23.94

So 45.71 - 23.94 = 21.77

Answer:

$520

Step-by-step explanation:

Since this is a 5% discount, you must subtract 5 from 100% which is 95%.

This will be written as 0.95.

Expression: [tex]x*0.95=494\\\\0.95x=494\\\\\frac{0.95x}{0.95} =\frac{494}{0.95}[/tex]

The answer will be $520.

Answer:

[tex]\boxed{520}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\text{ Price before discount - discount} & = & \text{sale price}\\b-0.05b & = & 494\\0.95b & = & 494\\\\b & = & \dfrac{494 }{0.95}\\\\& = & \mathbf{520}\\\end{array}\\\text{The number from the set that matches } b \text{ is }\boxed{\mathbf{520}}[/tex]

Answer:

see below

Step-by-step explanation:

z = 9 + 3i

This is in the form a+bi   where a is the real part and b is the imaginary part

1.The real part is 9

2. The imaginary part is 3

The complex conjugate is a-bi

3. complex conjugate 9-3i

4. 3i - z = 3i - (9+3i) = 3i -9 - 3i = -9

5. z-9 = 9+3i - 9 = 3i

6.  9-z = 9- (9+3i) = 9-9-3i = -3i