What additional information is needed to prove triangle LMN is congruent to triangle KMN using the HL theorem?

QUESTION 1

The given logarithm is

[tex]\log_{243}(27)[/tex]

Let [tex]\log_{243}(27)=x[/tex].

We rewrite in exponential form to get;

[tex]27=243^x[/tex]

We rewrite both sides of the equation as an index number to base 3.

[tex]3^3=3^{5x}[/tex]

Since the bases are the same, we equate the exponents.

[tex]3=5x[/tex]

Divide both sides by 5.

[tex]x=\frac{3}{5}[/tex]

[tex]\therefore \log_{243}(27)=\frac{3}{5}[/tex]

QUESTION 2

The given logarithm is

[tex]\log_{25}(\frac{1}{5} )[/tex]

We rewrite both the base and the number as power to base 5.

[tex]\log_{5^2}(5^{-1})[/tex]

Recall that: [tex]\log_{a^q}(a^p)=\frac{p}{q} \log_a(a)=\frac{p}{q}[/tex]

We apply this property to obtain;

[tex]\log_{5^2}(5^{-1})=\frac{-1}{2}\log_5(5)=-\frac{1}{2}[/tex]

➷ We'll work from here:

9x = 180

To isolate x, you would need to divide both sides by 9

x = 180/9

Solve:

x = 20

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer: ❤️Hello!❤️ x = 20

Step-by-step explanation:  Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

2*x+3*x+4*x-(180)=0  

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  9x - 180  =   9 • (x - 20)  

Step  2  :

Equations which are never true :

2.1      Solve :    9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2      Solve  :    x-20 = 0  

Add  20  to both sides of the equation :  

                     x = 20  

Answer:

d.   a_n = 6n - 4.

Step-by-step explanation:

The common difference (d)  is 8-2 = 14-8 = 20-14 = 26-20 = 6.

This is an Arithmetic Sequence with the first term (a1) is 2.

The general form of the explicit formula is a_n = a1 + d(n - 1)  so this sequence has  the formula:

a_n = 2 + 6(n - 1)

a_n = 2 + 6n - 6

a_n = 6n - 4.

The sequence is an illustration of an arithmetic sequence.

The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

We have:

[tex]a_1 = 2[/tex] -- the first term

Next, we calculate the common difference (d)

[tex]d = a_2 - a_1[/tex]

So, we have:

[tex]d = 8 -2[/tex]

[tex]d = 6[/tex]

The explicit formula is calculated using:

[tex]a_n = a_1 + (n - 1)d[/tex]

So, we have:

[tex]a_n =2 + (n - 1) \times 6[/tex]

Open bracket

[tex]a_n = 2 + 6n - 6[/tex]

Collect like terms

[tex]a_n = 6n - 6 + 2[/tex]

[tex]a_n = 6n - 4[/tex]

Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]

Read more about arithmetic sequence at:

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Answer:

Step-by-step explanation:

[tex]n,\ n+2,\ n+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)+(n+4)=-72\\\\n+n+2+n+4=-72\qquad\text{combine like terms}\\\\3n+6=-72\qquad\text{subtract 6 from both sides}\\\\3n+6-6=-72-6\\\\3n=-78\qquad\text{divide both sides by 3}\\\\\dfrac{3n}{3}=-\dfrac{78}{3}\\\\n=-26\\\\n+2=-26+2=-24\\\\n+4=-26+4=-22[/tex]

Answer:

The 3 angles are 36.87, 53.13 and 90 degrees.

Step-by-step explanation:

This right  triangle ABC  has sides 3, 4 and 5 units.

To find the angles:

sin A - 3/5  gives m <  A =  36.87 degrees

sin B = 4/5 gives m < B = 53.13 degrees.

[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]

Since [tex]f'(x)\le9[/tex], we have

[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]

so 19 is the largest possible value.

Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.

In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).

Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.

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Dana’s waking rate in miles per hour is 3 mph.

I did 3/4 x 4 = 3 because she walked 1/4 a mile and I needed to figure out the miles per one whole hour.

I hope this made sense and helped you.

Answer:

35° and 85°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Since one angle = 60° then the sum of the other 2 angles = 120°

Sum the parts of the ratio 7 + 17 = 24 parts, hence

[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence

7 parts = 7 × 5° = 35°

17 parts = 17 × 5° = 85°

note that 60° + 35° + 85° = 180°

Answer:

length of base is 10

Step-by-step explanation:

The area of the entire firgure is 1600 cm^2.  There are 4 equal sized pennants, so each pennant is 1600/4 = 400

the bottom pennant has area 400 and is triangular shaped.  the area of a triangle is 1/2 b h.  

A = 1/2 b h       given height is 80 and area is 400.  plug these values in

400 = 1/2 b (80)

400 = 40 b       divide both sides by 40

b = 10

Answer:

I think it's 53 miles

Step-by-step explanation:

After flat fee of $1.75 leaves him $13.25. Then use the remainder to calculate miles. Each dollar allows 4 miles × 13 = 52+1=53

The inequality is:

             [tex]1.75+0.25x\leq 15[/tex]

The solution of the inequality is:

                    [tex]x\leq 53[/tex]

Let Eddie could travel x miles.

It is given that:

A cab charges $1.75 for the flat fee and $0.25 for each mile.

This means that the fee charged by Eddie if he travels x miles excluding the flat fee is:

                   $  0.25x

Total amount the cab will charge Eddie is:

              1.75+0.25x

Also, it is given that:

He has only $ 15 to spend this means that he can spend no more than 15 on riding in a cab.

Hence, the inequality is given by:

            [tex]1.75+0.25x\leq 15[/tex]

Now on solving the inequality i.e. finding the possible values of x from the inequality.

We subtract both side of the inequality by 1.75 to obtain:

[tex]0.25x\leq 13.25[/tex]

Now on dividing both side of the inequality by 0.25 we get:

[tex]x\leq 53[/tex]

Hence, Eddie could travel less than or equal to 53 miles .

Answer:

87777777777777777777777777

Step-by-step explanation:

Answer:

$38.50/mo

Step-by-step explanation:

Rate of change = change in balance/time.

Change in balance = $731 - $500 = $231

Rate of change = $231/6 mo = $38.50/mo  

Answer:

31.60%

Step-by-step explanation:

(731−500)÷731=0.3160

0.3160×100=31.60%

Hope it helps!

Answer:

Part a) The volume of the prism Q is two times the volume of the prism P

Part b) The volume of the prism Q is two times the volume of the prism P

Step-by-step explanation:

Part 18) we know that

The volume of a rectangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=B(2h)=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

so

The volume of the prism Q is two times the volume of the prism P

b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?

Volume of prism Q

[tex]VQ=(2B)h=2(Bh)[/tex]

Volume of prism P

[tex]VP=Bh[/tex]

Compare

[tex]VQ=2VP[/tex]

The volume of the prism Q is two times the volume of the prism P

Answer:

480 feet

Step-by-step explanation:

Answer:

x+3

Step-by-step explanation:

Factor x² + 6x + 9 = (x+3)(x+3)

Factor x² + 5x + 6 = (x+3)(x+2)

We can see that (x+3) is the LCM since it goes into  x² + 6x + 9 and

x² + 5x + 6

Answer: 233/23

Step-by-step explanation:

[tex]\bold{Hey\ there!}[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& enjoy\ your\ day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The answer is c 226.9 m2

Step-by-step explanation:

Hope this helps

Answer:

a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

Step-by-step explanation:

The given system of equation is

[tex]9x-4y-5z=9[/tex]

[tex]7x+4y-4z=-1[/tex]

[tex]6x-6y+z=-5[/tex]

The coefficient matrix is :

[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]

The constant matrix is

[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]

The augmented matrix is obtained by  combining the coefficient matrix and the constant matrix.

[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]

The correct choice is A

Answer:

The answer is d

Step-by-step explanation:

A line segment is a portion of an infinite line separated by two end points

The mean altitude will be -54 per minute

We are given with altitude change as -378 feet over 7 minutes

Now

We need feet per minute

So -378 / 7 will give us the altitude change per minute

-378 / 7 = -54

Therefore the mean change of altitude in feet per minute is -54 per minute

Answer:

852

Step-by-step explanation:

Answer:

Step-by-step explanation:

2  on  top goes  to  last  on  the  bottom  or  b  goes  to  d

1st one one top goes to the 2nd one on bottom or a goes to b

last one on top goes to the third one on bottom or d goes to c

The last two witch are 3rd on top and first one together

Hope this helped it took me a long time :)

The x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A unit circle refers to a circle with unit radius (r = 1 unit) and positioned at center ( coordinates of origin = (h,k) = (0,0))

Thus, the equation of unit circle would be:

[tex]x^2 + y^2 =1[/tex]

Getting expression for y in terms of x,

[tex]x^2 + y^2 =1\\\\y = \pm \sqrt{1 - x^2}[/tex]

Using this equation to evaluate x for all given y:

[tex]\pm \dfrac{\sqrt{5}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{5}{9} = 1 - x^2\\\\x^2 = \dfrac{4}{9}\\\\x = \pm \dfrac{2}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get:

[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex]

[tex]\pm \dfrac{\sqrt{7}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{7}{9} = 1 - x^2\\\\x^2 = \dfrac{2}{9}\\\\x = \pm \dfrac{\sqrt{2}}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex]

[tex]\pm \dfrac{3}{5} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{9}{25} = 1 - x^2\\\\x^2 = \dfrac{16}{25}\\\\x = \pm \dfrac{4}{5}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex]

[tex]\pm \dfrac{2\sqrt{2}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{8}{9} = 1 - x^2\\\\x^2 = \dfrac{1}{9}\\\\x = \pm \dfrac{1}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]

Thus, the x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

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Answer: first option

Step-by-step explanation:

To form an arithmetic sequence, you have that for the sequence [tex]7,6k,22[/tex]:

[tex]6k-7=22-6k[/tex]

Therefore, to calculate the value of k to form an arithmetic sequence, you must solve for k, as following:

- Add like terms:

[tex]6k+6k=22+7\\12k=29[/tex]

- Divide both sides by 12. Then you obtain;

[tex]k=\frac{29}{12}[/tex]

Answer:

[tex]k=\frac{29}{12}[/tex]

Step-by-step explanation:

The given sequence is 7, 6k, 22.

For this to be an arithmetic sequence, there must be a common difference.

[tex]6k-7=22-6k[/tex]

Group similar terms;

[tex]6k+6k=22+7[/tex]

Simplify;

[tex]12k=29[/tex]

Divide by 12

[tex]k=\frac{29}{12}[/tex]

in short, we simply split the total amount by the given ratio, so we'll split or divide 1020 by (15 + 2) and then distribute accordingly.

[tex]\bf \cfrac{petunias}{geraniums}\qquad 15:2\qquad \cfrac{15}{2}~\hspace{7em}\cfrac{15\cdot \frac{1020}{15+2}}{2\cdot \frac{1020}{15+2}}\implies \cfrac{15\cdot \frac{1020}{17}}{2\cdot \frac{1020}{17}} \\\\\\ \cfrac{15\cdot 60}{2\cdot 60}\implies \cfrac{900}{120}\implies \stackrel{petunias}{900}~~:~~\stackrel{geraniums}{120}[/tex]

The total number of geraniums in the greenhouse is 120. This was determined by calculating the value of each 'part' in the provided petunia to geranium ratio and then multiplying the number of geranium 'parts' by this value.

The question provides a ratio of petunias to geraniums in the greenhouse, which is 15:2. This is the same as saying for every 15 petunias, there are 2 geraniums. If you combine the parts of the ratio, you get a total of 17 parts (15 petunias + 2 geraniums). We know that the total number of flowers in the greenhouse is 1020.

Now, we'll figure out what each 'part' is equal to in the real world. To do that, we divide the total number of flowers by the total number of parts, so 1020 ÷ 17 = 60. This tells us each 'part' in our ratio is equal to 60 flowers.

From there, since we need to find the number of geraniums, we multiply the number of geranium 'parts' by the value of each 'part'. So, the number of geraniums in the greenhouse is 2 (The geranium 'parts') x 60 = 120 geraniums.

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The correct answer would be A.

A.

You can distribute the 8

Distribute 8 to a and multiply them = 8a

Distribute 8 to -6 and multiply them = -48

= 8a-48

Answer:

  2 and 3/7 pounds

Step-by-step explanation:

Convert the mixed number to an improper fraction

12 1/7 becomes 85/7

This represents 5 bags, so divide it by 5 to see what one bag should weigh...

(85/7)/5 becomes (85/7)/(5/1)

which becomes

(85/7)*(1/5)      (division is the same as multiplying by the reciprocal)

   85/35  

     17/7      (reduce the fraction by factoring out a 5 from top and bottom)

       2 and 3/7 pounds

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

[tex] {l}^{2} = {h}^{2} + {b}^{2} [/tex]

[tex]{l}^{2} = {20}^{2} + {15}^{2} [/tex]

[tex]{l}^{2} = 400 + 225[/tex]

[tex]{l}^{2} = 625[/tex]

[tex]l= \sqrt{625} = 25ft[/tex]

Answer:

25

Step-by-step explanation:

Answer:

p = 4

j = 21

Step-by-step explanation:

Joey = j

Pat = p

j = p + 17

(j+6) = 2*(p + 6) + 7      Simplify this. Remove the brackets.

j + 6 = 2p + 12 + 7        combine like terms    

j + 6 = 2p + 19               Subtract 6 from both sides

j +6-6 = 2p +19-6

j = 2p + 13

================

Equation j = 2p + 13 and j = p + 17

2p + 13 = p + 17                 Subtract p from both sides

2p-p+13 =p-p + 17

p + 13 = 17                         Subtract 13 from both sides

p = 17-13

p = 4

============

j = p + 17

j = 4 + 17

j = 21

Answer:

Joey is 21; Pat is 4

Step-by-step explanation:

The problem statement supports two equations in Joey's age (j) and Pat's age (p):

j - p = 17

(j +6) -2(p +6) = 7

Subtracting the second equation from the first, we have ...

(j -p) -((j +6) -2(p +6)) = (17) -(7)

p +6 = 10 . . . . . simplify

p = 4 . . . . . . . . . subtract 6

J = 17 +4 = 21

Joey is 21; Pat is 4.