Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN Triangles M L Q and N P Q are connected at point Q. A line is drawn from points M to N to form triangle M N Q. Which congruence theorem can be used to prove △MLQ ≅ △NPQ? AAS SSS ASA SAS

Answer:

TRUE

Step-by-step explanation:

Notice that point P is at the center of the circle. Notice also that it is being crossed by two diameters (segments RT and SQ). Then, the central angles RPS and TPQ must be equal because they are opposed by their vertex (center point P). Notice as well that the two triangles formed (triangle SRP, and triangle TPQ) are both isosceles triangles since they have the two sides that are adjacent  to the central angles mentioned above, equal to the circle's radius. Therefore, the sides opposite to the central angles (RS in one triangle, and QT in the other) must be equal among themselves.

Answer:

Step-by-step explanation:

Unfortunately, f(x)=(15)x is not an exponential function.  I will assume that you meant

f(x) = 5^x

The second table fits this function.  Note that if x = -2, f(-2) = 5^(-2) = 1/25.

Answer:

Step-by-step explanation:

Permutation has to do with arrangement.

To form different word by rearranging the word KINDNESS, this can be done in the following way;

The total letters present in kindness = 8 letters

Repeated letters are 2N's and 2S's

The arrangement is done in [tex]\frac{8!}{2!2!}[/tex] ways

[tex]= \frac{8!}{2!2!} \\= \frac{8*7*6*5*4*3*2!}{2!*2}\\ = 8*7*3*5*4*3\\= 10,080 \ different\ words[/tex]

For MATHEMATICIAN;

The total letters present in kindness = 13 letters

Repeated letters are 2M's, 2T'S 2I'sand 3A's

The number of words formed =

[tex]\frac{13!}{2!2!2!3!} \\= \frac{13*12*11*10*9*8*7*6*5*4*3!}{6*3!}\\= 13*2*11*10*9*8*7*6*5*4\\= 172,972,800\ different\ words[/tex]

Answer:

Please find attached the required graph and

Step-by-step explanation:

The values for the information given can be written down as follows;

Time, seconds             Volume mL

0,                                    500

12,                                   450

24,                                  400

36,                                  350

48,                                  300

60,                                  250

72 250

84 250

96 250

108 250

120 250

132 250

144 250

156 250

168 250

180 250

192 250

204 250

216 250

228 250

240 250

252 250

264 250

276 250

288 250

300 250

312 225

324,                                        200

336,                                         175

348,                                         150

360,                                         125

372,                                         100

384,                                         75

396,                                        50

408,                                        25

420,                                        0

Answer:

-15c - 30

Step-by-step explanation:

-5(3c+6)

Expand or distribute the term outside the bracket to the terms inside.

-5(3c) - 5(6)

-15c - 30

Answer:

The answer is -15c - 30

Step-by-step explanation:

You have to apply Distributive Law :

[tex]a(m + n) = am + an[/tex]

So for this question :

[tex] - 5(3c + 6)[/tex]

[tex] = - 5(3c) - 5(6)[/tex]

[tex] = - 15c - 30[/tex]

Answer:

Out of 8000 students, 10% take tuition in various subjects before the exam.

10% of 8000 is:

10/100 * 8000 = 800

Among the 800, 40% take tuition in English only and 20% take tuition in Math only.

80 students take tuition in other subjects, therefore, in percentage:

80/800 * 100 = 10%

Therefore, the percentage of students that take tuition in both Math and English is:

100% - (40% + 20% + 10%) = 100% - 70% = 30%

30% of the 800 students take tuition in both subjects. That is:

30/100 * 800 = 240 students

Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.

In percentage:

240/8000 * 100 = 3%

3% of students take tuition in both English and Math.

In Ratio:

3 : 100

3 out of 100 students take tuition in English and Math.

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Answer:

proved

Step-by-step explanation:

prove that : (sin^2 θ)/(1+cosθ)=1-cosθ

(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =

sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:

(sin^2Ф)(1-cosФ)/sin^2Ф =

1-cosФ     (sin^2Ф/sin^Ф=1)

proved

Answer:

Step-by-step explanation:

take it befor delete

Answer:

option B is the correct option.

Solution,

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

x-4=_+√5

X=4_+√5

Hope this helps...

Good luck on your assignment...

Answer:

(x-4)^2 =5

x^2-16=5

x^2=5+16

x^2=21

√x^2=√21

x=√21

Step-by-step explanation :

First of all open the bracket which has square

Secondly change the position of 16

Note: when a number changes its place , the symbol also changes

then when you get the value take the square root on both sides

and you'll get the answer

Answer:

5x4^10

Step-by-step explanation:

Hope this helps have a nice day :)

Answer:

5. [tex]4^{9}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = 20 ÷ 5 = 80 ÷ 20 = 320 ÷ 80 = 4

This indicates the sequence is geometric with n th term

[tex]a_{n}[/tex] = a . [tex]r^{n-1}[/tex]

Here a = 5 and r = 4 , thus

[tex]a_{10}[/tex] = 5. [tex]4^{9}[/tex]

Answer:

Step-by-step explanation:

Analysis

Answer:

49 x 3 = 147

147 + 173 = 320

Step-by-step explanation:

Step 1 Henrik grew 3 times as many potatoes as Derek grew. Derek managed to grow 49 potatoes.

49 x 3 = 147

Step 2  Henrik already had 173 potatoes harvested from his other field.

173 + 147

Answer:

A:C = 9:20

Step-by-step explanation:

The computation of the ratio is shown below:

We can say that

Surface area ratio = Ratio square

i.e

[tex](\frac{A}{B})^2 = \frac{9}{16}[/tex]

Now squaring both sides

[tex]\frac{A}{B} = \sqrt{\frac{9}{16} } \\\\ \frac{A}{B} =\frac{3}{4}[/tex]

The ratio is 3: 4

Now in the other case

Volume ratio = Cube ratio

i.e

[tex](\frac{B}{C})^3 = \frac{27}{125}[/tex]

Now cubing root both sides

So,

[tex]\frac{B}{C} = \frac{3}{5}[/tex]

Therefore  

B : C = 3:5

Now for making the equivalent ratios

A:B:C = 9:12:20

So,

A:C = 9:20

Step-by-step explanation:

y isn't directly proportional with x because the graph doesn't cross O the origin, it starts from a y-intercept wich is not a property for proportional portions

Answer:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Or:

[tex]x + 5 = 5y[/tex]

Step-by-step explanation:

We have the function:

[tex]y=5x-5[/tex]

And we want to find its inverse.

To find the inverse of a function, we:

Hence:

[tex]x=5y-5[/tex]

Solve for y. Add:

[tex]\displaystyle x + 5 = 5y[/tex]

Divide:

[tex]\displaystyle y = \frac{x+5}{5}[/tex]

Simplify. Hence:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

In conclusion, the inverse function is:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Answer:

Option B.

Step-by-step explanation:

From the given graph it is clear that the related line passes through the points (0,3) and (2,4).

So, the equation of related line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]

[tex]y-3=\dfrac{1}{2}x[/tex]

Add 3 on both sides, we get

[tex]y=\dfrac{1}{2}x+3[/tex]

The related line is a solid line and shaded portion lies below the line. So, the sign of inequality must be ≤.

[tex]y\leq \dfrac{1}{2}x+3[/tex]

Therefore, the correct option is B.

Answer:

y ≤ one-halfx + 3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

in 1 years it grows 15% of $200= $30+200=$230

in x yrs it grows to $500

.... number of yrs= 500/230= 2.17 yrs

Answer:

Children 188

Adults. 115

Step-by-step explanation:

Let the no. of children be x and adults be y

x + y = 303

x = 303 - y. .... .....(1)

1.75x + 4.80y = 881. ...........(2)

Substituting,

1.75(303-y) +4.80y = 881

530.25 -1.75y + 4.80y = 881

530.25 + 3.05y = 881

3.05y = 881 - 530.25

y = 350.75 / 3.05 = 115 = adults

Children = 303-115 = 188

Answer:

  e/f

Step-by-step explanation:

Common factors in the numerator and denominator cancel.

  [tex]\dfrac{e\times e\times e\times e\times f}{e\times e\times e\times f\times f}=\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{f}\times\dfrac{f}{f}=1\times1\times1\times\dfrac{e}{f}\times1=\boxed{\dfrac{e}{f}}[/tex]

The required simplification of the expression is [tex]\dfrac{e}{f}[/tex].

We have to the given expression, e x e x e x e x f ÷ e x e x e x f x f.

The given expression is simplify in the following steps given below.

Expression; [tex]\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}[/tex]

Then,

The simplification of the given expression,

[tex]=\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}\\\\[/tex]

Cancel out the same term from denominator and numerator,

[tex]= \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{f}{f} \\\\= 1 \times 1 \times 1 \times \dfrac{e}{f} \times 1 \\\\= \dfrac{e}{f}[/tex]

Hence, The required simplification of the expression is [tex]\dfrac{e}{f}[/tex]

To know more about Multiplication click the link given below.

https://brainly.com/question/16871801

Answer:

Third one

Step-by-step explanation:

The circumference of a circle is given by the formula:

P= 20π ⇒ d*π = 20π ⇒ d= 20

The volume of a sphere is given by the formula:

V= [tex]\frac{4}{3}[/tex]*π*10³

V= 1333.33*π

Answer:

   B.  (10, 10, 0)

Step-by-step explanation:

Each component of the sum is the sum of corresponding components:

  r + v = (7, 3, 9) +(3, 7, -9) = (7+3, 3+7, 9-9) = (10, 10, 0)

Answer:

The times are t = 9, t = 10, t = 11 and t = 12

Step-by-step explanation:

For the train to be more than 16 km South and since south is taken as negative,

d(t) > -16

t³ - 9t² + 6t > -16

t³ - 9t² + 6t + 16 > 0

Since -1 is a factor of 16, inserting t = -1 into the d(t), we have

d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)

So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16

Factorizing  t² - 10t + 16, we have

t² - 2t - 8t + 16

= t(t - 2) - 8(t - 2)

= (t -2)(t - 8)

So t - 2 and t - 8 are factors of d(t)

So (t + 1)(t -2)(t - 8) > 0

when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0

when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0

when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0

when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0

Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8

Since t ∈ (0, 12]

In the interval 0 < t < 2 the only value possible for t is t = 1

d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2

Since d(1) < -16 this is invalid

In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.

So,

d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km

d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km

d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km

d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km

Answer:

7. a = 50 degrees

b = 50 degrees

c= 50 degrees

d = 75 degrees

8.

Step-by-step explanation:

7.

a. Vertically opposite angles are equal

b. Vertically opposite angles are equal

c Alternate angles

d. Angles on a straight line.

8. 45 + 45 + 65 + 35 + 40 + 30 = 200m

Hope this helps

Step-by-step explanation:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Solution :

Let “x km/hr” be the speed of 1st car

Let “y km/hr” be the speed of the 2nd car

Time = Distance/Speed

Speed of both cars while they are traveling in the same direction = (x – y)

Speed of both cars while they are traveling in the opposite direction = (x + y)

5 = 100/(x -y)

x – y = 100/5

x - y = 20

x - y - 20 = 0 ---(1)

1 = 100/(x + y)

x + y = 100

x + y - 100 = 0--b----(2)

x/(100 + 20) = y/(-20 + 100) = 1/(1 + 1)

x/120 = y/80 = 1/2

x/120 = 1/2 y/80 = 1/2

x = 120/2 y = 80/2

x = 60 y = 40

So, the speed of first car = 60 km/hr

Speed of second car = 40 km/hr

Answer:

B. (2, 2)

Step-by-step explanation:

In order for the coordinate to be a solution of the systems of inequalities, it has to be in the shaded region (not on the line since both are dotted). Only B fits in the shaded region.

Answer:

The answer is

Step-by-step explanation:

To find the graph which shows (f + g)(x) we must first find (f + g)(x)

That's

f(x) = - x² + 3x + 5

g(x) = x² + 2x

To find (f + g)(x) add g(x) to f(x)

That's

(f + g)(x) = -x² + 3x + 5 + x² + 2x

Group like terms

(f + g)(x) = - x² + x² + 3x + 2x + 5

We have (f + g)(x) as

(f + g)(x) = 5x + 5

Since (f + g)(x) is linear the graph which shows (f + g)(x) is the last graph

Hope this helps you

Answer:

last graph or D

Step-by-step explanation:

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = [tex]\frac{187.84}{307} \times sin(78)[/tex]

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Answer:

See text below or attached figure

Step-by-step explanation:

Given arcs

AC=70

CR=18

therefore AR = 88

RB=80

BE=130

therefor EA = 360-(70+18+80+130) = 360-298 = 62

angles will be denoted (1) for angle 1, etc.

We ASSUME

ARD is a straight line

PFRB is a straight line

FCE is a straight line

Using inscribed angle theorem, angles subtended by chords/arcs equal to half the arc central angle.

Therefore

(4)=80/2=40

(13)=130/2=65

(12)=62/2=31

(11)=70/2=35

(5) = (70+18)/2 = 44

Consider triangle AEG,

(7)=(13)+(11)=65+35=100   [exterior angle]

Consider triangle EGB,

(10)=180-100-31 = 49      [sum of angles of a triangle]

Consider triangle AEH,

(3) = 180-(4)-(13)-(11) = 180-40-65-35 = 40  [sum of angles of a triangle]

From cyclic quadrilateral ARBE,

ARB+AEB=180 =>

ARB=180-AEB=180-(35+49) = 96

By the intersecting secants theorem,

(2) = (130-18)/2 = 56     [secants FE, FB]

(1) = (130+62 - (18+70))/2 = 104/2 = 52  [secants PA,PB]

(8) = (130+62 -80)/2 = 112/2 = 56

ARD is straight line  (see assumptions above)

(9) = 180-96 = 84    [sum of angles on a line]

ARP = (9) = 84     [vertically opposite angles]

Consider triangle ARP

(14) = 180-52-84 = 44

Consider tangent PA

(15) = 180-(44+40+65) = 31    [sum of angles of a triangle]

Consider triangle ABD

(6) = 180 - (40+44+56) = 40   [sum of angles of a triangle]

This completes the search for all sixteen angles, as shown in the diagram, or in the text above.

Answer:

88° and 132°

Step-by-step explanation:

The sum of angles in a pentagon ( a 5-sided shape) is given as

= (5 - 2) 180°

= 540°

The angles ∠EAB and ∠AED are supplementary hence the sum is 180° Therefore,

∠AED + 110 = 180

∠AED = 180 - 110

= 70°

Given that the sum of the angles in a pentagon is 540° then

110 + 70 + 2k + 140 + 3k = 540

5k + 320 = 540

5k = 540 - 320

5k = 220

k = 220/5

= 44°

Hence the angle ∠ABC

= 2 × 44

= 88°

∠CDE

= 3 × 44

= 132°

Answer:

This sequence is a geometric sequence.

The common ratio of the sequence is

3/9 = 1/3

Hope this helps