Joe and Susan share a sum of money in the ratio 1:5. What fraction of the money does Joe receive?

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:

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:

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:

3, 6, and 15

Step-by-step explanation:

Notice that if 60 is a multiple, the numbers in question could have the same factors as 60.

So let's look at 60's prime factors:

60 = 2 * 2 * 3 * 5

we also know that 3 is a factor, so the factor 3 must be included in all three options, we also know that 4 is NOT a factor, so both factors 2 cannot be included (but only one of them could).

So, in order to build the lowest possible numbers that verify such conditions, we can use:

3

3 * 2 = 6

since 3 or 2 cannot be repeated, the next smaller would be:

3 * 5 = 15

Answer: 12 friends.

Step-by-step explanation:

the data we have is:

Mei Su had 80 coins.

She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:

The maximum number of friends that could have coins is when:

friend 1 got 1 coin

friend 2 got 2 coins

friend 3 got 3 coins

friend N got N coins

in such a way that:

(1 + 2 + 3 + ... + N) ≥ 79

I use 79 because "she gave most of the coins", not all.

We want to find the maximum possible N.

Then let's calculate:

1 + 2 + 3 + 4 + 5 = 15

15 + 6 + 7 + 8 + 9 + 10 = 55

now we are close, lets add by one number:

55 + 11 = 66

66 + 12 = 78

now, we can not add more because we will have a number larger than 80.

Then we have N = 12

This means that the maximum number of friends is 12.

Answer:

12

Step-by-step explanation:

my

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:

210°

Step-by-step explanation:

By inscribed angle theorem:

[tex] m\angle DFG = \frac{1}{2} \times m\widehat{(EDG)} \\\\

105\degree = \frac{1}{2} \times m\widehat{(EDG)} \\\\

105\degree\times 2= m\widehat{(EDG)} \\\\

\huge \red {\boxed {\therefore m\widehat{(EDG)} = 210\degree}} [/tex]

Answer:

There are no restrictions on x, so the domain is (-∞,∞)

When x = 2, 5|x - 2| = 0, so the range is [4,∞)

Step-by-step explanation:

The domain and range of the function ƒ(x) = 5|x - 2| + 4 is (-∝, ∝) and [4, ∝) respectively. So, the 4th option is correct.

A function's domain is the set of all values for which the function is defined, and its range is the set of all values that the function takes.

The given function is ƒ(x) = 5|x - 2| + 4.

This function is not undefined for any x-values. So, the domain of this function is (-∝,∝).

We know that

|x - 2| ≥ 0

i.e. 5|x - 2| ≥ 0

i.e. 5|x - 2| + 4 ≥ 4

i.e. f(x) ≥ 4

So, the range of this function is [4,∝).

Therefore, the domain and range of the function ƒ(x) = 5|x - 2| + 4 is (-∝, ∝) and [4, ∝) respectively. So, the 4th option is correct.

Learn more about domain and range of a function here -

https://brainly.com/question/4334924

#SPJ2

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:

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:

[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:

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 area of the shaded region = (36·π - 72) cm²

The perimeter of the shaded region = (6·π  + 12·√2) cm

Step-by-step explanation:

The given figure is a sector of a circle and a segment of the circle is shaded

We have that since the arc AC subtends an angle 90° at the center of the circle, the sector is a quarter of a circle, which gives;

Area of sector = 1/4×π×r²

As seen the radius, r = AB = 12 cm

∴ Area of sector = 1/4×π×12² = 36·π cm²

The area of the segment AB = Area of sector ABC - Area of ΔABC

Area of ΔABC = 1/2×Base ×Height =

Since the base and the height = The radius of the circle = 12 cm, we have;

Area of ΔABC = 1/2×12×12 = 72 cm²

The area of the segment AB = 36·π cm² - 72 cm² = (36·π - 72) cm²

The area of the shaded region = The area of the segment AB = (36·π - 72) cm²

The perimeter of the shaded region = 1/4 perimeter of the circle with radius r + Line Segment AC

The perimeter of the shaded region =  1/4 × π × 2 × r + √(12² + 12²) = 1/4 × π × 2 × 12 + 12·√2 = (6·π  + 12·√2) cm

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:

  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:

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:

second option

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and

x² = - 5 ( take the square root of both sides )

x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]

Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]

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:

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:

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:

-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:

   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:

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

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:

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:

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:

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:

104 inches

Step-by-step explanation:

To solve this, we use a circle theorem. The circle theorem to use is that a line from the center of a circle is perpendicular to a chord and it divides the chord into exactly two equal parts.

So therefore, we shall be having a right angled triangle if we join the edge of the chord to the center of the circle.

So in this circle, we have the distance from the center of the circle to the chord, the radius of the circle and half the length of the chord.

The length of the radius serves as the hypotenuse.

Let’s call the radius r.

The other two sides measure; 40 and 96 respectively.

Mathematically, using Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides;

r^2 = 40^2 + 96^2

r^2 = 10,816

r = √(10,816)

r = 104 inches