If today is Sunday, then Theodore is either playing soccer or watching television. If Theodore is playing soccer (regardless of the day of the week), it means that he hasn't finished his homework or taken out the trash. If the trash is taken out, and Theodore is watching television, then he has finished his homework. Today is Sunday and the trash is taken out. Then it has to be true that:

A) His homework is finished
B) His homework isn't finished
C) This situation is impossible
D) There isn't one right answer

Answer:

see proof below

Step-by-step explanation:

Let

p1,p2 = half lengths of chord p

q1,q2 = half length of chord q

By the intersecting chord theorem,

p1*p2 = q1*q2,    substituting p1=p2, q1=q2

p1^2 = q1*2

Take square-roots and reject negative roots

p1 = q1

therefore

p1=p2 = q1=q2, or

two parts of one chord are equal to the two parts of the other.

Answer:

[tex]4.14*10^{-6}[/tex]

Step-by-step explanation:

Well scientific notation is (something*10^(other thing))

so we count have many zeroes there are, and there are 6, so we move the decimal point 6 times and get

[tex]4.14*10^{-6}[/tex]

Answer: It would take 6 "jumps" the left of 4.14 x 10^-6 to move the decimal back to where it actually is when not in scientific notation.   0.00000414

Step-by-step explanation:

hope this helps you :)

Answer:

The lengths of the diagonals are;

15.49 cm and 5.66 cm

Step-by-step explanation:

The given area of the parallelogram = 30 cm²

Also the length of 2 adjacent sides are 6 cm and 10 cm

Given that the formula for the area of a parallelogram = Base × Height, h where the base is either of the sides of the parallelogram we have;

When the base b = 10 m and the other side, a = 6 cm the diagonal, d is given by the relationship, d² = (a + √(b² - h²))² + h²

10 × h₁ = 30

h₁ = 30/10 = 3

d₁² = (b + √(a² - h₁²))² + h₁² = (10 + √(6² - 3²))² + 3² = 239.92 cm²

d₁ = √(239.92 cm²) = 15.49 cm

The other diagonal can be found from the following relationship;

d₂² = (b - √(a² - h₁²))² + h₁²

d₂² = (10 - √(6² - 3²))² + 3² = 32.08 cm²

d₂ = √(32.08 cm²) = 5.66 cm.

Answer:

x=60°

Step-by-step explanation:

Let's say the point where angle x is, be K

Because ABCD and PQRS are paralelograms,

∡PSR = ∡PQR =130°

and

∡DAB=∡DCB=70°

and by angles between parallels

∡SPQ + ∡PQR = 180°

∡SPQ + 130° = 180°

∡SPQ = 50°

by angles opposite by vertex

∡PKC = ∡BKQ = x

So in triangle PKC the sum of all angles must add up to 180°

so

∡SPQ + ∡PKC + ∡DCB = 180

50 + x + 70 = 180

x = 60

Answer:

24.8 km

Step-by-step explanation

To do this we would just multiply 24.8 by 10,000 which is 248000 and if we divide that by 10000 (to get km) we would get 24.8km

Answer:

Yes

Step-by-step explanation:

Well to figure out if 210879 is divisible by 3 we do,

210879 / 3

= 70 293.

Thus,

210879 is divisible by 3.

Hope this helps :)

Answer: Yes

Explanation: To determine whether 210,879 is divisible by 3, first we need to find the sum of the digits.

Image is provided below.

The divisibility rules tell us that if the sum of the digits is divisible by 3,

then the number is also divisible by 3.

So since 27 is divisible by 3, 210,879 must also divisible by 3.

So our answer is yes, 210,879 is divisible by 3.

Answer:

Step-by-step explanation:

3y + 10= 5y-25

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

that's

3y - 5y = - 25 - 10

Simplify

- 2y = - 35

Divide both sides by - 2

Hope this helps you

Answer:

y=35/2 or 17.5

Step-by-step explanation:

1) 3y + 10= 5y-25

-3y          -3y

2) 10 = 2y - 25

3) 10 = 2y - 25

  +25        +25

35= 2y

4)Divide both sides by 2

y=35/2 or 17.5

Answer:

20

Step-by-step explanation:

She will be 10 in 5 years witch means she is 5

Double five you get 10

10 + 10 = 20

Answer:

the answer is B.) 20 years old

Step-by-step explanation:

if in 5 years melissa is 10, then right now she is 5 years old. since laura is twice as old as melissa, then laura is currently 10 years old. and if Kim is 10 years older then laura, then Kim is 20 years old

Tl;Dr:

10-5=5

5x2=10

10+10=20

Answer:

sq. root(330)

Step-by-step explanation:

[tex] \sqrt{-55 \sqrt[3]{-216} } = \sqrt{-55(-6)} = \sqrt{330} [/tex]

[Cube root of -216 = -6]

Answer:

[tex]\sqrt{3}x^2y+x^3-x[/tex]

Step-by-step explanation:

In an expression that is a polynomial, the exponent of the variables (x and y) are natural numbers bigger or equal to 0. So, the only expression that is a polynomial is [tex]\sqrt{3}x^2y+x^3-x[/tex], because we have the exponents equal to 2, 3, and 1 for x and an exponent equal to 1 for y.

The other expressions have exponents that are negatives, rational or the exponent is the same variable.

Answer:

JK = 16√2

Step-by-step explanation:

This triangle is a special case right triangle, where you have 1 90-degree angle and 2 45-degree angles. The sides that correspond to the 45-degree angles are scalable by 1 and the hypotenuse is scalable by √2. Sometimes these are called 1-1-√2 triangles, describing the measurements of the sides.

Since this has a side of 16, the hypotenuse will be 16√2.

Cheers.

Answer:

a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population

Step-by-step explanation:

a. The first female had 4 pups.

If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.

b. 1st generation                        =     1 pup

2nd generation = 4 ×  1 pup      =    4 pups

3rd generation  = 4 ×  4 pups    =  16 pups

4th generation  = 4 × 16 pups    = 64 pups

5th generation  = 4 × 64 pups = 256 pups

The sequence is           1,   4, 16, 64, 256, …

We can also write it as 4⁰, 4¹, 4²,  4³,   4⁴, …

Note that the exponent is one less than the number of the generation.

Thus, the general formula for the nth term, aₙ, is

aₙ = 4ⁿ⁻¹, where

n = the number of the generation

a = the number of pups in that generation.

c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion

The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.

There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,

Answer:

f(x) = -2x + 1

Step-by-step explanation:

The given expression is [tex]\frac{64^x}{4^{5x-1}}[/tex]

By solving the given expression further,

[tex]\frac{64^x}{4^{5x-1}}[/tex] = [tex]\frac{[(4)^{3}]^x}{(4)^{5x-1}}[/tex] [Since 64 = 4³]

        = [tex]\frac{4^{3x}}{4^{5x-1}}[/tex]

        = [tex]4^{3x}\times 4^{-(5x-1)}[/tex] [Since [tex]\frac{1}{a}=a^{-1}[/tex]]

        = [tex]4^{3x-5x+1}[/tex] [Since [tex]a^x\times a^y=a^{(x+y)}[/tex]]

        = [tex]4^{(-2x+1)}[/tex]

By comparing the result with [tex]4^{\text{f(x)}}[/tex]

f(x) = -2x + 1

Therefore, f(x) = (-2x + 1) will be the answer.

Answer: y=1/4x-3/4

Step-by-step explanation:

We have our equation of a line formula y=mx+b

Then we substitute the given and get y=1/4x-3/4

In other words, f(x) grows faster after a certain point. This is true when comparing any exponential curve to a linear one.

Choice B is false as it contradicts choice A.

Choice C is false as the tables show the function outputs are equal at x = 2, not the rates of change

Choice D is false because there are infinitely many intervals where f(x) grows slower compared to g(x). That's why I mentioned the "after a certain point" portion.

Answer:

A

Step-by-step explanation:

Answer:

3.9

Step-by-step explanation:

Pythagorean theorem:

a^2 + b^2 = c^2

a^2 + 1^2 = 4^2

a^2 + 1 = 16

a^2 = 15

a = sqrt(15)

a = 3.9

Answer a = 3.9 yards

Answer:

[tex]\boxed{3.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

Apply Pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + 1^2 = 4^2[/tex]

[tex]a^2 + 1 = 16[/tex]

[tex]a^2 = 15[/tex]

[tex]a=\sqrt{15}[/tex]

[tex]a \approx 3.872983[/tex]

Answer:

21

Step-by-step explanation:

since it is a triangle subtract 180 by 137 and 22

180-(137+22) or 180-132-22

hope this helps

Answer:

21

Step-by-step explanation:

We khow that the sum of a triangle's angles sizes is 180°

substract the sum of the two khown angles from 180°

so m<0 = 21°

Answer:

The correct answer is D.

Step-by-step explanation:

Answer:

The answer is A.) (4,-128)

Step-by-step explanation:

Answer:

2).X= 3.464 m

3).X= 86.60m

4).X= 51.96 m

5).X= 30 m

6). X=3.193 m

7). X= 126.2 m

8).79.41m = x

9). 14.3km = x

10). 173.21 m= x

Step-by-step explanation:

For question 2

Distance of ladder from the foot

Tan60= 6/x

X= 6/tan 60

X= 3.464 m

For question 3

The height of the wall x is

Sin 60= x/100

X= 100*0.8660

X= 86.60m

Question 4

The distance between tree and tower is x

Tan30 = 30/x

X= 30/tan 30

X= 30/0.5774

X= 51.96 m

Question 5

If TanA= 3/4

And base = 40 m

TanA= x/40

Equating

X/40= 30/40

X= 30 m

Question 6

The length of ladder= x

Cos 20 = 3/x

X= 3/cos20

X=3.193 m

Question 7

Length of the string= x

Sin 31= 65/x

X= 65/sin 31

X= 126.2 m

Question 8

Height of kite= x

Tan ∅ = 15/8

∅= Tan^-1(15/8)

∅=61.93°

Sin∅= x/90

Sin61.93 *90= x

79.41m = x

Question 9

Height above ground= x

Tan 50= x/12

Tan 50 * 12 = x

14.3 km = x

Question 10

Height of balloon above ground= x

Sin60= x/200

Sin 60 *200 = x

173.21 m= x

Answer:

check the graph below

Step-by-step explanation:

Dilation involves changing the size and position of a point

The image of the dilation is (4,-3)

From the figure, the coordinates of point D and point P are:

[tex]D = (13,2)[/tex]

[tex]P = (1,11)[/tex]

The scale factor of dilation is given as:

[tex]k = \frac{1}{3}[/tex]

The rule of dilation about point P is then calculated as:

[tex](x,y) \to k(x_D - x_P, y_D - y_P)[/tex]

So, we have:

[tex](x,y) \to \frac 13 \times (13 - 1, 2- 11)[/tex]

Simplify

[tex](x,y) \to \frac 13 \times (12, -9)[/tex]

Expand

[tex](x,y) \to (\frac 13 \times 12, -\frac 13 \times9)[/tex]

[tex](x,y) \to (4, -3 )[/tex]

This means that, the image of the dilation is (4,-3)

See attachment for the image of the dilation

Read more about dilation at:

https://brainly.com/question/8532602

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

25%

Step-by-step explanation:

Given that a restaurant meal usually cost Nu 80 but on Thursdays it cost Nu 80.

To determine the discount, we have to find the ratio between the difference between the usual cost and the cost on Thursday to the usual cost of meals. It is given by:

Percent discount = (Usual cost - Cost of meal on Thursday)/ Usual cost × 100%

Percent discount = (80 - 60) / 80 × 100% = 20 / 80 × 100%

Percent discount = 25%

Answer:

292

Step-by-step explanation:

To factor this, we need to multiply 18 by 18 to get 324 because the ^2 means you have to multiply the number by itself twice. Then, we subtract 32 from 324 to get our answer 292.

Answer:

Our set of data is:

A. their first choice (12 people)

B their second choice (7 people)

C their third choice (3 people)

D their last choice (3 people)

The total number of people is:

12 + 7 + 3 + 3 = 25.

You already know the number of people for each situation, but let's calculate the percentage:

1st choice: The first choice of 12 people winned, and the total number of people is 25.

Now, 25 is our 100%, then 12 is equivalent to x;

Then we have

12*100% = 25*x

x = (12/25)*100% = 48%

This is:

The quotient between

Second choice:

Same reasoning as above, here the percentage is:

(7/25)*100% = 28%

Third choice:

Same reasoning as above, here the percentage is:

(3/25)*100% = 12%

Fourth/Last choice:

Same reasoning as above, here the percentage is:

(3/25)*100% = 12%

Answer:

3/8

Step-by-step explanation:

Hey there!

Well we need to turn 3 3/8 into an improper fraction.

3*8 = 24

24 + 3 = 27

27 ÷ 9 = 3

3/8

Hope this helps :)

The answer of the given equation is 0.375

Given that,

Based on the above information, the calculation is as follows:

[tex]= 3 \frac{3}{8} \div 9\\\\ = \frac{27}{8} \div 9\\\\ = 3.375 \div 9\\\\ = 0.375[/tex]

Learn more: https://brainly.com/question/12522729?referrer=searchResults

Answer:

2.4 bags

Step-by-step explanation:

Uh you can keep your brains.

Using the data table, we get:

1, 2, 2, 3, 4 as our data.

Finding the mean:

(1+2+2+3+4)÷5=

12÷5=

2.4 bags

Answer:

The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Step-by-step explanation:

Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).

To find the values in the domain where f(x) = 0, we look at the ordered pairs given.

We look for the pair in which f(x) = 0.

So f(x) = 0 in (-2.5, 0)

f(x) = 0 in (-0.75, 0)

and f(x) = 0 in (1, 0)

The corresponding values of x  in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Answer:

C. [tex]x=1[/tex]

Step-by-step explanation:

When x is 1, y is 0.

Answer:

80

Step-by-step explanation:

t is important to note that a square of any non-zero integer is positive, and therefore there is no advantage in using negative integers instead of positive integers to attain the greatest difference of squares. So we will not consider negative integers.

The greatest value of a^2 - b^2 occurs when a^2 is at its largest and b^2 is at its smallest.

The larger a, the larger a^2:

8 ^ 2 = 64

9 ^ 2 = 81

10 ^ 2= 100

Since a^2 can have at most two digits, a=10 is too large, and so a=9 is the largest integral value of a we can use.

Now, b^2 is at its smallest when b is closest to zero on the number line (the further b gets from zero, the larger its square becomes):

2 ^ 2 = 4

1 ^ 2 =1

0 ^ 2 = 0

Remember to go back to the original problem sometimes, to make sure you are taking everything into account. It states b doesn't =0, and therefore the b=1 is the closest b can get to zero as an integer. So, the greatest difference between b^2 and a^2 is when b=1 and a=9, giving the result:

a^2-b^2 =9^2-1^2 =81-1= 80.

So, 80 is your answer.

Answer: 85 = 3.75x + 12.25

The restaurant can have 19 loads

Step-by-step explanation:

The 85 accounts for the restaurant's budget.  The 3.75x accounts for the cost of each load.  The 12.25 accounts for the delivery fee.

85 = 3.75x + 12.25

Subtract 12.25

72.75=3.75x

Divide by 3.75

19.4=x

Round down

x = 19

Hope it helps <3

Answer:

19.4

Step-by-step explanation:

3.75x+12.25=85

subtract 12 from both sides, and divide to put the variable alone.

Then you have to get 19.53333333

Round up and its 19.4

Check if it is true

3.75×19.4+12.25=85

Answer:

The carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100

Step-by-step explanation:

Let x be the no. of dining chairs and y be the no. of rocking chair

Time taken by carpenter to make 1 dining chair = 1 hour

Time taken by carpenter to make x dining chairs = x hours

Time taken by carpenter to make 1 rocking chair = 2 hour

Time taken by carpenter to make y rocking chairs = 2y hours

He only has 40 hours available to work on the chairs.

[tex]\Rightarrow x+2y \leq 40[/tex]

He has enough wood to make 30 chairs.

[tex]\Rightarrow x+y\leq30[/tex]

He makes $60 profit on a dining chair and $90 profit on a rocking chair.

So, profit =60x+90y

Plot the equations on graph

Refer the attached figure

Coordinates of feasible region

(0,20),(20,10) and (30,0)

Profit =60x+90y

At(0,20)

Profit = 1800

At(20,10)

Profit = 1200+900=2100

At(30,0)

Profit=900

So,the carpenter can maximize profits by making  20 dining chairs and 10 rocking chairs . His total profit for all the chairs will be $2100