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:

not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem to see if it is a right triangle

a^2 + b^2 = c^2

15^2 + 12^2 = 21^2

225 + 144 = 441

369 = 441

This is not true so it is not a right triangle

Answer:

Step-by-step explanation:

A triangle is a right angled triangle if sum of squares of two sides is equal to the square of third side.

12²+15²=144+225=369

21²=441

so a²+b²≠c²

it is not a right angled triangle.

Answer:

7/16=x/4

4 times 7/16= 4 times x/4

7/4=x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{7}{16} = \frac{x}{4} [/tex]

Apply cross product property

[tex]16 x = 7 \times 4[/tex]

Multiply the numbers

[tex]16x = 28[/tex]

Divide both sides of the equation by 16

[tex] \frac{16x}{16} = \frac{28}{16} [/tex]

Calculate

[tex]x = 1.75[/tex]

Hope this helps...

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Answer:

The answer is C.

Step-by-step explanation:

The formula to find equation is y - y1 = m(x - x1).

Let (x1,y1) be (6,2) and m is -5/7.

So the equation is,

y - 2 = -5/7(x - 6)

Answer:

Step-by-step explanation:

Given the total number of games played by the softball team = 18 games

Total games won = 15 games

Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played

Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]

[tex]Ratio = \frac{15}{18}[/tex]

Expressing the ratio in its lowest term

[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]

Hence, the ratio of the softball team's wins to its total number of games played is 5:6

Answer:

120 miles

Step-by-step explanation:

Distance in 2nd hour: 40 miles

Distance in 1st hour:  

40/(4/3) = 30 miles

Distance in 3rd hour:  

(5/4) * 40 = 50 miles

Total distance:  

40 + 30 + 50 = 120 miles

Answer:

2400months

Step-by-step explanation:

6/100*40,000

maybe

Answer:

x-1

Step-by-step explanation:

| x-1|  x> 1

Since x is greater than x, the absolute value will be positive so we can remove it

x-1

Lets use a number to check

Let x = 4

| 4-1|    4>1

3  which is positive

Answer:

x - 1

Step-by-step explanation:

| x - 1 |

x > 1

x is greater than 1. The absolute value is not needed, since the value inside will only be for positive integers.

x - 1

We can check by plugging x as 2.

2 - 1 = 1 (positive)

2 > 1

Answer:

m=30e

Step-by-step explanation:

30 minutes for each evening, 2 evenings, 60 minutes

Hope this helped!

The most suitable equation that would express the time Duarte spends to play chess with his dad is m= 30e

Number of minutes each evening= 30 mins=m

They played together every evening= e.

Therefore, the equation that would express the time Duarte spends to play chess with his dad is m = 30e.

Learn more about equation here:

https://brainly.com/question/2972832

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Answer:

x² + 4x + y² + 10y + 20 = 0

Step-by-step explanation:

Step 1: Expand (x + 2)²

x² + 2x + 2x + 4 + (y + 5)² = 9

Step 2: Combine like terms

x² + 4x + 4 + (y + 5)² = 9

Step 3: Expand (y + 5)²

x² + 4x + 4 + y² + 5y + 5y + 25 = 9

Step 4: Combine like terms

x² + 4x + 4 + y² + 10y + 25 = 9

Step 5: Move 9 over

x² + 4x + 4 + y² + 10y + 25 - 9 = 0

Step 6: Combine like terms

x² + 4x + y² + 10y + 20 = 0

Answer:

x^2+y^2+4x+10y+20=0

Step-by-step explanation:

(x+2)^2+(y+5)^2=9

x^2+4x+4+y^2+10y+25-9=0

general form: x^2+y^2+4x+10y+20=0

Answer:

All numbers greater than 5, i.e., [tex]x>5[/tex] .

Step-by-step explanation:

The given inequality is  

[tex]80x>150+50x[/tex]

Isolate variable terms on one side to find the solution.

Subtract  50x from both sides.

[tex]80x-50x>150+50x-50x[/tex]

[tex]30x>150[/tex]

Divide both sides by 30.

[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]

[tex]x>5[/tex]

It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.

Answer:

4/9

Step-by-step explanation:

So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.

Answer:

4/9

Step-by-step explanation:

Answer:

241 mm^2.

Step-by-step explanation:

There are 10 mm in a cm so there are 10*10 = 100 mm^2 in  a cm^2.

So the answer is 2.41 * 100 = 241 mm^2.

Answer:

241mm²

Step-by-step explanation:

If 10mm = 1cm,

then 100mm² = 1cm²

2.41 × 100 = 241mm²

Answer: Graph is shown in the attached image below

This is a V shaped graph with the vertex at (3,0). The V opens upward

Explanation:

The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.

Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.

Answer:

20

Step-by-step explanation:

30(0)

= 0

50 + 0 - 30

= 50 - 30

= 20

Answer:

20

Step-by-step explanation:

We know that 30 × 0 = 0. Next, we can take 50 and add 0 which is still 50. Now, we take 50 - 30 which equals to 20.

Answer:

Step-by-step explanation:

The table tells you that Marci's monthly payment on a 2-year loan at 8.5% will be $45.46 on each $1000 borrowed. For her $5000 loan, her monthly payment will be 5 times the table value, or ...

  monthly payment = $5000/$1000 × $45.46

  monthly payment = $227.30

__

Her total of 24 payments will be ...

  total repaid = 24 × $227.30 = $5,445.20

That amount is $445.20 more than the amount borrowed, so that is Marci's finance charge.

__

Marci's monthly payment will be $227.30, and her total finance charge will be $455.20.

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = [tex]C(n,k)[/tex] not nk

Answer:

True

Step-by-step explanation:

apec

Answer:

Amount of solution = 15 liter

Step-by-step explanation:

Given:

One third of solution is acid

Amount of acid = 5 Liter

Find:

Amount of solution

Computation:

Amount of solution = Amount of acid (1 / One third of solution is acid)

Amount of solution = Amount of acid (3)

Amount of solution = (5)(3)

Amount of solution = 15 liter

Answer:

1,110

Step-by-step explanation:

calculator

Answer:

The best fit is A. Linear model

Step-by-step explanation:

Given:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

To find:

The type of model that best fits the given situation?

Solution:

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

[tex]y =mx+c[/tex]

Slope of a function:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]

So, the equation is:

[tex]y =-500x+c[/tex]

Putting x = 20, y = 5000:

[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]

[tex]\Rightarrow \bold{y =-500x+15000}[/tex]

Let us check whether (18, 6000) satisfies it.

Putting x = 18:

[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.

So, the answer is:

The best fit is A. Linear model

Answer:

Number of pieces of candy in the bowl=64

Step-by-step explanation:

Let

x=number of pieces of candy in a bowl

Shirley took=1/2 of x

=1/2x

Remaining

x-1/2x

= 2x-x/2

=1/2x

Rose took half of the pieces left in the bowl=1/2 of 1/2x

=1/2*1/2x

=1/4x

Remaining

1/2x-1/4x

=2x-x/4

=1/4x

Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x

=1/2*1/4x

=1/8x

Remaining 8

1/8x=8

x=8÷1/8

=8*8/1

=64

x=64

Answer:

8 inches

Step-by-step explanation:

3/4+(3/4*2)=3/4+6/4=9/4=2 1/4

2 1/4+6=8 1/4=8.25

Answer: 8.25 inches

Step-by-step explanation:

If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].

We're given

[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:

[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]

Multiply both sides by 2:

[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]

Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:

[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]

Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].

Answer:

Total number of fruits remaining =  25

Step-by-step explanation:

Let the number of

apples = 4x

bananas = 5x

Therefore

4x-2 / 5x = 2 / 3

Solve for x, cross multiply

3(4x-2) = 2(5x)

12x - 6 = 10 x

2x = 6

x = 3

Apples = 4*3 = 12

Bananas = 5*3 = 15

Apples remaining = 12-2 = 10

Total number of fruits remaining = 10+15 = 25

Answer:

[tex]\boxed{25 \ fruits}[/tex]

Step-by-step explanation:

Let apples be 4x and Bananas be 5x

So, the given condition is:

[tex]\frac{4x-2}{5x} = \frac{2}{3}[/tex]

Cross Multiplying

5x*2 = 3(4x-2)

10x = 12x - 6

Adding 6 to both sides

10x+6 = 12x

12x - 10x = 6

2x = 6

x = 3

Now, Fruits remaining in the bowl are:

=> 4x-2 + 5x

=> 12 - 2 + 15

=> 10+15

=> 25

Answer:

53.076923

Step-by-step explanation:

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Answer:

30

Step-by-step explanation:

The unknown number is x.

Start with x.

To increase x by 130%, you need to add 130%of x to x.

x + 130% of x

The sum equals 69.

x + 130% of x = 69

x + 130% * x = 69

1x + 1.3x = 69

2.3x = 69

x = 30

Answer: The number is 30.

Answer:

For f(x)+2, it goes along the y axis, 2 units.

For f(x+2), it goes along the x axis, -2 untis.

Step-by-step explanation:

Answer:

[tex]Probability = 51\%[/tex]

Step-by-step explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14 * 5^2[/tex]

[tex]Area = 3.14 * 25[/tex]

[tex]Area = 78.5[/tex]

Outer Circle

[tex]Area = \pi R^2[/tex]

[tex]Area = 3.14 * 7^2[/tex]

[tex]Area = 3.14 * 49[/tex]

[tex]Area = 153.86[/tex]

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

[tex]Probability = \frac{78.5}{153.86}[/tex]

[tex]Probability = 0.51020408163[/tex]

Convert to percentage

[tex]Probability = 0.51020408163 * 100\%[/tex]

[tex]Probability = 51.020408163\%[/tex]

Approximate

[tex]Probability = 51\%[/tex]

Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer:

Two remote interior angles.

Answer:

Step-by-step explanation:

i cant see answers help my insta is 813.caden

Answer:

y+1=4(x-2)

y=4x+11

8x-2y+6

Step-by-step explanation: