The speed of a boat in still water is 50km/h. It takes the same time for the boat to
travel 10km upstream as it does to travel 20km downstream. Find the speed of the
current.​

It is true that the solution set of an equation of a circle is all of the points that lie in the circle

The equation of a circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where:

Center = (a,b)

Radius = r

The points are represented by (x,y)

The (x,y) can take any value as long as it makes the equation (x - a)^2 + (y - b)^2 = r^2 to be true

Hence, it is true that the solution set of an equation of a circle is all of the points that lie in the circle

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Answer:

False

Step-by-step explanation:

The volume of cylinder is 1205.76 cubic inches

Solution:

We have to find the volume of cylinder

The volume of cylinder is given by formula:

[tex]V = \pi r^2h[/tex]

Where "r" is the radius and "h" is the height of cylinder

Given dimensions are:

Radius = 8 inches

Height = 0.5 feet

Convert feet to inches

1 feet = 12 inches

Therefore,

0.5 feet = 12 x 0.5 = 6 inches

Thus, we have got,

height = 6 inches

Substitute r = 8 inches and h = 6 inches in formula:

[tex]V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76[/tex]

Thus volume of cylinder is 1205.76 cubic inches

Answer:

18 and 335

Step-by-step explanation:

y = 18x + 11

x * y = 6030

x * (18x + 11) = 6030

18x^2 + 11x = 6030

18x^2 + 11x - 6030 = 0

(18x + 335)(x - 18) = 0

18x + 335 = 0                 x - 18 = 0

18x = -335                      x = 18

x = -335/18

x is gonna have to be a positive number...so x = 18

y = 18x + 11

y = 18(18) + 11

y = 324 + 11

y = 335

so ur numbers are 18 and 335

The two positive integer numbers are 18 and 335

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the two numbers be a and b

Now ,

Positive integer is 11 more than 18 times another

a = 11 + 18b   be equation (1)

And , product of a and b is 6030

a x b = 6030   be equation (2)

Now , substituting the value of equation (1) in equation (2) , we get

( 11 + 18b ) x b = 6030

18b² + 11b = 6030

Subtracting 6030 on both sides , we get

18b² + 11b - 6030 = 0   be equation (3)

On simplifying , we get

18b² - 324b + 335b - 6030 = 0

18b ( b - 18 ) + 335 ( b - 18 ) = 0

So ,

( 18b + 335 ) ( b - 18 ) = 0

Now , we got two values for b ,

( 18b + 335 ) = 0

b = -335 / 18

And ,

( b - 18 ) = 0

b = 18

Since , b is a positive integer , the value of b is 18

Now , substituting the value of b in equation (2) , we get

a x 18 = 6030

Divide by 18 on both sides , we get

a = 335

Hence , the two positive integer numbers are 18 and 335

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Answer:

43.65  grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed

Step-by-step explanation:

Let us assume the total capacity of the container  = m grams

Here, given: 80% of m = 100 grams

[tex]\implies \frac{80}{100} \times m = 100\\\implies m = \frac{100 \times 100}{80} = 125[/tex]

or, the TOTAL CAPACITY of container  = 125 grams

Now, the container already has 5 % seeds.

Calculating 5% of the capacity, we get:

[tex]\implies \frac{5}{100} \times 125 = 6.25[/tex]

So, the container already has 6.25 grams.

Now, the total filling of the container should be 40%.

Calculating 40% of the capacity, we get:

[tex]\implies \frac{40}{100} \times 125 = 50[/tex]

So, the weight of seeds that NEEDS To be in total  = 50 grams.

Also, it already has  6.35 grams.

So, the weight of seeds to be added  = 50 grams - 6.35 grams

                                                                   = 43.65 grams

Hence, 43.65  grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed.

43.75  grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed  

Percentage is a number or ratio that can be expressed as a fraction of 100.

Let the total mass of the container = x

Therefore,

80% of x = 100g of bird feed

80 / 100 × x = 100

80x = 10000

x = 10000 / 80

x = 125 grams

Therefore, 5% volume will be as follows;

Therefore, 40% volume is as follows:

Finally, the weight to be added to make the bird feed 40% seed is as follows;

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The total number of blue cards in the game = 48

Step-by-step explanation:

Total number of blue and yellow cards = 84

let the blue card denote B and yellow card as Y

B = 4

Y = 3

Total number of cards in one round = 7

number of rounds possible = total number of cards / number of cards in one round

= 84/7

= 12

number of blue cards = 12 x 4

= 48

  The total number of blue cards in the game = 48                                                                                                              

Answer:

48

Step-by-step explanation:

Answer:

Infinitely many solutions

Step-by-step explanation:

If we have a system of equation like:

2x+y=4

6x+3y=12

If we make y the subject in the first equation and substitute into the second equation, we get:

6x+3(4-2x)=12

We expand to get:

6x+12-6x=12

6x-6x+12=12

Now the variable adds out to give:

12=12

This statement is true so the equation has infinitely many solution.

Answer:

Explanation:

When the variable adds out means that after all the simplifications, at the end, it will not appear in the final sentence or expression.

Then, if the final sentence is true, and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.

That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.

This is an example:

1. Equation:

2. Remove the parenthesis:

3. Add like terms on the right side and transpose the variables to the left side:

4. Combine like terms on the left side:

Thus, the variable added out and the final sentence is true. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.

Answer:

Step-by-step explanation:

7/9x + 2 = 5/6.....multiply by the common denominator of 18

14x + 36 = 15 <=== re-written without fractions

14x = 15 - 36

14x = -21

x = -21/14

x = - 3/2...(or - 1 1/2)...ur solution

To rewrite the equation 7/9x + 2 = 5/6 without fractions, we multiply every term by the least common denominator (18) to get 14x + 36 = 15. Subtracting 36 from both sides and solving for x results in x = -21/14.

In order to rewrite the equation without fractions, we can eliminate the fractions by finding the least common denominator (LCD) and multiplying every term in the equation by it.

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Answer:

yes

Step-by-step explanation:

1 1/2 is greater than 1 4/10. Wich is 1/10 less then 1 1/2

Answer:

Yes

Step-by-step explanation:

1 1/2 > 1 4/10

Step 1:  Covert to Improper Fraction

1 1/2 = 2/2 + 1/2 = 3/2

1 4/10 = 10/10 + 4/10 = 14/10

Step 2:  Find Common Denominator

The least common denominator is 10

3/2 * 5/5 = 15/10

14/10 is already good

Step 3:  Evaluate

Is 15/10 more than 14/10?

Yes!!!!

So, 1 1/2 is more than 1 4/10

Answer: I think it's True :)

Answer:

I feel like it true. Happy yo help!!!

Step-by-step explanation:

Answer:

  C) -9

Step-by-step explanation:

Exponents in a polynomial must be positive integers. Since your ? has a minus sign in front, its value must be negative. The only such choice is C.

Answer:

z = -8.46 - 3.08i.

Step-by-step explanation:

cos 200 = -0.93969 so 9 * cos 200 = -8.46 to the nearest hundredth.

sin 200 = -0.3420 so 9 * sin 200 = -3.08 to nearest hundredth.

Answer:

B) y = x + 2 and y = -x - 4

Step-by-step explanation:

The equation of a line is represented with y = mx + b.

"x" and "y", when substituted, tell you if a point (x, y) is on the line.

"m" is slope, and tells if it goes up (positive slope) or down (negative)

"b" is the y-intercept, when the line hits the y-axis.

In the graph, we have two lines. One goes upwards (read from left to right), and the other goes downwards.

The graph that goes upwards hits the y-axis at positive "2".

The graph that goes downwards hits the y-axis at (negative) "-4".

Since the choices only have positive 1 or negative 1 as the slope, we only have to worry if it goes up or down.

Take the key information, slope and y-intercept, to write the equations.

"upwards slope, y-axis at 2"

y = x + 2

"downwards slope, y-axis at -4"

y = -x - 4

Answer:

1.17

Step-by-step explanation:

this is because first you would do 14÷12 as 14 is yearly and you want to find the monthly percentage this gives you 1.1666666667. then the next step is to round it so you would round 1.1666666667 to 1.17 for hundredth of a percent

14÷12=1.1666666667

round 1.1666666667 to 1.17

hoped this helped

84 pounds of Type B coffee is used

Solution:

Let "x" be the pounds of type A coffee

Let "y" be the pounds of type B coffee

Cost per pound of type A = $ 5.50

Cost per pound of Type B = $ 4.20

This month, Chau made 143 pounds of the blend

x + y = 143

x = 143 - y -------- eqn 1

For a total cost of $677.30. Thus we frame a equation as:

pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30

[tex]x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2[/tex]

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

[tex]5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84[/tex]

Thus 84 pounds of Type B coffee is used

To determine how many pounds of type B coffee were used in Chau's coffee blend, we set up a system of equations based on the total weight and total cost of the blend. By substituting one equation into the other, we can solve for the quantity of type B coffee.

Calculating the Blend of Coffee:

To solve the problem, let's use a system of equations to determine how many pounds of type B coffee Chau used in his coffee blend. We have two unknowns here: the amount of type A coffee (let's call it A) and the amount of type B coffee (let's call it B). The total weight of the coffee blend is given as 143 pounds, and the total cost of the blend is $677.30.

The first equation comes from the total weight of the blend:

A + B = 143

The second equation comes from the total cost:

5.50A + 4.20B = 677.30

We can use either substitution or elimination to solve this system. If we solve the first equation for A (i.e., A = 143 - B) and substitute it into the second equation, we get:

5.50(143 - B) + 4.20B = 677.30

After simplifying, we can solve for B to find out how many pounds of type B coffee were used.

Answer:50/50

Step-by-step explanation:

It’s a 50/50 chance because there is only two sides to a coin

Answer:

predictable

Step-by-step explanation:

the opposite of random is predictable

The opposite of 'random' would be a word like 'ordered' or 'systematic', which suggest a set plan or sequence, contrasting with the concept of randomness.

The opposite of the word 'random' would be a term that denotes a sense of order, structure, or predictability. In this context, one example of a word that is the opposite of 'random' is 'ordered' or 'systematic'. These words suggest that things are arranged or occur according to a set plan or sequence, thereby contrasting with the concept of 'random', which indicates a lack of any discernible order or pattern.

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Answer:

Length = 10.5units,Area = 68.25 unit²

Step-by-step explanation:

Perimeter =34 units

Width =6.5 units

Perimeter = l+l+w+w

Where l= length and w= width

34 = l + l + 6.5+ 6.5

34.= 2l + 13

Subtract 13 from both sides

2l = 34 - 13

2l = 21

Divide both sides by 2

L= 21/2

Length = 10.5units

If we are to find the area.

Area = length x width

Area = 10.5 × 6.5

Area = 68.25 unit²

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Answer:

Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Initial deposit = $ 7,000

Annual interest = 6.5% = 0.065 compounded continuously

Time of the investment = 4 years

Price of the used car Trafton wants to buy = $ 10,000

2. How much money will he need to pay in addition to what is in his savings account?

1. For answering the question, let's calculate how much money Trafton has in his savings account after 4 years, this way:

FV = PV * e ^ (i * t)

Where,

FV = Future value of the initial deposit after t time

PV = Initial deposit

e = Euler's number (2.7183)

i = 0.065 compounded continuously

t = 4 years

Replacing with the real values, we have:

FV = 7,000 * 2.7183^(0.065 * 4)

FV = 7,000 * 1.30 (Rounding to the nearest hundredth)

FV = $ 9,100

Now, we can elaborate how much money will Trafton need to pay in addition, as follows:

Money in addition = Price of the used car Trafton wants to buy - Future Value of the savings account after 4 years

Money in addition = 10,000 - 9,100

Money in addition = $ 900

Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.

Answer:

+56

Step-by-step explanation:

Answer:

2007

Step-by-step explanation:

we have

[tex]p(x)=0.65x^{2} -0.047x+2[/tex]

This is a vertical parabola open upward

The vertex represent a minimum

p(x) is the population in thousands for a species of fish

x is the number of years since 1997

Remember that p(x) is in thousands

so

If the population reach 66,530 fish

then

the value of p(x) is equal to

p(x)=66.53

substitute in the quadratic equation

[tex]66.53=0.65x^{2} -0.047x+2[/tex]

[tex]0.65x^{2} -0.047x+2-66.53=0[/tex]

[tex]0.65x^{2} -0.047x-64.53=0[/tex]

Solve the quadratic equation by graphing

The solution is x=10 years

see the attached figure

therefore

Find the year

Adds 10 years to 1997

1997+10=2007

Hmmm.... do you mean 0.8888...... or just 0.8888.

If you mean point eight repeating the fraction equivalent is just 8/9.

The answer is B (153) on Edge.

The X-ray machines were sold last year in total is 157.

A commission is a sum of money that a salesperson receives for each transaction they make. If a salesman is compensated on commission, their pay is based on how much they sell. Salespeople are paid only on commission.

We have,

The company can sell an x-ray machine which cost $508.17 to produce for $1.295.75.

So, the number of x-ray machines that were sold last year by Khybar inc.

= 79558.59/508.17

= 156.5

= 157

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The measure of BD ≈ 5.36

Step-by-step explanation:

Let 'x' be the measure of BD and EC.

BC = x+9.28+x

20 = 9.28 + 2x

2x = 20-9.28

x = 10.72/2

x = 5.36 (approx.)

∴ The measure of BD ≈ 5.36

Answer:

$110

Step-by-step explanation:

35+25(3)

Step-by-step explanation:

First term : 8 - 0 = 8

second term: 8 - 1 = 7

third term : 8 - 2 = 6

The expression demonstrates distributive property.

Explanation:

The given expression is [tex]17 \times 102[/tex]

Thus, solving the expression results in [tex]1734[/tex]

One student rewrote this expression as [tex]17(100+2)[/tex]

Then, simplified the expression as

[tex]1700+34[/tex]

Thus, [tex]17(100+2)=1700+34[/tex]

The expression demonstrates distributive property and the property can be generally written as

[tex]$a(b+c)=a b+a c$[/tex]

The given expression [tex]17(100+2)[/tex] is of the form [tex]$a(b+c)$[/tex]

Hence, The expression demonstrates distributive property.

Answer:

C

Step-by-step explanation:

120° is an angle in the second quadrant.

The reference angle is the related acute angle in the first quadrant, that is

reference angle = 180° - 120° = 60° → C

Answer:

C

Step-by-step explanation:

Answer:

5xA-5xB

Step-by-step explanation:

Answer: 5a-5b

Step-by-step explanation: Distribute the 5 and carry the negative sign over

Answer:

(8,8)

Step-by-step explanation:

The image point of (3,7) after translation 5 units to the right and 1 unit up is (8,8).

Translation of a point in a coordinate plane involves moving the point to a new location without changing its orientation or size.

To find the image of a point (3,7) after a translation of 5 units to the right and 1 unit up, we simply add the translation amounts to the original coordinates.

For a rightward movement, we add 5 to the x-coordinate, and for an upward movement, we add 1 to the y-coordinate.

Therefore, the new position of the point after translation will be:

So, the image point after the translation is (8,8).

Answer:

(4,3)

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .

The vertices are:

A(-2,5), B(6,5), and C(4,-1)

Slope of (6,5), and (4,-1) is

[tex]m = \frac{5 - - 1}{6 - 4} = 3[/tex]

Slope of altitude through A is

[tex] - \frac{1}{3} [/tex]

The equation of the altitude through A is

[tex]y - 5 = - \frac{1}{3} (x - - 2)[/tex]

[tex]y = - \frac{1}{3} x + \frac{13}{3} [/tex]

The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.

The equation of altitude through (4,-1) will be the vertical line x=4.

This implies that,

[tex]y = - \frac{4}{3} + \frac{13}{3} = 3[/tex]

Hence the orthocenter is (4,3)