Which one of these are Rational Numbers?
A) -7.9898...
B) 4.9832
C) 6.329...
D) 7

The required product of two rational numbers is 8y² - 28y + 4) / (6y² - 21y + 9).

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Calculation of the product of two rational numbers

Given two rational numbers,

8y - 4 / 10y - 5 and 5y -15 / 3y - 9

We need to multiply both the numbers i.e.

= (8y - 4 / 10y - 5) × (5y -15 / 3y - 9)

= (8y -4) × (5y - 15) / (10y - 5) × (3y - 9)

= (40y² - 140y + 20) / (30y² - 105y + 45)

= (8y² - 28y + 4) / (6y² - 21y + 9)

= (8y² - 28y + 4) / (6y² - 21y + 9)

The restriction is that the denominator, 6y² - 21y + 9 should not be 0.

Hence, the required product of two rational numbers is 8y2 - 28y + 4) / (6y2 - 21y + 9).

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Answer:

4:1, 20:5

Step-by-step explanation:

You can determine if a ratio is equivalent by dividing each term with the respective term in the other ratio. If you come out with 1, the ratios are equivalent.

Answer:

4:1 & 20:5

Step-by-step explanation:

These two ratios are equal and true to 12:3!

Hopefully this helps have a great day! :D

The correct option is (b) square root 112 units

By using Pythagoras theorem,

where a & b = legs of triangle and c = hypotenuse

Hence:

If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

Let x represent the number of months

Hence,

Formulate

$34.04x+24= $34.29x+(36.50/2)

Collect like terms

($34.04x -34.29x)= 24-(36.50/2)

0.25x=24-18.25

0.25x=5.75

Divide both side by 0.25x

x=5.75/0.25

x=23 months

Therefore If Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, the number of months that the cost of the memberships be the same is: 23 months.

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Answer:

The correct answer is 4(x-7)²-(x-7)+3.

Step-by-step explanation:

When we have captured (t*s)(x), that is as equivalent as t(s(x)). To solve this, we take the important role of s(x), x-7, and call in an alternative for it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.

The missing numbers are 17,66,13, 9 3 and 15 respectively .

The rules given to us are-

first row consist of a number which is the sum of two numbers of middle row

Third row consist of a number which is the product of two numbers of middle row

The first part

The sum of 6 and 11 is 17 and the product of 6 and 11 is 66

       17

6                11

       66

The second part

To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13

       13

4               9

       36

The third part

To find the numbers of middle row we need to find the factors of 45 that sum up to 18

The factors of 45 are 3*3*5

The factor 15 and 3 satisfy both the requirements

       18

3                15

       45

Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively

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After playing 100 times the player will loose $-16.67.

Given the outcomes and the probability is:

Outcome            Probability

-$10                       1 (cost to play)

$14 draw red          5/12

$12 draw yellow      4/12

therefore, expected probability = ∑x.p(x)

x is no of trials and

p(x) is probability of the results.

E(x) = (14)5/12 + (12)4/12 + (0)3/12 - 10

E(x) = -2/12

E(x) = -10.1667

For 100 games the expected value E(100x) =

E(100x) = E(x) × 100

E(100x) = -10.1667 × 100

E(100x) = -16.67 i.e loss after game.

Hence the player lose $-16.67 after 100 games.

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For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25

Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.

Step 2: balance the arguments.

Step 3: Solve the resultant equation.

Step 4: Double-check your answers.

Given,

1/2 log x + log 4 = 2

log x^(1/2) + log 4 = 2

using logₐ(m.n) = logₐ(m) + logₐ(n)

log e (4 (x^1/2)) = 2

e² = 4x^(1/2)

7.38 = 4√x

Squaring on both sides -

54.4644 = 16x

x = 54.4644 / 16

x = 34,040.25

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The measure of the angle that complements m∠W is 17°. Option C

Complementary angles are defined as angles that sum up to 90 degrees.

They are also called angles at right angle.

Example:

If x and y are termed complementary angles, then

x + y = 90°

From the information given, we have that;

m∠W is complementary to another unknown angle x

This is represented as;

x + m∠W = 90°

But m∠W = 73°

Substitute the value into the equation

x + 73° = 90°

collect like terms

x = 90 - 73

x = 17°

Thus, the measure of the angle that complements m∠W is 17°. Option C

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Answer:

is 7 more than 4 or 4 more than 7?

Step-by-step explanation:

JUST USE YOUR BRAIN!

Answer:

no

Step-by-step explanation:

of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no

Considering the definition of an equation and the way to solve it, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns.

The members of an equation are each of the expressions that appear on both sides of the equal sign.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of cupcakes baked by Cadence on Monday, and knowing that:

the equation in this case is:

3 + 2x= 45

Solving:

2x= 45 -3

2x= 42

x= 42 ÷ 2

x= 21

Finally, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.

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The correct order from best to worst of the sample groups is b→ a→ c.

The study conducted by the City Council of USA incorporates the reviewing for the funding for local sports-related activities.

There are 3 sample groups selected from the population of Anytown residents with an active interest in sports. They are:

a. High-school students at three different schools.

b. People randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar.

c. People randomly approached at a department store and at a shopping mall

All these groups are selected randomly.

But for (b), the people are obviously interested in sports activities, as they are selected from softball tournament, a swim meet, an athletic supply store, and a sports bar.

Next would be (a), because the students being younger is probably more interested in sports than elder ones.

The last would be the (c), people selected from the department store since they would be less aware of local- sports related activities.

So the order of samples from best to worst is b→ a→ c.

The question is incomplete. Find the complete question below:

The city council of Anytown, U.S.A., is reviewing the funding for local sports-related activities. To be better informed, it commissions a study. Order the sample groups, best to worst, based on how well they would represent the population of Anytown residents with an active interest in sports.

a. high-school students at three different schools

b. people randomly approached at a softball tournament, a swim meet, an athletic supply store, and a sports bar

c. people randomly approached at a department store and at a shopping mall

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The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.

From the information given, the product of two factors is 1 and one of the factors is 1.

Let the other number = y

The other number will be:

1 × y = 1

y = 1

Therefore, the other number is 1

In conclusion, the correct option is B.

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Answer:

5 and -5

This is because these 2 spots are exactly 5 spaces from 0.

After 4 stops both buses will have the same amount of riders that is 27.

So, Bus A: 15 people ( +3 at every stop)

Bus B: 35 people ( -2 at every stop)

Then,

Therefore, after 4 stops both buses will have the same amount of riders that is 27.

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The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

Answer:

Evan, Liza, Tasha, Devon

Step-by-step explanation:

The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.

Given that

To find

So, according to the question

we have,

                                                     = (9 ×5)/10

                                                     = 4.5 miles.

Now, from question

So, Total laps walk by your friend

             = ( Total distance walk by you)/(Total length of your friends track)

             = [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]

             = [tex]\frac{4.5\times 2}{3}[/tex]

             = 9/3 = 3

Answer:

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Step-by-step explanation:

4-digit number abcd

a >= 2

a×b = d

so, 2 <= b <= 4 to allow a single digit result of a×b, and if b would be 1 or 0, the result would be either a copy of a or of b violating the rule that no 2 digits are the same.

that means a >= 3, because with a = 2 and b <= 4 the number can't be larger than 2500.

and that again means 2 <= b <= 3 and 3 <= a <= 4 to allow a single digit result of a×b.

the sum of "my digit" ? I guess you mean the sum of all digits is 16.

a + b + c + d = 16

so, my first guess :

a = 3

b = 2

therefore

d = 3×2 = 6

that means we have already 11 as sum of the digits, that leaves 5 for c.

so, the number would be

3256

the only alternative would start with a = 4 and then b = 2.

but that would make d = a×b = 8. abd 8 + 4 + 2 = 14, and that leaves for c only 2 to sum up to 16, and that would duplicate b.

so, 3256 is the only solution.

The best approximation for the solution to the system of equation is option C) (-2.2 , -3)

According to the question we have been given two system of linear equation which are:

         y = -3          (1)

and   y = x - 0.8        (2)

Now solving these two equation and find the value of x

Substituting the value of y from equation (1) to the equation (2) we get

               -3 = x - 0.8

                -3 + 0.8 = x

                   x = -2.2

Thus the best approximation for the solution to the system of equation is option C) (-2.2 , -3)

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If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.

We are given a triangle with the condition that BA ≅ CA. This means that side BA has a length equal to that of side CA.

Now, an Isosceles triangle is defined as a triangle that has at least two sides of equal length. This means that the given triangle ABC is an Isosceles triangle.

Now, since Triangle ABC is an Isosceles triangle, it means that when we draw a perpendicular line through the point joining the two equal sides, it bisects the third side of the triangle.

Thus, it means that BD is congruent to CD.

If BD = 3, then it means that CD is also equal to 3 by definition of Isosceles triangle.

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Answer:

AD

Step-by-step explanation:

It is the only segment that meets a side of triangle ABC at a right angle.

Answer:

The weight of the popcorn is off but the potato chips are safe. Simply determine whether each value is within the limit of deviation from eachother.

An equivalent form of 5 / ( 2 + 2 i ) is ( 5 -5 i ) / 4 [ option I ]

Given,

5 / ( 2 + 2 i )

To find its equivalent form we need to simplify the term by using the concept of conjugates.

Conjugate of a term results in opposite power of the imaginary part.

The conjugate of 2 + 2 i = 2 - 2 i

Multiply and divide the term with the conjugate

=> 5 * ( 2 - 2 i ) / ( 2 + 2 i ) * ( 2 - 2 i )

=> 10 - 10 i / 2 ² - ( 2 i ) ²                [ ( a + b ) ( a - b ) = a ² - b ² ]

=> 10 - 10 i / 4 - (-4)                        [ i ² = - 1 ]

=> 10 - 10 i / 8

=> 5 - 5 i / 4

This matches with option I

Therefore, we get an equivalent form of 5 / ( 2 + 2 i ) as ( 5 -5 i ) / 4

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The value of the x is 1 in the linear equation. Thus, option C is correct.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is:

4x−3=−12x+13

Then

we have to solve it

4x−3=−12x+13

4x+12x = 3+13

16x = 16

x = 16/16

x =1.

When we put x =1 in the given equation and then i satisfy the equation and give same values after calculation.

So, The value of the x is 1 in the linear equation. Thus, option C is correct.

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The solution to the system where the system contains linear equations is (59/16, -65/32)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x + 12y = −17

3x + 2y = 7

Multiply through 3x + 2y = 7 by 6

So, we have

18x + 12y = 42

Subtract the equation 2x + 12y = −17 from 18x + 12y = 42

So, we have

18x - 2x + 12y - 12y = 42 + 17

Evaluate the like terms

So, we have

16x = 59

Divide both sides by 16

So, we have

x = 59/16

Substitute x = 59/16 in 3x + 2y = 7

3 x 59/16 + 2y = 7

This gives

177/16 + 2y = 7

So, we have

2y = 7 - 177/16

Evaluate the difference

2y = -65/16

Divide by 2

y = -65/32

Hence, the solution to the system where the system contains linear equations is (59/16, -65/32)

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Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Without any side lengths, the most three angles can determine is similarity, not congruency. This means you can determine the ratio of the lengths of the sides, but not any of the sides individually.

De acuerdo a la información se puede inferir que su hijo nació en el año 22 antes de Cristo.

Una recta numérica es una herramienta gráfica de las matemáticas que nos sirve para ubicar números positivos y negativos en un gráfico con el objetivo de organizarlos con respecto al número cero.

Las líneas de tiempo con fechas Antes y Después de Cristo se pueden asociar a una recta numérica debido a que los años Antes de Cristo se ubican en la parte negativa de la gráfica (a la izquierda del cero) y los número Después de Cristo se ubican en la parte positiva (a la derecha del cero).

Para identificar el año de nacimiento del hijo debemos tener en cuenta que las fechas que se ubican en la zona negativa de la recta numérica aumentan de forma invertida, es decir que si su hijo nació 28 años después de ella se debe restar este número a su fecha de nacimiento como se muestra a continuación:

50 - 28 = 22

Entonces, el año de nacimiento de su hijo sería el año 22 Antes de Cristo.

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