1.2.PS-12
Determine whether the given number belongs to each set.
Integers
72
72
Whole
Numbers
?
Vyriole
Numbers
Yes
?
integers
Yes
Rational
Numbers
?
Katorial
Numbers
No
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Answer:

0.2083

Step-by-step explanation:

The number of boxes of candy that Mariana sells is 3/10.

A fraction is a non integer that is made up of a numerator and a denominator. An example of a fraction is 3/10. 3 is the numerator and 10 is the denominator.

In order to determine the boxes of candy that Mariana sold, multiply the fraction of boxes that Mariana sold by the number of boxes of candy that Juan sold.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is x.

Boxes that Mariana sells = fraction of boxes that Mariana sells x number of boxes that Juan sold

1/10 x 3 = 3/10

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1) Sheryl was wrong, the solution of w² = 49 and w² +49 = 0 are not same.

2) The solution of 4x² - 9 = 0 this quadratic equation is 3/2 and -3/2 through using factoring method.

3)

4) The solution of both quadratic equations will give same results.

Explanation:

1) Sheryl says that the solutions of the quadratic equations w² = 49 and

w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.

Solution:-

 According to Sheryl says that the solutions w² = 49 and w² +49 = 0 are the same.

Let's find the solution of given quadratic equations

        w = √49      ( ∵√49 = 7 )

         w = ±7

    So the solution of this quadratic equation 7 and -7

        w² = -49

        w  = √(-49)      ( ∵√49 = 7 )

         w = ±7 √-1       ( ∵√-1 = i )

   So the solution of this quadratic equation 7i and -7i

2. Patricia says that it's more appropriate to use the method of factoring

than extracting square roots in solving the quadratic equation

4x² - 9 = 0. Do you agree with Patricia? Explain your answer.

Solution:-

Patricia says that it's more appropriate to use the method of factoring

than extracting square roots in solving the quadratic equation

       4x² - 9 = 0.

Now, let's solve that quadratic equation through factoring method.

      (2x)² - (3)² = 0                {∵ a²-b²= (a-b)(a+b)

   (2x-3)(2x+3) = 0

    If       (2x-3) = 0  

               2x-3 = 0      

                   2x = 3

                      x = 3/2

   And if  (2x+3) = 0

               2x+3 = 0      

                   2x = -3

                      x = -3/2

3. If you are to choose between completing the square and factoring in

finding the solutions of each of the following equations, which would you

choose? Explain and solve the equation using your preferred method.

a. 4x² - 20x = 11

b. x² + 7x + 12 = 0.

Solution:-

a. 4x² - 20x = 11

For solve this quadratic equation, we can use completing the square method, because this equation is very hard to get it's factors.

So,

    4x² - 20x = 11

[tex]x^2-5x+(\frac{5}{2})^2 = \frac{11}{4} +(\frac{5}{2})^2\\x^2-2\times \frac{5}{2} \times x+(\frac{5}{2})^2 = \frac{11}{4} +\frac{25}{4}\\(x-\frac{5}{2})^2 = \frac{11+25}{4}\\(x-\frac{5}{2})^2 = \frac{36}{4}\\(x-\frac{5}{2})^2 = 9\\(x-\frac{5}{2})^2 = (3)^2\\(x-\frac{5}{2}) = \pm (3)\\\\[/tex]

 For taking + sign,

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

    x = 3 + [tex]\frac{5}{2}[/tex]

    x = [tex]\frac{6+5}{2}[/tex]

     x = [tex]\frac{11}{2}[/tex]

  For taking - sign,

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

    x =  [tex]\frac{5}{2}[/tex] - 3

    x = [tex]\frac{5-6}{2}[/tex]

     x = [tex]\frac{-1}{2}[/tex]

b. x² + 7x + 12 = 0.

For solve this quadratic equation, we can use factoring method, because that is very easy to get it's factors.

So,

            x² + 7x + 12 = 0

      x² + 4x +3x + 12 = 0

          x(x+4) +3(x+4) = 0

                 (x+4)(x+3) = 0

                If       (x+4) = 0  

                           x+4 = 0      

                               x = -4

             And if  (x+3) = 0

                           x+3 = 0      

                               x = -3

4. The values of a, b, and e of a quadratic equation written in standard form are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively. Do you agree that the two equations have the same solutions? Justify your answer.

Solution:-

We know that the standard form of quadratic equation is

From question we have two values of a,b and c.

For 1st quadratic equation the value of a,b and c is -2, 8, and 3, respectively.

So, the quadratic equation is

For 2nd quadratic equation the value of a,b and c is 2, -8, and -3, respectively.

So, the quadratic equation is

Now, we have to find the solution of both equations are same or not.

So, the solution of 1st quadratic equation

       -2x²+8x+3 = 0

           2x-8x-3 = 0            (multiplying - with both sides)

Now, this equation convert in the form of 2nd quadratic equation. So we can say that the solution of both quadratic equations will give same results.

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Answer:−4x+60X,1,2,3y−14

Step-by-step explanation:
1. simplify 3x x 20 to 60x
−4x+60X,1,2,3y−5−9
2. Simplify 3y- 5-9 to 3y - 14
−4x+60X,1,2,3y−14

Answer: They are parallel

Step-by-step explanation:

Turn them both into slope-intercept form:

 y = -x + 8

y = -x - 1

Since the slope on both of them are the same (-1), they are parallel

3 chicken wings he buys after spending  $3.00

When you take a single number and multiply it by several, you are multiplying. There are a number of distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.

Tyshawn spent $23.00 on 23 chicken wings.

Therefore in $1 the chicken wings that can be brought will be
= 23 /23

= 1

As he spent $3.00 on the chicken wings then the quantity that he has brought will be

= $3 * 1

= 3

The number of chicken wings that were brought was 3.

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The equations that will represent the reflected function are:

(c)  [tex]f(x)=5(\frac{1}{5})^{-x}[/tex] and;

(d) [tex]f(x)=5(5)^{x}[/tex]

If two functions share the same domain and codomain and have values that are consistent across all domain elements, they are said to be equivalent.

Consider the function,

[tex]f(x)=5(\frac{1}{5})^{x}[/tex]

Now,

Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.

So,

[tex]f(-x)=f(x)[/tex]

The reflection of the function f(x) across the y axis will be:

[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]

Therefore, the equivalent function will be:

[tex]f(x)=5(\frac{1}{5})^{(-1)(x)}[/tex]

[tex]f(x)=5 \times ((\frac{1}{5})^{-1})^{x} \\f(x)=5(5)^{x}[/tex]

Therefore, the equations which represent the function are:

[tex]f(x)=5(\frac{1}{5})^{-x}[/tex] and;

[tex]f(x)=5(5)^{x}[/tex].

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The complete question is mentioned below:

The function [tex]f(x)=5(\frac{1}{5})^{x}[/tex] is reflected over the y-axis. Which equations represent the reflected function? Select two options.

(a) [tex]f(x)=\frac{1}{5}(5)^{-x}[/tex]

(b) [tex]f(x)=\frac{1}{5} \frac{1}{5} [\frac{1}{5} ]^{x}[/tex]

(c)  [tex]f(x)=5(\frac{1}{5})^{-x}[/tex]

(d) [tex]f(x)=5(5)^{x}[/tex]

(e) [tex]f(x)=5(5)^{-x}[/tex]

Using proportions, it is found that the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

The Ruiz family is exchanging Euros for USD dollars, considering the following currency rate:

1 euro = 1.35261 USD.

Considering that the amounts in USD are rounded to the nearest hundredth, the use the following rule

1 euro - 1.35 USD.

It asks if the Ruiz family will be getting the most accurate answer.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, we suppose a 1000 euros amount, them:

Hence the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.

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Answer:

Step-by-step explanation:

No. It has to be a whole number in order to be an integer, and 12/5 = 2.4, and therefore is not a whole number.

Answer: 54

Step-by-step explanation:

2[(4+5)⋅3]

⇒2[9⋅3]

⇒2[27]

⇒54

Answer: h=V/r²

h=4 cm

Step-by-step explanation:

V = r²h solve for h

V/r² = r²h/r²     ==> divide the formula by r² to isolate h

h=V/r²

h=36/(3)²

h=36/9

h=4 cm

Answer:

The answer to your question is 42

the answer is 42 because the parentheses around the -6 and the -7 mean to multiply them and that two negatives make a positive so -6 * -7 equals 42

Hope this helps!

The equation formed using the given data is 195 = x + 12 and your final score is 183 points.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say your final score is x

Given that,

Your final score x is 12 points less than your friend's final score.

So,

x = friend final score - 12

Now,

Friend final score = 195

So,

x = 195 - 12

x + 12 = 195

195 = x + 12

Now,

x = 195 - 12 = 183

Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".

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By solving a system of equations, we can see that the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.

Let's define the variables that we will need to write our system of equations:

We know that the chemist wants to make 600mL of a 5% acid solution, so we can write the system of equations:

x + y = 600

x*0.02 + y*0.10 = 600*0.05

If we isolate y on the first equation, then we get:

y = 600 - x

Now we can replace that on the other equation so we get:

x*0.02 + (600 - x)*0.10 = 30

With this, we can get the value of x.

x*0.02 + 60 - x*0.10 = 30

-x*0.08 = 30 - 60 = -30

x = 30/0.08 = 375

So the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.

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Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given the function [tex]h(t)=\frac{1}{t+1}[/tex], we can find [tex]h(\frac{1}{2} )[/tex] by substituting [tex]\bf{t=\frac{1}{2}}[/tex].

When t= [tex]\frac{1}{2}[/tex],

[tex]h(\frac{1}{2})[/tex]

[tex]=\frac{1}{\frac{1}{2}+1 }[/tex]

[tex]=\frac{1}{(\frac{3}{2} )}[/tex]

[tex]=\bf{\frac{2}{3}}[/tex]

Additional:

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We are to evaluate the expression:

[tex]6c + 5d - 4c - 3d + 3c - 6d[/tex]

Where:

[tex]c = 4[/tex], [tex]d = 2[/tex]

Here, we just have to replace the variables with their given values, as shown below:

[tex]6(4) + 5(2) - 4(4) - 3(2) + 3(4) - 6(2)[/tex]

Now, we calculate.

[tex]→24 + 10 - 16 - 6 + 12 - 12[/tex]

Final answer

[tex] = 12[/tex]

Answer:

Step-by-step explanation:

Time/mph

Answer:

d = 510 km

Step-by-step explanation:

She travelled the final 4 hours at a constant speed of 60 km/h.

distance = speed × time

distance = 60 km/h × 4 hours

distance = 240 km for the last 4 hours

She already had travelled 270 km in the first 3 hours.

d = total distance = 270 km + 240 km = 510 km

Answer: d = 510 km

Answer:

Below

Step-by-step explanation:

b = 180 - 81° (because of the Z angle law)

b = 99°

Answer:

Step-by-step explanation:

Answer: Simplify the expression.

Scientific Notation:

4 ⋅ 10^7

Expanded Form:

40000000

Step-by-step explanation:

by doing 2.7*10^(5) divided by 6.75*10^(3)

you get the answer or now saying its

4 ⋅ 10^7 miles away basically. hope this helped

Answer:

see explanation

Step-by-step explanation:

the function is positive for values of y above the x- axis

the line goes on forever on the left side and terminates at x = 15 on the right side.

the interval where the function is positive is (- ∞, 15 ]

the x- intercept is where the line crosses the x- axis ( y = 0 )

x- intercept = 15

the y- intercept is where the line crosses the y- axis (x = 0 )

y- intercept = 3

The number of students in each bus are 54 students .

Given that, 331 students went on a field trip. Six buses were filled and 7 students traveled in cars.

Now you may get that only 7 students out of 331 are travelled in cars whereas others travelled by bus.

number of total students travelled by bus are 331-7 = 324 students

Therefore 324 students travelled in 6 buses.

Number of students travelled in each bus = 324/6 = 54 students.

Therefore number of students travelled in each bus is 54 students .

verification:

number of buses = 6

number of students in each bus = 54

Therefore total number of students in 6 buses = 6*54 = 324 students.

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Answer X=43 ,4X=172, (8X-3)=101

Step-by-step explanation:

Perimeter = addition of all sides ie;

556=X+4X+8X-3

556=13X-3

556+3=13X

559/13=13X/13

X=43

replace x with 43 to get their

Answer:

[tex]\frac{4}{49}[/tex]

Step-by-step explanation:

4/7 × 1/7

= 4 × 1/7 × 7

= 4/49

Answer:

-1/3

Step-by-step explanation:

So we need to find the slope of a line that passes through (6, 1) and (-3, 4).

We know that the line passes through 2 points, and using this information, we can find the slope of this line using our slope formula which is [tex]\frac{y1-y2}{x1-x2}[/tex].

So we can do [tex]\frac{4-1}{-3-6}=-\frac{1}{3}[/tex].

That's your answer.

Let me know if you have any questions

The decay rate of a certain new cell phone is 0.333

For given question,

The average lifetime of a certain new cell phone is three years.

The manufacturer will replace any cell phone failing within two years of the date of purchase.

Also, the lifetime of these cell phones is known to follow an exponential distribution.

We need to find the decay rate.

We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.

since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333

Therefore, the decay rate of a certain new cell phone is 0.333

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Answer:

Solve for x: [tex]x = \frac{3y+1}{4y-2}[/tex]

Evaluate x for y = 1: [tex]x = 2[/tex]

Step-by-step explanation:

[tex]Original:y=\frac{2x+1}{4x-3}\\Multiply\ out\ the\ denominator:(4x-3)*y = 2x+1\\Distribute: 4xy - 3y = 2x+1\\Group\ Like\ Terms:4xy-2x = 3y+1\\Factor\ Out\ x: x(4y-2) = 3y+1\\Divide\ to\ get\ x\ alone:x = \frac{3y+1}{4y-2}\\\\Plug\ in\ the\ value\ for\ y:x = \frac{3(1)+1}{4(1)-2}\\Multiply:x = \frac{3+1}{4-2}\\Add:x = \frac{4}{2}\\Simplify/Divide:x=2[/tex]