3x – 2 ( 6x – 3 ) = 42

The solution of the inequality expression in interval notation is;

-1/2 < x < 2/3 and the number line is attached

We are given the Inequality expression  as;

6x² - x  < 2

To express the function in quadratic form, we subtract 2 from both sides to get;

6x² - x - 2 < 0

We now factorize this expression to get;

(2x +1)(3x - 2) < 0

This means that we have two inequalities solution which are expressed as; (2x + 1) < 0 and (3x - 2) < 0

For (2x + 1) < 0, add 1 to both sides to get;

2x < 1

divide both sides by 2 to get;

x < 1/2

Similarly, for (3x - 2) < 0;

Add 2 to both sides and then divide by 3 to get;

x < 3/2

Thus, the solution to the inequality is x = -1/2 and x = 3/2

Read more about Inequalities at; https://brainly.com/question/25275758

#SPJ1

If 24 out of our 40 stickers glow in the dark, we would have 16 that don't

As a fraction relative to our total 40 stickers, those 16 would be:

Simplifying,

hereby, 2/5 of the sticketrs don't glow in the dark

Let x represent the weight of the comic book to be sold

Let y represent the weight of the appraised book to be appraised

There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. It means that

15x + 8y = 49.9 equation 1

If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz, it means that

10x + 4y = 30.2 equation 2

Multiplying equation 2 by 2, it becomes

20x + 8y = 60.4 equation 3

Subtracting equation 3 from equation 1, it becomes

20x - 15x + 8y - 8y = 60.4 - 49.9

5x = 10.5

x = 10.5/5

x = 2.1

Substituting x = 2.1 into equation 2, it becomes

10(2.1) + 4y = 30.2

21 + 4y = 30.2

4y = 30.2 - 21 = 9.2

y = 9.2/4

y = 2.3

Weight of the comic(S) to be sold = 2.1 oz

The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Given the question:

(x + 4)^2 = 15 - 2x^2.

To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:

[tex](x+4)^2 = 15 -2x^2[/tex]

Expand the expression

[tex]x^{2} +8x+16=15-2x^2[/tex]

Move the expression to the left

[tex]x^{2} +8x+16-15+2x^2[/tex] = 0

Collect like terms

[tex]3x^{2} +8x+1=0[/tex]

Use the Quadratic formula:

x = [-b ± √(b2 – 4ac)]/2a

x = [-8 ± √(8^2 – 4x3x1)]/2x 3

Multiply and evaluate :

x = [-8± √(64 – 12)]/6]

Calculate:

x = [-8± 2√13]/6]

Separate the solutions

[tex]x_{1}[/tex] =  [-4 + 2√13]/3]

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Hence, The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Learn more about Quadratic Formula at:

https://brainly.com/question/9300679

#SPJ1

If the ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice as much on ham as you do on cheese. The amount spent in total is: $187.20.

Let number of ham bought = x + 4

Let number  of cheese bought = x - 3

Price of ham = $6.24

Price of cheese = $4.80

Hence,

Amount spent on ham = (x+4)×6.24

Amount spent on ham =6.24x + 24.96

Amount spent on cheese = (x−3)×4.80

Amount spent on cheese =4.80x−14.40

So,

6.24 x + 24.96 = 2 (4.80 x - 14.40)

6.24x + 24.96 = 9.60 x - 28.80

Combine like terms

24.96 + 28.80 = 9.60 x - 6.24 x

3.36 x = 53.76

Divide both side by 3.36x

x = 53.76/3.36

= 16x

Now let find the total money spent where x is 16

Total amount = 6.24(16) + 24.96+ 4.80(16) - 14.40

Total amount = $187.20

Therefore the amount of $187.20 was spent in total.

Learn more about total cost here: https://brainly.com/question/28339731

#SPJ1

Answer:

y=-x^2+16x-55

Step-by-step explanation:

Since two intercepts are given (the two x-intercepts in this case), we should probably use intercept form.
y=a(x-b)(x-c)
plug in the intercepts which are 5 and 11 in this case
y=a(x-5)(x-11)
to solve for a, use the remaining point and set x to 6 and y to 5. we can do this because (6,5) is given to us as a solution of one of the points on the graph.

5=a(6-5)(6-11)
5=a*(-5)
a=-1
so, the equation should be:

y=   -  (x-5)(x-11)
expand the parentheses to get:

y=-x^2+16x-55


(also 5 points isn't a lot of points...)

The shadow of the 4 feet stick is 3/4 feet or 0.75 feet.

It is a question of ratio and proportion.

It is given in the question that the 32 feet tall building had a shadow 6 feet long.

We have to find the length of the shadow of a 4 ft stick.

Let the  length of the shadow of a 4 ft stick be x.

We know that length and shadow of a 4 feet stick and a 32 feet building will be in proportion.

Hence, we can write,

Length of building/Length of stick = shadow of building/shadow of stick

32/4 = 6/x

8 = 6/x

x = 6/8 feet = 3/4 feet = 0.75 feet

x = 0.75 feet.

To learn more about ratio and proportion, here:-

https://brainly.com/question/26974513

#SPJ1

Using it's formula, the bond's price in the context of this problem is given as follows: $5350.

To calculate the bond price, we need to know the face value(given in the missing information subsection at the end of the answer) and the yield rate, given at the problem.

The bond price is the given by the multiplication of the face value and 100% plus the yield, hence, in the context of this problem, it is given as follows:

Bond Price = 5000 x 1.07 = $5350.

The complete problem is given as follows:

"A bond with a face value of $5,000 has a current yield of 7% and a coupon rate of 8%, what is the bonds yield?"

As the face value is needed to calculated the bonds price.

A similar problem, also involving a bond's yield, is given at https://brainly.com/question/14676033

#SPJ1

The solution to the given expression (x + 20 - 1) when x = 9 is: A. 28.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to evaluate the given expression and determine its solution. Therefore, we would evaluate the given expression  as follows:

x + 20 - 1

Substituting the value of x into the given expression, we have:

Expression = 9 + 20 - 1

Expression = 29 - 1

Expression = 28.

In conclusion, we can reasonably and logically deduce that 28 is the  solution to this expression (x + 20 - 1).

Read more on expressions here: brainly.com/question/17361494

#SPJ1

Answer:

a) 28

Step-by-step explanation:

Now we have to,

→ evaluate the expression.

The expression is,

→ x + 20 - 1

Solving the expression,

→ x + 20 - 1

→ 9 + 20 - 1

→ 9 + 19

→ 28

Hence, solution is 28.

Answer:

Sum of two rational no. = 17/4

One rational no. = 5/2

So, Let the other rational no. be "x".

Therefore,

\begin{gathered} = > \frac{5}{2} + x = \frac{17}{4} \\ \\ = > x = \frac{17}{4} - \frac{5}{2} \\ \\ = > x = \frac{17 - 10}{4} \\ \\ = > x = \frac{7}{4} \end{gathered}=>25+x=417=>x=417−25=>x=417−10=>x=47

Answer:

Hope the picture will help you

The measure of the angle b is 61°.

In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams.

Vertical Angles (Vertically Opposite Angles): The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.

The figure describes two angles 61° and b.

Now, from the figure the angles 61° and b are vertically opposite angles.

Therefore, the angles are equal.

b = 61°

Hence, the measure of angle b is 61°.

Learn more about angles here:

https://brainly.com/question/12162963

#SPJ1

The correct explanation for the expression 3.5p(4 − 0.3p) will be;

⇒ 14p - 1.05p²

Option C is true.

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called the Mathematical expression.

Given that;

The mathematical expression is;

⇒ 3.5p(4 − 0.3p)

Now, Solve the expression as;

The mathematical expression is;

⇒ 3.5p(4 − 0.3p)

Hence,

⇒ 3.5p(4 − 0.3p) = 3.5 x 4p - 3.5p x 0.3p

                         = 14p - 1.05p²

Thus, After simplify we get;

⇒ 3.5p(4 − 0.3p) = 14p - 1.05p²

Therefore, The correct explanation for the expression 3.5p(4 − 0.3p) will be;

⇒ 14p - 1.05p²

Option C is true.

Learn more about the mathematical expression visit:

https://brainly.com/question/4344214

#SPJ1

The written and solved equation to determine the cost of the desserts, d is  5(9.75 + d) = 63.75; d = 3.00

Five friends ate lunch and spent a total of $63.75.

They each bought the same meal for $9.75, and they each bought the same dessert.

The equation to determine the cost of the dessert, d can be represented as follows:

They are 5 friends,

Hence,

5 (9.75 + d) = 63.75

48.75 + 5d = 63.75

Therefore, let's use the equation to solve for d.

48.75 + 5d = 63.75

63.75 - 48.75 = 5d

15 = 5d

divide both sides by 5

15 / 5 = 5d / 5

d = 3

learn more on equation here: https://brainly.com/question/28788021

#SPJ1

The difference between the population in City A and City B is 8.27 x [tex]10^{4}[/tex] and 82,700.

The numbers are written in scientific notation. Scientific notation is a method that is used in mathematics to compress large numbers. In order to write a number in scientific notation, the number is written as a decimal number between 1 and 10 and multiplied by a power of 10. For example, 3 x 10² is equivalent to 300

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers.

8.59 x [tex]10^{4}[/tex] - 3.2 x 10³

(0.859 x [tex]10^{4 - 1}[/tex]) - ( 3.2 x 10³)

(0.859 x  10³)- (3.2 x 10³)

0.827 x  10³

8.27 x [tex]10^{4}[/tex] = 82,700

To learn more about  scientific notation, please check: https://brainly.com/question/18073768

#SPJ1

The domain of the function is (-1, 3, 5).

Hence the correct answer is Option(C).

Given function: (-1 3 5) (2 6 8).

Domain is the input values in a function i.e. here it is (-1 3 5).

To know more about the domain of a function visit:

https://brainly.com/question/13113489

#SPJ9

Step-by-step explanation:

I assume you need the slope-intercept form

y = ax + b

"a" is the slope of the line, "b" is the y- intercept (the y-value when x = 0).

the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

for l we go from (5, 20) to (8, 80) and get

x changes by +3 (from 5 to 8)

y changes by +60 (from 20 to 80)

the slope is therefore

+60/+3 = 20/1 = 20 = a

so, we have

y = 20x + b

the y- intercept looks to be -80, but to be sure we use a point (e.g. 5, 20)

20 = 20×5 + b = 100 + b

b = -80

yes, the equation is

y = 20x - 80

for m we go from (5, 20) to (8, -40) and get

x changes by +3 (from 5 to 8)

y changes by -60 (from 20 to -40)

the slope is

-60/+3 = -20/1 = -20

we have therefore

y = -20x + b

we use the same trick for b as before

20 = -20×5 + b = -100 + b

b = 120

and our full equation is

y = -20x + 120

Answer:

  1/36

Step-by-step explanation:

You want the fraction of villains that are both jay walkers and double-parkers, given that 1/9 of jay walkers are double-parkers and 1/4 of villains are jay walkers.

The fraction of villains that both jay walk and double park is 1/9 of 1/4 of all villains.

  1/9 × 1/4 = 1/(9×4) = 1/36

1/36 of all villains are both jay walkers and double parkers.

Answer:   20 is the answer hope you have a great day

!!!!!

Step-by-step explanation:

After evaluating, we get

In the given question, we are given two expressions that include numerical in Roots. We have to calculate their values for each.

These are examples of Products. Product is when two numbers or terms are multiplied together.

The first expression is represented by:

=> 3 *√25, Calculating this expression we get

=> 3 * 5

=> 15

The second expression is represented by:

=> √(2 * 50), calculating this expression we get

=> √(100)

=> 10

Hence, after calculating both A. and B. expressions we get values 15, and 10 respectively

To know more about Product of Numbers, Click here:

https://brainly.com/question/3211849

#SPJ9

Answer: 0

Step-by-step explanation: We have to 2 answers to choose between, 0 and 1. 0.0379 is closer to 0 because if your decimal was more than 0.5 it would round to 1 as its nearest whole number. Hope this helps!

[tex] = 2(3( {(9})^{2} - 5) + 5(3)) \\ = 2(3(81 - 5) + 15) \\ = 2( 3(76) + 15) \\ = 2(228 + 15) \\ = 2(243) \\ = 486[/tex]

ATTACHED IS THE SOLUTION

YOU DID NOT PROVIDE FULL OPTIONS THEREFORE I WON'T BE ABLE TO CHOOSE.

GOODLUCK .

The volume of the given cylinder is 37.68ft³.

So, according to the given image, the given solid is a cylinder.

Now, insert values in the formula as follows:

Therefore, the volume of the given cylinder is 37.68ft³.

Know more about cylinders here:

https://brainly.com/question/24159177

#SPJ9

Answer:

-11/12

Step-by-step explanation:

Do you have a picture of your question?

Send it please

ok, ready

1 = 0.76r - 9 - 0.36r

1 + 9 = 0.76r - 0.36r

Simplify like terms

10 = 0.4r

Solve for r

r = 10/0.4

r = 25

Result

r = 25

b)

Result

z = 20

It is given that,

By using parallelogram method,

The graph is as shown below:

We have the following:

1. Similar By SSS similarity

4/2= 2

7.3.5 = 2

6/3 = 2

2. Similar by AA similarity, same angles, 90°, 70° and 50°

3. Similar by SAS similarity

, same angles and related sides.::

4/2 = 2

6/3 = 2

4. Similar by SAS similarity, same angles and related sides:

12/6 = 2

8/4 = 2

Answer: 700

Step-by-step explanation:

105-35=70

0.10Xx=70

x=700

700