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3 years ago

Solve for x: 2 + 3x = 10x - 5

Mathematics

2 answers:

Arada [10]3 years ago

4 0

Answer: 1

Step-by-step explanation:

2+3 = 5

10 - 5 = 5

The x’s would be just 1 to make them equal since they don’t need to be multiplied

Pavel [41]3 years ago

3 0

Hey! The answer is 1. Here’s why: 10(1)-5=5 because 10x1 is 10 minus 5 is 5. And 3x1 is 3 and 3+2=10 they both equal 10. Hope this helped!

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Dan has bags of candy with two pieces in each. Bill has bags of candy with five pieces in each. Bill has six more bags than Dan.

Anna35 [415]

<u>Answer:</u>

Bill has bags of candy with five pieces in each. The Bill has 16 bags

<u>Solution:</u>

Given, Dan has bags of candy with two pieces in each.

Bill has bags of candy with five pieces in each.

Bill has six more bags than Dan.

Then, number of bags with bill = 6 + number of bags with dan.

The total number of pieces candy the two boys have 100.

Now, candies with bill + candies with dan = 100

⇒ 5 pieces per bag x number of bags with bill + 2 pieces per bag x number of bags with dan = 100

⇒ 5 x (6 + number of bags with dan) + 2 x number of bags with dan = 100

⇒ 30 + 5 x number of bags with dan + 2 x number of bags with dan = 100

⇒ (5 + 2) x number of bags with dan = 100 – 30

⇒ 7 x number of bags with dan = 70

⇒ Number of bags with dan = 10

So, number of bags with bill = 6 + 10 = 16

Hence, bill has 16 bags.

7 0

3 years ago

Convert 26\%26%26, percent to a fraction in simplest form.

Korolek [52]

26 percent?

A percent is a fraction out of a hundred. 5% is 5 out of one hundred, 20% is 20 out of one hundred, etc.

So 26/100 simplified is 13/50.

6 0

3 years ago

Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).

marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

$A=\frac{3\sqrt{3}}{2} a^2$

Where $A$ is the area of the regular hexagon

$a$ is the side length of the regular hexagon

Also, it's Perimeter is given by:

$P=6a$

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where $d$ is the distance.

$(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance $d$ )

Applying the above formula we get:

$d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4$

$\therefore d=4$

We know that this distance is the side length of the given regular hexagon.

$\therefore d=a=4$

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

$a_{small}=4-\frac{40}{100}\times 4=2.4$

Thus, the area of the smaller hexagon will be:

$A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96$ unit squared

and the new smaller perimeter will be:

$P_{small}=6a_{small}=6\times 2.4=14.4$ unit

Which are the required answers.

5 0

3 years ago

What is the equaiton of the line that goes through the point (6,-1) and is parallel to the line represented by the equautions y=

mixas84 [53]

parallel lines have the same slope

The slope-intercept form of a linear equatio is y=mx+b, where m stands for the "slope of the line" and b stands for the "y-intercept of the line"

They give you the equation y= -5/6x+3 Notice this is already on the slope-intercept form, so in this case the slope is -5/6 and the y-intercept is 3

You want an equation of the line that is parallel to the given line. The slopes must be the same, so m=-5/6

So far we have y=-5/6x + b

We don't have b yet but that can be found using the given point (6,-1) which tells you that "x is 6 when y is -1"

Replace that on the equation y=-5/6x + b and you get

-1 = (-5/6)(6) + b

-1 = -5 +b

4 = b

b = 4

We found b, or the y-intercept

Go back to the equation y = -5/6 x + b and replace this b with the b we just found

y = -5/6x + 4

6 0

3 years ago

The average number of customers per day at a home improvement store is given in the following table. Let x represent the day whe

nika2105 [10]

Answer:

A. $33.690\sin (0.887x + 1.337) + 81.684$ .

Step-by-step explanation:

We are given that,

x = Number of days where 1 = Sun of 1st week and 7 = Sat of first week.

The corresponding table for the data is given by,

Days Day Number Number of Customers

Sun 1 115

Mon 2 77

Tue 3 60

Wed 4 51

Thur 5 68

Fri 6 86

Sat 7 120

The general form of the regression model is $a\sin (bx+c)+d$ .

Using the sinusoidal regression calculator, we get that,

a = 33.690

b = 0.887

c = 1.337

d = 81.684

That is, the sine regression model is $33.690\sin (0.887x + 1.337) + 81.684$ .

Thus, option A is the sine regression model for the given data.

6 0

3 years ago

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