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8090 [49]
3 years ago
15

Solve for x in the diagram below

Mathematics
1 answer:
ella [17]3 years ago
8 0

Answer:

20

Step-by-step explanation:

3x + x + 100 = 180 (sum of angles on a straight line)

4x = 180-100

4x=80

divide both sides by 4

x=20

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A culture of bacteria has an initial population of 92000 bacteria and doubles every 7 hours. Using the formula P_t = P_0\cdot 2^
ludmilkaskok [199]

Answer:

im here for the a

Step-by-step explanation:

8 0
3 years ago
The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3
Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is 258.75\ in^3.

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

Volume = Length\times height\times width

Substitute all given value in above formula.

258.75 = (h-4)\times h\times 3

Rewrite the equation as:

258.75 = 3h(h-4)

258.75 = 3h^2-12h

3h^2-12h-258.75=0

whole equation divided by 3.

h^2-4h-86.25=0

Use quadratic formula with a = 1, b = -4,c=-86.25

h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}

Put these a, b and c value in above equation.

h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}

h=\frac{4\pm \sqrt{16+345}}{2}

h=\frac{4\pm \sqrt{361}}{2}

h=\frac{4\pm 19}{2}

For positive sign

h=\frac{23}{2}  

h = 11.5 in

For negative sign

h=\frac{-15}{2}

h = -7.5

We take positive value of h.

Therefore, the height of the box h = 11.5 in

4 0
3 years ago
Prove that the product of a nonzero rational number together with an irrational number is an irrational number.
melamori03 [73]
Each time they assume the sum<span> is </span>rational<span>; however, upon rearranging the terms of their equation, they get a contradiction (that an </span>irrational number<span> is equal to a </span>rational number<span>). Since the assumption that the </span>sum of a rational<span> and </span>irrational number<span> is </span>rational<span>leads to a contradiction, the </span>sum<span> must be </span>irrational<span>.</span>
7 0
3 years ago
A fitted multiple regression equation is Y = 28 + 5X1 - 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as w
ad-work [718]

Answer:

A. Increase by 2

Step-by-step explanation:

Given that a  fitted multiple regression equation is

Y = 28 + 5X_1 -4X_2 + 7X_3 + 2X_4

This is a multiple regression line with dependent variable y and independent variables x1, x2, x3 and x4

The coefficients of independent variables represent the slope.

In other words the coefficients represent the rate of change of y when xi is changed by 1 unit.

Given that x3 and x4 remain unchanged and x1 increases by 2 and x2 by 2 units

Since slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in y

i.e. for 2 units change in x1, we expect 10 units change in Y

Similarly for 2 units change in x2, we expect -2(4) units change in Y

Put together we have

10-8 =2 change in y

Since positive 2, there is an increase by 2

A. Increase by 2

5 0
3 years ago
Carpeting costs 9.99 a yard. If jan buys 17.4 yards, how much will it cost her (round your anwser to the nearest hundreth
aalyn [17]
To get the answer, multiply 9.99 x 17.4 yards. That will give you the answer 173.826. That rounds to 173.83
4 0
3 years ago
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