Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.

Answer: 50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

300(2) bcuz 300 guests and each person gets 2

600(12) bcuz 300(2) is 600 and a dozen is 12

=50

Answer:

10°C

Step-by-step explanation:

F = 50

C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10

Another form of the given expression using associative property is 10y + (-3y -6y)

Associative property shows that if two or more property are added or multiplied, the result remains the same. For instance;

a +(b + c) = (a+b) + c

Given the expression below;

-3y - 6y + 10y

Group to have

(-3y - 6y) + 10y

10y - 3y - 6y

This can also be grouped as;

(10y - 3y) - 6y = 10y + (-3y -6y)

Hence another form of the given expression using associative property is 10y + (-3y -6y)

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The investment in  Fund B is $2000.

To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.

If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).

For Example: If the investment is A and profit is x % then the profit is calculated by:

Profit =A×([tex]\frac{x}{100}[/tex])

Now in the given problem, let us consider the amount of investment into the Fund B be x.

Profit in Fund B=10%

Profit in Fund A is 3%.

Investment in Fund A=$5000

Total profit from both investments=3% of 5000+10% of x

[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]

Now the total investment=5000+x

The combined profit for both the Investments is 150+0.1x

But the combined profit is 5% for both investments.

profit=[tex]5\% of(5000+x)[/tex]

[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]

Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.

[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]

Thus we can conclude that she invested $2000 in the Fund B.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-2}x+8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-2\implies \cfrac{-2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-2}\implies \cfrac{1}{2}}}[/tex]

so, we're really looking for the equation of a line whose slope is 1/2 and that it passes through (6 , -2)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +2= \cfrac{1}{2} (x -6) \\\\\\ y+2=\cfrac{1}{2}x-3\implies \LARGE \begin{array}{llll} y=\cfrac{1}{2}x-5 \end{array}[/tex]

Answer:

946 gal

629 gal

Step-by-step explanation:

volume that evaporates = LWH

volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch

volume = 218,550 in.³

volume = 218,550 in.³ × 1 gal / 231 in.³

volume = 946 gallons

You must add 946 gallons.

The loss to evaporation is 2.35 in.

The amount of rain is 20 mm

The net loss is

2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm

39.69 mm × 1 inch / 25.4 mm = 1.563 in.

The net loss now is 1.563 in. instead of 2.35 in.

We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.

1.563/2.35 × 946 gal = 629 gal

With rain, then 629 gallons of water must be added.

Answer:

$200

Step-by-step explanation:

At 27% reduction, we pay 100%-27%=73% of the original price O.

73% * O = $146

O = $146 / 73%

O = $2 / 1%

O = $2 / (1/100) = $2 * 100 = $200

Answer:

$ 200

Step-by-step explanation:

27 % off means you pay 73%   ( or .73 in decimal)

.73 * x   = 146             x = original price

x = 146/.73 = $ 200

Answer:

11

Step-by-step explanation:

2x-3=19

2x=22

x=11

Answer: $120

Step-by-step explanation:

5 * 60 (5 cents every minute with 60 minutes in a hour makes 300 cents per hour)

300 * 40 (300 cents per hour multiplied by 40 hours makes 12000 cents)

12000 / 100 (12000 cents divided by 100 since 100 cents in a dollar)

120 is the answer

the expression of the variable for a = 2 and c = 3. 2a − (c + a)2

2a+b^2 2a +b2

2(-3) +(-2)^2 2(-3) + (-2)

-6 +4 -6 -4

-2 -10

An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .

Either the options are incorrect, or the problem is poorly written.

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Answer:

x+(90°-0.5x)=3x

Step-by-step explanation:

Each of the two unknown angles in the triangle is 90°-0.5x because the triangle is isosceles.

So, by the exterior angle theorem, x+(90°-0.5x)=3x.

Answer:

4/5 is the slope of the line

The polynomial function with degree 5 is formed as:

f (x) = x (x + 2)³ (x - 2).

(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.

0 is derived from the factor x.

2 is derived from of the factor (x - 2).

The factored polynomial function is:

f (x) = x (x + 2)³ (x - 2)

Thus, the polynomial function with degree 5 is composed.

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Using proportions and multiplication, it is found that the door's height is 4 times greater than the desk's height.

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.

The ratio between two amounts a and b is the proportion of a to b, that is, the division of a by b.

For this problem, we have that:

8/2 = 4, hence, the door's height is 4 times greater than the desk's height.

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Answer:

[tex]\frac{270}{197}[/tex]

Step-by-step explanation:

First I need a common denominator.  That number is 270

The number of line segments in the 100th pattern is equal to 201 line segments.

Triangles are polygons with three sides of equal length, herein we find constructions elaborated with equilateral triangles, in which two new line segments are added when an equilateral triangle is so. Then, the number of line segments can be modelled after the following linear progression formula:

n = 3 + 2 · (n - 1)

Where n is the number of equilateral triangles in the pattern.

If we know that n = 100, then the number of line segments is:

n = 3 + 2 · (100 - 1)

n = 3 + 2 · 99

n = 3 + 198

n = 201

The number of line segments in the 100th pattern is equal to 201 line segments.

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hi

if he takes 1/3 , then remains 2/3

then 2/3 X = 10

             X =  10 / 2/3

            X =  10 * 3/2

              X = 30/2

              X = 15

let's check :  

1/3 of  15 =   15/3 = 5

15 -5 = 10

all macth, so answer is correct

Value of Sine and Cosine of T is -1 and 0 respectively.

According to the question statement, P is at the point (0,-1)

We are supposed to find the value of trigonometric ratios sine and cosine of T

Let Point P (0,-1)

[tex]x=0, y=-1[/tex] and radius r = 1

[tex]sin(t) = \frac{y}{r}\\sin(t)=\frac{-1}{1} \\sin(t)=-1[/tex]

Therefore, sine of t is -1

[tex]cos(t)=\frac{x}{r} \\cos(t)=\frac{0}{1} \\cos(t)=0[/tex]

Therefore, cosine of t is 0

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The formula for the 'B' variable is V/MK

To solve for the variable B is to make it the subject of formula.

Subject of formula is the variable that is expressed in terms of the other variables in a given formula, expression, function or equation.

Example;

In the equation,  2x + y = 4, let's make 'y' the subject of formula

y = 4 - 2x

Given the expression;

V=BMK

To make 'B' the subject, we need to divide both sides by the coefficients of B, we have;

V/MK = BMK/MK

B = V/MK

Thus, the formula for the 'B' variable is V/MK

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We need to know about scientific notation to solve the problem. Convert the numbers to same power of ten for addition or subtraction.

When a number is too big or too small we write it with an exponent raised to 10, this makes the number easy to read and understand. Writing a number like this is called scientific notation. Inorder to add or subtract two numbers written in scientific notation we need to first convert the powers of 10 to the same power, so that we can add the decimal numbers with the power of 10 being the common factor. We can convert the power by either multiplying the number to powers of 10 or by dividing it by powers of 10.

Therefore for addition or subtraction of two numbers written in scientific notation we need to have same powers of 10.

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Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Using the relation between velocity, distance and time, the distances are given as follows:

A. d = 13/3 miles.

B. d = 4.25 miles.

C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

Velocity is distance divided by time, that is:

v = d/t.

Hence the distance is:

d = vt.

In item a, considering the time in hours, we have that:

v = 13, t = 20/60 = 1/3.

Hence:

d = 13/3 miles.

In item b, we have different definitions, then:

d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).

d = 15/12 + 15/5

d = 4.25 miles.

For item c, we have that:

d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

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Answer:

2 groups of 3/8 are in one

Step-by-step explanation:

making up 6/8 because you can add another 3/8 to it.

Answer:

=

15/4

(Decimal: 3.75)

Step-by-step explanation:

Answer:

3080983

Step-by-step explanation:

ihhueuhreuhefhuuufehuefefeh

Answer:

Step-by-step explanation:

its ''C''

Answer:

Step-by-step explanation:

8.2% of what amount is $2.87

2.87 : 8.2 * 100 =

35

The profit in 2012 must be 4.5(in hundreds of dollars) to break even.

Profit for a company is defined as the difference between the revenue and cost of a product.

Let us take an example to learn more about profit.

A company sells a product at a price of 'S' dollars and the company spends 'C' dollars to manufacture the product. Here C includes the cost of raw materials, labor cost, transport etc.. Now the net profit for the company for selling one unit of this particular product is given by

Profit=S-C

In the given chart it is shown the profit of the company is given as

2.5,1.75,-3.3 and -1.4 (in thousands of dollars) over 4 years.

Net profit over four years=[tex]2.5+1.75-3.3 -1.4=-0.45[/tex]

So over the past four years the company incurred a loss of

[tex]=0.45\times 1000\\[/tex]

[tex]=450[/tex] dollars

Now the company needs to break even in 2012.

So net profit must be zero over 5 years.

Therefore Profit in 2012=0-(-450)=450 dollars

Profit=4.5 (hundreds of dollars)

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a) The slope of the line is 6 / 7.

b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).

c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.

d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.

There are three different forms of the equation of the line:

Point-slope

y - y' = m · (x - x')                     (1)

Slope-intercept

y = m · x + k                             (2)

Standard

a · x + b · x + c = 0                   (3)

Where:

a) The slope that passes through the two given points is found by secant line formula:

m = [8 - 2] / [11 - 4]

m = 6 / 7

b) The point-slope form of the equation of the line is:

y - 2 = (6 / 7) · (x - 4)

c) The slope-intercept form of the equation of the line is:

y - 2 = (6 / 7) · x - 24 / 7

y = (6 / 7) · x - 17 / 7

d) The standard form of the equation of the line is:

7 · y = 6 · x - 17

- 6 · x + 7 · y + 17 = 0

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Answer:

24 seconds

Step-by-step explanation:

Strand A: 3 × 8 secons =24 seconds

Strand B: 2 × 12 seconds= 24 seconds