A woman is training for a cycling event. In the first week she cycles 20 km. In each subsequent week, she cycles 5 km more than she cycled the previous week.

How many kilometres has she cycled in total by the end of the 18th week?

Answer:

(x - 3) (5x + 1)(x + 1).

Step-by-step explanation:

5x^3 - 9x^2 - 17x - 3

As the first coefficient is 5 and the last -3, so product is -15, we could try if (x-3) is a factor:

By the Factor Theorem, if x-3 is a factor then f(3) = 0.

f(3) = 5(3)^3 - 9(3)^2 - 17(3) - 3

= 135 - 81 - 51 - 3 = 0

So, x - 3 is a factor.

Now divide:

x - 3)5x^3 - 9x^2 - 17x - 3(5x^2 + 6x + 1 <------- Quotient

       5x^3 - 15x^2

                    6x^2 - 17x

                    6x^2 - 18x

                                    x - 3

                                    x - 3

                                     .......

Factoring 5x^2 + 6x + 1:

= (5x + 1)(x + 1)

So, the answer is:

(x - 3) (5x + 1)(x + 1).

Answer:

Given:

Model : Ship = 3 : 400

The surface area of the model = 7200 cm²

To Find:

The surface area of the actual ship in m²

Let's start with the map scale given:

Model : Ship = 3 : 400

We start by adding in a unit. Usually, we choose the units associated with the model:

Model : Ship = 3 cm : 400 cm

Now, according to tot the question, we know that the actual ship is in m:

Model : Ship = 3 cm : 400 ÷ 100 m

Model : Ship = 3 cm : 4 m

The question asked for surface area, so the units have to be in squares:

Model : Ship = (3 cm)² : (4 m)

Model : Ship = 9 cm² : 16 m²

Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:

Model : Ship = 9 cm² : 16 m²

Model : Ship = 9÷9 cm² : 16÷9 m²

Model : Ship = 1 cm² : 16/9 m²

Finally, we can find the required units by multiplying both sides with the required units:

Model : Ship = 1 cm² : 16/9 m²

Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²

Model : Ship = 7200 cm² : 12800 m²

Answer: The surface area of the ship is 12800 m²

(by the way, this was copied from the same website)

hope this helps :)

Answer: C) 60

Step-by-step explanation: If you keep adding 12 the only number that I get on the list is 60.

The simplified expression of 7 * 2 * 7 * 5 is 490

The expression is given as

7*2*7*5

Rewrite the expression properly

This is done as follows

7 * 2 * 7 * 5

The factors of the expression have different basis

i.e. Basis = 7 , 2 and 5

This means that we cannot apply the law of indices

Solving further, we have the following equation:

7 * 2 * 7 * 5 = 7 * 2 * 7 * 5

Rearrange the factors

So, we have

7 * 2 * 7 * 5 = 7 * 7 * 2 * 5

Evaluate the products of 7 and 7 in the above equation

So, we have

7 * 2 * 7 * 5 = 49 * 10

Finally, we have

7 * 2 * 7 * 5 = 490

Hence, the simplified expression of the expression given as 7 * 2 * 7 * 5 is 490

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The simplified expression of the given 7 x 2 x 7 x 5 will be; 490

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is given as;

7 x 2 x 7 x 5

Rewrite the expression properly as follows;

7 x 2 x 7 x 5

The factors of the expression have different basis that is;

Basis = 7 , 2 and 5

Thus we can't apply the law of indices

Solving further, we have the equation;

7 x 5 x 7 x 2 = 7 x 2 x 7 x 5

Rearrange the factors;

7 x 2 x 7 x 5 = 7 x 7 x 2 x 5

7 x 2 x 7 x 5 = 49 x 10

Finally, we have the following

7 x 2 x 7 x 5 = 490

Hence, the simplified expression of the given 7 x 2 x 7 x 5 will be; 490

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Given:

It can be written as follows.

Dividing 5.44 by 6.8, we get

Hence the quotient is

Answer:

$302.69

Step-by-step explanation:

399 x 30% = 119.7 # finding how much you save

399 - 119.7 = 279.3 # how much the item costs with the sale

279.3 x 8.375 = 23.39 # the sales tax for the discounted item

297.3 + 23.39 = 302.69 # adding sales tax to the discounted item

I think this is right. I was never that great at sales tax and discount.

Write the inequality for the statement and solve for v

It means that v is less than or equal to -4. The solution set for this inequality is:

Given the right triangle:

The Pythagorean theorem states that:

From the problem, we identify:

And a is our missing value. Using the Pythagorean theorem:

Given

V(5, -2)

T(10, -3)

Procedure

For V:

The equation of the horizontal straight line corresponds to y = -2.

The equation of the vertical straight line corresponds to x = 5

For T:

The equation of the horizontal straight line corresponds to y = -3.

The equation of the vertical straight line corresponds to x = 10

The number of miles that is covered is  1458 miles.

The term gas mileage refers to the distance that have been covered by the car using a given volume of gas. It is common that the unit that is used to measure the volume of the gas is the US gallon.

We have been told that;

420 miles could be covered by the use of 20 gallons

1 mile can be covered by the use of 1 mile  * 20 gallons/ 420 miles

= 0.048 gallons

If 1 mile requires  0.048 gallons

x miles requires 70 gallons

x = 1 mile  * 70 gallons/0.048 gallons

x = 1458 miles

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The slope of the given lines are:

Graph 1 = 1/3

Graph 2 = -1/3

Graph 3 = 3

Graph 4 = -3

To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:

Slope of a line (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Find the slope of Graph 1:

Using two points on the line, (0, 0) and (3, 1):

Slope of graph 1 (m) = (1 - 0)/(3 - 0)

Slope of graph 1 (m) = 1/3

Find the slope of Graph 2:

Using two points on the line, (0, 0) and (-3, 1):

Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3

Slope of graph 2 (m) = -1/3

Find the slope of Graph 3:

Using two points on the line, (0, 0) and (1, 3):

Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1

Slope of graph 3 (m) = 3

Find the slope of Graph 4:

Using two points on the line, (0, 0) and (-1, 3):

Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1

Slope of graph 4 (m) = -3

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The operations which must be part of the inverse function g(x) are:

An inverse function can be defined as a type of function that is obtained by reversing or undoing a mathematical operation in a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.

Generally speaking, the inverse of multiplication is division while addition is the inverse of subtraction. In this context, we can reasonably and logically deduce that a "division by 2," followed by an "addition of 3" to the function f(x) are the operations that must be part of the inverse function g(x).

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Answer:

AC= 3.2

Step-by-step explanation:

two trianglesare similar

so AC : BC = DF : EF

AC : 4 = 3:2.4

4×3.2 = AC×4

12.8=4×AC >>>> (÷4) both sides

3.2= AC

Given the following question:

First expression:

Second expression:

The equation without fraction is 51 - 8x = 0

So, the equation is:

Rewrite in a more simplified form:

first, take the LCM, we get -

Now, take LHS denominator 3 to RHS:

Now, take 4 from RHS to LHS:

At last, decrease 9 by 60:

Therefore, the equation without fraction is 51 - 8x = 0

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Solution:

LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.

The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.

There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.

To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.

In this case, we get:

Then, the LCM would be:

so that, the correct answer is:

Answer:

625 pages

Step-by-step explanation:

Rate x time of the one printer + the rate x time of the second printer = 1000 pages

t= time

([tex]\frac{300}{10}[/tex] )t +( [tex]\frac{400}{8}[/tex]) t = 1000

30t + 50t = 1000

t(30 + 50) = 1000

80t = 1000   Divide both sides by 80

t = 12.5

It took 12.5 minutes to get this job done with both printers.

Look at printer b

[tex]\frac{400}{8}[/tex] (12.5) = pages

50 x 12.5 = 625 pages

By solving |4n+2|=34 solve for N we get 8 .

What is N factor?

The factorial of a non-negative integer n, denoted by n!, is the  product of all positive of  integers less than or equal to n. The factorial of n also  equals to the product of n with the next smaller factorial: For example, These are  value of 0! is 1, according to the  convention for an empty of product.

Sol-|4n+2|=34
Split into two equations
4n+2 = 34 or 4n+2=-34
4n+2 =34
Rearrange variable to the left side of the equation
4n =34-2
Calculate the sum or difference
4n=32
Devide both side of the equation by the coefficient of variable
n=32/4
Cross out the common factor
n=8
When n=8
LHS = |4×8+2|=34
RHS =34
LHS =RHS
Thus 8 is valid.

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SOLUTION.

AC and BD will intersect at the mid-point between points A and C.

So let's find the mid-point between points A and C

Point A(-2, 4) and point C(-6, 0)

This becomes

Therefore, the correct answer is option C.

Answer:

y = (-1/4)x - 10

Step-by-step explanation:

y = 4x - 1

y = -1/4x - 1

(4, -11),

(x₁, y₁)  

y - y₁ = m(x - x₁)

y - (-11) = (-1/4)(x - 4)

y + 11 = (-1/4)x + 1

   -11                 -11

-------------------------------

y = (-1/4)x - 10

I hope this helps!

we can made a visula representation of the problem so:

So we can made an equation like:

and we can solve for x so:

Answer: X=6

Step-by-step explanation: you can set AB plus BC to AC because they both are equal to the full line so..

2X-2+3=3X-5

First off add like terms so..

-2+3= 1 and then add 5 to the negative 5 and 1 which now leaves you with

2X+6=3X

Now you see more like terms ( 2X,3X)

Now subtract 2X from 3x which will leave you with

6=1X

Now to separate X and get you answer you see it’s 1X and 1X = X prior to defined answer, therefore you will be with X=6. Have a great day

The general slope intercept form is : y = m * x + b

Where m is the slope and b is y - intercept

Given the equation of the line : x + 3y = 8

Write the equation in slope intercept form to find the slope of the line

so, solve for y :

So, the slope of the given line = -1/3

The parallel lines have the same slope

so, the slope of the required line = -1/3

And the equation will be :

Find the value of b using the given point ( 5 , -6 )

When x = 5 , y = -6

So, the equation of the line will be :

it can be written as : 3y = -x - 13

In order to determine the value of the missing length b, use the Pithagorean theorem, given by:

h² = a² + b²

where:

h = 6.5 mm

a = 2.5 mm

solve the previous equation for b, as follow:

b = √(h² - a²)

b = √(6.5² - 2.5²)mm

b = √36 mm

b = 6 mm

Hence, the value of the missing length is 6 mm

Variance inflation factor can have a value as low as one (absence of multicollinearity). A VIF number greater than 5 or 10 generally denotes collinearity that is problematic.

The variance of bj is not inflated at all if the VIF is 1, which indicates that there is no association between the jth predictor and the other predictor variables.

VIF equal to 1 signifies that there is no correlation between the variables. A VIF of 1 to 5 indicates a moderate correlation between the variables. Variables are highly linked when the VIF is greater than correlated2.

VIF = 1.0 if all independent variables are orthogonal to one another. VIF = infinity if there is perfect correlation.

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Answer:

a) 199

f(-6)= 5(-6)^2 - 3 (-6) + 1 =199

b) 37

f(3)= 5(3)^2 - 3 (3) + 1 =37

Answer:

Step-by-step explanation:

From the given question

There are given that the :

After two weeks, the total miles is 276 and after 3 weeks, the total miles are 413

Now,

The total miles did they ride in the third week is:

Hence, the total miles in the third week is 137.

Compound interest exists as the interest you gain on interest. The balance in the account after 2 years is $42266.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

'Compound interest' simply indicates earning interest on your savings, and also, eventually, on the interest that those savings earn.

The appropriate formula is

A = P(1 +r/n[tex])^{(nt)[/tex]

where P = 19,000, r = 0.4, n = 365, t = 2.

substitute the values in the above equation, we get

A = 19,000(1 +0.4/365[tex])^{(365 \times2)[/tex]

simplifying the above equation, we get

A = 42266.7592

The balance in the account after 2 years is $42266.

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By using proportions, it is discovered that each favor costs $5.

Using the rule of three and proportions, this problem can be resolved.

The party's price is increased by $40 with the addition of 8 favors.

A proportion is an equation that sets two ratios at the same value.

Using the rule of three and proportions, this problem can be resolved.

The party's price is increased by $40 with the addition of 8 favors.

The threes rule states:

$40 for 8 favors

$1 for 1 favor

Cross-multiplication application

8x=40

x= 40/8

x = 5

There is a $5 fee for each favor.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).

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the reflection over the line y=x tells us to swap the points.

Therefore the point (0,-8) becomes (-8,0)