Find a recursive formula for the sequence:

3, -5, 11, -21

Answer:

D

Step-by-step explanation:

a) correct is 3/4.5=4/6; b) correct is 3.2/2.4=4/3; c) correct is 4/3.2=3/2.4; d) this is correct answer.

Answer:

f(x) = 60 + 15n

Step-by-step explanation:

if the start off amount is 60, so we can simply start it with 60 + ...

If she gets 15 for each customer, and the amount of customers is equal to n, then this can be written by 15n ( 12 * n )

Simply put these two parts together:

60 + 15n

So in a function:

f(x) = 60 + 15n

Answer:

2 km/h

Step-by-step explanation:

Let c represent the speed of the current of the river in km/h. Then the speed of the boat upstream is (10-c). In 3/4 hour, the distance traveled upstream is ...

... distance upstream = (3/4)·(10 -c)

The time taken to travel the same distance downstream is given as 3 hours. The speed in that direction is c, so we have ...

... 3 = distance upstream/c = (3/4)(10 -c)/c

Multiplying this equation by 4c, we get ...

... 12c = 3(10 -c)

... 15c = 30 . . . . . . . . add 3c

... c = 2 . . . . . . . . . . . divide by 15

The speed of the river current is 2 km/h.

Answer:

2km/h

Step-by-step explanation:

Answer:

77° or 103°

Step-by-step explanation:

All of the angles are either the given angle or its supplement. Corresponding angles are congruent, as are vertical angles. Any linear pair of angles will add to 180°.

Answer:

77° and 103°

Step-by-step explanation:

77° because it says one of the angles is 77°

103° because two parallel lines are equal to 180°

180°-77° is 103°

the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

Let's simplify each of the given expressions using properties of exponents:

1. [tex](2x^4 * y^-4 * z^-3) / (3x^2 * y^-3 * z^4)[/tex]

To simplify this expression, you can use the properties of exponents that state when you divide two terms with the same base, you subtract the exponents:

[tex](2x^4 / 3x^2) * (y^-4 / y^-3) * (z^-3 / z^4)[/tex]

Now, simplify each term separately:

[tex](2/3) * (x^(4-2)) * (y^(-4-(-3))) * (z^(-3-4))[/tex]

[tex](2/3) * x^2 * y^(-1) * z^(-7)[/tex]

The simplified expression is

[tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3x^2 * y^2 * z^4) / 2[/tex]

To simplify this expression, simply divide each term by 2:

[tex](3x^2 / 2) * (y^2 / 2) * (z^4 / 2)[/tex]

The simplified expression is:

[tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2x^2) / (3y * z^7)[/tex]

To simplify this expression, divide each term in the numerator by 3y and each term in the denominator by 3y:

[tex](2x^2) / (3y * z^7) = (2x^2 / 3y) * (1 / z^7)[/tex]

The simplified expression is:

[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2yz) / (3x^2)[/tex]

To simplify this expression, divide each term in the numerator by 3x^2:

[tex](2yz) / (3x^2) = (2 / 3x^2) * yz[/tex]

The simplified expression is:

[tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

This expression is already in a relatively simple form, and there are no common factors to further simplify it.

So, the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)\\[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3.[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

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Answer:

k = -2

Step-by-step explanation:

The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.

Subtracting f(x) from that equation, you get k = -2.

_____

Check

g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.

The value of k is found by examining the vertical distance between the graphs of y=f(x) and y=g(x) at the same x-coordinate. Without the visual graphs or specific points, the exact value of k cannot be provided.

The student is asking about the relationship between two functions, where g(x) is related to f(x) by the addition of a constant k.

To find the value of k, one would typically examine the vertical distance between the two function graphs at any given x-coordinate, since g(x) = f(x) + k. Without the graphical information provided, it is not possible to determine the exact value of k.

However, typically if you have two functions with graphs that are vertically shifted versions of each other, and you know two corresponding points on each graph with integer coordinates, you can subtract the y-values of these points to find k.

Answer:

The inequality [tex]f>40[/tex] represents the length of the femur for which the woman had a height greater than 160cm.

Step-by-step explanation:

The given equation is

[tex]h=60+2.5f[/tex]

Where, h is woman's height in centimeters and f is length of the femur in centimeters.

If woman's height is greater than 160cm, then

[tex]h>160[/tex]

[tex]60+2.5f>160[/tex]

Substract 60 from both sides.

[tex]2.5f>100[/tex]

Divide both sides by 2.5.

[tex]f>40[/tex]

Therefore the inequality  [tex]f>40[/tex] represents the lengths of the femur for which the woman had a height greater than 160cm.

QUESTION 1

a)

Let

[tex]s [/tex]

represent the amount Same earned and

[tex]k[/tex]

represent the amount Kevin earned.

We were told that, they earned $425 dollars together.

This implies that,

[tex]k+s= 425---eqn(1)[/tex]

It was also given that, Kevin earned $25 more than Same.

This implies,

[tex]k-s=25---eqn(2)[/tex]

For equation (1), when

[tex]s=0[/tex]

[tex]k=425[/tex]

We plot the point,

[tex](425,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=425[/tex]

We plot the point,

[tex](0,425)[/tex]

Similarly for the second equation when

[tex]s=0[/tex]

[tex]k=25[/tex]

This gives the point,

[tex](25,0)[/tex]

When

[tex]k=0[/tex]

[tex]s=-25[/tex]

We plot

[tex](0,-25)[/tex]

and draw a straight line through them.

We can see from the graph that the two points intersect at  

[tex](225,200)[/tex]

This implies that

[tex]k=225\:and\:s=200[/tex]

Therefore Kevin earned $ 225

and Same earned $ 200

QUESTION 2

The given system is

[tex]6=-4x + y---eqn(1)[/tex]

and

[tex]-5x-y=21---eqn(2)[/tex]

From equation (2),

[tex]y=-5x-21---eqn(3)[/tex]

Put equation (3) into equation (1).

This implies that,

[tex]6=-4x-5x-21[/tex]

Group like terms,

[tex]6+21=-4x-5x[/tex]

Simplify, to get,

[tex]27=-9x[/tex]

[tex]x=-3[/tex]

We substitute this value into equation (3) to get,

[tex]y=-5(-3)-21[/tex]

[tex]y=15-21[/tex]

[tex]y=-6[/tex]

Therefore the solution is

[tex](-3,-6)[/tex]

QUESTION 3

We want to solve,

[tex]2x+y=20---(1)[/tex]

and

[tex]6x -5y=12---(2)[/tex]

We multiply equation (1) by 3 to get,

[tex]6x+3y=60---(3)[/tex]

Equation (3) minus equation (2) will give us,

[tex]8y=48[/tex]

This means

[tex]y=6[/tex]

Put this value into equation (1) to get,

[tex]2x+6=20[/tex]

[tex]2x=20-6[/tex]

[tex]2x=14[/tex]

[tex]x=7[/tex]

The solution is

[tex](7,6)[/tex]

Answer:

Sam earns $200 and Kevin earns $225.

x , y= -3 , -6 by substitution

x , y= 7, 6 by elimination

Step-by-step explanation:

a) Let the amount earned by Sam = s and the amount earned by Kevin = k

We are given, that they both earn total $425 i.e. s + k = 425

Also, Kevin earns $25 more than Sam i.e. k = s + 25

Hence, the system of equations comes out to be:

s + k = 425

-s + k = 25

b) Take s = x and k = y. See the graph plotted below

c) As the intersection point from the graph comes out to be (s,k) = (200,225)

Therefore, Sam earns $200 and Kevin earns $225.

Now, we have the system

-4x + y = 6

-5x - y = 21

We need to use substitution method.

Take y= -5x - 21 from the 2nd equation and put it in the 1st.

We get, -4x - 5x - 21 = 6  i.e.  -9x = 27  i.e.  x= -3

Now, substitute this value of x in any of the equation to find y.

We get, -5*(-3) - y = 21  i.e.  y = 15 - 21  i.e.  y = -6

Now, we are given the system,

2x + y = 20

6x - 5y = 12

We need to use elimination method.

Multiply 5 by equation 1. We get,

10x + 5y = 100

6x - 5y = 12

Adding the above equations, we get, 16x = 112  i.e. x = 7

Put this value in any of the equation to find the value of y.

We get, y = 20 - 2x  i.e.  y = 20 - 2*7  i.e.  y = 20 - 14  i.e. y = 6

48 1/8

As written, it is evaluated as ...

... 47 + 9/8 . . . . . . . . parentheses are evaluated first

... = 47 + 1 1/8 . . . . . . then division

... = 48 1/8 . . . . . . . . then addition

_____

A decent calculator will evaluate this for you according to the order of operations. A Google or Bing search box will do that, too.

Answer:

Answer is: D. $40

Step-by-step explanation:

20+40=60

100-60=40

Answer:

A 48

Step-by-step explanation:

Answer:

19 yards

Step-by-step explanation:

A square has 4 equal sides, thus its area is given by the formula below.

[tex]\boxed{\text{Area of square}=\text{side}^2}[/tex]

Substitute the area of the square into the formula:

361= side²

Square root both sides:

Length of each side

= [tex]\sqrt{361}[/tex]

= 19 yards

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Answer:

The equation of the line would be y = -3/7x - 20/7

Step-by-step explanation:

To start finding the line of this equation, you need to find the slope. You can do this using the slope equation.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-2 - -5)/(-2 - 5)

m = (-2 + 5)/(-2 - 5)

m = 3/-7

m = -3/7

Now that we have the slope, we can use that and either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y + 5 = -3/7(x - 5)

y + 5 = -3/7x + 15/7

y = -3/7x - 20/7

To find the equation of the line that passes through (-2, -2) and (5, -5), calculate the slope, apply it to the point-slope form using one of the points, then simplify to slope-intercept form, resulting in y = (-3/7)x - 20/7.

To find the equation of the line that passes through the points (-2,-2) and (5,-5), we first need to calculate the slope of the line. The slope (m) can be found using the formula:

m = (y_{2} - y_{1}) / (x_{2}  - x_{1})

Substituting our points into the formula:

m = (-5 - (-2)) / (5 - (-2)) = (-5 + 2) / (5 + 2) = -3 / 7

Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1). Let's use the first point (-2, -2):

y - (-2) = (-3/7)(x - (-2))

Now we simplify and write the equation in slope-intercept form (y = mx + b):

y + 2 = (-3/7)x - 6/7

Subtract 2 from both sides of the equation to solve for y:

y = (-3/7)x - 6/7 - 14/7

y = (-3/7)x - 20/7

The equation of the line that passes through the points (-2,-2) and (5,-5) is y = (-3/7)x - 20/7.

[tex]\left\{\begin{array}{ccc}2x+3y=5&|\text{multiply both sides ny 3}\\3x+4y=4&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x+9y=15\\-6x-8y=-8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad \boxed{y=7}\\\\\text{put the value of y to the first equation}\\\\2x+3(7)=5\\\\2x+21=5\qquad\text{subtract 21 from both sides}\\\\2x=-16\qquad\text{divide both sides by 2}\\\\\boxed{x=-8}\\\\Answer:\ \boxed{x=-8\ and\ y=7}[/tex]

Answer:

9/10

Step-by-step explanation:

In ratio units, the relative lengths of the first, second, and third towels are ...

... 1 : 3/5 : (5/12)·(1 +3/5)

... = 1 : 3/5 : 2/3

Then the fraction the second towel is of the third towel is ...

... (3/5)/(2/3) = (3/5)·(3/2) = 9/10

answer:

the answer is 2/3

Answer:

The answer is: 8km - 4

Step-by-step explanation:

Given: (4k4m - 8)1/2 =

Simplify then multiply 1/2 by each term:

4k4m/2 - 8*1/2 =

16km/2 - 4

8km - 4

Hope this helps! Have an Awesome day!! :-)

Answer:

Step-by-step explanation:

I don't know how is to speak it English correctly but is the teoreme of whole probability

P(A1)=0.08*0.4=0,032 is probability to choose defective item line I

P(A2)=0.1*0.6=0.06  is probability to choose defective item line II

P(B)=P(A1)+P(A2)=0,032+0.06=0.092 probability to choose defective item

P(C)=1-P(B)=0.908 the probability that it is not defective

Answer:

The amount off the original price is $3.6.

Step-by-step explanation:

The original price of the sweater = $18.00

Amount off on the sweater = 20% of the original price of the sweater

=[tex]18.00\times\frac{20}{100}=$3.6[/tex]

The cost of the sweater on the sale = $18.00 - $3.6 = $14.4

The amount off the original price is $3.6.

Answer:

-2

Step-by-step explanation:

3.3÷(0.8−3)−0.5

First think of PEMDAS

So first do parenthese

(0.8-3)=-2.2

3.3÷-2.2-0.5

Now do division

3.3/-2.2=-1.5

and now subtraction

-1.5-0.5=-2

Use the definition of conditional probability:

[tex]P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}[/tex]

We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so

[tex]P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40[/tex]

Answer:

0.40

Step-by-step explanation:

the tale-tell fellow is the base of the exponent ˣ.

if that number is less than 1, is a decay factor, if it's more than 1, is growth.

1.09 is cleary more than 1, so is growth, at what rate?

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &P\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0.0r\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ f(x)=4.7(1.09)^x\implies f(x)=4.7(1+\stackrel{\stackrel{r}{\downarrow }}{0.09})^x \\\\\\ r=0.09\implies \stackrel{\textit{converting it to percentage}}{r=0.09\cdot 100}\implies r=\stackrel{\%}{9}[/tex]

Exponential functions are mostly used to represent growth of population.

The true option is: (d)  Exponential growth function; 9%

The function is given as:

[tex]\mathbf{f(x) = 4.7 \cdot 1.09^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{f(x) = a \cdot b^x}[/tex]

By comparison:

[tex]\mathbf{b = 1.09}[/tex]

When b is greater than 1, then the function is a growth function.

Next, we calculate the constant percentage rate of growth (r)

If b is greater than 1, then:

[tex]\mathbf{b = 1 + r}[/tex]

Substitute 1.09 for b

[tex]\mathbf{1 + r = 1.09}[/tex]

Subtract 1 from both sides

[tex]\mathbf{r = 0.09}[/tex]

Express as percentage

[tex]\mathbf{r = 0.09 \times 100\%}[/tex]

[tex]\mathbf{r = 9\%}[/tex]

Hence, the growth rate is 9%

Hence, the true option is: (d)  Exponential growth function; 9%

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Answer:

9 days.

Step-by-step explanation:

If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.

Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.

If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.

If you had to use an equation:

Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:

number of items = 40 items/day * x days = 60 items/day * (x - 3) days

40x = 60(x - 3) = 60x - 180

180 = 20x

x = 9

9 days is the desired answer.

Answer:

9

Step-by-step explanation:

3 seconds

For the given problem conditions, the parameters in your formula are ...

... h = 0

... r = 48

Putting these values into the equation, we can solve for t.

... 0 = 48t -16t²

... 0 = 16t(3 -t) . . . . . factored

This will be true for t=0 and for t=3

The ball will hit the ground after 3 seconds.

_____

Comment on answer choices

For the ball to take 456 seconds (more than 7 1/2 hours) to hit the ground, it would have to  be launched at 7296 ft/s, several times the speed of sound. Its maximum height would be over 157.5 miles, and all of the usual assumptions about a stationary flat Earth with a uniform gravity field and no air resistance could not apply.

So, we know that 456 seconds is an impossible choice (as are the higher values, such as 1863 seconds). Perhaps that should be 4 5/6 seconds. For that to be the answer, the launch speed would need to be 77 1/3 ft/s, not 48 ft/s.

___

If these are the actual answer choices associated with this problem, it would be a good idea to have your teacher show you how to work it.

I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.

That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.

_____

Using an equation

If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...

... 0.60x + 0.20(100 -x) = 0.52·100

... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20

... x = 32/0.40 = 80 . . . . . kg of 60% alloy

... (100 -80) = 20 . . . . . . . .kg of 20% alloy

Answer:

-x^3+5x^2-8x+1, which is choice A

======================================

Work Shown:

f(x) = x^3 - x^2 - 3

f(x) = (x)^3 - (x)^2 - 3

f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)

f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2

f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3

f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4

f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5

f(2-x) = -x^3+5x^2-8x+1

----------

note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.

note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2

note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.

note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.

note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2

Answer:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15

Step-by-step explanation:

–x3 + 5x2 – 8x + 1

–x3 + 7x2 – 16x – 15

x3 + 5x2 + 8x + 1

x3 – 7x2 + 16x – 15

Answer:

what do i do if my math skills are bad

Step-by-step explanation:

Let the Salary of Mr. O'Conell be : S

Given : Mr. O'Conell spends 15% of his Salary on Food

[tex]\mathsf{\implies 15\%\;of\;Salary(S) = (\frac{15}{100} \times S) = 0.15 \times S}[/tex]

Given : Mr. O'Conell spends 24% of his Salary on Transportation

[tex]\mathsf{\implies 24\%\;of\;Salary(S) = (\frac{24}{100} \times S) = 0.24 \times S}[/tex]

Given : After Spending on Food and Transportation, He saves $1830

Money Spent on Food + Money spent on Transportation + Remaining Money should be Equal to his Total Salary

[tex]\mathsf{\implies 0.15S + 0.24S + 1830 = S}[/tex]

[tex]\mathsf{\implies 0.39S + 1830 = S}[/tex]

[tex]\mathsf{\implies S - 0.39S = 1830}[/tex]

[tex]\mathsf{\implies 0.61S = 1830}[/tex]

[tex]\mathsf{\implies S = \frac{1830}{0.61} }[/tex]

[tex]\mathsf{\implies S = 3000}[/tex]

Mr. O'Conell's Salary is $3000

Answer:

Option C is correct.

The value of x nearest to tenth is, 21.4 units

Step-by-step explanation:

In a given right angle triangle;

by definition of tangent ratio i,e   [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]

[tex]\tan 25^{\circ} = \frac{10}{x}[/tex]

[tex]0.46630765815 = \frac{10}{x}[/tex]

or

[tex]x = \frac{10}{0.46630765815} = 21.4450692[/tex] units

Therefore, the value of x nearest to tenth is, 21.4 units

Answer:

D. x = 3 1/8

Step-by-step explanation:

x + 7/8 = 4

The first step is to subtract 7/8 from each side

x + 7/8 - 7/8 = 4 - 7/8

x = 4 - 7/8

We need to borrow from the 4. It become 3 8/8

x = 3 8/8 - 7/8

x = 3 1/8

Answer:

I believe the answer would be D.

Step-by-step explanation:

y = -4.2x +34

The differences between adjacent y-values are -4.2 for all data points given, so the data is best modeled by a linear function with a slope of -4.2. The value for x=0 (the y-intercept) will be 4.2 higher than the value for x=1, so will be 34.

Thus the model can be ...

... y = -4.2x + 34

_____

Comment on the attached graph

The graph shows an attempt to model the data with a quadratic function (the first on your answer list). The result is that the x² coefficient is zero, and the model is the equation of a line (as shown above).

Answer:

Linear

Step-by-step explanation:

I got it from passing a quiz

c - the number

The sum of 7 times a number and 9 is 5:

[tex]7c+9=5[/tex]     subtract 9 from both sides

[tex]7c=-4[/tex]          divide both sides by 7

[tex]\boxed{c=-\dfrac{4}{7}}[/tex]