Which of the following is the general term for the sequence a, -a, a, -a, . . . ?

Answer:

first option

(8, -1)

Step-by-step explanation:

We have the following system of linear equations

[tex]\left \{{{x+6y=2} \atop {5x+4y=36}} \right.[/tex]

To solve the system multiply the first equation by -5 and then add it to the second equation.

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

[tex]-5x -30y=-10\\5x+4y=36[/tex]

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

[tex]-26y = 26[/tex]

[tex]y = -1[/tex]

substitute [tex]y = -1[/tex] in any of the two equations and then solve for x

[tex]5x+4(-1)=36\\5x-4=36\\5x = 36+4\\5x = 40\\[/tex]

[tex]x =8[/tex]

The answer is the first option

(8, -1)

Answer:

[tex]a=0.1\\b=0.85[/tex]

Step-by-step explanation:

In this problem we are calculating the relative frequency conditional by columns.

Therefore the sum of the frequencies of each column must be equal to 1.

Then we use this condition to calculate the values of a and b

So:

[tex]0.9 + a = 1\\a = 1-0.9\\a = 0.1[/tex]

[tex]b +0.15 = 1\\b = 1-0.15\\b = 0.85[/tex]

Finally

[tex]a=0.1\\b=0.85[/tex]

Answer:

Values of a and b are:

a=0.1

and b=0.85

Step-by-step explanation:

As we can clearly see from the table that sum of each column is equal to 1.0

i.e. 0.9+a=1.0

and b+0.15=1.0

Hence, a=1.0-0.9

              = 0.1

and b=1.0-0.15

        =0.85

Hence, Values of a and b are:

a=0.1

and b=0.85

[tex]|\Omega|=3+4+5=12\\|A|=3+5=8\\\\P(A)=\dfrac{8}{12}=\dfrac{2}{3}\approx66.7\%[/tex]

[tex]xy(x+1)=x\cdot y\cdot (x+1)\\x(x+2)=x\cdot (x+2)\\\\\text{lcm}(xy(x+1),x(x+2))=x\cdot y \cdot (x+1)\cdot (x+2)=xy(x+1)(x+2)[/tex]

Answer:

-1\20

Step-by-step explanation:

As percentages: ? + -35% = -40%; -5% = ?

As decimals: ? + -0.35 = -0.4; -0.05 = ?

**-⅖ = -8\20 [Least Common Denominator]

Answer:

144 dollars

Step-by-step explanation:

Answer:

3 < third side < 13

Step-by-step explanation:

The third side must be greater than the difference of the two other sides

and less than the the sum of the two sides

8-5 < third side < 8+5

3 < third side < 13

Answer:

98 ft  and   38 ft

Step-by-step explanation:

We know that the initial length of the piece is  136 feet

Then the piece is cut into two pieces.

Let's call x the length of the first piece  of cable and call z the length of the second piece of cable.

So we know that

[tex]x + z = 136[/tex]

and

[tex]x = 3z-16[/tex]

Now we substitute the second equation in the first one and solve for the variable z

[tex]3z-16 + z = 136[/tex]

[tex]4z-16= 136[/tex]

[tex]4z= 136+16[/tex]

[tex]z= \frac{152}{4}[/tex]

[tex]z=38\ ft[/tex]

Now we find the length x

[tex]x + 38 = 136[/tex]

[tex]x= 136-38[/tex]

[tex]x= 98\ ft[/tex]

Answer:

-12-14i

Step-by-step explanation:

subtract real from real number and imaginary from imaginary number

Answer:

-12 -14i

Step-by-step explanation:

(2 + 2i) - (14+ 16i)

Distribute the negative sign

2+2i -14-16i

Subtract the real part

2-14 = -12

Subtract the imaginary part

2-16 = -14

Put them back together in the form a + bi where a is the real part and b is the imaginary part

-12 -14i

The order of magnitude is (1)

Step-by-step explanation:

50 = 5.0 x10^1

Final answer:

Order of magnitude provides an estimation of the scale of a value expressed in powers of 10. For the number of states in the United States, the order of magnitude is approximately 10¹.

Explanation:

Order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 represents a different order of magnitude. For example, 10¹, 10², 10³ are all different orders of magnitude. We can estimate that the number of states in the United States is of the order of magnitude 10¹. This means there are approximately 10 to the power of 1 states in the United States.

Answer:

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

Step-by-step explanation:

Let

x -----> the length of the deck

y ----> the width of the deck

we know that

The perimeter of the deck is equal to

[tex]P=2(x+y)[/tex]

[tex]P=90\ ft[/tex]

so

[tex]90=2(x+y)[/tex]

[tex]45=(x+y)[/tex]

[tex]x=45-y[/tex] -----> equation A

The area is equal to

[tex]xy\geq 450[/tex] -----> inequality B  

[tex](45-y)y\geq 450\\ \\-y^{2} +45y-450\geq 0[/tex]

Solve the quadratic equation by graphing

The possible width of the deck are the values of y in the interval

[15,30]

All real numbers greater than or equal to 15 ft and less than or equal to 30 ft

see the attached figure

The minimum value of the width is 15 ft and the maximum value of the width is 30 ft

Answer:

2

Step-by-step explanation:

Answer:

The slope of line p is 3.

The slope of line q is -3.

Step-by-step explanation:

Points on line p  = [tex](x_1,y_2),(x_2,y_2):(1,-1), (0.-4)[/tex]

Slope of line p ,m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-4-(-1)}{0-(1)}=3[/tex]

The slope of line p is 3.

Points on line q  = [tex](x_1,y_2),(x_2,y_2): (0,2), (1,-1)[/tex]

Slope of line q ,m'= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m'=\frac{-1-2}{1-0}=-3[/tex]

The slope of line q is -3.

Answer:

[tex]12.5 \div 100 \times 6000 \times 0.5 = 375.00[/tex]

you have to convert six months to years by dividing six by 12 because it must be in years

Step-by-step explanation:

6÷12=0.5years

%/rate × money × years

12.5 ÷100 always divide by 100 because it is percentages over 100

12.5÷100 ×6000 ×0.5=Rs375.00

Answer:

Rs 375.00

Step-by-step explanation:

12.5 ÷ 100 × 6000 × 0.5 = 375.00

Answer:

3:2

Step-by-step explanation:

To answer questions like this I would makeup an age for Alan

Like say Alan is 10 years old

John is 3 times the age of 10 so he is 30

Ralph is twice the age of 10 so he is 20

so 30/20 can be simplified to 3/2

There are other ways to solve it but that is how I would solve it

I hope it helped you

Answer:

3:2 or 3/2

Step-by-step explanation:

Let Alan's age be x

So according to the assumed variable, John's age will be three times of Alan's age

John's Age = 3x

Similarly,

Twice of Alan's age = 2x

so, Ralph's age = 2x

Since we have to find the ratio of John's age to Ralph's age that will be equal to

3x : 2x

which can also be written as:

3:2 or 3/2 ..

Answer:

5x - 1

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 3x - 2 + 2x + 1 ← collect like terms

               = 5x - 1

[tex](f+g)(x)=3x-2+2x+1=5x-1[/tex]

Answer: The width is 12 feet shorter than the length.

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width of the rectangle.

 We know that lenght of Jennie's yard is 30 feet, the width is [tex](30-x)ft[/tex] and the area is 540 square feet. Then:

[tex]l=30\\w=(30-x)\\A=540[/tex]

Substitute these values into the formula and then solve for "x":

[tex]A=lw\\\\540=30(30-x)\\\\540=900-30x\\\\30x=900-540\\\\x=\frac{360}{30}\\\\x=12[/tex]

Therefore, the width is 12 feet shorter than the length.

Answer:

C

Step-by-step explanation:

got it on edge

Answer: 2x

Step-by-step explanation: 18+2(x-7)=4+M. First distribute 2 to (x-7), then you will be left with 18+2x-14=4+M. You can further simplify the left side of the equation by subtracting 14 from 18, now you are left with 2x+4=4+M. Subtract 4 from both sides to solve for M, 2x=M.

Answer:

0.3x = 100

x = 1000/3 = 333 and 1/3

Answer:

f(x)=-1(x+4)(x-3)

or  f(x)=-(x+4)(x-3)

Step-by-step explanation:

We see zeros at x=-4 and x=3.

So the factors are (x+4) and (x-3).

So we have a function that looks like

f(x)=A(x+4)(x-3).

y=A(x+4)(x-3)

I see the point (1,10) is on the curve.

So that means

10=A(1+4)(1-3)

10=A(5)(-2)

10=A(-10)

A=-1

So the function is f(x)=-1(x+4)(x-3)

or                          f(x)=-(x+4)(x-3)

Answer:

Step-by-step explanation:

Givens

Let Phoebe = P

Let Andy = A

Let Polly = Po

Total = 270

Equations

P = 3*A

A = 2*Po

P + A + Po = 270

Solution

P + 2Po + Po = 270

P = 3*A                                       But A = 2Po. Substitue 2Po for A

P = 3(2*Po)                                 Combine the right

P = 6Po                                      Substitute 6Po for P  

6Po + 2Po + Po = 270               Combine the left

9*Po = 270                                 Divide by 9

9Po/9 = 270/9                           Do the division

Po = 30

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

A = 2*Po = 2* 30 = 60

A = 60

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

P = 3*A

P = 3*60

P = 180

Answer

Phoebe gets 180

Andy gets       60

Polly gets        30

there are 50 states, NY is the 27th largest so before NY there are other 26 states that are larger than NY.

if we take 50 to be the 100%, what is 26 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 26&x \end{array}\implies \cfrac{50}{26}=\cfrac{100}{x}\implies \cfrac{25}{13}=\cfrac{100}{x}\implies 25x=1300 \\\\\\ x=\cfrac{1300}{25}\implies x=52[/tex]

[tex]\bf \cfrac{x}{2}+\cfrac{y}{3}-\cfrac{z}{4}\implies \stackrel{\textit{using the LCD of 12}}{\cfrac{(6)x~~+~~(4)y~~-~~(3)z}{12}}\implies \cfrac{6x+4y-3z}{12}[/tex]

Question: Perform the indicated operation. [tex]\frac{x}{2}+\frac{y}{3}-\frac{z}{4} = ?[/tex]

Answer: [tex]\frac{6x+4y-3z}{12}[/tex]

Hope I helped!!! :)

(I had this same question)

Answer:

x > -8

Step-by-step explanation:

5 - (x+5) > -2(x+4)

5 - x - 5 > -2x -8

- x > -2x -8

-x +2x > -8

x > -8

The answer is X > -8

Here is it graphed:

Answer:

It is f(x) = -x^2 + 2x + 4.

Step-by-step explanation:

As it has a maximum the coefficents of x^2 will be negative.

f(x) = -x^2 + 2x + 4

The y-intercept occurs when x = 0 so

y-intercept = 0 + 0 + 4 = 4.

-

ANSWER

[tex]f(x) = - {x}^{2} + 2x + 4[/tex]

EXPLANATION

The graph of the function that will have a maximum and a y-intercept of 4 is

[tex]f(x) = - {x}^{2} + 2x + 4[/tex]

To check for the y-intercept, we put x=0 into the function.

[tex]f(0) = - {0}^{2} + 2(0)+ 4[/tex]

This implies that,

[tex]f(0) = 4[/tex]

We can see that the coefficient of the quadratic term is -1.

Since the coefficient of the quadratic term is less than zero, the graph will have a maximum point.

Answer:  THIRD OPTION.

Step-by-step explanation:

We need to remember that we can create a perfect square trinomial by squaring a binomial:

[tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Then we need need to pick the coefficient of the x term of the given expression, divide it by 2 and square it:

[tex](\frac{3}{2})^2=\frac{9}{4}[/tex]

Therefore, the number that should be added to the given expression  in order to create a perfect square trinomial is:

[tex]\frac{9}{4}[/tex]

Answer:

- Discontinuity at (-1,6)

 - The zero is at (-7,0)

Step-by-step explanation:

Given the function [tex]f(x)=\frac{x^2 + 8x + 7}{x+1}[/tex], you need to factor the numerator. Find two number whose sum be 8 and whose product be 7. These are 1 and 7, then:

[tex]f(x)=\frac{(x+1)(x+7)}{(x+1)}[/tex]

Then, the denominator is zero when [tex]x=-1[/tex]

Therefore, [tex]x=-1[/tex] does not belong to the Domain of the function. Then, (-1,6) is a discontinuity point.

Simplifying, you get:

[tex]f(x)=x+7[/tex]

You can observe that a linear function is obtained.

This function is  equal to zero when [tex]x=-7[/tex], therefore the zero of the function is at (-7,0).

ANSWER

Discontinuity:

[tex]x = - 1[/tex]

Zero:

[tex]x = - 7[/tex]

EXPLANATION

The given rational function is

[tex]f(x) = \frac{ {x}^{2} + 8x + 7 }{x + 1} [/tex]

We factor function to obtain:

[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1} [/tex]

This function is not continuous when

[tex](x + 1) = 0[/tex]

The function is not continuous at

[tex]x = - 1[/tex]

When we simplify the function, we get;

[tex]f(x) = x + 7[/tex]

The zero(s) occur at

[tex]x + 7 = 0[/tex]

[tex]x = - 7[/tex]

Answer:

opposite

Step-by-step explanation:

Answer:

(- x, y)

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Answer:

Scalene and Acute

Step-by-step explanation:

Since all of the leg measures of the triangle are not equal to each other, this triangle would be scalene.

In addition, all of the angle measures of the triangle is less than 90 making it an acute triangle.

Answer:

Scalene and Acute

Step-by-step explanation:

Since none of the sides have the same length: scalene

Isosceles ( 2 sides same length)  False

Equilateral( 3 sides same length) False

Acute: all angles less than 90 degrees:  True

Right:  one angle equal to 90 degree:  False

Obtuse:  One angle greater than 90 degrees:  False

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 10x + 14 ← is in slope- intercept form

with y- intercept c = 14 ⇒ (0, 14) → C

A new borrower cannot achieve a perfect credit score, but the number of points missed is not specific and varies individually. Fair credit decisions are based on facts, not personal attributes. Late payment fees and interest on carried balances also affect your credit score.

When you are building your payment history, it's essential to understand the impact of your actions on your credit score. A perfect credit score is typically seen as 850. As a new borrower, lacking a lengthy credit history, you may not have a perfect score, but the exact number of points you may miss cannot be precisely determined without considering individual credit activities. However, every lender has different criteria for evaluating credit scores, and it is fair practice that race, gender, religion, and other such attributes are not considered in credit scoring.

If you carry a credit card balance from month to month, you will incur interest charges, which can quickly accumulate and affect your credit utilization ratio, thereby potentially lowering your credit score. Promptly paying off credit card balances and keeping a low utilization rate are key strategies to maintain and improve your credit score.

Remember that late payments can result in additional charges, as in the case where a credit card company charges a $10 late fee and $5 daily until the payment is settled. Such penalties not only burden you financially but can also impact your credit score if late payments are reported to credit bureaus.

Final answer:

When starting to build your payment history, it's not possible to achieve a perfect credit score instantly due to the short credit history length and other factors. Payment history is the most significant component, affecting 35% of the FICO score. Keeping accounts in good standing and credit utilization under 30% are key steps to improving your score.

Explanation:

When you're building your payment history, establishing a perfect score immediately is not typically possible. A perfect FICO score is 850, and payment history is the most influential factor, accounting for 35% of your score. As a new credit user, your credit history length is shorter, which negatively affects your score. Unfortunately, it's not possible to quantify exactly how many points you'll miss from a perfect score as it varies depending on the individual credit report and the scoring model used.

It's important to keep your accounts in good standing to build a strong credit history over time. Also, being mindful of your Amounts Owed, which makes up 30% of the FICO score, can help improve your standing. Striving to utilize no more than 30% of your available credit is recommended. Over time, with good financial habits such as these, your credit score will naturally improve, moving closer to the ideal score of 700 or higher.

Other factors influencing your score include the length of your credit history (15%), new credit, and the mix of credit types you have. It's crucial to avoid opening too many new accounts at once, as this can lower your average account age and result in hard inquiries, both of which can reduce your score somewhat.