Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.

Answer: D

s > 0, V(s) > 0

Step-by-step explanation: edge

The question requires matching verbal descriptions of numbers with their corresponding numeric representations using decimal notation. The place value of each digit is used to determine the correct numeric form of the verbal description.

When matching the verbal descriptions to the correct number sentences, you will use the value of each place within a number to write it in decimal notation. For example, in the number 1837, the digit 7 is in the ones place (10⁰ = 1), the digit 3 is in the tens place (10¹ = 10), the digit 8 is in the hundreds place (10² = 100), and the digit 1 is in the thousands place (10³ = 1000). This helps us correctly identify the number sentences.

[tex]\frac{-5 + 2x^{2}}{7 - 8x}[/tex]

The denominator cannot equal zero.

7 - 8x ≠ 0

7       ≠  8x

    [tex]\frac{7}{8} \neq \frac{8x}{8}[/tex]

[tex]\frac{7}{8} \neq x[/tex]

Answer: [tex]\frac{7}{8}[/tex] is not in the domain

An asymptote is a vertical horizontal or oblique line to which the graph of a function progressively approaches without ever touching it.

To answer this question we observe the graph. All the values of x and y must be identified for which the graph of the function tends to infinity.

It is observed that these values are:

x = -1

x = 3

y = 0

The first two corresponds to the equations of a vertical line. The third corresponds to horizontal line, the axis of x. It can be seen that although the graph of the function is very close to these values, it never "touches" them

The asymptotes to the considered function are given as:

Suppose that we have the function f(x) such that it is continuous for all input values < a or > a and have got the values of f(x) going  to infinity or -ve infinity (from either side of [tex]x = a[/tex]) as x goes near a , and being not defined at [tex]x = a[/tex], then at that point, there can be constructed a vertical line [tex]x = a[/tex] and it will be called as vertical asymptote for f(x) at [tex]x = a[/tex]

The line [tex]y = a[/tex] is horizontal asymptote if the function f(x) tends to 'a' from upside of that line y = a, or from downside of that line.

For the given case, the line y = 0 is one of its horizontal asymptote.

If we make two straight lines at x = -1, and x = 3, we get two lines to which the graph of the function is going arbitrarily close, and going to +ve or -ve infinity.

Thus, they are its vertical asymptotes.

Therefore, the asymptotes to the considered function are given as:

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Answer:

use the butterfly method

Step-by-step explanation:

Answer:

9/4

Step-by-step explanation:

a pex

Javier's bank balance after 3 months would be $182.50

Using the parameters given for our Calculation;

The bank charge for the three month period ;

Balance after charges ;

Now we have ;

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First, combine like terms

-7x - 3x = -10x

-10x + 2 = -8x - 8

Isolate the x. Add 8x to both sides, and subtract 2 from both sides

-10x (+8x) + 2 (-2) = -8x (+8x) - 8 (-2)

-10x + 8x = -8 - 2

Simplify. Combine like terms

-2x = -10

Isolate the x. Divide 2 from both sides

(-2x)/-2 = (-10)/-2

x = -10/-2

x = 5

5 is your answer for x

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~Rise Above the Ordinary, Senpai

The solution of expression is,

x = 5

We have to given that,

Expression to solve,

-7x - 3x + 2 = - 8x - 8

Now, We can solve as,

-7x - 3x + 2 = - 8x - 8

First, combine like terms

-7x - 3x = -10x

-10x + 2 = -8x - 8

Add 8x to both sides, and subtract 2 from both sides

-10x (+8x) + 2 (-2) = -8x (+8x) - 8 (-2)

-10x + 8x = -8 - 2

Simplify. Combine like terms

-2x = -10

Divide 2 from both sides

(-2x)/-2 = (-10)/-2

x = -10/-2

x = 5

So, The solution of expression is,

x = 5

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Solving the system, we find [tex]\(x = 2.5\) and \(y = -1\)[/tex]. The product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex]. Answer: C) [tex]\(-\frac{2}{5}\).[/tex]

To find the product of [tex]\(x\) and \(y\)[/tex], we need to solve the given system of equations:

2x - 5y = 10

4x + 3y = 7

Let's solve this system using the substitution method:

From the first equation, we can express [tex]\(x\) in terms of \(y\)[/tex]:

[tex]\[2x = 10 + 5y\][/tex]

[tex]\[x = \frac{10 + 5y}{2}\][/tex]

[tex]\[x = 5 + \frac{5}{2}y\][/tex]

Now, substitute this expression for [tex]\(x\)[/tex] into the second equation:

[tex]\[4(5 + \frac{5}{2}y) + 3y = 7\][/tex]

[tex]\[20 + 10y + 3y = 7\][/tex]

[tex]\[13y = -13\][/tex]

[tex]\[y = -1\][/tex]

Now, substitute [tex]\(y = -1\)[/tex] into the expression for \(x\):

[tex]\[x = 5 + \frac{5}{2}(-1)\][/tex]

[tex]\[x = 5 - \frac{5}{2}\][/tex]

[tex]\[x = 5 - 2.5\][/tex]

[tex]\[x = 2.5\][/tex]

Finally, find the product [tex]\(xy\):[/tex]

[tex]\[xy = 2.5 \times (-1)\][/tex]

[tex]\[xy = -2.5\][/tex]

So, the product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex], which corresponds to option C) [tex]\(-\frac{2}{5}\).[/tex]

divide 3,326 by 3 and if she gets 842 it should be reasonable

Answer:

No her answer is not reasonable.  If you round 842 to 850 and multiplied that by 3 you would get 2,550.  

Step-by-step explanation:

I think you can google that really easily.

The solution is in the attached picture.

The perimeter of a shape is the sum of all visible side lengths of the shape. The perimeter of polygon qrst is 16 units.

Given that:

[tex]q = (-3,2)[/tex]

[tex]r = (1,2)[/tex]

[tex]s = (1,-2)[/tex]

[tex]t = (-3,-2)[/tex]

First, we calculate the distance between the vertices using distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

So, we have:

[tex]qr = \sqrt{(-3- 1)^2 + (2 - 2)^2} = \sqrt{16} = 4[/tex]

[tex]rs = \sqrt{(1- 1)^2 + (2 - -2)^2} = \sqrt{16} = 4[/tex]

[tex]st = \sqrt{(1--3)^2 + (-2 - -2)^2} = \sqrt{16} = 4[/tex]

[tex]tq = \sqrt{(-3--3)^2 + (-2 -2)^2} = \sqrt{16} = 4[/tex]

The perimeter (P) is the sum of all sides:

[tex]P = qr + rs + st + tq[/tex]

[tex]P = 4 + 4 + 4 + 4[/tex]

[tex]P = 16[/tex]

Hence, the perimeter is 16 units.

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Answer:

-3

Step-by-step explanation:

ANSWER

The factorization of   [tex]100x^2-20x+1[/tex]

 is [tex](10x-1)^2[/tex].

EXPLANATION

We want to factor [tex]100x^2-20x+1[/tex]

Comparing this to [tex]ax^2+bx+c[/tex]

[tex]a=100,b=-20,c=1[/tex]

[tex]ac=100[/tex]

We look for factors of 100  that add up to [tex]-20[/tex].

These factors are [tex]-10,-10[/tex]

We now split the middle term to obtain;

[tex]100x^2-10x-10x+1[/tex]

We factor to obtain;

[tex]10x(10x-1)-1(10x-1)[/tex]

This simplifies to  [tex](10x-1)(10x-1)=(10x-1)^2[/tex]

Answer:B

Step-by-step explanation:

For this one, plug in your x and y intercepts for the corresponding letters and see which one is true.  I always start with the first equation and then see which ones solve it first, that will cut your time down on a test.

Lets start with A. (4,5)

and the first equation y=x+1

5=4+1, which is true so A is a potential answer

B. (2,3)

3=2+1, B is a potential as well

C. (-2,1)

1=-2+1, which is false so C is out

D. (-4,-3)

-3=-4+1, which is true.

To cut down on time, do the same thing with the second equation and your final answer will be A. (4,5)

Answer:

Average change in temperature is - 2.8 Fahrenheit per hour.

Step-by-step explanation:

Average change in temperature is the change in temperature divided by the time taken for the change.

Change in temperature = (-11.2) F- 0 F

                                       = -11.2 F

Time taken for the change in temperature = 10 pm - 6 pm

                                                                       = 4 hours

Average change in temperature = Change in temperature / time taken for the change

                                                      = [tex]\frac{-11.2}{4}[/tex]

                                                      = - 2.8 Fahrenheit per hour

Final answer:

The average change in temperature per hour from 6 pm to 10 pm is calculated by dividing the total change in temperature by the number of hours. The result is a drop of -2.8°F per hour.

Explanation:

To find the average change in temperature per hour between 6 pm and 10 pm, you can use the following expression:

(Final Temperature - Initial Temperature) / Number of Hours = Average Change per Hour

Applying the given temperatures:

(-11.2°F - 0°F) / (10 pm - 6 pm) = Average Change per Hour

Since 10 pm is 4 hours after 6 pm, the expression simplifies to:

(-11.2°F - 0°F) / 4 hours = Average Change per Hour

Which evaluates to:

(-11.2°F / 4) = -2.8°F per hour

So the temperature dropped on average by -2.8°F each hour between 6 pm and 10 pm.

10.5821886 ounces is your answer

Answer:

ans is 56

Step-by-step explanation:

for u = 2, x = 9, and y = 6

substituting into u + xy = 2 + 9*6 = 2 + 54 = 56

Answer:

56

Step-by-step explanation:

2+9*6

=2+54

=56

Answer:

(1,2) (-1,-2)

Step-by-step explanation:

Given the equation of curve as y= 2x³ and slope of tangent line as 6 then

Find dy/dx

[tex]\frac{d}{dx} (y)=\frac{d}{dx}(2x^3)[/tex]

Apply the power rule

[tex]\frac{d}{dx} (x^n)=nx^{n-1}[/tex]

where n=constant

Hence, our equation will be;

[tex]\frac{dy}{dx} =2*3x^{3-1} \\\\\\\frac{dy}{dx} =6x^{2}[/tex]

But you know that dy/dx=slope=6

6x²=6--------------------divide both sides by 6

6x²/6=6/6

x²=1

x=√1=±1

x=1 and -1

Remember y=2x³

Substitute value of x to get value of y

y=2x³

y=2×1³

y=2×1=2

y=2

For x=-1, find y coordinate

y=2×-1³=2×-1=-2

coordinate will be (-1,-2)

Coordinates of the points will be (1,2) ,(-1,-2)

Number of units purchased = 117

Amount paid to purchase 117 units = $ 1250

Selling price of 117 units = $ 1601

Here, let us assume that all the units were sold at the same price.

So, profit on 117 units = [tex]1601-1250= 351[/tex]

Now, profit per unit will be,

[tex]\frac{351}{117} =3[/tex]

Hence, the profit earned per unit is $3.

Answer:

Measure of ∠P = 60°

Step-by-step explanation:

Consider triangle PMO.

Since PM is perpendicular to MO , hence m∠PMO = 90°

Also given that m∠MOP = m∠2 = 30°

And since sum of three angles of a triangle is 180°

⇒ m∠PMO + m∠MOP + m∠MPO = 180°

⇒m∠MPO = 180° - (m∠PMO + m∠MOP) = 180° - ( 90 + 30 ) = 60°

Hence m∠MPO that is m∠P is 60°

Answer:

m 2 = 30°, m P = 60

The correct choice is 60

$50

the sale price is [tex]\frac{5}{12}[/tex] × $120

[tex]\frac{5(120)}{12}[/tex] = $50

Answer:50

Step-by-step explanation:

you would do number of devisions (denominator of fraction) divided by the number of the original price then multiply it by the numer of the devision (numerator of fraction)

120/12=10*5=50

First you must know that is i∧2= -1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2-(-4)) =

= (x-4) (x∧2-(-1) *4) = (x-4) (x∧2- i∧2*2∧2) = (x-4) (x∧2-(2i)∧2) = (x-4) (x-2i) (x+2i)

Good luck!!!

A sidewalk is built 12 bricks wide by laying each brick side by side.

The size of each brick measures [tex]3\frac{3}{8}[/tex]

Convert the mixed fraction into improper fraction

[tex]3\frac{3}{8}= \frac{27}{8}[/tex]

The width of each brick is [tex]\frac{27}{8}[/tex]

To built side walk, 12 bricks are used

To find the width of side walk , we multiply the number of bricks with the width of each brick

[tex]12 * \frac{27}{8}[/tex]

We can cancel out 12  and 8

[tex]3 * \frac{27}{2}[/tex]

[tex]\frac{81}{2}[/tex]

[tex]40\frac{1}{2}[/tex] inches