karen and mary are saving money. karen has 150 and disposits an additional $25 a week. mary has $200 and deposits an additional $10 a week. what is the minimum number of weeks it will take for karen to have more saving then mary

The equation [tex]y = x^2 - 8x + 3[/tex] is an illustration of a quadratic equation

The vertex of the quadratic equation [tex]y = x^2 - 8x + 3[/tex] is (4,-13)

The equation is given as:-

[tex]y = x^2 - 8x + 3[/tex]

A quadratic equation is represented as:

[tex]y = ax^2 + bx + c[/tex]

By comparison, we have:

a = 1; b = -8; c = 3

The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]

So, we have:

[tex]x = \frac 8{2*1}[/tex]

[tex]x = 4[/tex]

Substitute 4 for y in [tex]y = x^2 - 8x + 3[/tex]

[tex]y = 4^2 - 8 * 4 + 3[/tex]

[tex]y = -13[/tex]

When x = 2 and 3, we have:

[tex]y = 2^2 - 8 * 2 + 3 = -9[/tex]

[tex]y = 3^2 - 8 * 3 + 3 = -12[/tex]

When x = 5 and 6, we have:

[tex]y = 5^2 - 8 * 5 + 3 = -12[/tex]

[tex]y = 6^2 - 8 * 6 + 3 = -9[/tex]

So, the table of values is:

x       y

2      -9

3      -12

4      -13

5      -12

6      -9

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What is k ? (k = y/x)

     If y is dollars earned and x is hours worked,

k = y/x

k = 150 dollars /20 hours

k = 7.50 dollars per hour

What is the equation for the direct variation situation? (y = kx)

y = kx

y = (7.50)(60)

y = 450

How much will she earn for working 60 hours?

y = $450

       She will earn $450 after working for 60 hours.

The standard form of the given equation  [tex]x^2+y^2-18x+8y+5=0[/tex] will be given as  [tex](x-9^2)+(y+4)^2=(2\sqrt{23} )^2[/tex]

The general form of the equation of the circle is given  as

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We have the equation

[tex]x^2+y^2-18x+8y+5=0[/tex]

By adding 81 and 16 on both sides

[tex]x^2-18x+81+y^2+8y+16=-5+81+16[/tex]

[tex](x-9)^2+(y+4)^2=92[/tex]

[tex](x-9)^2+(y+4)^2=(2\sqrt{23})^2[/tex]

Thus the standard form of the given equation  [tex]x^2+y^2-18x+8y+5=0[/tex] will be given as  [tex](x-9^2)+(y+4)^2=(2\sqrt{23} )^2[/tex]

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Answer:

x-9, y+4, & 92

Step-by-step explanation:

i did it

Answer:

872 square in.

Step-by-step explanation:

The formula for the surface area of a rectangular prism is:

[tex]A=2(wl*wh*lh)[/tex]

Where w is the width of the prism, l s the length of the prism, h is the height of the prism, and A is the surface area.

Plugging in the numbers given, you get the following equation:

[tex]A=2((20*18)*(20*2)*(18*2))[/tex]

Which when calculated out, is 872 square in.

Answer:

4.61

Step-by-step explanation:

Step-by-step explanation:

[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]

Find the LCM

[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]

Convert into lowest term

[tex] \frac{83}{16} \\ [/tex]

Answer:

1

(

π

3

)

)

Step-by-step explanation:

Explanation:

Substitute

tan

(

y

x

)

for

θ

tan

(

y

x

)

=

π

3

Obtain

y

x

on the left by using the inverse tangent on both sides:

tan

−

1

(

tan

(

y

x

)

)

=

tan

−

1

(

π

3

)

y

x

=

tan

−

1

(

π

3

)

Multiply both sides by x:

y

=

(

tan

−

1

(

π

3

)

)

x

Answer:

Solving for x;

-2x + 22 < 18

Get rid of constants:

-22          -22

-2x < -4

Isolate x, by dividing by -2 from both sides since the inverse operation of multiplication is division, and remember when dividing or multiplying by negative integers, you flip the inequality symbol around:

÷-2 ÷-2

x > 2

Answer:

[tex]x > 2[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x > 2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(2,\:\infty \:\right)\end{bmatrix}[/tex]

Given:

-2x + 22 < 18

Solve:

[tex]\mathrm{Subtract\:}22\mathrm{\:from\:both\:sides}[/tex]

[tex]-2x+22-22 < 18-22[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-2x < -4[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-2x\right)\left(-1\right) > \left(-4\right)\left(-1\right)[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]2x > 4[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]

[tex]\frac{2x}{2} > \frac{4}{2}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x > 2[/tex]

~Lenvy~

Answer:

(0, -22)

Step-by-step explanation:

       The y-intercept is the value of y when x is 0,

f(x) = -x² + 10x - 22

f(0) = -(0)² + 10(0) - 22

f(0) = - 22

                  The y-intercept is -22 at point (0, -22).

-> We can also see this when graphing, please see attached.

Note: If you want me to solve for f(x) = -x² + 10x - 12 as you wrote in text and not f(x) = -x² + 10x - 22 as the picture shows, let me know.

By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.

We define half-life as the time such that the initial amount is reduced to its half.

So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:

S(t) = A*e^{-t*ln(2)/T}

Where t is the variable in time units.

We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:

S(t) = 500mg*e^{-t*ln(2)/6h}

Then after 4 days (or 4*24h = 96h) the amount of medication is:

S(96h) =  500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.

If the initial dose was 750mg, after 4 days the person would have:

S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg

So the person would have:

0.0114 mg -  0.0076 mg = 0.038 mg more of medication.

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Answer:

27

Step-by-step explanation:

30% of 90 can be written as 30% × 90

= 30/100 × 90

= 27

Answer:1260

Step-by-step explanation: photo of the graded question attached

A math class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher

choose?

x3060

073

5040

1260

The amount of the refund Julia gets as a federal income tax will be $90.

It is given in the question:

Julia's gross pay = $500

federal income tax withholding from her pay was 13% of her gross pay

federal income tax she owes is = $495

To find out the refund we will first find the amount of Federal income which is 13% of the gross pay.

[tex]\rm federal \ amount =\dfrac{4500\times 13}{100} =585[/tex]

The refund Julia will get will be

[tex]=585-495=90[/tex]

Hence the amount of the refund Julia gets as a federal income tax will be $90.

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Answer:

9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true

Step-by-step explanation:

L * W =  area  length = width on a sqare so L * L = area too

(3x - 4) * (3x - 4)

use foil method

9x^2 - 24x + 16

Answer:

9x^2 − 24x + 16

Step-by-step explanation:

To find the area of a square, you use the formula

A = x^2

So we plug in 3x-4 for x

A = (3x-4)^2

A = 9x^2 − 24x + 16

The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.

In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

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Answer:

y = 71

z = 18

x = 14

Step-by-step explanation:

Figure on the right is simply figure on the left but flipped on its side. we know this because the question tells us the shapes are congruent (which means equal, the same)

Answer:

rational

Step-by-step explanation:

Hope this helps!

If not I am sorry

let's keep in mind that that same/same = 1 always, so then we can say

[tex]\cfrac{spaghetti}{spaghetti}~~ = ~~\cfrac{hippopotamus}{hippopotamus}~~ = ~~\cfrac{meatballs}{meatballs}~~ = ~~\cfrac{dog}{dog}~~ = ~~\cfrac{0.\overline{55}}{0.\overline{55}}~~ = ~~\textit{\huge 1}[/tex]

well, "1" is a whole number

"1" is also an integer oddly enough

"1" can be written as a ration like 1/1, so is also rational.

Answer:

a. 32%

B.8B.88

Step-by-step explanation:

100 -68=32%

32/100=x/275

100x=8800

x=88

Answer:

Third option

Step-by-step explanation:

Given the following question:

[tex]7x-4=5x+15[/tex]

To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.

[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]

Your answer is the third option or "19/2."

Hope this helps.

Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

Answer:

C. 5%

Step-by-step explanation:

if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent

The fraction of the compact disks ordered  by the owner of the music store that are Soft Rock is 13/28.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.

1 - (1/4 + 2/7)

1 -[ (7 + 8) /28]

1 - 15/28 = 13/28

the assumption being that "y" is encapsulating a function in "x" terms.

[tex]y+2=\cfrac{x^2}{2}-2sin(y)\implies \stackrel{\textit{taking the derivative to both sides}}{\cfrac{dy}{dx}+0=\cfrac{1}{2}(2x)\underset{chain~rule}{-2cos(y)\cdot \cfrac{dy}{dx}}} \\\\\\ \cfrac{dy}{dx}=x-2cos(y)\cfrac{dy}{dx}\implies \cfrac{dy}{dx}+2cos(y)\cfrac{dy}{dx}=x \\\\\\ \cfrac{dy}{dx}\left[ 1+2cos(y) \right]=x\implies \cfrac{dy}{dx}=\cfrac{x}{1+2cos(y)}[/tex]

Answer:

4/5 yd^3

Step-by-step explanation:

(2/3)(3/1)(2/5) = 12/15 = 4/5

Answer:

4/5 I believe?

Step-by-step explanation:

Multiply all the numbers together :)

Answer: a 5/24

Step-by-step explanation:

3 + 5 + 1 = 9

First = Pop Song     P = 3/9  = 1/3

Seconed = Hip Hop Song       P2 =  5/9-1   = 5/8

So P = 1/3 x 5/8 = 5/24

So that makes A the correct answer

Answer:

$81,728

Step-by-step explanation:

For reference: 1 pound = 16 ounces.

Therefore, 4 pounds of gold must be 16 * 4 = 64 ounces.

Since each ounce is $1,277, we must have the total cost of the gold to be $1,277 * 64 = $81,728.

The key word here is "per", which means to multiply.

Answer:Answer:5,108

Step-by-step explanation:

Answer:

A) (-5,0) and (-4,0)...

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]

X - intercepts are the points where the curve cuts x - axis ~

for the given curve (parabola), the intercepts are :

[tex]\qquad \sf  \dashrightarrow \:(-5,0) \: \: and \: \: (-4, 0)[/tex]

The Correct choice is A

[tex]➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖[/tex]

Answer:

5

Step-by-step explanation:

Answer:

The mean absolute deviation would be 10.

Step-by-step explanation:

I calculated the answer in Microsoft excel. I used a bunch of excel formulas. I do not know how to insert some of the math symbols neccessary to show you my steps. Here is a picture of the formula.

Answer:

2100

Step-by-step explanation:

Answer:

m = 3.75

Step-by-step explanation:

⇒ Angle opposing 3 in the left triangle is 53°