What is the exponential form of log9 5 = y

Answer:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Step-by-step explanation:

Let the items sold with price $1.5 = [tex]x[/tex]

Let the items sold with price $3.5 = [tex]y[/tex]

Initially, total number of items = 150

Items left at the end of the day = 41

So, number of items sold throughout the day = Total number of items - Number of items left

Number of Items sold = 150 - 41 = 109

So, the first equation can be written as:

[tex]\bold{x+y = 109} ....... (1)[/tex]

Now, let us calculate the sales done by each item.

Sales from item with price $1.5 = Number of items sold [tex]\times[/tex] price of each item

= (1.5)[tex]x[/tex]

Sales from item with price $3.5 = Number of items sold [tex]\times[/tex] price of each item

= (3.5)[tex]y[/tex]

Total sales = [tex]\bold{(1.5)x+(3.5)y = 227.50} ....... (2)[/tex]

So, the correct answer is:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Answer:

5/w -7

Step-by-step explanation:

quotient means division

5/w

less than means it comes after

5/w -7

Answer:

5/w-7

Step-by-step explanation:

First, let's write out "the quotient of a number 5 and w"

The quotient is the result from dividing two numbers. Therefore, we must divide 5 and w.

5/w

Now, let's add on "7 less than". Since it is "less than" it will come after the division. "Less" means subtract. So, subtract 7 from 5/w.

5/w-7

7 less than the quotient of a number 5 and w as an expression is: 5/w-7

Answer:

360

Step-by-step explanation:

Answer:

3x3÷2= 4.5cm^2

The formula is 1/2×base×slanted height

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = ¹/₃•(¹/₂•10•9)•10 = ¹/₃•45•10 = 15•10 = 150 in²

Answer: [tex]243/5[/tex]

[tex]3^2/3(3^4)/5\\=9/3(3^4)/5\\=3(3^4)/5\\=(3)(81)/5\\=243/5[/tex]

Answer:

  2

Step-by-step explanation:

The series is a geometric series with a common ratio (r) of 1/2 and a first term (a1) of 1/2^0 = 1. The sum of such a series is given by ...

  S = a1/(1 -r) 1/(1 -1/2) = 2

The sum of the series is 2.

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

Answer: [tex]y=\dfrac12x-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given, The equation of line WX is 2x + y = −5.

It can be written as [tex]y=-2x-5[/tex] comparing it with slope-intercept form y=mx+c, where m is slope and c is y-intercept, we have

slope of WX = -2

Product of slopes of two perpendicular lines is -1.

So, (slope of WX) × (slope of perpendicular to WX)=-1

[tex]-2\times\text{slope of WX}=-1\\\\\Rightarrow\ \text{slope of WX}=\dfrac{1}{2}[/tex]

Equation of a line passes through (a,b) and has slope m:

[tex]y-b=m(x-a)[/tex]

Equation of a line perpendicular to WX contains point (−1, −2) and has slope [tex]=\dfrac12[/tex]

[tex]y-(-2)=\dfrac{1}{2}(x-(-1))\\\\\Rightarrow\ y+2=\dfrac12(x+1)\\\\\Rightarrow\ y+2=\dfrac12x+\dfrac12\\\\\Rightarrow\ y=\dfrac12x+\dfrac12-2\\\\\Rightarrow\ y=\dfrac12x-\dfrac{3}{4}[/tex]

Equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2) [tex]:y=\dfrac12x-\dfrac{3}{4}[/tex]

Answer:

  55°

Step-by-step explanation:

Perhaps you want the measure of angle B. (There is no "b" in the figure.)

That measure is half the measure of the intercepted arc:

  m∠B = 110°/2 = 55°

Angle B is 55°.

Answer:

12

563 - (563x0.25) = 422.25 -> 422

16

422 -(422x0.25) = 316.5 -> 317

20

317 - (317x0.25) = 237.75 -> 238

24

238 - (238x0.25) = 178.5 -> 179

28 (continue the step by step process)

134.25 -> 134

32

100.5 -> 101

36

75.75 -> 76

40

57

44

42.75 -> 43

48

32.25 -> 32

52

24

56

18

Step-by-step explanation:

the time interval has to keep skipping by four hours because the medicine is filtered in that amount of time.

The multiplying by 0.25 part must be done first in order to show how much the kidney has filtered.

after this, you need to subtract that from how many milligrams of medicine are left in your system

note that if you do not subtract, you will only be showing how much the kidney has filtered. the question asks for how much is left in the SYSTEM overall, so subtracting is quite necessary to completely answer the question.

I hope this helped.

Answer:x=45

Step-by-step explanation:

Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Answer:

see below

Step-by-step explanation:

x + 3y = 5,

y = –x + 3

Substitute the point into each equation and verify that it is true

x + 3y = 5,  2 +3(1) = 5   5 = 5  true

y = -x +3    1 = -2+3     1=1  true

(2,1) is a solution

Answer:

D,A,A,A,

Step-by-step explanation:

that's the real answer

1d

2a

2a

2a

God bless

Answer:

See below.

Step-by-step explanation:

There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.

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

Explanation:

19 = h/3 - 8

19+8 = h/3 - 8+8  .... see note 1

27 = h/3

h/3 = 27

3*(h/3) = 3*27 .... see note 2

h = 81

----------

Answer:

(6x + 9y)(6x - 9y)

Step-by-step explanation:

We can use the difference of squares which states that a² - b² = (a + b)(a - b), in this case, a = 6x and b = 9y so the answer is (6x + 9y)(6x - 9y).

Answer:

Hey there!

Your answer is:

Hope this helps :)

Answer:

The correct option is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

Given the points

(-1, -8), (0, -1), (1, 2), we have;

The general quadratic function;

f(x) = a·x² + b·x + c

From the given points, when x = -1, y = -8, which gives

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8 =  a - b + c.....................................(1)

When x = 0, y = -1, which gives;

-1 = a·0² + b·0 + c = c

c = -1.....................................................(2)

When x = 1, y = 2, which gives;

2 = a·1² + b·1 + c = a + b + c...............(3)

Adding equation (1) to (3), gives;

-8 + 2 = a - b + c + a + b + c

-6 = 2·a + 2·c

From equation (2), c = -1, therefore;

-6 = 2·a + 2×(-1)

-2·a  = 2×(-1)+6 = -2 + 6 = 4

-2·a = 4

a = 4/-2 = -2

a = -2

From equation (1), we have;

-8 =  a - b + c = -2 - b - 1 = -3 - b

-8 + 3 = -b

-5 = -b

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1

The correct option is f(x) = -2·x² + 5·x - 1.

The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.

The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.

The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.

Answer:

Hi, there!!

Hope you mean the answers in the solution.

Hope it helps...

Answer:

Step-by-step explanation:

7)

JKLM is a isosceles trapezium.

KL // JM

∠K + ∠J =  180   {Co interior angles}

50 +∠J = 180

      ∠J = 180 - 50

      ∠J = 130

As it is isosceles, non parallel sides KJ = LM &  

∠L = ∠K

∠L = 50

∠M = ∠J

∠M = 130

8)JKLM is a isosceles trapezium.

KL // JM

∠K + ∠J =  180   {Co interior angles}

100 +∠J = 180

      ∠J = 180 - 100

      ∠J = 80

As it is isosceles, non parallel sides KJ = LM &  

∠L = ∠K

∠L = 100

∠M = ∠J

∠M = 80

6:40 or 6 hour 40 minutes,

if you go back(subtract) 1 hour and 40 minutes

i.e. 6hours 40 minutes- 1 hour 40 minutes

subtract minutes from minutes and hours from hours,

5:00

note that here the minutes value is not negative so it was not a problem, what If it was 6:40-1:50?

Answer:

discriminant is b²-4ac

= 2²-4(-8)(0)

= 0

one solution

hope this helps :)

Answer:

1) 0.3 ; 0.7

Step-by-step explanation:

Given the following :

Probability that product A launch : P(A) = 0.45

Probability that product B launch : P(B) = 0.60

Probability that both product launch : P(AnB) = 0.35

P(A alone) = p(A) - p(AnB)

P(A alone) = 0.45 - 0.35 = 0.1

P(B alone) = p(B) - p(AnB)

P(B alone) = 0.60 - 0.35 = 0.25

Probability that neither product will launch :

1 - [p(A alone) + p(B alone) + p(AnB)]

1 - [0.1 + 0.25 + 0.35]

1 - 0.7 = 0.3

Probability that at least one product will launch :

P(A alone) + p(B alone) + p(AnB)

0.1 + 0.25 + 0.35 = 0.7

Answer:

The watered area is approximately 3783 square feet.

Step-by-step explanation:

The area that is watered due to the rotation of the spankler is a circular section area ([tex]A[/tex]), whose formula is:

[tex]A = \frac{\theta }{2}\times \frac{1}{360^{\circ}}\times 2\pi \times d^{2}[/tex]

Where:

[tex]d[/tex] - Water distance, measured in feet.

[tex]\theta[/tex] - Rotation angle, measured in sexagesimal degrees.

Given that [tex]d = 85\,ft[/tex] and [tex]\theta = 60^{\circ}[/tex], the watered area is:

[tex]A = \frac{60^{\circ}}{2} \times \frac{1}{360^{\circ}}\times 2\pi \times (85\,ft)^{2}[/tex]

[tex]A \approx 3783\,ft^{2}[/tex]

The watered area is approximately 3783 square feet.

Answer:176

Step-by-step explanation:

6 times 29.33333333333333

[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]

$\frac1c=\frac{c_1+c_2}{c_1c_2}$

$\implies c=\frac{c_1c_2}{c_1+c_2}$

Answer:

Step-by-step explanation:

Hello, when you try to find the intersection point(s) you need to solve a system like this one

[tex]\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}[/tex]

So, you come up with a polynomial equation like.

[tex]ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0[/tex]

And then, we can estimate the discriminant.

[tex]\Delta=(b-m)^2-4*a*(c-p)[/tex]

If [tex]\Delta<0[/tex] there is no real solution, no intersection point.

If [tex]\Delta=0[/tex] there is one intersection point.

If [tex]\Delta>0[/tex] there are two real solutions, so two intersection points.

Hope this helps.

Step-by-step explanation: Ants are one of the most abundant insects on our planet and the reasons are their eusocial, complex societal behaviors and their ability to survive in many and various ecosystems. Like most other animal societies, reproduction is one of the core reasons why ants are so prevalent.

Acrobat Ant

Reproduction for ants is a complex phenomenon that involves finding, selecting and successfully fertilizing females to ensure that the eggs laid are able to survive and molt through the successive stages of the ant’s life cycle – larvae, pupae and adults.

Answer:

81

Step-by-step explanation:

Start: 50

After 1 day: 50 * 1.1

After 2 days: 50 * 1.1 * 1.1 = 50 * 1.1^2

After 3 days: 50 * 1.1^2 * 1.1 = 50 * 1.1^3

...

After 5 days: 50 * 1.1^5 = 80.53

Answer: 81

Answer:

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

[tex]A (n) = a ({r})^{n - 1} [/tex]

where

a is the first term

r is the common ratio

n is the number of terms

To find the eighth term we must first find the first term

4th term = 108

common ratio = 3

That's

[tex]A(4) = a ({r})^{4 - 1} [/tex]

[tex]108 = a ({3})^{3} [/tex]

[tex]27a = 108[/tex]

Divide both sides by 27

For the eighth term

[tex]A(8) = 4 ({3})^{8 - 1} [/tex]

[tex]A(8) = 4({3})^{7} [/tex]

The final answer is

Hope this helps you

Answer:

358.125

Step-by-step explanation:

Answer:

358 3/24

Step-by-step explanation:  

Answer:

$2.

Step-by-step explanation:

This is because the base price is $12, which means the constant is 12. The toppings are the only things you can add to the pizza, so the price of each additional topping is the slope of the pizza's cost. The slope is 2 dollars.

Hope this helps!

Answer:

2

Step-by-step explanation:

If we were to write a linear equation in slope-intercept form (y = mx + b where m = slope and b = y-intercept) of this situation, it would be y = 2x + 12 where y is the price and x is the number of toppings. This is because the price for every topping is 2x but the base price doesn't change, therefore it's a constant so it would be + 12. In this case, since m = slope, the slope is 2.