Five students sold lemonade and earned a total of $21.30. If they equally split their earnings, how much would each student receive?

The required expression in terms of logarithm of prim numbers are;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

Prime numbers are numbers that can only be divisible by 1 and itself.

From the given logarithmic expression, we will need to write 405, 8, and 81 as the product of prime numbers

405 = 3 * 3 * 3 * 3 * 5

405 = 3^4 * 5

8= 2* 2 * 2

8 = 2^3

81 = 3 * 3 * 3 * 3

81 = 3^4

The logarithm expression [tex]log_4405 \ and \ log_7(\frac{8}{81} )[/tex] can be expressed in terms of prime numbers as;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

Similarly;

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

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Answer:

8

Step-by-step explanation: 6 (half the perimeter). By truial and error, 2 units by 4 units.

Answer:

1

Step-by-step explanation:

Y2-Y1/X2-X1 would become 4-6/3-5 which would become-2/-2 and that equals 1 because its a whole number and when you divide or add two negative numbers, it becomes a positive

the answer of ur question is 0.25

Hey there!

I'm going to go in order from images.

1. The angle measure 60 is linear to angle 6, this would make them supplementary.

Angle 6: 180 - 60 = 120

Angle 6 is vertical to angle 2, this makes them congruent. If angle 6 equals 120 measure 2 also equals 120.

2. Measure 6 is vertical from measure 2. We established in the last problem measure 2 equals 120.

If angle 2 equals 120 measure 6 also equals 120.

3. The 2 equations are alternate exterior angles.

2x+5=8x-7

    +7     +7

2x+12=8x

-2x     -2x

12=6x

12/6= 2

x=2

4. I cannot explain this one without showing it visually lol.

Measure 5 equals 30 degrees.

5. Measure 1 is verticle to the measure that reads 60. Vertical angles are congruent.

If measure 1 is congruent to the measure that reads 60. Measure 1 equals 60.

I hope this helps!!!

Answer:

Step-by-step explanation:

2)f(x) = 2x² +4x - 3    

a = 2 ; b = 4 ; c = -3

1) Put x = -1 in the equation

f(x) = 2*(-1)² + 4*(-1) -3 = 2 - 4 -3 = -5

Vertex = (-1,-5)

2) Upward

3) Minimum

4) axis of symmetry = -b/2a = -4/2*2=-4/4= -1

x = -1

5) domain: all real numbers  (-∞ ,∞)

Range : y ≥ -5 ; [-5 , ∞)

3) f(x) = 3x² - 6x + 4

Vertex : (1,1)

Opening : upward

Minimum

Axis of symmetry: x = 1

Domain: all real numbers

Range: y ≥ 1 ; [1, ∞)

4)f(x) = -x² - 2x - 3

a) Vertex:  f(x) = -(-1)² - 2*(-1) - 3 = -1 + 2 - 3 = -2

Vertex( -1,-2)

b) downward

c) Maximum

d) Axis of symmetry: x = 2/-2 = -1  

x = -1

e) Domain: all real numbers

Range: y ≤ -2 ; (-∞ , -2]

5)f(x) = 2(x -2)²

a) Vertex: (2, 0)

b) Opening: upward

c) Minimum

d) x = 2

e)Domain: all real numbers

Range: y ≥ 0 ; [0,∞)

Answer:

y=-2x+8

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (8, -8) and has a slope of -2

We can write this equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope of the line, we can immediately plug it into the equation as m:

y=-2x+b

Now we need to find b

As the equation of the line passes through the point (8, -8), we can use it to help solve for b, since (8, -8) is a solution to the equation, meaning that it will yield a true statement when plugged into the equation

So substitute 8 as x and -8 as y:

-8=-2(8)+b

Multiply

-8=-16+b

Add 16 to both sides

8=b

Now substitute 8 as b into the equation:

y=-2x+8

Hope this helps!

.Equation of line in point slope form

[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\\ \sf\longmapsto y+8=-2(x-8)[/tex]

[tex]\\ \sf\longmapsto y+8=-2x+16[/tex]

[tex]\\ \sf\longmapsto 2x+y+8-16=0[/tex]

[tex]\\ \sf\longmapsto 2x+y-8=0[/tex]

Answer:

zero slope

Step-by-step explanation:

horizontal lines are zero slope because they are not slanted (slope)

this is a horizontal line.

Replace h with 34:

p(h) = 21(34)

Multiply :

21x 34 = 714

Answer: $714

Answer:

p=v-u/t440-500=-60 this is decreasing in the rent so it decreased

Answer:

The answer is C.

Step-by-step explanation:

The theory of vertical angles, often known as the theorem of vertically opposite angles. According to the theorem, two opposed vertical angles created when two lines cross one other are always equal (congruent) to each other no matter what the circumstances are.

Answer:

(x - 4)² - 9 = 0

Step-by-step explanation:

x² - 8x + 7 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 8x

x² + 2(- 4)x + 16 - 16 + 7 = 0

(x - 4)² - 9 = 0

Answer:

x= -64, y= 55

Step-by-step explanation:

x=-y-9

6(y-9)-5y=1

6y-54-5y=1

y=55

x=-55-9

x=-64

Answer:

{x=-4

{x= -5

Step-by-step explanation:

Substitute into one of the equations:6(- y -9) - 5y=1

Apply Multiplicative Distribution Law:- 6y-54-5y=1

Rearrange unknown terms to the left side of the equation:-6y -5y = 1+54

Combine like terms:- 11y= 1+54

Calculate the sum or difference:-11y=55

Divide both sides of the equation by the coefficient of variable:y= 55÷(-11)

Remove the parentheses:y = -55÷11

Calculate the product or quotient:y=-5

Substitute into one of the equations:x=-(-5)-9

Remove the parentheses:x=5-9

Calculate the sum or difference:x=-4

The solution of the system is:{x=-4

{x=-5.

Answer:

Step-by-step explanation:

Each boundary line equation is of the form ...

  y = mx + b

the value of m is the coefficient of x. The value of b is the constant. You find their values by matching the given relation to the form above, and identifying the matching parts.

  y ≤ 1/2x +2   ⇒   m = 1/2, b = 2

  y < -2x -3   ⇒   m = -2, b = -3

_____

The slope (m) in each case tells you how many units up (m>0) or down (m<0) the line will go for each unit to the right. The y-intercept (b) in each case gives you a starting point on the y-axis, making it easier to draw the line.

The < part of each inequality symbol tells you the graph will be shaded below the boundary line. (Y-values in the solution set are less than those on the line.) The "or equal to" part of the first inequality symbol tells you the boundary line will be solid. (Y-values on that line are part of the solution set.) The lack of that in the second inequality tells you the boundary line will be dashed.

The graph is shown in the attachment.

Answer:

104%

Step-by-step explanation:

Answer:

yes they are

Step-by-step explanation:

they are both congruent because they are the same shape and size, they are just on opposite sides

(congruent means that 2 objects are the same shape and size)

Answer:

yes they are

Step-by-step explanation:

Answer:

-2p/3+3

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

12+8 = 20

20*6 = 120

Answer:

Its 53 because 1=1 and 2=2

Step-by-step explanation:

The mapping of the strip pattern onto itself is a Glide reflection.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Glide reflection is a combination of reflection over a line and then translation along that line.

As we can see, the mapping of the strip pattern onto itself is a Glide reflection.

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Answer:

A: Half-turn

Step-by-step explanation:

i took the test and got it wrong due to the wrong answer above.

Answer:

100 yes there are trust me

Answer: inverse operation, subtraction

Step-by-step explanation: The key insight here is that we want to solve for x , and in doing so, we need to undo any operation being applied to it. Right now, only 5 is being added to it, so to solve for it, we need to do the inverse operation, subtraction

If you mean this: How to solve multiplication property of equality?

Multiplication Property of Equality

For all real numbers a, b, and c: If a = b, then a • c = b • c (or ab = ac).

I hope this is right :)

Total up the Consumption,Investment, Government Spending and Exports then minus the Total Imports. So the correct answer is C. $4,100

Answer:

Perpendicular

Step-by-step explanation:

The equation of the graph is y = 1/3x  + 4

The slope 1/3 and 3 are opposite reciprocals, which indicates that the two lines are perpendicular.

-Chetan K

Answer:

The baker baked 375 loaves of bread that day.

Step-by-step explanation:

The baker baked a total of x loaves of bread.

240 loaves were sold by the end of the day.

The baker was then left with 9/25 of the number of loaves that were baked.

We get the equation:

x-240 = 9x/25

When you solve the equation, you will see that x=375.

Therefore, the baker baked 375 loaves of bread that day.

Answer:

5x - y = 3

Step-by-step explanation:

Standard form of a linear equation is expressed as Ax + By = C

In order to express the given equation in this form, we need to isolate the constant.  We can achieve this by subtracting 5x from both sides:

y = 5x - 3

y - 5x = -3

If possible, we want A to be positive, so we can multiply both sides by -1:

-1(y - 5x) = -1(-3)

-y + 5x = 3 or 5x - y = 3

Answer:

15 Dimes and 75 Nickles

Step-by-step explanation:

N = Nickles

D = Dimes

5D + D = 90

6D= 90

D= 15

90 - 15 = 75

N = 75

There are 75 nickels and 15 dimes does she​ have.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Susan has a collection of 90 nickels and dimes.

And, The number of nickels is five times the number of​ dimes.

Now,

Since, The number of nickels is five times the number of​ dimes.

Let number of dimes = x

Then, Number of nickels = 5x

Since, Susan has a collection of 90 nickels and dimes.

Hence, We can formulate;

⇒ 5x + x = 90

⇒ 6x = 90

⇒ x = 15

Thus, The number of dimes = 15

And, Number of nickels = 5 × 15  = 75

Therefore, There are 75 nickels and 15 dimes does she​ have.

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Length = 4m

Width = ½ of length = ?

Then width will be,

→ 4 × 1/2

→ 4 ÷ 2 × 1

→ 2 × 1 = 2

Thus, 2 is the width.