Which expression is NOT equivalent to 24 + 12

Group of answer choices

3(8+4)

2(12+10)

2(12+6)

6(4+2)

The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

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By using the graph of y = f(x), the graph of the function g(x) = f(x + 3) include the following: D. graph D.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to write an equation that models the graph of g(x), we would have to apply a horizontal translation to f(x) by 3 units left:

y = f(x)

g(x) = f(x + 3)

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By using the head to tail, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5).

In Geometry, a vector is typically composed of two end points. First, is the starting point which is commonly known as a "tail" and the second (ending) point that is commonly known as a "head."

Additionally, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

Next, we would add the two (2) vectors algebraically as follows;

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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The amount for one dose of IV vancomycin for this child is 350 mg.

The recommended dosage of IV vancomycin is 40 mg/kg/day divided q6h.

The child weighs 35 kg.

To calculate the amount for one dose, we need to first calculate the total daily dose and then divide it by the number of doses per day.

Total daily dose = 40 mg/kg/day x 35 kg = 1400 mg/day

Since the medication is divided q6h (every 6 hours), there are 4 doses per day.

Amount for one dose = Total daily dose / Number of doses per day

= 1400 mg/day / 4 doses per day

= 350 mg/dose

Therefore, the amount for one dose of IV vancomycin for this child is 350 mg.

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Answer: 226.795 paperclips

Step-by-step explanation:

    First, we need to know how many grams are in a pound.

[tex]\boxed{\text{1 pound = 453.59 grams}}[/tex]

    Next, we will divide 453.59 grams by the 2 grams per paper clip to see how many paper clips would balance the scale with one pound.

     453.59 / 2 = 226.795 paperclips

Check the picture below.

The calculated measure of m∠DEF is 45 degrees

From the question, we have the following parameters that can be used in our computation:

The image of the protractor

The reading from the protactor is

Angle = 0 degrees + 45 degrees

Evaluate the sum

So, we have

Angle = 45 degrees

This reading represents the angle DEF

Hence, the measure of m∠DEF is 45 degrees

The required difference cannot be calculaed from the given parameter

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The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.

Let

Number of chickens = x

Number of pigs = y

x + y = 53

2x + 4y = 138

From (1)

x = 53 - y

Substitute x = 53 - y into (2)

2x + 4y = 138

2(53 - y) + 4y = 138

106 - 2y + 4y = 138

- 2y + 4y = 138 - 106

2y = 32

divide both sides by 2

y = 32/2

y = 16

Substitute y = 16 into

x + y = 53

x + 16 = 53

x = 53 - 16

x = 37

Therefore, there are 37 chickens and 16 pigs respectively.

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Answer:

( x - 3 ) 3 .

Step-by-step explanation:

Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=3√x+3 f - 1 ( x ) = x 3 + 3 is the inverse of f(x)=(x−3)3 f ( x ) = ( x - 3 ) 3 .

Answer:

you got them all right except graph 4 is a function! The trick is to use the vertical line test. Put your pencil vertically on your paper and move it across the graph. If your pencil passes through the same point twice, it's not a function. :)

Step-by-step explanation:

Answer:

n = -6

Step-by-step explanation:

We can allow n to represent the unknown number.

Now, we can set the two expressions equal to each other to find the number, n:

[tex]2n-1=4n+11\\2n=4n+12\\-2n=12\\n=-6[/tex]

Finally, we can check if the number fits the equation and the verbal expression by plugging in -6 for n:

Algebraically:

2(-6) - 1 = 4(-6) + 11

-12 - 1 = -24 + 11

-13 = -13

Verbally:

Two times the number -6 is -12 and 1 less than - 12 is -13

Four times the number -6 is -24 and 11 more than this is -13

Answer: x= -6

Step-by-step explanation:

Each word in a word problem translates to a mathematical symbol

> 1 less than =>  - 1

> two times a number => 2x

put that together 1 less than two times a number means:

2x-1

> is => =

> 11 more  => 11+

> four times the number  => 4x

put it all together

2x-1=11+4x     bring all like terms to each side

-2x = 12         solve for x

x= -6

The coordinates of the solution that lies in quadrant I are

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x² + 4y² = 100    ......equation 1.

4y - x² = -20  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (6, 4).

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Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

We know that,

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:

= (7/8) ÷ (1/6)

To divide fractions, we need to invert the second fraction and multiply:

= (7/8) × (6/1)

Simplifying the fractions, we get:

(7 × 6)/(8 × 1) = 42/8 = 5 1/4

Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

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The solution is the number in polar form 4 - 4i is

4 Root(2) (cos(-45) + i sin(-45)).

We know that,

Polar form of a complex number is r( cos(theta) + i sin(theta) )

r is equal to the total distance created by the rectangular coordinates of the complex number

r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)

To find theta, if a > 0, use arctan(b/a), where:

a = the first number

b = the second number

arctan (-4/4) = -45 degrees (-0.7854 radians)

The answer is 4 Root(2) (cos(-45) + i sin(-45))

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complete question;

Express the number in polar form 4 - 4i

The linear equations of the lines are y = 1/3x and y = 4x + 17, respectively

The parallel line

The equation is given a

x - 3y = 9

So, we have

3y = x - 9

y = x/3 - 3

Slope = 1/3

The slopes of parallel lines are equal

So, the slope of the required line is 1/3

The equation is then calculated as

y = mx + c

So, we have

y = 1/3x + c

Using the points, we have

2 = 1/3 * 6 + c

c = 0

So, we have

y = 1/3x

The perpendicular line

The equation is given a

y + 1/4x - 5 = 0

So, we have

y = -1/4x + 5

Slope = -1/4

The slopes of parallel lines are opposite reciprocals

So, the slope of the required line is 4

The equation is then calculated as

y = mx + c

So, we have

y = 4x + c

Using the points, we have

5 = 4(-3) + c

c = 17

So, we have

y = 4x + 17

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If 75% of Brannan's class attended her twelfth birthday party, we can find the number of students who came to the party by multiplying the total number of students in the class by the percentage that attended.

First, we need to convert 75% to a decimal by dividing by 100:

75% = 75/100 = 0.75

Next, we can multiply the total number of students in the class by the decimal that represents the percentage who attended:

Number of students who came to the party = 0.75 * 24

Number of students who came to the party = 18

Therefore, 18 students came to Brannan's twelfth birthday party.

The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.

When a pizza is cut into 12 equal pieces, each piece has a central angle of:

360 degrees / 12 pieces = 30 degrees/piece

If Johnson ate 4 adjacent pieces, then he ate a total central angle of:

4 pieces * 30 degrees/piece = 120 degrees

Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).

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The graph of the linear and quadratic equation is attached below

A linear and quadratic system can be represented by a line and a parabola in the xy-plane. Each intersection of the line and the parabola represents a solution to the system.

A line and a parabola can intersect zero, one, or two times, which means a linear and quadratic system can have zero, one, or two solutions.

If a graph of the system is not provided, then the ability to quickly draw graphs based on equations is essential.

However, in this problem, we have the equation given and we can easily draw the graph using a graphing calculator.

The solution to the problem is attached below;

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The value of X, given the matrices, can be found to be X = [ [ 4 ], [-1.5 ] ].

We are told that the value of X can be found to be :
2X + A = B

Solving this would give:
X = (B - A) / 2

We can then apply this to the matrices to give:
B - A = [ [ 11 - 3 ], [1 - 4 ] ]

B - A =  [[ 8 ],  [ -3 ] ]

X = [ [ 8 / 2 ], [ -3/2 ] ]

X = [ [ 4 ], [-1.5 ] ]

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Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

The principal amount was £1260, and the annual interest rate is 5.5%.

Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.

SI = principal × rate × time / 100

So,

P + 5pr = £1606.50

P = £1606.50 - 5pr............(i)

P + 6pr = £1675.80

P = £1675.80 - 6pr.........(ii)

Therefore,

£1606.50 - 5pr = £1675.80 - 6pr

Pr = 69.3

Put the value of pr in eq(i)

P + 5(69.3) = 1606.50

P = 1606.5 - 346.5

P = 1260

Now,

(1260)r = 69.3

r = 0.055

The annual interest is 5.5%

Hence, the principal amount was £1260, and the annual interest rate is 5.5%.

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Answer: there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Step-by-step explanation: Let's denote the number of children, parents, and grandparents as "c", "p", and "g", respectively.

We are given three pieces of information:

The total number of people in attendance is 400:

c + p + g = 400

There were twice as many parents as grandparents:

p = 2g

There were 50 more children than parents:

c = p + 50

We can use this system of equations to solve for the unknown variables.

First, we can use equation (2) to express "p" in terms of "g":

p = 2g

Next, we can substitute this expression for "p" into equation (3) to get:

c = 2g + 50

Now, we can use equations (1) and (4) to eliminate "p" and "c" from the system and express "g" in terms of only known quantities:

c + p + g = 400

2g + 50 + p + g = 400 (substituting c=2g+50)

3g + p = 350 (simplifying)

We can then substitute the expression for "p" from equation (2) into this last equation to obtain:

3g + 2g = 350

Simplifying:

5g = 350

Solving for "g", we get:

g = 70

Now, we can use equation (2) to find "p":

p = 2g = 2(70) = 140

Finally, we can use equation (3) to find "c":

c = 2g + 50 = 2(70) + 50 = 190

Therefore, there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

The total change in All - Plus stock, given the change in one day and the dip the next day, would be - $ 3.125.

In the one day shown on the table, the price of All - Plus stock dropped by $ 2.50 dollars. The very next day, the price of the stock still dropped but this time by 1 / 4 of the fall in the first day so the fall was ;

= 1 / 4 x 2. 50

= $ 0. 625

This means that the total change in price can be found to be :

= Change in price first day + change next day

= 0. 625 + 2. 5

= $ 3. 125

This means prices of All - Plus stock changed by - $ 3.125.

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In the words that your describing it, I supposed we are talking about the pythagorean theorem

What is the formula for the theorem?

a^2+b^2= C^2

A being the height

B being the Bottom

C being the slant or hypotenuse

How to Solve?

Well supposed 9 is a and 6 is b

[tex]9^{2}[/tex]+[tex]6^{2}[/tex]=[tex]c^{2}[/tex]

9 squared is 81 and 6 squared is 36

81+36= 117

So, 117=[tex]c^{2}[/tex]

Which means [tex]\sqrt{117}[/tex] is the answer or 10.8

Hope this helped!

The total at 0 id 100 hours and rate if increasing is 50 per hour.

From the given graph;

Let x represents the total hours

And y represents total pay

Then,

(a) When x = 0

Then from graph we have y = 100

So total pay is 100 dollars.

(b) When x = 1 then y = 150

Therefore,

Rate of increasing = (150-100)/(1-0) = 50

So it is increasing 50 per hour.

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Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

The solution of the equation 39=2x+1 is 19

The given equation is 39=2x+1

We have to find the solution of the equation

2x+1=39

Let us find the value of x

Subtract 1 from both sides

2x=38

Divide both sides by 2

x=19

Hence, the solution of the equation 39=2x+1 is 19

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The value of the expression l/2 when l=50 is 25.

Given information:

The expression l/2 means "half of l".

The expression is l/2 where l is variable.

In this case, the value of l is given as 50. So to calculate the expression, you just need to substitute 50 for l in the expression and simplify:

If l = 50, then

l/2 = 50/2 = 25

Therefore, the value of the expression l/2 when l=50 is 25.

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