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3 years ago

Which expression represents the algebraic phrase “the sum of negative three-eighths and four times x minus nine times z”?

Mathematics

2 answers:

7nadin3 [17]3 years ago

8 0

Answer:

-3/8+4x-9z

Step-by-step explanation:

"The sum of -3/8" means -3/8+ some number, which we find out (later in the expression) to be 4×x (that is 4 times x), or 4x. So we add on 4x to the expression, which becomes -3/8+4x. Then, it says "minus 9 times z", so we just take away 9×z. So, the final expression is -3/8+4x-9z.

Hope this helps! I got it right on Edgen.; you should trust me

MAXImum [283]3 years ago

7 0

An algebraic phrase or expression is a mixture of integer constants, variables and algebraic operations like addition, subtraction, multiplication, division and exponentiation. In this problem, you need to isolate first what is grouped together or what needs to be done first which in this sentence, "the sum of negative three-eighths and four. By substitution, it would be (-3/8+4). Then you multiply their sum by x so it would result to (-3/8+4)x. After that it is said that you need to minus that to nine times z which is 9z. This will result to an expression like this (-3/8 +4)x-9z. In the simplest term, the answer would be 9/8x-9z.

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3 years ago

Sandy plays tennis once every 6 six days. Jim plays once every 8 eight days. If they both played tennis today, in how many days

tiny-mole [99]

Answer: 24 days

Step-by-step explanation:

Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.

To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.

The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.

6 = 6, 12, 24, 30

8 = 8, 16, 24, 32

The lowest common multiple is 24.

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4 years ago

Bruno says30% of 50 is smaller than 50% of 30Is Bruno right ? Explain your answer.

lora16 [44]

Answer:

He's wrong.

Step-by-step explanation:

30% of 50 is 3/10 * 50 = 15
50% of 30 is 1/2 * 30 = 15
As you can see, 30% of 50 is the same as 50% of 30.

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2 years ago

Write the fractions in lowest terms:

never [62]

Part 1:

A and B are already in lowest terms

C 3/8

D 7/9

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A 5 * 11

B 3 * 3 * 3

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4 years ago

Find the critical points of the given function and then determine whether it is a local maximum, local minimum, or saddle point.

irga5000 [103]

Answer:

Therefore the critical point is (x,y)= $(-\frac12,0)$ .

Therefore $(-\frac12,0)$ is local minimum.

Step-by-step explanation:

Given function is

$z=f(x,y)=8x^2+2xy+5x+y^2+y+6$

The partial derivatives of z are

$\frac{\partial z}{\partial x}= 8.2x+2y+5=16x+2y+5$

and

$\frac{\partial z}{\partial y}=2x+2y+1$

To find the critical point, setting the partial derivatives equal to zero.

∴16x+2y+5 =0......(1) and 2x+2y+1=0.......(2)

Now solving the above equation,

Subtract equation (2) from equation (1)

16x+2y+5-( 2x+2y+1)=0

⇒16x+2y+5-2x-2y-1=0

⇒8x+4=0

⇒ 8x = -4

$\Rightarrow x=-\frac{4}{8}$

$\Rightarrow x= -\frac{1}{2}$

Now putting the value of x in (2)

$2.(-\frac12)+2y+1=0$

$\Rightarrow -1 +2y+1=0$

⇒2y=0

⇒y=0

Therefore the critical point is (x,y)= $(-\frac12,0)$ .

Second order partial derivatives are

$\frac{\partial^2 z}{\partial x^2 }= 16$ , $\frac{\partial^2 z}{\partial y^2 }= 2$ and $\frac{\partial^2 z}{\partial x \partial y}= \frac{\partial^2 z}{\partial y \partial x} =2$