MATHEMATICS HIGH SCHOOL

Seven less than twice a number is greater then five more than the same number. which integer satisfies this inequality? 1
2
12
13

Answers

Answer 1
Answer: 13
just use trial and error. PLUS since *the integer x 2* needs to be greater than that *integer + 5*, you already know that the number needs to be greater than 5.

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If xy < zy < 0, is y positive? x < z x is negativeStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Answers

Answer:

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked

Step-by-step explanation:

Given statement 1 :

xy < zy < 0,

The product of two numbers are negative if either of the numbers are negative.

∵ if xy < 0 ⇒ Case 1 : x > 0 and y < 0

Case 2 : x < 0 and y > 0,

Thus, Statement is not sufficient to prove y is positive,

Now, Statement 2 :

x < z, x is negative,

That is, x < 0

Combining statements (1) and (2),

We get,

xy < 0, x < 0,

⇒ y > 0

That is, y is positive.

Hence, Both statements (1) and (2) TOGETHER are sufficient to answer the question asked

Phil and Nick are selling fruit for a fundraiser. Customers can buy small and large boxes of tangerines. Phil sold 11 small boxes and 10 large boxes of tangerines for a total of $146. Nick sold 5 small boxes of tangerines and 12 large boxes of tangerines for a total of $126. Write the systems of equations.
What is the cost of a large box of tangerines?

Answers

Answer:

11s + 10l = 146

5s + 12l = 126

$8

Step-by-step explanation:

Let :

Small box = s

Large box = l

11s + 10l = 146 - - - - (1)

5s + 12l = 126 - - - - (2)

Multiply (1) by 5 ; (2) by 11

55s + 50l = 730

55s + 132l = 1386

Subtract

-82l = - 656

l = 8

11s + 10(8) = 146

11s + 80 = 146

11s = 66

s = $6

Hence, the price of a large box of tangerine = $8

Confirm that f and g are inverses by showing that f(g(x))=x and g(f(x))=x.f(x)=x-8/x+7 and g(x)=-7x-8/x-1

Answers

Good day! Please see the attached document to know how to substitute and simplify both functions to check if they are inverses of each other.

Which logarithm is equivalent to log3^10 – log3^2?

Answers

log_(3)(10) - log _(3) (2)

Apply log rule:

log _(c)(a)-log _(c) (b) = log _(c) ( (a)/(b) )

log _(3) (10)-log _(3) (2) = log _(3) ( (10)/(2) )

log _(3) ( (10)/(2) )

Divide 10 by 2  :

log _(3) (5)

hope this helps!

T/9=35/6 what is this portion

Answers

Hello,this is your answer. :)

Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.

Answers

f(x) = 3x^2 : axis of symmetry is x = 0.
g(x) = x^2 - 4x + 5 = (x - 2)^2 + 1 : axis of symmetry is x = 2
h(x) = -2x^2 + 4x + 1 = -2(x - 1)^2 + 3 : axis of symmetry is x = 1

Therefore, based on their axis of symmetry, f(x) < h(x) < g(x)
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