MATHEMATICS HIGH SCHOOL

Let r varies inversely as u, and r = 8 when u =5. Find r if u=55

Answers

Answer 1

Answer:

Step-by-step explanation:

Given that, r varies inversely with u. r=k÷u, k being the constant.

Therefore, k=8×5, ( after making k the subject of your formula).

This implies that k=40.

Now, according to the formula r=k÷u,

r=40÷55

Therefore, r=0.72

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What would be the price for a product that started at $27 and get marked up by 30%

Answers

Answer:

$35.10

Step-by-step explanation:

Which statement accurately describes how adding a number, n, to the function f(x)=sin(x) affects its graph?A. There is a vertical shift of n units.
B.The x-intercepts will shift n units.
C. There is a change in amplitude of n units.
D. The range will change by a factor of 2n units.

Answers

The correct answer is:

A) There is a vertical shift of n units.

Explanation:

When a parent function is transformed, each type of transformation results ina different change in the graph.

The parent function in this question is f(x) = sin(x).

Adding n units to the end of this function would result in f(x) = sin(x) + n.

When a function is transformed by adding a constant to the end of a function results in a vertical shift by that number of units. In this case, it would be a vertical shift n units.

Answer:

Step-by-step explanation:

A on edge

What is 782,444 rounded to the nearest hundred thousand

Answers

782,444 rounded to the nearest hundred thousand would be 800,000.

This is because we know that the hundred thousands place has a 7 in it, so it would be 700,000. However, because 8 is greater than 5, we have to round up instead of down.

Hope this helps!

What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

Answers

so we want to know the vertex point of the equation f(x)=-(x+8)(x-14). First lets simplify the equation: f(x)=-x^2+6x+112. Now lets calculate the vertex by transforming the function to the form: f(x)=a(x-h)^2 + k where h and k are vertex coordinates. So: f(x)= (-x^2+6x+9)+121=-(x-3)^2+121 and the vertex point is (3,121).

Answer:

D.121

Step-by-step explanation:

Which numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), if any, will solve this equation?2x + 3 = 5x - 3

Answers

Answer:

Step-by-step explanation:

2(2)+3=7

5(2)-3=7

Answer:

Step-by-step explanation:

2 multiplied by 2 is 4+3=7 and 5x2=10-3=7

A recipe for sparkling grape juice 1 1/2 quarts of sparkling water and 3/4 of grape juice. How much sparkling water woild you need to mix with 9 quarts of grape juice. How much grape juice would you need to mix with 15/4 quarts of sparkling water?

Answers

According to the recipe the ratio of sparkling water to grape juice = 1 1/2 : 3/4.

Let us convert 1 1/2 into improper fraction and that is 3/2.

Now, 3/2: 3/4 or 3/2 ÷ 3/4 = 3/2 × 4/3 = 2/1 or 2:1.

Therefore, sparkling water quantity is two times of the quantity of grape juice.

Now, we need to find the number of quarts of sparkling water need to mix in 9 quarts of grape juice.

Since, sparkling water quantity is two times of the quantity of grape juice.

Therefore, we need 2 × 9 = 18 quarts of sparkling water to mix in 9 quarts of grape juice.

And now we need to find the number of quarts of grape juice would we need to mix with 15/4 quarts of sparkling water.

Therefore, we need 1/2 × 15/4 = 15/8 quarts of grape juice to mix with 15/4 quarts of sparkling water.

Answer:

a) $x = 18\,qt$ , b) $y = 1\,(7)/(8)\,qt$

Step-by-step explanation:

a) The amount of sparkling water needed is determined by simple rule of three:

$x = (9\,qt)/((3)/(4)\,qt)* (3)/(2)\,qt$

$x = 12* (3)/(2)\,qt$

$x = 18\,qt$

b) The amount of grape juice needed is found by simple rule of three:

$y = ((15)/(4)\,qt)/((3)/(2)\,qt ) * (3)/(4)\,qt$

$y = (30)/(12)* (3)/(4)\,qt$

$y = (90)/(48)\,qt$

$y = (15)/(8)\,qt$

$y = 1\,(7)/(8)\,qt$

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