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2 years ago

= 2. Given the quadratic equation 3x2 – 8x + k = 0 has no real roots. Find the range of values of k.

1 answer:

6 0

$\text{If there are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)$

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A seamstress needs to cut 15 inches pieces of ribbon from a roll of ribbon that is 9 feet in length what is the greatest number

Natali [406]

Answer: 36

Step-by-step explanation:

One roll is of length = 9 feet

1 foot = 12 inches

9 feet = 12 *9 = 108 inches

Since there are 5 rolls

So, total length of 5 rolls = 108 * 5 = 540 inches

Since we are given that A seamstress needs to cut 15-inch pieces of ribbon from a roll of ribbon that is 9 feet in length.

We are supposed to find . What is the greatest number of 15-inch pieces the seamstress can cut from 5 of these rolls of ribbon

So, number of 15-inch pieces the seamstress can cut from 5 of these rolls of ribbon:

Hence the greatest number of 15-inch pieces the seamstress can cut from 5 of these rolls of ribbon is 36

4 0

3 years ago

A fishing lodge wants to build a new boat ramp. The slope of the ramp must be 8° to the horizontal. The total height of the bank

Likurg_2 [28]

Answer:

The length of the sloping section of the ramp is 20.12 m

Step-by-step explanation:

Given;

the total height of the bank, h = 2.8 m

The slope of the ramp must be 8° to the horizontal, i.e, θ = 8°

Let the length of the sloping section = L

let the horizontal distance between the height of the bank and sloping section = b

Thus, h, L and b forms three sides of a right angled-triangle, with L as the hypotenuse side, h (height of the triangle) as the opposite side and b (base of the triangle) as the adjacent side.

We determine L by applying the following formula;

Sinθ = opposite / hypotenuse

Sin θ = h / L

L = h / Sin θ

L = 2.8 / Sin 8

L = 2.8 / 0.13917

L = 20.12 m

Therefore, the length of the sloping section of the ramp is 20.12 m

6 0

3 years ago

Sterre charges $ 3 5 $35dollar sign, 35 to file tax returns, but files for free if she only needs the easiest form. Then she don

blagie [28]

Given:

$35 is charged per form, but $0 if only the easiest form is filed.
$2 donated for every single tax return filed (since it is not explicitly mentioned otherwise, I will assume she donates $2 whether she charges $35 or does it for free)
Total amount charged for the full year = $7245
Total amount donated for the full year = $1242

To Find: The number of forms for which Sterre charged $35 and the number of forms Sterre did it for free.

Concept:

We can make use of the Unitary Method here. Given the number of units in a group, the Unitary Method can be used to find the value of a single unit or and individual unit when we are given the value for a group.

So,

Value of Single Unit = Value of Entire Group of Units ÷ Number of Units in the Group

Explanation & Calculation:

We are given that Sterre charged $7245 for the full year. Taking each Unit as the $35 type of form, and value of each Unit would be the amount that Sterre charges per form which is obviously $35, we can find the number of $35 forms using the expression written above.

So, putting in the values into the expression,

$35 = $7245 ÷ number of $35 forms

Therefore, number of $35 forms = $7245 ÷ $35

Using simple division, number of $35 forms = 207

Next, we are given Sterre donated $1242 in the full year and she donates $2 for every form (whether it is the $35 form or the free form).

If this time, we define each Unit as being each form (both $35 form and free form), value of each unit we define as the $2 donation money, we see that the value of the full group of units is $1242.

So, putting the values into the expression,

$2 = $1242 ÷ total number of forms

Therefore, total number of forms = $1242 ÷ $2

Using simple division, total number of forms = 621

Conclusion:

Sterre has filed a total of 621 tax returns (both charged and for free).

Of these 621 returns filed, for 207 forms, Sterre charged $35.

The number of returns Sterre filed for free (that is, the easiest forms) is

Total number of forms - Chargeable forms = 621 - 207 = 414

Thus, Sterre filed 414 tax returns for free.

8 0

3 years ago

What can be used to determine the length of segment AB?

Vikki [24]

It depends on what you mean by "what can be used", you can use a protractor or ruler since it's a line segment. OR you can use the formula a^ + b^ = c^ to find out all the measurements.......

If you still can't find it, then, you can try to find the other measurements around that specific line segments. And it DEPENDS on what you choose to find the length of this segment.

( There's no picture on my screen, so I'm guessing that you didn't put any.. )

Well, I hope this can help you :3

STAY SAFE!! :)

6 0

3 years ago

Guyys!! Im helping my lil sister here but I completely forgot it?

iren [92.7K]

Answer:B:72

Step-by-step explanation:

Because you are doing multiplication and division in this problem

5 0

3 years ago