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Gekata [30.6K]
3 years ago
7

Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y ≤

20, which represents the situation, is shown. What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If Eula buys 7 notebooks, what is the greatest number of binders she can buy?
Mathematics
2 answers:
Anarel [89]3 years ago
8 0

Answer:

5, 10  and 1 are the answers

Step-by-step explanation:


professor190 [17]3 years ago
4 1
If there are no notebooks purchased, then Eula may buy 5 binders. If no binders are bought, then Eula may buy 10 notebooks. If 7 notebooks are purchased, then one binder may be purchased; this will also cause Eula to have $2 extra (maybe for tax).
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Express the sum of the polymonial 3x^2+15x-56 and the square of the binomial (x-8) as a polynomial in standard form.
tester [92]

Given:

Polynomial is 3x^2+15x-56.

To find:

The sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form.

Solution:

The sum of given polynomial and the square of the binomial (x-8) is

3x^2+15x-56+(x-8)^2

=3x^2+15x-56+x^2-2(x)(8)+8^2    [\because (a-b)^2=a^2-2ab+b^2]

=3x^2+15x-56+x^2-16x+64

On combining like terms, we get

=(3x^2+x^2)+(15x-16x)+(-56+64)

=4x^2-x+8

Therefore, the sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form is 4x^2-x+8.

7 0
3 years ago
I GOT STUCK ON THIS QUESTION ON MY MATH TEST SO .. PLS HELP ME <3
HACTEHA [7]

Answer:

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3 0
3 years ago
PLEASE HELP!! WILL MARK BRAINLIEST!!!
Rus_ich [418]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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baherus [9]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = \frac{\sqrt3}{2}

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}

Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

                             ⇒ cos 330 = 2 cos² 165 - 1

                             ⇒ 2 cos² 165  = cos 330 + 1

Given:                        2 \cos^2 165  = \dfrac{\sqrt3}{2} + 1

                              \rightarrow 2 \cos^2 165  = \dfrac{\sqrt3}{2} + \dfrac{2}{2}

Divide by 2:               \cos^2 165  = \dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \dfrac{2\sqrt3+4}{8}

Square root:             \sqrt{\cos^2 165}  = \sqrt{\dfrac{4+2\sqrt3}{8}}

Scratchwork:            \cos^2 165  = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2

                             \rightarrow \cos 165  = \pm \dfrac{\sqrt3+1}{2\sqrt2}

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

                             \rightarrow \cos 165  = - \dfrac{\sqrt3+1}{2\sqrt2}

LHS = RHS \checkmark

4 0
3 years ago
A cone has a base area of 420mm and height of 180mm. What is the volume of the cone.
luda_lava [24]

Cone Volume = PI * radius^2 * height / 3, which can br rewritten as

Cone Volume = base area * height / 3

Cone Volume = 420mm * 60

Cone Volume = 25,200 cubic mm

3 0
3 years ago
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