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Mariana [72]
3 years ago
9

The inequality 10x ≤ –0.6x + 7 can be broken into two related inequalities. Review the graphs of the two related inequalities.

Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

Answer:

B) -3

Step-by-step explanation:

just got it right on edge

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Simliar-AA is your answer 
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Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses. How ma
xeze [42]
4 1/5 divided by 3/5 = 7 
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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).
KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

2x^2-3x-6=0

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}

We have to find the value of (a+2)(b+2).

Putting the values:

(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4

3 0
2 years ago
Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.
sesenic [268]

Answer:

Step-by-step explanation:

If it is a parallelogram the opposite sides will a have the same slope.

Using the diagram  we see from the coordinates of A and B:

Slope of AB = (5 - -1)/(-1 - -5)

= 6/4

= 3/2.

In the same way

slope of CD = (2 - -4) / (1 - -3)

= 3/2.

So AB and  CD can be shown to be parallel.

Similarly the lines BC and AD are parallel.

So the figure is a parallelogram

Finding the perimeter (counting the units between the points):

Perimeter = 2AB + 2BC

By Pythagoras:

AB =   sqrt (6^2 + 4^2) = sqrt 52

BC = sqrt (3^2 + 2^2) = sqrt 13

So Perimeter = 2sqrt52 + 2sqrt13

= 4sqrt13 + 2 sqrt13

= 6sqrt13

or 21.63 unit^2 to 2 decimal places.

Area = sqrt52 * perpendicular distance between the lines AB and CD.

8 0
3 years ago
Which expression is equivalent to 4^ 5x4^ -7÷4 ^-2?
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\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad  a^n\implies \cfrac{1}{a^{-n}}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4^5\cdot 4^{-7}\div 4^{-2}\implies \cfrac{4^5\cdot 4^{-7}}{4^{-2}}\implies \cfrac{4^{5-7}}{4^{-2}}\implies \cfrac{4^{-2}}{4^{-2}}\implies 4^{-2}\cdot 4^2 \\\\\\ 4^{-2+2}\implies \boxed{4^0}\implies 1

5 0
3 years ago
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