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ser-zykov [4K]
3 years ago
5

If f(a)=(a•a•a)-(a•a) + a-1 what is the value of f(-3)?

Mathematics
1 answer:
Elena L [17]3 years ago
3 0

Answer:

-40

Step-by-step explanation:

f(a) = a³ - a² + a - 1

f(-3) = (-3)³ - (-3)² + (-3) - 1

f(-3) = (-27) - (9) + (-3) -1

f(-3) = -27 - 9 -3 - 1

f(-3) = -40

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After buying some new coins, Andre has 80 coins in his collection. Last month, he had 50 coins. The size of his current collecti
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Answer:

160%

Step-by-step explanation:

5 0
3 years ago
Match the circle equations in general form with their corresponding equations in standard form. Not all will be used. 
Xelga [282]
<span>The standard form of the equation of a circumference is given by the following expression:

</span>(x-h)^{2}+(y-k)^{2}=r^{2} \\ \\ where \ (h, k) \ is \ the \ center \ of \ the \ circumference \ and \ r \ the \ radius
<span>
On the other hand, the general form is given as follows:

</span>x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}<span>

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

</span>\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46

Equations in General Form:

\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0

\bold{6)} \ x^{2}+y^{2}+2x-12y

So let's match each equation:

\bold{From \ a)} \\ \\ (h,k)=(6,4),\ r=2\sqrt{14} \\ D=-12, \ E=-8 \\ F=-4

Then, its general form is:

x^{2}+y^{2}-12x-8y-4=0

<em><u>First. a) matches 5) </u></em>

\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20

Then, its general form is:

x^{2}+y^{2}-4x+12y-20=0

<em><u>Second. b) matches 1) </u></em>

\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5

Then, its general form is:

x^{2}+y^{2}+4x+6y-5=0

<em><u>Third. c) matches 3)</u></em>

\bold{From \ d)} \\ \\ (h,k)=(-1,6),\ r=\sqrt{46} \\ D=2, \ E=-12, \ F=-9

Then, its general form is: x^{2}+y^{2}+2x-12y-9=0

<em><u>Fourth. d) matches 6)</u></em>
6 0
3 years ago
Read 2 more answers
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
Novay_Z [31]

Answer:  3+\sqrt{2}

Step-by-step explanation:

Given the following expression shown in the picture:

\frac{7}{3-\sqrt{2} }

You need to use a process called "Ratinalization".

By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.

Then, in order to simplify the expression, you can follow the following steps:

<em>Step 1</em>. You need to multiply the numerator and the denominator of the fraction by  3+\sqrt{2}, which is the conjugate of the denominator  3-\sqrt{2}.

<em>Step 2</em>. Then you must apply the Distributive property in the numerator.

<em>Step 3</em>. You must apply the following property in the denominator:  (a+b)(a-b) = a^2 - b^2

Therefore, applying the procedure shown above, you get:

=\frac{(7)(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}=\frac{21+7\sqrt{2}}{3^2-(\sqrt{2})^2}=\frac{21+7\sqrt{2}}{9-2}=\frac{21+7\sqrt{2}}{7}

<em>Step 4</em>.  You can observe that the expression can be simplified even more. Since:

 \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}

You get:

\frac{21+7\sqrt{2}}{7}=\frac{21}{7}+\frac{7\sqrt{2}}{7}=3+\sqrt{2}

3 0
2 years ago
32 = 4(n – 5) and -s + 11 = 17 please solved Both of the following​
valina [46]

Answer:

n=13 s=-6

Step-by-step explanation:

Hope this helps :)

4 0
2 years ago
Read 2 more answers
william bougght canned goods at 2.40 per can.he wants to increase the price per can so that he makes a 25% profit. what will the
NemiM [27]

Answer:

The answer is 3

Step-by-step explanation:

25% of 2.40 equals 0.6

so 3 will be the total price and he will get 0.6 profit.

7 0
2 years ago
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