MATHEMATICS MIDDLE SCHOOL

the graph of F(x), shown below, has the same shape as the graph of G(x) = x^2, but it is shifted down 4 units and to the right 3 units. What is its equation?

Answers

Answer 1

Answer:

Answer:

$F(x)=(x-3)^(2)-4$

Step-by-step explanation:

The graph of F(x) is a translation of the graph of G(x) by 4 units down and 3 units right.

$G(x)=x^(2)$

4 units down is the vertical shift. Vertical shift is obtained by adding or subtracting a number from the function value. Subtraction indicates a downward shift and addition indicates an upward shift. Since the graph is shifted 4 units down, the new equation after this translation will be:

$x^(2) - 4$

3 units to the right is the horizontal shift. Horizontal shift is obtained by adding or subtracting a number from x. Subtraction indicates a shift towards right and addition indicates a shift towards left. Since the graph is being shifted 3 units to right, the new equation after this transformation will be:

$F(x)=(x-3)^(2)-4$

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A European swallow flies about 11 meters in 1 second.How many kilometers could it flyvin 5 minutes.

Answers

tha answer is 555 i think ok? dont get mad if it is wrong everyone makes mistakes

Kira makes 93 greeting cards for a craft fair. She sells the cards in packs of 5. How many full packs of greeting cards does Kira make?

Answers

The correct answer is 18. Hope that helps!

She makes 18 full packs. 93 is not divisible by 5 to get a whole number so you would round it to 90 then divide it by 5.

Reasoning What number has factors of 2 and 3 and multiples of 12 and 18?

Answers

2x3= 6 so that's a check

12/6=2 so there's another check

18/6=3 so there's a 3rd check

SIX is the correct answer (:

We will get 1 as the answer .

Please Please Please Help in Questions 24 and 25!!!!! PLEASE!!!!

Answers

a, b and c are the zeros of a polynomial: w(x) = (x - a)(x - b)(x - c).

$24.\nw(x)=(x-6)[x-(-5-2i)][x-(-5+2i)]\n\nw(x)=(x-6)(x+5+2i)(x+5-2i)\n\nw(x)=(x-6)[(x+5)+2i][(x+5)-2i]\n\n\text{use}\ a^2-b^2=(a-b)(a+b)\n\nw(x)=(x-6)[(x+5)^2-(2i)^2]\n\n\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and}\ (ab)^n=a^nb^n\n\nw(x)=(x-6)(x^2+2(x)(5)+5^2-2^2i^2)\n\nw(x)=(x-6)(x^2+10x+25-4(-1))\n\nw(x)=(x-6)(x^2+10x+25+4)$

$w(x)=(x-6)(x^2+10x+29)\n\n\text{use distributive property}\ a(b+c)=ab+ac\n\nw(x)=(x)(x^2)+(x)(10x)+(x)(29)+(-6)(x^2)+(-6)(10x)+(-6)(29)\n\nw(x)=x^3+10x^2+29x-6x^2-60x-174\n\n\text{combine like terms}\n\nw(x)=x^3+(10x^2-6x^2)+(29x-60x)-174\n\n\boxed{w(x)=x^3+4x^2-31x-174}$

$25.\nw(x)=(x-i)(x-(-i))(x-6i)(x-(-6i))\n\nw(x)=(x-i)(x+i)(x-6i)(x+6i)\n\n\text{use}\ a^2-b^2=(a-b)(a+b)\n\nw(x)=(x^2-i^2)(x^2-(6i)^2)\n\n\text{use}\ (ab)^n=a^nb^n\ \text{and}\ i^2=-1\n\nw(x)=(x^2-(-1))(x^2-6^2i^2)\n\nw(x)=(x^2+1)(x^2-36(-1))\n\nw(x)=(x^2+1)(x^2+36)\n\n\text{use distributive property}\ a(b+c)=ab+ac\n\nw(x)=(x^2)(x^2)+(x^2)(36)+(1)(x^2)+(1)(36)\n\nw(x)=x^4+36x^2+x^2+36\n\n\boxed{w(x)=x^4+37x^2+36}$

Trey has 180 coins in his piggy bank.of these coins,1/12 of the coins are dimes,2/9 are quarters,1/6 are nickels,and the rest are pennies.how many pennies does trey have in his piggy bank?

Answers

180 coins total.

You need to find out how many pennies there are out of the 180 coins in Trey's piggy bank. So, you need to first find the total number of the other coins in the piggy bank. To do so, multiply each fraction by 180.

Dimes:
1/12 * 180 = 15 dimes

Quarters:
2/9 * 180 = 40 quarters

Nickels:
1/6 * 180 = 30 nickels

Now, you can add up the dimes, quarters, and nickels and subtract that from the total 180 coins to find out how many pennies Trey has in his piggy bank.

180-(15+40+30)=95
180-85=95

total=pennies+dimes+quarter+nickles
total-dimes-quarters-nickles=pennies

find how many of each
1/12 of all are dimes
1/12 times 180=15 dimes

2/9 of all are quarters
2/9 times 180=40 quarters

1/6 are of all are nickles
1/6 times 180=30 nickles

toatl=180
180-15-40-30=pennies
95=pennies

he has 95 pennies
(anohter harder way is to add alll fractions and find the fraction of pennies)

1/12+2/9+1/6=3/36+8/36+6/36=17/36
17/36+pennies=total=36/36
pennies=19/36 of total
pennies=19/36 times 180
pennies=95

95 pennies

Explain how you can use mental math to compare 7 pounds to 120 ounces.

Answers

16 oz=1 pound
we either convert 7 pounds to oz or 120 ounces to pound
I would ocnvert ounces to pounds since it is bigger to make it smaller
120/16=60/8=30/4=15/2=7.5

120oz=7.5pounds

so we compare 7 to 7.5 (pounds)

You could use mental math if you know how many ounces = 1 pound, which is 16, so you could easily multiply 16 times 7 in your head which will equal 112, and you could see dat 120 ounces > 7 pounds, (120 ounces is greater than 7 pounds), and DAT'S how you could use mental math! =D
I hope I helped! =D

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