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Natalija [7]
3 years ago
14

Identify the vertex for the graph of y = −3x^2 + 6x − 4

Mathematics
1 answer:
algol [13]3 years ago
3 0

Answer:

the vertex is (1,-1)

Step-by-step explanation:

y = −3x^2 + 6x − 4


the vertex is at

h= -b/2a  where ax^2 +bx+c

h= -6/2(-3)

h= -6/-6

h=1

substitute this in to find the y value

y = -3(1)^2 +6(1)-4

y = -3+6-4

y = -1

the vertex is (1,-1)

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All 930 students enrolled at a school either walk to school or ride the bus. Of these students, there are exactly 5 times as man
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7 0
3 years ago
Ella has 0.5 lb of sugar. how much water should she add to make the following concentrations? Tell Ella how much syrup she will
makkiz [27]

Answer:

For 50% syrup, add 0.5 lb of water for 1 lb of syrup; for 5% syrup, add 9.5 lb of water for 10 lb of syrup; for 75% syrup, add 0.17 lb of water for 0.67 lb of syrup; for 1.5% syrup, add 32.8 lb of water for 33.3 lb of syrup.

Step-by-step explanation:

Let x represent the amount of water added.  This means the total mass of the syrup is represented by 0.5+x.

To find percentages, we divide the part by the whole.  For a 50% syrup, we need the part (sugar) compared to the whole (sugar + water) to equal 50%, or 0.50:

Multiply both sides by 0.5+x:

Using the distributive property, we have

0.5 = 0.5(0.5)+0.5(x)

0.5 = 0.25+0.5x

Subtract 0.25 from each side:

0.5-0.25 = 0.25+0.5x-0.25

0.25 = 0.5x

Divide both sides by 0.5:

0.25/0.5 = 0.5x/0.5

x = 0.5

For 50% syrup, add 0.5 lb of water.  This makes the total mass 0.5+0.5 = 1 lb.

For 5% syrup, we change the equation to equal 0.05 (5% = 5/100 = 0.05) and leave everything else the same:

Multiply both sides by 0.5+x:

Using the distributive property,

0.5 = 0.05(0.5)+0.05(x)

0.5 = 0.025 + 0.05x

Subtract 0.025 from both sides:

0.5-0.025 = 0.025+0.05x-0.025

0.475 = 0.05x

Divide both sides by 0.05:

0.475/0.05 = 0.05x/0.05

x = 9.5

For 5% syrup, add 9.5 lb of water; the total mass will be 9.5+0.5 = 10 lb.

For 75% syrup, set the equation equal to 0.75:

Using the distributive property,

0.5 = 0.75(0.5)+0.75(x)

0.5 = 0.375 + 0.75x

Subtract 0.375 from each side:

0.5 - 0.375 = 0.375 + 0.75x - 0.375

0.125 = 0.75x

Divide both sides by 0.75:

0.125/0.75 = 0.75x/0.75

0.17 = x

For 75% syrup, add 0.17 lb of water; the total mass is 0.17+0.5 = 0.67 lb.

For 1.5% syrup, set the equation equal to 0.015:

Using the distributive property,

0.5 = 0.015(0.5) + 0.015(x)

0.5 = 0.0075 + 0.015x

Subtract 0.0075 from each side:

0.5-0.0075 = 0.0075 + 0.015x - 0.0075

0.4925 = 0.015x

Divide both sides by 0.015:

0.4925/0.015 = 0.015x/0.015

32.8 = x

For 1.5% syrup, use 32.8 lb of water; the total mass is 32.8+0.5 = 33.3 lb.

I hope this is right and have a good day

3 0
3 years ago
Read 2 more answers
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
professor190 [17]

Answer:

25

Step-by-step explanation:

The formula for the Pythagorean Theorem is:

\sqrt{a^2+b^2}=c

Now,

A=7

B=24

7x7=49

24x24=576

Add,

576+49=625

Last,

Take the square root of 625

The square root of 625 is 25

c=25

To Check if the hypotenuse is correct:

a^2+b^2=c^2

7^2+24^2=25^2

7x7=49

24x24=576

25x25=625

49+576=625

625=625,

Therefore the hypotenuse is 25.

5 0
2 years ago
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