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earnstyle [38]
2 years ago
13

A car was travelling at a constant speed of 19 m/s, then accelerated for 10 seconds. The distance travelled, during this time, "

d" metres, is given by the formula d = 19t + t^2, where "t" is the time in seconds since the acceleration began. How long did it take the car to travel 200m? Give the answer to the nearest tenth of a second. Solve algebraically.
Mathematics
1 answer:
gregori [183]2 years ago
5 0

Answer:

7.5 seconds.

Step-by-step explanation:

Substitute the distace  220m in the given equation:

d = 19t + t^2

200 = 19t + t^2

t^2 + 19t - 200 = 0

t = [-19 +/- sqrt(19^2 - 4*1*-200)]  / 2

t = -19 +/- sqrt(1161) / 2

t = ( -19 +/- 34.07) / 2

t = 7.535 seconds

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A shoe factory produces 1.81 × 104 pairs of shoes each month. Estimate how many pairs of shoes the factory will produce if it ma
quester [9]

Answer:

2*10 ^6 shoes in 10 years

Step-by-step explanation:

1.81 × 10^4 pairs of shoes each month

1.2 × 10^2 months in 10 years

Multiply these together to determine the number of shoes in 10 years

1.81 × 10^4 * 1.2 × 10^2

We want to estimate so 1.81 is approximately 2 and 1.2 is approximately 1

2 × 10^4 * 1 × 10^2

Multiply the numbers

2*1 = 2

Add the exponent

10 ^ ( 4+2)

10 ^6

Put this back together

2*10 ^6

4 0
2 years ago
Read 2 more answers
Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27
densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

or

y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

Step-by-step explanation:

Vertex form of equation : f (x) = a(x - h)^2 + k,where (h, k) is the vertex of the parabola.

y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

Hence, the vertex form of the equation is y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

8 0
2 years ago
Read 2 more answers
Ava bought some pens for $ 2 each and some pencils for $ 1 each. She bought 3 more pens than pencils and spent a total of $ 12.
Rudiy27

Answer:

Step-by-step explanation:

price of 1 pen= $ 2

price of 1 pencil= $1

total money spent= $12

Let the number of pen be a and number of pencil be b.

 2 a + b = 12   ----------------Equation 1

We have, she bought 3 more pens than pencils

  a - b = 3   ------------------  Equation 2

 Equation 1 +Equation 2,  

   2 a + b +  a - b = 12 + 3

                     3a = 15

                     a = 5

 Substituting in  equation

           5 - b = 3

               b = 2

 Number pencils Ava bought = 2

5 0
2 years ago
Shane, Cheryl, and Isaac went to the store to buy school supplies. Shane bought 4 pens, 3 folders, and 2 notebooks for a total o
vladimir1956 [14]

Answer: 3.00

Step-by-step explanation:

8 0
1 year ago
Please help!!!!!!!!!
shepuryov [24]
A, the first one only, this parabola only has a minimum and no maximum.  the other statements are also just false 
7 0
2 years ago
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