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2 years ago

Y=x^2+bx+c;(-2,3)

Mathematics

1 answer:

Maksim231197 [3]2 years ago

8 0

<h3>Answer: b = 4 and c = 7.</h3>

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Explanation:

Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.

The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.

Plug those three values into the vertex form below

y = a(x-h)^2 + k

y = 1(x-(-2))^2 + 3

y = (x+2)^2 + 3

Then expand everything out and simplify

y = x^2+4x+4 + 3

y = x^2+4x+7

We see that b = 4 and c = 7.

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the seating capacity of basketball stadium is 5782 the seats are arranged in 24 sections of the same size any seats over from th

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5782/24=240 since we round down to s whole.

Multiply again by 24.
240*24=5760

There are 5782-5760=22 priority seats.

The correct answer is 22.

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3 years ago

A marching band is arranged in rows of 7 the first row has 3 band members and each row after the first has 2 more band members t

pav-90 [236]

Answer:

$a_{n}$ = 1+2n and 63

Step-by-step explanation:

the question belongs to arithmetic sequence and $a_{n}$ can be determined by the formula

$a_{n}$ = a1 + d (n-1)

Let " $a_{n}$ " represents the number of band members in the nth row

and 'd' represents the common difference.( as stated each row has 2 more band members than the row before it)

therefore, d=2

'a1' represents first row that has three members. So, a1 = 3

->Rule for nth term will be:

$a_{n}$ = 3 + 2(n-1)

$a_{n}$ = 3 + 2n -2

$a_{n}$ = 1+2n

-> In order to find total number of band members ' $S_{7}$ '

Let $S_{n}$ represent total number in n rows

We'll use the formula, i.e $S_{n}$ = n/1 ( $a_{1}$ + $a_{n}$ )

where, n is the number of terms, $a_{1}$ is the first term and $a_{n}$ is the last term

So,

n=7

$a_{7}$ = 1 + 2(7)= 15

=> $S_{7}$ = 7/2 (3 + 15)

$S_{7}$ = 63

The total number of band members are 63

8 0

3 years ago

Ahmad wants to practice free-throws. He estimates the distance from the free-throw Line to the hoop and marks it with chalk. Ahm

const2013 [10]

Answer: 10%

Step-by-step explanation:

The difference between his estimated and actual distance is 15 - 13.5 = 1.5

The percentage of error is the difference divided by the actual value.

1.5÷15 = 0.10

Converted to a percentage, it is 10%

4 0

3 years ago

Read 2 more answers

The cost of renting a car is $42 a day plus 25 cents per mile. How far can Alex drive in one day if he only has $162

earnstyle [38]

Answer:

Alex can drive 480miles in one day period.

Step-by-step explanation:

$162- $42 =$120

$120/0.25¢=480

480miles

8 0

3 years ago

1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)

Sveta_85 [38]

Answer:

1. $-5x+3y+44=0$

2. $2x+y-2=0$

3. $2x+y-4=0$

Step-by-step explanation:

Standard form of a line is $Ax+By+C=0$ .

If a line passing through two points then the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope, i.e., $m=\dfrac{y_2-y_1}{x_2-x_1}$ .

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

$y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)$

$y+3=\dfrac{-5}{-3}(x-7)$

$y+3=\dfrac{5}{3}(x-7)$

$3(y+3)=5(x-7)$

$3y+9=5x-35$

$-5x+3y+9+35=0$

$-5x+3y+44=0$

Therefore, the required equation is $-5x+3y+44=0$ .

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to $2 x + y =-5$ .

Slope of the line : $m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2$

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

$y-2=-2(x-0)$

$y-2=-2x$

$2x+y-2=0$

Therefore, the required equation is $2x+y-2=0$ .

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to $2x + y =-5$ .

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

$y-0=-2(x-2)$

$y=-2x+4$

$2x+y-4=0$

Therefore, the required equation is $2x+y-4=0$ .

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3 years ago