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3 years ago

What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?

Mathematics

2 answers:

MakcuM [25]3 years ago

7 0

Answer:

(-1, -4)

Step-by-step explanation:

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are numbers.

In the equation

y = x² + 2x - 3

a = 1

b = 2

c = -3

We can calculate the x-coordinate of the vertex (xv) using the following expression.

xv = -b / 2a

xv = -2 / 2.1

xv = -1

We can replace this value in the equation to find the y-coordinate of the vertex (yv).

yv = (-1)² + 2.(-1) - 3

yv = -4

The coordinates of the vertex are (-1, -4).

Ilia_Sergeevich [38]3 years ago

4 0

$\bf \textit{vertex of a parabola}\\ \quad \\

\begin{array}{llccll}
y=&1x^2&+2x&-3\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

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If the lines are parallel with angle a measuring 5x + 8 and angle b measuring 8x - 7, the measure of angle a would be ___ degree

Mandarinka [93]

The value of angle a will be 33°.

It should be noted that when we've parallel lines, then the angles will be equal. In this case, the value of angle a will be equal to that of angle b and this will be:

5x + 8 = 8x - 7.

Collect like terms .

8x - 5x = 8 + 7

3x = 15

Divide both side by 3

3x/3 = 15/3

x = 5

Therefore, the value of angle a will be:

= 5x + 8

= 5(5) + 8

= 25° + 8°

= 33°

The measure of angle a is 33°.

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3 years ago

A number n plus 7 is less than or equal to 9

devlian [24]

N ≤ 2, if n plus 7 is less than or equal to 9 (n+7 ≤ 9) then carry the 7 over to create n ≤ 9-7 giving the answer n ≤ 2 (n less than or equal to 2)

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3 years ago

Segment AE is congruent to segment EB

Rudiy27

EF for sure u got to really pay attention to the inches

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3 years ago

A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

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4 0

3 years ago

Simplify the following math expression: 5+4(6-3)+4/2

lesantik [10]

Answer:

you have to solve the brackets first(6-3=3)

Then solve the division (4/2=2)

lastly the addition (5+4=9)

so we have 9×3=27

27+2=29.

3 0

2 years ago

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