2 PointsWhat is the vertex of the graph of the function below?
y = x2 + 10x + 24
O A. (-4,-1)
O B. (-5, -1)
O C. (-5,0)
O D. (4,0)
SUBMIT

Answers

Answer 1

Answer:

$\bf \textit{vertex of a vertical parabola, using coefficients} \n\n y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+10}x\stackrel{\stackrel{c}{\downarrow }}{+24} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \n\n\n \left( -\cfrac{10}{2(1)}~~,~~24-\cfrac{10^2}{4(1)} \right)\implies (-5~,~24-25)\implies (-5~,~-1)$

Answer 2

Answer:

Final answer:

The vertex of the quadratic function y = x² + 10x + 24 is located at point B. (-5, -1). This is found by using the formula -b/2a for the x-coordinate and substituting the x coordinate into the function for the y-coordinate.

Explanation:

The vertex of a quadratic function (a function in the form of y=ax²+bx+c) is the point that represents the minimum or maximum of the function graph. In this case, we are looking to find the vertex of the function y = x² + 10x + 24. The formula to find the x-coordinate of the vertex of a quadratic function is -b/2a. In this function, a = 1 and b = 10, giving us -10/(2*1) = -5 for the x-coordinate of vertex. We then substitute -5 into the function for x to determine the y-coordinate, resulting in y = (-5)² + 10*-5 + 24 = -1. Therefore, the vertex of the function is (-5,-1). So, the correct choice is B. (-5, -1).

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Answers

2sin^2 - x - Sinx =1 and sec x csc x (tanx+ cotx) = sec^2x + csc^2x is not an identity. Option B and C is correct.

Out of Four options are given, which of them is not an identity is to be determined.

What is identity?

An identity is the common case formula that helps to solve mathematics.

$2cos^2x-1 = 1 - 2 sin^2x\n \ncos2x =cos2x$

It is also a perfect identity.

$secx cscx(tanx+ cotx) = sec^2x + csc^2x\n\n\nsec x cscx (sinx/cos x + cosx/sinx) = sec^2 + csc^2x\n\nsecx cscx (sin^x+cox^2x/cosxsinx) = sec^2x +csc^2x$

It is also not an identity.

3) 2sin^2-X- Sinx=1

It's not an identity cause it is form of equation and contain -x.

$sin^2x+ tan^2x + cos^2x = sec^2x\n sin^2x + cos^2x = sec^2x -tan^2x = 1$

It is a perfect identity.

Thus, 2sin^2- x - Sinx =1 and sec x csc x (tanx+ cotx) = sec^2x + csc^2x is not an identity. Option B and C is correct.

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Answer:

C. 2 sin^2x-sinx=1

Step-by-step explanation:

a p e c

How can I solve this system of linear equations by substitution 3x-2y=9 and y=2x-7

Answers

y=2x-7
therfor we can SUBSITUTE 2x-7 for y whereever we see y in the other equation

3x-2(2x-7)=9
3x-4x+14=9
-x+14=9
minus 14 both sides
-x=-5
mulitly -1
x=5

sub back

y=2x-7
y=2(5)-7
y=10-7
y=3

(5,3)

Lucy is a dressmaker she sews 4/7 of a dress in 3/4 hour. At this rate, how many dresses Lucy sew in one hour

Answers

4/7 divided by 3 = 4/21 per 1/4 hour. multiply that by 4 to get 16/21

she would be able to make 16/21 of a dress.

A baby weighed 3.2 kg at birth. She gained 0.17 kg per week. She now weighs 5.75 kg. How old is she now?

Answers

5.75 (weight now) - 3.2 (weight at birth) = 2.55 (how much weight she has gained)

2.55 (how much weight she has gained) / 0.17 (weight gained per week) = 15 weeks

The baby is 15 weeks old.

X = 8, y = 20. Find y when x = 42

Answers

Create proportions to do this question
When x is 8, y is 20
when x is 42, y is ?

$(8)/(20)$ = $(42)/(?)$

Do cross multiplication:

8 × ? = 20 × 42
8 × ? = 840

Divide by 8 to isolate the unknown

$(8*?)/(8)$ = $(840)/(8)$
8 and 8 cancels out

? = 105

y is 105 when x is 42

8 / 20 = 42 / y;
Then, y = ( 42 × 20 ) / 8 ;
y = 840 / 8 ;
y = 105;

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