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Vadim26 [7]
2 years ago
8

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x 2. What is the function’s vertex? (one-half, seven-

quarters) (one-half, three-halves) (1, 1) (1, 3).
Mathematics
1 answer:
nydimaria [60]2 years ago
3 0

Vertex of the quadratic equation is the highest or the lowest point of the quadratic equation.

<h3>Given-</h3>

The given equation in the question is,

f(x) = x^2 - x +2

<h3>Vertex of the quadratic equation</h3>

Vertex of the quadratic equation is the highest or the lowest point of the quadratic equation.

To find the vertex of the equation we need to compare the given equation with the following equation.

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

Here h and k are the vertex of the equation.

The given equation is,

f(x) = x^2 - x +2

Rewrite the equation,

f(x) = x^2 - x +(\dfrac{1}2)^2} +2-(\dfrac{1}2)^2}

f(x) = x^2 - x +\dfrac{1}{4} +2-\dfrac{1}4}

f(x) =(x-\dfrac{1}{2} )(x-\dfrac{1}{2} )+2-\dfrac{1}{4}

f(x) =(x-\dfrac{1}{2} )^2+\dfrac{7}{4}

Thus the vertex of the quadratic equation is 1/2 and 7/4.

Learn more about the vertex of the quadratic equation here;

brainly.com/question/6356924

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the area of a rectangle is 96m^2 and the circumference is 39.2m. Determine the dimensions if the rectangle​
goldenfox [79]

Answer:

Dimension => 10 m × 9.6 m

Step-by-step explanation:

From the question given above, the following data were obtained:

Area (A) = 96 m²

Circumference (C) = 39.2 m

Dimension =.?

Next, we shall determine the Lenght and breadth of the rectangle. This can be obtained as follow:

Let L be the Lenght

Let B be the breadth

Area of a rectangle = L × B

96 = L × B ..... (1)

Circumference of rectangle = 2(L + B)

39.2 = 2(L + B) .... (2)

From equation 2, make L the subject

39.2 = 2(L + B)

Divide both side by 2

39.2 /2 = L + B

19.6 = L + B

Rearrange

L = 19.6 – B ....(3)

Substitute the value of L in equation 3 into equation 1

96 = L × B

L = 19.6 – B

96 = (19.6 – B ) × B

Clear bracket

96 = 19.6B – B²

Rearrange

B² – 19.6B + 96 = 0

Solving by factorisation

B² – 10B – 9.6B + 96 = 0

B(B – 10) – 9.6(B – 10) = 0

(B – 9.6)(B – 10) = 0

B – 9.6 = 0 or B – 10 = 0

B = 9.6 or B = 10

Substitute the value of B into equation 3:

L = 19.6 – B

B = 9.6

L = 19.6 – 9.6

L = 10

Or

L = 19.6 – B

B = 10

L = 19.6 – 10

L = 9.6

Since the length is always longer than the breadth,

Length (L) = 10 m

Breadth (B) = 9.6 m

Finally, we shall determine the dimension of the rectangle. This can be obtained as follow:

Length (L) = 10 m

Breadth (B) = 9.6 m

Dimension =?

Dimension = L × B

Dimension = 10 m × 9.6 m

5 0
3 years ago
X to the 2nd power plus x equal 5
mr Goodwill [35]
X^2 + x = 5
hope that helps

................
4 0
3 years ago
Read 2 more answers
Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square increasing when the area of the s
diamong [38]
Area of a square = length²
A = x²
16 = x²; x = 4
dA/dx = 2x cm²/s
dx/dt = 6 cm/s
Using chain rule:
dA/dt = dA/dx * dx/dt
dA/dt = 2x * 6
dA/dt = 12x
At x = 4,
dA/dt = 12(4) = 48 cm²/s
7 0
3 years ago
Find the determinant of A.<br><br><br>A.29<br>B.2<br>C.-2<br>D.13<br>​
strojnjashka [21]

Answer:

Step-by-step explanation:

The determinant of a matrix is a special number that can be calculated from a square matrix.

...

To work out the determinant of a 3×3 matrix:

Multiply a by the determinant of the 2×2 matrix that is not in a's row or column.

Likewise for b, and for c.

Sum them up, but remember the minus in front of the b.

7 0
3 years ago
Zara is shopping at a furniture store with a budget of $1,500
Burka [1]

The Estimated total cost was $1564. Zara do not have eough money to buy the sofa and coffee table.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

She wants to buy a sofa for $924 and a coffee table for $640, hence:

Estimated total cost = 924 + 640 = $1564

The Estimated total cost was $1564. Zara do not have eough money to buy the sofa and coffee table.

Find out more on equation at: brainly.com/question/1214333

3 0
2 years ago
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