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2 years ago

Michael is an art elective programme student who

Mathematics

1 answer:

Elena L [17]2 years ago

4 0

Answer:

Step-by-step explanation:

find the prime factors of given numbers:

126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors

108= 2*2*3*3*3 - same as above

As per prime factors, the squares can be of sizes:

2×2, 3×3, 6×6, 9×9 and 18×18

The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square

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Austin's Coffee Shop makes a blendd that is a mixture of two types of coffee. Type a coffee costs bill $5.70 per pound and type

IceJOKER [234]

Answer:

He use 97 pound of type A coffee

Step-by-step explanation:

Let's call A the pounds of type A coffee that Austin used this month and B the pounds of type B coffee that Austin used this month.

From the sentence: Type A coffee costs bill $5.70 per pound and type B coffee costs $4.65 per pound and the total cost is $943.50, we can formulated the equation 1 as:

5.70*A + 4.65*B=943.50

Because the total cost is the sum of the cost of every type of coffee.

Additionally, from the sentence: This month bill made 181 pounds of the blend, we can formulate the equation 2 as:

A + B = 181

Solving for B, we get:

B = 181 - A

Now, for find the value of A we need to replacing this last equation on equation 1, and solving for A as:

5.70*A + 4.65*B=943.50

5.70*A + 4.65*(181-A)=943.50

5.70*A + 841.65 - 4.65*A = 943.50

5.70*A - 4.65*A = 943.50 - 841.65

1.05*A = 101.85

A = 101.85/1.05

A = 97

So, this month, he use 97 pound of type A coffee.

5 0

3 years ago

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the grap

aliya0001 [1]

The coordinates of the vertex of the graph are (-2, -9).

<h3>Further explanation</h3>

The quadratic function is described by the standard equation $\boxed{ \ f(x) = ax^2 + bx + c \ }.$ The graph of a quadratic function is called a parabola.

We have the quadratic function $\boxed{ \ f(x) = x^2 + 4x - 5 \ }.$

We identify the coefficients a, b, and c. For this equation, $\boxed{ \ a = 1, b = 4, and \ c = -5 \ }$
The axis of symmetry is $\boxed{ \ x = h = -\frac{b}{2a} \ }$ , i.e., $\boxed{ \ x = h = -\frac{4}{2(1)} \rightarrow h = -2 \ }.$ Thus, the statement in the question for the symmetry axis x = -2 is correct.
The vertex (or turning point) is $\boxed{ \ (h, k) \ },$ where $\boxed{ \ k = f(h) \ }$ or $\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }$
The parabola opens upward because a > 0, resulting in a vertex that is a minimum.

Finding the minimum value is as follows:

$\boxed{ \ k = f (-2) = (-2)^2 + 4(-2) - 5 \rightarrow k = -9 \ }, or$
$\boxed{ \ k = \frac{4^2 - 4(1)(-5)}{-4(1)} = -\frac{36}{4} \rightarrow k = -9 \ }$

Therefore, the coordinates of the vertex of the graph are (h, k), i.e., $\boxed{\boxed{ \ (-2, -9) \ }}$

Other components:

The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point $\boxed{ \ (0, -5) \ }.$
The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at $\boxed{ \ (-5, 0) \ and \ (1, 0) \ }$

<h3>Learn more</h3>

Which is the graph of f(x) = (x - 1)(x + 4) brainly.com/question/2334270
Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) brainly.com/question/1332667
The midpoint brainly.com/question/3269852

Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value