Please help me with the math

For a quadratic function ƒ(x)=ax2+bx+c, ƒ(−1)<1, ƒ(1)>−1, and ƒ(3)<−4. What could be the sign of a?

denis23 [38]

Answer:

"a" must be negative

Step-by-step explanation:

The slope between points (-1, 1) and (1, -1) is a minimum of (-1-1)/(1-(-1)) = -1.

The slope between points (1, -1 and (3, -4) is a maximum of (-4-(-1))/(3-1) = -3/2.

Thus, as x increases, the slope is decreasing. In order for that to be the case, the value of a must satisfy a < 0.

4 0

4 years ago

The scale of a map is 1in:15miles. How many miles is it from Philadelphia, Pa to Boston, Ma if they are 20.4 inches apart on the

cupoosta [38]

Answer:

if 1in=15miles

then20.4in=? miles

1in by ? miles and 20.4in by 15miles

1in ? miles= 306in miles

divide both sides by 1in

? miles= 306 miles

therefore 20.4in = 306miles

4 0

2 years ago

Which expression does NOT have a Greatest Common Factor?

Misha Larkins [42]

Answer:

4x^2-9

Step-by-step explanation:

i just took the quiz

3 0

3 years ago

What is factorisation

liubo4ka [24]

Factorization is a method of writing numbers as the product of their factors or divisors.

Solution:

Factorisation:

Factorization is a method of writing numbers as the product of their factors or divisors.

In other words we can say, Finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

Methods of factorisation:

Factoring out the GCF

The sum-product pattern

The grouping method

The perfect square trinomial pattern

The difference of squares pattern

Factoring out the GCF:

This methods means that factoring out common factors

For example:

$12x^2 + 3x = 3x(4x + 1)$

This can be used when each term in given expression shares a common factor

The sum-product pattern

A quadratic equation may be expressed as a product of two binomials

For example:

$x^2 + 7x + 12 = (x + 3)(x + 4)$

This method can be used for quadratic equations of form $ax^2 + bx + c = 0$

The grouping method

If the polynomial is of the form $ax^2 + bx + c$ and there are factors of ac that add up to b , we can use this method

For example:

$2x^2 + 7x + 3\\\\2x^2 + 6x + 1x + 3\\\\2x(x + 3) + 1(x + 3)\\\\(x + 3)(2x + 1)$

The perfect square trinomial pattern

If the first and last terms are perfect squares and the middle term is twice the product of their square roots , we can use this method

For example:

$x^2 + 10x + 25\\\\(x + 5)^2$

The difference of squares pattern

If the expression represents a difference of squares, we can use this method

Because $a^2 - b^2 = (a + b)(a - b)$

For example:

$x^2 - 25\\\\x^2 - 5^2\\\\(x + 5)(x - 5)$

6 0

4 years ago

Negitive 7 over 18 minus negitive 9 over 4 equals?

Inessa [10]

Answer:

1 31/36 is your answer

Step-by-step explanation:

Find common denominators. Note that what you do to the denominator, you must do to the numerator;

(-7/18)(2/2) = (-14/36)

(-9/4)(9/9) = (-81/36)

Combine the terms:

(-14/36) - (-81/36)

Note that two negative signs directly next to each other equals a positive sign.

(-14/36) + 81/36

-14/36 + 81/36

(-14 + 81)/36

Combine like terms. Solve the parenthesis:

(67)/36

Change to a mixed fraction:

(67/36) = 1 31/36

1 31/36 is your answer.

~

5 0

3 years ago