Find two numbers a and b whose sum a+b is −1, and whose difference a−b is 1.

Anna35 [415]

This is a parabola, first, locate the line of symmetry.
the line of symmetry is x=-b/2a
in this case, b=-2, a=-1, so the line of symmetry is x=-1
when x=-1, f(x)=-(-1)²-2(-1)-3=-2
locate the point (-1,-2) on the grid. this point is the vertex.
get two pairs of points with x=-1 as the symmetry line:
(0, -3) and (-2, -3); (1,-6) and (-3,-6)
connect these five points into a parabola, stick out at the ends because it will extend forever downward.

3 0

3 years ago

Sandy has 28 pencils and 72 erasers. She wants to make the greatest number of bags that have the same number of pencils and eras

aalyn [17]

Answer:

she can make a maximum of 4 bags.

peach bags containing 7 pencils and 18 erasers.

Step-by-step explanation:

find all the factors each numbers are divisible by:

28 => 1, 2, 4, 7, 14, 28

72 => 1, 2, 3, 4, 8, 9, 18, 24, 36, 72

choose the maximum common denominator.

7 0

3 years ago

Read 2 more answers

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

4 0

3 years ago

Tay-Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, th

LuckyWell [14K]

Answer:

Step-by-step explanation:

Given that Tay-Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that each of their offspring will develop the disease is approximately 0.25.

Let X be the no of children having this disease out of 4 occasions

Then X has two outcomes and each trial is independent of the other trial

Hence X is binomial with n =4, and p = 0.25

a) $P(X=4) = 4C4 (0.25)^4 = 0.003906$