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3 years ago

What integer is the opposite of –7?(a)1/7 (b)7 (c)-7 (d)-1/7

1 answer:

6 0

Hi

-7 -6 -5 -4 -3 - 2 -1 0 1 2 3 4 5 6 7

The distances d₁ = -7 to 0 and d₂ = 0 to 7 are the same

<span>Answer: b) 7</span>

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Olivia baked 16 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in

lukranit [14]

Answer:

The number of whole loaves at each location = 5 loaves

Step-by-step explanation:

This problem is essentially testing your ability to use simple division within remainders, and the number of whole loaves is calculated as follows:

Numer of loaves of bread = 16

number of locations = 3

next, we will divide the number of loaves by the number of locations since Olivia placed an equal number of loaves in 3 different locations:

$= \frac{16}{3} = 5\frac{1}{3}$

This means that there will be 5 whole loaves and 1 loaf that will be divided equally into the three places.

Therefore, the number of whole loaves at each location = 5 loaves

<em>but remember that there will be a remainder of 1 loaf.</em>

4 0

3 years ago

Find an equation in standard form of the parabola passing through these points: (0,-6),(-1,-12),(3,0)

Elan Coil [88]

One form of the equation of a parabola is
y = ax² + bx + c

The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)

Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)

Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1

The equation is
y = -x² + 5x - 6

Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6

y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.

Answer: y = -(x - 2.5)² + 0.25

3 0

4 years ago

The floor of a round hut has a diameter of 4 meters. What is the floor's circumference? Use 3.14 for .

7nadin3 [17]

Answer:

12.56

Step-by-step explanation:

C= 2 x 3.14 x 2

(the other 2 is half of the circumference)

3 0

4 years ago

Show work and Factor 4x^2+xy-18y^2

grigory [225]

Answer:

$4x^2+xy-18y^2=(4x+9y)\,(x-2y)$

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

$(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2$

so we want the following to happen:

$a\,c = 4\\ad+bc=1\\bd--18$

Notice as well that $ad+bc =1$ means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product $bd=-18$ , then we can consider the case in which one of this (b or d) is the negative factor. So let's then assume that $a\,\,and \,\,c$ are positive.

We can then try combinations for $a\,\,and \,\,c$ such as:

$a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4$

Just by selecting the first one $(a=4;\,\,c=1)$

we get that $4d_b=1\\b=-4d-1$

and since

$bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0$

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

$d=-18/(-2)\\d=9$

Now we have a good combination of parameters to render the factoring form of the original trinomial:

$a=4; \,\,b=9;\,\,c=1;\,\,d=-2$

which makes our factorization:

$(4x+9y)\,(x-2y)=4x^2+xy-18y^2$

6 0

3 years ago

A plumber is fitting A water pipe that is 3/4 foot long on to a water pipe that is 2/12 foot long.How long will the finish pipe

viktelen [127]

Add 3/4 foot to 2/12 foot. The LCD here is 12.

Thus, add 9/12 foot to 2/12 foot. Answer: 11/12 foot.

Are you sure you copied down that "2/12" correctly? Note that 2/12 = 1/6

3 0

3 years ago

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