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Camille's kitchen has an area of 80 square feet. The kitchen is 8 times as many square feet as Camille's pantry. If the pantry i

Inessa05 [86]

Answer:

Length of the pantry = 5 feet

Step-by-step explanation:

Camille's kitchen has an area of 80 square feet. The kitchen is 8 times as many square feet as Camille's pantry.

Step 1

Area of Camille's kitchen = 8(Area of Camille's pantry)

Area of Camilla kitchen = 80 square feet

80 square feet = 8(Area of Camille's pantry)

Area of Camille's pantry = 80 square feet/8

Therefore:

Area of Camille's pantry = 10 square feet

Step 2

If the pantry is 2 feet wide, what is the length of the pantry?

The shape of the pantry is rectangular hence:

The area of the pantry = Length × Width

Area of the pantry = 10 square feet

Width = 2 feet

Length = Area of the pantry/Width

Length = 10 square feet/2 feet

Length = 5 feet

5 0

3 years ago

Find the coordinates of the y-intercept and x-intercepts of the following. (image!)

marissa [1.9K]

Answer:

Step-by-step explanation:

We can do this a couple of ways. We can graph it -- see below. Or we can do the math.

Math

y = x^2 - 2x - 15

This trinomial factors into

y = (x - 5)(x + 3)

from which

x - 5= 0

x = 5

and

x + 3 = 0

x = - 3

The y intercept is the value obtained when all the xs on the right = 0

y = 0^2 - 2*0 - 15

y = - 15

Answer

x intercepts: (-3,0),(5,0)
y intercept: (0,-15)

The graph is below.

4 0

2 years ago

Solve for X Explain if possible :)

sweet-ann [11.9K]

The two labeled angles are alternate interior angles, and as such, they are the same.

From this result you can build the equation

$15x-2 = 13x+2$

and solve it for x: subtract 13x from both sides to get

$2x-2=2$

and add 2 to both sides to get

$2x = 4 \implies x = 2$

Check: if we plug the value we found we have

$13\cdot 2 + 2 = 26+2 = 28 = 15\cdot 2 - 2 = 30-2$

So the angles are actually the same, as requested.

4 0

3 years ago

How to factor expressions? For example 4n + 4 • 2, 10t + 10 • 3, 7v + 7 • 8

TiliK225 [7]

Answer:

8(n + 1)

30(t + 1)

56(v + 1)

Step-by-step explanation:

(4n + 4)(2)

4(n + 1)(2)

8(n + 1)

(10t + 10)(3)

10(t + 1)(3)

30(t + 1)

(7v + 7)(8)

7(v + 1)(8)

56(v + 1)

6 0

3 years ago

If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by

PIT_PIT [208]

Answer:

The family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

$\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}$ (1)

Where:

$\theta$ - Angle between vectors, in sexagesimal degrees.

$\|\vec a\|, \|\vec b \|$ - Norms of vectors $\vec {a}$ and $\vec{b}$

If $\theta$ is acute, then the cosine function is bounded between 0 a 1 and if we know that $\vec {a} = (p, 3, -7)$ and $\vec {b} = (p, -p, 4)$ , then the possible values for $p$ are:

Minimum ( $\cos \theta = 0$ )

$\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0$

Maximum ( $\cos \theta = 1$ )

$\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1$

With the help of a graphing tool we get the family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

7 0

3 years ago