Over the weekend, I bought a dress for $23.96, a pair of

A hotel has a number of meeting rooms , m , available for events each meeting room has 325 chair write an equation to represent

Sati [7]

Let c represent the total number of chairs in all of the meeting rooms at the hotel.

325M = C
325 (#of chairs per meeting room) M (# of meeting rooms) = C total # of chairs at the hotel

6 0

2 years ago

The area of a rectangle is 525 sq cm. the ratio of the length to the width is 7:3. find the length and width.

nalin [4]

Suppose the length is 7x, the width is then 3x
7x*3x=525
21x²=525
x²=25
x=5
so the length is 7*5=35, and the width is 3*5=15

3 0

2 years ago

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

Write a linear inequality in two variables that has (-1, 3) as a solution but does not have (4,0) as a solution.

Stels [109]

Answer: y ≤ -x + 2

<u>Step-by-step explanation:</u>

There are an infinite number of possible solutions.

Plot the two points, draw any line between them such that the two points are NOT connected, then choose the inequality symbol that shades (-1, 3).

Here is one solution that satisfies the requirements. y ≤ -x + 2

Here is another: y < -x + 3

And another: y > x + 3

And one more: y ≥ x + 4

3 0

3 years ago

SomeonePLEASE help if u do ily:(

pav-90 [236]

Answer:

4

Step-by-step explanation:

Pythagorean Theorem

a^2+b^2=c^2

C is the hyptonuse A and B are legs.

a^2+3^2=5^2

a^2+9=25

a^2=16

a= sqrt16

a=4

Hope this helps!

6 0

2 years ago