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Elena L [17]
3 years ago
6

The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and

length of this rectangle?
PLS HELP ASAP!!!!!!!!!!!!!!!!!
Mathematics
1 answer:
krok68 [10]3 years ago
7 0

Answer:

width is 2 1/4 length 5 5/12

Step-by-step explanation:

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Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t
WINSTONCH [101]

Answer:

Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

Step-by-step explanation:

Let v_1 be the speed and  t_1 be the time Barbara drives in clear weather, and let v_2 be the speed and t_2 be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). v_2 = v_1 -22

Also,

(2). v_1t_1 = 45miles

(3). v_2 t_2 = 57,

and

(4). t_1+t_2 = 2.25hr

From equations (2) and (3) we get:

t_1 = \dfrac{45}{v_1}

t_2 =\dfrac{57}{v_2}

putting these in equation (4) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25

and substituting for v_2 from equation (1) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25

This equation can be rewritten as

2.25v_1^2-151.5v_1+990=0

which has solutions

v_1 = 60

v_1 = 7.33

We take the first solution v_1 =60 because it gives a positive value for v_2:

v_2 = v_1 -22

v_2 = 60 -22\\

v_2 = 38.

Thus, Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

4 0
3 years ago
Two factors whose product is 84 are 12 and _[blank]_.
djyliett [7]

Answer: 7

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You know that a multiplication has the following form:

a*b=c

Where a and b are the factors and c is the product.

2. You know one of the factor, then you can find the second one as following:

12*b=84

b=84/12

b=7

Therefore the answer is 7.

7 0
3 years ago
How many unit cubes would it take to completely fill the prism with no gaps between unit cubes?
Lemur [1.5K]

Answer:

72 cubes

Step-by-step explanation:

Top view of the rectangular prism shows the unit cubes arranged in two rows along the length.

In each row number of unit cubes arranged = 9

Right view side of the prism shows the unit cubes arranged in two columns.

Number of unit cubes in each column = 4

Total number of cubes arranged in the prism = (Number of cubes in each row × Number of cubes arranged in two columns) × Number of columns

= (9 × 4) × 2

= 72

Therefore, number of cubes filled completely in the prism with no gaps = 72

6 0
3 years ago
How do you this question (pre-cal)
Novay_Z [31]

The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).

So I'll take the left hand side and try to turn it into \csc^2( B )

One way we can do that is through the following steps:

\frac{\tan(B) + \cot(B)}{\tan(B)} = \csc^2(B)\\\\\frac{\tan(B)}{\tan(B)} + \frac{\cot(B)}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\frac{1}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\cot(B) = \csc^2(B)\\\\1 + \cot^2(B) = \csc^2(B)\\\\1 + \frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)}{\sin^2(B)}+\frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)+cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{1}{\sin^2(B)} = \csc^2(B)\\\\\csc^2(B)=\csc^2(B) \ \ {\Large \checkmark}\\\\

Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.

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Decompose the figure into regions that are closest to each
Korolek [52]

The image is decomposed as follows: H1 and H2. Where original graph is Hx.

<h3>Are the images (attached) valid decompositions of the original graph?</h3>

  • Yes, they are because, H1 and H1 are both sub-graphs of Hx; also
  • H1 ∪ H2 = Hx
  • They have no edges in common.

Hence, {H1 , H2} are valid decomposition of G.

<h3>What is a Graph Decomposition?</h3>

A decomposition of a graph Hx is a set of edge-disjoints sub graphs of H, H1, H2, ......Hn, such that UHi = Hx

See the attached for the Image Hx - Pre decomposed and the image after the graph decomposition.

Learn more about decomposition:
brainly.com/question/27883280
#SPJ1

7 0
1 year ago
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