3x/4-7/2=1/4 what does x equal

Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coor

Alex787 [66]

The correct answer is:

C. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.

Using the distance formula,

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

the lengths of the sides of BRAD are:

$\text{BR}=\sqrt{(7-6)^2+(3-4)^2}=\sqrt{1^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}\\\\\text{RA}=\sqrt{(6-3)^2+(4-3)^2}=\sqrt{3^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{AD}=\sqrt{(3-6)^2+(3-2)^2}=\sqrt{(-3)^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{DB}=\sqrt{(6-7)^2+(2-3)^2}=\sqrt{(-1)^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}$

The lengths of the sides of KELY are:

$\text{KE}=\sqrt{(2-0)^2+(11-9)^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\\\\\text{EL}=\sqrt{(0-2)^2+(9-3)^2}=\sqrt{(-2)^2+6^2}=\sqrt{40}=2\sqrt{10}\\\\\text{LY}=\sqrt{(2-4)^2+(3-9)^2}=\sqrt{(-2)^2+(-6)^2}=\sqrt{40}=2\sqrt{10}\\\\\text{YK}=\sqrt{(4-2)^2+(9-11)^2}=\sqrt{2^2+(-2)^2}=\sqrt{8}=2\sqrt{2}$

Each side of KELY is twice the length of the corresponding side on BRAD. This makes the ratio of the sides 2:1 and the figures are similar.

8 0

3 years ago

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20. The sum of two consecutive even integers is 158. Find the least of the two integers.

Mumz [18]

Answer:

78

Step-by-step explanation:

The tricky part of this is figuring out how to assign the unknowns. We are told that we are working with two consecutive even integers. Consecutive means "next to" or "in order" and sum means to add. If we use 2 and 4 as examples of our 2 consecutive even integers and assign x to 2, then in order to get from 2 to 4 we have to add 2. So the lesser of the 2 integers is x, and the next one in order will be x + 2. (2 and 4 are just used as examples; they mean nothing to the solving of this particular problem. You could pick any 2 even consecutive integers and find the same rule applies. All we are doing here with the example numbers is finding a rule for our integers.) Now we have the 2 expressions for the integers, we will add them together and set the sum equal to 158:

x + (x + 2) = 158

The parenthesis are unnecessary since we are adding, so when we combine like terms we get

2x + 2 = 158 and

2x = 156 and

x = 78

That means that the lesser of the 2 integers in 78, and the next one in order would be 80, and 78 + 80 = 158

6 0

3 years ago

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Solve for 44. 51° 64 = [?] 44 42=72° 57° I

Anastaziya [24]

Answer:

look at the picture i have sent

6 0

3 years ago

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-2/3a+5/6a-1/6 simplify

ratelena [41]

Answer:

$\frac{1}{6} a-\frac{1}{6}$

Step-by-step explanation:

$-\frac{2}{3} a+\frac{5}{6}a-\frac{1}{6}$

$=-\frac{4}{6} a+\frac{5}{6}a -\frac{1}{6}$

$= \frac{1}{6} a-\frac{1}{6}$

8 0

3 years ago

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Given the first type of plot indicated in each pair, which of the second plots could not always be generated from it?

Kisachek [45]

Answer:

d. box plot, stem and leaf

Step-by-step explanation:

The box plot depicts the five number summary minimum, 1st quartile, median, third quartile and maximum while stem and leaf plot shows every observation in data. So, when the box plot is given, we can't generate stem and leaf plot for the data because we don't have sufficient information in this scenario i.e., we don't have every data value to generate stem and leaf plot. Whereas, If the stem and leaf plot is given first then we can generate box plot from it because we have every data value to compute 5-number summary to generate box plot.

a. From dot plot, the histogram can be generated because dot plot represents every data value in the form of dots and from every data value, we can generate histogram.

b. From dot plot, the stem and leaf plot can be generated because dot plot represents every data value in the form of dots and from every data value, we can generate stem and leaf plot.

c. From stem and leaf plot, the dot plot can be generated because stem plot represents every data value in the form of stem and leaf i.e. 12 can be represented as 1 for a stem and 2 for a leaf (1 2) and so, from every data value we can generate dot plot.

d. From box plot, the stem and leaf plot can't be generated and the reason is explained in first paragraph. So, when the first type of plot is box plot then from it second plot stem and leaf plot can't be generated.

6 0

3 years ago