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Lina20 [59]
3 years ago
11

Find the value of each measure.

Mathematics
1 answer:
zloy xaker [14]3 years ago
4 0

The two congruent base angles tell us that this is an isosceles triangle, meaning the triangle has two congruent sides. Therefore, we can set these two expressions equal to each other and solve from there.

15x + 7 = 23x - 17

7 = 8x - 17

8x = 24

x = 3

Side = 15(3) + 7 = 45 + 7 = 52

Hope this helps!

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Question 1b.
Ainat [17]

Answer:  i) Reasonably symmetric

=============================================================

Explanation:

The data set is

35,40,45,49,51,54,57,58,58,64,68,68,75,77

Erase the outer pair of values (35 and 77) to end up with this smaller set

40,45,49,51,54,57,58,58,64,68,68,75

Repeat and erase off the outer values (40 and 75) to end up with

45,49,51,54,57,58,58,64,68,68

Keep going until we have either one or two elements left

  • 49,51,54,57,58,58,64,68
  • 51,54,57,58,58,64
  • 54,57,58,58
  • 57,58

At this point, we see that the center is between these two last values. So the median is (57+58)/2 = 57.5

--------------------------------

The center is at 57.5

Let L = {35,40,45,49,51,54,57} consist of the set of numbers lower than the median

Let U = {58,58,64,68,68,75,77} be the upper set of values larger than the median.

The middle of set L is 49 and the middle of set U is 68. So Q1 and Q3 are 49 and 68 respectively.

From that, we see the IQR = Q3 - Q1 = 68-49 = 19

Let A and B be the lower and upper fence

We would then say

A = Q1 - 1.5*IQR = 49-1.5*19 = 20.5

B = Q3 + 1.5*IQR = 68 + 1.5*19 = 96.5

Notice how all of the given data values are between A = 20.5 and B = 96.5, which means we don't have any outliers.

Furthermore, if we plotted a box-and-whisker plot (see below), we can see that the two whiskers are fairly the same length. It's not perfect but they're reasonably symmetric. Similarly, the median is somewhat in the middle of the box itself. So this gives a rough idea that the data set we're dealing with is fairly symmetric.

More confirmation can be in the form of a histogram which is also part of the image below. This histogram is fairly symmetric as the left half is nearly (not perfectly) a mirror image of the right half, and vice versa. No one side pulls too far out to create a highly skewed distribution.

8 0
3 years ago
Corey is visiting the Jefferson
lutik1710 [3]

Answer:

Step-by-step explanation:

He wants to estimate the height of the statue of Thomas Jefferson. Corey stands so that his line of vision to the top and base of the statue form a right angle as shown in the diagram. ... So, the total height of the statue is about 159 + 68 or 227 inches, which is equivalent to 18 ft 11 in. ANSWER: 18 ft 11 in.

8 0
2 years ago
Find the value of y.<br> Picture below
olga2289 [7]

We have trapezoid with congruent legs.

30x + 11y = 2x + 3

28x +11y = 3

Also we have

30x + 11y = 12

We got 2 equations:

30x + 11y = 12

28x +11y = 3 (*-1) -----> -28x -11y = -3

30x + 11y = 12

<u> -28x -11y = -3</u>

2x = 9

x=9/2

30x + 11y = 12 ------> 30*9/2 +11y =12 ------> 135+11y =12, ---> 11y = - 123,

y= - 123/11

6 0
3 years ago
A store pays $10.56 fora map of Africa and marks the price up by
nignag [31]

Essentially, 50% of $10.56 is $5.28.

This means that all we have to do is add $10.56 to $5.28, making <u>$15.84</u>


Side note: Another way that you can do this is by simply doing 1.5(10.56).

6 0
3 years ago
Kevin is three years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
GarryVolchara [31]

Answer:

I believe that Kevin is 6 years old now.

Step-by-step explanation:

I used the guess and check method to figure this out.

First, I began by making Daniel 1 years old, two years ago. Kevin was 4 times as old as Daniel two years ago, so he would be 4 at the time. Now, Daniel would be 3 and Kevin would be 6 years old. The statement that Kevin is three years older than Daniel would confirm this, because 6-3=3.  Hope this helps, this is my first time answering:)

3 0
3 years ago
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