Find the constant of proportionality on the graph.

A student solved the following problem and made an error: Triangles ABC and DEF. Angles A and F are congruent and measure 135 de

dmitriy555 [2]

We have that
triangle ABC coordinates
A (0,2) B(2,4) C(0,0)

triangle DEF coordinates
D (2,0) E ( 4,4) F (4,2)

using a graph tool
see the attached figure

therefore

Line 1 Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE
so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct

Line 2 ∠A ≅ ∠F------> is correct

Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83

find the distance AB
d=√[(4-2)²+(2-0)²]--------> d=√[4+4]-----> d=√8-----> d=2.83
AB=2.83
so
Line 3 is correct

Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47

find the distance DE
d=√[(4-0)²+(4-2)²]--------> d=√[16+4]-----> d=√20-----> d=4.47
DE=4.47
so
Line 4------> is correct

Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct

therefore

the answer is
the student make the first mistake in line 5

6 0

3 years ago

How do I write a decimal or fraction as a percent for 2/5

AleksandrR [38]

Answer:

40%

Step-by-step explanation:

Make it so the denominator is 100 since a percentage is out of a 100.

2/5 x 20/20 = 40/100

Now turn 40/100 into a percent. Should be simple. 40 out of 100 is 40%.

4 0

3 years ago

Administrators at a large public high school are interested in their students’ standardized test scores. Last year, the mean sco

ratelena [41]

Answer:

The appropriate hypotheses for performing a significance test is:

$H_0: \mu = 51$

$H_1: \mu > 51$

Step-by-step explanation:

Last year, the mean score on the state’s math test was 51. The administrators have trained the teachers in a new method of teaching math hoping to raise the scores on this standardized test this year.

At the null hypothesis, we test if the mean score this year is the same as last year, that is:

$H_0: \mu = 51$

At the alternate hypothesis, we test if the mean score improved this year from last, that is:

$H_1: \mu > 51$

The appropriate hypotheses for performing a significance test is:

$H_0: \mu = 51$

$H_1: \mu > 51$

8 0

2 years ago

A rectangular prism has a base area of 56 square feet and a volume of 840 cubic feet. The length of the base is longer than the

katovenus [111]

The answer is 8 ft.

The base area of rectangular prism is: A = l * w = 56 ft²
The length of the base is longer than the width: l > w

The volume of the prism is: V = l * w * h = 840 ft³
The sum of the length and width of the base is equal to the height of the pyramid: l + w = h

So:
l * w = 56
l * w * h = 840
___
56 * h = 840
h = 840 / 56
h = 15 ft

Now, we know that
l + w = 15 ⇒ w = 15 - l
l * w = 56
___
l * (15 - l) = 56
15l - l² = 56
0 = l² - 15l + 56

Or: l² - 15l + 56 = 0

Let's solve the quadratic function:
l = (-b +/-√(b² - 4ac)/(2a)
= (15 +/-√(-15)² - 4 * 1 * 56))/(2*1)
= (15 +/- √(225 - 224))/2
= (15 +/- √1)/2
= (15 +/-1)/2

l = (15+1)/2 = 16/2 = 8
or
l = (15-1)/2 = 14/2 = 7

If l = 8, then w = 15 - 8 = 7. So, l > w
If l = 7, then w = 15 - 7 = 8. So, l < w

Therefore, l = 8 ft.

6 0

3 years ago

5 days = blank hours

artcher [175]

24 hours in a day. 5 x 24 = 120 hours

6 0

2 years ago