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katrin [286]
3 years ago
11

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse

. Find the length of the hypotenuse.
Mathematics
1 answer:
nata0808 [166]3 years ago
3 0

Answer:

25 cm.

Step-by-step explanation:

If the hypotenuse is  x cm long the 2 legs are  x-5 and x-10 cm long.

So by the Pythagoras theorem:

x^2 = (x - 5)^2 + (x - 10)^2

x^2 = x^2 - 10x + 25 + x^2 - 20x + 100

x^2 - 30x + 125 = 0

(x - 5)(x - 25) = 0

x = 5, 25

We can discard x = 5 because that would make the lengths of the legs negative so the hypotenuse = 25 cm long.

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Answer:

34+24.5h

Step-by-step explanation:

8.5(4+3h)-h\\\\=8.5(4)+8.5(3h)-h\\\\=34+25.5h-h\\\\=34+24.5h

4 0
3 years ago
Read 2 more answers
Based on the Pythagorean Theorem, which of
aleksley [76]

Answer:

G is not TRUE.

Step-by-step explanation:

using the law A+B = B+A

PYTHAGOREAN THEOREM

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So for A²,

B² - c² = A. remember if a positive number move from the left to the right over an equal sign it becomes negative and vice versa

B²

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6 0
2 years ago
Please help... need help ASAP due today... which ones are the answers?
andrey2020 [161]

Answer:

Choices 1 and 4 are correct.

Step-by-step explanation:

We first need to find what the slope of the line is. That way, we can find out which possible answers are perpendicular to it:

\frac{4-(-2)}{3-1}=\frac{6}{2}=3

Since we now have the slope, we need the negative reciprocal of it. Remember: if x is the slope, it's negative reciprocal will be -\frac{1}{x}. Therefore, if the line's slope is 3, then we need to find answers with a slope of-\frac{1}{3}.

The first answer is correct, as you have marked. The second answer, while written a little weirdly, does show the slope as 3, which we know as wrong. The third choice is not correct, however. This equation is written in point-slope form, wherey-y_{1}=m(x-x_{1}). The only variable we have to worry about is m, which, in the third choice, is 3. The fourth answer is correct, which sounds weird at first. Let's put that equation into slope-intercept form:

x+3y=9\\3y=9-x\\y=3-\frac{1}{3}x\\y=-\frac{1}{3}x+3

Equations like these can be real sneaky, so it's important not to jump to conclusions with them.

6 0
3 years ago
11.1 x 0.8 x 1.16 x 0.4
makkiz [27]
Answer: 4.12032 which is also equivalent to 4:12
3 0
3 years ago
A researcher compares differences in positivity between participants in a low-, middle-, or upper-middle-class family. If she ob
777dan777 [17]

Answer:

(2, 12)

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

If we assume that we have 3 groups and on each group from j=1,\dots,n_j we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=k-1=3-1=2 where k =3 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=15-3=12.  

And the total degrees of freedom would be df=N-1=15 -1 =14  

And the correct answer would be 2 degrees of freedom for the numerator and 12 for the denominator

(2, 12)

3 0
3 years ago
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