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kiruha [24]
3 years ago
13

What is the gcf of 54 and 32

Mathematics
2 answers:
natima [27]3 years ago
8 0
The greatest common factor is 2
alex41 [277]3 years ago
7 0
2 should be the gcf
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Solve for x: 3(x + 1) = −2(x − 1) − 4.
Vlad [161]

Answer:

Multiply the first bracket by 3

Multiply the second bracket by -2

3x+3=-2x+2-4

3x+2x+3=-2x-2   negative (-) number and positive number (+)= negative number

Just rearranging

5x+3=-2

5x+3-3=-2-3

5x=-5

Dividing by 5

5x/5=-5/5

x=-1

Check answer by using substitution method

3(-1+1)=-2(-1-1)-4

0=-2(-2)-4 negative number and negative number = positive number

0=4-4

0=0

Answer is x=-1

6 0
3 years ago
Triangle BCD is rotated counterclockwise to form
IRISSAK [1]

Answer:

The answer is 90 degrees. Have a good day!

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The number of salmon swimming upstream to spawn is approximated by the following function:
umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

S'(x) = -3\cdot x^{2}+4\cdot x +405 (Eq. 1)

S''(x) = -6\cdot x +4 (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for x:

-3\cdot x^{2}+4\cdot x +405 = 0

And all roots are found by Quadratic Formula:

x_{1} \approx 12.305\,^{\circ}C, x_{2}\approx -10.971\,^{\circ}C

Only the first root is inside the given interval of the function. Hence, the correct answer is:

x \approx 12.305\,^{\circ}C

Now we evaluate the second derivative at given result. That is:

S''(12.305) = -6\cdot (12.305)+4

S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

5 0
3 years ago
Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *​
krek1111 [17]

Here are a couple I found:

<u>Similarities</u>:

  • They have the same y-intercept of (0,5).
  • They are both in slope-intercept form.

<u>Differences</u>:

  • The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
  • They have different x-intercepts. (y = 2x + 5 intersects (-\frac{5}{2}, 0) while y = -13x + 5 intersects at (\frac{5}{13}, 0)

<u></u>

<u>Explanation</u>:

Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).

As for differences, we can see that the coefficient in place of that "m" is positive in y = <u>2x</u> + 5 and negative in y = <u>-13x</u> + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.

4 0
2 years ago
A triangle has sides with lengths of 43 millimeters, 52 millimeters, and 65 millimeters. Is it a right triangle
Mrrafil [7]
Use pythagora's theorem to test if it is a right triangle

c^2 = a^2 + b^2
65^2 = 52^2 + 43^2
4225 = 2704 + 1849
4225 =/= 4553
therefore it is not a right triangle as it does not comply to pythagora's theorem
7 0
2 years ago
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