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3 years ago

Factor completely x^2 − 10x + 25.

Mathematics

2 answers:

Olenka [21]3 years ago

8 0

The answer is a.
x^2 -10x+25 = x*x-2*5*x+5*5 => (x-5)(x-5)

ivanzaharov [21]3 years ago

5 0

We're looking for two numbers that when multiplied, give 25, and when added, give -10.

Factoring 25 leads to 5*5 or -5*-5. The second alternative also fits -5+-5 = -10.

So (x-5)(x-5) is the factorization.

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Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

Sati [7]

Answer:

$x = 2-t$ and $y = -5\cdot t +21$

Step-by-step explanation:

Given that $y = 5\cdot x + 11$ and $t = 2-x$ , the parametric equations are obtained by algebraic means:

1) $t = 2-x$ Given

2) $y = 5\cdot x +11$ Given

3) $y = 5\cdot (x\cdot 1)+11$ Associative and modulative properties

4) $y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11$ Existence of multiplicative inverse/Commutative property

5) $y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11$ Associative property

6) $y = -5\cdot (-x)+11$ $\frac{a}{-b} = -\frac{a}{b}$ / $(-1)\cdot a = -a$

7) $y = -5\cdot (-x+0)+11$ Modulative property

8) $y = -5\cdot [-x + 2 + (-2)]+11$ Existence of additive inverse

9) $y = -5 \cdot [(2-x)+(-2)]+11$ Associative and commutative properties

10) $y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11$ Distributive property

11) $y = (-5)\cdot (2-x) +21$ $(-a)\cdot (-b) = a\cdot b$

12) $y = (-5)\cdot t +21$ By 1)

13) $y = -5\cdot t +21$ $(-a)\cdot b = -a \cdot b$ /Result

14) $t+x = (2-x)+x$ Compatibility with addition

15) $t +(-t) +x = (2-x)+x +(-t)$ Compatibility with addition

16) $[t+(-t)]+x= 2 + [x+(-x)]+(-t)$ Associative property

17) $0+x = (2 + 0) +(-t)$ Associative property

18) $x = 2-t$ Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is $x = 2-t$ and $y = -5\cdot t +21$ .

5 0

3 years ago

Helpppppppppp there are 2 pics attached

fiasKO [112]

Answer:

Option A

Option B

Option E

Option G

Option A and E go together

and

Option B and G go together.

4 0

3 years ago

Jen’s goal is to run a total of 22 miles in five days. The table below shows her log for the number of miles she ran on Monday,

Ronch [10]

Answer: 5.875 miles run on Friday to reach her goal by Jen

Step-by-step explanation:

Since we have given that

Part of distance covered on Monday by Jen is given by

$4\frac{3}{4}=\frac{19}{4}$

Part of distance covered on Tuesday by Jen is given by

$5\frac{1}{8}\\\\=\frac{41}{8}$

Part of distance covered on Wednesday by Jen is given by

Part of distance covered on Thursday by Jen is given by

$6\frac{1}{4}\\\\=\frac{25}{4}$

Total part of distance covered in these four days by Jen is given by

$\frac{19}{4}+\frac{41}{8}+0+\frac{25}{4}\\\\=\frac{38+41+0+50}{8}\\\\=\frac{129}{8}=16.125\ miles$

Remaining part of distance will be covered on Friday to reach her goal which is given by

$22-16.125=5.875\ miles$

Hence, 5.875 miles run on Friday to reach her goal by Jen.

5 0

3 years ago

Read 2 more answers

Why can't we find the area of this parallelogram

Ira Lisetskai [31]

Answer:

To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply. The base and height of a parallelogram must be perpendicular.

Step-by-step explanation:

parallelogram is easy to find

4 0

3 years ago

Solve this equation using an algebraic method: (x + 4)( x - 4) = 9<br> Help me out please

Artyom0805 [142]

You have to FOIL out the (x+4)(x-4) and then subrtract away the 9 in order to get a quadratic that you can solve for x. As it is, you can't do it.
$(x+4)(x-4)= x^{2} -4x+4x-16= x^{2} -16$
Now if you move the 9 over with it, you get this:
$x^{2} -16-9=0$
which simplifies to
$x^{2} -25=0$
Now you can either solve this by recognizing that is the difference of perfect squares, or you can move the 25 over to the other side and take the square root of both sides, like this:
$x^{2} =25$
$\sqrt{ x^{2} } = \sqrt{25}$
$x=+/-5$

5 0

3 years ago