Please help me find the values of a and b so that the system shown had the given solution

What is the slope for (5,7) (-4,-2)

Wewaii [24]

Answer:

Slope = 1

Step-by-step explanation:

7 0

2 years ago

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5. To get to the library from his house, Robert biked 6 kilometers due east and then

AURORKA [14]

Answer:

24 kilometers.

Step-by-step explanation:

The shortest path between two points is a straight segment that connects the two points.

Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.

The two shorter segments are the two legs, and
The longer segment that joins the library and the house is the hypotenuse.

The length of the hypotenuse can be found with the Pythagorean Theorem.

$\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{Leg 1})^{2} + (\text{Leg 2})^{2}}\\&= \sqrt{6^{2} + 8^{2}}\\&= \sqrt{36 + 64} \\&= \sqrt{100}\\&= \rm 10\;km\end{aligned}$ .

The length of the round-trip will equal to the sum of the length of the three segments: $\rm 6\;km + 8\;km + 10\;km = 24\;km$ .

5 0

3 years ago

...................................................................

Genrish500 [490]

Answer:

12 cm

Step-by-step explanation:

The Pythagorean Theorem is as follows:

$a^{2} +b^{2} =c^{2}$

A and B represent the side lengths (legs) and C represents the hypotenuse.

The length of one leg equals 5cm. (This can be represented by either a or b)

The hypotenuse equals 13 cm.

Plug these into the equation from above:

$a^{2} + (5^{2}) = (13^{2})$

Solve for the other leg:

$a^{2} + 25 = 169$ Square what's in the parentheses from above

$a^{2} = 144\\$ Subtract 25 from 169

$\sqrt{a^{2} } = \sqrt{144}$ Square root both sides

a = 12 cm

Thus, the length of the other leg is 12 cm.

Let's check our answer:

$12^{2} +5^{2} =13^{2}$ Square everything

144 + 25 = 169 Add

169 = 169

Because both sides are equal it means that 12 cm is the correct answer.

Hope this helps!!

3 0

2 years ago

Use an algebraic approach to solve the problem.

qaws [65]

Answer:

Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.

Step-by-step explanation:

Use the formula for the mean: sum of elements / number of elements

Let x represent her first exam score.

Her second exam score can be represented by x + 11, since it was 11 points better than her first.

Her third exam score can be represented by (x + 11) + 5, since it was 5 points better than her second.

Plug in all of these expressions into the mean formula. Plug in 87 as the mean, and plug in 3 as the number of elements (since there are 3 scores):

mean = sum of elements / number of elements

87 = ( (x) + (x + 11) + (x + 11) + 5 ) / 3

Add like terms and solve for x:

87 = (3x + 27) / 3

261 = 3x + 27

234 = 3x

78 = x

So, her first score was a 78.

Find her second score by adding 11 to this:

78 + 11 = 89

Find her third score by adding 5 to the second score:

89 + 5 = 94

Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.

6 0

3 years ago

Simplify this expression.<br> <img src="https://tex.z-dn.net/?f=2%5Csqrt5%2813%2B%5Csqrt2%29" id="TexFormula1" title="2\sqrt5(13

andreyandreev [35.5K]

Step-by-step explanation:

everything can be found in the picture

5 0

2 years ago

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