1+1(2)-5+96-4(67+9)+59+10

Which equation could be used to find the length of the hypotenuse?

Komok [63]

Answer:

<h3>(base)² + (altitude)² = (hypotenuse) ²</h3>

Therefore,

2²+5² = c² will be matched.

7 0

3 years ago

For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x

Alla [95]

The correct answer is:

D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

Explanation:

We solve each system to find the correct answer.

For A:
$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

Since we have the coefficients of both variables the same, we will use elimination to solve this.

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
$\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. 
\\
\\6x=23$

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is not the x-coordinate of the answer we are looking for, so A is not correct.

For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is not the y-coordinate of the answer we're looking for, so B is not correct.

For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is not the y-coordinate of the answer we're looking for, so C is not correct.

For D:
Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

$\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. 
\\
\\-8y=-24$

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so D is the correct answer.

7 0

3 years ago

Solve the equation: x^2 - 6x = 7 A. x = 7 , 1 B. x = -7 , 1 C. x = 7 , -1

Alex777 [14]

x^2 - 6x = 7
(x - 7)(x + 1)= 0
x = 7, - 1

The answer is: x = 7, -1.

6 0

3 years ago

I need you guys to answer all of this sorry please help me before 11:59 I beg

Igoryamba

Answer:

M<1 = 106

M<2 = 74

M<3 = 106

M<4 = 74

M<5 = 106

M<6 = 74

M<7 = 106

M<8 = 74

Step-by-step explanation:

7 0

3 years ago

Two sides of a parallelogram measure 60 centimeters and 40 centimeters. If one angle of the parallelogram measures 1320, find th

UkoKoshka [18]

Answer:

b. about 91.7 cm and 44.6 cm

Step-by-step explanation:

The lengths of the diagonals can be found using the Law of Cosines.

Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).

For diagonal "d" and sides "a" and "b" and corner angle D, we have ...

d² = a² +b² -2ab·cos(D)

The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...

d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)

d² ≈ {1988.2, 8411.8}

d ≈ {44.6, 91.7} . . . . centimeters

The diagonals are about 91.7 cm and 44.6 cm.

4 0

3 years ago