Answer:
The correct option is option B. It has one solution, and it's x=-3
Step-by-step explanation:
We have the following system of equations:
5x+7 = 2y (1)
y-9x=23 (2)
Step 1: Solve for 'y' in equation (2):
y-9x = 23
y = 9x + 23
Step 2: Substitute in equation (1):
5x + 7 = 2y
5x + 7 = 2(9x + 23)
5x + 7 = 18x + 46
Step 3: Solve for x:
7 - 46 = 18x - 5x
-39 = 13x
x= -3
So the correct option is option B. It has one solution, and it's x=-3
Answer:
x = 9
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Sum the given angles and equate to 360
90 + 109 + 9x - 5 + 85 = 360, that is
9x + 279 = 360 ( subtract 279 from both sides )
9x = 81 ( divide both sides by 9 )
x = 9
Answer: 12in
Step-by-step explanation:
Length+width+length+width
In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
What we know:
quotient 9.2 x 10^6/ 2.3 x 10²
in quotients exponents are subtracted of they have the same base, for example 10^6 and 10² have the same base of 10
What we need to find: quotient 9.2 x 10^6/ 2.3 x 10²
9.2 x 10^6
-------------- = 4 x 10^4
2.3 x 10²
Here in this problem I divided 9.2 by 2.3 and got 4, since the solution was simple and clean meaning no repeated decimals I went ahead and divided the 10^6 by 10^2 and got 10^4.
Another method would be to expand both numbers then divide and do scientific notation again.
Remember to change to normal notation you move the decimal to the right using the number of the exponent.
9.2 x 10^6= 9200000
2.3 x 10²= 230
920000/230=40000
40000= 4 x 10^4 scientific notation
Use the method that is best for you or just know you can use either method to check your work.
