Answer:
The number would be 22.
Step-by-step explanation:
In order to solve for the number, we need to make both statements into numerical statements.
Fifteen more than four times a number = 15 + 4x
difference between 191 and four times the number = 191 - 4x
Now we set them equal to each other.
15 + 4x = 191 - 4x -----> Add 4x to each side
15 + 8x = 191 ------> Subtract 15 from both sides
8x = 176 -------> Divide by 8
x = 22
5x³ + 8x² - 7x - 6
1)
x + 2 is a factor because when using synthetic division, the remainder is zero.
-2 | 5 8 -7 -6
<u>| ↓ -10 4 6 </u>
5 -2 -3 0 ← remainder is zero
2)
x + 2 is not a factor because when using synthetic division, the remainder is not zero.
-1 | 5 8 -7 -6
<u>| ↓ -5 -3 10 </u>
5 3 -10 4 ← remainder is not zero
Answer:
a) 2
b) -
c) y = 2x + 1
Step-by-step explanation:
a)
First put the equation into slope intersept form (y=mx+b) by...
- Move the variable to the right-hand side and change its sign : -y = -4 -2x
- Change the signs on both sides of the equation: y = 4 + 2x
- Use the commutative property to reorder the terms : y = 2x + 4
Slope intersept form : y = 2x + 4
Parallel lines have the same slope so.... a parallel slope is 2
b)
First put the equation into slope intersept form (y=mx+b) by...
- Move the variable to the right-hand side and change its sign : -y = -4 -2x
- Change the signs on both sides of the equation: y = 4 + 2x
- Use the commutative property to reorder the terms : y = 2x + 4
Slope intersept form : y = 2x + 4
To find a perpendicular slope flip the slope and change the sign : -
c)
First put the equation into slope intersept form (y=mx+b) by...
- Move the variable to the right-hand side and change its sign : -y = -4 -2x
- Change the signs on both sides of the equation: y = 4 + 2x
- Use the commutative property to reorder the terms : y = 2x + 4
Slope intersept form : y = 2x + 4, parellel slope : 2
- Substitute the x and y values with the given ordered pair: 3 = 2(1) + b
- Calculate the product: 3 = 2 + b
- Move the variable to the left-hand side and change its sign: -x = 2 - 3
- Calculate the difference and change the signs : b = 1
Use the slope and y-intersept (b) to write the new line : y = 2x + 4
112-37=75
75/5=15
So 15 weeks until she has 112 cards
Answer:
The length of hypotenuse is 45 kilometers
Step-by-step explanation:
Assuming that given lengths are of perpendicular and hypotenuse, and the triangle is a right angled triangle
Perpendicular = P = 27 km
Base = B = 36 km
Hypotenuse = H = ?
We can use Pythagoras theorem for finding the length of hypotenuse
The Pythagoras theorem is given by:

Putting the values, we get

Taking square root on both sides

Hence,
The length of hypotenuse is 45 kilometers