Let the width be x, the length is then 3x-10
Area of a rectangle is length times width: x(3x-10)=77 => 3x^2-10x-77=0
Factor this quadratic equation: (x-7)(3x+11)=0 =.x=7 or x=-11/3
width cannot be negative, so the only answer is x=7
width is 7m, length is 11m
Answer:
1, 4,9,16,25
Step-by-step explanation:
√1 = 1 √4 =2 √9= 3 √16= 4 √25 =5
Answer:
I'm sorry I can't help because I don't know what part is shaded. Note: Since a square has the same length for each side all the sides are 16 cm.
Area and Perimeter for WHOLE square:
A: 256 sq cm
P: 64 cm
Answer:
1. Statement: ∠RVS ≅ ∠SVT
2. Statement: m∠RVS + m∠SVT = 180°
3. Statement: m∠RVS + m∠RVS = 180°
4. Statement: m∠RVS = 90°
5. Statement: Line RT ⊥ Line SU
1. Reason: Given
2. Reason: Angles forming a linear pair sum of 180°
3. Reason: Substitution
4. Reason: Algebra
5. Reason: Defintion of perpendicular lines
Step-by-step explanation:
First, write the given (line 1).
Next, use the fact that angles forming a linear pair sum to 180° to show m∠RVS + m∠SVT = 180° (line 2).
Next, substitute m∠RVS for m∠SVT in m∠RVS + m∠SVT=180° (line 3).
Next, use algebra to show m∠RVS = 90° (line 4).
Finally, use the definition of perpendicular lines to prove that Line RT ⊥ Line SU (line 5).
Hope this helps :D
Given that:
- Amber can peel this amount of potatoes:
![10\frac{1}{2}\text{ }potatoes](https://tex.z-dn.net/?f=10%5Cfrac%7B1%7D%7B2%7D%5Ctext%7B%20%7Dpotatoes)
- And she can peel them in this time:
![\frac{1}{3}\text{ }hour](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Ctext%7B%20%7Dhour)
You can determine that the Unit Rate is the number of potatoes she can peel per hour.
Since the number of potatoes is given as a Mixed Number, you can convert it to an Improper Fraction as follows:
1. Multiply the Whole Number part by the denominator.
2. Add the Product to the numerator.
3. The denominator does not change.
Then:
![10\frac{1}{2}=\frac{(10\cdot2)+1}{2}=\frac{20+1}{2}=\frac{21}{2}](https://tex.z-dn.net/?f=10%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%2810%5Ccdot2%29%2B1%7D%7B2%7D%3D%5Cfrac%7B20%2B1%7D%7B2%7D%3D%5Cfrac%7B21%7D%7B2%7D)
Now you can set up that:
![Unit\text{ }Rate=\frac{\frac{21}{2}\text{ }potatoes}{\frac{1}{3}\text{ }hour}](https://tex.z-dn.net/?f=Unit%5Ctext%7B%20%7DRate%3D%5Cfrac%7B%5Cfrac%7B21%7D%7B2%7D%5Ctext%7B%20%7Dpotatoes%7D%7B%5Cfrac%7B1%7D%7B3%7D%5Ctext%7B%20%7Dhour%7D)
Solving the Division, you get:
![\begin{gathered} Unit\text{ }Rate=\frac{21\cdot3}{2\cdot1}\frac{potatoes}{hour} \\ \\ Unit\text{ }Rate=\frac{63}{2}\frac{potatoes}{hour} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20Unit%5Ctext%7B%20%7DRate%3D%5Cfrac%7B21%5Ccdot3%7D%7B2%5Ccdot1%7D%5Cfrac%7Bpotatoes%7D%7Bhour%7D%20%5C%5C%20%20%5C%5C%20Unit%5Ctext%7B%20%7DRate%3D%5Cfrac%7B63%7D%7B2%7D%5Cfrac%7Bpotatoes%7D%7Bhour%7D%20%5Cend%7Bgathered%7D)
Hence, the answer is: