Answer:
The Answer is: y = -1/4x + 6
Step-by-step explanation:
Given point: (4, 5)
Given equation: y = -1/4x - 11
Slope: m = -1/4, a parallel line will have the same slope.
Start with the point slope form and solve for y:
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
y - 5 = -1/4x + 1
y = -1/4x + 1 + 5
y = -1/4x + 6
Proof:
f(x) = -1/4x + 6
f(4) = -1/4(4) + 6
= -1 + 6 = 5, giving (4, 5)
Hope this helps!! Have an Awesome day!!! :-)
Answer:
About 41.5%
Step-by-step explanation:
<em>Given:</em>
<em>A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape.</em>
<em>To Find:</em>
<em>What is the probability that both grapes are red?</em>
<em>Answer choices:</em>
<em>about 39.7%</em>
<em>about 41.5%</em>
<em>about 42.5%</em>
<em>about 44.5%</em>
<em>Solution:</em>
<em>Since, there are 8 green grapes and 15 red grapes, the total number of grapes is 23 .</em>
<em>As the red grapes are 15..</em>
<em>Thus,</em>
<em>The probability of choosing a red grape the first time is 15/23.</em>
<em>Because out of the total 23 grapes only 15 were red grape.</em>
<em>The probability of choosing the red grape the second time will be 14/22. Because the number of red grapes has already decreased by one and so is the total number of grapes after first choice</em>
<em>Hence, the probability of choosing or eating two red grapes will be :</em>
<em>15/23×14/22</em>
<em>=105/253</em>
<em>=0.415</em>
<em>= 41.5%</em>
<em>Therefore, the probability that both grapes are red is about 41.5%</em>
Answer:
The patio is a rectangle
Step-by-step explanation:
Since it is given that we have 2 pairs of two parallel sides, which implies 4 sides, this thus shows that the shape is a quadrilateral since, only quadrilaterals have 4 sides. Also, 2 pairs of sides are the same length, and are parallel, it shows that the shape is likely a rectangle.
Finally, there are 4 square corners on the shape which implies 4 right angles. This confirms that our shape is a rectangle since only a rectangle has 2 pairs of two parallel sides and 2 pairs of sides that are the same length there are 4 square corners.
So, the patio is a rectangle.
Using relations in a right triangle, considering c as the hypotenuse, we have that the length of side A is: 
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
From the information given, we can build the following relation:
cos(A) = a/c.
More can be learned about relations in a right triangle at brainly.com/question/26396675
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Associative property of multiplication which states :
(a * b) * c = a * (b * c)
