Answer:
59°
Step-by-step explanation:
In triangle DAB, by Pythagoras theorem:
Next, in triangle DCB, by Pythagoras theorem:
Now, by sin rule.
Answer:
Therefore either a:b = 5:4 or a:b=-5:4
Step-by-step explanation:
ax²-5bx+4a=0
Since the quadratic equation has two real root.
Then b²-4ac>0
Here a= a , b= -5b and c=4a
∴(-5b)²-4.a.4a=0
⇔25b²=16a²
⇔5b=±4a
Therefore either a:b = 5:4 or a:b=-5:4
Dilation is a transformation of scaling that requires a center of scaling and a factor of scaling.
Similarity is a relationship between two figures when there is a special transformation that transforms one figure into another.
This transformation can include any combination of rotation, shift and dilation.
That's why a pair of a source and its image after dilation are similar, but not all similar figures can be connected by dilation. For instance, rotation and/or shift transform a figure into another, similar one to the original, but not related through dilation..
Answer:
Step-by-step explanation:
Apply the 30-60-90 formula
side between 60 and 90 is x
side between 90 and 30 is 
side between 90 and 30 is 2x
If =
then x=
Answer:
4<em>s</em> + 10<em>p</em> <= 100
<em>p</em> >= 5
Step-by-step explanation:
So it's important to remember here that this isn't one linear inequality to represent everything, it's a system. One of the inequalities that are part of the answer won't answer the entire question by itself, so don't worry about that. It might sound like tedious work, but you can break it down pretty easily into logic.
So the soil costs Marsha $4 per bag, and the plants cost her $10 each. She can't spend more than $100 dollars.
Let <em>p</em> = number of plants and let <em>s</em> = number of bags of soil
If each soil bag costs her $4, then 4<em>s</em> is the amount she spends on soil (4 [which is the cost of each individual soil bag] x number of bags = total cost of soil bags).
If each plant costs her $10, then 10<em>p</em> is the amount she spends on plants (same logic).
Because she can't spend more than $100 on both soil and plants together,
4<em>s</em> + 10<em>p</em> has to be less than or equal to 100.
4<em>s</em> + 10<em>p</em> <= 100
Since she wants to buy at least 5 plants, <em>p</em> has to be greater than or equal to 5.
<em>p</em> >= 5
And there you have it! Your system of inequalities is:
4<em>s</em> + 10<em>p</em> <= 100
<em>p</em> >= 5
Pretty simple c:
