If you could help me with this i would be very thankful
1 answer:
Answer:
Δ QRS is an obtuse triangle ⇒ according to its angle
Δ QRS is an isosceles triangle ⇒ according to its sides
Step-by-step explanation:
In Δ QRS
∵ m∠Q = 8x - 17
∵ m∠R = 19x + 4
∵ m∠S = 5x + 1
→ The sum of the interior angles of a Δ is 180°
∴ m∠Q + m∠R + m∠S = 180°
→ Substitute their values in the equation above
∵ 8x - 17 + 19x + 4 + 5x + 1 = 180
→ Add the like terms
∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180
∴ 32x + (-12) = 180
∴ 32x - 12 = 180
→ Add 12 to both sides
∵ 32x - 12 + 12 = 180 + 12
∴ 32x = 192
→ Divide both sides by 32
∵ =
∴ x = 6
→ Substitute the value of x in each measure of angles to find them
∵ m∠Q = 8(6) - 17 = 48 - 17
∴ m∠Q = 31°
∵ m∠R = 19(6) + 4 = 114 + 4
∴ m∠R = 118°
∵ m∠S = 5(6) + 1 = 30 + 1
∴ m∠S = 31°
∵ m∠R > 90°
∴ ∠R is an obtuse angle
∴ Δ QRS is an obtuse triangle
∵ m∠Q = m∠S
→ In any Δ if two angles are equal in measures, then the two sides
opposite to these angles are equal in length and the Δ is isosceles
∴ RQ = RS
∴ Δ QRS is an isosceles triangle
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Answer:
P(Z < 2.37) = 0.9911.
Step-by-step explanation:
We are given that Let z denote a random variable that has a standard normal distribution.
Let Z = a random variable
So, Z ~ Standard Normal(0, 1)
As we know that the standard normal distribution has a mean of 0 and variance equal to 1.
Z = ~ N(0,1)
where, = mean = 0
= standard deviation = 1
Now, the probability that z has a value less than 2.37 is given by = P(Z < 2.37)
P(Z < 2.37) = P(Z < ) = P(Z < 2.37) = 0.9911
The above probability is calculated by looking at the value of x = 2.37 in the z table which has an area of 0.9911.
Answer:
A
Step-by-step explanation:
We have the expression:
And we want to find its sign given that a>0 and b<0.
Notice that the expression is already negative since we have -4.
a>0 means that a is positive. Therefore, we can ignore it since it won’t do anything.
b<0 means that b is negative. Therefore, we will have two negatives being multiplied together. Hence, this will make a positive.
Therefore, the sign of our expression will be positive.
We can see this with an example. Let a=1 (1>0) and let b=-1 (-1<0). Then:
So, the sign is positive.
Hence, the answer is A.
Answer:
80
Step-by-step explanation:
Think of it as a Venn diagram. One circle is the people who like dogs, and one circle is the people who like cats. The overlap is people who like both dogs and cats.
190 people in the survey said they like dogs. That includes the people who like both dogs and cats.
141 people in the survey said they like cats. That includes the people who like both dogs and cats.
If we simply add the two numbers together, we'll be counting the overlap twice. So to find the total number of people who like dogs or cats, we have to subtract one overlap.
dogs or cats = 190 + 141 − x
Therefore:
190 + 141 − x + 88 = 339
419 − x = 339
x = 80
80 people said they liked both cats and dogs.
