Answer:
5 + 2(3 + 2x) = x + 3(x + 1) has no solution
Step-by-step explanation:
Answer:
C. Similarity cannot be determined
Step-by-step explanation:
Two triangles are considered similar when all three angles are equal and also when the ratio of their corresponding side lengths are equal.
Since we only know the angles of the two triangles given and we are not given the side lengths to determine if their corresponding ratio is the same, we therefore cannot determine if the two triangles are similar in anyway.
The estimate would be 1200.
We will set up a proportion for this. 10 out of 60 of the sample were tagged, so that is the first ratio. The 200 that were tagged would be in the numerator of the second ratio (10 was the portion tagged, and 200 is the portion tagged, so they both go on top). We do not know the total number so we use a variable:
10/60 = x/200
Cross multiply:
10*x = 60*200
10x = 12000
Divide both sides by 10:
10x/10 = 12000/10
x = 1200
Answer:
The scale factor is 18 to 1 for the painting
Step-by-step explanation:
Here we want to get the scale factor of the original to what is reproduced
Let us have same units first
Mathematically;
1 foot = 12 inches
3 feet = 36 inches
2 feet = 24 inches
So 36 to 2 and 24 to 1 1/3
That will be ratio 36/2 = 18 to 1
same as 25 divided by 1 1/3 = 18 to 1
Vertex form of a parabola
<span>y = a (x - h)^2 + k </span>
<span>where (h, k) is the vertex </span>
Substituting the values of h and k.
we get,
<span>y = a(x + 4)^2 + 2 </span>
<span>substituting in the point (0, -30) for x and y
</span><span>-30 = a (0 + 4)^2 + 2
</span>solve for a,
<span>-30 = 16 a + 2 </span>
<span>-32 = 16 a </span>
<span>-2 = a </span>
<span>y = -2(x + 4)^2 + 2 </span>
<span>Put y = 0 </span>
<span>-2 x^2 - 16 x - 30 = 0 </span>
<span>-2(x^2 + 8 x + 15) = 0 </span>
<span>x^2 + 8 x + 15 = 0 </span>
<span>(x + 3)(x + 5) = 0 </span>
<span>x = -3
x = -5</span>
