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ASHA 777 [7]
3 years ago
15

Given the conditional statement, match the following. Conditional statement: If two lines intersect, then their intersection is

one point.
Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
8 0

Answer:

If two lines meet at exactly one point, then those two lines intersect.

Step-by-step explanation:


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At a construction job for a mansion there are 37 painters. Of these painters, 67.6% of them paint the interior of the mansion. H
Inessa05 [86]
This is a relatively easy question to answer. You want to find 67.6% OF 37 mean you need to multiply. 37*0.676≈25. There should be 25 painters painting the interior.
3 0
3 years ago
Brian pays £475.29 a year on his car insurance. The insurance company reduces the price by 2.1%.
Nookie1986 [14]

Answer:

470.12??? not sure!!!!

Step-by-step explanation:

3 0
3 years ago
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135,000 total annual income . What is the amount is budgeted for clothing ???
Natalija [7]
15%/100%×$135,000
=15/1×$1,350
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$20,250 Is Budgeted For Clothing.
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4 years ago
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Two improper fractions that have the same decimal form as 188/11
Savatey [412]
Double then triple both the numerator and denominator
remember any number divide by itself is 1(value will not change)
188/11 x 2/2= 376/22
188/11 x 3/3= 564/33

they all reduce to 188/11= 17.09

hope this helps
6 0
3 years ago
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Find the extreme values of f subject to both constraints f(x,y) = 2x^2+3y^2-4x-5, x^2 + y^2 <=16
Softa [21]
f(x,y)=2x^2+3y^2-4x-5
f_x=4x-4=0\implies x=1
f_y=6y=0\implies y=0

f(x,y) has only one critical point at (x,y)=(1,0). The function has Hessian

\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}4&0\\0&6\end{bmatrix}

which is positive definite for all (x,y), which means f(x,y) attains a minimum at the critical point with a value of f(1,0)=-7.

To find the extrema (if any) along the boundary, parameterize it by x=4\cos t and y=4\sin t, with 0\le t. On the boundary, we have

f(x(t),y(t))=F(t)=2(4\cos t)^2+3(4\sin t)^2-4(4\cos t)-5=32\cos^2t+48\sin^2t-16\cos t-5
F(t)=35-16\cos t-8\cos2t

Find the critical points along the boundary:

F'(t)=16\sin t+16\sin2t=16\sin t+32\sin t\cos t=16\sin t(1+2\cos t)=0
\implies t=0,\dfrac{2\pi}3,\pi,\dfrac{4\pi}3

Respectively, plugging these values into F(t) gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when F(t)=47.

Now, solve for x,y for both cases:

t=\dfrac{2\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=2\sqrt3\end{cases}

t=\dfrac{4\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=-2\sqrt3\end{cases}

so f(x,y) has two absolute maxima at (x,y)=(-2,\pm2\sqrt3) with the same value of 47.
5 0
3 years ago
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