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15 days ago

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and peach pie, p, requires 8 apples. The bake

r receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?
t ≤ 40
p ≤ 184
t ≤ 40
8p ≤ 184
t ≤ 40
p + 8t ≤ 184
t ≤ 40
8p + t ≤ 184
the answer is D is the answer

Mathematics

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Sam receives the following scores on his English tests: 63, 84, and 96. What average score does he need on the last two tests in

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Sam needs to score 97 on his upcoming test to keep his average at 85. If you total 63, 84, 96, and 97, the sum is 340. Dividing 340 by four test scores yields an exact average of 85.

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2 months ago

Suma numerelor de forma a4b cu produsul cifrelor 24 este egala cu

AnnZ [12381]

Answer:

The correct response is: b)

Step-by-step explanation:

a4b=24, where a × 4 × b = 24 implies a × b = 6

The pairs of numbers with a product of 6 include: {1,6} and {2,3}

In base 10, a4b translates to 100a + 40 + b

Calculating gives us:

100×1+40+6=146

100×6+40+1=641

100×2+40+3=243

100×3+40+2=342

Summing these results yields: 146 + 641 + 243 + 342 = 1372

The correct answer is: b)

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3 months ago

Write f(x) = 2x2 44x + 185 in vertex form. to write f(x) = 2x2 44x + 185, factor out from the first two terms. next, form a perf

zzz [12365]

The equation is:
f(x) = 2x² - 44x + 185
f(x) = 2(x² - 22x + 121 - 121) + 185 =
= 2(x² - 22x + 121) - 242 + 185 =
= 2(x - 11)² - 57
Conclusion:
The vertex is located at (11, -57) and the vertex form is: f(x) = 2(x - 11)² - 57

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2 months ago

Read 2 more answers

A flat circular plate has the shape of the region x2 + y2≤1. The plate, including the boundary where x2 + y2 = 1, is heated such

Leona [12618]

Setting both partial derivatives to zero results in a single critical point at $(x,y)=\left(\dfrac12,0\right)$ , located within the unit disk.

At this given point, the derivative value of the Hessian matrix is

$|H|=\begin{vmatrix}T_{xx}&T_{xy}\\T_{yx}&T_{yy}\end{vmatrix}=\begin{vmatrix}2&0\\0&4\end{vmatrix}=8>0$

and the second-order partial derivative with respect to $x$ yields

$T_{xx}\bigg|_{(x,y)=(1/2,0)}=2>0$

This suggests that the critical point represents a local minimum, marking it as the coldest area on the plate with a temperature of $T\left(\dfrac12,0\right)=-\dfrac14$ .

To find the hottest area on the plate, it must be located along the boundary. Let $x=\cos\theta$ and $y=\sin\theta$ , so that

$T(x,y)=T(\theta)=\cos^2\theta+2\sin^2\theta-\cos\theta$
$T(\theta)=\dfrac32-\cos\theta-\dfrac12\cos2\theta$

Thus, the plate's boundary (the circle $x^2+y^2=1$ ) is treated as a single variable function $\theta$ examined over $\theta\in[0,2\pi)$ . A single differentiation gives

$T'(\theta)=\sin\theta+\sin2\theta=0$
$\implies\theta=0,\theta=\dfrac{2\pi}3,\theta=\pi,\theta=\dfrac{4\pi}3$

You will discover that $T(\theta)$ achieves three extrema on the interval $(0,2\pi)$ , with relative maxima occurring at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , and a relative minimum at $\theta=\pi$ (and $\theta=0$ , if you wish to include that).

Our minimum has already been identified inside the plate - which you can check to have a lower temperature than at the points noted by $T(\theta)$ - and we identify two maxima at $\theta=\dfrac{2\pi}3$ and $\theta=\dfrac{4\pi}3$ , both showing a maximum temperature of $T=\dfrac94$ .

Reverting to Cartesian coordinates, these points match up with $\left(-\dfrac12,\pm\dfrac{\sqrt3}2\right)$ .

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