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Anit [1.1K]
3 years ago
6

Use substitution to solve the system of equations.

Mathematics
2 answers:
polet [3.4K]3 years ago
8 0
The answer is (3,-6)
murzikaleks [220]3 years ago
4 0
X-3*(-2x)=21
x+6x=21
7x=21
X=21/7
X=3
Now you substitute x=3 in the other equation
Y=-2*3
Y=-6
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Maria works as a part- time waitress and earns $30 per day plus 2% of all sales of food and drinks during the day
ollegr [7]

Answer:

y = 30 + 0.02x

Step-by-step explanation:

Required

Write an equation to present her daily earnings?

Let daily sales be represented by x and daily earnings be represented by y.

y is calculated as thus;

y = Earnings + Commission * Sales

y = 30 + 2\% * x

Convert percentage to decimal

y = 30 + 0.02 * x

y = 30 + 0.02x

Hence, her daily earnings is y = 30 + 0.02x

5 0
3 years ago
A cola company decides to test five different brands of soft drink. The different brands have been labeled F, G, H, I, and J. Th
Yuki888 [10]

The answer is B) 20

Because you have 5 brands and you combine each with the 4 others, so 5*4=20


8 0
3 years ago
Read 2 more answers
Please help w this! Its a calculus question! look at the picture for the problem,
neonofarm [45]

Since you mentioned calculus, perhaps you're supposed to find the area by integration.

The square is circumscribed by a circle of radius 6, so its diagonal (equal to the diameter) has length 12. The lengths of a square's side and its diagonal occur in a ratio of 1 to sqrt(2), so the square has side length 6sqrt(2). This means its sides occur on the lines x=\pm3\sqrt2 and y=\pm3\sqrt2.

Let R be the region bounded by the line x=3\sqrt2 and the circle x^2+y^2=36 (the rightmost blue region). The right side of the circle can be expressed in terms of x as a function of y:

x^2+y^2=36\implies x=\sqrt{36-y^2}

Then the area of this circular segment is

\displaystyle\iint_R\mathrm dA=\int_{-3\sqrt2}^{3\sqrt2}\int_{3\sqrt2}^{\sqrt{36-y^2}}\,\mathrm dx\,\mathrm dy

=\displaystyle\int_{-3\sqrt2}^{3\sqrt2}(\sqrt{36-y^2}-3\sqrt2)\,\mathrm dy

Substitute y=6\sin t, so that \mathrm dy=6\cos t\,\mathrm dt

=\displaystyle\int_{-\pi/4}^{\pi/4}6\cos t(\sqrt{36-(6\sin t)^2}-3\sqrt2)\,\mathrm dt

=\displaystyle\int_{-\pi/4}^{\pi/4}(36\cos^2t-18\sqrt2\cos t)\,\mathrm dt=9\pi-18

Then the area of the entire blue region is 4 times this, a total of \boxed{36\pi-72}.

Alternatively, you can compute the area of R in polar coordinates. The line x=3\sqrt2 becomes r=3\sqrt2\sec\theta, while the circle is given by r=6. The two curves intersect at \theta=\pm\dfrac\pi4, so that

\displaystyle\iint_R\mathrm dA=\int_{-\pi/4}^{\pi/4}\int_{3\sqrt2\sec\theta}^6r\,\mathrm dr\,\mathrm d\theta

=\displaystyle\frac12\int_{-\pi/4}^{\pi/4}(36-18\sec^2\theta)\,\mathrm d\theta=9\pi-18

so again the total area would be 36\pi-72.

Or you can omit using calculus altogether and rely on some basic geometric facts. The region R is a circular segment subtended by a central angle of \dfrac\pi2 radians. Then its area is

\dfrac{6^2\left(\frac\pi2-\sin\frac\pi2\right)}2=9\pi-18

so the total area is, once again, 36\pi-72.

An even simpler way is to subtract the area of the square from the area of the circle.

\pi6^2-(6\sqrt2)^2=36\pi-72

6 0
3 years ago
Find the slope of the line graphed
Marrrta [24]

Answer:

Slope = -1.5

Step-by-step explanation:

The two points are: (1, 1) and (3, -2)

Slope = (-2 - 1) / (3 - 1)

Slope = -1.5

3 0
3 years ago
Read 2 more answers
The vertices of the image of GHJK after a translation are given. Choose the vector that describes the translation.
Lady_Fox [76]

Answer:

Option B

Step-by-step explanation:

Let's take a vertex G of quadrilateral GHJK to understand the rule for the translation,

From the graph attached,

Coordinates of G → (-5, 5)

Coordinates of the image point G' after the translation → G'(-5, 5)

Let the point G is translated 'a' units to the right and 'b' units down,

Rule for this translation,

G(x, y) → G'(x + a, y - a)

By this rule,

G(-5, 5) → G'(-5 + a, 5 - a)

-5 + a = -5 ⇒ a = 0

5 - a = 5 ⇒ a = 0

Therefore, vector that defines the translation will be,

<0, 0>

Option B is the the correct option.

8 0
3 years ago
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