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2 years ago

A pair of equations is shown below: y = 6x + 9 y = 7x + 7 What is the solution to the pair of equations?

Mathematics

1 answer:

dimaraw [331]2 years ago

4 0

Answer:

x=2, y= 21

Step-by-step explanation:

y = 6x + 9

y = 7x + 7

Since both equations are equal to y, we can set them equal to each other

6x+9 = 7x+7

Subtract 6x from each side

6x+9-6x = 7x -6x+7

9 = x+7

Subtract 7 from each side

9-7 = x+7-7

x=2

Now we need to find y

y = 6x+9

y = 6(2) +9

y = 12 +9

y = 21

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Find the measure of each angle indicated. Show work.

kirza4 [7]

Answer:

? = 109 degrees

Step-by-step explanation:

45 + 75 + _ = 180 ( look for vertical angles)

45 + 75 + 60 = 180

60 +79 + _ = 180 (look for a straight line that forms 180 degrees)

60 + 79 + 41 = 180

68 + 41 + _ = 180 (look for a triangle that adds up to 180)

68 + 41 + 71 =180

180 - 71 = 109 (look for a linear pair)

3 0

2 years ago

Find the derivative.

Aleksandr [31]

Answer:

Using either method, we obtain: $t^\frac{3}{8}$

Step-by-step explanation:

a) By evaluating the integral:

$\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du$

The integral itself can be evaluated by writing the root and exponent of the variable u as: $\sqrt[8]{u^3} =u^{\frac{3}{8}$

Then, an antiderivative of this is: $\frac{8}{11} u^\frac{3+8}{8} =\frac{8}{11} u^\frac{11}{8}$

which evaluated between the limits of integration gives:

$\frac{8}{11} t^\frac{11}{8}-\frac{8}{11} 0^\frac{11}{8}=\frac{8}{11} t^\frac{11}{8}$

and now the derivative of this expression with respect to "t" is:

$\frac{d}{dt} (\frac{8}{11} t^\frac{11}{8})=\frac{8}{11}\,*\,\frac{11}{8}\,t^\frac{3}{8}=t^\frac{3}{8}$

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:

"If f is continuous on [a,b] then

$g(x)=\int\limits^x_a {f(t)} \, dt$

is continuous on [a,b], differentiable on (a,b) and $g'(x)=f(x)$

Since this this function $u^{\frac{3}{8}$ is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:

$\frac{d}{dt} \int\limits^t_0 {u^\frac{3}{8} } } \, du=t^\frac{3}{8}$

5 0

2 years ago

Use the diagram below to answer the question.

Lunna [17]

Answer:

The length of shadow is 69 foot.

Step-by-step explanation:

We are given a shadow of lighthouse.

Length of top of lighthouse to end of shadow is 90 ft.

Angle make at top of lighthouse is 50°

Distance from foot of lighthouse to end of shadow is x ft.

we need to find the length of shadow i,e x ft

Using trigonometry ration:

$\sin\theta=\dfrac{P}{H}$

$\sin50^\circ=\dfrac{x}{90}$

$x=90\times 0.766$

$x=68.94\approx 69\text{ ft}$

Hence, The length of shadow is 69 foot.

7 0

3 years ago

What is the measure of YB ?

BARSIC [14]

Answer:

YB = 12

Step-by-step explanation:

The product of the measures of the parts of one chord are equal to the product of the measures of the parts of the other chord, that is

7YB = 6 × 14 = 84 ( divide both sides by 7 )

YB = 12

3 0

2 years ago

L 7.8.2 Test (CST): Area, Surface Area, and Volume Question 24 of 30 Find the area of the sector of the circle below. The radius

lawyer [7]

Answer:

28.26 cm^2

Step-by-step explanation:

Mathematically, we have the area of a sector as;

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Substituting these values;

90/360 * 3.14 * 6^2 = 28.26 cm^2

6 0

2 years ago