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2 years ago

Graph the following exponential function given the table of values.

Mathematics

1 answer:

Radda [10]2 years ago

7 0

Answer:

Step-by-step explanation:

Here, we want to select the graph of the given exponential function values

Let us take a look at the y-intercept

At the y-intercept, the value of x is 0

The y-intercept for this particular equation is 1

This mean that the y-intercept value is 1

hence, the graph will touch the y-axis at the point y = 1

looking at the graphs , only the graph D provides this, and that should be our answer

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Can someone help me draw this out to visualize it?

Vedmedyk [2.9K]

Answer:

Solution given:

South distance :base[b]=80milea

East distance :perpendicular [p]=35miles

Now

<S=?

we have

$\tan( \alpha ) = \frac{p}{b} = \frac{35 }{80}$

$\alpha = \tan {}^{ - 1} ( \frac{7}{16} )$

$\alpha = 23.629°$ =24°

24° bearing should be taken from south airport to East airport.

3 0

3 years ago

3. What are the intersection points of the line whose equation is y=3x +3 and the

densk [106]

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

→ (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = $\frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}$

x = $\frac{-7\pm \sqrt{169}}{10}$

x = $\frac{-7\pm13}{10}$

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

6 0

3 years ago

Write the following quotient in the form a+bi.<br> -7i/2-7i

Helga [31]

Answer:

$\large\boxed{\dfrac{49}{53}-\dfrac{14}{53}i}$

Step-by-step explanation:

$\text{Use}\\\\i=\sqrt{-1}\to i^2=-1\\\\(a-b)(a+b)=a^2-b^2\to(a-bi)(a+bi)=a^2+b^2\\\\\text{distributive property}\ a(b+c)=ab+ac\\---------------------\\\\\dfrac{-7i}{2-7i}=\dfrac{-7i}{2-7i}\cdot\dfrac{2+7i}{2+7i}=\dfrac{-7i(2+7i)}{2^2+7^2}=\dfrac{(-7i)(2)+(-7i)(7i)}{4+49}\\\\=\dfrac{-14i-49i^2}{53}=\dfrac{-14i-49(-1)}{53}=\dfrac{-14i+49}{53}\\\\=\dfrac{49}{53}-\dfrac{14}{53}i$