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3 years ago

The graph below could be the graph of which exponential function?

Mathematics

2 answers:

Akimi4 [234]3 years ago

8 0

Consider this option:
according to the attached graph there is a decreasing function.
If a decreasing function is an exponential function y=a× it means, that a∈(0;1).
This property is performed in answer 'B' only, its equation is y=2*(0,5)×.

answer: B.

Aneli [31]3 years ago

7 0

Answer:

The correct option is B.

Step-by-step explanation:

The general form of an exponential function is

$f(x)=ab^x$

Where, a is the initial value of the function and b is the growth factor.

If b>1, then f(x) is an increasing function and if b<1, then f(x) is an decreasing function

From the given graph it is noticed that the initial value of the function is 2. It means the value of a is 2.

The graph shows that the function is a decreasing function, therefore the value of b must be less than 1.

It means the required function is in the form of

$F(x)=2(b)^x$

Where, b<1.

In option B, b=0.5<1, therefore option B is correct.

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Which equation best fits the graphed data?

fenix001 [56]

Answer:

hmm

Step-by-step explanation:

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2 years ago

The sum of three consecutive positive numbers is 147. Find the product of the greatest and the

Dima020 [189]

Answer:

2400

Step-by-step explanation:

x+y+z=147

x+(x+1)+(x+2)=147

3x+3=147

3x=144

x=48

The three consecutive positive numbers are 48, 49, and 50.

48 • 50 = 2400

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2 years ago

Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k

masha68 [24]

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

−2k−4k+12

D=k^2-6k+13D=k

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

6 0

3 years ago

In the xy-plane, line l has a y-intercept of -13 and is perpendicular to the line with the equation y=-2/3x. If the point (10, b

AlekseyPX

Answer:

The value of $b$ is 2.

Step-by-step explanation:

The standard form of the equation of the line is of the form:

$y = m\cdot x + k$

Where:

$x$ , $y$ - Independent and dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$k$ - y-intercept, dimensionless.

Given that line $l$ is perpendicular to $y = -\frac{2}{3}\cdot y$ , the slope is equal to:

$m = -\frac{1}{m_{\perp}}$

Where $m_{\perp}$ is the slope of the perpendicular line, dimensionless.

If $m_{\perp} = -\frac{2}{3}$ , then:

$m = -\frac{1}{\left(-\frac{2}{3}\right) }$

$m = \frac{3}{2}$

If $x = 0$ and $y = -13$ , the y-intercept of the line $l$ is:

$-13 = \frac{3}{2}\cdot (0) +k$

$k = -13$

The equation of the line $l$ is $y = \frac{3}{2}\cdot x -13$ . Given that $y = b$ and $x = 10$ , the value of $b$ is:

$b = \frac{3}{2}\cdot (10)-13$

$b = 15-13$

$b = 2$

The value of $b$ is 2.

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3 years ago

If 3/7 is written as a decimal,will the digits after the decimal repeat

LekaFEV [45]

Answer:

Step-by-step explanation:

5 0

3 years ago