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3 years ago

Solve the following problems. Find x, y

Mathematics

2 answers:

natta225 [31]3 years ago

7 0

Step-by-step explanation:

by using similarity and enlargement

10/8 = 7+y/7

70=56+8y

8y=14

y= 7/4

10/8 = 5+x/5

50=40+8x

x = 8/10 = 4/5

siniylev [52]3 years ago

3 0

Step-by-step explanation:

7/7+y=8÷10

46+8y=70(Cross multiply)

8y=70-46

y=24÷8

y=3

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Which of these statements is true for f(x)=(1/10)^x

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Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Analyzing option A)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Putting $x = 1$ in the function

$f\left(1\right)=\:\left(\frac{1}{10}\right)^1$

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Therefore, the statement that '' The graph contains $\left(1,\:\frac{1}{10}\right)$ '' is TRUE.

Analyzing option B)

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The range of the function is the set of values of the dependent variable for which a function is defined.

$\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k$

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$\mathrm{Range\:of\:}\left(\frac{1}{10}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

Therefore, the statement that ''The range of $f(x)$ is $y > \frac{1}{10}$ " is FALSE

Analyzing option C)

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$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The domain of the function is the set of input values which the function is real and defined.

As the function has no undefined points nor domain constraints.

So, the domain is $-\infty \:$

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$\mathrm{Domain\:of\:}\:\left(\frac{1}{10}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Therefore, the statement that ''The domain of $f(x)$ is $x>0$ '' is FALSE.

Analyzing option D)

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$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

As the base of the exponential function is less then 1.

i.e. 0 < b < 1

Thus, the function is decreasing

Also check the graph of the function below, which shows that the function is decreasing.

Therefore, the statement '' It is always increasing '' is FALSE.

Keywords: function, exponential function, increasing function, decreasing function, domain, range

Learn more about exponential function from brainly.com/question/13657083

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