One step equation

If log10(x^{2}y^{3})=7 and log10 (x/y)=1 , then x=__ and y= __

yuradex [85]

Answer:

$x=100$

$y=10$

Step-by-step explanation:

we are given

$log_1_0(\frac{x}{y})=1$

Firstly, we will get rid of log

so, we will take exponent over 10 on both sides

$10^{log_1_0(\frac{x}{y})}=10^{1}$

now, we can simplify it

$\frac{x}{y}=10$

now, we can solve for x

$x=10y$

we are given

$log_1_0(x^2y^3)=7$

Firstly, we will get rid of log

so, we will take exponent of 10 on both sides

$10^{log_1_0(x^2y^3)}=10^7$

$x^2y^3=10^7$

now, we can plug back x from first equation

$(10y)^2y^3=10^7$

now, we can solve for y

$100y^5=10000000$

$\frac{100y^5}{100}=\frac{10000000}{100}$

$y^5=100000$

now, we can take radical 5

$y=\sqrt[5]{100000}$

$y=10$

now, we can find x

$x=10\times 10$

$x=100$

So, solution is

$x=100$

$y=10$

4 0

4 years ago

What is the area of ABC?

notsponge [240]

Let D be the Intersection of Height of the Triangle and Base of the Triangle BC

From the Figure, We can notice that Triangle ADB is a Right angled Triangle.

We know that, In a Right angled Triangle :

$\bigstar$ (Hypotenuse)² = (First Leg)² + (Second leg)²

In Triangle, ADB : AB is the Hypotenuse, AD is the First leg and BD is the Second leg

Given : AB = 15 and BD = 9

Substituting the values, We get :

$:\implies$ (15)² = (AD)² + (9)²

$:\implies$ 225 = (AD)² + 81

$:\implies$ (AD)² = 225 - 81

$:\implies$ (AD)² = 144

$:\implies$ (AD)² = (12)²

$:\implies$ AD = 12

We know that, In a Right angled Triangle :

$\bigstar\;\;\boxed{\mathsf{Tan\theta = \dfrac{Opposite\;Side}{Adjacent\;Side}}}$

Now, Consider Triangle ADC : With respect to 45° Angle, AD is the Opposite Side and DC is the Adjacent Side

$:\implies \mathsf{In\;Triangle\;ADC,\;Tan45^{\circ} = \dfrac{AD}{DC}}$

$\mathsf{:\implies 1 = \dfrac{12}{DC}}$

$:\implies$ DC = 12

$:\implies$ Total Length of the Base (BC) = BD + DC

$:\implies$ Total Length of the Base (BC) = 9 + 12

$:\implies$ Total Length of the Base (BC) = 21

We know that, Area of the Triangle is given by :

$\bigstar\;\;\boxed{\mathsf{Area = \dfrac{1}{2} \times Base \times Height}}$

In Triangle, ABC : AD is the Height and BC is the Base

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times BC \times AD}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times 21 \times 12}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = (21 \times 6)}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = 126}$

7 0

4 years ago

The first figure contains 2 dots, the second 6 dots, and the third 12 dots. If the pattern continues, how many dots would the te

PIT_PIT [208]

Answer: 110

The 3 figures showed the same pattern by multiplying 2 consecutive whole numbers starting from one. Multiplying 1 by 2 gets 2, 2 by 3 gets 6, 3by 4 results to 12 and so on. If this pattern continues, then 4 will be multiplied by 5, 5 by 6, 6 by 7, 7 by 8, 8 by 9, 9 by 10, and lastly the 10th figure 10 by 11 which is equal to 110.

4 0

3 years ago

I =125 r=6% t=1 what is p

vfiekz [6]

There is no P in here, you can't solve for P without a P, Or I just don't get the question.

4 0

4 years ago

Provide an example of a trig function that includes multiple transformations. Describe how it is different from the standard tri

klio [65]

An example of a trig function that includes multiple transformations and how it is different from the standard trig function is; As detailed below

<h3>How to interpret trigonometric functions in transformations?</h3>

An example of a trigonometric function that includes multiple transformations is; f(x) = 3tan(x - 4) + 3

This is different from the standard function, f(x) = tan x because it has a vertical stretch of 3 units and a horizontal translation to the right by 4 units, and a vertical translation upwards by 3.

Another way to look at it is by;

Let us use the function f(x) = sin x.

Thus, the new function would be written as;

g(x) = sin (x - π/2), and this gives us;

g(x) = sin x cos π/2 - (cos x sin π/2) = -cos x

This will make a graph by shifting the graph of sin x π/2 units to the right side.

Now, shifting the graph of sin xπ/2 units to the left gives;

h(x) = sin (x + π/2/2)

Read more about Trigonometric Functions at; brainly.com/question/4437914

#SPJ1

5 0

2 years ago