K - 5 = 12. Solve the equation

Show that Circle R with center (2, -9) and radius 5 is similar to Circle Q with center (-4, 3) and radius 3 by using a series of

faltersainse [42]

Answer:

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

Step-by-step explanation:

We can demonstrate that Circle R is similar to Circle Q by translating the center of the former one to the center of latter one. Meaning that every point of circle R experiments the same translation. Vectorially speaking, a translation is defined by:

$O'(x,y) = O(x,y) + T(x,y)$ (1)

Where:

$O(x,y)$ - Original point.

$O'(x,y)$ - Translated point.

$T(x,y)$ - Translation vector.

If we know that $O(x,y) = (2,-9)$ and $O'(x,y) = (-4,3)$ , then the translation vector is:

$T(x,y) = O'(x,y)-O(x,y)$

$T(x,y) = (-4,3) - (2,-9)$

$T(x,y) = (-6,12)$

It can be proved that the circle R is similar to the circle Q by translating the circle R a displacement of (-6, 12).

4 0

3 years ago

What is the inverse of the function f(x) = x +3?

MAXImum [283]

Answer:

f⁻¹(x) = x - 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Functions
Function Notation
Inverse Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x + 3

Step 2: Find

Swap: x = y + 3
[Subtraction Property of Equality] Isolate y: x - 3 = y
Rewrite: f⁻¹(x) = x - 3

6 0

3 years ago

the sum of the perimeter of two squares is 40cm while the sum of the area is 58cm². Find length the side of the square.

tia_tia [17]

$a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}$

$\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}$

8 0

4 years ago

A finite geometric series is the sum of a sequence of numbers. Take the sequence 1, 2, 4, 8, … , for example. Notice that each n

Anna [14]

Answer:

Step-by-step explanation:

3 0

3 years ago

The mean hourly wage for employees in industries is currently $24.57. Suppose we take a sample of employees from the manufacturi

Mashutka [201]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ = $24.57

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $24.57

(b) The P-value of the test statistics is 0.1212.

(c) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using P-value approach.

(d) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using critical value approach.

Step-by-step explanation:

We are given that a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the U.S industries.

Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour.

Let $\mu$ = population mean hourly wage in the manufacturing industry.

(a) Null Hypothesis, $H_0$ : $\mu$ = $24.57 {means that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $24.57 {means that the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the U.S industries}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean wage in the manufacturing industry = $23.89/hr

σ = population standard deviation = $2.40/hr

n = sample of employees from the manufacturing industry = 30

So, the test statistics = $\frac{23.89-24.57}{\frac{2.40}{\sqrt{30} } }$

= -1.55

The value of z test statistics is -1.55.

(b) Now, the P-value of the test statistics is given by;

P-value = P(Z < -1.55) = 1 - P(Z $\leq$ 1.55)

= 1 - 0.9394 = 0.0606

For two-tailed test P-value is calculated as = 0.0606 $\times$ 2 = 0.1212

Since, the P-value of the test statistics is higher than the level of significance as 0.1212 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.

(d) Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.

6 0

3 years ago