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3 years ago

Which transformation will always create congruent figures

1 answer:

5 0

Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figureis not changed, then the figures are congruent.

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What is an equation of a circle whose center is (1,4) and diameter is 10?

nexus9112 [7]

Answer:

$x^{2} - 2x + y^{2} - 8y = 8$

Step-by-step explanation:

Standard form for a circle is:

$(x - h)^{2} + (y - k)^{2} = r^{2}$ (h, k) is the center r is the radius

$(x - 1)^{2} + (y - 4)^{2} = 5^{2} \\x^{2} - 2x + 1 +y^{2} - 8y + 16 = 25\\x^{2} - 2x + y^{2} - 8y = 8$ $x^{2} - 2x + y^{2} - 8y = 8$

6 0

3 years ago

Rewrite <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bn%5E%7B3%7Dp%5E%7B4%7D%20%20%7D" id="TexFormula1" title="\sqrt{n^{3}p^{4} }

givi [52]

Answer:

${n}^{1\frac{1}{2}}{p}^{2}$

Step-by-step explanation:

According to the Definition of Rational Exponents, use this formula to rewrite this as an exponential expression:

$a^{\frac{m}{n}} = \sqrt[n]{a}^{m}$

NOTE: Since we have exponents in our radical, we have to multiply all exponents by one-half, since raising something to its half power is the exact same as taking the square root of something:

$[{n}^{3}{p}^{4}]^{\frac{1}{2}} = {n}^{1\frac{1}{2}}{p}^{2}$

* Do not forget to remove the radical in the beginning because you are once again, rewriting this as an exponential expression.

I am joyous to assist you anytime.

6 0

4 years ago

Read 2 more answers

In a survey of 1005 adults, a polling agency asked, "When you retire, do you think you will have enough money to live comfort

Sphinxa [80]

Answer: (0.504, 0.556)

Step-by-step explanation:

Given : Sample size : n= 1005

Number of adults stated that they were worried about having enough money to live comfortably in retirement = 531

Then the proportion of adults stated that they were worried about having enough money to live comfortably in retirement : $p=\dfrac{531}{1005}\approx0.53$

Significance level : $\alpha: 1-0.90=0.1$

Critical value : $z_{\alpha/2}=1.645$

The confidence interval for population proportion is given by :-

$p\pm\ z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.53\pm(1.645)\sqrt{\dfrac{0.53(1-0.53)}{1005}}\\\\\approx0.53\pm0.026\\\\=(0.504,\ 0.556)$

Hence, the 90% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement = (0.504, 0.556)

6 0

3 years ago

You purchase a new guitar and take out a loan for $450. You have 18 equal monthly payments of $28 each. What is the simple inter

Daniel [21]

18*28/450=1.12
(1.12-1)*100=12%
Simple interest rate of the loan is 12%

8 0

4 years ago

A gift box of cookies has 4 chocolate chip cookies and 7 peanut butter cookies. Use c to represent the cost of each chocolate ch

dimulka [17.4K]

Answer:

20 chocolate and 35 peanut butter ( 4c+7p=1 )

Step-by-step explanation:

multiply both sides by 5

4 0

3 years ago