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3 years ago

Which equation is the inverse of 5 y + 4 = (x + 3) squared + one-half?

Mathematics

2 answers:

telo118 [61]3 years ago

8 0

Answer:

The correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot

Step-by-step explanation:

the given equation is $5y + 4 =(x+3)^{2} + \frac{1}{2}$

Therefore we can write $5y\hspace{0.1cm} = (x+3)^{2} + \frac{1}{2} - 4 \hspace{0.3cm} \Rightarrow \hspace{0.2cm} 5y = (x+3)^{2} - \frac{7}{2} \hspace{0.3cm} \Rightarrow \hspace{0.3cm} y = \frac{(x+3)^{2}}{5} - \frac{7}{10}$

To find the inverse of the above function let us replace x with y and y with x.

Therefore we get

$x = \frac{(y+3)^{2}}{5} - \frac{7}{10}$

Now we write the above equation with only y on the Left hand side and we will obtain the inverse of the given function

$y = \pm \sqrt{5 (x + \frac{7}{10} )} \hspace{0.1cm} - \hspace{0.1cm} 3 \hspace{0.1cm} \Rightarrow\hspace{0.1cm} y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}$

Therefore the correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot , $y = \pm \sqrt{5x + \frac{7}{2} } - \hspace{0.1cm} 3 \hspace{0.1cm}$

ohaa [14]3 years ago

4 0

Answer:

y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot

Step-by-step explanation:

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Can someone help please

elena-s [515]

Answer:

I'm sorry I can help you maybe a little bit if that's okay. Btw what grade are you in?

Step-by-step explanation:

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3 years ago

The base of a right circular cylinder has a diameter of 5.00 inches. Sally measured the circumference of the base cylinder and r

LUCKY_DIMON [66]

Answer:

The percent of error in her measurement is 1.3%

Step-by-step explanation:

we know that

The circumference of a circle is equal to

$C=\pi D$

where

D is the diameter

we have

$D=5\ in$

assume

$\pi=3.14$

substitute

$C=(3.14)(5)=15.7\ in$ ----> This value represent the 100% (theoretical value)

Find the difference between the theoretical value and the measured value

$15.7-15.5=0.2\ in$

Find the percentage by proportion

$15.7/100=0.2/x\\ x=100*0.2/15.7\\ x=1.3\%$

4 0

3 years ago

How can I solve this math equation?

alukav5142 [94]

Answer:

Graphing

Step-by-step explanation:

1) You can graph this equation by using y=mx+b. You can replace that equation with y=3x-1.

M=3

X=x

B=-1

On a graph you would down 1 since it's negative and make a point. Then you would put a 1 under the 3 to make it a fraction. 3/1. Then you would divide 1 by 3 (1 ÷ 3). Then you would go to the right 0.33 because it's positive, and the up 1. Then you would make a second point.

This would only give you one line which wouldn't give you an intersection.

6 0

3 years ago

Read 2 more answers

Center: (-2,5), radius:7

Firlakuza [10]

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question. I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

5 0

3 years ago

The article "Students Increasingly Turn to Credit Cards" (San Luis Obispo Tribune, July 21, 2006) reported that 37% of college f

Sloan [31]

Answer:

Step-by-step explanation:

Hello!

There are two variables of interest:

X₁: number of college freshmen that carry a credit card balance.

n₁= 1000

p'₁= 0.37

X₂: number of college seniors that carry a credit card balance.

n₂= 1000

p'₂= 0.48

a. You need to construct a 90% CI for the proportion of freshmen who carry a credit card balance.

The formula for the interval is:

p'₁± $Z_{1-\alpha /2}*\sqrt{\frac{p'_1(1-p'_1)}{n_1} }$

$Z_{1-\alpha /2}= Z_{0.95}= 1.648$

0.37±1.648* $\sqrt{\frac{0.37*0.63}{1000} }$

0.37±1.648*0.015

[0.35;0.39]

With a confidence level of 90%, you'd expect that the interval [0.35;0.39] contains the proportion of college freshmen students that carry a credit card balance.

b. In this item, you have to estimate the proportion of senior students that carry a credit card balance. Since we work with the standard normal approximation and the same confidence level, the Z value is the same: 1.648

The formula for this interval is

p'₂± $Z_{1-\alpha /2}*\sqrt{\frac{p'_2(1-p'_2)}{n_2} }$

0.48±1.648* $\sqrt{\frac{0.48*0.52}{1000} }$

0.48±1.648*0.016

[0.45;0.51]

With a confidence level of 90%, you'd expect that the interval [0.45;0.51] contains the proportion of college seniors that carry a credit card balance.

c. The difference between the width two 90% confidence intervals is given by the standard deviation of each sample.

Freshmen: $\sqrt{\frac{p'_1(1-p'_1)}{n_1} } = \sqrt{\frac{0.37*0.63}{1000} } = 0.01527 = 0.015$

Seniors: $\sqrt{\frac{p'_2(1-p'_2)}{n_2} } = \sqrt{\frac{0.48*0.52}{1000} }= 0.01579 = 0.016$

The interval corresponding to the senior students has a greater standard deviation than the interval corresponding to the freshmen students, that is why the amplitude of its interval is greater.

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3 years ago