Consider the equation:
6x+55=x^2
1) Rewrite the equation by completing the square.
Your equation should look like (x+c)^2=d(x+c)
2
=dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c)
2
=dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d.
2) What are the solutions to the equation?

Answer:

The length of side x is [tex]x = \sqrt{6}[/tex]

Step-by-step explanation:

Pythagorean Theorem:

In a right triangle, with sides a and b, and hypothenuse h, we have that:

[tex]a^2 + b^2 = h^2[/tex]

In this question:

The vertical line on the sides means that both are equal, that is, measuring x, so [tex]a = b = x[/tex].

Hypothenuse is the square root of 12. So [tex]h = \sqrt{12}[/tex]

[tex]x^2 + x^2 = (\sqrt{12})^2[/tex]

[tex]2x^2 = 12[/tex]

[tex]x^2 = \frac{12}{2}[/tex]

[tex]x^2 = 6[/tex]

[tex]x = \sqrt{6}[/tex]

The length of side x is [tex]x = \sqrt{6}[/tex]

Answer:

see explanation

Step-by-step explanation:

first fill out all sides of the triangle (use pythagorean theorem).

9^2 = 4^2+x^2

x^2 = 81-8 --> x^2 = 73 --> x = √73

csc theta --> hyp/opp

sin theta --> opp/hyp

cot theta --> adj/opp

hyp = 9, adj = 4, opp = √73

csc = 9/√73 --> 9√73/73

sin = √73/9

cot = 4/√73

Answer:

5

Step-by-step explanation:

It will remain 5 because two negatives make a positive.

-(-5) = 5

Hope this helps.

Answer:

5 ( REMEMBER TWO NEGATIVES MAKE A POSITIVE)

Step-by-step explanation:

When there is a - in front of an expression in parentheses, change the sign of each term in the expression 5

Answer:

Step-by-step explanation:

We can do this the easy way and just set up an inequality and let the factoring do the work for us. The inequality will look like this:

[tex]-16t^2+112t>192[/tex] We will move the constant over and get

[tex]-16t^2+112t-192>0[/tex] and when you factor this you get that

3 < t < 4

Between 3 and 4 seconds is where the projectile reaches a height higher than 192 feet. With a little more work and some calculus you can find the max height to be 196 feet.

Answer:

its A

Step-by-step explanation:

got it right

Answer:

12 posts are needed

Step-by-step explanation:

60 divided by 5 is 12

Answer:

Step-by-step explanation:

4-3(6)-1

= 4 - 18 - 1

= 4 - 19

= -15 (Ans)

Answer:

It should be in quadrant 1

Step-by-step explanation:

The quadrants of a coordinate plane can be counted counter-clockwise starting from quadrant 1, if you know the exact point you're trying to find, you can use the x and y to figure out which quadrant it's in.

If the x and y values are both positive, the point is in quadrant 1.

If the x value is negative and the y value is positive, the point is in quadrant 2.

If the x and y values are both negative, the point is in quadrant 3.

If the x value is positive and the y value is negative, the point is in quadrant 4.

Answer:

it's 4488 Wich would make 187

Answer:

the answer is 3800mm.because 1m is 1000mm

WHAT IS THIS

AM CONFUSEDDDD

DO YOU NEED HELP WITH HOEMWORK

Answer:

a ?

Step-by-step explanation:

Answer:

I'm pretty sure it's A? makes more sense

Step-by-step explanation:

missing where ?

I guess you mean that there is one element missing between 51 and 33 (based on the readable answer options).

if that is true, then the missing element is 42.

the difference between 60 and 51 is 9.

the difference between 51 and 33 is 18.

if there is an engender missing in between 51 and 33, then it is logical to put it in the middle cutting the interval of 18 in half to 2 times 9. which is also supported by the first interval between 60 and 51 (9).

so, it would be 51 -9 = 42

Answers:

These values are approximate

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Explanation:

The circumference formula is

C = 2*pi*r

which rearranges to

r = C/(2pi)

when solving for r.

Plug in the given circumference to find that

r = C/(2pi)

r = (39,750)/(2pi)

r = 6,326.40898790283

For the sake of the most accuracy possible, I'm using my calculator's stored version of pi (and not something like pi = 3.14); if your teacher requires you to use pi = 3.14 then follow those instructions of course.

The radius is roughly 6326 km when rounded to the nearest integer.

Keep in mind that the earth isn't a perfect sphere, but rather a slightly squished one. This means the earth is slightly fatter than it is tall. However, for the sake of this problem, we'll assume it's a sphere.

------------------------

Once you determine the circumference, aka distance around the circle, we can figure out the next problem: determining the distance from the north pole to the equator. This distance runs along a line of longitude, so it's a north-south distance.

Again, imagine the earth is a perfect sphere. This means that the equator circumference is the same as the circumference as a full longitude line when we travel the globe only along that line. In other words, start at the north pole, travel along that specific longitude only until you reach the south pole. Then staying on that line, travel back to the north pole going around the backend of the earth.

That full circular path we traveled will get cut into 1/4 because 1/2 the circumference is the portion from north to south pole, and then we cut that distance in half when going from north pole to the equator.

(1/4)*(6,326.40898790283) = 1,581.6022469757

That rounds to 1582 km

------------------------

Side notes:

Answer:

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Step-by-step explanation:

Before solving the question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Test if a lower proportion of men favor stricter gun control than women:

At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So

[tex]H_1: p_M - p_W < 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.

This means that:

[tex]p_W = \frac{313}{564} = 0.555[/tex]

[tex]s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209[/tex]

In a random sample of 588 men, 307 favored stricter gun control laws.

This means that:

[tex]p_M = \frac{307}{588} = 0.522[/tex]

[tex]s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206[/tex]

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_M - p_W = 0.522 - 0.555 = -0.033[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.033 - 0}{0.029}[/tex]

[tex]z = -1.12[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.

Looking at the z-table, z = -1.12 has a p-value of 0.1314.

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Answer:

a. [ 2 , ∞ )

Step-by-step explanation:

Answer:

boxers get injured but it is good to have some security on your fist and for those who do do boxing it's nice to have some security

Answer:

Volume = 288 in.³

Step-by-step explanation:

Volume of the solid = volume of the cube + volume of the square pyramid

V = a³ + ⅓*a²*h

a = 6 in.

h = 12 - 6 = 6 in.

Plug in the values into the volume formula

Volume = 6³ + ⅓*6²*6

Volume = 216 + 72

Volume = 288 in.³

Answer:

So, if we say Jiri's age is j (we can pick any letter), then Pamela's age is 2j, right?

j + 2j = 72

j is the same as 1j, but we wouldn't call you 1James, just James.

3j = 72

To isolate j, we do the opposite operation to both sides.

3j/3 = 72/3

j/j = 1, so that cancels out. 72/3 = 24.

j = 24

Jiri is 24 years old.

Answer:

Jiri is 7 years old.

explanation:

3j + j = 28

4j = 28

4j/4 = 28/4

j = 7

this can be proven:

Pamela's age: 3×7 = 21

the sum of their ages = 28

7 + 21 = 28

Answer:

OMGGGG OMGGG I NEEDTHIS QUESTION TOOOOOO

hope it helps you see the attachment for further information

Answer:

Probability[Number of 6 random sample do not have cavities] = 0.8

Step-by-step explanation:

Given:

Number of student do not have cavities = 60%

Number of random sample = 9 children

Find:

Probability[Number of 6 random sample do not have cavities]

Computation:

n = 9

p = 60% = 0.6

P(At least 6)  

Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)  

Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)

Probability[Number of 6 random sample do not have cavities] = 0.8

The probability of 9 children selected from this school, at least 6 do not have cavities is 0.80.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Sixty percent of all children in a school do not have cavities.

The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities will be

n = 9

p = 0.60

Then we have

[tex]\rm P = 1 - P(less \ than \ or \ equal \ 6)\\\\P = 0.8[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

I need more information to answer this

Answer:

The sale price of the TV is $ 300.

Step-by-step explanation:

Given that a television costs $ 450, but during a special sale, it’s marked 1⁄3 off, to determine what’s the sale price of the TV the following calculation must be performed:

1/3 = 0.333

1 - 0.333 = 0.666

450 x 0.666 = X

300 = X

Therefore, the sale price of the TV is $ 300.

Answer:

4.9

Step-by-step explanation:

Use the butterfly method.

13*13 = 8*u

39 = 8u

(divide by 8)

4.875 = u

4.875 is about 4.9

Answer:

4.875

Step-by-step explanation:

1. multiply 13 times 3 and then 8 times u

2. set equal to each other so you get 39=8u

3. divide both sides by 8 to isolate u

4. solve 39/8 which is 4.875

Answer:

The volume is increasing at a rate of 25,133 mm/s.

Step-by-step explanation:

Diameter is 40mm

Radius is half the diameter, so [tex]r = \frac{40}{2} = 20[/tex]

How fast is the volume increasing when the diameter is 40mm?

We have to apply implicit differentiation, of V and r in function of t. So

[tex]V = \frac{4}{3} \pi r^3[/tex]

[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 5 mm/s.

This means that [tex]\frac{dr}{dt} = 5[/tex]

Then

[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = 4\pi (20)^2(5)[/tex]

[tex]\frac{dV}{dt} = 25133[/tex]

The volume is increasing at a rate of 25,133 mm/s.

Answer:

f(x) = 12x = 10

Step-by-step explanation:

We need a linear equation in the slope-intercept form.

y = mx + b

where y = total pay, m = hourly salary, x = number of hours worked, and b = y-intercept, or initial value

Let's look in the table.

1 hour: $22

2 hours: $34

The difference in pay between 1 hour and 2 hours is $34 - $22 = $12.

The difference in time between 1 hour and 2 hours is 1 hour.

In 1 hour he earns $12. That means the slope is 12.

We know he earns $22 for working a total of 1 hour.

Start at 1 hour and $22 on the table.

Subtract 1 hour from 1 hour to get 0 hours.

Subtract $12 form $22 to get $10.

That means for 0 hours he gets $10. b = 10

The equation is

y = 12x + 10

In function form, we have:

f(x) = 12x = 10

Here we want to find a linear relation with only using the data in a table, we will find that the line is:

[tex]y = 12\cdot x + 12[/tex]

We know that Damian's earns a set amount plus an hourly wage, then this can be modeled with a linear equation:

[tex]y = a\cdot x + b[/tex]

Where a is the slope, which in this case is the hourly wage, and b is the y-intercept, which in this case is the set amount.

Such that x is the number of hours and y is the pay.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be given as:

[tex]a = \frac{x_2 - x_1}{y_2 - y_1}[/tex]

By looking at the table we can find two points of our line, for example, if we use the first and third points:

(1, 22) and (2, 34) then the slope will be:

[tex]a = \frac{34 - 22}{2 - 1} = 12[/tex]

Then the line is something like:

[tex]y = 12\cdot x + b[/tex]

To find the value of b, we can use one of the points, for example, the point (1, 22) means that when x = 1, we must have y = 22.

Replacing that in the above equation we have:

[tex]22 = 12\cdot1 + b\\\\22 = 12 + b\\\\22 - 12 = b = 12[/tex]

Then the equation of the line is:

[tex]y = 12\cdot x + 12[/tex]

If you want to learn more, you can read:

https://brainly.com/question/22901085

Answer: Since he had fourteen, and he gave away six of them, he has eight left.

Step-by-step explanation:

The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8.

A way to express or represent numbers is through the number system.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

As per the given,

Total number of apples = 14

Number of apples that make a pie = 6

Left = 14 - 6 = 8

Hence "The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8".

For more about the number system,

https://brainly.com/question/22046046

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