Consider this quadratic equation
X^2+2x+7=21

Answers

Answer 1

Answer:

x = sqrt(15) - 1 or x = -1 - sqrt(15)

Step-by-step explanation:

Solve for x:

x^2 + 2 x + 7 = 21

Subtract 7 from both sides:

x^2 + 2 x = 14

Add 1 to both sides:

x^2 + 2 x + 1 = 15

Write the left hand side as a square:

(x + 1)^2 = 15

Take the square root of both sides:

x + 1 = sqrt(15) or x + 1 = -sqrt(15)

Subtract 1 from both sides:

x = sqrt(15) - 1 or x + 1 = -sqrt(15)

Subtract 1 from both sides:

Answer: x = sqrt(15) - 1 or x = -1 - sqrt(15)


Related Questions

Joe earns $750 each week working his full time job. His employer has a
9.75% tax deduction on all monies earned each week.

Answers

Answer:

After tax deduction he makes $676.875  a week

Step-by-step explanation:

9.75% of 750 is 71.125

750-71.125 is 676.875

256 divided by -16 with steps.

Answers

Answer:

256÷-16=16

Step-by-step explanation:

The complete expression is 256 divided by -16 is -16

How to determine the solution to the equation

From the question, we have the following parameters that can be used in our computation:

256 divided by -16 = what

When represented as an equation, we have

Result = 256 divided by -16

Make the result the subject of the formula

So, we have

Result = 256/-16

Rewrite as

Result = -256/16

Evaluate the quotient

Result = -16

Hence, the number is -16


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EASY

A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures?

t ≤ 33° F

t ≥ 33° F

t > 33° F

t < 33° F

Answers

Answer: t ≥ 33

Step-by-step explanation:

So the temperature has to equal to 33 or less than 33.It can't be greater than 33.

6
An ordinary fair dice is thrown once.
(a) On the probability scale mark with a cross (X) the probability ti
the dice lands on an even number.
1
2
(b) Write down the probability that the dice lands on a number les
than 3.​

Answers

Answer:

(a) 1/2(b) 1/3

Step-by-step explanation:

(a) 3 of the 6 numbers on the die are even, so the probability that one of them will show is 3/6 = 1/2.

__

(b) 2 of the 6 numbers on the die are less than 3, so the probability that one of them will show is 2/6 = 1/3.

Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??

Answers

Answer: [tex]3(3-4x+2y)[/tex]

Step-by-step explanation:

[tex]9-12x+6y[/tex]

[tex]3(3-4x+2y)[/tex]

what is the best college to go to?

Answers

It is different for everyone especially what you want to do in the future. What do you want to major in?

Answer:

The the best college to go to is the one where you feel comfortable.

Step-by-step explanation:

It is so important to understand the sence of what is actually "the best" college to go to.

You can look at that from a viriety of perspectives, and it is debatable to just go for the college which holds the highest rank on some site.

There are a lot of factors to consider, and what is generally considered the best college does not necassarilly the right one for you.

Ask your loved ones for advice and if you can take a look at yourvtop thee collages.

The the best college to go to is the one where you feel comfortable.

Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.

Answers

Answer:

A. p + q = b

D. p · q = c

Step-by-step explanation:

It's best to look at an example, such as this:

[tex]x^2 - 12x + 35[/tex]

And it's factored form is:

(x - 5) (x - 7)

As you can see, if you add -5 (p) and -7 (q), you get -12 (b). Then, if you multiply -5 (p) and -7 (q), you get 35 (c).

Answer:

A and D

Step-by-step explanation:

STOP REPORTING MY ANSWER!!

Kono Dio Da!!!

A fraction that is equivalent to 6/-5?

Answers

Answer:

12/-10

Step-by-step explanation:

Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.

Answer:

12/-10

Step-by-step explanation:

6/-5

6×2= 12

-5×2=-10

12/-10

A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.

Answers

Answer:

D. Observational Study

Explanation:

An observational  study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.  

This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study  is subject to bias because a positive or negative result might be because of other factors not related to the study.

What is the volume of this cube with a side length of 6 centimeters
6 cm

Answers

Answer:

V = 216 cm^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = (6)^3

V = 216 cm^3

Answer:216 cm^3

Step-by-step explanation:

In cube, the length of all sides are equal

length of side=6cm

Volume of cube=length x length x length

Volume of cube=6 x 6 x 6

Volume of cube=216

Volume of cube=216 cm^3

a clock chimes once at 1, twice at 2

Answers

Answer:

3 times at 3

Step-by-step explanation:

Brittany Monroe is a legal secretary. Her biweekly salary is $1,650.00 what is her annual salary?

Answers

Answer:

$42,900 a year

Step-by-step explanation:

so there are 26 bi-weeks in a year. (fun fact)

you take $1,650 and multiply that biweekly to get her annual salary.

1650*26=42,900

How to factor this trinomial(a=1)?

Answers

Answer:

The answer is (x+8)(x-3) .

Step-by-step explanation:

First, you have to elaborate out :

[tex] {x}^{2} + 5x - 24[/tex]

[tex] = {x}^{2} - 3x + 8x - 24[/tex]

Next, you can factor out the like terms :

[tex] {x}^{2} - 3x + 8x - 24[/tex]

[tex] = x(x - 3) + 8(x - 3)[/tex]

[tex] = (x - 3)(x + 8)[/tex]

Answer:(x-3)(x+8)

Step-by-step explanation:

x^2+5x-24

We first find two numbers whose product is -24 and whose sum is 5,the two numbers are 8 and -3,we then removed +5x from the equation and replace it with +8x-3x

x^2+8x-3x-24

We factorise

x(x+8)-3(x+8)

We factorise the like terms which is (x+8)

(x-3)(x+8)

Using the information below, Solve for x. Show Your Work with your answer.
X + 2y = 5
2x + y = 12


-2(x + 2y = 5)
-2x - 4y = - 10


-2x - 4y = -10
2x + 6y = 12
_____________
2y = 2
————————
2 2


y=1

Answers

[insert answer here]

Step-by-step explanation:

A self storage center is a storage room that is 8 feet long, 6 feet wide, and 10 feet high. What is the volume of the room? 24 cubic feet 48 cubic feet 140 cubic feet 480 cubic feet

Answers

Answer:

Step-by-step explanation: answer is 480 cubic feet. Just do 8 x 6 x 10.

Employees that work at a fish store must measure the level of nitrites in the water each day. Nitrite levels should remain lower than 5 ppm as to not harm the fish. The nitrite level varies according to a distribution that is approximately normal with a mean of 3 ppm. The probability that the nitrite level is less than 2 ppm is 0.0918.
1. Which of the following is closest to the probability that on a randomly selected day the nitrite level will be at least 5 ppm?
(A) 0.0039
(B) 0.0266
(C) 0.0918
(D) 0.7519
(E) 0.9961

Answers

Answer: .0039

Step-by-step explanation:

Classify this triangle.


Acute scalene triangle
Obtuse isosceles triangle
Right isosceles triangle
Right scalene triangle

Answers

right scalene triangle

Answer: right isosceles

Step-by-step explanation:

the angle at the bottom is right therefore you need to figure out the lengths of the sides to conclude if it is isosceles or scalene. because two of the sides are the same length and the other is not it is isosceles

Please help ASAP! Will give BRAINLIEST! Please read the questionTHEN answer correctly! No guessing.

Answers

Answer:D

Step-by-step explanation:

(4/5)^0

4^0/5^0=1/1=1

what is the degree of x^4-3x+22​

Answers

Answer:

4

Step-by-step explanation:

The degree is the highest power on the exponent when they are lined up from highest to lowest

The degree is 4

What is the slope of a line that is parallel to the line
represented by the equation y- 4x = 1?

Answers

Answer:

m=4

Step-by-step explanation:

First get the equation in slope intercept form

y -4x =1

Add 4x to each side

y - 4x+4x = 4x+1

y = 4x+1

This is in the form

y = mx+b where m is the slope and b is the y intercept

The slope is 4

Parallel lines have the same slope

m =4

Graph the circle (x-3)^2+(y-7)^2=4

Answers

The equation is in the form of the equation of the circle. x^2+y^2=r^2. This equation is for the centre, (0,0).

x-3 and y-7 represents the shift in the centre of the circle in the respective axis. Therefore the centre is (3,7). r=2. d=4. So this circle’s centre is at (3,7) with radius 2.

A local retailer claims that the mean waiting time is less than 8 minutes. A random sample of 20 waiting times has a mean of 6.3 minutes with a standard deviation of 2.1 minutes. At α = 0.01, test the retailer's claim. Assume the distribution is normally distributed. Round the test statistic to the nearest thousandth.

Answers

Answer:

The claim is not true

Step-by-step explanation:

We are given that A local retailer claims that the mean waiting time is less than 8 minutes.

[tex]H_0:\mu=8[/tex]

[tex]H_a:\mu<8[/tex]

A random sample of 20 waiting times has a mean of 6.3 minutes with a standard deviation of 2.1 minutes.

[tex]\bar{x}=6.3[/tex]

s = 2.1

n = 20

Since n <30 and population standard deviation is unknown

So,we will use t test

So,[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t=\frac{6.3-8}{\frac{2.1}{\sqrt{20}}}[/tex]

t=-3.62

α = 0.01

Degree of freedom = df=n-1=20-1=19

[tex]t_{df,\frac{\alpha}{2}}=t_{19,\frac{0.01}{2}}=2.861[/tex]

t calculated < t critical

So, we failed to reject null hypothesis

Hence the claim is not true

help plz now quick if right brain list

Answers

Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

Factor x2 – 8x + 15.

Which pair of numbers has a product of ac and a sum of b?

Answers

Answer:

(x - 5)(x - 3)

Step-by-step explanation:

[tex] {x}^{2} - 8x + 15 \\ = {x}^{2} - 5x - 3x + 15 \\ = x(x - 5) - 3(x - 5) \\ = (x - 5)(x - 3) \\ \\ ac = ( - 5) (- 3) = 15 \\ a + c = - 5 - 3 = - 8[/tex]

Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?

Answers

Answer:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]

We have the following data given:

[tex]n_1 =20[/tex] represent the sample size for group 1

[tex]n_2 =20[/tex] represent the sample size for group 2

[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1

[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2

[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1

[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]

And the deviation would be just the square root of the variance:

[tex]S_p=3.678[/tex]

The statistic is givne by:

[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]

The degrees of freedom are

[tex]df=20+20-2=38[/tex]

And the p value is given by:

[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

What are the hypothesis tested?

At the null hypothesis, it is tested if there is no difference, that is:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if there is a difference, that is:

[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]

What is the mean and the standard error of the distribution of differences?

For each sample, we have that they are given by

[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]

[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]

Hence, for the distribution of differences, the mean and the standard error are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]

What is the test statistic?

It is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{3.3 - 0}{1.163}[/tex]

[tex]t = 2.84[/tex]

What is the decision?

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].

Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

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Which fraction is in simplest form 4/20 6/9 5/13 14/21

Answers

Answer: 5/13

Step-by-step explanation:

Answer:

5/13 is in simplest form, because it cannot be reduced any further.

Step-by-step explanation: 4/20 can be reduced to 1/5, 6/9 to 1/3, and 14/21 can be reduced to 2/3

Find two numbers for which the sum is 101 and the difference is 47

Answers

Answer:

74 and 27

Step-by-step explanation:

let x and y be the numbers

x + y =101........eqn 1

x - y = 47.......eqn 2

solve simultaneously

from equation 2, make x the subject

x= 47 + y........eqn 3

put eqn 3 into eqn 1

(47+y) + y = 101

47 + 2y = 101

       2y= 101 - 47

       2y=54

         y= 54/2

         y= 27

put y=27 into eqn 3

x = 47 + 27

x = 74

74 and 27

74+27=101
74–27=47

Plzzz mark as brainleast plzzz plzzz

Need help with this math problem

Answers

Answer:

[tex]f(x)=-5x-3[/tex].

Step-by-step explanation:

From the given machine diagram it is clear that:

[tex]f(x)=-8[/tex] at [tex]x=1[/tex]

[tex]f(x)=-13[/tex] at [tex]x=2[/tex]

[tex]f(x)=-18[/tex] at [tex]x=3[/tex]

It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.

Since the function changing at a constant rate, therefore it represents a linear function.

If a linear function passing through two points, then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is

[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]

[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]

[tex]y+8=-5(x-1)[/tex]

[tex]y=-5x+5-8[/tex]

[tex]y=-5x-3[/tex]

So, the required function is [tex]f(x)=-5x-3[/tex].

3(12−5)+(8x8)-45? Answer?

Answers

Answer:

its 40

Step-by-step explanation:

i think

40
Pemdas
Ones you solve what’s in the parenthesis it leaves you with 3x7+64-45 now you do the multiplication which leaves you with 21+64-45 ones you add it gives you 85-45 and now you have 40

Equations
What is the solution of the system of linear equations?
-3x + 4y = -18
2x - y = 7

(-2,-3)
(-2,3)
(2, -3)
(2, 3)​

Answers

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y =   28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

The solution of the system of linear equations given is (2,-3), the correct option is C.

What is System of Linear Equation?

The system of linear equation is set of equations which have a common solution.

The equations are

-3x+4y = -18

2x-y =7

The linear equations can be solved using substitution method

y = 2x -7 from equation 2 will be substituted in equation 1

-3x +4 ( 2x -7) = -18

-3x +8x -28 = -18

5x = 10

x = 2

y = 2 * 2 -7 = -3

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