find the circle through (-4,sqrt(5) with center (0,0)

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

Answer:

a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°

Step-by-step explanation:

Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.

Answer:

A) 144 yd²

Step-by-step explanation:

Base= 8x8=64

Side = 1/2*8*5=20

64+20+20+20+20=144 yd²

Answer:

168 sq yds

Step-by-step explanation:

5x8/2x2=40

8x8/2x2=64

8x8=64

40+64+64=168

Answer:

(-5, 0) and (0,4)

Step-by-step explanation:

Given equation: -4x + 5y = 20

Sub. in the values

When x = -5 and y = 0 (-5,0),

[tex] - 4( - 5) + 5(0) = 20 [/tex]

When x = 0 and y = 4 (0,4),

[tex] - 4(0) + 5(4) = 20[/tex]

That's how I would do it, not sure if your school has another method. Hope this helps :)

Answer: x = -5 and y = 4

Step-by-step explanation: its the first option do you need me to exlain how cuz its multiple choice  

Answer:

a) 5[tex]cm^{3}[/tex]

Step-by-step explanation:

Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.

When raising to 3, these dimensions are included and therefore  5[tex]cm^{3}[/tex] is a measure of volume.

Answer:

5cm^3

Step-by-step explanation:

Volume for a form will always be in cubic units.

Area of a shape will always be in squared units.

Length will not be in cubic or squared units.

Hence, the first option is a measure for volume.

The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.

The third option represents a measurement of length, for example the length of a line segment or the height of a figure.

Answer:

-9p -4q + 69

Step-by-step explanation:

5p +4q + (-9p +69)

=> 5p + 4q -9p +69

=> -4p +4q +69

Now, we need to subtract 5p +8q from -4p + 4q +69

=> -4p +4q +69 - (5p +8q)

=> -4p + 4q +69 - 5p -8q

=> -9p -4q + 69

Answer:

Subtraction property

Step-by-step explanation:

Answer:

Subtraction

Step-by-step explanation:I took the test

Answer:

b

Step-by-step explanation:

b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

Here,

The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.

We know that,

[tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ=1

Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

Learn more about Right triangle and Hypotenuse here

https://brainly.com/question/2869318

#SPJ2

Answer:  19.2222

Step-by-step explanation:

given data;

no of tornadoes = 2,1,0 because it’s fewer than 3.

period = 14 years

probability of a tornado in a calendar year = 0.12

solution:

probability of exactly 2 tornadoes

= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )

= 0.0144 * 0.2451 * 1092

= 3.8541

probability of exac one tornado

= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )

= 0.12 * 0.2157 * 182

= 12.7109

probability of exactly 0 tornado

= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )

= 1 * 0.1898 * 14

= 2.6572

probability if fewer than 3 tornadoes

= 3.8541 + 12.7109 +2.6572

= 19.2222

Answer: The answer in a is No while the answer in b is Yes

Step-by-step explanation:

Find the explanation in the attached file.

Answer:

[tex]t \: = 3.92 \: sec[/tex]

Step-by-step explanation:

When (t =0)

Height of cliff = 248 feet = 75.5m

Using Newton's equations of motion:

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

75.5 = 0 * t + 4.9 * t^2

Solving further :

[tex]t \: = 3.92 \: sec[/tex]

Answer:

x1 = -4

x2 = 6

Step-by-step explanation:

The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive

For Example

|-3| = 3

So we can ignore if the answer we get is positive or negative because it will forced to be a positive

|3 x 4| = 12

|x - 2| = 4

x1 = 6

x2 = -2

Answer:

(2,2) (-1,-1)

Step-by-step explanation

i think this is there answer im sorry if im wrong

Answer:

Option (1)

Step-by-step explanation:

Monica earned a bonus = $60

Per hour earning in addition to bonus = $8.50

Let she worked for 'h' hours this week.

Then total earning from the hourly rate = $8.50h

Total earning for the week = Earning of 'h' hours + Bonus earned

                                             = $(8.50h + 60)

Therefore, Option (1) will represent Monica's earnings for the week.

Answer:

8.50h + 60

Step-by-step explanation:

Step-by-step explanation:

your required answer is 60°.

Hello,

Here, in the figure;

angle 1= 120°

To find : m. of angle 2.

now,

angle 1 + angle 2= 180° { being linear pair}

or, 120° +angle 2 = 180°

or, angle 2= 180°-120°

Therefore, the measure of angle 2 is 60°.

Hope it helps you.....

Answer:

20 hours

Step-by-step explanation:

10*8*4=320 (volume of the pool)

320/16=20 hours

Answer:

20 hours

Step-by-step explanation:

10x8x4 = 320

320 / 16 = 20

it takes 20 hours to fill the empty pool

Answer:

No solution

Step-by-step explanation:

Given equation is,

[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}-\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}=0[/tex]

[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}=\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}[/tex]

[tex]\frac{(x+1)}{\sqrt{x}(1-x)}+\frac{(\sqrt{x}-1)}{\sqrt{x}(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]

[tex]\frac{(\sqrt{x}+1)(x+1)+(\sqrt{x}-1)(1-x)}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]

[tex]\frac{x\sqrt{x}+x+\sqrt{x}+1+\sqrt{x}-1-x\sqrt{x}+x}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2x+2\sqrt{x}}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2(\sqrt{x}+1)}{(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]

[tex]\frac{2}{1-x}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]  if x ≠ ±1

[tex](\frac{2}{1-x})^2=\frac{4+x}{1-x}[/tex]  [Squaring on both the sides of the equation]

[tex]\frac{4}{(1-x)}=(4+x)[/tex]

4 = (1 - x)(4 + x)

4 = 4 - 4x + x - x²

0 = -3x - x²

x² + 3x = 0

x(x + 3) = 0

x = 0, -3

But both the solutions x = 0 and x = -3 are extraneous solutions, given equation has no solution.

Answer:

Could you please help me Genius??????

Answer:

We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

Step-by-step explanation:

We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.

Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.

[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.

So, Null Hypothesis, : = 490      {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}

Alternate Hypothesis, : 490     {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                               T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~ [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3

[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2

[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3

[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3

[tex]n_1[/tex] = sample of children born to cocaine users = 190

[tex]n_2[/tex] = sample of children not exposed to cocaine = 186

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3

So, the test statistics =   ~

                                     =  -2.908

The value of t-test statistics is -2.908.

Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:

Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by

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

Null hypothesis:

[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]

Test statistic:

[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]

Alternative Hypothesis:

[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]

Rejection Criterion

[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]

Given value:

[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]

here

[tex]\to t_0 < -t_{0.05,374}[/tex]

hence rejecting the [tex]H_0[/tex]

Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.

Find out more about the alternative hypothesis here:

brainly.com/question/18831983

Answer:

2

Step-by-step explanation:

2,8 to 4,12 has a rise of 4 and a run of 2.

4/2 = 2

The slope is 2.

Remember rise/run!

Answer:

2

Step-by-step explanation:

We take take two points and use the slope formula

m = (y2-y1)/(x2-x1)

m = (12-8)/(4-2)

   = 4/2

   = 2

Answer:

6

Step-by-step explanation:

Given, 3sin2x−7sinx+2=03sin2⁡x-7sin⁡x+2=0

⇒(3sinx−1)(sinx−2)=0⇒3sin⁡x-1sin⁡x-2=0

⇒sinx=13 or 2⇒sin⁡x=13 or 2

⇒sinx=13    [∵sinx≠2]⇒sin⁡x=13    [∵sin⁡x≠2]

Let  sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα

now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)

⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]

Hence, required number of solutions are 6

Answer:

4

Step-by-step explanation:

Length of one side=8

Area=32

Length of another side=x

8 into x = 32

X=32/8

=4

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer:

6

Step-by-step explanation:

36 - 20 - 32 x 1/4

=> 36 - 20 - 32/4

=> 36 - 20 - 8

=> 36 - 28

=> 6

Answer:

46

Step-by-step explanation:

(14+x)/4 = 15

14 + x = 60

x = 46

Answer:

46

Step-by-step explanation:

Let a to d be number 1 to 4 respectively.

15 = (a + b + c + d) / 4

(a + b + c + d) = 60 ------> total sum of the 4 numbers

Since the sum of 3 numbers (assuming a to c) is 14,

Fourth number (d) = 60 - 14

= 46

That's how I would do it, hope this helps :)

Answer:

-16

Step-by-step explanation:

8q

Let q = -2

8*-2

-16

Answer:

I believe it's a 12 percent increase.

Step-by-step explanation:

50/100= 50%

62/100= 62%

62%-50%=12%

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Answer:

a). Function (4)

b). Function (2)

c). Function (3)

Step-by-step explanation:

Characteristics of the functions given,

Function (1),

Form the given graph,

Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

          = [tex]-\frac{4}{1}[/tex]

          = -4

Y- intercept of the given function = 2

Function (2),

From he given table,

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

         = [tex]\frac{5-3}{0+1}[/tex]

         = 2

y-intercept = 5 [Value of y for x = 0]

Function (3),

y = -x - 1

By comparing this equation with y = mx + b

Where 'm' = slope

and b = y-intercept

Slope = (-1)

y-intercept = (-1)

Function (4),

Slope = 5

y-intercept = (-4)

(a). Greatest slope of the function → Function (4)

(b). y-intercept greater than 3 → Function (2)

(c). Function with y-intercept closest to 0 → Function (3)

Answer:

  145 degrees

Step-by-step explanation:

Adjacent angles in a parallelogram are supplementary.

  d2 = 180° -d1 = 180° -35°

  d2 = 145°

Answer:

No the sample does not show that the average age  was different in 2010      

Step-by-step explanation:

From the question we are told that

   The sample size is n =  50

    The  sample mean is  [tex]\= x = 38.5[/tex]

    The population mean is  [tex]\mu = 37[/tex]

     The standard deviation is  [tex]\sigma = 16[/tex]

     The level of significance is  [tex]\alpha = 5 \% = 0.05[/tex]

 The null hypothesis is  [tex]H_o : \mu = 37[/tex]

  The alternative hypothesis is  [tex]H_a : \mu \ne 37[/tex]

The critical value of the level of  significance obtained from the normal distribution table is  ([tex]Z_{\alpha } = 1.645[/tex] )

Generally the test statistics is mathematically evaluated as

          [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]        

         [tex]t = 0.663[/tex]

Now looking at the value  t and  [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.

This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010