Please help solve x and round all answers to the nearest tenth

[tex]\sf \: {x}^{2} - 5[/tex]

[tex]\sf \: Use \: the \: algebraic \: identity \\ \sf \: a {}^{2} - {b}^{2} = (a - b)(a + b)[/tex]

[tex]\sf \: Substitute \: the \: value \: of \: a \: and \: b \: in \: the \: identity.[/tex]

[tex]\sf \: a = \sqrt{x ^{2} } = x \\ \sf \: b = \sqrt{5} [/tex]

[tex]\sf \: the \: identity \: becomes \: [/tex]

[tex]\sf {x}^{2} - 5 \\ \sf = (x - \sqrt{5} )(x + \sqrt{5} ) \\ [/tex]

Answer ⟶ [tex]\boxed{\bf{(x - \sqrt{5} )(x + \sqrt{5} )}}[/tex]

Answer:

63

Step-by-step explanation:

a=9

7a

7(9)

63

Answer:

\left(-32ux+19u^2x^3-12u^6x^7\right)\:divided\:by\:\left(-4u^2x^3\right)

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

\frac{8}{ux^2}\:-\frac{19}{4}+3u^4x^4

Answer:

25.

Step-by-step explanation:

Let the number of pupils be x, then:

there are 0.6x girls and 0.4x boys.

From the given information:

0.6x - 0.4x = 5

0.2x = 5

x = 5/0.2

= 50/2

= 25.

Answer:

a) 272 used at least one prescription​ medication.

b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

Step-by-step explanation:

Question a:

86.6% out of 3149, so:

0.866*3149 = 2727.

272 used at least one prescription​ medication.

Question b:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 3149, \pi = 0.866[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876[/tex]

For the percentage:

0.856*100% = 85.6%

0.876*100% = 87.6%.

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Suppose that we have:

Then, we get:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)

For this case, we have:

Part (a):

The number of subjects used at least one prescription​ medication is:

[tex]\dfrac{3149}{100} \times 86.6 \approx 2727[/tex]

Thus, the sample proportion we get is:

[tex]\hat{p} = \dfrac{2727}{3149} \approx 0.8659[/tex]

For level of significance 0.10, we get: [tex]Z_{\alpha/2} = 1.645[/tex]

Thus, the confidence interval needed is:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099[/tex]

Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]

Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Learn more about population proportion here:

https://brainly.com/question/7204089

Answer,

C

Step-by-step explanation:

I had the same question 2 days ago

Answer:

5/3

Step-by-step explanation:

3^5 = 27 ^x

Rewrite 27 and 3^3

3^5 = 3^3^x

We know that a^b^c = a^(b*c)

3^5 = 3^(3x)

The bases are the same so the exponents are the same

5 = 3x

Divide by 3

5/3 =x

Answer:

x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]3^{5} = 27^{x}[/tex]

These problems are getting you ready to work with exponential functions,

and ultimately with logarithms. The point here is that with variable exponents (notice the exponent is an x (on the right one) and not a number. Variable exponents can not be solved with regular algebra "rules" you need new ones.

The new ones will be Logs....

For now (until you learn logs) , you have to use some "tricks"

the "trick" in this problem is that you have to realize that 27 = [tex]3^{3}[/tex]...

with "common bases" this problem becomes trivial

[tex]3^{5} =(3^{3} ) ^{x}[/tex]

so now the bases are the same and the equals sign suggests that

3x = 5

thus x = [tex]\frac{5}{3}[/tex]

Answer:

Step-by-step explanation:

The rectangle has 4 corners of 90 degrees.

Here a rectangle is divided into two right triangles. In right-angled triangles, the opposite side at a 30-degree angle is half a chord...I replace x instead of length.. So x / 2 = 4--->x:8

The perimeter of a rectangle is equal to (length + width) × 2--->(8+4)×2=24m^2

Answer:

[tex]\text{(D) }16\sqrt{3}\:\mathrm{m^2}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:2x:x\sqrt{3}[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.

The rectangle shown forms two 30-60-90 triangles. The side labelled 4 meters is opposite to the 30 degree angle. Therefore, the side on top must be [tex]x\sqrt{3}\text{ for }x=4[/tex]. Let the length of the top base be [tex]w[/tex]:

[tex]w=4\sqrt{3}[/tex]

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Thus, the area of the rectangle is:

[tex]A=4\cdot 4\sqrt{3},\\A=\boxed{16\sqrt{3}\:\mathrm{m^2}}[/tex]

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K

Answer:

The height above sea level at B is approximately 1,604.25 m

Step-by-step explanation:

The given length of the mountain railway, AB = 864 m

The angle at which the railway rises to the horizontal, θ = 120°

The elevation of the train above sea level at A, h₁ = 856 m

The height above sea level of the train when it reaches B, h₂, is found as follows;

Change in height across the railway, Δh = AB × sin(θ)

∴ Δh = 864 m × sin(120°) ≈ 748.25 m

Δh = h₂ - h₁

h₂ = Δh + h₁

∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m

The height above sea level of the train when it reaches B ≈ 1,604.25 m

Answer:

See graph

[tex](x +3)^{2}[/tex] + [tex](y + 1)^{2}[/tex] = 9

(-3 , -1) is the center.

[tex]\sqrt{9}[/tex] = 3 = radius

Step-by-step explanation:

[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex]

center (h,k)

radius = r

Answer:

QXV=WXV

Step-by-step explanation:

Step-by-step explanation:

First sentence

Let the number be X

second sentence

X-5

Third sentence

X-5=14

X=19

The number is 19

Hi there!  

»»————-　★　————-««

I believe your answer is:

19

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Step-by-step explanation:

The answer is 4.

Once you add 4, you get:

x^2 -2x + 4 = 7.

The left side is factorable:

(x-2)^2 = 7.

There is your perfect square.

Answer:

the answer is as follows:

Step-by-step explanation:

a)

The equation has the following integer solutions:

5*x+25=-3*xy+8*y^2

Number of solutions found: 3

x1=-31; y1=-10

x2=-7; y2=-2

x3=-5; y3=-0

b)

The equation has the following integer solutions:

2*y^2+x+y+1=x^2+2*y^2+xy

Number of solutions found: 2

x1=0; y1=-1

x2=2; y2=-1

 Do not forget to give appriciation.

Answer:

(x-12)^2+(y-2)^2=4

Step-by-step explanation:

Answer:

[tex]VR=5[/tex]

Step-by-step explanation:

From the question we are told that:

No of Pulleys =5

Generally Greatest VR is achieved if it has no friction to the pulleys

Therefore

[tex]W=5P[/tex]

Generally the equation for Efficiency  is mathematically given by

[tex]n=\frac{MA}{VR}[/tex]

Where

MA=mechanical advantage

Therefore  at Greatest VR

[tex]n=100 \%[/tex]

[tex]MA=VR[/tex]

[tex]VR=\frac{W}{P}[/tex]

[tex]\frac{W}{P}=5[/tex]

[tex]VR=5[/tex]

Answer:

1) The length of [tex]DC[/tex] is 20.

2) The length of [tex]PS[/tex] is 17.

Step-by-step explanation:

1) If [tex]DR = RE[/tex] and [tex]CS = SB[/tex], then we can use the following proportionality ratio:

[tex]\frac{DE}{DR} = \frac{32 - x}{26 - x}[/tex] (1)

Where [tex]x[/tex] is the length of segment [tex]\overline{CD}[/tex].

If [tex]DE = 2\cdot DR[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{32-x}{26-x}[/tex]

[tex]52 - 2\cdot x = 32 - x[/tex]

[tex]20 = x[/tex]

The length of [tex]DC[/tex] is 20.

2) If [tex]QV = VP[/tex] and [tex]RW = WS[/tex], then we can use the following proportionality ratio:

[tex]\frac{QP}{QV} = \frac{x-7}{12-7}[/tex] (2)

Where [tex]x[/tex] is the length of segment [tex]\overline{PS}[/tex].

If [tex]QP = 2\cdot QV[/tex], then the value of [tex]x[/tex] is:

[tex]2 = \frac{x-7}{5}[/tex]

[tex]10 = x-7[/tex]

[tex]x = 17[/tex]

The length of [tex]PS[/tex] is 17.

hope this helps! feel free to clarify if unsure

Answer:

C

Step-by-step explanation:

y=-x^2+1. y is a decreasing function as x^2 is an increasing function

Answer:

1) -7929

2) -2401

3)-5414

4) -7592

5) 12888

6)-237726

7) 7287

8)-4588

9)-394495

10) 891856

Answer:

D. [tex] \frac{15}{8} [/tex]

Step-by-step explanation:

Recall: SOH CAH TOA

Thus,

Tan A = Opposite/Adjacent

Reference angle (θ) = A

Length of side Opposite to <A = 15

Length of Adjacent side = 8

Plug in the known values

[tex] Tan(A) = \frac{15}{8} [/tex]

Answer:

next 3 terms are -15, -28, -41. The formula would be n= (n-1)-13 to get the nth term

Step-by-step explanation:

Answer:

-0.301

Step-by-step explanation:

Correct Question :-

If log 2 = 0.301 , find log 0.5

Solution :-

We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .

[tex]\rm\implies log_{10}2= 0.301 [/tex]

And we are supposed to find out the value of log 0.5 . We can write it as ,

[tex]\rm\implies log_{10}(0.5) = log _{10}\bigg( \dfrac{5}{10}\bigg)[/tex]

Simplify ,

[tex]\rm\implies log _{10}\bigg( \dfrac{1}{2}\bigg)[/tex]

This can be written as ,

[tex]\rm\implies log_{10} ( 2^{-1})[/tex]

Use property of log ,

[tex]\rm\implies -1 \times log_{10}2 [/tex]

Put the value of log 2 ,

[tex]\rm\implies -1 \times 0.301 =\boxed{\blue{-0.301}} [/tex]

Hence the value of log (0.5) is -0.301 .

*Note -

Here here there was no use of log 5 in the calculation .

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

Step 1:  Solve for x

Since there are two parallel lines and one perpendicular line through the middle, that means that all of the angles are equal.  Therefore, we can make an equation 21x + 6 = 90 and solve for x

[tex]21x + 6 - 6 = 90 - 6[/tex]

[tex]21x / 21 = 84 / 21[/tex]

[tex]x = 4[/tex]

Answer:  [tex]x = 4[/tex]

Answer:

Kristi will pay $22.77 for the shirt.

Step-by-step explanation:

First, determine the sales price of the shirt. If the full price is $27.99, a 25% reduction is $7. Subtract the discount from the full price to get a sales price of $20.99 for the shirt.

Next, determine the amount of tax Kristi will pay for the shirt. In her state, the sales tax is 8.5% (0.085). Multiply $20.99 by 0.085 and you will see that the sales tax is $1.78. Add the amount of the tax, $1.78, to the sales price of the shirt, $20.99, and you will get $22.77 as the cost of the shirt after the sales tax is added.