4x + 1 -5x =2x +4(x-5)

Answer:

D. a line and a point not on that line

Step-by-step explanation:

That is how you determine a plane.

The factors which determine a plane are a line and a point not on that line.

In geometry, a plane is a flat surface that extends into infinity.

In a three dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.

Therefore, the factors which determine a plane are a line and a point not on that line.

Hence, option D is correct.

Learn more about plane here:

https://brainly.com/question/17458011

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We want to maximize [tex]x^3y^4z[/tex] subject to the constraint [tex]x+y+z=30[/tex].

The Lagrangian is

[tex]L(x,y,z,\lambda)=x^3y^4z-\lambda(x+y+z-30)[/tex]

with critical points where the derivatives vanish:

[tex]L_x=3x^2y^4z-\lambda=0[/tex]

[tex]L_y=4x^3y^3z-\lambda=0[/tex]

[tex]L_z=x^3y^4-\lambda=0[/tex]

[tex]L_\lambda=x+y+z-30=0[/tex]

[tex]\implies\lambda=3x^2y^4z=4x^3y^3z=x^3y^4[/tex]

We have

[tex]3x^2y^4z-4x^3y^3z=x^2y^3z(3y-4x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\z=0,\text{ or}\\3y=4x\end{cases}[/tex]

[tex]3x^2y^4z-x^3y^4=x^2y^4(3z-x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\3z=x\end{cases}[/tex]

[tex]4x^3y^3z-x^3y^4=x^3y^3(4z-y)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}4z=y\end{cases}[/tex]

Let's work with [tex]x=3z[/tex] and [tex]y=4z[/tex], for which we have

[tex]x+y+z=8z=30\implies z=\dfrac{15}4\implies\begin{cases}x=\frac{45}4\\y=15\end{cases}[/tex]

The smallest of these is C. 15/4.

Answer:

(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.

Step-by-step explanation:

The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.

If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.

So the initial weight would occur at (0, 79.5) which is the positive y-intercept.

And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.

Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.

Cheers.

Answer:

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

   Let Pn represent the nth term in the sequence

   Then Pn = (1/3)^n-1

   From this P14 = (1/3)^13 = 1/1594323

5. The sum of the first n terms of a GP beginning a with ratio r is given by

   Sn = a* (r^n+1 - 1)/(r - 1)

   With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500

Answer:

Step-by-step explanation:

Hello, we can write

(1) p(x)=(x-a)q(x)+r

[tex]\boxed{\sf v}[/tex] True

It means that p(a)=0 * q(a) + r = r

so the first one is true.

[tex]\boxed{}[/tex] False

The second one is not to be proven true from the remainder theorem.

[tex]\boxed{\sf v}[/tex] True

For x different from a we can divide the equation (1) by (x-a).

[tex]\boxed{}[/tex] False

We cannot say anything on q(a).

[tex]\boxed{\sf v}[/tex] True

If the rest is 0 then it means that p(a) = 0

[tex]\boxed{\sf v}[/tex] True

If p(a) = 0 it means that the rest r = 0 and then p(x)=q(x)(x-a)

Thank you

Answer:

The product decreases 2022.

Step-by-step explanation:

(x + 1)(y - 1) = xy + 2020

xy - x + y - 1 = xy + 2020

-x + y = 2021

(x - 1)(y + 1) = xy + x - y - 1

  + 2021   =       -x + y

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

(x - 1)(y + 1) + 2021 = xy - 1

(x - 1)(y + 1) = xy - 2022

The product decreases 2022.

Answer:

x≤−8

Step-by-step explanation:

2x+3≤x−5

Subtract x from each side

2x-x+3≤x-x−5

x+3≤−5

Subtract 3 from each side

x+3-3≤−5-3

x≤−8

Answer:

[tex]\huge \boxed{x \leq -8}[/tex]

Step-by-step explanation:

[tex]2x+3 \leq x-5[/tex]

[tex]\sf Subtract \ x \ from \ both \ parts.[/tex]

[tex]2x+3 -x\leq x-5-x[/tex]

[tex]\sf Simplify \ the \ inequality.[/tex]

[tex]x+3 \leq -5[/tex]

[tex]\sf Subtract \ 3 \ from \ both \ parts.[/tex]

[tex]x+3-3 \leq -5-3[/tex]

[tex]\sf Simplify \ the \ inequality.[/tex]

[tex]x \leq -8[/tex]

Answer:

The coefficient is 6

Step-by-step explanation:

The coefficient is the number in front of the variable

The variable is x

The coefficient is 6

Answer:

6

Step-by-step explanation: The coefficient of this would be the real number that is in front of a variable that is not a variable like x, and that number is 6. So, the coefficient of 6x is 6.

Answer :

[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]

Step-by-step-explanation :

I did the explanation in the picture.

Answer:

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

Answer:

The answer is 55, -275, 1375, -6875......

Step-by-step explanation:

Answer:

B = 32

Step-by-step explanation:

Since this is an isosceles triangle, C is also equal to 74 degrees

 the angles of a triangle add to 180

A + B+ C = 180

74+ B + 74 = 180

148 + B = 180

B = 180-148

B =32

Answer:

  0 ≤ x ≤ 10

Step-by-step explanation:

The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...

  -x^2 +10x ≥ 0

  x(10 -x) ≥ 0

The two factors in this product will both be positive only for values ...

  0 ≤ x ≤ 10 . . . . the domain of f(x)

Answer:

$350

Step-by-step explanation:

1. Set up the equation. The sale price of $259 is 74% of the original price.

[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]

2. Cross multiply

74x = 25900

3. Solve

x = 350

Answer:

The probability that the selected adult has liver problems is 0.08

Step-by-step explanation:

In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.

Let E(L) be the event that an adult has liver problems.

The probability is directly obtainable from the question and it is given as 8%

Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08

Answer:

There is no sufficient evidence to support the claim

Step-by-step explanation:

From the question we are told that

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

     The  sample proportion is  [tex]\r p = 0.08[/tex]

     The  sample size is  [tex]n = 250[/tex]

Generally for normal sampling distribution can  be used

     [tex]n * p > 5[/tex]

So  

     [tex]n* p = 250 * 0.12 = 30[/tex]

Since  

     [tex]n * p > 5[/tex] then  normal sampling distribution can  be used

The null hypothesis is  [tex]H_o : p = 0.12[/tex]

  The alternative hypothesis is  [tex]H_a : p > 0.12[/tex]

The  test statistic is evaluated as

            [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }[/tex]

substituting values

            [tex]t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }[/tex]

            [tex]t = -1.946[/tex]

The  p-value is obtained from the z  table and the value is

        [tex]p-value = P(t > -1.9462) =0.97512[/tex]

Since the [tex]p-value > \alpha[/tex]

    Then we fail to reject the null hypothesis

Hence it means there is no sufficient evidence to support the claim

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??????

-1.5

Step-by-step explanation:

So, you do 7.25 - 1 (because it is) and you get 6.25. Make it a fraction inton 25/4 and divide bu 75/8 (9 3/8 simplified) and you get -1.5 voila.

Answer:

x = 3/2

Step-by-step explanation:

7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4

9 3/8 = 9 + 3/8 = 72/8 + 3/8 = 75/8

then:

7 1/4 x = 29x/4

29x/4 - x = 75/8

29x/4 - 4x/4 = 75/8

25x/4 = 75/8

x = (75/8)/(25/4)

x = (75*4)/(8*25)

x = 300/200

x = 3/2

Checking:

(29/4)(3/2) = (29*3)(4*2) =  87/8

87/8 - 3/2 = 75/8

3/2 = 12/8

then:

87/( - 12/8 = 75/8

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

Answer:

r = 19

Step-by-step explanation:

( r-5) /2 = ( r+2) /3

The least common denominator is 6

3/3 *( r-5) /2 = ( r+2) /3 * 2/2

3( r-5) /6 = 2( r+2) /6

Since the denominators are the same, the numerators are the same

3( r-5) = 2(r+2)

Distribute

3r -15 = 2r+4

Subtract 2r from each side

3r-2r -15 = 2r+4-2r

r-15 =4

Add 15 to each side

r-15+15 = 4+15

r = 19

Answer:

65%

Step-by-step explanation:

If 14 are male, then 26 are female.

To find the percent female, divide the number of females by the total.

26/40 = 0.65

So, the percentage of the class that is female is 65%

Answer:

C. 65%

Step-by-step explanation:

We know that of the 40 total students, 14 are male, which means the remaining students are female.

To find how many are female, we subtract 14 from 40:

40 - 14 = 26 females

Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:

(26 / 40) * 100 = 65

The answer is thus C, 65%.

~ an aesthetics lover

Answer:

Critical F value  = 4.9503

Step-by-step explanation:

Given that:

The sample size of the numerator = 7

The sample size of the denominator = 6

The degree of freedom for the numerator df = n -1

The degree of freedom for the numerator df = 7 - 1

The degree of freedom for the numerator df = 6

The degree of freedom for the denominator df = n - 1

The degree of freedom for the denominator df = 6 - 1

The degree of freedom for the denominator df = 5

The assume that the test is two tailed and using a level of significance of ∝ = 0.10

The significance level for the two tailed test = 0.10/2 = 0.05

From the standard normal F table at the level of significance of 0.05

Critical F value  = 4.9503

Answer:

Below

Step-by-step explanation:

First method:

● f(x)= (x^3-2x+1)×(x-3)

● f'(x)= (x^3-2x+1)' ×(x-3) + (x^3-2x+1)×(x-3)'

●f'(x)= (3x^2-2)×(x-3) + (x^3-2x+1) × 1

●f'(x) = 3x^3-9x^2-2x+6 + x^3-2x+1

● f'(x)= 4x^3-9x^2-4x+7

■■■■■■■■■■■■■■■■■■■■■■■■■■

Second method:

●f(x) = (x^3-2x+1)×(x-3)

●f(x) = x^4-3x^3 -2x^2+6x+x-3

●f(x) = x^4-3x^3-2x^2+7x-3

●f'(x) = 4x^3-9x^2-4x+7

We got the same result using both methods.

Answer:

1.3859

Step-by-step explanation:

The formula for Margin of Error is given as:

Margin of Error = Critical value × Standard Error

Critical value = z score

In the question, we are given a confidence interval of 95%.

Z score for a 95% confidence level is given as: 1.96

Hence, critical value = 1.96

Standard Error = σ / √n

Where n = number of samples = 98 chicken eggs

σ = Standard deviation = 7 milligrams

Standard Error = 7/√98

Standard Error = 0.7071067812

Hence, Margin of Error = Critical value × Standard Error

Margin of Error = 1.96 × 0.7071067812

Margin of Error = 1.3859292911

Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859

Answer:

first = flour, second = oats, third = sugar

Step-by-step explanation:

Since the labels are "wrong", we know that the third drawer doesn't have oats or flour, therefore it has sugar. Since the first doesn't have oats, it must have flour and that makes the second drawer oats.

Answer:

first drawer has flour, second has oats, third is sugar

Step-by-step explanation:

on the first drawer, it is labelled oats, so it cannot be oats. on the second it cannot be flour, and on the third it cannot be oats or flour, which means it HAS to be sugar leaving oats and flour to be in either the first, or second.

i know it may sound a little confusing but please let me know if you dont understand

Answer:

b = 10.5

Step-by-step explanation:

2(b-9) = 3

then:

2*b + 2*-9 = 3

2b - 18 = 3

2b = 3 + 18

2b = 21

b = 21/2

b = 10.5

check:

2(10.5 - 9) = 3

2*1.5 = 3

Answer:

the 4 and 8 are exponents

Step-by-step explanation:

4 zeroes basically means [tex]10^4[/tex]

$80=2^3\cdot 10$ and $70=7\cdot10$

there will be $10^2$ when you take the product not $10^4$

hence it will have 2 zeroes not 4

Answer:

12.5 minutes

Step-by-step explanation:

When working together,It takes two computers 10 minutes to send out an email

It takes the slower computer 50 minutes to send out an email

Let x represent the time taken by the faster computer to do the job in its own

Therefore, the time required by the faster computer can be calculated as follows

1/x + 1/50= 1/10

Collect the like terms

1/x= 1/10-1/50

1/x= 4/50

Cross multiply both sides

4 × x = 50×1

4x=50

Divide both sides by the coefficient of x which is 4

4x/4=50/4

x= 12.5

Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes