25 Points!! :D

Complete the interphase part of the data from your data table.

Answer:

3pw + w^2 - 3p^2 - pw = 2pw + w^2 - 3p^2

Step-by-step explanation:

Multiply every term of the first binomial by every term of the second binomial.

(w - p)(3p + w) = 3pw + w^2 - 3p^2 - pw = 2pw + w^2 - 3p^2

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

the graph of f(x)=×2 called a parabola

Answer:

6y = -5x + 6

y = -5/6 x + 1

Step-by-step explanation:

y = -5/6 x + b

1 = b

Answer:

Step-by-step explanation:

From the given angles ∠ABC and ∠GHK,

m∠ABC = m∠GHK [Given]

m∠ABC = m∠GHL + m∠KHL [Since, ∠GHL + ∠KHL = ∠GHK]

(6x + 2)° = (5x - 27)° + (3x + 1)°

6x + 2 = 8x - 26

8x - 6x = 28

2x = 28

x = 14

m(BC) = m(HK) [Given]

3z + 6 = 8z - 9

8z - 3z = 6 + 9

5z = 15

z = 3

m(AB) = m(GH)

5y - 8 = 3y

2y = 8

y = 4

m∠ABC = mGHK = (6x + 2)

                            = 6(14) + 2

                            = 86°

m(AB) = m(GH) = 3y

                        = 3(4)

                        = 12 units

m(BC) = m(HK) = (3z + 6)

                        = 3(3) + 6

                        = 15 units

m(∠KHL) = (3x + 1)°

              = 3(14) + 1

              = 43°

Answer:

m(∠C) = 18°

Step-by-step explanation:

From the picture attached,

m(arc BD) = 20°

m(arc DE) = 104°

Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.

m(∠C) = [tex]\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}][/tex]

Since, AB is a diameter,

m(arc BD) + m(arc DE) + m(arc EA) = 180°

20° + 104° + m(arc EA) = 180°

124° + m(arc EA) = 180°

m(arc EA) = 56°

Therefore, m(∠C) = [tex]\frac{1}{2}(56^{\circ}-20^{\circ})[/tex]

m(∠C) = 18°

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

42

Step-by-step explanation:

prime factorisation of 1764 = 2^2 × 3^2 × 7^2

hence,

√1764 = √(2^2 × 3^2 × 7^2) =2 x 3 x 7 = 42

Answer:

42

Step-by-step explanation:

1764 = 2 * 882

        = 2 * 2 * 441

        = 2 * 2 *  3 * 147

        = 2 * 2 * 3 * 3 * 49

        = 2 * 2 * 3 * 3 * 7 * 7

[tex]\sqrt{1764} = \sqrt{2*2*3*3*7*7} = 2*3*7 = 42[/tex]

Answer:

Step-by-step explanation:

Answer:

see your answer in pic

mark me brainlist

Step-by-step explanation:

Answer:

Red line: y=-1/2x+1  Blue line: y=-1/3x-2  Green line: y=x

Step-by-step explanation:

f(x) red line m=-1/2 b=1

g(x) blue line m=-1/3 b=-2

h(x) green line m=1 b=0

Answer:

0

Step-by-step explanation:

g[f(x)] = x^2 - 3

= 3x^2

if gf(0) = 3(0)^2

= 0

Step-by-step explanation:

-6>t-(-13)

= -6>t+13

= -6-13>t

= -19>t

= t<-19

Answer:

t < - 19

Step-by-step explanation:

Given

- 6 > t - (- 13) , that is

- 6 > t + 13 ( subtract 13 from both sides )

- 19 > t , then

t < - 19

HOPE ITS HELPFUL ^_^

x = number of hours

want to find probability (P) x >= 13

x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.

P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

To convert that to percentage, multiply 100, to get 84.13%

Answer:

Sample 1 MOE = 37.24%

Sample 2 MOE = 29.4%

Sample 3 MOE = None

Step-by-step explanation:

We are told that 250 sheep grazes over a 40-acre pasture.

Thus, number of sheeps per acre = 250/40 = 6.25 ≈ 6

Thus, n = 6

For the samples given, we can find sample proportions as;

Sample 1: p_o = 4/6 = 0.67

Sample 2: p_o = 1/6 = 0.17

Sample 3: p_o = 9/6 = 1.5

Formula for test statistic here is;

z = √(p_o(1 - p_o)/n)

For sample 1;

z = √(0.67(1 - 0.67)/6)

z ≈ 0.19

For sample 2;

z = √(0.17(1 - 0.17)/6)

z ≈ 0.15

For sample 3;

z = √(1.5(1 - 1.5)/6)

z = √−0.125

We are not given confidence level but we will use 95%.

Value of z_α at 95% Confidence level is 1.96. Thus, we can find the margin of error for the samples;

For sample 1;

Margin of error at z = 0.19 is;

1.96 × 0.19 = 0.3724 = 37.24%

For sample 2;

Margin of error at z = 0.15 is;

1.96 × 0.15 = 0.294 = 29.4%

For sample 3;

Since test statistic has a negative square root, then it has no margin of error.

Answer:

y=4x+7

Step-by-step explanation:

use the slope intercept formula to find the equation.

y =4

passess through (-1,3)

Answer:

8.6023

Step-by-step explanation:

length = √[(x2-x1)^2+(y2-y1)^2]

=√[(1-6)^2+(-1--8)^2] =√74 =8.6023

Answer:

B. 0.024

The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before testing the hypothesis, 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.

1999:

Of 100, 20 were in the bottom thid. So

[tex]p_B = \frac{20}{100} = 0.2[/tex]

[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]

2001:

Of 100, 10 were in the bottom third, so:

[tex]p_A = \frac{10}{100} = 0.1[/tex]

[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]

To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.

Can also be rewritten as:

[tex]H_0: p_B - p_A = 0[/tex]

[tex]H_1: p_B - p_A > 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.

0 is tested at the null hypothesis:

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

From the sample:

[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]

[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]

Value of the test statistic:

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

[tex]z = \frac{0.1 - 0}{0.05}[/tex]

[tex]z = 2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.

Looking at the z-table, z = 2 has a p-value of 0.976.

1 - 0.976 = 0.024, so the p-value is given by option B.

The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Answer:

80m

Step-by-step explanation:

(20x2) =40m + 40m= 80m

Answer:

2x-24

I think that you changes the problem...

you went from a derivative to an inverse ???

y = 1/2x + 14

x = 1/2 y + 14

2x = y + 24

y = 2x-24

Step-by-step explanation:

Answer:

[tex]f^{-1}[/tex] (x) = 2x - 28

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{1}{2}[/tex] x + 14 ( multiply through by 2 to clear the fraction )

2y = x + 28 ( subtract 28 from both sides )

2y - 28 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = 2x - 28

Answer:

4sqrt(3)

Step-by-step explanation:

If the triangle is equilateral, the hypotenuse is 2x

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (2x)^2

x^2 + 144 = 4x^2

144 = 4x^2 -x^2

144 = 3x^2

48 = x^2

Taking the square root of each side

sqrt(48) = sqrt(x^2)

sqrt(16*3) = x

4 sqrt(3) =x

Answer:

The option which represents the inequality is option D ; stated as x ≥ 0

Step-by-step explanation:

The marked or dotted position is 0 ; which represents the position of x, when graphing inequality statements, if the point IS SHADED, then it means GREATER THAN EQUAL TO.

Option A is incorrect, the inequality sign is not the same as the direction of the arrow.

Option B, says LESS THAN EQUAL TO, instead of GREATER THAN EQUAL TO

Option C SAYS GREATER THAN instead of GREATER THAN EQUAL TO.

Therefore, Option D is the correct expression which means x is GREATER THAN EQUAL TO.

Learn more : https://brainly.com/question/24065770

Answer:

There are sixteen lines.

Answer:

x = 10

Step-by-step explanation:

7x - 15 = 4x + 15

7x - 4x = 15 + 15

3x = 30

x = 10

Answer:

x = 10

Step-by-step explanation:

Given that AC and BD are congruent , then

7x - 15 = 4x + 15 ( subtract 4x from both sides )

3x - 15 = 15 ( add 15 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Answer:

D

Step-by-step explanation:

(the line is a / shape, so the slope is positive)

(the line crosses the y axis at (0,-2)

(using the above information, the equation is y=2x-2)

Answer:

y = 2x - 2

Step-by-step explanation:

Start with

y = mx + b

The graph shows the y-intercept -2.

We have y = mx - 2

slope = m = rise/run

The slope is rise of 2 and run of 1, so m = 2.

y = 2x - 2

Answer:

C

Step-by-step explanation:

You are correct

*Per something means multiplication*

20 per 4 weeks = 20 × 4

Answer:

(0.5,3.5)

Step-by-step explanation:

First, we can draw the image, as shown. The diagonals in the rectangle are the following lines:

from (-2,9) to (3,-2)

from (-5, 6) to (6,1)

To find where they intersect, we can start by making an equation for the lines. For an equation y=mx+b, m represents the slope and b represents the y intercept, or when x=0

For the first line, from (-2,9) to (3,-2), we can calculate the slope by calculating the change in y/change in x = (y₂-y₁)/(x₂-x₁). If (3,-2) is (x₂,y₂) and (-2,9) is (x₁,y₁), our slope is

(-2-9)/(3-(-2)) = -11/5

Therefore, our equation is

y= (-11/5)x + b

To solve for b, we can plug a point in, like (3,-2). Therefore,

-2=(-11/5)*3+b

-2=-33/5+b

-10/5=-33/5+b

add 33/5 to both sides to isolate b

23/5=b

Our equation for one diagonal is therefore y=(-11/5)x+23/5

For the second line, from (-5, 6) to (6,1), if (6,1) is (x₁,y₁) and (-5,6) is (x₂,y₂), the slope is (1-6)/(6-(-5)) = -5/11 . Plugging (6,1) into the equation y=(-5/11)x+b, we have

1=(-5/11)*6+b

11/11 = -30/11 + b

add 30/11 to both sides to isolate b

41/11 = b

our equation is

y = (-5/11) x + 41/11

Our two equations are thus

y = (-5/11) x + 41/11

y=(-11/5)x+23/5

To find where they intersect, we can set them equal to each other

(-11/5)x+23/5 = y = (-5/11) x + 41/11

(-11/5)x + 23/5 = (-5/11)x + 41/11

subtract 23/5 from both sides as well as add 5/11 to both sides to make one side have only x values and their coefficients

(-11/5)x + (5/11)x = 41/11-23/5

11*5 = 55, so 55 is one value we can use to make the denominators equal.

(-11*11/5*11)x+(5*5/11*5)x=(41*5/11*5)-(23*11/5*11)

(-121/55)x+(25/55)x = (205/55) - (253/55)

(-96/55)x = (-48/55)

multiply both sides by 55 to remove the denominators

-96x=-48

divide both sides by -96 to isolate x

x=-48/-96=0.5

plug x=0.5 into a diagonal to see the y value of the intersection

(-11/5)x + 23/5 = y = (-11/5)* 0.5 + 23/5 = 3.5