Daniel wrote the following two-column proof for the given information.

Answer:

y = -5x - 11

Step-by-step explanation:

We are given that a line passes through the point (-3,4) and also has a slope of -5.

We want to write an equation of this line.

The equation of the line can be written in 3 different ways:

Since the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.

Because we are already given the value of the slope, we can immediately plug that into the equation.

Replace m with -5.

y = -5x + b

Now we need to find b.

As the equation passes through the point (-3, 4), we can use its values to help solve for b.

Substitute -3 as x and 4 as y.

4 = -5(-3) + b

Multiply

4 = 15 + b

Subtract 15 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = -5x - 11

Topic: finding the equation of the line

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The ratio of blue paint to yellow paint is 2 : 3.

The total number of blue paint he used on the first and second day is 10.

The number of yellow paint he used on the first and second day is 15.

On the third day, the highest number of can of blue paint he can use is 2

On the third day, the highest number of can of yellow paint he can use is 3.

The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3

Total blue paint cans used on the first and second day = 4 + 6 = 10

Blue paint cans remaining = 14 - 10 = 4

Total yellow paint cans used on the first and second day = 6 + 9 = 15 cans

Yellow paint cans remaining = 20 - 15 = 5 cans

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Step-by-step explanation:

0 <= income <= 31000 : 10.8%

31000 < income <= 31000+36000 = 67000 : 12.75%

67000 < income < anything above 67000 : 17.4%

the total income is

$85,000

the taxes paid are

10.8% of 31000 = $3348

12.75% of 67000 - 31000 = 12.75% of 36000 = $4590

17.4% of 85000 - 67000 = 17.4% of 18000 = $3132

so, out of $85000 you paid

3348

4590

3132

----------

$11,070

taxes

100% = 85000

1% = 100%/100 = 85000/100 = 850

how many % are 11070 ?

well, as many as how often 1% fits into that amount :

11070 / 850 = 13.02352941...% ≈ 13.02%

There's nothing particularly tricky about the limits of integration. The upper limit is a telescoping series converging to 2,

[tex]\displaystyle \sum_{n=1}^\infty \frac4{4n^2-1} = 2 \sum_{n=1}^\infty \left(\frac1{2n-1} - \frac1{2n+1}\right) \\\\ ~~~~~~~~ = 2 \left(\left(1-\frac13\right)+\left(\frac13-\frac15\right) + \left(\frac15 - \frac17\right) + \cdots\right)[/tex]

The lower limit reduces to 0 using the Riemann-Liouville definition of the fractional derivative. For [tex]q\in\Bbb Q[/tex], let

[tex]\displaystyle \frac{d^q}{dx^q} f(x) = \frac1{\Gamma(\lceil q\rceil-q)} \frac{d^{\lceil q\rceil}}{dx^{\lceil q\rceil}} \int_a^x (x-t)^{\lceil q\rceil-q-1} f(t) \, dt[/tex]

With [tex]a=0[/tex], [tex]q=\frac12[/tex] and [tex]\lceil q\rceil=1[/tex], it follows that

[tex]\displaystyle \frac{d^{1/2}}{dx^{1/2}} 1 = \frac1{\Gamma\left(\frac12\right)} \frac d{dx} \int_0^x (x-t)^{-1/2} \, dt = \frac1{\sqrt{\pi x}}[/tex]

Let

[tex]\displaystyle I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx[/tex]

Observe that

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

is its own inverse, so by substituting [tex]\frac{2-x}{1+2x}\mapsto x[/tex], we get the equivalent integral

[tex]\displaystyle \int_0^2 \frac{\tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]

We have the identity

[tex]\tan^{-1}(x) + \tan^{-1}\left(\dfrac{2-x}{1+2x}\right) = \tan^{-1}(2)[/tex]

so that

[tex]\displaystyle I + I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right) + \tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]

[tex]\implies \displaystyle I = \frac{\tan^{-1}(2)}2 \int_0^2 \frac{dx}{(x-2)^2-5}[/tex]

The remaining integral is trivial,

[tex]\displaystyle \int_0^2 \frac{dx}{(x-2)^2-5} = \int_{-2}^0 \frac{dx}{x^2-5} \\\\ ~~~~~~~~ = \frac1{2\sqrt5} \int_{-2}^0 \left(\frac1{x-\sqrt5} - \frac1{x+\sqrt5}\right) \, dx \\\\ ~~~~~~~~= -\frac{\ln(2+\sqrt5)}{2\sqrt5} \\\\ ~~~~~~~~ = -\frac1{\sqrt5} \tanh^{-1}\left(\dfrac2{\sqrt5}\right)[/tex]

Then the integral we want is

[tex]I = \displaystyle \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx = \boxed{-\frac1{2\sqrt5} \tan^{-1}(2) \, \tanh^{-1}\left(\dfrac2{\sqrt5}\right)} \approx -0.357395[/tex]

The best option is C. Provide multiple worksheets with pictures of the basic shapes for children to colour.

The process of learning has often been described to include all but not limited to the following:

Children according to experts learn faster and easily remember what they see. Hence, providing multiple worksheets with pictures of the basic shapes for children to colour is the most cost-efficient strategy to support children in learning about shapes.

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Answer:

954 passengers

Step-by-step explanation:

We can use ratios to solve

15 buses                   18 buses

--------------             = ---------------

795 passengers      x passengers

Using cross products

15 * x = 18 * 795

15x = 14310

Divide each side by 15

15x/15 = 14310 /15

x =954

18 buses can carry 954 passengers

The probability of rolling an even number first and an odd number second is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of rolling an even number first and an odd number second = (numbers that have the even number first and odd number second / total sample space)

9/36 = 1/4

Here is the complete question:

The table below shows all of the possible outcomes for rolling two six-sided number cubes. What is the probability of rolling an even number first and an odd number second?

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Answer:

the answer is=21

Step-by-step explanation:
u have to sum all of its sides
(length+breadth+height).

Answer: C, (-1, -5)

Step-by-step explanation:

A = 2, B = 4, C = -3

We know the graph opens up because a is positive.

This rules out A and D

We are left with B and C as options.

Let's change this into vertex form

[tex]y=a(x-h)^2[/tex]

Complete the square

[tex]2(x+1)^2-5[/tex]

now a = 2, h = 1, k = -5

The vertex is (h, k)

plug in values:

(-1, -5)

Answer:

Step-by-step explanation:

Hello

   If a line's equation has the form [tex]\boldsymbol{\rm{y-y1=m(x-x1)}}[/tex], then it's considered to be in point-slope form.

In that formula,

Now you know why this equation is called point-slope form!

Now that we're familiar with the equation, let's plug in the information that's given to us...

[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x-(-1)}}[/tex] | simplify

[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x+1)}}[/tex]

[tex]\pmb{\tt{done~!!}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

Using the spread sheet we can easily get the answers:

The statistical section helps find answers by putting the accurate formula or the graphing calculator.

ANOVA      

Source of Variation SS   df     MS         F        P-value      F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.4677      

Total              2359.882 16    

The APA style refers to Times New Roman Font 12 pts.

The effect size of the result is 0.6233 medium

Part A

ANOVA      

Source of Variation SS   df     MS F        P-value F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.4677      

Total        2359.882 16    

1) The null and alternative hypotheses are

H0: u1=u2=u3

Ha: Not all means are equal

2) The significance level is alpha = 0.05

3) The test statistic F = sb²/sw²

Which if H0 is true has an F distribution with ν1=2 and  v2= 14 degrees of freedom.

The computations are

Anova: Single Factor            

Groups Count Sum Average            Variance  

Column 1      6          373    62.16666667      78.96666667  

Column 2 4 324              81             60.66666667  

Column 3 7 402        57.42857143     51.95238095  

ANOVA      

Source of Variation SS   df     MS F        P-value F crit

Between Groups 1471.33    2 735.68 11.59   0.001072834 3.7389

Within Groups 888.55 14 63.46768707      

Total        2359.882353 16  

5) The critical region is F ≥ F(0.05)(2,14) = 3.74

6) Conclusion:

Since the computed value F= 3.73 does not fall in the critical region F> 3.74 so we accept H0 and conclude that there is no significant difference in the three means.

Part D: The effect size of the result is 0.6233 medium and  calculated by

η²= ss between/ ss between + ss error

η²= 1471/1471+889

η²= 0.6233

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f(x) moves 6 unit towards right side along X-axis and forms the function g(x).

Given that, the original function is

[tex]f(x)=x^2[/tex]

and now the function is

[tex]g(x) =(x-6)^2[/tex]

When f(x)=0 then we can get by calculating that,

[tex]x^2=0[/tex]

x=0

So, the f(x) function satisfied by point (0,0).

Now when g(x)=0 then by calculating that we get,

[tex](x-6)^2=0[/tex]

x-6 = 0

x = 6

So g(x) function satisfied by (6,0).

In geometrical words we can say that if we transform from f(x) to g(x) then (0,0) tranformed to (6,0).

That suggests that the function moves 6 unit right along X axis, which is towards positive X axis.

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Answer:

volume= [tex]912.9ft^{3}[/tex] (not sure how you want to round the answer. it could be rounded to 913 or left as 912.9)

Step-by-step explanation:

volume of cone: to find the height of the cone, subtract the cylinder height from the total height (H-h= cone height)

[tex]V=\pi r^2\frac{h}{3} \\V=\pi (5.6)^2(\frac{6.8}{3} )\\V=\pi (31.36)(2.2666...)\\V=71.08057\pi \\V=223.3062[/tex]

volume of cylinder:

[tex]V=\pi r^2h\\V=\pi (5.6)^2(7)\\V=\pi (31.36)(7)\\V=219.52\pi \\V=689.6424[/tex]

add them together:

[tex]V=223.3062+689.6424\\V=912.9486[/tex]

Answer:

in fraction form it is : 5 11/16

Decimal form it is : 5.6875

Step-by-step explanation:

convert the mixed number into improper fractions: 11 3/8 = 91/8

= 91/8 / 8/2

Apollyon the fraction rule: a/b / c = a / b * c

= 91/8 * 2

Multiply the numbers: 8 * 2 = 16

= 91/15

convert the improper fractions into mixed numbers: 91/16 = 5 11/16

Final answer of:
= 5 11/16

Answer: x=9

Step-by-step explanation:

Since this shape is a parallelogram, the diagonals perpendicularly bisect each other. So EH =HG

5x-3=2x+24

3x=27

x=9

Substituing x=9 to EH and HG

EH: 5(9)-3=42

HG: 2(9)+24=42

Answer:

35 years from now.

Step-by-step explanation:

The quantity of moose as a function of time is as follows:

[tex]M(t) = 3000(1.02)^{t}.[/tex]

Thus, for [tex]M < 6000:[/tex]

[tex]3000(1.02)^{t} < 6000\\\\1.02^{t} < 2\\\\t < \frac{log\,2}{log\,1.02}\\\\ t < 35.003\,\,years.[/tex]

Answer:

6

Step-by-step explanation:

i took the test

Since the angles of elevation of the top of two vertical towers is 45° & 60°, the ratio of the height of the towers is 0.58:1

Since the angles of elevation of the top of two vertical towers as seen from the middle point of the lines joining the foot of the towers are 45° & 60°.

The height of the tower, the line of sight and the ground form a right angled trangle

Let

Using trigonometric ratios, we have that

tanФ = h/d

= h/L/2

= 2h/L

So, h = LtanФ/2

= Ltan45°/2

= L/2 × 1

= L/2

Let

Using trigonometric ratios, we have that

tanФ' = h'/d

= h'/L/2

= 2h'/L

So, h' = LtanФ'/2

= Ltan60°/2

= L/2 × √3

= √3L/2

So, the ratio of the height of the towers is n = h/h'

= L/2 ÷ √3L/2

= 1/√3

= 1/1.732

= 0.577

≅ 0.58

So, the ratio of the height of the towers is 0.58:1

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Answer: [tex]y=26^{\circ}[/tex]

Step-by-step explanation:

Using linear pairs, we can determine the two angles in the picture attached.

Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]y=26^{\circ}[/tex]

The rate is 1.2%.

Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account.

Given:

P = 5000

T =6 month= 1/2 year

SI= 300

We know,

SI= P*R*T/100

300= 500* R * 1 /200

60000= 500R

R= 60000/500

R= 120

R= 1.2%

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Answer:

[tex]\huge{\boxed{ \huge{\sf 10^{\frac{4}{5} } x^\frac{1}{5} }}}[/tex]

Explanation:

Exponent rules:

Given expression:

breakdown

rewrite expression

Answer: a = 2√3

First method (Pythagoras theorem):

a² + b² = c²

a² + 2² = 4²

a² = 16 - 4

a = √12

a = 2√3

Second method (sine rule):

opposite/hypotenuse = sin(x)

a/4 = sin(60)

a = 4sin(60)

a = 2√3

Third method (tan rule):

opposite/adjacent = tan(x)

a/2 = tan(60)

a = 2tan(60)

a = 2√3

Answer:

2√3

Step-by-step explanation:

From inspection of the given triangle:

As we cannot be sure that ΔABC is a right triangle since it is not marked as such, use the cosine rule to find the exact length of side a.

Cosine Rule

[tex]a^2=b^2+c^2-2bc \cos A[/tex]

where a, b and c are the sides and A is the angle opposite side a

Given:

Substitute the given values into the formula and solve for a:

[tex]\implies a^2=2^2+4^2-2(2)(4) \cos 60^{\circ}[/tex]

[tex]\implies a^2=4+16-16\left(\dfrac{1}{2}\right)[/tex]

[tex]\implies a^2=20-8[/tex]

[tex]\implies a^2=12[/tex]

[tex]\implies a=\sqrt{12}[/tex]

[tex]\implies a=\sqrt{4 \cdot 3}[/tex]

[tex]\implies a=\sqrt{4}{\sqrt{3}[/tex]

[tex]\implies a=2\sqrt{3}[/tex]

Therefore, the exact length of side a is 2√3.

To find out if ΔABC is a right triangle, use Pythagoras Theorem to solve for side a:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies a^2+2^2=4^2[/tex]

[tex]\implies a^2+4=16[/tex]

[tex]\implies a^2=12[/tex]

[tex]\implies a=\sqrt{12}[/tex]

[tex]\implies a=2\sqrt{3}[/tex]

As the measure of side a is the same as the solution found when using the cosine rule, we can conclude that ΔABC is a right triangle.

Two bikers meet at a park at A

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles.

By following of the above statement the triangle is formed shown in  the image attached below.

Thus, without using cosine formula, by drawing the triangle according to
the statement. At point A both the bikers were meet

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The number of ways committees of 2 men and 3 women can be formed is 60.

The method of arranging objects in order is called Permutation and the method of selecting things from a group of objects such that the order doesn't matter is called Combination.

Total Men = 6

Total Women = 4

Committee should consists of 2 men and 3 women

2 men from 6 men can be selected in [tex]\rm ^6 C _2[/tex] ways

3 women from 4 women can be selected in [tex]\rm ^4C_3[/tex] ways

The number of ways committees of 2 men and 3 women can be formed can be determined by Multiplication Principle

[tex]\rm ^6 C _2[/tex] *  [tex]\rm ^4C_3[/tex]

15 * 4

= 60 ways

Therefore the number of ways committees of 2 men and 3 women can be formed is 60.

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The domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).

The domain of a function f(x) is the set of all real values of x, for which real f(x) exists.

In the question, we are asked to find the domain of the function f(x) = 3/x + 2 - √(x - 3).

To find the domain of f(x), we need to check the real values of x, for which real f(x) exists.

We check each part of f(x):

For 3/x, every x gives a real value except x = 0.

For 2, every x gives a real value as it is not dependent on x.

For √(x - 3), real values exist when x - 3 ≥ 0, as negative square roots are not real.

Therefore, after assessing each term, we can say that the domain for f(x) is x - 3 ≥ 0, or x ≥ 3.

Therefore, the domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).

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The trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]

Since we have 4cos(-5B) sin3B

Using the trigonometric identity

sin(x + y) - sin(x - y) = 2cosxsiny

So, cosxsiny = [sin(x + y) - sin(x - y)]/2

Since we have 4cos(-5B) sin3B, comparing cos(-5B) sin3B with cosxsiny, we have

x = -5B and y = 3B

So, we have cos(-5B)sin3B = [sin(-5B + 3B) - sin(-5B - 3B)]/2

= [sin(-2B) - sin(-8B)]/2

=  [-sin(2B) - {-sin(8B)}]/2 [since sin(-2B) = -sin(2B)]

=  [-sin(2B) + sin(8B)]/2

= [sin(8B) - sin(2B)]/2

So, 4cos(-5B)sin3B = 4 × [sin(8B) - sin(2B)]/2

= 2[sin(8B) - sin(2B)]

So, the trigonometric identity 4cos(-5B) sin3B is equivalent to 2[sin(8B) - sin(2B)]

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Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.

Las utilidades (U') se obtienen de sustraer los costes de producción (Cp) a las utilidades netas (U). Los costes de producción (Cp) son la suma de costes variables (C') y costes fijos (C). y la utilidades netas proceden de la venta de botellas. En consecuencia, tenemos la siguiente expresión:

U' = U - Cp

U' = U - C' - C

A continuación, desarrollamos y resolvemos la ecuación resultante:

30000 = 4.50 · x - 2.50 · x - 18500

1.50 · x = 11500

x = 7667

Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.

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Answer:

Step-by-step explanation:

Proportional relationship is:

We have the ordered pair (1, 5/4), which represents:

When x = 1, the y- coordinate is equal to the coefficient of proportionality.

In this case it represents a score for one correct answer.