Condense the logarithmic expression using logarithmic properties.

3 log x + 2 log y - log y

Answer:

D. 7n - 3 = 32 Because is contains the neccesary amount of variables needed to be considered as an expression.

Step-by-step explanation:

Hope this helps you! :D

The area of one lateral face of the triangular prism could be 20 ft².

a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first base, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Since the base of the prism is triangular so there will be three lateral faces.

Dimensions of rectangular lateral faces are:

1)8 feet by 2.5 feet

2)8 feet by 6 feet

3) 8 feet by 6. 5 feet

Area of the lateral face with dimension 8 feet by 2.5 feet = 8*2.5 =20 ft²

Area of the lateral face with dimension 8 feet by 6 feet = 8*6 =48 ft²

Area of the lateral face with dimension 8 feet by 6.5 feet = 8*6.5 =51 ft²

Therefore, the area of one lateral face of the triangular prism could be 20 ft².

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Answer:

what's up w u people and not giving context

Step-by-step explanation:

1. add ur complete problem

2. show a picture or add the question(s)

3. ur done at that point

Answer:

x>5, so

let x=6

6-3=3

+

6+2=8

-

6-5=1

3+8-1=10

answer=10

Answer:

35 percent

Step-by-step explanation:

1050 / 3000 as a percent

1050 / 3000 = 105 / 300

Divide both sides by 3:

300 / 3 = 100

105 / 3 = 35

35 / 100 = 35 percent

34%

This is because when you divide 1,050 by 3,000 you get 0.34 then turn that into a percent then there you go

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

For completion of table you should know the basics formulas :-

[tex]\sf{=}{\sf{\dfrac{Sum \:of\: class \:interval }{ 2}}}[/tex]

That is,

[tex]\sf{=}{\sf{\dfrac{ = 18 + 25}{2}}}[/tex]

[tex]\sf{=}{\sf{\dfrac{ = 43}{2}}}[/tex]

[tex]\sf{= 21.5 }[/tex]

[ For more calculation ,Please refer the attachment ]

[tex]\sf{ fx = frequency {\times} midpoint }[/tex]

[tex]\sf{ fx = 8 {\times} 21.5 }[/tex]

[tex]\sf{ fx = 172 }[/tex]

[ For more calculation please refer the attachment ]

We have to calculate mean, median and mode of the given data

We know that the,

Mean = Sum of all observation / no. of observation

That is

[tex]\sf{ Mean = }{\sf{\dfrac{ {\sigma}fx}{{\sigma}x}}}[/tex]

Subsitute the required values,

[tex]\sf{ Mean = }{\sf{\dfrac{ 1811 }{ 187.5}}}[/tex]

[tex]\sf{ Mean = 9.65}[/tex]

Hence, The mean of the given data is 9.65

We know that, For odd numbers

[tex]\sf{ Median = l + }{\sf{\dfrac{ (n/2 - c)}{ f}}}{\sf{ h }}[/tex]

Here,

[tex]\sf{ n = }{\sf{\dfrac{ 50 + 1}{ 2}}}[/tex]

[tex]\sf{ n = }{\sf{\dfrac{ 50 }{ 2}}}[/tex]

[tex]\sf{ n = 25 }[/tex]

Subsitute the required values in the above formula :-

[tex]\sf{ Median = 34 + }{\sf{\dfrac{ (25-20)}{ 14}}}{\sf{ 7 }}[/tex]

[tex]\sf{ = 34 + }{\sf{\dfrac{ 5}{ 14}}}{\sf{ {\times}7 }}[/tex]

[tex]\sf{ = 34 + }{\sf{\dfrac{ 35}{ 14}}}[/tex]

[tex]\sf{ = 34 + 2.5}[/tex]

[tex]\sf{ = 36.5 }[/tex]

Hence, The median of the given data is 36.5 .

We know that,

[tex]\sf{ M= l }{\sf{\dfrac{ (f1 - fo)}{ 2f1 - fo - f2 }}}{\sf{ {\times} h }}[/tex]

Subsitute the required values,

[tex]\sf{ M= 34 }{\sf{\dfrac{ (14 - 12)}{ 2(14)- 12 - 12 }}}{\sf{ {\times} 7 }}[/tex]

[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 28 - 24 }}}{\sf{ {\times} 7 }}[/tex]

[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 2}{ 4 }}}{\sf{ {\times} 7 }}[/tex]

[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 1}{ 2 }}}{\sf{ {\times} 7 }}[/tex]

[tex]\sf{ M= 34{\times}}{\sf{\dfrac{ 7}{ 2 }}}[/tex]

[tex]\sf{ M= 34 + 3.5 }[/tex]

[tex]\sf{ M= 37.5 }[/tex]

So,

Hence ,The mode of the given data is 37.5 .

Answer:

1770

Step-by-step explanation:

multiply the mass value by 1000

that is the easy way

Answer:

6x² + 4x + 10

Step-by-step explanation:

(2x - 2)(3x + 5)

2x(3x + 5) - 2(3x + 5)

6x² + 10x - 6x + 10

6x² + 4x + 10 ans.

hope this helps you !

Answer:

4

Step-by-step explanation:

Answer:

Option 4 is correct.

Step-by-step explanation:

To find: Polynomial whose solution are not real numbers.

Given Polynomials are Quadratic Polynomial.

So, we can check if solution of quadratic polynomial by find & checking value of discriminant.

Standard form of Quadratic polynomial is given by

ax² + bx + c

then Discriminant, D = b² - 4ac

If, D > 0 ⇒ Solutions are distinct real numbers

if, D = 0 ⇒ Solutions are equal real numbers

if, D < 0 ⇒ Solutions are not real numbers (They are complex conjugates)

Option A:

By comparing with standard form

a = 1 , b = -6 , c = 3

D = (-6)² - 4 × 1 × 3 = 36 - 12 = 24 > 0

Thus, Solutions are Real numbers.

Option B:

By comparing with standard form

a = 1 , b = 4 , c = 3

D = (4)² - 4 × 1 × 3 = 16 - 12 = 4 > 0

Thus, Solutions are Real numbers.

Option C:

By comparing with standard form

a = -1 , b = -9 , c =-10

D = (-9)² - 4 × (-1) × (-10) = 81 - 40 = 41 > 0

Thus, Solutions are Real numbers.

Option D:

By comparing with standard form

a = 1 , b = 2 , c = 3

D = (2)² - 4 × 1 × 3 = 4 - 12 = -8 < 0

Thus, Solutions are not Real numbers.

Therefore, Option 4 is correct.

Unit conversion is a way of converting some common units into another without changing their real value. The amount that is paid by the family in mortgage per month is equal to $1200.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

As it is given to us that the family uses 12,986.64 Swiss francs per year to pay a mortgage. Therefore, the amount that is paid by the family in mortgage per month can be written as,

[tex]\text{Mortgage for a month} = \dfrac{\text{Mortgage of the family for a complete year}}{\text{Number of Months}}\\\\\\\text{Mortgage for a month} = \dfrac{\rm 12,986.64\ Swiss\ francs}{12} = 1082.22\rm \ Swiss\ francs[/tex]

Thus, the family needs to pay 1082.22 swiss francs every month in the mortgage.

Now, it is mentioned in the problem that 1 Swiss franc = 1.11 US dollars, therefore, 1082.22 swiss francs when converted to US dollars will be equal to,

[tex]\rm 1\ Swiss\ francs = \$1.11 \\\\1082.22\ Swiss\ francs = 1082.22 \times 1.11 = \$1,201.26 \approx \$1,200[/tex]

Hence, the amount that is paid by the family in mortgage per month is equal to $1200.

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What is [tex]\sf{\displaystyle\frac{1}{4}}[/tex] of 12?

In order to find it, we should divide 12 by 4:-

3

Now, solve our word problem:-

Matthew bought 12 roses. [tex]\sf{\displaystyle\frac{1}{4} }[/tex] of these roses were white.

And we already know how to solve this problem :)

Hence,

[tex]\bigstar{\boxed{\pmb{3~of~the~roses~were~white}}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

huh

Step-by-step explanation:

Using compound interest, it is found that you would have $1524.86.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, we have that the values of the parameters are given by: P = 1250, r = 0.05, n = 4, t = 4. Hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(4) = 1250\left(1 + \frac{0.05}{4}\right)^{4 \times 4} = 1524.86[/tex]

Tou would have $1524.86.

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Answer:

-4, 10.

Step-by-step explanation:

(x – 3)^2 = 49

x - 3 = ±√49

x = 3 ± 7

= -4, 10.

Answer: ASA

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

It all adds up. Ex; 2*2=4   4-3=1

and continues through the rest of the table

Answer:

10x + 12y -15 =0

Step-by-step explanation

Answer:

Step-by-step explanation:

h = -5t^2 - 6t + 44

I'll assume 0 meters is the ground height.  That would mean we want to know the time, t, for h to be = 0 meters:

h = -5t^2 - 6t + 44

0 = -5t^2 - 6t + 44

5t^2 + 6t -44 = 0

Solve using the quadratic equation:  2.43 and - 3.63 seconds.  We'll use the positive value:  2.43 seconds for the ball to reach the ground.  Save the -3.63 value for the Klingons.  

We can also solve by graphing the function, as per the attached image.  Note that the starting time of 0 seconds, the ball is at 44 feet.  It reaches the x axis at 2.43 seconds (where x = 0, the ground).

Answer:

t = 2.43 s (nearest hundredth)

Step-by-step explanation:

Given equation: [tex]h=44-6t-5t^2[/tex]

where:

When the ball hits the ground, h = 0

[tex]\implies 44-6t-5t^2=0[/tex]

[tex]\implies 5t^2+6t-44=0[/tex]

Using the quadratic formula when [tex]ax^2+bx+c=0[/tex] and where:

[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

  [tex]=\dfrac{-(6)\pm\sqrt{(6)^2-4(5)(-44)}}{2(5)}[/tex]

  [tex]=\dfrac{-6\pm\sqrt{916}}{10}[/tex]

  [tex]=\dfrac{-6\pm2\sqrt{229}}{10}[/tex]

  [tex]=\dfrac{-3\pm\sqrt{229}}{5}[/tex]

  [tex]=2.43, -3.63 \ \textsf{(nearest hundredth)}[/tex]

As time is positive, t = 2.43 s (nearest hundredth)

The trigonometry identity sin(x + y) = sinx cosy + cosx siny.

sin(x + y) is one of the identities in trigonometry for compound angles.

The angle (x + y) represents the compound angles.

sin(x + y) = sinx cosy + cosx siny

To prove sin(x + y) = sinx cosy + cosx siny

Consider OX as a rotating line anti-clockwise. Let angle XOY = a

the making of an acute angle b the rotation in the same direction is

angleYOZ = b , angle XOZ = a + b

From triangle PTR,

∠TPR = 90 - ∠PRT , ∠ROX = a

From the right-angled triangle PQO

sin(a + b) = PQ/OP

= (PT + TQ) / OP

= PT/OP + TQ/OP

= PT/PR × PR/OP + RS/OR × OR/OP

= cos (∠TPR ) sinb + sina cosb

= sina cosb + cosa sinb

if we replace a=x and b=y

Therefore, sin(x + y) = sinx cosy + cosx siny.

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Answer:

12.39cm

Step-by-step explanation:

cos 25°=AB/12.5

AB=12.5 cos 25°

cos 25°=0.9912

AB=12.5×0.9912

=12.39cm

By taking the quotient between the volumes, we conclude that he must use the blue cup 16 times or the green cup 4 times.

The volume of the sink is 512π in^3.

The blue cup is a cylinder of diameter = 4 in and a height = 8 in, then its volume is:

V = π*(4in/2)^2*8in = 32π in^3

The number of times that he needs to use this cup is given by:

N = (512π in^3)/(32π in^3) = 512/32 = 16

He needs to use 16 times the blue cup.

The green cup has a diameter = 8in and a height = 8in, then its volume is:

V' =π*(8in/2)^2*8in = 128π in^3

The number of times that he must use this cup is:

N' = (512π in^3/ 128π in^3) = 512/128 = 4

He needs to use 4 times the green cup.

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Given -

ps - use 3.14 for π

To find -

Solution -

We know to find the circumference of a circle we use the formula C=2πr.

Doing the same,

C = 2 × 3.14 × 2

C = 12.56 feet

[tex]\sf\large\underline{Given:-}[/tex]

[tex]\rightarrow[/tex] Radius(r) of the circle = 2 ft.

[tex]\rightarrow[/tex] Value of Pie(π) = 3.14

[tex]\sf\large\underline{To\: Find:-}[/tex]

[tex]\rightarrow[/tex] Circumference of the circle.

[tex]\sf\large\underline{Formula \: Used:-}[/tex]

[tex]\rightarrow[/tex] Circumference of circle = [tex]\sf{2πr}[/tex]

[tex]\sf\large\underline{Solution:-}[/tex]

[tex]\rightarrow[/tex] Circumference of circle = [tex]\sf{2πr}[/tex](putting the value of π and r from the above given)

[tex]\rightarrow[/tex] [tex]\sf{=2×3.14×2}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=12.56\: ft.}[/tex]

Therefore, circumference of the given circle = [tex]\sf{12.56\: ft.}[/tex]

_____________________________

Hope it helps you:)

Answer:

ο Neither is correct.

Step-by-step explanation:

1) the vertex has coordinates (5;-7) the equation must be made up according to the rule: y=(x-x₀)²-y₀, where (x₀;y₀) - the coordinates of the vertex;

2) according to the rule above the equation of the given graph is:

y=(x-5)²-7;

3) finally, 'neither is correct'

Answer:

the answer is 16

Step-by-step explanation:

look at the photo

Answer:

27

Step-by-step explanation:

we know that 4 multiplied with something is 36

=>     4x = 36

=>     x = 36/4

=>     x = 9

so we have to multiply 3 with 9

=>     3*9 = 27

The major axis, which is horizontal, is of the length [tex]2\sqrt{7.29} = 5.4[/tex] ft, the miror axis, which is vertical, is of the length [tex]2\sqrt{6.25} = 5[/tex] ft.

Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:

[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1[/tex]

For the considered case, the equation of the considered ellipse is:

[tex]\dfrac{x^2}{(\sqrt{7.29})^2} + \dfrac{y^2}{(\sqrt{5.4})^2} =1[/tex]

Thus, the major axis, which is horizontal, is of the length [tex]2\sqrt{7.29} = 5.4[/tex] ft,

the miror axis, which is vertical, is of the length [tex]2\sqrt{6.25} = 5[/tex] ft.

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Answer:

The mirror has a vertical orientation and is 5.4 ft tall.

Step-by-step explanation:

Got it right. The major axis is vertical (the ellipse has a vertical orientation) because the y^2 term comes first. It is 5.4 ft tall because if you take the square root of the number under the y^2 term (square root of 7.29), it is equal to 2.7. This is only the distance from the center to one vertex on the major axis, and so twice 2.7 is 5.4, and the mirror is 5.4 ft tall.

Also I know I am weeks late, but maybe this will help others at some point. Sorry I didn't get here in time!

The probability density function of the time to failure of an electronic component in a copier (in hours) is [tex]\rm P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}[/tex].

Probability Density Function is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

The given function is;

[tex]\rm =\dfrac{ e^\frac{-x}{1074}}{1074}[/tex]

The probability density function of the time to failure of an electronic component in a copier (in hours) is given by;

[tex]\rm P(a < x < b) =\int\limits^a_b {p(x)} \, dx[/tex]

For the electronic component, the probability will be:

[tex]\rm P(a < x < b) =\int\limits^a_b {\rm \dfrac{ e^\frac{-x}{1074}}{1074}} \, dx\\\\ P(a < x < b) =\int\limits^a_b {\rm \dfrac{1074}{1074} e^\frac{-x}{1074}}} \, dx\\\\P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}[/tex]

Hence, the probability density function of the time to failure of an electronic component in a copier (in hours) is [tex]\rm P(a < x < b) =e^\frac{-b}{1074}-e^\frac{-a}{1074}[/tex].

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The value of  [tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  or  [tex]\rm cot\theta = -\frac{8}{3}[/tex] the option first is correct.

It is given that the  [tex]\rm tan\theta = -\frac{3}{8}[/tex]

It is required to find which expression is equivalent to [tex]\rm cot\theta[/tex].

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have  [tex]\rm tan\theta = -\frac{3}{8}[/tex] , which is a ratio of side opposite side of an angle to the side adjacent to the angle.

We know [tex]\rm cot\theta[/tex] is a ratio of the side adjacent to the angle to the side opposite to the angle ie. it is the opposite of the [tex]\rm \tan\theta[/tex] ie.

The  [tex]\rm tan\theta = \frac{1}{cot\theta}[/tex]

or    [tex]\rm cot\theta = \frac{1}{tan\theta}[/tex]

Putting the value of [tex]\rm tan\theta[/tex] in the above equation, we get:

[tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  

Or

[tex]\rm cot\theta = -\frac{8}{3}[/tex]

Thus, the value of  [tex]\rm cot\theta = \frac{1}{ -\frac{3}{8} }[/tex]  or  [tex]\rm cot\theta = -\frac{8}{3}[/tex].

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Answer:

first option

Step-by-step explanation: