5. Find the quadratic equation with root alpha and beta,given that alpha-beta=2 and alpha^2-beta^2=3.​

Answer:

X equals 10.

8x - x = 70

Step-by-step explanation:

8 x 10 = 80

80 - 10 = 70

The value of A and B is 5 , 10 ;The average temperature for first ten hours is  -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)

A function is a mathematical statement used to correlate two variables.

The function given is

T(h) = - A - B * cos((pi*h)/12)

T is the temperature in degrees Fahrenheit and

h is the number of hours from midnight (0 <= h <= 24)

a. The initial temperature at midnight was - 15 degrees * F and

at Noon of New Year's Day it was 5 degrees * F

At midnight h = 0

T(h) = -15 degrees F

-15 = -A-B* cos 0

-15 = -A-B

A+B = 15------------------- (1)

At noon , h = 12 , T(h)= 5

- A - B*  cos(pi) = 5

-A - B (-1) = 5

B -A = 5 ----------------------- (2)

Solving equation 1 and 2

2B = 20

B = 10

A = 5

The value of A and B is 5 , 10

The average temperature for first ten hours is  -7.466 degree F

Find an expression for the rate that the temperature is changing with respect to h

dt/dh = +B sin ((pi*h)/12)

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Answer: B=16 and m=6

Step-by-step explanation:

in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.

The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

To purchase 13700 worth of restaurant equipment for her business.

Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.

The total amount Maria ended up paying for the equipment will be

Total amount = 371.16 × 3 × 12 + 1500

Total amount = $14,861.76

The interest of Maria on the loan will be

Interset = [(14861.76 – 13700) / 13700] x 100

Interset = 8.48%

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Answer:

Let the cost price be X

A Sells to B

profit = 20%

= cost price + 20%

= X + 20/100 of X

= 6x/ 5

B sells to C

profit = 25%

= Cost price + + 25%

= cost price + 25%

= 6x/5 + 25/100*6x/5

= 6x/5.+ 3x/10.

= 3x/2

3x/2 = 225.

3x = 450

x = 150.

sp = C. p + profit

S. p - profit = C. p

X - X/5

4x/5

4(150)/5.

120

Answer:

40%

Step-by-step explanation:

We already have our first value 20 and the second value 8. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

Step 1 ⇒ Y = 8/20

By multiplying both numerator and denominator by 100 we will get:

Step 2 ⇒ Y = 8/20 × 100/100 = 40/100

Step 3 ⇒ Y = 40

Finally, we have found the value of Y which is 40 and that is our answer.

Step-by-step explanation:

hope you can understand

Answer:

x = -31/4  or x = 17/4

Step-by-step explanation:

|4x + 7| − 4 = 20

⇔ |4x + 7| − 4 + 4 = 20 + 4

⇔ |4x + 7| = 24

⇔ 4x + 7 = 24  or 4x + 7 = -24

⇔ 4x = 24 - 7 or 4x = -24 - 7

⇔ 4x = 17 or 4x = -31

⇔ x = 17/4 or x = -31/4

Answer:

x = [tex]\frac{17}{4}[/tex]    (17/4 = 4.25)

or x =  [tex]-\frac{31}{4}[/tex]  (-31/4 = -7.75)

Step-by-step explanation:

| | is notation for absolute value

absolute value - the distance that a number is from 0

> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |

if we have | x | = 20, we could really have (without the | | ) two versions of x

either | x | = 20  ; or | -x | = 20  {because a negative x inside of the | | has the same value as positive x}

we set this up as two equations:

x = 20        or         -x = 20

                                ^ {multiply by -1}

x = 20  or   x = -20

now, let's plug our understanding into the equation

|4x + 7| - 4 = 20

first, we should simplify our equation to:

|4x + 7| - 4 = 20

           + 4   + 4

 |4x + 7|   =   24

now, let's separate this absolute value equation into two separate equations:

4x + 7 = 24:

      - 7    - 7  {subtract 7 from both sides to isolate x}

4x = 17

÷4  ÷4        {divide both sides by 4 to get 1x}

x= [tex]\frac{17}{4}[/tex]

or,

4x + 7 = -24:

      - 7    -7   {subtract 7 from both sides to isolate x}

4x     =    -31

÷4           ÷4   {divide both sides by 4 to get 1x}

 x = [tex]-\frac{31}{4}[/tex]

so, we know that

x = [tex]\frac{17}{4}[/tex]    (17/4 = 4.25)

or x =  [tex]-\frac{31}{4}[/tex]  (-31/4 = -7.75)

hope this helps!!

Answer:

3 months

Step-by-step explanation:

The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.

The second runner: $50 starting out, plus 60x for $60 each month.

To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.

155 + 25x = 60x + 50

105 = 35x

x = 3

Brainliest, please :)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex] \texttt{ \:The absolute maxima of f is f(-8) = 6} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Absolute maxima is the maximum possible value for a given x, of a function.

and here, the maximum value is at -8, and the maximum value is 6.

[tex]\qquad \tt \rightarrow \: maximum - \: \: f( - 8) = 6[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The value of e³ = 20.079.

e is an irrational number , It is a numerical constant used in mathematical constant .

The value of e = 2.718

It is asked in the question to determine the value of e³

Therefore

e³ = ( 2.718)³

e³ = 20.079

Therefore the value of e³ = 20.079.

The image of the calculation is attached with the answer.

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The answers are as follows:

a) X denotes the number of the california residents that have adequate earthquake insurance

b)  x = 1 ,2 ,3 ......

c) P( X=x ) = 0.3(1-0.3) ^ (x-1)

d)  P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

e) 0.49

f)0.42

g)0.33

It is a branch of mathematics that deals with the occurrence of a random event.

The complete question is

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?

given that 30% of California residents have adequate earthquake supplies.

a) variable X denotes the number of the california residents that have adequate earthquake insurance

b) x = 1 ,2 ,3 ......

c) p=0.3

P( X=x ) = 0.3(1-0.3) ^ (x-1)

d) P( X=1) +  P( X=2)  + P( X=3) +  P( X=4)

= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...

e) P( X≥ 3) = 1- P(X<3)

= 1- (P(X=1) + (X=2))

= 1- 0.051

= 0.49.

f) E(X)= 1/P

p is the resident who does not have adequate earthquake supplies

p= 1-0.3

p = 0.7

E(X) = 1/0.7

= 0.42

g) E(X) =  1/q

= 1/0.3

= 3.333

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The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]

[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]

[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

=21-21i

After converting into the exponential form:

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

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Based on the calculations, the equation of this hyperbola in standard form is: A. [tex]\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex].

Mathematically, the equation of a hyperbola in standard form is given by:

[tex]\frac{x\;-\;h}{a^2} + \frac{x\;-\;k}{b^2} = 1[/tex]

Given the following data:

Center (h, k) = (7, 0)

Vertex (h+a, k) = (7, 4)

Focus = (h+c, k) = (7, 5)

Also, we can deduce that the value of a and c are 4 and 5 respectively.

For the value of b, we would apply Pythagorean's theorem:

c² = a² + b²

b² = c² - a²

b² = 5² - 4²

b² = 9.

Substituting the parameters into the standard equation, we have:

[tex]\frac{x\;-\;7}{4^2} + \frac{y\;-\;0}{3^2} = 1\\\\\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex]

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Answer:

write three methods of writing set. Give one example of each methods.

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Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

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

Given:  [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution: We need to first solve for y in the equation that was provided so we can determine the slope.  Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

Divide both sides by 4

Plug in the values

Simplify and distribute

Subtract 3 from both sides

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75

Answer:

The costco basmati rice

Step-by-step explanation:

Under the label it is given that the bag is 18.14 kg

When converted to lbs= 18.14*2.2~39.91

39.91lbs>10lbs, so it has more quantity of rice: Costco Basmati

Answer:

The Costco bag is a better deal as each pound is $0.65 cheaper

Step-by-step explanation:

Let make the weight of each bag in a common unit

18.14kg = about 40 pounds (formula: multiply the mass value by 2.205)

Now find how much it cost per pound for each bag,

Costco: 49.99 / 40 = $1.25 per pound

Bulkmarket: 18.99 / 10 = $1.90 per pound

1.25 < 1.90

Answer:

12x^18

Step-by-step explanation:

Answer:

[tex]52\sqrt{3} ft^{2}[/tex]

Step-by-step explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x [tex]4\sqrt{3}[/tex]

[tex]=44\sqrt{3} ft^{2}[/tex]

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]

Area of Trapezoid = Area of Rectangle + Area of Triangle

[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]

Answer:

A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)

   = 2[tex]\sqrt{3}[/tex] × 26

   = 52[tex]\sqrt{3}[/tex] ft²

   ≈ 90.1 ft² ( to the nearest tenth )

Answer:

B

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].

We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].

Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]

Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].

Answer:

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

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )

m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]

Answer:

D. x = -2; x = 3/4

Step-by-step explanation:

[tex] \huge \tt \underline {\green{Answer}}[/tex]

If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees

ie. $1 = Rs 66.79

$ 1 = 66.79 × 1

$ ? = 110.66

$ = New / old

$ = 110.66 / 66.79

$ = 1.65683485552

or

$1.66 = 110.66

7.5 pounds of the $0.82 per lb candy must be used in the mixture.

First, let's define the variables:

We want to make 9 lb of mixture, then:

x + y = 9.

And the price of these 9 pounds must be $0.91, then we can write:

x*$0.82 + y*$1.36 = 9*$0.91 = $8.19

Then we have a system of equations:

x + y = 9.

x*$0.82 + y*$1.36 = $8.19

We can isolate y on the first equation so we get:

y = 9 - x

Now we can replace that on the other equation:

x*$0.82 + (9 - x)*$1.36 = $8.19

And now we can solve this for x.

x*($0.82 - $1.36) = $8.19 - 9*$1.36

-x*$0.54 = -$4.05

x = (4.05/0.54) = 7.5

So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.

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Answer:

angle M = angle P ( 90°)

so MN is parallel to pq

MN makes 90° with UT so it is perpendicular