x2+3y=4 solve for x. (someone help asap)

Answer:

B) x+(2x+5)=29

Step-by-step explanation:

Micah = x

Aria =2x+5

x+(2x+5)=29

Answer:

let micah age be X and Aria age be Y then go through with question what did it say .

Answer:

The first and the fourth one.

The ones that could be rationalized are automatically the ones you should pick.

Answer:

They wrapped their school textbooks with paper.

Step-by-step explanation:

Susie King Taylor was born in 1848, a period when African Americans were not allowed to learn how to read and write. She lived with her grandmother and siblings. Taylor would secretly go to the house of her grandmother's friend known as Mrs. Woodhouse. For two years, she would do this secretly with her brother, wrapping her textbooks with paper so as not to be seen by the policemen.

She also made a white friend known as Katie O'Connor who promised to teach her if she did not tell her father. Katie did this for four months. Later, their landlord's son also volunteered to teach Susie.

Answer:

The direction cosines are:

[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex]  and  [tex]\frac{4}{\sqrt{42} }[/tex]  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = [tex]\frac{a . i}{|a| . |i|}[/tex]               ---------------------(i)

cos β = [tex]\frac{a.j}{|a||j|}[/tex]               ---------------------(ii)

cos γ = [tex]\frac{a.k}{|a|.|k|}[/tex]             ----------------------(iii)

And from these we can get the direction angles as follows;

α =  cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )

β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )

γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i =  (5i + j + 4k) . (i)

a . i = 5         [a.i is just the x component of the vector]

a . j = 1            [the y component of the vector]

a . k = 4          [the z component of the vector]

Also

|a|. |i| = |a|. |j| = |a|. |k| = |a|           [since |i| = |j| = |k| = 1]

|a| = [tex]\sqrt{5^2 + 1^2 + 4^2}[/tex]

|a| = [tex]\sqrt{25 + 1 + 16}[/tex]

|a| = [tex]\sqrt{42}[/tex]

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = [tex]\frac{5}{\sqrt{42} }[/tex]

cos β =  [tex]\frac{1}{\sqrt{42} }[/tex]              

cos γ =  [tex]\frac{4}{\sqrt{42} }[/tex]

From the value, now find the direction angles as follows;

α =  cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )

α =  cos⁻¹ ( [tex]\frac{5}{\sqrt{42} }[/tex] )

α =  cos⁻¹ ([tex]\frac{5}{6.481}[/tex] )

α =  cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )

β = cos⁻¹ ( [tex]\frac{1}{\sqrt{42} }[/tex] )

β = cos⁻¹ ( [tex]\frac{1}{6.481 }[/tex] )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )

γ = cos⁻¹ ([tex]\frac{4}{\sqrt{42} }[/tex])

γ = cos⁻¹ ([tex]\frac{4}{6.481}[/tex])

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

Conclusion:

The direction cosines are:

[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex]  and  [tex]\frac{4}{\sqrt{42} }[/tex]  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

hope it will help you.......

Answer:

B. Ordinal

Step-by-step explanation:

The level of measurement used for a variable in statistical analysis determines what summary statistics and analysis are possible. In statistical analysis, we have three types of level of measurement.

Nominal , Ordinal  , Interval/ Ratio

The nominal is the most basic level of measurement. It is the  qualitative level of measurement such as color or number.  Data in Nominal scale of measurement are  stored as a word or  as numerical code.

Ordinal level of measurement  are variables based on ranks or hierarchy. Ordinal level of measurement posses a sequential step-wise order but the intervals between the variables are not  equal. They are usually expressed in frequencies.

Therefore, the level of measurement of variable that determines the livability rankings for cities based on their ranks or hierarchy is Ordinal.

The interval/ratio level of measurement  is the highest  level of measurement where  data are  being measured and ordered in a sequential process.

Answer:

I'd ont now that your questions

Answer:

The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].

Step-by-step explanation:

Given the extremes of the diameter of the sphere, its center is the midpoint, whose location is presented below:

[tex]C(x,y,z) = \left(\frac{4+8}{2},\frac{1+3}{2},\frac{6+8}{2}\right)[/tex]

[tex]C(x,y,z) = (6,2,7)[/tex]

Any sphere with a radius [tex]r[/tex] and centered at [tex](h,k,s)[/tex] is represented by the following equation:

[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]

Let be [tex](x,y,z) = (4,1,6)[/tex] and [tex](h,k,s) = (6,2,7)[/tex], the radius of the sphere is now calculated:

[tex](4-6)^{2}+(1-2)^{2}+(6-7)^{2}=r^{2}[/tex]

[tex]r = \sqrt{6}[/tex]

The equation of a sphere with endpoints at (4, 1, 6) and (8, 3, 8) is [tex](x-6)^{2}+(y-2)^{2}+(z-7)^{2} = 6[/tex].

Answer:

x = 9 or x = -21

Step-by-step explanation:

Solve for x over the real numbers:

x^2 + 12 x - 189 = 0

The left hand side factors into a product with two terms:

(x - 9) (x + 21) = 0

Split into two equations:

x - 9 = 0 or x + 21 = 0

Add 9 to both sides:

x = 9 or x + 21 = 0

Subtract 21 from both sides:

Answer: x = 9 or x = -21

Answer:

Step-by-step explanation:

Hello, the sum of the roots is -9=-4-5 and the product is 20=(-4)*(-5) so we can write

[tex]x^2+9x+20=(x+4)(x+5)[/tex]

thanks

Answer:

( x + 4 ) ( x + 5 )

Step-by-step explanation:

For this polynomial, we will factor the coefficient of the x^2 term and the constant.

The coefficient of x^2 is 1, which just factors to 1.

The constant 20 factors into 2 * 2 * 5.

Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9.   4 + 5 = 9, so we will choose that.

Using the standard binomials, we will factor the polynomial:

( x^2 + 9x + 20 )

= ( x + 4 ) ( x + 5)

We can check by performing foil:

= ( x + 4 ) ( x + 5 )

= ( x * x + x * 5) + ( 4 * x + 4 * 5)

= ( x^2 + 5x ) + ( 4x + 20 )

= ( x^2 + 9x + 20 )

Thus, we have successfully factored our polynomial.

Cheers.

Answer:

y = 7(1 + x/5)

Step-by-step explanation:

7x - 5y = -35

-5y = -35 - 7x

5y = 35 + 7x

y = (35 + 7x) / 5

y = 7 + 7x/5

y = 7(1 + x/5)

Answer: 2,269

Step-by-step explanation: Divide by 2 to get half of a number

Answer:

2269

Step-by-step explanation:

just simply divide 4538 by 2

Here is the correct format for the question.

[tex]x'_1 = 7x_1 +4x_2+ 12x_3 , \ \ x'_2 = x_1 + 2x_2 + x_3 , \ \ x'_3 = -3x_1 -2x_2 -5x_3[/tex] . Then find the solution that satisfies  [tex]x \limits ^{\to} = \left[\begin{array}{c}0\\1\\-2\end{array}\right][/tex]

Answer:

[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]

Step-by-step explanation:

From the figures given above:

the matrix can be computed as,

[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] x \limits ^{\to} = \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = x \limits ^{\to} = \left[\begin{array}{c}x_1'\\x_2'\\x_3'\end{array}\right][/tex]

The first thing we need to carry out is to determine the eigenvalues of A,

where:

[tex]A = \left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right][/tex]

[tex]|A-rI|=0[/tex]

[tex]\begin {vmatrix} 7-r&4&12\\1&2-r&1\\-3&-2&-5-r \end {vmatrix}=0[/tex]

the eigenvalues are r = 0, 1, 3

However, the eigenvector correlated to each eigenvalue can be calculated as follows.

suppose  r = 0

(A - rI) x = 0

[tex]\left[\begin{array}{ccc}7&4&12\\1&2&1\\-3&-2&-5\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right] = \left[\begin{array}{c}0\\0\\0\end{array}\right][/tex]

now the eigenvector is [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]

However, for eigenvalue = 1, we have :  [tex]\left[\begin{array}{c}-4\\1\\2\end{array}\right][/tex]

for eigenvalue = 3, we have:[tex]\left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]

The solution now can be computed as :

[tex]x(t)= c_1 \left[\begin{array}{c}-4\\1\\2\end{array}\right] + c_2e^t \left[\begin{array}{c}-4\\3\\1\end{array}\right]+ c_3e^{3t} \left[\begin{array}{c}-2\\-1\\1\end{array}\right][/tex]

Similarly, the fundamental matrix solution is:

[tex]\left[\begin{array}{ccc}-4&-4e^t&-2e^{3t}\\1&3e^t&-e^{3t}\\2&e^t&e^{3t}\end{array}\right][/tex]

[tex]-4c_1 -4c_2-2c_3 =0 \\ \\ c_1 + 3c_2 -c_3 = 1\\ \\ 2c_1+c_2 +c_3 = -2[/tex]

Solving the above equation, we get:

[tex]\mathbf{c_1 = -3, c_2 = 2, c_3 = 2}[/tex]

Answer: (3,-10)

Step-by-step explanation:

Using the translated rule that x is increase by 5 and y  is decreased by 7 put it into the equation and solve for  the coordinates of k.

(-2 +5 ) = 3

(-3 -7) = -10

So now the coordinates will be (3,-10)

Answer:

Each book costs 26 dollars

Step-by-step explanation:

Let b be the price of each book

8*b +17 = 225

Subtract 17 from each side

8b+17-17 = 225-17

8b =208

Divide by 8

8b/8 = 208/8

b =26

Each book costs 26 dollars

Answer:

1). Mass of water present= 18000 kg

2).4/3 meters deep

Step-by-step explanation:

Area of the rectangle= 6*3= 18m²

Volume of water in the pool

= Deepness of water*area of rectangle

= 1*18

= 18 m³

density of water is about 1 gram per cubic centimeter

In kg per m³= 1000 kg/me

Mass of water present= density*volume

Mass of water present= 1000*18

Mass of water present= 18000 kg

2)6000 kilograms of water is added to 18000 of

Total mass present= 6000+18000

Total mass present=24000 kg

If density= 1000kg/m³

Volume present= mass/density

Volume present= 24000/1000

Volume present= 24 m³

Area of the rectangle= 18 m²

deepness of the pool= volume/area

deepness of the pool= 24/18

deepness of the pool= 4/3 meters deep

Answer:

0.0893

Step-by-step explanation:

Let A be the event that the individual has the disease

Let Aⁿ be the event that the individual doesn't have the disease

Let B be the event of a positive result showing.

Now,

We are told One in 1000 adults is afflicted with the disease.

Thus;

P(A) = 1/1000 = 0.001

P(Aⁿ) = 1 - 0.001 = 0.999

Also,we are told that when an individual has the disease, a positive result will occur 98% of the time.

Thus;

P(A|B) = 98% = 0.98

Also, we are told that an individual without the disease will show a positive result only 1% of the time. Thus;

P(Aⁿ|B) = 1% = 0.01

Now, from fundamental rule, let's find P(B). Thus;

P(B) = [P(A|B) × P(A)] + [P(Aⁿ|B) × P(Aⁿ)]

P(B) = (0.98 × 0.001) + (0.01 × 0.999)

P(B) = 0.01097

Now, from Baye's theorem, If a randomly selected individual is tested and the result is positive, the probability that the individual has the disease is given by;

P(A|B) = [P(A|B) × P(A)]/P(B)

P(A|B) = (0.98 × 0.001)/0.01097

P(A|B) = 0.0893

Answer:

10.95 or 11 if rounded up

Step-by-step explanation:

The side length of a pool shaped like a square with an area 120ft² is

S = [tex]\sqrt{120}= 10.954[/tex]

Given,

 Let side of the pool = S

      Area of the pool = S² = 120

      Hence, the side of the pool = S = [tex]\sqrt{120}= 10.954[/tex] ft

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Answer:

The tree is approximately 22.707 meters tall.

Step-by-step explanation:

The geometric diagram of the problem is included below as attachment. The height of the tree is found by means of trigonometric functions:

[tex]\tan \alpha = \frac{h}{w}[/tex]

Where:

[tex]\alpha[/tex] - Elevation angle, measured in sexagesimal degrees.

[tex]h[/tex] - Height of the tree, measured in meters.

[tex]w[/tex] - Length of the tree shadow, measured in meters.

The height of the tree is cleared in the equation:

[tex]h = w\cdot \tan \alpha[/tex]

If [tex]w = 51\,m[/tex] and [tex]\alpha = 24^{\circ}[/tex], the height is:

[tex]h = (51\,m)\cdot \tan 24^{\circ}[/tex]

[tex]h \approx 22.707\m[/tex]

The tree is approximately 22.707 meters tall.

Answer:

A function is a mathematical device that converts one value to another in a known way. ... The set of allowable inputs to a given function is called the domain of the function. The set of possible outputs is called the range of the function.

Step-by-step explanation:

Hopefully this was mindfull

The input set of a function is called the "Domain" of the function.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For any function, the values which we are putting form a set of intervals called domain.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Hence "The input set of a function is called the "Domain" of the function".

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Answer:

D.

(-7, 3)

Step-by-step explanation:

Given equation

y - 3 = 4(x + 7)

points are in form of (x,y) that is first value represent value of coordinate and

second value y represents value of y coordinates.

to find which point lies on given line equation we need to substitute value of x and see if value of y obtained is same as given in the option or not.

______________________________________

A.

(7, 3)

substituting x with 7 in the equation

y - 3 = 4(7 + 7)

=> y - 3 = 4(14)

=> y - 3 = 56

=> y = 56+3 = 59

Thus, we see value of y when x is 7 is 59

which is not equal to 3 as given in option A hence option A is not correct choice

B.

(7, -3)

As seen above for x = 7 , y is 59 hence option B is also incorrect

C.

(-7, -3)

substituting x with -7 in the equation

y - 3 = 4(-7 + 7)

=> y - 3 = 4(0)

=> y - 3 = 0

=> y = 0+3 = 3

Thus, we see value of y when x is -7 is 3

which is not equal to -3 as given in option C hence option C is not correct choice

D.

(-7, 3)

As calculated above value of y when x is -7 is 3

hence

option D is correct choice.

Answer:

its the 3rd 1

Step-by-step explanation:

Answer:

4/16 pieces are in 2/8, 5/8 pieces are in 10/16, 8/8 pieces are in 4/4

Step-by-step explanation:

multiply or divide both the numerator (top number) and the denominator (bottom number) by a number that will give you a common denominator

[tex]\frac{2*2}{8*2} =\frac{4}{16} \\\frac{10/2}{16/2} =\frac{5}{8} \\\frac{4*2}{4*2}=\frac{8}{8}[/tex]

Answer: Fabio is four feet above the ground level.

Step-by-step explanation:

Answer:

  $1108.25

Step-by-step explanation:

Danielle's commission on $4300 in sales is ...

  0.0775 × $4300 = $333.25

That, added to her base salary, gave her weekly earnings of ...

  $333.25 +775 = $1108.25 . . . . Danielle's pay last week

Answer:

$117.00

Step-by-step explanation:

-earns $7.00 per hour as a cashier

-earns $6.00 per hour as a bagger

-earns $5.00 per hour as a stocker

-works 4 hours as a cashier

-works 9 hours as a bagger

-works 7 hours as a stocker

First, find the amount of money earned in the week while working as a cashier.  We know from the information we picked out that Surge works $7.00 per hour as a cashier and he works 4 hours that week.  Therefore, we need to multiply the amount of money made per hour by the amount of hours worked in a week.:

$7.00/hr * 4 hrs=$28.00 made as a cashier

Next, find the amount of money Surge made as a bagger.  Do the same thing as you did with the cashier calculations, except that this time, he earns $6.00 per hour and he works 9 hours as a bagger.:

$6.00/hr * 9 hrs=$54.00 made as a bagger

Then, find the amount of money made as a stocker.  It's the same as everything else, just that Surge know earns $5.00 per hour and he works 7 hours as a stocker.  So, do the last set of multiplication:

$5.00/hr * 7hrs=$35.00 made as a stocker

Finally, the question asks for the average amount of money made per week, so add up all you calculations to get that average amount:

$28.00+$54.00+$35.00=$117.00

Surge makes an average of $117.00 in a given week.

The serge average pay per hour will be $117.00.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that earns $7.00 per hour as a cashier, earns $6.00 per hour as a bagger, earns $5.00 per hour as a stocker, and works 4 hours as a cashier -works 9 hours as a bagger -works 7 hours as a stocker.

First, find the amount of money earned in the week while working as a cashier.  We know from the information we picked out that Surge works $7.00 per hour as a cashier and he works 4 hours that week.  Therefore, we need to multiply the amount of money made per hour by the number of hours worked in a week.:

$7.00/hr  x  4 hrs=$28.00 made as a cashier

Next, find the amount of money Surge made as a bagger.  Do the same thing as you did with the cashier calculations, except that this time, he earns $6.00 per hour and he works 9 hours as a bagger.:

$6.00/hr x 9 hrs=$54.00 made as a bagger

Then, find the amount of money made as a stocker.  It's the same as everything else, just that Surge now earns $5.00 per hour and he works 7 hours as a stocker.  So, do the last set of multiplication:

$5.00/hr x  7hrs=$35.00 made as a stocker.

Finally, the question asks for the average amount of money made per week, so add up all your calculations to get that average amount:

$28.00+$54.00+$35.00=$117.00

Therefore,  the serge average pay per hour will be $117.00.

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Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{62}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{x ° + 118 ° = 180 ° }[/tex]

( Sum of angle in straight line )

Move 118 to right hand side and change it's sig

⇒[tex] \sf{x ° = 180 ° - 118 °}[/tex]

Calculate

⇒[tex] \sf{x = 62 °}[/tex]

Hope I helped!

Best regards!!

Answer:

The angle of elevation of the sun to the nearest hundredth of a degree is 44.07°

Step-by-step explanation:

Here is the complete question:

A building 86.53 feet tall has a shadow that is 89.39 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree.

Step-by-step explanation:

Please see the attachment below for an illustrative diagram:

From the diagram

/AC/ is the height of the building

/CB/ is the length of the shadow

/AC/ = 86.53 feet

/CB/ 89.39 feet

θ is the angle of elevation

Consider triangle ABC

/AC/ is the opposite

and /CB/ is the adjacent

From

tanθ =[tex]\frac{Opposite}{Adjacent}[/tex]

Then,

tanθ = [tex]\frac{/AC/}{/CB/}[/tex]

tanθ = [tex]\frac{86.53}{89.39}[/tex]

tanθ = 0.9680

∴θ = tan⁻¹(0.9680)

θ = 44.0686°

θ = 44.07° (to the nearest hundredth of a degree)

Hence, the angle of elevation of the sun to the nearest hundredth of a degree is 44.07°

Answer:

(-∞,∞)

Range (-∞,∞)

Step-by-step explanation: