SAT Math Question
Correct Answer: D

I was confused with A and D while solving this problem.

I get why D is the right answer but why is A wrong?

Answer: 105

Step-by-step explanation:

105 * .2 = 21 :)

The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.

The properties of a rhombus are:

The given rhombus BCDE has B(n, p) and E(0, 0).

Since the diagonals of a rhombus are perpendicular bisectors,

EO = OC or BO = OD

Where O is the midpoint of EC and BD.

In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.

So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).

Thus, we have B(n, p), D(n, -p), and E(0, 0)

Consider the coordinates of C as (x, y).

The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])

⇒ coordinates of O = (n, 0)

So,

The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])

⇒ coordinates of O = (x/2, y/2)

⇒ (n, 0) = (x/2, y/2)

∴ x = 2n and y = 0

Then, the coordinates of C are (2n, o)

Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).

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Answer:

56kg

Step-by-step explanation:

If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg

16*3.5 = 56 kg

Answer:

Step-by-step explanation:

16 + 12 + 5 + 3 = 36

16 prefer email, 36 total students surveyed

16:36 / 4 = 4:9

4 out of 9 students prefer email

4:9 x 680 = 302.222

302 students can be expected to prefer email.

Using the z-distribution, the 95% confidence interval for the proportion is given as follows:

(0.4576, 0.5824).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The other parameters for the interval are given as follows:

[tex]n = 246, \pi = 0.52[/tex].

The lower and upper bound of the interval, respectively, are given by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]

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Using the probability concept, the likelihood of landing on 2 or 3 is given by:

[tex]p = \frac{3}{8}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, considering the areas of 2 and 5 counting twice, the spinner has 8 areas, out of which 3 are 2 or 3, hence the probability is given as follows:

[tex]p = \frac{3}{8}[/tex]

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Check the picture below.

notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.

Here is the solution process:

                     3 x² -  2 x  -   6                      

x² + 0x + 2 | 3 x⁴ -  2 x³ +  0  x² -     x -   4

                    3  x⁴ + 0 x³ +  6  x²                

                             - 2 x³  -  6  x² -      x -   4

                             - 2 x³  + 0  x² -   4 x        

                                        -  6  x² +  3 x  -  4

                                        -  6  x²  + 0 x  -  12

                                                        3 x  + 8

Long division:

Therefore, the correct option is "A".

Answer:

78000

Step-by-step explanation:

5000/1 times 52/10 times 3)1

Answer:

4*1/1000+6*100+8*10+5*1

Step-by-step explanation:

Step-by-step explanation:

important of festival in nepali languages for class seven

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Comment

√15 = 3.87

√12 = 3.46              Subtract these 2

Difference = 0.41

she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

she would pay $400 per month to rent a station and keep all of her earnings.

Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.

Therefore,

let

x = number of haircut

Hence,

4x = 400

divide both sides by 4

4x / 4  = 400 / 4

x = 100

Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

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Answer:

bx/a (3rd choice)

Step-by-step explanation:

The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is

s = rΘ

Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.

x = aΘ

Solve for Θ:

Θ = x/a      Eq. 1

Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.

s = bΘ

Solve for Θ:

Θ = s/b      Eq. 2

Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.

x/a = s/b

Multiply both sides by ab.

abx/a = abs/b

bx = as

as = bx

s = bx/a

Answer: bx/a

Answer:

35,000 - 8000=27,000 altitude

The expression that will help him to determine the total cost is as follows:

y = 60 + 4x

He signed up to provide snacks for his daughter and her school group's camping trip.

He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.

He also wanted to buy some boxes of fruit snacks, which were $4 each.

The number to buy and the total cost can be expressed as follows:

let

y = total cost

x = number of boxes of fruit juice.

Therefore, the  expression that will help him to determine the total cost is as follows:

y = 60 + 4x

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Answer: yes, as long as you haven't used them. :)

Step-by-step explanation:

Answer: 171.75

Step-by-step explanation:

[tex]687/4 = 171.75[/tex]

Answer:

To find the result we have to divide, in a fraction the numerator is always divided by the denominator and the final result is 171.75

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I hope help you :)

Kind regards, Antonio.

By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.

The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:

m∠BDC = ½ × m∠BAC.

For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

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Answer:

plato

Step-by-step explanation:

m∠BAC m∠BDC

50° 25°

70° 35°

90° 45°

125° 62.5°

150° 75°

Answer:

3:8 3 sodas for 8 drinks

Step-by-step explanation:

6/16

3/8

The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:

(x,y) -> (x - 3, y - 3).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:

(x,y) -> (x - 3, y - 3).

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For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.

Simply put, a set in mathematics is a grouping of different items.

An element of the set is any component of the set. When writing a set, curly brackets are utilized.

The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.

According to the question,

A = {11,22,33,44}

The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]

[ by linear pair ]

[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]

[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]

[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]

[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]

[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]

[tex]\qquad❖ \: \sf \:x = 35[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

By the quotient rule for differentiation,

[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]

According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].

On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].

Then

[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]

The possible rational roots of the given equation are 1 and -3

From the question, we are to determine all the possible rational roots of the given equation

The given equation is

x⁴ -2x³ -6x² +22x -15 = 0

To determine the rational roots, we will test for values that make the equation equal to zero

(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15

1 + 2 - 6 - 22 -15

= -40

∴ -1 is not a root of the equation

(1)⁴ -2(1)³ -6(1)² +22(1) -15

1 - 2 - 6 + 22 -15

= 0

∴ 1 is one of the roots of the equation

(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15

16 + 16 - 24 - 44 -15

= -51

∴ -2 is not a root of the equation

(2)⁴ -2(2)³ -6(2)² +22(2) -15

16 - 16 - 24 + 44 -15

= 5

∴ 2 is not a root of the equation

(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15

81 + 54 - 54 -66 -15

= 0

∴ -3 is one of the roots of the equation

(3)⁴ -2(3)³ -6(3)² +22(3) -15

81 - 54 - 54 + 66 -15

= 24

∴ 3 is not a root of the equation

The other roots of the equation are irrational roots.

Hence, the possible rational roots of the given equation are 1 and -3

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Answer:

[tex]5x^{2} -4x-9[/tex]

Step-by-step explanation:

f(x)+g(x)

[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]

The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9

Given that:

Functions, f ( x ) = 3x² - 6x + 2

And g ( x ) = 2x² + 2x - 11.

Then find f ( x ) + g ( x ).

To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.

To find f(x) + g(x), add the coefficients of the corresponding terms:

f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)

Now, combine like terms:

f(x) + g(x) = 5x² - 4x - 9

So, the sum of the two functions is:

f(x) + g(x) = 5x² - 4x - 9

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Answer :LF is the abbreviation for linear feet Sq ft is the abbreviation for square feet L – lenght (e.g. room length) W – width (e.g. room width)

Liters to Cubic Feet formula. ft³ =. L * 0.035315. Show working Show result in exponential format More information: Cubic Feet.

Step-by-step explanation:

Step-by-step explanation:

=(7x)^2-(y)^2

=(7x+y) (7x-y)

Therefore, a^2-b^3

=(a+b) (a-b)

Answer:

no solution

Step-by-step explanation:

16x - 32y = 27 → (1)

8x - 16 = 16y ( subtract 16y from both sides )

8x - 16 - 16y = 0 ( add 16 to both sides )

8x - 16y = 16 → (2)

multiply (2) by - 2 and add to (1)

- 16x + 32y = - 32 → (3)

add (1) and (3) term by term

0 + 0 = - 5

0 = - 5 ← not possible

this indicates the system has no solution

(b)

the solution to a system is the point of intersection of the 2 lines

since there is no solution, no point of intersection, then

this indicates the lines are parallel and never intersect

Answer:

a) no solution

b) the two lines never intersect

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]

To solve by linear combination (elimination):

Step 1

Write both equations in standard form: Ax + By = C

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 8x-16y=16[/tex]

Step 2

Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]

Step 3

Subtract one of the equations from the other to eliminate one of the variables:

[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]

Therefore, as 0 ≠ 5, there is no solution to this system of equations.

Part (b)

The solution to a system of equations is the point(s) of intersection.

As there is no solution to the given system of equations, this tells us that the two lines never intersect.

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109×50

100×50+9×50=5000+450

5450

Answer:

5450

Step-by-step explanation:

You can just use a caculater to get the answer.

Answer:

The no. of student failed is 36.

Step-by-step explanation:

Given, the number of student enrolled= 216

Let us suppose number of student failed = x

Given,

no. of student passed is 5 times no. of student failed.

Then, no. of student passed = 5x

x +5x = 216

6x = 216

x = 216/6

x = 36

Thus, the no. of student failed is 36.