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1 year ago

2/3 x + 2 = 2 1/3 Solve for X. A. 0 B. 1/2 C. -2 D.2

Mathematics

2 answers:

TEA [102]1 year ago

6 0

Answer:

B. 1/2

Step-by-step explanation:

Our equation:

2/3x + 2 = 2 1/3

Let's isolate x to find our value:

Subtract 2 from both sides of the equation.

2/3x = 1/3

Multiply both sides of the equation by 3/2, or 1/5:

(This is used to make x = 1)

x = 1/2

B. 1/2 is your correct option.

leva [86]1 year ago

3 0

Answer: B. 1/2

Isolate the variable by diving each side by factors that don’t contain the variable.

1. Subtract 2
2/3x+ 2 = 2 1/3
-2 -2

2. Divide 2/3
2/3X = 1/3
2/3 2/3

3. X = 1/2

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Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48

Oksana_A [137]

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$ .

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

$x - h = 4\cdot p \cdot (y-k)^{2}$

Where:

$h$ , $k$ - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

$p$ - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

$p = x_{D} - x_{V}$

$p = \frac{1}{48}-0$

$p = \frac{1}{48}$

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$ .

6 0

2 years ago

Someone please help me with this ASAP

Natasha_Volkova [10]

Answer:

y= -11

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

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6 0

2 years ago

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -

rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

$y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\$

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by D and its formula is

$D=b^2-4ac\\$

Where

a= the coefficient of the $x^{2}$

b= the coefficient of $x$

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .

Let us start with

$y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\$

Hence we have two real roots for this equation.

$y = 2x^2 - 6x + 5\\$

$y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D$

Hence we do not have any real root for this quadratic

$y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\$

Hence D>0 and thus we have two real roots for this equation.

$y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\$

Hence we have one real root to this quadratic equation.

7 0

2 years ago

Write the equation for a parabola with a focus at (0,-5) and a directrix at y=-3

Olenka [21]

-4y -16 = x^2
All done

7 0

3 years ago