Solve for X.

-3/2(x-2)=45/14

Please show work.

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.

A value of [tex]x[/tex] is a zero of the quadratic function if and only if [tex]y = 0[/tex]. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: [tex]A(x,y) = (r_{1}, 0)[/tex], [tex]B(x,y) = (r_{2},0)[/tex] and [tex]C(x,y) = (x,y)[/tex]

Based on such information, we form the following system of linear equations:

[tex]a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0[/tex] (2)

[tex]a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0[/tex] (3)

[tex]a\cdot x^{2} + b\cdot x + c = y[/tex] (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

[tex]a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

[tex]c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]

[tex]c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]

And finally we obtain the equation of the quadratic function given two zeroes and a point.

Answer:

y = -7x - 11

Step-by-step explanation:

Answer:

In order:

Distributive Property

Subtraction Property of Equality

Division Property of Equality or Reciprocal Property

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

simplify the radical by breaking the redicand up into a product of known factors, assuming positive real numbers.

Answer:

try 4

Step-by-step explanation:

basically need to find number that when multiplied 3 times equals 64 so 4*4*4=64

Answer:

[tex]m \angle A = m \angle C[/tex] by reason [tex]\overline{AB} \cong \overline{BC}[/tex] and [tex]m \angle B = m \angle M = m \angle P[/tex].

[tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem

Step-by-step explanation:

We proceed to demonstrate the statement by Geometric means:

1) [tex]\overline{AB} \cong \overline{BC}[/tex], [tex]\overline {AM} \cong \overline {PC}[/tex], [tex]m\angle AMO = m\angle CPO[/tex] Given.

2) [tex]\frac{AM}{AB} = \frac{PC}{BC}[/tex] Proportionality.

3) [tex]\frac{AM}{AM + MB} = \frac{PC}{BP + PC}[/tex] Definition of line segments.

4) [tex]\frac{1}{1+\frac{MB}{AM} } = \frac{1}{\frac{BP}{PC}+1}[/tex] Algebra.

5) [tex]\frac{BP}{PC} + 1 = 1 +\frac{MB}{AM}[/tex] Algebra.

6) [tex]\frac{BP}{PC} = \frac{MB}{AM}[/tex] Algebra.

7) [tex]BP = BM[/tex] By 1)

8) [tex]m \angle B = m \angle M = m \angle P[/tex] By 1), 7)

9) [tex]\triangle AMO \sim \triangle ABC[/tex], [tex]\triangle CPO \sim \triangle ABC[/tex] By 1), 7), 8). Defintion of simmilarity.

10) [tex]\frac{AM}{MO} = \frac{AB}{BC}[/tex], [tex]\frac{PO}{PC} = \frac{AB}{BC}[/tex] Definition of proportionality.

11) [tex]\frac{AM}{MO} = \frac{PO}{PC}[/tex] Algebra.

12) [tex]AM^{2} = PO\cdot MO[/tex] Algebra.

13) [tex]PO = MO[/tex] By 12) and Algebra.

14) [tex]\overline{PO} \cong \overline{MO}[/tex] By 13).

15) [tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem/Result.

Answer:

first step - make x² the subject of the formula

x² = 25

second step :

find the square root of both sides

√x² = √25

x = 5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = 2x - 10 ( add 10 to both sides )

y + 10 = 2x ( divide both sides by 2 )

[tex]\frac{y+10}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{2}[/tex] = [tex]\frac{1}{2}[/tex] x + 5 → D

Step-by-step explanation:

hope it is helpful to you ☺️

Answer:

Same side interior angles

Step-by-step explanation:

Same side interior angles are interior angles and on the same side. Sorry don't know how to better explain.

Answer:

7 students

Step-by-step explanation:

1+2+4=7students

Answer:

[tex]x=0, \\x=\pi[/tex]

Step-by-step explanation:

Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].

Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:

[tex]2\sin x\cos x=2\sin x[/tex]

Subtract [tex]\sin x[/tex] from both sides:

[tex]2\sin x\cos x-2\sin x=0[/tex]

Factor out [tex]2\sin x[/tex] from both terms on the left:

[tex]2\sin x(\cos x-1)=0[/tex]

We now have two cases:

[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]

Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:

[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]

Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].

Answer:

It should be B,  180 cm

Step-by-step explanation:

x = circumference of  circle D

18/360 = 9/x

9*360 = 18x

9*360/18 = x

x = 180

Answer:

0.64 feet or 7.68 inches of snow on average over the 5 days.

Step-by-step explanation:

3.2/5

0.64ft

7.68in.

Answer:

yo congratulations on finishing 10th grade (congratulate me on finishing 8th)

hamood spelled backwards is doomah so...um...

also do u mean 7/2/21..bc 6/2/21 is like in June and we're in July

Answer:

13.86

Step-by-step explanation:

In ∆ ABC ,

Answer:

x = 6

Step-by-step explanation:

6 is x so this is the answer

Answer:

Step-by-step explanation:

The youth shirt is 12 dollars

The adult shirt is 15 dollars

So the number of adult shirts is x

The number of youth shirts   is y

15 x + 12y = 489

You are not asked to solve this. You are just asked to find it.

Answer:

From what I learn it is 360 degrees

Answer:

11. B.

12. C.

13. A.

14. D.

Step-by-step explanation:

for 11: we know that angles D and J are congruent from the tick marks, we also know that ∠FKD and ∠LKJ are congruent (vertical angles are congruent) therefore we need the sides between them

for 12: we know that ∠STU and ∠TUG are congruent, we also know that line TU is congruent to TU (reflexive property), therefore we need the angles adjacent to the first angles listed.

for 13: we know that ∠PQR and ∠CQR are congruent, we also know that lines RQ and RQ are congruent (reflexive property), therefore we need the other angles to which line RQ is between.

for 14: we know ∠B is congruent to ∠T and line AB is congruent to line ZY. therefore the angle cannot be connected to lines AB and ZY.

Step-by-step explanation:

simply take the average of the x and y coordinates

Answer:

42

Step-by-step explanation:

Perimeter is [tex]2l+2w[/tex]

Answer: 42

Hope this helped! Please mark brainliest :)

Answer:

P=-2.3662299854

Step-by-step explanation:

6.87p = - 7.056 -9.2

So 6.87p= - 16.256

P=-2.3662299854

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the variance is given by:

[tex]v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}[/tex]

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

[tex]M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76[/tex]

Then the variance will be:

[tex]v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14[/tex]

The correct option is C, 14.

Answer:

sorry i cannot help you

Answer:

3,082,000

Step-by-step explanation:

THE ANSWER IS 3,082,000 HOPE IT HELPS

Answer:

31.80°

Step-by-step explanation:

In ∆ ABC :-

Answer:

58

Step-by-step explanation: