Triangles FEG and FDH are similar. If segment DH is 28 units, what is the
measure of segment EG?

9514 1404 393

Answer:

  B

Step-by-step explanation:

Angles A and C are vertical angles; angles B and C are alternate interior angles. Only line 3 of the proof is in error.

The applicable description is found in choice B.

Answer:

5/36

Step-by-step explanation:

Answer:

the probability of getting a total greater than 8 is  10/36=5/18

Step-by-step explanation:

Of the 36 different possible results of rolling a die twice, 10 of them have a total greater than 8.

Therefore, the probability of getting a total greater than 8 is  10/36 which equals 5/18

Answer:

40

Step-by-step explanation:

"Find all real solutions of" basically means solve for x. You're looking for the real numbers x such that the given equation is satisfied. "Zeros" is synonymous with "solutions".

It looks like the first equation is

3x³ + x² - 38x + 24 = 0

It's not immediately obvious whether this can be factorized, so we first carry out the rational zero test to see if there are any rational solutions. *If* this equation has any rational solutions, then they must take the form of (divisor of 24)/(divisor of 3). That is, take any divisor of the constant coefficient and divide it by any divisor of the leading term's coefficient.

We have

• divisors of 24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

• divisors of 3 : ±1, ±3

Sadly, there are 64 possible roots to test, but we only need one to make the rest of the problem easier.

• Let x = +1 / +1 = 1. Then plugging x = 1 into the equation gives

3•1³ + 1² - 38•1 + 24 = -10 ≠ 0

so x = 1 is *not* a solution

• Let x = +2 / +1 = 2. If x = 2, then

3•2³ + 2² - 38•2 + 24 = -24 ≠ 0

so x = 2 is *not* a solution.

• Let x = +3 / +1 = 3. If x = 3, then

3•3³ + 3² - 38•3 + 24 = 0

so x = 3 is a solution.

By the remainder theorem, this means that x - 3 divides 3x³ + x² - 38x + 24. Using long or synthetic division,

(3x³ + x² - 38x + 24) / (x - 3) = 3x² + 10x - 8

so that

3x³ + x² - 38x + 24 = 0

is the same as

(x - 3) (3x² + 10x - 8) = 0

We factorize the remaining quadratic to get

3x² + 10x - 8 = (3x - 2) (x + 4)

and so the original equation is equivalent to

(x - 3) (3x - 2) (x + 4) = 0

Solve for x :

x - 3 = 0   or   3x - 2 = 0   or   x + 4 = 0

x = 3   or   x = 2/3   or   x = -4

The other equations can be solved similarly, though some of the others you included are much simpler.

For the second problem (note that you left out an exponent), we solve the equation

x³ - 2x² - 23x + 60 = 0

Again, not immediately obvious how to factorize this. But using the rational root test, we have

• divisors of 60 : ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

• divisors of 1 : ±1

If you follow the same steps as before, you'll find the first rational solution with x = 3. So x - 3 divides x³ - 2x² - 23x + 60, and long division gives

(x³ - 2x² - 23x + 60) / (x - 3) = x² + x - 20

and the resulting quadratic is easily factored,

x² + x - 20 = (x - 4) (x + 5)

So, we have

x³ - 2x² - 23x + 60 = (x - 3) (x - 4) (x + 5) = 0

which means

x - 3 = 0   or   x - 4 = 0   or   x + 5 = 0

x = 3   or   x = 4   or   x = -5

For the third problem, we can factor by grouping.

x³ - 4x² - x + 4 = 0

x² (x - 4) - (x - 4) = 0

(x² - 1) (x - 4) = 0

(x - 1) (x + 1) (x - 4) = 0

Then

x - 1 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = -1   or   x = 4

For the fourth problem, we use the rational root test again, but twice this time.

x⁴ - 6x³ + 7x² + 6x - 8 = 0

• divisors of -8 : ±1, ±2, ±4, ±8

• divisors of 1 : ±1

We find that x = 1 and x = 2 are both rational roots, so both x - 1 and x - 2 divide x⁴ - 6x³ + 7x² + 6x - 8. By long division,

(x⁴ - 6x³ + 7x² + 6x - 8) / ((x - 1) (x - 2)) = x² - 3x - 4

and factoring this gives

x² - 3x - 4 = (x + 1) (x - 4)

So, we have

x⁴ - 6x³ + 7x² + 6x - 8 = (x - 1) (x - 2) (x + 1) (x - 4) = 0

which means

x - 1 = 0   or   x - 2 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = 2   or   x = -1   or   x = 4

For the last problem,

x⁴ + 4x³ + 7x² + 16x + 12 = 0

we use the rational root test again.

• divisors of 12 : ±1, ±2, ±3, ±4, ±6, ±12

• divisors of 1 : ±1

We find that both x = -1 and x = -3 are rational solutions, and dividing gives

(x⁴ + 4x³ + 7x² + 16x + 12) / ((x + 1) (x + 3)) = x² + 4

which we cannot factorize further over the real numbers. So we end up with

x⁴ + 4x³ + 7x² + 16x + 12 = (x + 1) (x + 3) (x² + 4) = 0

so that

x + 1 = 0   or   x + 3 = 0   or   x² + 4 = 0

x = -1   or   x = -3

(We omit the third equation here because it has no real solution since x² + 4 ≥ 4 for all real x.)

Answer:

Answered is x= 55x

Step-by-step explanation:

13x+10 * 12x+20

soln:

or, 13x+12x+10+20

or, 25x+30

:., therefore, x=55x

Answer:

x > 5

Step-by-step explanation:

14 -14 - 3 x < -1 -14

-3 x < -15

-3 x / -3 < -15 / -3

x > 5

Answer:

10

Step-by-step explanation:

There are two 1/8 in one 1/4. There are eight 1/8 in 1. 8/8 + 1/8 + 1/8 = ten 1/8.

Answer:

$34

Step-by-step explanation:

374/11=34

Answer:

One ticket cost $34

Step-by-step explanation:

Tito purchased 11 tickets for $374 so divide $374 by 11 and you get $34

[tex]xy =-21~~.....(i)\\\\x+ y=20~~....(ii)\\\\\text{From equation (i):}\\\\xy = -21 \implies y = -\dfrac{21}x~~.....(iii)\\\\\text{Substitute y in equation (ii):}\\\\x - \dfrac{21}x = 20\\\\\implies x^2 -20x -21= 0\\\\\implies x^2 - 21x + x-21=0\\\\\implies x(x-21) +(x-21) =0\\\\\implies (x+1)(x-21)=0\\\\\implies x = -1 ~~\text{or}~~ x =21\\\\\text{Substitute x in equation (iii):}\\\\y = 21 ~~ \text{or}~~ y = -1\\\\\text{Hence,}~ (x,y)=(21,-1) ~~ \text{or}~~ (x,y) = (-1,21)[/tex]

Answer:

5^6

Step-by-step explanation:

5 was multiplied repeatedly 6 times, so it's 5 to the power of 6

Answer:

5 to the power of 6 or 5^6

Step-by-step explanation:

Answer:

unknown number = 1

Step-by-step explanation:

Let the unknown number be x.

(8×x)-6=2

   8x-6=2

       8x=2+6

           =8

         x=8÷8

           =1

Hence, unknown number = 1.

Answer:its the first one

Step-by-step explanation:

becuase it tells more explanation if you look at the answer or what im saying is problem to make it more simpler.

Answer:

Your answer would be x=2±√5

Step-by-step explanation:

Using simple interest, it is found that the principal loan amount was of $156,491.6.

The amount of money after t years in simple interest is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

In this problem, she paid $984 monthly for 22 years, hence:

[tex]t = 22, A(t) = 984(22)(12) = 259776[/tex]

Interest rate of 3%, hence [tex]r = 0.03[/tex]

Then:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]259776 = A(0)[1 + 0.03(22)][/tex]

[tex]A(0) = \frac{259776}{1 + 0.03(22)}[/tex]

[tex]A(0) = 156491.6[/tex]

The principal loan amount was of $156,491.6.

A similar problem is given at https://brainly.com/question/13176347

Answer:

C(-1, -4)

Step-by-step explanation:

see the point reflected over the line through the vertex point

Answer:

D. Q′ (−4, −3)

Step-by-step explanation:

From looking at the graph it looks like the answer would be

Q= (3, -4) if the X-axis goes first

Q= (-4, 3) if the Y-axis goes first

Answer:

Question is missing

Step-by-step explanation:

Question missing

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(3*x+7)^2+5-((7*x-9)^2*x+5)=0

Step by step solution :

STEP1:

Equation at the end of step 1

(((3x+7)2)+5)-(x•(7x-9)2+5) = 0

STEP2:

Checking for a perfect cube

2.1 -49x3+135x2-39x+49 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: -49x3+135x2-39x+49

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -39x+49

Group 2: -49x3+135x2

Pull out from each group separately :

Group 1: (-39x+49) • (1) = (39x-49) • (-1)

Group 2: (49x-135) • (-x2)

Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

Find roots (zeroes) of : F(x) = -49x3+135x2-39x+49

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is -49 and the Trailing Constant is 49.

The factor(s) are:

of the Leading Coefficient : 1,7 ,49

of the Trailing Constant : 1 ,7 ,49

Let us test ....

Equation at the end of step

2

:

-49x3 + 135x2 - 39x + 49 = 0

STEP

3

:

Cubic Equations:

3.1 Solve -49x3+135x2-39x+49 = 0

Future releases of Tiger-Algebra will solve equations of the third degree directly.

Meanwhile we will use the Bisection method to approximate one real solution.

Approximating a root using the Bisection Method :

We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).

The function is F(x) = -49x3 + 135x2 - 39x + 49

At x= 3.00 F(x) is equal to -176.00

At x= 2.00 F(x) is equal to 119.00

Intuitively we feel, and justly so, that since F(x) is negative on one side of the interval, and positive on the other side then, somewhere inside this interval, F(x) is zero

Procedure :

(1) Find a point "Left" where F(Left) < 0

(2) Find a point 'Right' where F(Right) > 0

(3) Compute 'Middle' the middle point of the interval [Left,Right]

(4) Calculate Value = F(Middle)

(5) If Value is close enough to zero goto Step (7)

Else :

If Value < 0 then : Left <- Middle

If Value > 0 then : Right <- Middle

(6) Loop back to Step (3)

(7) Done!! The approximation found is Middle

Next Middle will get us close enough to zero:

F( 2.596896529 ) is 0.000000414

The desired approximation of the solution is:

x ≓ 2.596896529

Note, ≓ is the approximation symbol

One solution was found :

x ≓ 2.596896529

Answer:

use this equation: GPE=mgh

Step-by-step explanation:

GPE = gravitational potential energy = J

m = mass = Kg

g = gravitational field = N/kg = world's gravitational field is 9.8N/kg

h = height = m

Answer:

its the first one

Step-by-step explanation:

Answer:

The answer would be D

Step-by-step explanation:

5 1/3 ÷ 2/3 = 8

16/3 ÷ 2/3 = 8

16 ÷2 = 8

Answer:(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

(x - 3)² + (y - 2)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (3, 2 ) and r = 5 , then

(x - 3)² + (y - 2)² = 5² , that is

(x - 3)² + (y - 2)² = 25 ← equation of circle

Answer:

The right answer is letter C.

Step-by-step explanation:

I hope it's help

have a nice day and night

Answer: $113.89

Step-by-step explanation:

108.99 * 0.045

= 4.90455

108.99 + 4.90455

= 113.89455

$113.89

Answer:

Total Cost = $113.89

Step-by-step explanation:

Total Cost = Cell phone cost + sale Tax % ( cell phone cost)

Total Cost = $108. 99 + .045 × $108.99

Total Cost = $108.99 + $4.90455

Total Cost = $108.99 + $4.90

Total Cost = $113.89

By isosceles triangle theorem,

Angle ZXY = Angle ZYX

The sum of the angles in a triangle is 180 degrees.

106 + 2 same angles (-106) = 180 (-106)  (Subtract 106 by both sides)

2 same angles (/ 2) = 74 (/ 2)   (Divide 2 by both sides)

V = 37

Answer:

The value of v is 37°.

Step-by-step explanation:

Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:

Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,

∠ZXY + ∠ZYX + ∠XZY = 180°

v + v + 106° = 180°

2v + 106° = 180°

2v = 180° - 106°

2v = 74°

v = 74 ÷ 2

v = 37°

Answer:

A- 8x+9

Step-by-step explanation:

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

5x + 3 (x + 2) + 3

5x + 3x + 6 + 3

8x + 6 + 3

8x + 9

<3

=======================================================

Explanation:

Let point A be the center of the circle.

The inscribed angle CED doubles to the central angle CAD due to the inscribed angle theorem.

angle CAD = 2*(angle CED)

angle CAD = 2*(7x+6)

angle CAD = 14x+12

Angle CAD is the same as minor arc CD. These are two different ways to describe the same thing more or less. This is because the central angle subtends or cuts off the minor arc CD.

-----------

The three arc pieces CE, ED and CD all combine to form a 360 degree circle.

(arc CE) + (arc ED) + (arc CD) = 360

(18x+1) + (13x+1) + (14x+12) = 360

(18x+13x+14x) + (1+1+12) = 360

45x+14 = 360

45x = 360-14

45x = 346

x = 346/45

This approximates to roughly x = 7.6889, but I have a feeling your teacher will want the fraction form.