Complex Roots Problem #5

Answer:

a

Step-by-step explanation:

104 is the only number inside the box

The value of ∠1  is 38 degree , Option B is the correct answer.

Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.

From the figure given

One of the angle is 104 degree

when two lines are parallel and intersected by a transversal

then the sum of the consecutive interior angles is 180 degree

∠1  +  ∠2 =  180 -104 = 76 degree

similarly the other two lines are parallel with each other

so  ∠1  =  ∠4

∠3 =   ∠2

Therefore the diagonals are bisecting the angle and so

the value of ∠1   = 76 / 2 = 38 degree

Therefore , The value of ∠1  is 38 degree , Option B is the correct answer.

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Answer:

f^-1(x) = (x +7)/5

Step-by-step explanation:

Set x = f(y) and solve for y.

... x = 5y -7

... x+7 = 5y

... (x+7)/5 = y . . . . this is the inverse function

f^-1(x) = (x +7)/5

Answer:

3 brownies

Step-by-step explanation:

To find this answer we need to divide the 0.81 by 0.27 to find out how many brownies total 0.81:

0.81 ÷ 0.27 = 3

So he needs to sell 3 brownies.

Answer:

2l + 3 = 39

Step-by-step explanation:

the equation is 3 + 2L = C, where L is Lindsay's age and C is Carol's age

3 + 2L = 39

Answer: 6.3093

Step-by-step explanation:

[tex]3^{\frac{x}{5}} = 4[/tex]

[tex]ln3^{\frac{x}{5}} = ln4[/tex]

[tex]\frac{x}{5} ln3 = ln4[/tex]

xln3 = 5ln4

[tex]x = \frac{5ln4}{ln3}[/tex]

x = 6.3093

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Answer: 5, 3, [tex]\frac{1}{5}[/tex], D

Step-by-step explanation:

a) x ≤ 0 so, f(-5) = | -5 | = 5

   x ≤ 0 so, f(-3) = | -3 | = 3

   x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]

b) graph D

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Answer: [tex]\frac{\pi}{12}[/tex]

Step-by-step explanation:

 [tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]

=  [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]

=  [tex]\frac{\pi}{12}[/tex]

Answer:

2

Step-by-step explanation:

We can find the average rate of change by using the formula

rate of change = (y2-y1) /(x2-x1)

                         = (5-3)/(1-0)

                         = 2/1

                            =2

Answer:

A. 2

Step-by-step explanation:

average rate of change from x1 to x2 is

[f(x2) - f(x1)]/(x2 - x1)

Here we have x1 = -3; f(x1) = -3; x2 = 1; f(x2) = 5

average rate of change from x1 to x2 =

= [f(x2) - f(x1)]/(x2 - x1)

= [5 - (-3)]/(1 - (-3))

= 8/4

= 2

Answer:

B

Step-by-step explanation:

We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.

We can use Pythagorean Theorem [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side length x. a=6, b=11 and c=x.

[tex](6)^{2} +(11)^{2} =x^{2}[/tex]

[tex]36+121=x^2\\157=x^2\\\sqrt{157}=x\\ 12.5=x[/tex]

Answer:

125 candy bars

Step-by-step explanation:

[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]

[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]

Answer: The meaning y-intercept is the initial value of a rare coin is 6.

Step-by-step explanation:

Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.

The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.

i.e. , we need to put t=0, we get

[tex]f(0) = 6\times 2^0=6[/tex]

The meaning y-intercept is the initial value of a rare coin is 6.

25 friends because 7*5=35

Answer:

A

Step-by-step explanation:

The transformation is [tex]h(x)=4*g(x+5)[/tex].

The answer is A.  The graph of h is the graph of g vertically stretched by a factor of 4 and shifted 5 units to the left.

Answer: A for plato users

Answer: D

Step-by-step explanation:

Inverse is when the x's and y's are swapped

x   |   y        Inverse

-3 |   5         (5, -3)

-2 |  -3         (-3, -2)

0 |   3          (3, 0)

1  |  -5         (-5, 1) ← this matches choice D

2  |   6          (6, 2)

3  |  10          (10, 3)

well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MN=\sqrt{[4-5]^2+[-8-(-3)]^2}\implies MN=\sqrt{(4-5)^2+(-8+3)^2} \\\\\\ MN=\sqrt{(-1)^2+(-5)^2}\implies MN=\sqrt{26}[/tex]

Answer:

This team can lose 6 games and still achieve this goal.

Step-by-step explanation:

In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.

Ratio = Total  

2/5 = x/15

Now cross multiply

15*2 = 5x

30 = 5x

6 = x

This means the team can lose 6 games and still keep the necessary ratio.

Answer:

x = 32

Step-by-step explanation:

This is an equilateral triangle, all three sides equal.  Since all three sides are equal, all three angle are equal.  180/3 = 60.  That means each angle is equal to 60 degrees.

2x-4 = 60

Add 4 to each side

2x-4+4 = 60+4

2x =64

Divide each side  by 2.

2x/2 = 64/2

x = 32

Answer: [0, 6) ∪ (6, 15]

Step-by-step explanation:

The particle is moving to the right when the velocity is positive.

[tex]s(t)=\dfrac{t^3}{3} -\dfrac{12t^2}{2}+36t[/tex]

v(t) = s'(t)

     = t² - 12t + 36

First, find the zeros of v(t): ⇒ v(t) = 0

  0 = t² - 12t + 36

     = (t - 6)²

0 = t - 6

6 = t

The zero occurs when t = 6

Next, find when v(t) > 0

Choose a test point between 0 and 6:

v(5) = (5 - 6)²

     =     (-²)

     =      (+)

Since velocity is positive between 0 and 6, the particle is moving to the right during that interval.

Choose a test point between 6 and 15:

v(7) = (7 - 6)²

     =    (+)²  

     =    (+)

Since velocity is positive when t > 6, the particle is moving to the right.

Answer:

14.4 yards

Step-by-step explanation:

Each shirt needs 0.8 yards so 18 shirts needs 18 * 0.8 = 14.4 yards of material.

14.4 yards of material will be needed to make 18 shirts.

Multiplication is when you take one number and add it together a number of times.

Given that, one shirt is of 0.8 yards of material,

18*0.8 = 14.4

Hence, 14.4 yards of material will be needed to make 18 shirts.

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Answer:

190 percentage of the weight limit is 114 pounds.

Step-by-step explanation:

Given: A rocking horse has a weight limit of 60 pounds.

We have to find what percentage of the weight limit is 114 pounds.

x percentage of the weight limit is 114 pounds.

⇒ x% of 60 = 114

[tex]\frac{x}{100} \times 60 = 114[/tex]

Solve for x;

[tex]\frac{6x}{10} = 114[/tex]

Multiply both sides by 10 we get;

[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]

[tex]6x = 1140[/tex]

Divide both sides by 6 we get;

[tex]x = \frac{1140}{6}[/tex]

Simplify:

x = 190%

Therefore, 190 percentage of the weight limit is 114 pounds.

To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.

To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:

Percentage = (114 pounds / 60 pounds) * 100

Simplifying this equation, we get:

Percentage = 190%

Therefore, 114 pounds is 190% of the weight limit of 60 pounds.

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Answer:

hello :

the graph passes by ( -4; 7/128)  : f(-4) = 7/128

a/ (-4)^4 = 7/128

a / 256 = 7/128

a/2 = 7

a = 14

We have the point:

[tex]\left(-4,\ \dfrac{7}{128}\right)[/tex]

Put the coordinates of the point to the equation of the function f:

[tex]f(x)=\dfrac{a}{x^4}\to y=\dfrac{a}{x^4}\\\\\left(-4,\ \dfrac{7}{128}\right)\to x=-4,\ y=\dfrac{7}{128}\\\\\dfrac{a}{(-4)^4}=\dfrac{7}{128}\\\\\dfrac{a}{256}=\dfrac{7}{128}\qquad\text{multiply both sides by 256}\\\\a=\dfrac{7}{128}\cdot256\\\\\boxed{a=14}[/tex]

Answer: [tex]\bold{\dfrac{1}{36}}[/tex]

Step-by-step explanation:

The first die can be any number:  [tex]P = (\dfrac{6}{6}) = 1[/tex]

The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]

The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]

1st die   and   2nd die   and    3rd die  =  Probability of success

   1          x          [tex]\dfrac{1}{6}[/tex]             x          [tex]\dfrac{1}{6}[/tex]         =               [tex]\dfrac{1}{36}[/tex]

[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]

[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]

Answer:

angle C is 60 degrees

Step-by-step explanation:

First you would solve for X

once you have that plug it in angle C

2(30)=60

Answer:

60°

Step-by-step explanation:

∠B is a right angle and all right angles are 90°, so if ∠B = 3*x then to find x you divid 3 by 90 to get x because 3*x = 90 once you do that you get 30 so x=30 then to find ∠C you just multiply 2 by 30 which gives you 60 which means the measure of ∠C = 60°

hope this helps :D

Answer:

When f(x) is 0, then x is -1.8.

Step-by-step explanation:

To find this, you simply have to look for the place where the line crosses the x axis. This is where y (or f(x)) is equal to 0. Since this graph only crosses that axis at x = -1.8, that is the number we are looking for.

The first thing to notice is that the smaller triangle on the left is equilateral, because of the same single tickmarks on each of the three sides. For any equilateral triangle, each interior angle is 60 degrees as you have marked it on the drawing.

Once you determine that, you would solve for the 120 degree angle (60+120 = 180). Afterward, solve the equation 120+x+x = 180 to find that x = 30. The equation 120+x+x = 180 refers to adding up the three angles of the smaller triangle on the right side (with angles 120, x, x). The two missing angles are both x due to the fact that this triangle is isosceles.

Answer:

Step-by-step explanation:

Since ∆ABC is equilateral, all of its angles would be the same (60°). Since a line is 180°, the other part of ∠C is 120°. Since we also know that △BCD is isosceles, we know that angles ∠B and ∠D are equal. If a triangle is 180°, and we already know that ∠C is 120°, we can do 180-120, which is 60°. If angles ∠B and ∠D are equal, we can do 60/2=30. Therefore, ∠D is 30°.