Which equation is equivalent to StartRoot x squared + 81 EndRoot = x + 10?

the probability of getting a black one given that in the first draw we got a black one is P = 1/2 = 0.5

We will assume that all the beads have the same probability of being randomly selected.

Then the probability of picking a black bead is equal to the quotient between the number of black beads and the total number of beads.

Originally, there are 4 black ones and 3 red ones ( a total of 7).

We want to get the probability of getting a black one given that in the first draw we got a black one.

If in the first draw we got a black one, then now there are 3 blacks and 3 reds (a total of 6 beads).

So the probability of getting another black one is:

P = 3/6 = 1/2 = 0.5

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Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.

Hence the time in years is found as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]

[tex](1.0033)^{12t} = 1.3[/tex]

[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]

[tex]12t\log{1.0033} =  \log{1.3}[/tex]

[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]

t = 6.6

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By using trigonometric relations, we will see that the distance between Carlos and the tree is:

D = 781.23 ft

We can model this with a right triangle. We know that Carlos is 6ft tall, and the height of the tree is 275ft.

Then one of the cathetus of the triangle is equal to:

275ft - 6ft = 269ft.

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

Replacing that, we get:

tan(19°) = 269ft/D

Solving for D, we get:

D = 269ft/tan(19°) = 781.2ft

So we conclude that Carlos is at 781.23 ft of the tree.

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The following represents the factorization of the trinomial is -3x [ (x+2)(x+4)].

What is Trinomial?

A trinomial is a polynomial consisting of three terms or monomials.

Given polynomial:

-3x³-18x²-24x

Taking -3x as common, we get

=-3x(x²+6x+8)

Now, by factorization

=-3x (x²+4x+2x+8)

= -3x[x(x+4) + 2(x+4)]

= -3x [ (x+2)(x+4)]

Hence, the factorization is -3x [ (x+2)(x+4)].

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The values for time is  1.361 and 0.828.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given: h=-16t²+35t+2

so if the height is going to be 20ft,

20 = 2+35t-16t²

16t²-35t18=0

Solve the above quadratic equation

x= -b±√b²-4ac/2a

a=16, b=-5, c=18

x=[-(-35)±√(-35)²-4*16*18]/2*16

x= [35±√73]/32

x= 35+√73/32  and x= 35-√73/32

x=1.361 and 0.828.

Hence, the values for time is  1.361 and 0.828.

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Answer:

she will need about 7 baskets, the proper number is 6.7 but round up and its 7

Step-by-step explanation:

hope this helps!

Answer:

B.) 4,096 feet

Step-by-step explanation:

You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".

t = (1/4)√x                                         <--- Original equation

16 = (1/4)√x                                      <--- Plug 16 in "t"

64 = √x                                            <--- Divide both sides by (1/4)

4,096 ft = x                                    <--- Square both sides

The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height  x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:

16 = 1/4 √x

Simplify the equation by multiplying both sides by 4:

4⋅16= √x

64= √x

Now, square both sides to isolate x:

64²=x

4096 = x

Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

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The volume of the sphere with a diameter of 12 ft is calculated as: 288π feet cubed.

The volume of a given sphere with a radius (r) is given as: V = 4/3πr³.

Given the following:

Volume of the sphere = 4/3π(6³)

Volume of the sphere = 288π feet cubed

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Answer:

288 Is the answer : )

Step-by-step explanation:

I got it right on the test (100%)

The graph that shows the information on the table is On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).

The independent variable is the number of ounces of salad dressing which means that it will be shown on the x axis.

The total calories is the dependent variable which means that it will be on the y axis.

The line drawn will pass through the points on the table of (2,300) and (4 ,600) so option A is correct.

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Answer:

d

Step-by-step explanation:

your answer to your question is D

By applying concepts of linear functions, the graphs are related to the following expressions:

Graphically speaking, lines are described by linear functions, a kind of polynomials of grade 1, whose standard form is presented below:

y = m · x + b     (1)

Where:

Please notice that the slope is represented graphically by the change in the y-variable divided by the change in the x-variable and the intercept is the location where the line passes through the y-axis. Hence, the resulting expressions are shown in this order:

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The length of EF which lie on line EC is 8.66 units.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines.

Here,    EG = 6.9 ,        FC = 6.4,           GD = 5.1

Also. FG || CD

By Basic Proportionality Theorem,

               [tex]\frac{EF}{FC} = \frac{EG}{GD}[/tex]

               [tex]EF = \frac{EG . FC}{GD}[/tex]

               EF =  (6.9 X 6.4) / 5.1

               EF = 8.66 units

Thus, The length of EF which lie on line EC is 8.66 units.

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Answer:

slope is undefined

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (6, - 2 )

m = [tex]\frac{-2-4}{6-6}[/tex] = [tex]\frac{-6}{0}[/tex]

division by zero is undefined, therefore the slope of the vertical line is undefined.

Answer:

290 m²

Step-by-step explanation:

The volume of the figure can be found by taking the sum of the volumes of the 2 cuboid.

[tex]\boxed{\text{Volume of cuboid}=\text{length}\times\text{breadth}\times\text{height}}[/tex]

Top cuboid

Length= 4 m

Breadth= 5 m

Height= 7 m

Volume= 4(5)(7)= 140 m²

Bottom cuboid

Length= 5 m

Breadth= 6 m

Height= 5 m

Volume= 5(6)(5)= 150 m²

Total volume

Total volume

= volume of top cuboid +volume of bottom cuboid

= 290 m²

Additional:

For a similar question on volume of composite figures, do check out the following!

Answer:

Not similar

Step-by-step explanation:

If you have scratch paper, its best to label the angles and sides given. You can also rotate the orientation of one of the triangles if that helps visually.

First lets look at the sides.

Notice the common factor between side AB and side XY.

14/7=2

Notice the common factor between side AC and side XZ.

22/11=2

So far so good right? Well, IF these triangles are similar, that means that angle X must correspond to angle A. Since corresponding angles of similar triangles are equal to each other, lets check of angle X is equal to angle A.

Angle X = 29 degrees

Angle A = 28 degrees

28 does not equal 29 degrees. Therefore, the triangles are not similar. If angles X and A were equal, than the triangles would have been similar due to the Side-Angle-Side rule (SAS).

Answer:

101 degrees

Step-by-step explanation:

The third angle in the first triangle would be  180 - (26+53) = 101 degrees

the angle in triangle 2 could be the 101 degree one

Answer:

-2(x^2+2)

Step-by-step explanation:

1. x^2-3x^2-4
= -2x^2-4
2. -2(x^2+2) factor completely :)

Answer: - 2 (x² + 2)

Step-by-step explanation:

x² - 3x² - 4 ⇒ -2x² - 4 ⇒ - 2 (x² + 2)    factor out - 2

Answer:

A=108

B=22

C=51

D=28

Step-by-step explanation:

A= AFB is a vertical angle opposite 108

B= congruent angles congruent sides, 11 x 2 sides

C= using angle rules, alternate interior angles of 21 puts 21 in the

triangle with 108, all triangles sum total 180, so (180-21=51)

for the 3rd angle ACD

D=last answer

The ratio of f to g to h is:

1:3:5

First, we know that g is the 60% of h, then we can write:

g = 0.6*h

Now we can write the 0.6 as a fraction, then 0.6 = 3/5.

g = (3/5)*h

So we can write:

5*g = 3*h

So the ratio of g to h is 3:5

Now, we know that f is a third of g:

f = (1/3)*g

3f = g

So the ratio of f to g is:

1:3

notice that the value that represents the proportion of g is 3 in both ratios, so we can just write:

The ratio of f to g to h is:

1:3:5

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Answer:

y=3x-10

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(2-8)/(4-6)

slope= -6/-2 = 3

Point: (6,8)

Slope-intercept: y-y1=m(x-x1)

y-8=3(x-6)

y-8=3x-18

y=3x-10

Answer:

C

Step-by-step explanation:

the 2 angles form a linear pair and sum to 180° , that is

3x + 12 + x = 180

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

1 |      2   -5   3

  | 2   -5    3  0

1 |      2     -3  

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     [tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  2  |     2  2    

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   [tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

-2 |      -12    10     -2

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         [tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]

                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]

Answer:

3/4 (A)

Step-by-step explanation:

replace x with -2 in the function

3 · 2^-2  = 3 · 0.25

3 · 0.25 = 0.75

0.75 = 3/4

Answer:

choose option 1

Step-by-step explanation:

option one is going to take a longer time to pay off but option 2's annual fees are going to make you spend at least $200 more dollars than option 1

Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as

SA=16.094711 ft^2

Generally, the equation for the surface area of a cone is mathematically given as

SA=πr(rπ+√(h^2+r^2))

Therefore

SA=πr(rπ+√(h^2+r^2))

SA=π*1(1+√(4^2+1^2))

SA=16.094711 ft^2

In conclusion,  the amount of steel Kassidy will need is

SA=16.094711 ft^2

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Answer:

4.25 gallons of juice

Step-by-step explanation:

4 quarts = 1 gallon

3 quarts = 3/4 gallon

2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4

4 1/4 = 4.25

give brainliest please

hope this helps :)

Based on the statement below,  if d is the midpoint of the segment AC, the  length of the segment AB  is  4.5cm.

in the question given,

AC = 3cm,

Therefore,  AD and DC will be = 1.5cm segments each.  

We are given C as the midpoint of segment DB.

So CB = 1.5cm.

The representation of the line segment is:

A-----------D------------C-------------B

     1.5           1.5            1.5

Since AD, DC and CB are each 1.5cm segments. Then the equation will be:

= 1.5 + 1.5 + 1.5

= 4.5

Therefore, The length of the segment AB is 4.5cm.

See full question below

If D is the midpoint of the segment AC and C is the midpoint of segment DB , what is the length of the segment AB , if AC = 3 cm.

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Answer:

150 square inches.

Step-by-step explanation:

[tex]V=s^3[/tex]

s=125

[tex]s=\sqrt[3]{125} =5[/tex]

Therefore, total surface of a cube = [tex]6*s^2[/tex]

=6×5×5

[tex]150 in^2[/tex]