Consider the equation -5\cdot e^{10t}=-30−5⋅e
10t
=−30minus, 5, dot, e, start superscript, 10, t, end superscript, equals, minus, 30.
Solve the equation for ttt. Express the solution as a logarithm in base-eee.
t=
Approximate the value of ttt. Round your answer to the nearest thousandth.
t=

The ball's maximum height is 30.25 feet.

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, b, are the coefficients, c is the constant term, and x is the variable.

Given:

h= -16t²+36t+10

Differentiate w.r.t. 't',

h' = -32t+36

When h=0, that will be the maximum height

32t= 36

t= 9/8

t= 1.125 sec.

So, The maximum height is

h(1.123)= -16(1.125)² + 36*1.125+10

h(1.125) = 30.25 feet.

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[tex]\huge \boxed{\sf x=2}\\\\\\\displaystyle \sf AC=AB+BC\\\\41=3x-1+14x+8\\\\41=17x+7\\\\Subtracting\ 7\ from\ each\ side \\\\ 41-7=17x+7-7 \\\\ 34=17x\\\\Dividing\ each\ side\ by\ 17 \\\\ \frac{34}{17}=\frac{17x}{17} \\\\ 2=x[/tex]

Wealthy Romans relied on servants to run their households.

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Answer:

The correct answer is Wealthy Romans relied on servants to run their households.

Step-by-step explanation:

I got it right on edge 2022

Answer: 8

Step-by-step explanation:

[tex]\frac{180(n-2)}{n}=135\\180(n-2)=135n\\180n-360=135n\\-360=-45n\\n=\boxed{8}[/tex]

Answer:

36960 yards

Step-by-step explanation:

294/14=21

1 gallon is 21 miles

1 mile is 1760 yard

21 miles is 36960 yards

36960 yard is the answer assuming 14 gallons is a full tank of gas

Answer:

A) [tex]\displaystyle x=\frac{-8\pm\sqrt{40}}{2}[/tex]

Step-by-step explanation:

We know that the discriminant is [tex]b^2-4ac=(8)^2-4(1)(6)=64-24=40[/tex], so it cannot be B or C.

Also, because [tex]2a=2(1)=2[/tex], then the denominator must be 2, which means that A is the correct un-simplified solution for the quadratic equation.

Answer:

Choice A

Step-by-step explanation:

Let's solve to check.

Given:

x^2 + 8x + 6 = 0

Solution:

We know that,

[tex] \implies \rm \: x = \cfrac{ { - b±} \sqrt{ {b}^{2} - 4(ac)} }{2a} [/tex]

So substitute them:

[tex] \implies \rm \: x = \cfrac{ - 8± \sqrt{ {8}^{2} - 4(1 \times 6)} }{2 \times 1} [/tex]

[tex] \implies \rm \: x = \cfrac{ - 8± \sqrt{64 - 4 \times 6 } }{2} [/tex]

[tex] \implies \rm \: x= \cfrac{ - 8 ±\sqrt{64 - 24} }{2} [/tex]

[tex]\boxed{ \implies \rm \: x = \cfrac{ - 8 ±\sqrt{40}}{2}}[/tex]

Hence, choice A[x = {8±√(40)/2}] shows the un-simplified solution for x2 + 8x + 6 = 0.

Answer:

6

Step-by-step explanation:

First order them from least to greatest:

1, 3, 6, 7, 9

The median is 6 because it is the middle value.

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The value of x will be equal to 2.477.

The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The given expression will be solved as follows;-

[tex]5^{x-2}= 8[/tex]

Taking Log on both sides.

[tex]Log_e 5^{x-2}=Log_e8[/tex]

(x-2) Log5 = Log 8

( x-2) = Log8 / Log 5

(x - 2) = Log 8 - Log 5

(x - 2 ) = Log 3

x-2 = 0.477

x  =  2.477

Therefore the value of x will be equal to 2.477.

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Answer: A translation left 3 units and up 6 units

In order to find the translation of a shape in the graph.

Take particular one point from the original shape: (0, 2)

Take particular one point from the translated shape: (-3, 8)

Let the translation be (x, y)

   Original + Translation = Translated Image

This implies the shape has been translated 3 units left and 6 units up.

282.5 of 10 tickets were sold in the rock concert by the promoter

To do this, we make use of the following representations:

The 475 tickets that were sold means that:

x + y + z = 475

The income means that:

10x + 15y + 20z = 6300

Also, we have:

10y = 4z

Divide both sides by 10

y = 0.4z

Substitute y = 0.4z in 10x + 15y + 20z = 6300

10x + 15*0.4z + 20z = 6300

10x + 6z + 20z = 6300

Evaluate the like terms

10x + 26z = 6300

Substitute y = 0.4z in x + y + z = 475

x + 0.4z + z = 475

Evaluate the like terms

x + 1.4z = 475

Make x the subject

x = 475 - 1.4z

Substitute x = 475 - 1.4z in 10x + 26z = 6300

10(475 - 1.4z) + 26z = 6300

Expand

4750 - 14z + 26z = 6400

Evaluate the like terms

12z = 1650

Divide both sides by 12

z = 137.5

Substitute z = 137.5 in x = 475 - 1.4z

x = 475 - 1.4 * 137.5

Evaluate

x = 282.5

Hence, 282.5 of 10 tickets were sold

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The amount of plywood needed by Trenton = total surface area of the triangular prism-shaped ramp = 21 ft².

Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).

The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.

We are given the parameters:

Total surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)

= (18) + (3)

Total surface area = 21 ft²

Trenton will need 21 square feet of plywood.

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Answer:

Step-by-step explanation:

We can use the quadratic formula to get the answer to this

Quadratic Formula: -b +- √b² - 4ac/2a

Once we input A, B, and C into this, and solve any multiplication, we get

x = -1  +- √1 + 20/2

We divide by 2a, which 2a = 2.

-0.5 +- 10.5.

these are the following values of x:

x = 10

x = 11

Pretty sure this is it, hope it helps!

The combined total of their contracts is $1,296,250

The values of the contracts are given as:

The combined total is represented as:

Total = Exxon Mobil + Aerospace

Substitute known values

Total = $756,733 + $539,517

Evaluate the sum

Total = $1,296,250

Hence, the combined total of their contracts is $1,296,250

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The regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39

The attached table represents the missing information in the question.

Next, we enter the data values in a graphing technology

Using the graphing technology, we have:

a =2.13; b = 0.13 and c = 6.39

A quadratic regression is represented as:

y = ax^2 + bx + c

So, we have:

y = 2.13x^2 + 0.13x + 6.39

Hence, the regression equation of the data values is y = 2.13x^2 + 0.13x + 6.39

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Real life scenarios of acute angles are:

As a general rule, an acute angle, x is represented as: x < 90

This means that acute angles are less than 90 degrees.

The real life scenarios that involve acute angles are scenarios that whose measure of angle is less than 90 degrees.

Sample of the real life scenarios that satisfy the above definition are:

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The speed is the distance covered by an object at a particular time. The speed of the helicopter is equal to 10 kilometer/minute.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given the helicopter travels 30 kilometers in 3 minute. Therefore, the speed of the helicopter is equal to,

Speed = 30 kilometer/ 3minutes = 10 kilometer/minute.

Hence, the speed of the helicopter is equal to 10 kilometer/minute.

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The number of acorns that each animal hid is 48

An equation is formed when two algebraic expressions are equated by an equal sign.

It is asked to calculate the number of acorns that each animal hid.

Total number of acorns hid  =  number of acorns hid per tree * number of trees    

Let   T be the number of trees chipmunk used

For chipmunk:    = 3*T

For squirrel:   = 4*(T-4)

 As both the animals hid same number of acorns.

    3T = 4(T-4)      

    3T = 4T - 16      

      16 = T

Therefore the chipmunk hid 16 * 3 = 48 acorns

and the squirrel hid 4(16-4) = 48 acorns.

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Answer:

For Questions 1 , 2 and 3 check the attached diagram

4. How many outcomes are in the event "Toss a tails, spin yellow"? 

There is only one outcome ‘TY’ in this event .

5. What is the probability of tossing tails and spinning yellow?

[tex]p\left( TY\right) =\frac{1}{6}[/tex]

Step-by-step explanation:

Diagram

Step-by-step explanation:

that is a large gift. wow ! you have a lucky teacher ...

the surface of a block consists of 6 (3 pairs of) areas :

front and back

left and right

top and bottom

you know that the area of a rectangle is length × width ?

so,

front and back are

2× 9×13.5 = 18×13.5 = 243 m²

let and right are also

2× 9×13.5 = 243 m²

top and bottom are

2× 9×9 = 2 × 81 = 162 m²

so, for the whole package you need

243 + 243 + 162 = 648 m²

the money for that amount of wrapping paper alone would be way more than I ever spent on a teacher in my life ...

t = 0

t = 5

Step-by-step explanation:

(-10t^2+50t)/(t^2+4t+3)

I'm making t into x so its not confusing with the plus sign

(-10x^2+50x)/(x^2+4x+3)

with (x^2+4x+3) :

what 2 numbers when multiplied make 3 and when added make 4 ?

they are 1 and 3

(x+1)(x+3)

(-10x^2+50x)/(x+1)(x+3)

(-10x(x-5))/(x+1)(x+3) =0

(-10t(t-5))/(t+1)(t+3)=0

t = 0

t = 5

Answer:312

Step-by-step explanation: multiply 6*4*13

By solving a quadratic equation, we will see that the ball hits the ground after 2.6 seconds.

Here we need to solve the equation:

h(t) = 0 = -16t² + 40t + 4

This represents that the ball hits the ground.

So we just need to solve that quadratic equation, using the general formula we get:

[tex]t = \frac{-40 \pm \sqrt{(40)^2 - 4*4*(-16)} }{2*-16} \\\\t = \frac{-40 \pm 43.1 }{-32}[/tex]

We only care for the positive solution, which is:

t = (-40 - 43.1)/-32 = 2.6s

So the ball hits the ground after 2.6 seconds.

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Answer:

2

Step-by-step explanation:

The rise is two using the slope formula

rise/run

2/3

2 is the rise

Give brainliest please.

Hope this helps

Answer:

2

Step-by-step explanation:

Remember the rise-run formula

rise ÷ run

The rise is 2, and the run is 3, making this two-over-three.

Answer:

h(x) = 1 / 4x

last choice

Step-by-step explanation:

y = 4x becomes x = 4y

we want to solve for y,

divided both sides by 4

x / 4 = 4y / 4

x / 4 = y

Answer:

[tex]h(x) = \dfrac 14 x[/tex]

Step-by-step explanation:

[tex]y = f(x) = 4x\\\\\text{Replace x with y and then solve for y:}\\\\~~~~~x = 4y\\\\\implies y = \dfrac x4\\\\\implies f^{-1}(x) = \dfrac 14x[/tex]

Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:

c = 9.01/1.7 = 8.42 litros.

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Answer: Given y=3x-3, find y if x=4

              y=3x-3

              x=4

              y=3(4)-3

              y=12-3

              y=9

Step-by-step explanation: hopes this helps

                                        please mark me as a brainliest

Answer:

11i+4j

Step-by-step explanation:

add the i's together and the j's together.