Ben is climbing a tree with a lot of branches. His height off the ground at time $t$ is $2t^2-5t+29$ feet. To the nearest foot, what will his minimum height be?

Answers

Answer 1

Using the vertex of the quadratic equation, it is found that his minimum height will be of 25.875 feet.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.

In this problem, the equation is:

h(t) = 2t² - 5t + 29.

Hence the coefficients are a = 2 > 0, b = -5, c = 29, and the minimum height in feet is given by:

[tex]y_v = -\frac{(-5)^2 - 4(2)(29)}{4(2)} = 25.875[/tex]

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

Answer 2

Ben minimum height above the ground when climbing the tree would be 25.875 feet

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

h(t) = 2t² - 5t + 29

The minimum height is at h'(t) = 0, hence:

h'(t) = 4t - 5

4t - 5 = 0

t = 5/4

h(5/4) = 2(5/4)² - 5(5/4) + 29 = 25.875 feet

Ben minimum height above the ground when climbing the tree would be 25.875 feet

Find out more on equation at: https://brainly.com/question/2972832


Related Questions

Help pls!!! No links pls and ty <33

A circle has a circumference of 51 centimeters. What is the circle's
diameter? Use 3.14 for pi and round your answer to the nearest tenth

Answers

Answer:

16.2

Step-by-step explanation:

just divide the circumference by 3.14

Answer:

diameter= 16.2338

Step-by-step explanation:

D = C/π

c means CircumferenceD means diameterπ means pi

=> D = 51/3.14

D = 16.2338

D = 16.2

Find the new side lengths if the scale factor is 2/5. 35 inches 15 iches NEED ANSWER ASAP PLEASEEEE​

Answers

Answer:

l = 14 inches , b = 6 inches

Step-by-step explanation:

multiply length l and breadth b by the scale factor , then

new length = [tex]\frac{2}{5}[/tex] × 35 = 2 × 7 = 14 inches

new breadth = [tex]\frac{2}{5}[/tex] × 15 = 2 × 3 = 6 imches

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Need help with this

Answers

Answer:

6

Step-by-step explanation:

PLS GIVE ME BRAINILIEST!

211,207,203,...
Find the 38th term.

Answers

Answer:

63

Step-by-step explanation:

Using the formula attached, we can setup the equation:

[tex]211 + (38 - 1) - 4[/tex]

Then using a calculator you can solve

The required 38th term of the given arithmetic sequence is 63.

What is arithmetic progression?

Arithmetic progression is the series of numbers that have common differences between adjacent values

What is geometric progression?

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

here,
Given sequence,
211,207,203,...
First term, a = 211
Common difference, d = 207 - 211 = -4

Now.
Nth term of an arithmetic progression,
Nth term = a + (n -1)d
Nth term of given sequence
Nth term = 211 - (n - 1)4

Now, put n = 38
38th term = 211 - (38 - 1)4
38th term = 211 - [37](4)
38th term = 211 - 148 = 63

Thus, the required 38th term of the given arithmetic sequence is 63.

Learn more about arithmetic progression here: https://brainly.com/question/20334860
#SPJ2

help me PLEASEE i really don’t understand

Answers

Area =Length(L) x Length(L)
Area = L^2
625 = L^2
L = √625
L= 25 m

Perimeter = 4L = 4 x 25 = 100 m
Answer = 100 meters

Geometry math work! help needed please.

Answers

Answer:

I decided to use the actual formula this time and got 25.7

Step-by-step explanation:

first we find the length of the arc of bca

360-65

so its 295

then after I use the arc length formula which is

x/360 times 2(pie)r

295/360 times 2(pie)5

295/360 times 31.4159

9267.6983/360 (I multplied 295 and 31.4159)

Then we divide and get

25.743

What is the simplified expression for:

Answers

I think it is for the original amount

A circle has a circumference of 26 millimeters. What is the circle's
radius? Use 3.14 for pi and round your answer to the nearest tenth

PLS HELP!!! No links pls and ty <333

Answers

Answer:

22.5

Step-by-step explanation:

Radius = Circumference/(2*PI)

If the simple interest on $5,000 for 6 years is 1,200 then what is the interest rate?

Answers

Answer:

4%

Step-by-step explanation:

You can use the formula below to find the simple interest rate.

Simple interest = P r t / 100

Here,

P ⇒ Principle ⇒ $ 5000

r ⇒ rate ⇒ ??

t ⇒ time ⇒ 6 years

simple interest ⇒ $ 1200

Let us find it now.

Simple interest = P r t / 100

1200 = 5000 × r × 6 / 100

1200 × 100 = 30000r

120000 = 30000 r

Divide both sides by r.

4 = r

Therefore, the interest rate is 4%

HELP ME WITH THIS NOOOOWWWW

Answers

Answer:

A

Step-by-step explanation:

BD = 12

BC = 12/2 => 6

using Pythagoras theorem

AB² = AC² + BC²

AB² = 3² + 6²

AB² = 9 + 36

AB² = 45

AB = √45 (A)

Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in this
situation?
a full standard deck of cards
a spinner divided evenly into four sections, with each section a different color
a six-sided number cube
0 a bag containing 12 chips in three different colors, with four of each color
two coins

Answers

The simulation tool to use is (d) a bag containing 12 chips in three different colors, with four of each color

How to determine the simulation tool?

From the question, we have the following parameter:

Group, n = 3

The probability of selecting a group is:

p = 1/3

This means that the simulation tool to select must have a probability value of 1/3

From the question, the option (d) has a probability of 1/3

This is so because, we have:

Chips = 12Colors = 3Chip of same color = 4

So, the probability of selecting each color is 4/12 or 1/3

Hence, the simulation tool to use is (d)

Read more about probability at:

https://brainly.com/question/251701

Answer:

a bag containing 12 chips in three different colors, with four of each color

and i think

a six-sided number cube

Step-by-step explanation:

plato?

What is the missing value (-15)+18=

Answers

Answer:

3

Step-by-step explanation:

(-15) + 18 = 3

We can check our answers by adding 15 to 3 when doing inverse operations.

Answer:

3

Step-by-step explanation:

-15 + 18 = 3

Find the number to add to x^2 + 14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.

Answers

Answer:

Option 2

Step-by-step explanation:

Divide the co efficient of 'x' by 2 and the square the result.

14 ÷2 = 7

7² = 49

To make it a perfect trinomial, 49 should be added

x² +14x + 49 = x² + 2*x *7  + 7²        {Compare with a²+ 2ab + b² = (a +b)²}

                   = (x +7)²

100 Points!!!! Please Show Steps!

1. Given f(x)=x^2 - 2 and g(x) =4x + 1 Find

a. f(g(x))
b. g(f(x))

Answers

f(x) = x² - 2g(x) = 4x + 1

Go from right to left in such function questions

a. f(g(x))

⇒ f(4x + 1)

⇒ (4x + 1)² - 2

⇒ 16x² + 8x + 1 - 2

⇒ 16x² + 8x - 1

b. g(f(x))

⇒ g(x² - 2)

⇒ 4(x² - 2) + 1

⇒ 4x² - 7

Answer:

[tex]f[g(x)]=16x^2+8x-1[/tex]

[tex]g[f(x)]=4x^2-7[/tex]

Step-by-step explanation:

Given functions:

[tex]f(x)=x^2 - 2[/tex]

[tex]g(x) =4x + 1[/tex]

[tex]f[g(x)][/tex] means to substitute g(x) in place of x in f(x):

[tex]\begin{aligned}\implies f[g(x)] & =[g(x)]^2-2\\ & =(4x+1)^2-2\\ & = (4x+1)(4x+1)-2\\ & = 16x^2+8x+1-2\\ & = 16x^2+8x-1\end{aligned}[/tex]

[tex]g[f(x)][/tex] means to substitute f(x) in place of x in g(x):

[tex]\begin{aligned}\implies g[f(x)] & =4[f(x)]+1\\ & = 4(x^2-2)+1\\ & = 4x^2-8+1\\ & = 4x^2-7\end{aligned}[/tex]

If the slope of a line is 4/5, does the line rise (from left to right), fall (from left to right), horizontal or vertical?

Answers

slope: 4/5 is a positive slope

positive slopes rises from left to rightpositive slopes falls from right to leftneither horizontal or vertical.

The picture below shows some examples of equation with positive slope.

Answer:

rise from left to right

Step-by-step explanation:

Linear equation: [tex]y=mx+b[/tex]

(where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept)

Positive slope: rise from left to right

[tex]m[/tex] is a positive number

[tex]\textsf{e.g.}\:y=\dfrac45x+4[/tex]

Negative slope: fall from left to right

[tex]m[/tex] is a negative number

[tex]\textsf{e.g.}\:y=-\dfrac45x+4[/tex]

Zero slope: horizontal line

[tex]m=0[/tex]

[tex]\textsf{e.g.}\:y=0x+\dfrac45\implies y=\dfrac45[/tex]

Therefore, a horizontal line is [tex]y = a[/tex] (where [tex]a[/tex] is some constant)

Infinite slope: vertical line

[tex]m= \infty[/tex]

[tex]\sf slope\: (m)=\dfrac{change\:in\:y}{change\:in\:x}[/tex]

There is no change in x-values for a vertical line, so:

[tex]\sf \implies slope=\dfrac{change\:in\:y}{0}=\infty[/tex]

We also usually call the slope of this line undefined.

Therefore, a vertical line is [tex]x = a[/tex] (where [tex]a[/tex] is some constant)

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

Attached graph:

Positive slope: black line

Negative slope: blue line

Zero slope: green line

Infinite slope: red line

5x + 3y -5.70 2x+10y+3.60

Answers

Answer:

I`m not really sure what i`s asking to solve but here`s my best answer.

5x + 3 - 5.70 = 2x + 10y + 3.60

3x + 3 - 5.70 = 10y + 3.60

3x + 3 = 10y + 9.30

3x = 10y + 6.30

^^^That`s the most it can be simplified without any new fractions or decimals

3x = 10y + 6.30

x = 3.33y + 2.10

^^^That`s the most it can be simplified to solve for x.

A new washing machine is purchase by the hamilton family it cost 324.50 how much will the washing machine cost after 6% sales tax is
applied

Answers

Answer:

343.97

Step-by-step explanation:

price of vending machine is 100% = 324.50

100% + 6% sales tax = 106%=1.06

324.50*1.06

343.97

Which statement about the simplified binomial expansion of (a – b)n, where n is a positive integer, is true? all terms of the expansion are positive. all terms in the expansion are negative. the first term in the expansion is positive. the first term in the expansion is negative.

Answers

If the value of n is a positive integer then the first term is always positive. Then the correct option is C.

What is binomial expansion?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

The binomial expression is given (a – b)ⁿ.

If the value of the n is positive then the condition will be

There is a negative sign between a and b so it is impossible to have all the terms positive as well as negative.

But the first term will always be positive.

More about the binomial expansion link is given below.

https://brainly.com/question/12249986

Answer:c

Step-by-step explanation:

edge 2022 slay

An exponential function and a linear function are graphed below.



Over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?

Answers

Answer:

x = 1.79 to x = 3

Step-by-step explanation:

I think this is correct because the linear function grows at a constant rate so the point where the exponential function's line starts going up faster means that the growth rate is increasing. At the point (1.79,7.17) is when both lines intersect but the exponential function is growing at a faster rate than the linear function.

Answer:

x = 1.79 to x = 3

Step-by-step explanation:

An isosceles right triangle has legs of equal length. If the
hypotenuse is 18 centimeters long, find the length of each leg.

Answers

Step-by-step explanation:

hope you have a great day going so far today

Given the points (0, 5), (1, 7), and (-2, -5), find the equation of the quadratic polynomial that contains
these points. Show your work.

Answers

Answer:

y=-x²+3x+5.

Step-by-step explanation:

1) the common view of the quadratic function is y=ax²+bx+c, where a, b and c - numbers;

2) according to the equation above, it needed to substitute the given coordinates and to make up the system of the equations:

point (0;5): c=5;

poit(1;7): a+b+5=7 ('c' is already known, 5);

point(-2;-5): 4a-2b+5=-5 (c=5);

3) to solve the system:

[tex]\left \{ {{a+b+5=7} \atop {4a-2b+5=-5}} \right. \ = > \ \left \{ {{a=-1} \atop {b=3}} \right.[/tex]

4) finally, if a=-1, b=3 and c=5, then

y=-x²+3x+5.

Please help guys much love

Answers

Step-by-step explanation:

1) Ans 3

2) Ans 6

3) Ans 4

4) Ans 1/5

5) Ans 1/23

What is the slope of a line that is parallel to the line y = 3/4x + 2?
-4/3
-3/4
3/4
4:3

Answers

Answer: The Slope Is 3/4

Step-by-step explanation:

y = 3/4x + 2

This is given in slope intercept form y = mx+b where m is the slope

Parallel lines have the same slope

The slope is 3/4y = 3/4x + 2

Answer:

x is - 7

Step-by-step explanation:

as you do  4+3=7 then there  is a - sign  in front of it

You are standing next to a really big circular lake. You want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! You decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400π m400, pi, start text, space, m, end text.
What is the diameter of the lake?

Answers

Answer:

diameter = 400 m

Step-by-step explanation:

Perimeter of circle = pi * d

 400 pi                  = pi * d

d = 400 meters  

Cos²(90° -X).tan(180°-X).cos(180°+X)/sin(180°-X)

Answers

Recall some identities:

tan(x) = sin(x) / cos(x)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

This means we have

• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²

… = sin²(x)

• tan(180° - x) = sin(180° - x) / cos(180° - x)

… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]

… = sin(x) / (-cos(x))

… = -tan(x)

(and we also get sin(180° - x) = sin(x))

• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)

… = -cos(x)

So, the given expression reduces to

sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)

since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.

60 points) khan academy geometry practice. Need help i in any way cannot miss this question please help!!

Answers

93 degrees (all triangles degrees add to be 180)

(3+1)(6x9)-23
Using Pemdas explain and answer this question

Answers

Answer:

193

Step-by-step explanation:

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

3+1 can be simplified to 4

6 times 9 is 54

(4)(54)-23

216-23

193

area = 756 cm^2
h = 18 cm
a = 39 cm
b = ?​

Answers

Answer:

given,

area= 756cm^2

h = 18cm

a = 39cm

then,

area = (a+b)h/2

756 = (39+b)18/2

756= 351+9b

756-351= 9b

405 = 9b

405/9= b

b = 45cm

Simplify the expression below: 3(7x) – 2(4 – x)

A. 13 – 2x

B. 13 + 2x

C. 23x – 8

D. 20x – 8

Answers

Answer:

C

Step-by-step explanation:

3(7x)=21x

-2(4-x)= -8+2x

21x-8+2x=23x-8

i just need the answer and ill do the labels​

Answers

By the vertical angle theorem, the two angles '5y + 12' and '82' are equal

    ⇒ [tex]5y + 12 = 82[/tex]

        [tex]5y = 70\\y = 14[/tex]

Thus x = 14

Hope that helps!

p.s. Definition of Vertical Angle Theorem: angles that are opposite each other and formed by two intersecting straight lines, are congruent

p.s. Diagram for what is Vertical Angle Theorem:

Answer:

y = 14

Step-by-step explanation:

82° = (5y + 12)°

5y = 82 - 12

5y = 70

y = 14

    {calculate carefully{

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