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Answer: At [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.

Step-by-step explanation:

Since we have given that

Distance at which Selena is standing on a rock cliff = 52 feet

Height of boulder above a rock cliff = 12 foot

So, the given quadratic equation would be

[tex]p(t)=-16t^2+12t+52[/tex]

First we derivative it w.r.t  t,

[tex]p'(t)=-32t+12[/tex]

Now, we will find the critical value,

[tex]-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}[/tex]

Now, we will check whether it is maximum or not.

[tex]p''(t)=-32<0[/tex]

So, we get that it is maximum.

Hence, at [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.

Answer:

The answer is t=3/8

Answer:

[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Step-by-step explanation:

Given:

Two functions are given:

[tex]f(x)=5x^{3} +3x^{2} -3[/tex]

[tex]g(x)=x^{2} +x-5[/tex]

Find [tex]f(x)+g(x)[/tex]

Solution:

[tex]f(x)+g(x)=(5x^{3} +3x^{2} -3)+(x^{2} +x-5)[/tex]

[tex]f(x)+g(x)=5x^{3} +3x^{2} -3+x^{2} +x-5[/tex]

[tex]f(x)+g(x)=5x^{3} +(3x^{2} +x^{2})+x-3-5[/tex]

[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Therefore, the function of [tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]

Answer:I believe it's y=log(x-3)

Step-by-step explanation:

Answer:

(2, 1).

Step-by-step explanation:

f(x)=2x^2-8x+9

Find -b/2a first, it's -(-8)/2(2)=8/4=2.

Then find the y-coordinate of the vertex.

2(2)^2-8(2)+9=2(4)-16+9=8-16+9=-8+9=1

420 trees

210 minutes in 3 1/2 hours

x2 per minute

=420 trees in 3 1/2 hours

There are 420 trees will be sold in three and a half hours.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Every minute, there are two Christmas trees sold at the tree farm.

Now,

Since, Every minute, there are two Christmas trees sold at the tree farm.

Hence, Number of sold Christmas tree in 1 hour = 2 × 60

                                                                          = 120

So, Number of sold Christmas tree in 3 1/2 hour = 120 × 3 1/2

                                                                          = 120 × 7/2

                                                                          = 420

Thus, There are 420 sold Christmas tree in 3 1/2 hour.

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Answer:

127, 255  are the next 2 terms.

Step-by-step explanation:

The difference in terms  are 2,4,8,16,32 and so on.

Answer:

Amount of screen time

Step-by-step explanation:

Explanatory variables are those variables that are not totally independent and are used to predict or explain differences in the response variable.

Having pointed what an explanatory variable is, we'll list the explanatory variable(s) in the question, using the definition above.

The Variable used to predict results here is the amount of screen time.

In that case, it is the explanatory variable.

And it's of numerical type.

In the described study, the explanatory or independent variable is the amount of computer screen time each day, as it is the variable that is being manipulated by the researcher in order to examine its effect on REM sleep.

In this particular research study, the explanatory variable, or the independent variable, is the amount of computer screen time each day. This is because the explanatory variable is the factor manipulated by the researcher to observe any potential effects on the outcome variable, which in this case, is the amount of REM sleep.

The participants were divided into four different groups, each exposed to a different amount of screen time: 2 hours, 4 hours, 6 hours, and 8 hours. These varying hours of exposure were purposely manipulated by the researcher to observe and measure any differences in the REM sleep duration. Therefore, the computer screen time is the explanatory variable or cause, and the observed alterations to the REM sleep will be the response, or the dependent variable.

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Answer:

Step-by-step explanation:

3^-6 × (3^4 ÷ 3^0)^2 = 3^-6 × (3^4 ÷ 1 )^2           {any number raise to zero = 1}

     = 3^-6 × (3^4 )^2

   =  3^-6 × (3^8)             [ (a^m)^n = a^ m*n ]

     = 3^ -6 + 8 = 3^2 = 3 * 3 = 9

Answer:

The 3rd one

Step-by-step explanation:

The steepest slope is basically the slope with the greatest absolute value. You can find slope by finding rise over run when given the graphs and finding change in y/change in x in the tables.

Function 1: -3

Function 2: (13-10)/(6-3) = 3/3 = 1

Function 3: 2

Function 4: (-4-(-12))/(2-4) = 8/-2 = -4

Function 4's slope has the greatest absolute value.

answer: the fourth one

Answer:

see the explanation

Step-by-step explanation:

step 1

Identify the equation of the given line

we know that

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]m=5\\b=-1[/tex]

substitute

[tex]y=5x-1[/tex]

step 2

Identify the coordinates of four points on the line

First point

The given y-intercept

point (0,-1)

Second point

The x-intercept

For y=0

[tex]0=5x-1[/tex]

[tex]x=\frac{1}{5}=0.20[/tex]

point (0.20,0)

Third point

For x=1

[tex]y=5(1)-1=4[/tex]

point (1,4)

Fourth point

For x=2

[tex]y=5(2)-1=9[/tex]

point (2,9)

Answer:

  see attached

Step-by-step explanation:

The translation is 1 unit left and 5 units down. It is easy enough to count squares. It is just as easy to add (-1, -5) to each of the preimage coordinates.

Answer:

20 = 3x+2y

Step-by-step explanation:

one box of crackers is $3 (3x)

one box of granola bars is $2 (2y)

Answer:

20/3

Step-by-step explanation:

Answer:

10%

Step-by-step explanation:

Good morning,

Answer:

Step-by-step explanation:

Let x be the cost price and

     y the final sell price

     p gain percent

the gain precent p = (20/100)-(10/100)-[(20×10)/(100×100)]

                               = (20-10)/100 - 2/100

                               = 10/100 - 2/100

                               = 8/100

example : x=20

x(1+20/100)(1-10/100) = 20(1+20/100)(1-10/100) = 20(120/100×90/100)

                                                                           = 20(10 800÷10 000)

                                                                           = 21.6

20+20p% =21.6 then 20p%=1.6 then p%=1.6/20=16/200=8/100 then p=8.

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Sofia can spend at most $20.83 each week.

Step-by-step explanation:

Given,

Amount of given by Sofia's parent = $125

Number of weeks = 6

Let,

x represent the amount that Sofia can spend each week.

As Sofia has $125, therefore, she can spend maximum $125 or less than that.

[tex]6x\leq 125[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}\leq \frac{125}{6}\\x\leq 20.83[/tex]

Sofia can spend at most $20.83 each week.

Keywords: inequality, division

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Rita has hiked 1.38 miles so far.

Step-by-step explanation:

Given,

Total length of the hiking trail = 13.8 miles

Distance covered by Rita so far = [tex]\frac{1}{10}\ of\ the\ trail[/tex]

Distance covered in miles = [tex]\frac{1}{10}*13.8[/tex]

Distance covered in miles = 1.38 miles

Rita has hiked 1.38 miles so far.

Keywords: fraction, division

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Answer:

The arc length, radius and the included angle are related as

r\theta=\widehat {XYZ}  where  \theta  is in radians.

The radius  r  is given by

r=\frac{\widehat {XYZ} }{\theta} \\ r=\frac{10.8}{1.8} \\ r=6\;units  

Correct choice is (B).

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(x+3)/3 =(y+2)/2

x/3 +3/3 = y/2 +2/2

x/3 +1 = y/2 +1

x/3 = y/2

Final answer:

To find how many text messages, x, Tim sent last month, use the equation: Total cost = fixed cost + variable cost. Given that Tim's phone bill was $30.58, the equation is $30.58 = $25.08 + $0.22x. Solving the equation gives x ≈ 25, so Tim sent approximately 25 text messages last month.

Explanation:

To find the number of text messages, x, Tim sent last month, we can use the equation:
Total cost = fixed cost + variable cost

Given that Tim's phone bill was $30.58, the fixed cost is $25.08. The variable cost is $0.22 per text message sent. Let's represent the number of text messages sent by x.

So, the equation becomes:
$30.58 = $25.08 + $0.22x

To solve for x, we need to isolate x. Subtract $25.08 from both sides of the equation:

$30.58 - $25.08 = $0.22x

Simplify:

$5.50 = $0.22x

Divide both sides of the equation by $0.22:

x = $5.50 / $0.22

x ≈ 25

Therefore, Tim sent approximately 25 text messages last month.

Answer:

x = 12

y = 5

Step-by-step explanation:

a triangle's side is divided by an angle bisector that bisects the opposite angle. Their relative lengths equals to the relative lengths of the other two sides of the triangle

x / 8 = 9 / 6

x = 9/6 * 8 = 12

(y-3) / 3 = 4 / 6

y - 3 = 4/6 * 3 = 2

y = 5

Answer:

f(x) - g(x) = (1/x) + 2 - 3x      or (f - g)(x)

Step-by-step explanation:

f(x)  = 1/x+2

-g(x) = 3x

can be summarized on line line as:

f(x) - g(x) = (1/x) + 2 - 3x      or (f - g)(x)

A relation is a function if there is exactly one output for each input ⇒ b

Step-by-step explanation:

Let us revise the meaning of relation and function

Examples:

{(1 , 2) , (-2 , 3) , (1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ The input 1 has two output 2 and 5

∴ The set above is a relation

{(1 , 2) , (-2 , 3) , (-1 , 5) , (2 , 4)}

∵ x is the input

∵ y is the output

∵ Each input has only one output

∴ The set above is a function

A relation is a function if there is exactly one output for each input

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Here are the steps:

1. Arrange the polynomial in descending order.

2. Write down all the factors of the constant term. These are all the possible values of p.

3. Write down all the factors of the leading coefficient. ...

4. Write down all the possible values of . ...

5. Use synthetic division to determine the values of for which P( ) = 0.

Answer:

Step-by-step explanation:

Arrange the polynomial in descending order.

Write down all the factors of the constant term. These are all the possible values of p.

Write down all the factors of the leading coefficient.

Answer:

Step-by-step explanation:

2x=(360÷4)

2x = 90

Dividing by 2

x = 90/2

x = 45

By following the steps of simplifying, isolating, and solving for x, we find that x = 45 is the value that satisfies the given equation.

To solve the equation 2x = (360 ÷ 4) for x, we need to isolate x on one side of the equation. Follow these steps to find the value of x:

Step 1: Simplify the expression on the right side of the equation.

360 ÷ 4 = 90

Step 2: Replace the right side of the equation with its simplified value.

2x = 90

Step 3: To isolate x, divide both sides of the equation by 2.

(2x) ÷ 2 = 90 ÷ 2

This simplifies to:

x = 45

The solution to the equation is x = 45. To verify, you can substitute x = 45 back into the original equation:

2(45) = 90

90 = 90

Since both sides of the equation are equal, x = 45 is indeed the correct solution.

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Answer:

Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]

Or

Scale : 3 mm = 1 m

Step-by-step explanation:

Let the scale used be 1 mm = 'x' m

Given:

Actual width of kitchen is 12 m.

Length used by Kate in drawing is 36 mm.

So, 36 mm in drawing is equivalent to 12 m in actual.

Therefore, 1 mm in drawing is equivalent to 'x' m in actual.

Taking proportions and solving by cross multiplication, we get

[tex]\frac{36}{12}=\frac{1}{x}\\36x=12\\x=\frac{12}{36}\\x=\frac{1}{3}\ m[/tex]

Therefore, 1 mm in drawing is equal to [tex]\frac{1}{3}\ m[/tex] in actual.

Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]

Or

Scale : 3 mm = 1 m

47 / 14 ≈ 3.36

Firstly, let's covert the fraction 47 / 14 to a decimal. The decimal format of 47 / 14 will be

Finally, let's approximate the decimal to the nearest hundredth

Always remember to use the approximate symbol when you approximate an answer.

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Final answer:

To round 47/14 to the nearest hundredth as a decimal, divide 47 by 14 to get 3.3571..., and then round this to 3.36 since the third decimal place is 7.

Explanation:

To convert the fraction 47/14 to a decimal rounded to the nearest hundredth, you first divide 47 by 14. This gives you the decimal form. After obtaining the decimal, you look at the third decimal place. If it's 5 or more, you round the second decimal place up. If it's less than 5, you leave the second decimal place as is.

Dividing 47 by 14 gives us 3.3571... To round it to the nearest hundredth, we look at the third decimal place, which is a 7, so we round up the second decimal place from 5 to 6, thus the answer is 3.36.

First find m<HGC.

m<HGC=14 degrees (through vertical angles)

So...

m<HGE=14+78=92 degrees (through adjacent angles)

Now we have two parallel line cut by a transversal. And so... <HGE and <CEG are same side interior angles which means they are supplements (sum to 180 degrees)

m<HGE+m<CEG=180

92+m<CEG=180

m<CEG=88 degrees

<CEG and <CEB make a linear pair and are thus are supplements as well.

So...

m<CEG+m<CEB=180

88+m<CEB=180

m<CEB=92 degrees

m<CEB=4x=92

x=92/4=23 degrees

answer: 23 degrees

Final answer:

Both lawn care services, Green Lawn and Grass Team, will cost the same after 3 months, with each service costing a total of $136 at that point.

Explanation:

The student asked at how many months will both lawn care services, Green Lawn and Grass Team, cost the same and what will be that cost. To solve this, we set up an equation with Green Lawn's cost model: $49 (startup fee) + $29 per month (monthly fee) and Grass Team's cost model: $25 (startup fee) + $37 per month (monthly fee). Let m represent the number of months.

The equation will look like this:
49 + 29m = 25 + 37m

To find the number of months where the costs are the same, we will solve for m:

Therefore, both services will cost the same after 3 months. The total cost at this point will be calculated by substituting m back into either cost model (we will use Green Lawn's model):