A ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 18 feet up the tree. What is the angle created between the ladder and tree? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.

Answer:

[tex]\huge\boxed{x=8;\ y=1\to(8;\ 1)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}[/tex]

[tex]\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}[/tex]

Answer:

(8, 1).

Step-by-step explanation:

y = x - 7

5 + 2y = 7

5 + 2(y) = 7

5 + 2(x - 7) = 7

5 + 2x - 14 = 7

Subtract 5 from both sides

2x - 14 = 2

Add 14 to both sides

2x = 16

Divide both sides by 2

x = 8

Since x = 8...

y = x - 7

y = 8 - 7

y = 1.

To check our work...

5 + 2y = 7

5 + 2 * 1 = 7

5 + 2 = 7

7 = 7

Since it works out, your answer is (8, 1).

Hope this helps!

Answer:

  x = 10

Step-by-step explanation:

Use the Pythagorean theorem. The sum of the square of the sides is the square of the hypotenuse.

  x² +(√200)² = (√300)²

  x² = 300 -200

  x = √100 = 10

The length of the unknown side is 10 units.

Answer:

Step-by-step explanation:

Hello!

To compare different prices of several brands of a product the best is to express the price for the same quantities of product.

Since the three options are original in 300g, 450g and 600g, I'll express all prices on a base of 100g of product. You can use simple rule of three for this:

Option 1

300g cost $3.89

100g cost [tex]\frac{100*3.89}{300} = $1.296[/tex]

Option 2

450g cost $ 4.77

100g cost [tex]\frac{100*4.77}{450}= $1.06[/tex]

Option 3

600g cost $ 6.59

100g cost [tex]\frac{100*6.59}{600}= 1.098[/tex]

So:

Option 1: $1.296/ 100g

Option 2: $1.06/100g

Option 3: $1.098/100g

The cheapest option is number 2

I hope this helps!

Answer:

Terrance is incorrect

Step-by-step explanation:

Supplementary angles add to 180 degrees

4x+30 + 2x+6 = 180

Combine like terms

6x+36 = 180

Subtract 36 from each side

6x+36-36 = 180 -36

6x =144

Divide by 6

6x/6 = 144/6

x =24

Answer:

No solutions.

Step-by-step explanation:

we have y=3x

to get y=3x+4

we just move every point of y=3x ,4 units up

and to get y=3x+7

we just move every point of y=3x, 7 units up

and it's pretty clear they are parallels, because it's the same line, just moved.

Answer:

No solutions.

Step-by-step explanation:

Answer:

a. 24

b.600

c.36

d. No

Step-by-step explanation:

a.You know the approximate number of gallons is about 24 gallons because each tank holds twelve and your family used 2 of them.

b. You know you drove about 600 miles. This is because you used 24 gallons And each gallon should get you 25 miles. multiply The 2 together to get 600 miles. Or you could set a thing like 1/25=24/x and solve for x.

c. It cost 36 dollars because each gallon is 1.5 and you used 24 gallons so mul the two together to get 36

d. First find the amount of gallons used by dividing 350 by 25 to get 14. Then multiply 14 by 1.5 to get 21. 21 is greater than 20 so you don’t have enough money.

Answer:

You have relative maximum at x=1.

Step-by-step explanation:

-Note that f' is continuous and smooth everywhere. f therefore exists everywhere on the domain provided in the graph.

f' is greater than 0 when the curve is above the x-axis.

f' greater than 0 means that f is increasing there.

f' is less than 0 when the curve is below the x-axis.

f' is less than 0 means that f is decreasing there.

Since we are looking for relative maximum(s), we are looking for when the graph of f switches from increasing to decreasing. That forms something that looks like this '∩' sort of.

This means we are looking for when f' switches from positive to negative. At that switch point is where we have the relative maximum occurring at.

Looking at the graph the switch points are at x=0, x=1, and x=2.

At x=0, we have f' is less than 0 before x=0 and that f' is greater than 0 after x=0.  That means f is decreasing to increasing here. There would be a relative minimum at x=0.

At x=1, we have f' is greater than 0 before x=1 and that f' is less than 0 after x=1. That means f is increasing to decreasing here. There would be a relative maximum at x=1.

At x=2, we have f' is less than 0 before x=2 and that f' is greater than 0 after x=2. That means f is decreasing to increasing here. There would be a relative minimum at x=2.

Conclusion:

* Relative minimums at x=0 and x=2

* Relative maximums at x=1

Using the graph and the second derivative test, it is found that the relative maximum on the graph of f(x) is at [tex]x = 1[/tex].

The critical points of a function f(x) are the values of [tex]x_0[/tex] for which:

[tex]f(x_0) = 0[/tex].

The second derivative test states that:

In this problem, the critical points are: [tex]x = 0, x = 1, x = 2[/tex].

For each of the critical points:

A similar problem is given at https://brainly.com/question/2256078

Answer:

[tex]\boxed{D = 15/8}[/tex]

Step-by-step explanation:

=> [tex]x^2-\frac{1}{2} x +\frac{1}{2} = 0[/tex]

Comparing it with the standard form of quadratic equation [tex]ax^2+bx+c = 0,[/tex] we get

a = 1, b = -1/2 and c = 1/2

Discriminant = [tex]b^2-4ac[/tex]

[tex]D = (-1/2)^3+4(1)(1/2)\\D = -1/8 + 2\\D = \frac{-1+16}{8} \\D = \frac{15}{8}[/tex]

Answer:

2 times

Step-by-step explanation:

Well let's first graph the quadratic equation,

Look at the image below ↓

By looking at the image below we can tell that the graph touches the x axis 2 times at,

(-1,0)

(1 1/3,0)

Thus,

the parabola touches the x axis twice.

Hope this helps :)

Answer:

3

Step-by-step explanation:

Answer:

r = 18m

Step-by-step explanation:

h = 50 m

Volume of cone = 5400π m³

[tex]\frac{1}{3}\pi r^{2}h=5400\pi \\\\\\\frac{1}{3}\pi r^{2}*50=5400\pi \\\\\\r^{2}=\frac{5400* \pi *3 }{\pi * 50}\\\\\\r^{2}=108*3\\\\r^{2} = 324\\\\\\r=\sqrt{324}\\\\\\[/tex]

r = 18 m

You should use a T distribution to find the critical T value based on the level of confidence. The confidence level is often given to you directly. If not, then look for the significance level alpha and compute C = 1-alpha to get the confidence level. For instance, alpha = 0.05 means C = 1-0.05 = 0.95 = 95% confidence

Use either a table or a calculator to find the critical T value. When you find the critical value, assign it to the variable t.

Next, you'll compute the differences of each pair of values. Form a new column to keep everything organized. Sum everything in this new column to get the sum of the differences, which then you'll divide that by the sample size n to get the mean of the differences. Call this dbar (combination of d and xbar)

After that, you'll need the standard deviation of the differences. I recommend using a calculator to quickly find this. A spreadsheet program is also handy as well. Let sd be the standard deviation of the differences

The confidence interval is in the form (L, U)

L = lower bound

L = dbar - t*sd/sqrt(n)

U = upper bound

U = dbar + t*sd/sqrt(n)

Step-by-step explanation:

Hello!!

Given that,

one is 75 cm and other is 1m.

now, let's convert 1m into cm.

so, 1m=100cm.

now,

ratio of 75cm to 100 cm = 75/100

=3/4

= 3:4 ...is answer.

Therefore, the ratio is 3:4.

Hope it helps..

Answer:

Ahhh

Step-by-step explanation:

I have this question too!!!

Answer:

144 m²

Step-by-step explanation:

top triangle area: (8 x 6) / 2 = 24

bottom triangle area: (8 x 6) / 2 = 24

back rectangle area: 8 x 4 = 32

left rectangle area: 6 x 4 = 24

right rectangle area: 10 x 4 = 40

add all: 144 m²

Answer:

There are 5 surfaces for which you will have to calculate area.

the back is 4 by 8  = 32 mi^2

The bottom is 4 by 6 = 24 mi^2

the tilted ramp 4 by 10 = 40 mi^2

There are 2 side triangles 8 by 6  area of 1 triangle = 8*6/2 = 24 mi^2

area of BOTH triangles = 2 * 24 = 48 mi^2

Total area = 32 + 24 + 40 + 48 = 144 mi^2

Step-by-step explanation:

Answer:

On day 0 (starting day), the percentage of petri dish occupied by bacteria was 2.44%

Step-by-step explanation:

Rate of growth = 2  (i.e. doubles every day)

Petri dish was filled to 100% on day 12.

Let

P(0) = percentage of Petri dish occupied on day 0, then

equation of percentage a  function of time in x days

P(x) = P(0)*r^x  ......................(1)

where

100% = P(12) = p(0) * 2^12 = 4096 P(0)

=>

P(0) = 100% / 4096 = 0.0244%

Next, to find percentage on February 14 (Valentine's day!)

Day 0 is February 9, so February 14 is the fifth day, so x=5.

Substitute x=5 in equation (1) above,

P(x) = P(0)*r^x  

P(5) = P(0)*2^5

P(5) = 0.0244*2^5 = 0.0244*32 = 0.781%

Ans. the 0.781% of the petri dish was filled with bacteria after 5 days on February 14th.

Answer:

0.0244%

Step-by-step explanation:

A = p(1 + r)^t

The future amount is 100, for 100 percent. From February 9 to February 21, there are 12 days. The rate of growth is 100% since the amount doubles each day. t = 12, for 12 days. p = beginning percentage.

100 = p(1 + 1)^12

log 100 = log [p(1 + 1)^12]

2 = log p + 12 log 2

log p = 2 - 12 log 2

p = 10^(2 - 12log 2)

p = 0.0244

Answer 0.0244%

Answer:

A) a=25

B) b=14

Step-by-step explanation:

A) a/5+3=8

First you need to subtract 3 from both sides.

(a/5+3)-3=(8)-3

Then simplify

a/5=5

Multiply both sides by 5

(a/5)*5=(5)*5

Then simplify

a= 25

B )3b/7-1=5

First you need to add 1 to both sides

(3b/7-1)+1=(5)+1

Simplify

3b/7=6

Multiply both sides by 7

(3b/7)*7=(6)*7

Simplify

3b=42

Divide both sides by 3

(3b)/3=(42/3)/3

Simplify

b= 14

(Brainliest???) :P

Answer:

There are four possible outcomes for each spin: red, blue, yellow, green.

Answer:

i have a Similar question I’m stuck on, just remember z rule, vertically opposite etc.

Answer:

o.5

Step-by-step explanation:

Answer:

[tex]Angle = 54[/tex]

Step-by-step explanation:

Given

Kano = 45;

Kwara  = 410;

Ogun = 105;

Ondo = 126;

Oyo = 154

Total Distribution = 840

Required

Determine the angle subtended by Ondo (in a pie chart)

The general formula to calculate subtended angle in a Pie chart is;

[tex]Angle = 360 * \frac{Frequency}{Total\ Frequency}[/tex]

In this case of Ondo

Frequency = 126

Total Frequency = Total Distribution = 840

Substitute these values in the given formula;

[tex]Angle = 360 * \frac{126}{840}[/tex]

[tex]Angle = \frac{360 *126}{840}[/tex]

[tex]Angle = \frac{45360}{840}[/tex]

[tex]Angle = 54[/tex]

Hence, the angle subtended by Ondo is 54

Answer:

264 ft³

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Height (h) = 21 ft

Radius (r) = 2 ft

Volume (V) =..?

The volume of the cylinder can be obtained as follow:

V = πr²h

V = 3.14 × 2² × 21

V = 3.14 × 4 × 21

V = 264 ft³

Therefore, the of the cylinder is 264 ft³

Answer :

A. add x, subtract 1, divide by 4

D. subtract 3x, subtract 4, divide by -4

Step-by-step-explanation : Further explanation

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\1+3x-1=-x+4-1\\Simplify\\3x=-x+3\\\mathrm{Add\:}x\mathrm{\:to\:both\:sides}\\3x+x=-x+3+x\\Simplify\\4x=3\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4x}{4}=\frac{3}{4}\\x=\frac{3}{4}[/tex]

I hope it helps:)

Answer:

The equation for renting a car is ;

y = 3.5x + 220

where y is the rental cost and x is the number of miles driven

The cost of rising 388 miles is $1,578

Step-by-step explanation:

88 miles cost $428 while 158 miles cost 673, now we want to create an equation that represents renting a car from Hertz

We can make this in form of a plot with us having 2 data points here.

let the value y represent the cost of driving and x represent the number of miles driven.

So the kind of relationship we want to establish is a linear one that looks like ;

y = mx + c

Now let’s calculate the slope m with the two data points

The two points are; (88,428) and (158,673)

So the slope would be; (673-428)/(158-88) = 245/70 = 3.5

So what is left is the y intercept. To find this , we can make use of any of the two data points

Let’s say (88,428) in this case , so we have

528 = 88(3.5) + c

c = 528-88(3.5) = 528 - 308 = 220

So this means that our equation takes the form;

y = 3.5x + 220

where y represents the cost of traveling and x represents the number of miles driven

Now to the second part of the question, we want to know the cost of driving 388 miles

Just substitute the value 388 into the equation

y = 3.5(388) + 220

y = 1358+ 220 = $1,578

Answer:

10

Step-by-step explanation:

68.362/7.12

Multiply the top and bottom by 1000

68362/7120

Rounding to the nearest 1000

70000/7000

10

Answer:

Step-by-step explanation:

We know that the bull's eye target has a diameter of 20 centimeters, which equals 200 milimeters.

So, we find the area

[tex]A_{target}= \pi (100mm) ^{2} =(3.14)(10000) mm^{2} =31,400 mm^{2}[/tex]

Therefore, the right answer is B.

Answer:

D. 31,400mm^2

Step-by-step explanation:

Area of a triangle is 1/2 x base x height.

The graphed triangle has height of 2 and base of 2.

Area = /2 x 2 x 2 = 2 square units.

The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4

Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.

The answer is C) 8

Answer:

x+5

Step-by-step explanation:

We are adding fish

There were x and then we added 5

There are now

x+5

Answer:

x+5

Step-by-step explanation:

since there are x fish, adding five more would make it x+5        

Answer:

210 students

Step-by-step explanation:

The total number of students surveyed was

19+14+30+23+14 = 100

The fraction that picked Yosemite is 14/100

Multiply that fraction by the total number of students

1500* 14/100 = 210

Answer:

210 students

Step-by-step explanation:

vote me brainliest plz

Answer:

(1, −2)  (0, 1) (−1, 1)

Step-by-step explanation:

−2x+y≥−4

Substitute the points into the inequality and see if it is true

(0, −5)

-2(0) + -5 ≥−4

0-5 ≥−4

-5≥−4

False  not a solution

(1, −2)

-2(1) -2 ≥−4

-2-2 ≥−4

-4≥−4

True    it is a solution

(3, −1)

-2(3) -1 ≥−4

-6 -1 ≥−4

-7 ≥−4

False, not a solution

(0, 1)

-2(0) +1 ≥−4

0+1 ≥−4

1 ≥−4

True it is a solution

(−1, 1)

-2(-1) +1≥−4

2+1≥−4

3≥−4

True it is a solution

Answer:

(1.-2)

(0.1)

(-1,.-1)

Step-by-step explanation:

To solve this we have to plug in each point to see which one would work.

Inequality: -2x + y >= -4

First let's plugin (0,-5):

-2x + y >= -4

-2(0) + (-5) >= -4

0 - 5 >= -4

-5 >= -4 is wrong.

Now let's plugin (1,-2)

-2x + y >= -4

-2(1) + (-2) >= -4

-2 - 2 >= -4

-4 >= -4 is correct

Now let's plugin (3,-1):

-2x + y >= -4

-2(3) + (-1) >= -4

-6 - 1 >= -4

-7 >= -4 is wrong

Now let's plugin (0,1):

-2x + y >= -4

-2(0) + (1) >= -4

0 + 1 >= -4

1 >= -4 is correct

Now let's plugin (-1,1):

-2x + y >= -4

-2(-1) + (1) >= -4

2 + 1 >= -4

3 >= -4 is correct

Would appreciate if you gave me brainliest :)

Answer:

radius ≈ 10.77 cm

Step-by-step explanation:

The segment from the centre O to the chord is a perpendicular bisector.

Thus 2 right triangles are formed with legs 10 cm and 4 cm ( half of XY )

The radius r is the hypotenuse.

Using Pythagoras' identity, then

r² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )

r = [tex]\sqrt{116}[/tex] ≈ 10.77 cm ( to 2 dec. places )

Answer:

Step-by-step explanation:

perpendicular from center always bisects the chord of circle.

1/2 of chord=1/2×8=4 cm

[tex]r=\sqrt{4^2+10^2} =\sqrt{16+100} =\sqrt{116} \approx 10.77 ~cm[/tex]