Darius uses the shadow method to estimate the height of the flagpole. He finds that a 5-foot stick casts a 4-foot shadow. At the same time , he finds that the flagpole casts a 20-foot shadow . What is the height of the flagpole. Sketch a diagram.

Answer:

A

Step-by-step explanation:

-3×5+4×3+10×2

=-15+12+20

=17

Answer:

A: 3x5 + 4x3 +10x2

Step-by-step explanation:

The simplified expression is:

[tex]g(x)-f(x) = x^2-6x-1[/tex]

Solution:

Given that the expression is:

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

We have to simplify the expression

The expression can be simplified by combining the like terms

Like terms are terms that have the same variables and powers. The coefficients do not need to match

From given,

[tex]g(x) - f(x) = (x^2-x+3)-(5x+4)\\\\Remove\ the\ paranthesis\ and\ solve\\\\g(x) - f(x) = x^2-x+3-5x-4\\\\Combine\ the\ like\ terms\\\\g(x)-f(x) = x^2-x-5x+3-4\\\\Add\ the\ like\ terms\\\\g(x)-f(x) = x^2 -6x + 3 - 4\\\\Add\ the\ constants\\\\g(x)-f(x) = x^2 -6x -1[/tex]

Thus the expression is simplified

Final answer:

The sum of 8/15 and 2/5 is 14/15, which is closer to 1 than to 0 or 1/2 after finding a common denominator and adding the fractions.

Explanation:

To determine whether 8/15 + 2/5 is closer to 0, 1/2, or 1, you need to first find a common denominator for the fractions. The least common denominator for 15 and 5 is 15. You can then rewrite the second fraction, 2/5, with 15 as the denominator by multiplying both the numerator and denominator by 3, which gives you 6/15.

Now add the two fractions:

8/15 + 6/15 = 14/15

This sum is very close to 1, but still less than 1. Therefore, 14/15 is closest to 1.

To conceptualize this, you can think about the fractions in terms of division: 8 divided by 15 is a bit more than half, and 2 divided by 5 is exactly 0.4, which is also slightly less than half. Their sum is thus nearly a whole but not quite there, clearly indicating it's closer to 1 than to 0 or 1/2.

Conviction of DUI results in increased fines and jail time if aggravating factors such as high alcohol levels or prior offenses are present.

If you are convicted of DUI (driving under the influence), your fine and jail time will typically be increased if certain aggravating factors are present. These can include having a high blood alcohol content, previous DUI convictions, causing an accident while DUI, especially if injury or death occurred, having minors in the vehicle, and others. The penalties are enhanced due to the increased risk and harm these factors represent.

Answer:

2(x+4)=6+x

Step-by-step explanation:

Let x be our variable.

We want to write about equation using x that gives us -2 as solution.

We can write many of such equation.

An example is:

[tex]2( x + 4) = 6 + x[/tex]We cross check.

Let us expand:

[tex]2x + 8 = 6 + x[/tex]

Group similar terms:

[tex]2x - x = 6 - 8[/tex]

Combine similar terms:

[tex]x = - 2[/tex]

Answer:

  f(3) = g(3)

Step-by-step explanation:

The graph shows f(3) = 6, and it shows g(3) = 6. Then ...

  f(3) = g(3)

To determine if two functions f and g are equal at certain points, one must refer to their definitions or graphs. If f(x) and g(x) are defined as x², they are the same function as they produce identical outputs for any numerical input.

The student's question pertains to function comparison and the evaluation of these functions at specific points. The statement "f(6) = g(3)" implies that the value of the function f when x is 6 is equal to the value of function g when x is 3.

The answer to the question will rely on the specific definitions or graphical representations of the functions f and g, provided in the original question or accompanying materials.

For the functions defined by f(x) = x² and g(s) = s², f and g are indeed the same function since they both return the square of their input, regardless of the variable used to represent that input.

Since both function names are simply placeholders for the operation being performed (squaring), f and g yield the same output for any identical numeric input.

Based on the examples in the reference information, we can see that two different functions could have the same graph if they result in the same set of points on a Cartesian plane. This would make them the same function in the context of their graphical representation.

Answer:17

Step-by-step explanation:trust me use mathaway;)  mathaway dot com

Answer:

x=-41/3, y=6 (-41/3, 6).

Step-by-step explanation:

3x+4y=-17

y=-6*-1

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

3x+4y=-17

y=6

3x+4(6)=-17

3x+24=-17

3x=-17-24

3x=-41

x=-41/3

Answer:

[tex](-\infty,+\infty)[/tex]

Step-by-step explanation:

The given inequality is 3x-2>4 or [tex]5x-3\leq 7[/tex]

We group similar terms to obtain: 3x>4+2 or [tex]5x\le7+3[/tex]

Simplify to get:

3x>6 or [tex]5x\le10[/tex]

x>2 or [tex]x\le 2[/tex]

This implies that the solution set is all real numbers.

The solution in interval notation is [tex](-\infty,+\infty)[/tex]

Answer:

Don't forget to include a ± sign in your equation once you have taken the square root. Next, if the coefficient of the squared term is 1 and the coefficient of the linear (middle) term is even, completing the square is a good method to use. Finally, the quadratic formula will work on any quadratic equation.

Step-by-step explanation:

x² + 4x = 15 can be solved best using the completing the square method.

2x(x−3)=0 can be best solved using the zero product property.

Answer:

Actual mean: 223 pages

Predicted mean / estimate: 225 pages

Explanation below

Step-by-step explanation:

Mean = total amount ÷ # of numbers

155 + 214 + 312 + 198  + 200 + 170 + 250 + 260 + 215 + 256

Add

2,230

# of numbers = 10

2,230 ÷ 10 = 223

The exact mean is 223

If I were to predict the mean, I would say that a good estimation would be around 225, because I see that the highest number in the data set is 312, and the lowest is 155. If 312 is rounded down to 300, and 155 is rounded down to 150, the number exactly in the middle of 300 and 150 is 225.

Actual mean: 223 pages

Predicted mean: 225 pages

Hope this helps :)

Answer:

B

Step-by-step explanation:

Could be wrong

The length of KM is,

⇒ KM = 80 units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Line a is the perpendicular bisector of KM.

Now, We can formulate;

Two sides are isosceles triangle are equal.

Hence we get;

9x - 5 = 7x + 7

9x - 7x = 12

2x = 12

x = 6

Thus, The length of KL is,

KL = 6x + 4

KL = 6 x 6 + 4

KL = 40

So, The length of KM is,

⇒ KM = 2 KL

⇒ KM = 2 × 40

⇒ KM = 80 units

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Answer:L F and K G

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is not A because:

lines gk and kg are the same line

The answer is not B because:

lines il and gk are perpendicular if they were to touch

The answer is not C because:

line fl and il are perpendicular

The answer IS D because:

lines fl and gk are parallel because they will never touch

Answer: 4.5

Step-by-step explanation: because, 3x4=12 then you have 1.5 left and 1.5 is half of three so you would have .5 and you then add 4+.5 to get 4.5

Answer:

the answer is 4.5 h

Step-by-step explanation:

Answer:

The distance between the cruise ship and the sail boat is 517 feet.

Step-by-step explanation:

The cruise ship is 236 feet tall, and the sailboat is 236 tall; this means the distance between the top of the cruise ship and the top of the sail boat is

236 feet - 27 feet = 209 feet.

We also know that the angel of depression from the top of the cruise ship to the bottom of the cruise ship is 22°. This forms a right triangle as shown in the figure attached.

Now from trigonometry we get:

[tex]tan \: \theta = \dfrac{209}{d}[/tex]

[tex]d= \dfrac{209}{tan\:\theta }[/tex]

[tex]\boxed{d=517ft}[/tex]

The distance between the cruise ship and the sailboat is 517 feet.

Final answer:

To calculate the horizontal distance between the cruise ship and the sailboat, we subtract the sailboat's height from the cruise ship's height to get 209 feet, use the angle of depression and tangent function, and find that the distance between them is approximately 517.57 feet.

Explanation:

To find the distance between the cruise ship and the sailboat, we need to apply trigonometry. First, we determine the difference in height between the two, which is the cruise ship's height above the water subtracted by the sailboat's height. This will be 236 feet - 27 feet = 209 feet. Since the angle of depression from the cruise ship to the sailboat is 22 degrees, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

The opposite side, in this case, is the difference in height (209 feet), and the adjacent side is the horizontal distance between the ships, which we're trying to find. Thus:

tangent(22 degrees) = opposite/adjacent

adjacent = opposite/tangent(22 degrees)

= 209 feet / tangent(22 degrees)

Now we calculate the tangent of 22 degrees and then divide 209 feet by this amount to find the distance between the two vessels.

Using a calculator, tangent(22 degrees) ≈ 0.4040, so:

adjacent ≈ 209 feet / 0.4040 ≈ 517.57 feet

Therefore, the horizontal distance between the cruise ship and the sailboat is approximately 517.57 feet.

Answer:

49/10

Step-by-step explanation:

when you plug in 490% into your calculator, it shlukd be 49/10.

Answer:

Step-by-step explanation:

49/10 divide the numerator and denominator by gif.490/100=2x5x7 with the power of two=2x5x7with the power of two /2x5 both with th power of two divided 2x5=7 with the power of two/2x5=49/10

Answer:

13.1mi

Step-by-step explanation:

Length(l) = 4.1mi

Breadth(b) = 2.5 mi

Perimeter of a rectangle = addition of all sides that is = l + l + b + b as a rectangle has 2 opposite equal length and also breadth.

Therefore perimeter = 4.1 + 4.1 + 2.5 + 2.5

= 8.1 + 5

=13.1 mi

I hope this was helpful, Please mark as brainliest

Answer:

13.2 mi

Step-by-step explanation:

Perimeter of a rectangle

= 2 (L + W)

From the question

L = 4.1

W = 2.5

Using the above formula , we have P = 2 (4.1 + 2.5)

Using the distributive property

2x4.1 + 2x2.5

8.2 + 5

13.2mi

Answer:

look at shown picture.

Answer:

The answer is 4

Step-by-step explanation:

Why?...Because this is a site where everything is fake and incorrect.

Final answer:

To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.

Explanation:

To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.

Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.

Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:

Thus, one of the roots of the equation is 1/2, which corresponds to option C.

The value of x in the equation  2.14x - 12.18 = 5.76 is  8.38.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for x or find the value of x in the equation

2.14x - 12.18 = 5.76.

2,14x = 5.76 + 12.18.

2.14x = 17.94.

x = (17.94/2.14).

x = 8.38.

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Answer:

i) Therefore option A is Correct.   Δ ECD   [tex]\sim[/tex] Δ ACB by the SAS ( Side Angle Side) Similarity Theorem.

ii) Yes it can be proven that ED || AB after proving that Δ ECD   [tex]\sim[/tex] Δ ACB

Step-by-step explanation:

i) CE = [tex]\frac{1}{2}[/tex] AC ..... given

ii)  CD =  [tex]\frac{1}{2}[/tex] CB .... given

iii)  Therefore [tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{1}{2}[/tex]

iv)  Angle ACB or ∠C is common to Δ ACB and Δ CED.

v) Therefore from the above 4 equations we can say that by

   SAS theorem the two triangles are similar , that is ,  Δ ECD   [tex]\sim[/tex] Δ ACB .

 Therefore option A is Correct.

 vi)  Yes it can be proven that ED || AB after proving that Δ ECD   [tex]\sim[/tex] Δ ACB.

Since Δ ECD   [tex]\sim[/tex] Δ ACB , therefore ∠CED = ∠CAB  and ∠CDE = ∠CBA.

Therefore we can say that ED is parallel to AB or that ED || AB.

Answer:

x = 10/3

Step-by-step explanation:

(x - 1)/5*35 = (4x + 3)/35*35

7(x - 1) = 4x + 3

7x - 7 - 4x + 7 = 4x + 3 - 4x + 7

3x/3 = 10/3

x = 10/3

Answer:

110.1

Step-by-step explanation:

So, we just need to figure out 734% of 15.

734% can be written as 734/100.

734*15=11010.

11010/100 = 110.1

In the photo, the beetle is 110.1 millimeters

Answer:

x>7

Step-by-step explanation:

2x+6>20

2x>20-6

2x>14

x>14/2

x>7

Answer:

60 hours

Step-by-step explanation:

you multiply 5×12 and then you get 60

Answer:

1. 8n + 4

2. 5x +13

3. X + 3

4. X - 6

5. 4x + 1

Step-by-step explanation:

1.

2n + 6 and 6n -2 so simply addition will be

2n +6 +6n -2

8n +4

2.

3x + 9 + 2x + 4

5x + 13

3.

3x + 5 - 2x -2

X +3

4.

4x + 3 - 3x -9

X -6

5.

6x + 2 - 2x -1

4x + 1

Answer:

55 square feet

Step-by-step explanation:

We can represent the area as a sum of two rectangles.

A = 8 * 5 + 5 * 3 = 40 + 15 = 55 square feet

Answer:

Step-by-step explanation:

Area of rectangle at top

length =5ft; breadth = 3 ft

Area = 5*3 = 15 sq.ft

Area of rectangle at bottom

length = 8ft ; breadth =8-3 = 5 feet

Area = 8*5 = 40 sq.ft

Area of the figure = 15 + 40 = 55 sq.ft

Answer:

k(x)=x^3+9x+5x^2+45

Step-by-step explanation:

k(x)=x^3+5x^2+9x+45

k(x)=x^2(x+5)+9(x+5)

K(x)=(x+5)(x^2+9)

k(x)=x^3+9x+5x^2+45

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