on a football field, the 20-foot-tall goal post casts a 60-foot shadow. at the same time, another post casts a shadow that is 24 feet long when standing perpendicular to the ground. what is the height, in feet, of the second post?

On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.

[tex]2-inch, 3 inch, 4-inch[/tex]

triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2

[tex]2-inch, 3 inch, 5-inch[/tex]

This is doesn't make  a triangle as  [tex]2+5 > 3, and 3+5 > 2,[/tex]

2+3 is not more  than 5,, they cannot make triangle.

[tex]2-inch, 4 inch, 5-inch[/tex]

triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2

[tex]3-inch, 4 inch, 5-inch[/tex]

a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3

Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

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For the given polar equation the cartesian form of the equation is x² - y² = 1

The term polar equation in math is defined as  another way to represent a complex number.

The general form the complex number is written as

=> z = a + bi

It is also known as the rectangular coordinate form of a complex number. And the horizontal axis is the real axis and the vertical axis is the imaginary axis.

Here we have given an equation r²2cos(2θ) = 1.

It can be rewritten as,

=> r²cos2θ − r²sin2θ = 1

Then here we substitute x as rcosθ and y as rsinθ, we get the cartesian equation as,

=> x² − y² = 1.

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here is your Answer.

hope it is helpful,

Please mark me brainiest

Answer:

x =1

Step-by-step explanation:

4 + 3x = x + 6

minus 4 from both side

6-4 = 2

3x = x + 2

then minus x from both side

3x-x=2

(pretend there's a 1 beside the x)

2x = 2

then divide 2 from both side and 2/2 =1

s0 x=1

that doesn't make sense but ye

There is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.

The probability of all 5 employees selected at random from the company having college degrees is calculated by using the following formula: P = (0.8)^5.  Substituting 0.8 for the probability of having a college degree, this equation simplifies to P = 0.32768.

Therefore, P = (0.8)^5 = 0.32768.

This implies that there is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.

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The only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.

The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b], then there exists some c in the interval such that

f'(c) = (f(b) - f(a)) / (b - a).

In the case of f(x) = x(x-3) , on the closed interval [0,3], we can solve for c using the equation above.

We begin by calculating f'(c), which is equal to 2c - 3. Then, we set the equation equal to (f(3) - f(0)) / (3 - 0), which is equal to -3 / 3.

Substituting this into our equation for f'(c), we get 2c - 3 = -1, which simplifies to c = 2.

Therefore, the only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.

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1 and 7/12

Divide the 2 fractions (multiply by reciprocal.)

1/4 + 1/2 × 8/3

1/4 + 8/6

Find common denominators.

6/24 + 32/24

38/24

Turn that into a mixed number.

1 14/24

Simplify.

1 7/12

Nature of roots of the quadratic equation 4x^2 - 12x - 9 = 0 are real and unequal by Discriminant method.

Given quadratic equation is 4x^2 - 12x - 9 = 0

Comparing the given equation with the standard form i.e ax^2 - bx - c = 0.

 Here we have, a = 4

                           b = -12  and

                           c = -9

Now discriminant, D = b^2 - 4ac

                                  = (-12)^2 - 4(4)(-9)

                                  = 144 - (-144)

                               D = 288    

Now check for discriminant D, D=288 and 288 >0

                                 Therefore, (D>0)

Hence the roots of given equation are real and unequal.

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Answer:

Step-by-step explanation:

The system of inequalities can be written as follows:

x ≥ 14

x + y ≥ 15

0.5x + 0.1y ≤ 1

We can graph the system by plotting the three lines representing the three inequalities.

The first inequality, x ≥ 14, is a vertical line with x-intercept at (14, 0).

The second inequality, x + y ≥ 15, is a line with a slope of 1, passing through the point (0, 15) and with y-intercept at (0, 15).

The third inequality, 0.5x + 0.1y ≤ 1, is a line with a slope of -5, passing through the point (2, 0.2) and with y-intercept at (0, 0.2).

The solution to the system of inequalities is the region below the line representing the first inequality, above the line representing the second inequality, and to the right of the line representing the third inequality.

One possible solution is x = 16 and y = 1. This means that Taylor has 16 nickels and 1 dime, which is exactly 15 coins worth a maximum of $1 combined.

Answer: the person is right above just made sure that .5 is .05 since it’s cents. A nickel is worth .05 cents not .5 cents.

Step-by-step explanation:

A visual representation of data where numbers on the left side of a chart show one part of each value and numbers on the right side of the chart show the other is called a bar chart. A bar chart is a chart that uses rectangular bars to represent different values or categories. Each bar has a length that represents a value or a category. The left side of the chart is called the y-axis, or the vertical axis, and the right side of the chart is called the x-axis, or the horizontal axis. The x-axis typically shows the categories, and the y-axis shows the values of those categories. The height of each bar represents the value of the data point, with the height on the y-axis and the categories on the x-axis. This type of graph is useful for comparing the relative sizes of different groups or categories, as well as spotting trends and patterns.

On solving the provide question, we can say that by plotting data they can own 8 to 10 video games.

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

Here,

We can therefore deduce from the provided number that the cluster owns between 8 to 10 video games.

How do we know the range is 8 to 10 then? In the example figure, the dots are referred to as the cluster.

Based on this, we may deduce that our range is between 8 and 10, the amount of games that are owned as a minimum and maximum, respectively.

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The complete question is " A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.

What is the range of video games owned for the cluster?"

No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .

What is a Triangle ?

A triangle can be defined as the closed figure , that is made up of three line segments .

The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .

The sides of triangle are given to be : 2cm , 3cm and 5cm ;

on adding the two sides ,

we get ;

⇒ 2 + 3 = 5 > 5 ; False

⇒ 3 + 5 = 8 > 2 ; True

⇒ 2 + 5 = 7 > 3 ; True

All the conditions are not met ,

Therefore , the given sides cannot form a triangle .

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The following algebraic expression are trinomial.

The term expression in math is also known as algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we must know what is meant by trinomial,

The term trinomial is referred as

Here we have given algebraic expression that is written as  x³ + x² - √x is a trinomial with one variable ‘x’ and it having three non-zero terms.

Then the next given algebraic expression which is 2x³ - x², is NOT a trinomial. Because this expression is a binomial with one variable ‘x’, having two non-zero terms.

Then the another given algebraic expression that is 4x³ + x² - 1/x, is a trinomial with one variable ‘x’, having three non-zero terms.

Finally the given algebraic expression which can be written as x⁶ - x +√6, is a trinomial with one variable ‘x’, having three non-zero terms.

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Answer:

(x – 3)2 = 49 can be written as (x – 3) = ± √49.

To solve for x, we can square root both sides:

x -3 = ±7

Now we can add 3 to both sides:

x = 3 ±7

So the values of x are:

x = 3 + 7 = 10

x = 3 - 7 = -4

Hence the values of x are -4 and 10.

Step-by-step explanation:

Answer: Did you mean (x - 3)² = 49? If so, the answers are -4 and 10

Step-by-step explanation: This equation is a simple quadratic. We can square root both sides to get:

x - 3 = -7

OR

x - 3 = 7

(Remember 49 has a positive square root and a negative square root)

Now simple rearranging will yield our two answers: 10 and -4.

Answer:

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

Given system of inequalities:

Plot the inequality and the given points to determine which of them fall into solution area.

See attached.

As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).

(Answer:

(6, 5)

Step-by-step explanation:

For this question, there are not two correct choices.

Given systems:

y ≤ 2/3x + 1

y > -1/4x + 2

For the first equation, the y-intercept is 1, and the rate of change is 2/3 (rise over run). The inequality symbol is less than or equal to (≤), meaning this will be a solid line and the area shaded will be below the line.

For the second equation, the y-intercept is 2, and the rate of change is -1/4 (this means it is decreasing in number, therefore the line is going down). The inequality symbol is greater than (>), meaning this will be a dashed line and the area shaded will be above the line.

the area overlapped is where the solution will be. The answer is (6, 5) because it lies on the solid line of the first inequality, indicating it does satisfy the first inequality. Any point on the solid line satisfies the inequality. The point also lies above the second inequality, meaning it is a solution to the system.

Also, if you plug it into the system of inequalities, all the outcomes will make sense.

Answer:

A, 6:00 P.M. EST

Step-by-step explanation:

The time difference between EST and PST is -3 hours

11 am - 9am = 2 hours

2 - (-3) = 2+3 = 5 hours

The flight time is 5 hours

Then:

The time difference between PST and EST is +3 hours

5 + 3 = 8

If the fly leaves Los Angeles at 10:00 AM PST

10 + 8 = 18

The plane will arrive at 6:00PM EST

The solution for the compound inequality is -2>x≥-4. Therefore, option C is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is 3<-2x-1≤7.

Here, 3<-2x-1

Add 1 on both the sides of an inequality, we get

4<-2x

Divide -2 on both the sides of an inequality, we get

-2>x

Here, -2x-1≤7

Add 1 on both the sides of an inequality, we get

-2x≤8

Divide -2 on both the sides of an inequality, we get

x≥-4

The solution is -2>x≥-4

Therefore, option C is the correct answer.

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Three ratios that are equivalent to 18:21 are 6 : 7, 36 : 42 and 72 : 84

An equivalent ratio is a ratio that represents the same relationship between numbers as another ratio, but with different values.

You can create equivalent ratios by multiplying or dividing both parts of the ratio by the same non-zero number. For example, if a ratio is 4:8, an equivalent ratio would be 2:4.

Thus, 3 ratios that are equivalent to 18:21 can be:

18 : 21 = 6 : 7 (divide both sides by 3)

18 : 21 = 36 : 42 (multiply  both sides by 2)

18 : 21 = 72 : 84 (multiply  both sides by 4)

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The area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².

The area of the semicircle is the space occupied by it. It can be given as,

[tex]A_{s} = \frac{d^{2} }{8} \pi[/tex]

Here, (d) is the diameter of the semicircle.

Each side of the square measures 4 centimeters. The area of the square is square of its side. Thus,

Area of the square, [tex]A_{s}[/tex] = 4² = 16cm²

3 semicircles are connected to 3 sides of a square. Thus, the diameter of the semicircle is equal to 4 cm. The area of 3 semicircles is,

[tex]A_{sc} = 3 *\frac{4^{2} }{8} \pi\\A_{sc} = 6\pi[/tex]

The area of the composite figure is,

[tex]A = A_{s} + A_{sc} \\A = (6\pi + 16) cm^{2}[/tex]

Thus, the area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².

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Answer:

We know that the distance between Paris and Nice is about 920,000 meters. To convert this distance to kilometers we divide by 1000: 920,000/1000= 920 kilometers

We also know that the train travels at a speed of 230 kilometers per hour. To find out how long it will take Lola to travel from Paris to Nice, we divide the distance by the speed:

920/230 = 4 hours

So it will take Lola 4 hours to travel from Paris to Nice by train.

Answer: 4 hours actually kinda ez not gonna lie

Step-by-step explanation: 230 kilometers = 230000 meters. 230 * 1000 = 230000. Distance / speed = time. 920000/230000 = T(as in time). T = 4

The equation for the given quadratic polynomial is f(x) = x^2-33x+242.

When the highest degree term in a second-degree polynomial equals 2, the polynomial is said to be quadratic. A quadratic equation has the generic form ax^2 + bx + c = 0. Here, x is the unknown variable, a and b are coefficients, and c is the constant term.

A polynomial with an exponent degree of 2 or higher is said to be quadratic. A quadratic polynomial has the general form f (x) = ax^2 + bx + c, where a 0 and b a n d c are real numbers. A parabola is the name of the quadratic polynomial's curve.

f(x) = (x-11)(x-22)

f(x) = x^2-33x+242

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Answer: The answer is 3

Step-by-step explanation:

(-7)-(-10)

=(-7)+10

=10-7

=3

Answer: 3

Step-by-step explanation: First, to make this easy, let's rewrite the equation:

-7 + 10

I did this because whenever you change subtraction to an addition problem, with decimals, you need to change the sign of the number on the right side (always) So, (-7) - (-10) is the same as (-7) + 10.

So, to make this even easier, we can model this as 10 - 7, which is 3. As we know, it's the same as (-7) + 10 because we are adding 10 more to (-7) which is 3. Also, if you can, using a numberline really helps to! I hope this helped!

The missing coefficient of the linear equation 4 · x + 10 = __ · x + 8 such that it has no solutions is equal to 4.

In this problem we find a linear equation of the form a · x + b = c · x + d, where a, b, c, d are real coefficients. This kind of equation has no solution for the case when a = c. The complete procedure is shown below.

First, write the incomplete expression:

4 · x + 10 = __ · x + 8

Second, add the missing coefficient according to the definition for linear equations with no solutions:

4 · x + 10 = 4 · x + 8

Third, use algebra properties to simplify the expression:

10 = 8 (CRASH!)

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Answer:[tex]x = 18[/tex]

* also think you meant x instead of c*

Step-by-step explanation:

[tex]\frac{x}{6} - 7 = -4[/tex] --> +7 on both sides

[tex]\frac{x}{6} - 7 + 7 = -4 + 7[/tex]

[tex]\frac{x}{6} = 3[/tex] --> multiple by 6 by both sides

[tex]6 * \frac{x}{6} = 3 * 6[/tex] --> the 6 and the [tex]\frac{x}{6}[/tex] cancel out

[tex]x = 18[/tex]

The area of the triangle ΔKLM, obtained using Routh's theorem is 4/13

Routh Theorem outlines the ratio relationship between the triangle formed by three cevians of a triangle and the area of the original triangle.

Mathematically it states that the ratios (x, y, and z) of the segments formed the intersection of the cevians and the three sides of the triangle produces the area of the triangle when expressed in the form;

A = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1)).

The specified dimensions are;

BD : DC = CE : EA = A_F: FB  = 1 : 3

The point of intersection of AD, BE and CF = K, L, and M

Area of triangle ΔABC = 1

The area of triangle ΔKLM is found as follows;

Where the length of AB = 4 units, we get;

Length of A_F = 1 unit and the length of FB = 3 units

We get;

BD/DC = x, CE/EA = y, A_F/FB = z

x = y = z = 1/3

Routh's theorem states that the area of the triangle formed by AD, BE, and CF is obtained using the formula;

Area of ΔKLM = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1))

Plugging in the values of x, y, z, we get;

x = y = z, therefore;

Area of ΔKLM, A = (x³ - 1)² ÷ ((x² + x + 1)·(x² + x + 1)·(x² + x + 1))

A = (x³ - 1)² ÷ ((x² + x + 1)³)

x = 1/3, therefore;

A = ((1/3)³ - 1)² ÷ (((1/3)² + (1/3) + 1)³) = 4/13

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Step-by-step explanation and Answer

Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:

Interest = Principal x Rate x Time

In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months

So, Interest = 2000 x 0.05 x 4.5/12 = 50

The same applies to the second loan of 1000, so the interest on this loan is:

Interest = 1000 x 0.05 x (4.5/12) = 25

To find the total amount returned, we add the interest on both loans to the total principal borrowed:

total = 2000 + 1000 + 50 + 25 = 3075

Therefore, the total amount returned is Ks 3075

Answer:

formula:

c^2 = a^2 + b^2 - 2abcos(C)

where c is the length of the diagonal, a and b are the lengths of the legs of the triangle (the non-parallel sides of the trapezoid), and C is the angle between them.

In this case, a = b = 7 feet and C = (180 - 140)/2 = 20 degrees. We can plug these values into the formula to find:

c^2 = 7^2 + 7^2 - 2(7)(7)cos(20)

c = sqrt(98 + 49cos(20))

To use the Law of Sines to find the length of the shorter base, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.

Since we know a and b, we can use the formula to find:

x/sin(140) = 7/sin(20)

x = 7sin(140) / sin(20)

Note that the value of c will be in squared units, so you need to take the square root to get the actual length of the diagonal.

Answer: 2.4 inches per guest

Step-by-step explanation:
2.4 inches per guest

2.4 x 5 = 12

The values of variables in the kite is - x = 35°, y = 12.5°. The angles measures of the kite are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.

What is a kite?

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry. Another name for kites is deltoids.

The given angles of the kite are -

∠a = (3x+5)°

∠b = y°

∠c = (2y-20)°

∠d = (4x-30)°

According to the properties of kite -

The two angles are equal where the unequal sides meet.

So, ∠a = ∠d

(3x+5)° = (4x-30)°

3x - 4x = -30 - 5

-x = -35

x = 35°

Substituting to find the value of ∠a -

∠a = (3x+5)°

∠a = [3(35)+5]°

∠a = (105+5)°

∠a = 110°

Substituting to find the value of ∠d -

∠d = (4x-30)°

∠d = [4(35)-30]°

∠d = (140-30)°

∠d = 110°

According to the properties of the kite ∠ADC = 90°.

So, ∠c = 90°/2 as line BD is a bisector.

(2y-20)° = 90°/2

2(2y-20)° = 90°

(4y - 40)° = 90°

4y = 90° - 40°

4y = 50°

y = 12.5°

Substituting to find the value of ∠b -

∠b = y°

∠b = 12.5°

Substituting to find the value of ∠c -

∠c = (2y-20)°

∠c = [2(12.5)-20]°

∠c = (25-20)°

∠c = 5°

Therefore, the value of angles are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.

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The length of the rectangle is 2.4 and breadth is 1.8

Now, According to the question:

The given information is :

The length of a rectangle multiplied by 3 is equal to 4 times its width.

The perimeter is 8[tex]\frac{2}{5}[/tex].

To find the length and the width.

We take,

Length=L

Width=W

3L=4W

Divide by 3 on both sides

L = [tex]\frac{4}{3}[/tex]W

We know that, The perimeter of rectangle:

Perimeter of rectangle is = 2(L + W)

2W + 2L=8.4

2W + 2([tex]\frac{4}{3}[/tex]W) = 8.4

2W + [tex]\frac{8}{3}[/tex]W=8.4

[tex]\frac{6}{3}[/tex]W +  [tex]\frac{8}{3}[/tex]W = 8.4

[tex]\frac{14}{3}[/tex]W =  8.4

14W = 25.2

Divide by 14 on both sides.

W = [tex]\frac{25.2}{14}[/tex]

W =1.8

L = 4/3W

L= [tex]\frac{4}{3}1.8[/tex]

L=2.4

L=2.4; W=1.8

Hence, The length of the rectangle is 2.4 and breadth is 1.8

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