From the top of a 450-foot cliff, a hiker looks down at a river below. Her angle of
depression to the near and far banks of the river are 80° and 50° respectively, as
shown in the picture. Based on this information, how wide is the river?

The value of AB in the triangle is 2.5 cm and the value of x in the triangle is 10 units

From the question, we have the following parameters that can be used in our computation:

The triangle

On the triangle, we have the following equivalent ratio

AB : 4 = 10 : 16

Express as fraction

So, we have

AB/4 = 10/16

This gives

AB = 4 * 10/16

Evaluate

AB = 2.5

Here, we understand that the line bisects the angle BAC

This means that

x = 20 - x

So, we have

2x = 20

Divide

x = 10

Hence, the value is 10

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Answer:

l is parallel to m and u is parallel to t

Step-by-step explanation:

Parallel line means that never meet each other

The area of a trapezoid with the given parallel sides and height is 4x+8 square units. Therefore, option B is the correct answer.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (b₁+b₂)×h.

where (A) is the area of a trapezoid, 'b₁' and 'b₂' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between b₁ and b₂).

1) Given that, b₁=x-3, b₂=x+7 and the height=4

Now, area of a trapezoid = 1/2 (x-3+x+7)×4

= 2×(2x+4)

= 4x+8 square units

Hence, option B is the correct answer.

2) The given polynomials are -3x²-7x+9 and -5x²+6x-4.

Here, sum = -3x²-7x+9+(-5x²+6x-4)

= -3x²-7x+9-5x²+6x-4

= -8x²-x+5

Hence, option 1 is the correct answer.

Therefore, the area of a trapezoid is 4x+8 square units.

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Answer: D, 9.4

Step-by-step explanation:

(pi*2*12) *45/360 = 9.4

Answer:

9.4 is correct

Step-by-step explanation:

C=2πr = 2x3.14x12=75.36

arc AB=(45/360)x75.36=9.42

The number of penguins at the zoo is 48.

Percentage is a measure of frequency that determines the value of a number as an amount out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply by 100.

Number of penguins = percentage of penguins x number of birds

50% x 96

(50/100) x 96 =

0.5 x 96 = 48

Here is the complete question:

There are 96 birds at the Parkdale Zoo. 50% of the birds are penguins. How many penguins are at Parkdale Zoo?​

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Answer: 7:5

Step-by-step explanation:

Answer:

A

I believe because p→q

q→p

The item reached its highest point at 78.4 meters by quadratic form of equation.

Suppose a quadratic form of equation has the following form

y=a[tex](x-h)^2[/tex] + k

Once in vertex form, it is said to be. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)

Using the data shown above, we can determine that

-4.9[tex]t^2[/tex] + 19.6 t + 58.8 = 0

The equation will naturally be converted to vertex form after the square is finished:

where h is the amount of time needed to reach a height of k.

Next, square the half of the linear term and add it to both sides.

-4.9([tex]t^2[/tex]-4t)=-58.8

-4.9([tex]t^2[/tex]-4t+4)=-58.8-19.6

-4.9([tex](t-2)^2[/tex])=-78.4

s(t)=-4.9([tex](t-2)^2[/tex])+78.4

As can be seen, the vertex is (2,78.4).

The maximum height is 78.4m.

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Question: An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t)=−4.9[tex]t^2[/tex]+19.6t+58.8. What is the maximum height of the object?

It will take 15 revolutions per minute.

What is the unit rate?

An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Here, we have

Given: a wheel for a wheel of winning game makes one revolution in 4 seconds.

Take a time for 1 revolution = 4 seconds

Assume that the unit rate in terms of revolutions per minute is x.

1 rev/4 second = x rev/60 second

4x = 60

x = 15

Hence, it will take 15 revolutions per minute.

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Answer:

(4,4)

By using a graphing we can see that the lines intersect at (4,4).

therefore, 4 is the solution

don't forget to say thanks

The value of x is 18.

The value of y is 15.6.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

From the figure,

Sin 30 = 9/x

1/2 = 9/x

x = 9 x 2

x = 18

Now,

Using the Pythagorean theorem.

x² = 9² + y²

18² = 81 + y²

y² = 325 - 81

y = √244

y = 15.6

Thus,

x = 18

y = 15.6

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It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.

To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t

First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600

Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400

Simplifying the right side of the equation gives us:
t = 40

So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.

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Answer:

Below

Step-by-step explanation:

     Since :   .35 x = 28       Given    ( where x = total sweets)

x = 80 sweets total

28 are red ( given )   then  02.  * 80 = green = 16

80 - 28 - 16 = 36 remaining

                                     and are divided between  pink : white in ratio of 2:1

                                   pink are 2 out of (2+1) = 2/3

                                             2/3 * 36 remaining = 24 pink

                                                    then 12 are white

Python formats all floating point numbers to two decimal places when outputting using the print statement. (FALSE)

The if statement causes one or more statements to execute only when a Boolean expression is true. ( TRUE)

Floating point  is a number format that can be used to represent a large or small value.

In writing this number is done by writing it in exponential form, so that the number has a base number, the exponential number and the base number.

The following is writing scientific notation in floating point. example in decimal numbers

261,000,000,000 written 2.61 x 10¹¹

0.000000000261 is written 2.61 x 10^-10

The Floating point representation itself has two parts, namely the mantissa part and the exponent part. The mantissa determines the digits, while the exponent determines the value of how many powers the mantissa is, as follows:

±S * B±E

S = Significant also called mantissa

E = Exponent

B  = Base

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She have 1 hour 17 minutes remaining for the second section.

what is total time ?

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.

Given:

Total time : two hours

Time taken to complete the first section =  forty-three minutes

Now , minutes she have remaining on the second section

= Total time - Time taken to complete the first section

= 2 hours - 43 minutes

= 1 hour 17 minutes

Hence , she have 1 hour 17 minutes remaining for the second section.

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360 guests were at the gala

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

Since the ratio of staff to guests at the gala was 3 to 5.

Let S and G represent the number of staff and guests respectively. From the given information, we can write:

S/G = 3/5

S + G = 576

Thus, S = 576 - G

Put S = 576 - G in S/G = 3/5 and solve for G. That is:

(576 - G)/G = 3/5

3G = 5(576 - G)

3G = 2880 - 5G

3G + 5G = 2880

8G = 2880

G = 2880/8

G = 360

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The intervals on which the function is increasing is (0, 1). Option D

A polynomial is a type of mathematical expression that has variables that are raised to whole number powers.

Since the factors of 5 are 1 and 5, we'll try to factor the polynomial by assuming that (x-1) and (x-5) are factors.

The product of (x-1) and (x-5) is (x² - 6x + 5), which is the polynomial we're given.

⇒ (x² - 6x + 5) is the factored form of the polynomial.

A polynomial is increasing on the intervals where it's greater than zero. So we just need to look at the sign of (x² - 6x + 5) for values between 1 and 5.

For values between 1 and 5, the function is always positive, so it's increasing on the interval (1, 5). Therefore, the increasing interval is (1, 5).

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Minda must view 76 movies to make Movie Prime the better deal

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, The number of movies be 'x' and from the given information the two equations can be formed as,

5.95x and 150 + 3.95x.

And  to make Movie Prime the better deal,

150 + 3.95x < 5.95x.

2x > 150.

x > 75.

So, Minda must watch greater than 75 movies.

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An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35. Thus, option 3 is correct.

It represents a relationship between variables and constants and is used to describe the behavior of a function or system. Equations can be linear or nonlinear and can have one or multiple variables. They can be used to solve real-world problems, such as finding the slope of a line, calculating distances, or determining the minimum or maximum value of a function. Equations are also used in advanced mathematical disciplines, such as calculus, algebra, and geometry.

When x = 0, y-intercept = 35.4 ≈ 35

And when x increases, the value of y decreases, so slope is negative

From the given options

There is only two negative slope equation but only one with y-intercept = 35. i.e.

y = -0.3x + 35

Thus, An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35.

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Answer:

Rounding to the nearest cent implies approximating a money amount to two decimals (which represent the number of cents), applying the following rules: If the third decimal digit is lower than 5, we leave the second decimal digit as it is. E.g., $4.563 ≈ $4.56.

The correct steps for bisecting line segment AB using a reflective device is given below:

Cutting a line exactly in half is known as bisecting it. Due to the fact that the line you are drawing will be at a right angle to the initial line, it is also sometimes referred to as creating a perpendicular bisector.

A compass, pencil, and ruler are required.

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Answer:

= 6 years old.

Step-by-step explanation:

Let your age 2 year ago be = x

= 2x

again

Let your age 2 years from now be x

= 2x

therefore

= 2x +2x = 24

= 4x = 24

= 4x/4 = 24/4

= x = 6

therefore you're 6 years old.

Algebraic expression to represent the given situation would be, P = 2N - 7

What is algebraic expression?

When we utilize numbers and words to solve a mathematical problem, we are using algebraic expressions.

Let P represent the number of pennies in Greg's pocket.

We know that the number of pennies is 7 less than twice the number of nickels, which can be written as:

P = 2N - 7

This expression represents the number of pennies in terms of the number of nickels.

Therefore, Algebraic expression to represent the given situation would be, P = 2N - 7

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Rafael will take 75 minutes to run 10 miles at the same rate.

Solution:

We know that Rafael can run 4 miles in 30 minutes.

So, we can find his pace, as follows:

30 minutes/ 4 miles = 7.5 minutes per mile.

So, for 10 miles he will take 7.5* 10 = 75 minutes.

Hence, it will take Rafael 75 minutes to run 10 miles.

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Answer:51. 2%

Step-by-step explanation:

24+32+(16×4)+7(2+16)=24+32+64+126=246

26g of Epsom salt contains 126g of water of crystallisation.Hence, 100g of Epsom salt contains 100×126/246The % of H2​O in MgSO4​.7H2​O=

Step 1: Equation for Roller Coaster Height.

The general form for the equation of a circle at the origin is:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Equation of a Circle (at origin):}}\\\\x^2+y^2=r^2\\\\\bullet \ \text{where 'r' is the radius of the circle}\end{array}\right}[/tex]

It is given that the height of the roller coaster is 30 feet. Thus, r = 30. Plug this into the equation above and solve for 'y.'

[tex]\Longrightarrow x^2+y^2=(30)^2\\\\\\\\\Longrightarrow x^2+y^2=900\\\\\\\\\therefore \boxed{\boxed{y=\sqrt{900-x^2} }}[/tex]

Step 2: Graph of Roller Coaster Model.

Refer to the attached image(s).

Step 3: Equation for Horizontal Distance of Beams.

Going back to the equation we got in step (1), we can solve for the variable ‘x.’

[tex]\Longrightarrow y=\sqrt{900-x^2}\\\\\\\\\therefore \boxed{\boxed{x=\pm\sqrt{900-y^2}}}[/tex]

Step 4: Algebraic Solution for Beam Placement.

Given a height, y = 25 ft. We can plug this into the equation above and solve for 'x.'

[tex]\Longrightarrow x=\pm\sqrt{900-(25)^2}\\\\\\\\\Longrightarrow x=\pm\sqrt{275}\\\\\\\\\Longrightarrow x=\pm5\sqrt{11}\\\\\\\\\therefore \boxed{\boxed{x\approx\pm16.58 \ ft}}[/tex]

Step 5: Placement of Beams.

The beams should be placed 16.58 feet from either side of the origin.

Step 6: Graph of Cable and Strut.

Refer to the attached image(s).

Step 7: Algebraic Intersection of Cable and Strut.

To find the point of intersection, set the two given equations (from model 2) equal to each other and solve for 'x.'

[tex]y=\sqrt{2x+8} \ \text{and} \ y=x-8\\ \\\\\\\Longrightarrow \sqrt{2x+8}=x-8 \\\\\\\\\Longrightarrow 2x+8=(x-8)^2 \\\\\\\\\Longrightarrow 2x+8=x^2-16x+64\\\\\\\\\Longrightarrow x^2-18x+56=0\\\\\\\\\Longrightarrow (x-14)(x-4)=0\\\\\\\\\therefore x=\{14,-4\}[/tex]

In order to determine which value of 'x' is correct we must verify the solution.

When x = 14:

[tex]\Longrightarrow 2(14)+8=(14-8)^2\\\\\\\\\Longrightarrow 36=36 \checkmark[/tex]

When x = -4:

[tex]\Longrightarrow 2(-4)+8=(-4-8)^2\\\\\\\\\Longrightarrow 0\neq 144[/tex]

Thus, the correct x-value is 14. Plug this into either given equations and solve for 'y.'

[tex]\Longrightarrow y =x-8\\\\\\\\\Longrightarrow y =14-8\\\\\\\\\therefore y=6[/tex]

Thus, the point of intersection is (14, 6).

Step 8: Graph of Two Struts.

Refer to the attached image(s).

Step 9: Algebraic Solution for Beam Placement.

To find the x-value of the beam placement, you need to find the point where the two strut equations are 2 feet apart. Set up an equation using the given functions and solve for 'x.'

[tex]\Longrightarrow y=\sqrt{x+8}-\sqrt{x-4}; \ y=2\\\\\\\\\Longrightarrow 2=\sqrt{x+8}-\sqrt{x-4}\\\\\\\\\Longrightarrow 2+\sqrt{x-4}=\sqrt{x+8}\\\\\\\\\Longrightarrow 4\sqrt{x-4}+x=x+8\\\\\\\\\Longrightarrow 4\sqrt{x-4}=8\\\\\\\\\Longrightarrow \sqrt{x-4}=2\\\\\\\\\Longrightarrow x-4=4\\\\\\\\\therefore \boxed{\boxed{x=8}}[/tex]

Step 10: Placement of Beam.

The beams will need to be placed 8 feet from either side of the origin.

The closet square inch that is needed to cover the cuboid is 208 inches ( option A)

A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges.

The surface area of cuboid is given as;

SA = 2(lb+lh+bh)

lb = 33/4 × 4 = 33 in

lh = 23/4 × 4 = 23 in

bh = 23/4 × 33/4 = 759/16

SA = 2( 23+33+759/16)

SA = 46+66+47.44

SA = 207 in

therefore the closet square inches is 208 in²

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Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.

To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.

In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:

(x+1)(x+4) = 0

This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:

x+1 = 0 or x+4 = 0

x = -1 or x = -4

These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.

It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.

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Answer:

x = 24°

Step-by-step explanation:

See the attached worksheet.   Let a and b stand for the two unknown angales as shown on the worksheet.  Since the sum of angles across a straight line is 180°, we can express the two angles as:

a = 180°-x, and

b = 180° - 111° or b = 69°

The sum of the interior angles of a quadrilateral is 360°.  Set the four angles equal to 360° and solve for x.

x = 24°