4. What is the area of the triangle shown on the graph below?
(1) 10
(2) 11
(3) 14
(4) 25

Answer:

Step-by-step explanation:

To find the arc length of the polar curve r = 8cosθ between 0 and π/4, we can use the formula for arc length:

L = ∫a^b √(r^2 + (dr/dθ)^2) dθ

Substituting in the values for r and dθ, we get:

L = ∫0^(π/4) √(8^2cos^2θ + (-8sinθ)^2) dθ

= ∫0^(π/4) √(64cos^2θ + 64sin^2θ) dθ

= ∫0^(π/4) √(64) dθ

= ∫0^(π/4) 8 dθ

= 8(π/4 - 0)

= 8π/4

= 2π

Therefore, the arc length of the polar curve r = 8cosθ between 0 and π/4 is 2π.

Answer:

i don't know but its not B or D and my guess is A

Step-by-step explanation:

The equation is x^2-8 x-15=0.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Given, sum of the roots of a quadratic equation is 8 and their product is 15 We know that the quadratic equation is given as [tex]$\mathrm{x}^2-$[/tex](Sum of the roots) [tex]$\mathrm{x}+$[/tex] (product of the roots)[tex]$=0$[/tex] [tex]$\Rightarrow x^2-8 x-15=0$[/tex]

Hence, the equation is x^2-8 x-15=0.

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Answer:

  x² +8x -15 = 0

Step-by-step explanation:

You want a quadratic such that the sum of the roots is -8 and their product is -15.

When the roots of a quadratic are p and q, its factored form is ...

  (x -p)(x -q) = 0

The expanded form of this is ...

  x² -(p+q)x +pq = 0

That is, the coefficient of x is the opposite of the sum of the roots, and the constant is the product of the roots.

Here, we want the sum of roots to be -8, so the x-coefficient will be the opposite of that: 8. The constant will be the product of the roots: -15. That makes the desired quadratic be ...

  x² +8x -15 = 0

__

Additional comment

The attachment shows the quadratic, its roots, and their sum and product.

Answer:

i think A is a function because when you search what it looks like it looks kind of like A so i am sure it is A

Step-by-step explanation:

After solving, the maximum height of the ball is 90.25 feet.

In the given question,

A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.

The quadratic function

h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.

We have to find the maximum height of the ball.

Height is given that;

h(t) = -16t^2+52t + 48

Now comparing the given equation by the standard equation ax^2+bx+c=0

Here b = 52, a = -16

For maximum height put t= -b/2a

t = -52/2(-16)

t = 52/32

t = 1.625

Maximum height

h(1.625) = -16(1.625)^2+52(1.625) + 48

h(1.625) = -42.25+ 84.5 + 48

h(1.625) = 90.25 feet

The maximum height of the ball is 90.25 feet.

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Yes, a triangle can be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters this is in the case whereby the lengths of any two sides combined is longer than the length of the 3rd side.

Triangle inequality, in Euclidean geometry, theorem  can be described as the theorem that states that the  sum of any two sides of a triangle is greater than or equal to the third side.

This can be represented using the  symbols, {a + b ≥ c.}  and this can be explained that the the shortest distance between two points is a straight line.

Then cherck this illustration to confirm that we are right:

7.3 + 4.6 > 11

7.3 + 11 > 4.6

4.6 + 11 > 7.3

Hence from this we can see that triangle can be drawn

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1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that A survey of 2000 subscribers to a certain news paper revealed that 1800  people subscribe to the daily morning edition  

And 1000 subscribe to both the daily and the sunday editions.  

Let x denote the number who subscribe to the Sunday edition.  

Then the addition rule with overlap tells us that is;

1800 + x – 1000 = 2000

800 + x = 2000  

x = 1200  

so, 1500 subscribe to the Sunday edition and 1200 – 1000 = 200 subscribe to the Sunday edition only.

Hence, 1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

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The equation of the function represented by the graph is (d) g(x) = √(x + 9) - 1

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

The parent function of the graph is a square root function

This is represented as

f(x) = √x

First, we have the transformation to be:

The function is translated left by 9 units

Next, we have:

The function is translated down by 1 unit

Mathematically, this can be represented as

g(x) = f(x - 9) - 1

When represented as an equation, it is

g(x) = √(x + 9) - 1

Hence, the transformation is (d) g(x) = √(x + 9) - 1

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The probability that the blood pressure of woman is more than 130 by given normal distribution is 0.9505

What is z-value?

The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean.

We are given a normal distribution with a mean value 115 and standard deviation 9

And we are asked to find the probability that a woman selected at random has blood pressure greater than 130

We first find the z-value

z= (x-μ)/σ

z= (130-115)/9

z= 15/9

z= 1.6666

Now the corresponding value is

Probability is 0.95

Hence the probability is 95%

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Step-by-step explanation:

Riders must be at least 48 inches. "At least" means greater than or equal to. Therefore, the inequality is:

h ≥ 48

To graph this, we draw a solid dot at the 48 mark (because it can equal 48) and an arrow to the right (because it can be greater than 48).

The sum of 3/4 and 4/5 is 31/20 and To divide the common denominators by the individual denominators without using fractions or decimals, we need common denominators or the LCM of the two denominators.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, are two fractions 3/4 and 4.5 and their sum is,

= 3/4 + 4/5.

= (15 + 16)/20.

= 31/20.

So, the answer of the student is wrong.

We need common denominators or LCM of the two denominators so that we can divide the common denominators by the individual denominators without having fractions or decimals.

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When the card is a jack, there is a 0.25 probability that you will receive a spade.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application. Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

P(Spade) = 13/52 = 1/4 P(Jack) = 4/52

= 1/13 P(Spade and Jack)

= (1/4)(1/13) = 1/52 P(Spade/Jack)

= P(Spade and Jack)/P(Jack)

= (1/52)/(1/13) = (1/52)(13/1)

= 13/52 = 1/4 = 0.25

Hence, When the card is a jack, there is a 0.25 probability that you will receive a spade.

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Complete question-

A single card is drawn from a standard 52- card deck. Find the conditional probability that the card is a spade, given that it is a jack.?

Answer:

If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X

The required value of y for the given inverse relation is 30.78

What is the inverse variation?

Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.

In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.

Given, y varies inversely as [tex]x^{2}[/tex]

That is, y∝ 1/ [tex]x^{2}[/tex]

or, y = k/ [tex]x^{2}[/tex]

or,  [tex]x^{2}[/tex]y = k

And, y=38 when x=18

Then,  [tex]18^{2}[/tex]*38 = k

k = 12312

Now, if x=20 then y=?

[tex]x^{2}[/tex]y = 12312

or,  [tex]20^{2}[/tex]*y = 12312

or, 400y = 12312

or, y = 12312/400 = 30.78

Hence, the required value of y is 30.78

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The required graph is as follows.

The graph of an equation in x and y is the value of y for the

corresponding value of x.

Given,

y = -x - 2

or x + y = -2

The line cuts x axis when y = 0 and cuts y axis when x = 0.

Therefore, the line cuts x axis at x = -2

                  the line cuts y axis at y = -2

Hence, required graph is:

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Answer:

Data set 1: 20

Data set 2: 25

Step-by-step explanation:

Range is where you take the lowest value and subtract it from the highest value. So with data set 1, the highest number is 40 and the lowest is 20.cSo 40-20=20. Answer 20. Then with data set number 2, the highest number is 60 and the lowest is 35. So 60-35=25. Answer 25.

I hope this helps!!!

Answer:

hola

Step-by-step explanation:

Answer: You say Hola

Step-by-step explanation:

Which sounds like (Ohw·laa)  = This means Hi or Hello

Answer:

This is because the function is an exception - it is a special type of function called a Separatrix Separation Function.

Step-by-step explanation:

The Separatrix Separation Function theorem helps us prove through complex conjugates the reason why there is no hole at x =2.

Answer:  1.8  divided by 0.6 is 3

The equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number 1.8 is divided by the number 0.6. The mathematical model for the division can be written as:-

E = 1.8 / 0.6

Hence, the equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.

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The volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event is [tex]1000m^{3}[/tex].

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Basically, the volume of a liquid is measured in liters, where 1 liter is equal to 1000 cubic centimeters.

1 liter = 1000 cubic centimeters = 0.001 cubic meters

Hence,

1 cubic meters = 1000 liters

Given,

[200m x 100m = [tex]20000m^{2}[/tex]]

[5cm x 1m/ 100cm = 0.05m]

20,000m2 x 0.05m = [tex]1000m^{3}[/tex]

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Answer:

44

Step-by-step explanation:

BxH/2=Area

8x11=88

88/2=44

area=44

Answer:

Step-by-step explanation:

The number of apples x will be 10 and the number of bananas y will be 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether.

The number of apples and bananas will be calculated as,

0.75x +0.30y = 6

x + y = 14 or x = 14 - y

0.75(14-y) = 0.30y = 6

10.5-0.75y + 0.30y = 6

y = 10

x = 14  - y

x = 14 - 10 = 4

Therefore, the number of apples x will be 10 and the number of bananas y will be 4.

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Answer: 14.0328

Step-by-step explanation:

Answer: 14.032

Step-by-step explanation: you just have to move the decimal point

The antenna's height is determined to be 10 m using right triangle relations.

Following are the relationships in a right triangle:

The sine of an angle is equal to the length of the hypotenuse divided by the length of the side opposite the angle.

The cosine of an angle is equal to the neighboring side's length divided by the hypotenuse's length.

The tangent of an angle is calculated by dividing the length of the angle's adjacent side by its opposite side.

So, n this case, the side opposite to the 17o angle is the vertical height from her eyes to the top of the antenna, and the next side is the horizontal distance of 29 m, then:

tan 17° = h/29

h = 29 tan 17°

h = 8.87

Including eye height:

h = 8.87 + 1.51 = 10.38 m.

The antenna is 10 meters tall, rounded to the nearest meter.

Therefore, the antenna's height is determined to be 10 m using right triangle relations.

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Answer:

Alex will have a total of $990 in 5 years.

Step-by-step explanation:

Using the formula [tex]i=prt[/tex] we get [tex]i=900[/tex] × [tex]0.2[/tex] × [tex]5[/tex] which equals 90

[tex]900 + 90 = 990[/tex]

The total weight of the carton after packing the apples is 29.825 kg.

Empty carton: 8.350 kg

Apples: 21.475 kg

Since we are placing the apples inside the empty carton, now the carton will also contain the weight of the apples, additional to its own weight.

8.350 kg + 21.475 kg= 29.825 kg.

The total weight of the carton after packing the apples is 29.825 kg.

Answer:

Step-by-step explanation: h(t)=-16t2+85

Let h(t)=0 to find when the object will hit the ground

0=-16t2+85

Solve for t=?

We need to get t term on its own

Take 85 from both sides

0-85=-16t2+85-85

-85=-16t2

To get t term on its own

Divide both sides by -16

-85/-16=-16t2/-16

5.3=t2

We have to solve for t squared that means we must take the square root of both sides

the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds