1 Point) (a) Find The Discriminant Of The Equation 5x9x+6=0Discriminant =(b) Use The Discriminant To (2024)

The concept of the unit circle is presented throughout it's answer.

What is the unit circle?

The unit circle is a circle with a radius of 1 unit that is centered at the origin (0,0) of a coordinate plane. It is a fundamental concept in trigonometry and geometry, and it is used to define the trigonometric functions (sine, cosine, and tangent) of angles in the Cartesian plane.

The format of each coordinate on the unit circle is given as follows:

[tex](\cos{\theta}, \sin{\theta})[/tex].

Hence we can calculate the trigonometric measures for any angle, as the tangent, the secant, the cossecant and the cotangent of an angle are all functions of the sine and the cosine obtained by the unit circle.

Missing Information

The problem is incomplete, hence the unit circle concept is presented in this answer.

More can be learned about the unit circle at https://brainly.com/question/26284611

#SPJ1

The estimated area of the sidewalk that is getting wet is 706.5 square feet

The area of the sidewalk that is getting wet can be estimated by using the formula for the area of a circle: A = πr2, where "r" is the radius of the circle, which in this case is 15 feet. (A = π(152) = 706.5).

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

For such more questions on radius of circle:

https://brainly.com/question/24375372

#SPJ11

a) The average daily balance for the billing period is $285.29.

b) The finance charge to be paid on February 13 is $3.42.

c) The balance due on February 13 is $288.71.

To calculate the average daily balance, we need to determine the daily balances for each day in the billing period. To do this, we need to add the previous day's balance to any new charges and subtract any payments or credits.

Day Transaction Daily Balance

Jan 13Starting balance$221.33

Jan 17Charge of $50$271.33

Jan 22Payment of $100$171.33

Feb 4Charge of $100$271.33

Feb 6Charge of $100$371.33

Feb 10Payment of $100$271.33

Feb 13Finance charge$288.71

To calculate the average daily balance, we add up the daily balances and divide by the number of days in the billing period:

(221.33 * 4) + (271.33 * 5) + (371.33 * 3) + (288.71 * 1) / 13 = $285.29

To calculate the finance charge, we multiply the average daily balance by the interest rate and the number of days in the billing period:

285.29 * 0.012 * 31 = $3.42

To calculate the balance due on February 13, we add the finance charge to the average daily balance:

285.29 + 3.42 = $288.71

Learn more about Financial Transactions:

https://brainly.com/question/30023427

#SPJ4

Answer:

Step-by-step explanation:

To find this answer you need to find the vertex of the parabola. Do this by using the formulas for h and k as follows:

[tex]h=\frac{-b}{a}[/tex] and [tex]k=c-\frac{b^2}{4a}[/tex], where a, b, and c come from the quadratic equation.

Filling in for h:

[tex]h=\frac{10}{2(.2)}=25[/tex]

Filling in for k:

[tex]k=650-\frac{100}{4(.2)} =525[/tex]

Thus, the coordinates for the vertex are (25, 525). The h value interprets the number of bowls that should be produced to minimize the cost of production (25) and the minimum production cost is the k value (525).

The access to a full is [tex]23[/tex] m in height.

What kind of height is that?

Height is a measurement of vertical distance, or how high or some someone is (how tall they were) "The altitude of an aircraft in flight is around 10,000 m," for instance.

How can I determine my height?

Ensure that your shoulders are level, arms are at your sides, and legs are straight. The youngster or adolescent should maintain a straight gaze that is parallel to the ground. Measure the kid or adolescent when they are standing with their head, shoulders, buttocks, & heels on a flat surface.

The calculation of the total screen height is displayed below;

[tex]= a + b[/tex]

where

[tex]a = 21 * tan 17[/tex] degrees

[tex]= 21 * 0.305[/tex]

[tex]= 6.4 m[/tex]

And

[tex]b = 21 * tan 38[/tex] degree

[tex]= 21 * 0.781[/tex]

[tex]= 16.4 m[/tex]

So, the height of the entire screen is

[tex]= 6.4 m + 16.4 m[/tex]

[tex]= 22.8 m[/tex]

[tex]= 23 m[/tex]

To know more about height visit:

https://brainly.com/question/20714736

#SPJ1

The rate of change of each given function are:

f(x) = 5x² + 3x - 7; f'(x) = 10x + 3g(x) = [tex]\frac{-5x + 7}{2x - 3}[/tex]; [tex]g'(x)=\( \frac{-10x+11}{(2x-3)^2} \)[/tex]

To find the rate of change of given functions, we have to differentiate the given function w.r.t the variable provided. We will solve each part of the question and differentiate the functions step by step.

(a) f(x) = 5x² + 3x - 7

The function is, f(x) = 5x² + 3x - 7

Differentiating the above function, we get;

f'(x) = (5x² + 3x - 7)/dx

f'(x) = 10x + 3

Therefore, the rate of change of function f(x) = 5x² + 3x - 7 is 10x + 3.

Now, let us solve the second part of the question.

(b)[tex]\( g(x)=\frac{-5 x+7}{2 x-3} \)[/tex]

The function is,[tex]\( g(x)=\frac{-5 x+7}{2 x-3} \)[/tex]

Differentiating the above function using the quotient rule, we get;

[tex]\[\begin{aligned} g'(x)&=\frac{(2x-3)\cdot (-5)-(7)\cdot(2)}{(2x-3)^2}\\ &=\frac{-10x+11}{(2x-3)^2}\end{aligned}\][/tex]

Therefore, the rate of change of function [tex][tex]\( g(x)=\frac{-5 x+7}{2 x-3} \) is \( \frac{-10x+11}{(2x-3)^2} \).[/tex][/tex]

Learn more about Rate of Change here: brainly.com/question/29518179

#SPJ11

The values would be

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

What is an expression?

In mathematics, an expression is a combination of symbols and/or numbers that represents a value or a relationship between values. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions. Expressions can be used to describe relationships between variables, to represent mathematical formulas or equations, and to perform calculations.

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

Hence, the values would be

[tex]15. = \frac{1}{1000y^3}\\\\16. =-\dfrac{1024}{n^5}\\\\17. =\dfrac{1}{32k^{10}}\\\\18. =$\dfrac{49}{36c^2}$\\\\\\19. = $64^t$\\\\20. = $5 \cdot 5^t$\\\\21. = $81 \cdot 3^{4t}$\\\\22. = $\dfrac{2^{2t}}{2}$ or $2^{2t-1}$[/tex]

To know more about expression visit :

https://brainly.com/question/1859113

#SPJ1

1 hot dog costs amount $8.00 and 1 hamburger costs $10.80.

Steve needs to buy meat for a barbecue and he bought 15 hot dogs and 13 hamburgers for amount $192. He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. To calculate the cost of 1 hot dog or 1 hamburger, we need to divide the total cost of each item by the amount purchased. For the hot dogs, we divide $780 by 75, which gives us $8.00. For the hamburgers, we divide $780 by 45, which gives us $10.80. Therefore, the cost of 1 hot dog or 1 hamburger is $8.00 and $10.80 respectively.

Hot Dogs : ($192 + $780) / (15 + 75) = $8.00

Hamburgers : ($192 + $780) / (13 + 45) = $10.80

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

Points found on y = h(x) are (7, -6) and (-2,-1).

Using these two points, we will solve for the exact equation of y = h(x).

To solve the equation, we will get the slope (m) of the two points first using the following formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-1-(-6)}{-2-7} =\dfrac{5}{-9} =-\dfrac{5}{9}[/tex]

Now that we have a slope, we can now proceed in solving the equation using Point-Slope Formula.

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-6)=-\dfrac{5}{9}(x-7)[/tex]

[tex]y+6=-\dfrac{5}{9}(x-7)[/tex]

[tex]9y+54=-5x+35[/tex]

[tex]9y=-5x+35-54[/tex]

[tex]9y=-5x-19[/tex]

[tex]y=-\dfrac{5}{9}x-\dfrac{19}{9}[/tex]

Now that we have the equation of the dashed line, we will now solve for its inverse function y = h^-1 (x).

To solve for the inverse, we will reverse y and x with each other. The new equation will be:

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

From that equation, we will now equate or isolate y.

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

[tex]x=-\dfrac{5y-19}{9}[/tex]

[tex]9x=-5y-19[/tex]

[tex]5y=-9x-19[/tex]

[tex]y=-\dfrac{9}{5}x -\dfrac{19}{5}[/tex]

In this equation, our slope (m) here is -9/5 and our y-intercept is at (0, -19/5). The graph for this equation will look like this.

Drag the endpoints of the solid segment to the coordinates shown above to graph y = h^-1 (x).

Or drag the endpoints to (-6,7) and (-1,-2). It's the same graph anyway.

The area under the curve of the given function from x=1 to x=5 is -64.17.

The area under a curve is the area between the curve and the x-axis in a certain range. To calculate the area under a curve, we will use the definite integral of the function. The definite integral of a function f(x) from x=a to x=b is defined as

[tex]∫baf(x)dx[/tex]

For the given function f(x) = x^3 - 5x^2 + 2x + 8, the definite integral from x=1 to x=5 is

[tex]∫51(x^3 - 5x^2 + 2x + 8)dx = [x^4/4 - 5x^3/3 + x^2 - 8x]5[/tex]

Substituting x=1 and x=5 gives

[54 - 5(125)/3 + 25 - 8(5)] = -64.17

Learn more about definite integral here:

https://brainly.com/question/29974649

#SPJ4

The solution of the absolute inequality is as follows:

x < 22 / 5 or x > 6 / 5

How to solve absolute inequalities?

The absolute inequalities can be solved as follows:

An absolute value inequality is an inequality that has an absolute value sign with a variable inside, modulus of a complex number.

Therefore,

|14 - 5x| > 8

let's find x as follows:

|14 - 5x| > 8

14 - 5x > 8 or 14 - 5x < - 8

-5x > 8 - 14 or - 5x < - 8 - 14

-5x > -6 or - 5x < - 22

Therefore,

x > 6 / 5 or x < 22 / 5

learn more on inequality here: https://brainly.com/question/27906262

#SPJ1

The lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

To calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment, we need to take into account the uncertainty in the initial mass and the change in mass.

The initial mass of the chemicals is given as 73 g, rounded to 2 significant figures. This means that the actual value of the initial mass could lie anywhere between 72.5 g and 73.4 g, since the last significant digit (the 3) is uncertain.

Similarly, the change in mass during the experiment is given as 8.2 g, rounded to 2 significant figures. This means that the actual value of the change in mass could lie anywhere between 8.15 g and 8.25 g.

To find the lower bound of the mass at the end of the experiment, we assume that the initial mass was at its upper bound (73.4 g) and the change in mass was at its lower bound (8.15 g):

Lower bound = 73.4 g - 8.15 g = 65.25 g

To find the upper bound of the mass at the end of the experiment, we assume that the initial mass was at its lower bound (72.5 g) and the change in mass was at its upper bound (8.25 g):

Upper bound = 72.5 g - 8.25 g = 64.25 g

Therefore, the lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

To learn more about rounded Click here:
brainly.com/question/29878750

#SPJ4

Domain: [-6,-2], Range: [-4,3) and Function: Yes, this graph can be expressed as a function as it passes the vertical line test.

What is Function?

A function is a set of instructions used to perform a specific task. It is a fundamental building block of computer programming, and it is used to create programs that can perform specific tasks. A function is a named block of code that performs a specific task. It can take one or more arguments as input and return a value as output. Functions can be used to divide a large program into smaller, more manageable pieces. Functions are also useful for code reuse, since the same code can be used multiple times within a program. In addition, functions can help improve program efficiency since code does not need to be written multiple times.

To learn more about Function
https://brainly.com/question/25638609
#SPJ1

The domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).

What is function?

Function is an operation that takes one or more input values and produces one or more output values. It is a mathematical concept that is used in programming to create programs that can be used to solve problems. Functions can be used to organize code blocks into reusable pieces, making it easier to debug and maintain the code. A good example of a function is the mathematical function f(x) = x2, which takes an input value x and produces an output value of x2.

The domain of the inverse of a function is the range of the original function, and the range of the inverse is the domain of the original function. Therefore, since the domain of the original function is [-1, 0) and the range of the original function is [-3, ∞), the domain of the inverse function is [-3, ∞).

To learn more about function
https://brainly.com/question/11624077
#SPJ1

Complete Question is attached below:

The volume of the solid is the amount of space value is k = 32.

What is volume in maths?.

Volume in mathematics refers to the quantity of space within a certain 3D object. A fish tank, for example, has measurements of 3 feet long by 1 foot wide and 2 feet high. If you increase the length, breadth, and height by 3x1x2, which is equal to six, you can calculate the volume.

The volume of the solid is represents in cubic units. Thus

k = ∛v/4

k³ = v/4

v = 4k³ ( k≥0)

when k = 1, v = 4

k = z, v = 4.z³ = 32

∴ points (1,1) , (7,32) are on the graph.

Learn more about volume

brainly.com/question/1578538

#SPJ1

Step-by-step explanation:

To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.

y = 5x – 2 is already in slope-intercept form, so its slope is 5.

These two slopes are not equal, so the lines are not parallel.

B) x + y = 0 can be rearranged to y = −x, so its slope is −1.

y = x + 7 is already in slope-intercept form, so its slope is 1.

These two slopes are not equal, so the lines are not parallel.

C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.

4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.

These two slopes are not equal, so the lines are not parallel.

D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.

y = 2x + 2 is already in slope-intercept form, so its slope is 2.

These two slopes are not equal, so the lines are not parallel.

E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.

y = 3x − 10 is already in slope-intercept form, so its slope is 3.

These two slopes are equal, so the lines are parallel.

Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.

Number of people with AB+ blood type = 3.4 / 100 x 300 .Number of people with AB+ blood type = 10.Therefore, of the 300 people who donated blood, approximately 10 people would have been AB+.

Assuming the distribution of blood types in Springfield are the same as the distribution in the US, then the percent of AB+ blood type donors would be 3.4%. Therefore, of the 300 people who donated blood, approximately 10 people would have been AB+. This calculation is based on the following formula: Percent of AB+ blood type donors = Number of people with AB+ blood type / Total number of people who donated Number of people with AB+ blood type = Percent of AB+ blood type donors / 100 x Total number of people who donated Number of people with AB+ blood type = 3.4 / 100 x 300 .Number of people with AB+ blood type = 10.

Learn more about Number here:

https://brainly.com/question/28210925

#SPJ4

The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.

What is simple interest?

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

What kinds of simple interests are there?

When the time is measured in days, simple interest can be divided into two groups. They have common and straightforward interests. The comparable number of days in a year for ordinary simple interest is 360 days. In contrast, precise simple interest (SI) is a SI that requires exactly 365 days in a regular year or 366 days in a leap year.

The simple interest is given by the formula:

SI = PRT/ 100

where, P is the principal = $4999 - $999 = $4000.

R is the rate.

T is the time = 3.

Given that the total accumulated amount is $7000.

That is:

4000 + SI(3) = 7000....(1)

SI = (4000)(R)(3)/100

SI = 120R.......(2)

Substitute the value of SI in equation 1:

4000 + 120(3)R = 7000

36R = 3000

R = 83.33

R = 0.83%

The monthly repayments are:

SI = (4000)(0.83)(3)/100

SI = 99.6

Hence, the monthly payments are 99.6.

The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.

Learn more about simple interests here:

brainly.com/question/25845758

#SPJ4

According to the formula, the area of rhombus JKI M is approximately 315.3 square centimeters.

What is area of rhombus formula?

The formula for the area of a rhombus is half the product of its diagonals. That is,

Area of rhombus = (diagonal 1 x diagonal 2)/2

where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the rhombus.

Let D be the intersection of diagonals JK and IM.

Since JK and IM are perpendicular bisectors of each other, D is the midpoint of both diagonals. Let AD = x and BD = y. Then, we have:

[tex]$$\begin{aligned} x + y &= \frac{1}{2} JM = \frac{1}{2}(KL + KM) = \frac{1}{2}(2 \cdot 12.7 + 25.1) = 25.25 \ y - x &= \frac{1}{2} KL = \frac{1}{2} \cdot 12.7 = 6.35 \end{aligned}$$[/tex]

Solving for x and y, we get:

x = [tex]\frac{25.25 - 6.35}{2}[/tex]= 9.95cm

y = [tex]\frac{25.25 + 6.35}{2}[/tex] = 15.8cm

Therefore, the diagonals of rhombus JKI M have lengths 2x = 19.9 cm and 2y = 31.6 cm, respectively. The area of the rhombus is half the product of the diagonals, so we have:

[tex]$$\begin{aligned} A &= \frac{1}{2} \cdot 19.9 \cdot 31.6 \ &= 315.32 , \text{cm}^2 \end{aligned}$$[/tex]

Rounding to the nearest tenth, we get:

[tex]$$A \approx 315.3 , \text{cm}^2$$[/tex]

Therefore, the area of rhombus JKI M is approximately 315.3 square centimeters.

To learn more about the area of rhombus visit:

brainly.com/question/16205763

#SPJ1

The equation is y = ax² + bx + c, standard form of the parabola is y = ax² + bx + c.

The equation for a parabola in standard form is given by:

y = ax² + bx + c

where a, b, and c are constants and x and y are variables.

To convert from vertex form to standard form, you can follow these steps:

Expand the squared term in the vertex form to get the x² term in standard form. For example, if the vertex form is:

y = a(x - h)² + k

then expand (x - h)² to get x² - 2hx + h², giving:

y = a(x² - 2hx + h²) + k

Distribute the 'a' term to get the coefficient of x². This gives:

y = ax² - 2ahx + ah² + k

Combine the constant terms to get the constant coefficient. This gives:

y = ax² - 2ahx + (ah² + k)

Therefore, the standard form of the parabola is y = ax² + bx + c, where:

a = the coefficient of x², which is a

b = the coefficient of x, which is -2ah

c = the constant term, which is (ah² + k)

To learn more about equation click here

brainly.com/question/4074088

#SPJ4

we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

We know that JKLM is a parallelogram, which means that its opposite sides are parallels, such that: JK // ML and JM // KL.

So, we know that the angle MLJ equals 25°, and JK // ML, from this we can say that angles LJK and MLJ are equal, because they are ''internal alternate angles'', since that they are inside the parallels.

So, angle LJK is 25, and JKL is a triangle, which has the angle at K vertex equal to 130°. We know that internal angles in a triangle must sum 180°.

Since that, two angles, in the triangle JKL, measure 130° + 25° = 155°; we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

learn more about parllelogram,

https://brainly.com/question/29249343

#SPJ4

By trignometric property, The 630 .18 feet tall is the gateway arch .

What is the definition of trigonometry?

Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc).

As given

The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.

Now by using the trignometric property

tanθ = perpendicular/base

As diagram is given below .

θ = 39

tan39° = AB/CB

CB = 778 feet

tan39° = 0.81 (approx)

0.81 = AB/778

AB = 0.81 × 778

AB = 630 .18 feet

Therefore, the 630 .18 feet tall is the gateway arch .

Learn more about trignometric property

brainly.com/question/29024806

#SPJ1

We can see that the sequence 1, 3, 9, 27 is not arithmetic.

Is the given sequence arithmetic?

An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference d.

Generally, the recursive relation for these sequences is:

a(n) = a(n - 1) + d

Here we have the sequence:

1, 3, 9, 27, ...

Taking the differences between consecutive terms of the sequence we get:

3 - 1 = 2

9 - 3 = 6

27 - 9 = 18

The differences are different, so there is no common difference, meaning that this sequence is not arithmetic.

Learn more about sequences at:

brainly.com/question/6561461

#SPJ1

• The number 4: Because there are four cards with the number four in a regular deck of 52 cards (4 suits each containing a four), the chance of getting a four is 4/52, which may be reduced to 1/13 or about 0.077.

• The number 7 or a Jack: A regular deck of cards has four sevens and four jacks, for a total of eight cards that are either a seven or a jack. Picking a 7 or a Jack has a chance of 8/52, which may be reduced to 2/13 or roughly 0.154. • A red card or a Queen: A normal deck has 26 red cards (13 diamonds and 13 hearts) and 4 queens. to avoid counting them twice, we must remove the two red queens. As a result, the total number of red or queen cards is 26 + 4 - 2 = 28. Picking a red card or a queen has a chance of 28/52, which may be reduced to 7/13, or roughly 0.538. • A Spade or an Ace: A regular deck of cards has 13 spades and 4 aces, but we must deduct the ace of spades to avoid counting it twice. Therefore there are 13 + 4 - 1 = 16 cards that are either a spade or an ace. As a result, the chance of selecting a spade or an ace is 16/52, which may be reduced to 4/13 or roughly.

learn more about cards here:

https://brainly.com/question/7570270

#SPJ4

We can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

Given the triangles EFG and BCD, you can identify that:

By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.

In this case, you can identify that you know two pairs of corresponding sides. Then, you can find that they are in proportion. Set up that:

[tex]\frac{EF}{BC}=\frac{FG}{CD}[/tex]

Substituting values and simplifying, you get:

[tex]\frac{18}{90}=\frac{16}{80}\\\\\frac{1}{5}=\frac{1}{5}[/tex]

Notice that they are in proportion.

You can also identify that the corresponding angles F and I are congruent because they have equal measures.

Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

learn more about Side-Angel-Side Theorem (SAS).

https://brainly.com/question/22995265

#SPJ4

Answer:

A

Step-by-step explanation:

we know that

tan x=sin x/cos x

if

then

x belongs to the II quadrant or IV quadrant

sin 30°=

cos 30°=

therefore

tan 30°=

the angle theta has a 30-degree reference angle and is located in Quadrant II or IV

Answer:

A

Step-by-step explanation:

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. This statement is not correct.

When a pyramid and a prism have the same base and height, the volume of the pyramid is one-third ([tex]\frac{1}{3}[/tex]) the volume of the prism.

This can be seen from the formula for the volume of a rectangular prism, which is:

[tex]The volume of the prism = base area x height[/tex]

And the formula for the volume of a rectangular pyramid is:

The volume of the pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Since the base area and height of the pyramid and prism are the same, we can compare their volumes by dividing the volume of the pyramid by the volume of the prism:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex] x base area x height/base area x height

Simplifying this expression, we get:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex]

Therefore, the volume of a pyramid with the same base and height as a prism is one-third [tex](\frac{1}{3})[/tex] the volume of the prism.

The complete question is:-

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. True/False.

To learn more about the volume of the pyramid, refer:-

https://brainly.com/question/17615619

#SPJ4

Step-by-step explanation:

The proportion of similar triangles are

[tex] \frac{3}{4} = \frac{9}{r} [/tex]

Solving for r

[tex] \frac{4}{3} = \frac{r}{9} [/tex]

[tex] \frac{9 \times 4}{3} = r[/tex]

[tex]12 = r[/tex]

The total distance traveled by the particle from 0 ≤ t ≤ 6 is: 216 units

How to find the total distance travelled?

The position of the particle is given by the equation:

x(t) = 3t³ - 27t² + 72t + 14.

Now, To find the times when the particle changes direction, you just need to find the critical numbers of the function x(t). These would be the possible times when the particle changes direction.

x(t) = 3t³ - 27t² + 72t + 14.

x'(t) = 9t² - 54t + 72

Using quadratic equation calculator, we have:

t = 2 or 4

Then you can find the position of the particle at these times. We will also need to find its position at our end points: t = 0, 7. Basically all we are doing here is finding the global max/min values of the function up to this point.

x(0) = 3(0)³ - 27(0)² + 72(0) + 14 = 14

x(2) = 3(2)³ - 27(2)² + 72(2) + 14 = 74

x(4) = 3(4)³ - 27(4)² + 72(4) + 14 = 62

x(6) = 3(6)³ - 27(6)² + 72(6) + 14 = -202

Thus:

Total distance = (74 - 14) + (62 - 74) + (-202 - 62)

= -216

This is 216 in the negative direction

Read more about Total Distance Travelled at: https://brainly.com/question/29409777

#SPJ1

Answer:

b

d

. ._-_-_-__---_--_--_----___-_--------_--------------------------__-_______--_-__-________---_-_--___-----__--