Find the measure of the missing angles.

If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units

The length of the hypotenuse = 13.5 units

The angle = 41 degrees

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

In this question hypotenuse and angles are given and we have to find the opposite side.

sin θ= opposite side /  Hypotenuse

Substitute the values in the equation

sin 41 = Opposite side / 13.5

Opposite side = sin 41×13.5

= 8.86 units

Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.

Learn more about trigonometric functions here

brainly.com/question/14746686

#SPJ1

The function to show how quickly the weeds grow each day is "f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily. Option B

f(x) = 4(1.15)x = 4(1+ 0.15)x ................... (1)

Given that there are seven days in a week, the daily growth rate of the weeds may be estimated using equation (1) by dividing 0.15 (which stands for the 15% weekly growth rate) in the following manner:

f(x) = 4(1.15)x = 4(1+ 0.15/7)x

f(x) = 4(1 + 0.02)x

f(x) = 4(1.02)x

Since 0.02 is the same as 2%, this implies that the rate at which the weeds grow each day is 2%.

Learn more about the function here:

https://brainly.com/question/12431044

#SPJ1

The solution for the inequality is x < 11/130.

The problem we dealing with is related to inequality which is referred to as An inequality in mathematics could be a relationship that produces a non-equal comparison between two integers or other numerical expressions.

Since we are provided with inequality which is 81 - 11/5x < 55

Now multiplying both by 5x we get

81 × 5x - (11/5x) × 5x < 55 × 5x

=> 405x - 11 < 275x

=> 405x - 275x < 11

=> 130x < 11

=> x < 11/130

so it is the solution for the inequality 81 - 11/5x < 55

to know more about inequality  refer to the link https://brainly.com/question/20383699?referrer=searchResults.

#SPJ1

Applying the slope formula, we have:

16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.

17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.

See explanation below for the rest answers.

Slope of a line = change in y / change in x.

The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.

In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".

16. Given, (3, 7) and (7, -2):

Slope (m) = (-2 - 7)/(7 - 3)

Slope = -9/4

Parallel slope = -9/4

Perpendicular slope = 4/9.

17. Given, y = -4x + 2,

Slope = -4

Parallel slope = -4

Perpendicular slope = 1/4.

18. Rewrite 5x - 2y = 8 in slope-intercept form:

-2y = -5x + 8

y = 5/2x - 4

Slope = 5/2

Parallel slope =  5/2

Perpendicular slope = -2/5.

19. Rewrite  4x + 3y = 2 in slope-intercept form:

3y = -4x + 2

y = -4/3x + 2/3

Slope (m) = -4/3

Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):

y - (-5)) = -4/3(x - 2)

y + 5 = -4/3(x - 2) [point-slope form]

20. Given, y = -5x + 2

Slope (m) = -5

Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):

y - (-6) = -5(x - (-4))

y + 6 = -5(x + 4) [point-slope form]

21. Rewrite 9x - 3y = 6 in slope-intercept form:

-3y = -9x + 6

y = 3x - 2

The slope of y = 3x - 2 (9x - 3y = 6) is 3.

The slope of -3x - 5 is -3.

Therefore, the lines are neither parallel nor perpendicular.

Learn more about slope on:

https://brainly.com/question/13861479

#SPJ1

The simplified form of like terms in -3(u+6) -4(u+5) is 7u = -38.

Similar variables and powers are defined as like terms. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

Given that,

Expression is -3(u+6) -4(u+5)

Simplifying the equation,

-3u-18-4u–20 = 0

-7u -38 = 0

-7u = 38

7u = -38

Therefore 7u = -38 is the simplifief form of like term in -3(u+6) -4(u+5).

To know more about simplification of an expression, visit:

https://brainly.com/question/2192729

#SPJ9

Let Bailey drive x miles.

So, Kacie drove 2x miles.

Kaiden drove 2x + 10 miles.

According to the question,

x + 2x + 2x + 10 = 50

x = 8

Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.

To Learn More, https://brainly.com/question/15172156

#SPJ4

The most appropriate choice for exponent will be given by-

Keiko is not correct because the exponent [tex](-1)^n[/tex] does not always give -1

What is exponent?

Exponent denotes how many times a number is multiplied by itself.

For example in [tex]2^4[/tex] = [tex]2 \times 2 \times 2 \times 2[/tex], here 2 is multiplied 4 times.

Suppose [tex]a^m = a \times a \times a \times a[/tex][tex].....[/tex] (m times), here a is the base and m is the power.

Here,

The given exponents are[tex](1)^n[/tex] and [tex](-1)^n[/tex]

[tex](1)^n = 1 \times 1 \times 1\times.....\times 1[/tex] (n times)

      = 1

For [tex](-1)^n[/tex]

If n is even,  [tex](-1)^n[/tex] = 1

If n is odd ,  [tex](-1)^n[/tex] = -1

But Keiko told that [tex](-1)^n[/tex] always results in -1

So, Keiko is not correct.

To learn more about exponents, refer to the link -

https://brainly.com/question/10339517

#SPJ9

[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]

I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF

[tex] {x}^{2} [/tex]

and the constant number then find the factors that will give me the coefficient of x.

ATTACHED IS THE SOLUTION

Step-by-step explanation:

are you sure this is the whole information ?

because

6² = 5x + 6

is not called a quadratic equation.

it is a quadratic equation, when there is one term in x² involved.

I assume therefore, that your problem is

6x² = 5x + 6

that is then as basic quadratic equation

6x² - 5x - 6 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -5

c = -6

x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =

= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =

= (5 ± 13)/12

x1 = (5 + 13)/12 = 18/12 = 3/2

x2 = (5 - 13)/12 = -8/12 = -2/3

so, the 2 solutions for the quadratic equation are

x = 3/2 and x = -2/3

Answer:

1/4^3

Step-by-step explanation:

I WILL USE THE LAWS OF EXPONENTS WHEN WE MULTIPLY POWERS OF THW SAME BASES WE KEEP ONE POWER AND ADD THE EXPONENTS.

[tex] = 7^{ - 5} \times 7^{2} \\ = {7}^{ - 5 + 2} \\ = {7}^{ - 3} \\ = \frac{1}{ {7}^{3} } \\ = \frac{1}{343} [/tex]

ATTACHED IS THE SOLUTION

US$ the tourist received finally is US$985.

BD$2000 is there.

BD$1 = US$0.50

Bank charged a commission of 1.5%.

Solution:

For one BD i.e., BD$1 he gets US$0.50.

It is half the value of BD$.

By cross multiplication technique, you can find this.

Then for,

BD$2000 he will get US$ 1000.

Bank charges =  1.5%.

That is,

1.5/100*1000 = $15

US$ the tourist received finally = 1000-15

= $985

US$ the tourist received finally is US$985.

To learn more about conversion sums, refer

https://brainly.com/question/23718955

#SPJ13

Answer:

perpendicular

Step-by-step explanation:

The equations represent a vertical and horizontal line, respectively, which are perpendicular to each other.

Step-by-step explanation:

the set of prime numbers that, when multiplied together, give

13824:

2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3

Answer:

24

Step-by-step explanation:

To solve this question, find the 4 first terms of the sequence.

The first term is a₁

a₁ is given and a₁ = 7

The second term is a₂

Given:

Then, let's find a₂ using the value of a₁

The third term is a₃

let's find a₃ using the value of a₂

The fourth term is a₄

let's find a₄ using the value of a₃

Answer:

The four first terms are:

a₁ = 7

a₃ = 12

a₃ = 17

a₄ = 22

Diameter = 13.93771776 cm

Answer:

x = 1 +sqrt(5)

x = 1 -sqrt(5)

Step-by-step explanation:

y= x^2 -2x -3

Let y = 1

1= x^2 -2x -3

Subtract 1 from each side

1-1= x^2 -2x -3-1

0 = x^2 -2x -4

Using the quadratic formula

x = - (-2) ±sqrt( (-2) ^2 -4(1)(-4))

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

                      2(1)

x = 2 ±sqrt( 4 +16)

     ------------------------

                      2

x = 2 ±sqrt( 20)

     ------------------------

                 2

x = 2 ±sqrt( 4*5)

     ------------------------

                 2

x = 2 ±sqrt(5)

     ------------------------

                 2

x = 1 ±sqrt(5)

The rate/speed at which one must travel to cover 227.5 miles in 3.5 hours is 65 miles per hours.

Speed or rate is simply referred to as distance traveled per unit time.

It is expressed as;

r = d / t

Where r is the speed/rate, d is the distance and t is time elapsed.

Given the data in the question;

To determine the rate at which one must travel to cover 227.5 miles in 3.5 hours, plug the given values into the equation above and solve for r.

r = d / t

r = 227.5 miles / 3.5 hours

r = 65m/h

r = 65mph

Therefore, the speed/rate one must travel is 65mph.

Option A)65mph is the correct answer.

Learn more about speed here: brainly.com/question/7359669

#SPJ1

Answer:

5

Step-by-step explanation:

he needs $85 and he has $25,

so it will be 85-25=60

that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.

By using the Unitary method, $468 was spent on newspapers in 52 weeks.

Unitary method is a method used for finding the unit cost in which we divide the total cost by the total number of articles and to find the cost of more than one article, we multiply the unit cost by the number of articles required.

Cost of newspapers in a week from monday to saturday = $(1 x 6) = $6

Cost of newspaper only on sunday of a week = $3

Cost of newspapers in a week = $(6 + 3) = $9

Therefore, the cost of newspapers in 52 weeks = $(52 x 9) = $468.

Learn more about unitary method, visit- https://brainly.com/question/28276953

#SPJ4

The domain and the range pf the curve was solved and the correct answer to the question is the last option which is

The domain are the input values and are represented in the x axis while the range are the output values and represented in the y axis

From the graph

We can conclude that the last option is the correct answer

Read more on domain and range here: https://brainly.com/question/2264373

#SPJ1

Answer: C

Step-by-step explanation:

Starting off we need to understand what the circles are in inequalities.

A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.

So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.

Because the angles on the first quadrant of the bottom horizontal line are equal, we conclude that the two parallel lines are FM and GB,

We know that two lines are parallel if when intersected by the same line, the two give the same angles.

In the image, we can see only one pair of equal angles, which are the two ones represented by a red quarter circle.

Both of these angles are on line MB, this means that the two parallel lines are the ones that intersect MB (in this case are the two vertical lines).

Then we can conclude that the two parallel lines are FM and GB.

Learn more about parallel lines:

https://brainly.com/question/24607467

#SPJ1

0.020 is a probability for student selects at least 6 .

What is a probability simple definition?

There are two ways to do it. You can either interpret this as

One minus the probability that the student will guess 5 or fewer

correct answers with a probability of a correct answer being = 1/4  ⇒      

0.0197277069

The probability that the student will guess 4 or fewer wrong answers

with a probability of a wrong answer being = 3/4

  binomcdf (10,3/4,4)

     = 0.0197277069

Either way it rounds to 0.020

Learn more about probability

brainly.com/question/11234923

#SPJ13

Answer: y=x2+3x−1

Hope this helps! :)

Each person gets 1/12 fraction of the original cake.

What is a fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Composite fractions, complicated fractions, and combined numeral fractions are examples of uncommon fractions that use numerators and denominators.

Each person gets = 1/2 x 1/6 = 1/12

Hence, each person gets 1/12 fraction of the original cake.

To know more about fractions, click on the link

https://brainly.com/question/7678465

#SPJ9

Scientific notation of the given expression divided -6.5 × 10^-7 by

9.88 ×10^-8 with two decimal places is equal to  6.58 × 10^0.

As given in the question,

Divided  -6.5 × 10^-7 by  9.88 ×10^-8 we have,

= ( -6.5 × 10^-7 ) /( 9.88 ×10^-8 )

= ( -6.5 / 9.88) × 10^(-7 +8)

= 0.65789 × 10^1

Express above quotient in scientific notation form with two decimal is equal to

= 6. 58 × 10^0

Therefore, scientific notation of the given expression divided -6.5 × 10^-7 by  9.88 ×10^-8 with two decimal places is equal to 6.58 × 10^0.

Learn more about scientific notation here

brainly.com/question/18073768

#SPJ1

I WILL TAKE THE POINTS (0,7) AND (2,1) FROM THW GRAPH AND USE THEM TO GET THE GRADIENT.

[tex]m \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 7}{2 - 0} \\ m = \frac{ - 6}{2} \\ m = - 3[/tex]

I WILL USE THE POINT (0,7) TO FIND THE VALUE OF C IN THE GENERAL EQUATION.

[tex]7 = - 3(0) + c \\ c = 7[/tex]

THE EQUATION IS

[tex]y = - 3x + 7[/tex]

ATTACHED IS THE SOLUTION