Answers
Answer:
Step-by-step explanation:
X=y
[tex]\[ \csc(\theta) = \frac{15}{12} = \frac{5}{4} \][/tex] Option C. 15/12 is the Right Choice.
In a right triangle, the cosecant ([tex]\(\csc\)[/tex]) of an angle is the ratio of the length of the hypotenuse to the length of the side opposite the angle. In this scenario, we're given an angle [tex]\( \theta \)[/tex] and the side opposite to it measures 12 units. The length of the hypotenuse is denoted as [tex]\( r \)[/tex], and the length of the other side is 9 units.
To find the length of the hypotenuse ([tex]\( r \)[/tex]), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ r^2 = 12^2 + 9^2 \][/tex]
[tex]\[ r^2 = 144 + 81 \][/tex]
[tex]\[ r^2 = 225 \][/tex]
Taking the square root of both sides, we get [tex]\( r = 15 \)[/tex].
Now that we have the length of the hypotenuse ([tex]\( r = 15 \)[/tex]), we can find the cosecant ([tex]\(\csc\)[/tex]) of angle [tex]\( \theta \)[/tex]. The definition of [tex]\(\csc\)[/tex] in a right triangle is:
[tex]\[ \csc(\theta) = \frac{r}{\text{opposite side}} \][/tex]
Substituting the values we have, we get:
[tex]\[ \csc(\theta) = \frac{15}{12} \][/tex]
Simplifying this expression, we find that:
[tex]\[ \csc(\theta) = \frac{5}{4} \][/tex]
Therefore, the value of [tex]\( \csc(\theta) \)[/tex] is [tex]\( \frac{5}{4} \)[/tex]. Hence, the correct answer is C. 15/12.
Related Questions
What’s the length of a leg of an isosceles right triangle whose hypotenuse is 100?
Answers
Answer:
The length of a leg of the isosceles triangle is 50√(2
Step-by-step explanation:
Since it is an isosceles right triangle, the length of the adjacent and the opposite is the same value which is let’s say x.
Mathematically; the square of the hypotenuse equals the square of the adjacent plus the square of the opposite according to Pythagoras.
Thus;
100^2 = x^2 + x^2
10000 = 2x^2
divide the through by 2, we have;
x^2 = 10,000/2
x^2 = 5,000
x = √5,000
x = √2,500 * 2
x = 50√2
Mei-ling invested $2,000 in a simple interest account for 3 years. At the end of 3 years, she had earned $150 in interest. What was the simple interest rate of the account?
Answers
Answer:
2.5%
Step-by-step explanation:
Simple Interest formula : V = P + P*r*t
I = Prt
$150 = $2000*r * 3
r = $150 / ($2000*3) = 5/200 = 0.025 = 2.5%
1 Quincy created the table of x and y
values shown here.
1
2
3
y
10
8
6
4
Which equation represents the relationship
between the x values and the y values in
the table?
A y=-2x + 12
B y= 5x + 5
Cy= 4x+6
D y=-2x - 12
Answers
Final answer:
The correct equation representing the relationship between x and y values is y = -2x + 12. This is found by recognizing the pattern in the table and using the slope-intercept form to find the slope and y-intercept. Thus, option A is correct.
Explanation:
The student is asking to determine which equation represents the relationship between the x values and the y values in the given table. To find the correct equation, we examine the pattern of changes in the x and y values.
The y values decrease by 2 as the x values increase by 1, indicating a slope of -2.
Starting with the x value of 1, which corresponds to a y value of 10, we apply the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
We find that the y-intercept, b, must be 12 to satisfy the equation when x is 1 (10 = -2(1) + b).
Thus, we can conclude that the equation representing the relationship between x and the y values is y = -2x + 12, which is option A.
This type of equation is a linear equation and the slope-intercept form is particularly useful for quickly identifying the slope and y-intercept of the line represented by the equation.
Felipe takes a commuter train to get to work. He pays a one-time fee to store his bike at the train station. He pays a
monthly fee for train passes. The total cost c for Felipe to travel to work for m months is given by the equation
80m + 50. What do the numbers 80 and 50 represent?
Answers
Answer:
80 represents the monthly fees and 50 represents the fixed one-time fee to store the bike at the train station.
The number 80 represents the monthly train pass cost, while 50 represents the one-time bike storage fee. Multiply the monthly fee by the number of months and add the bike storage fee to get total cost c for m months.
The number 50 is the initial, one-time cost to store Felipe's bike at the train station. To calculate the total commuting cost c for Felipe for m months, you multiply the number of months m by the monthly train pass cost, and then add the one-time bike storage fee.
You open a business selling school supplies and tutoring sessions. In your first week, you had $9,000 in sales. You ran a promotion on tutoring sessions totaling $900 in discounts. Your returns equaled $150. Calculate total net sales.
Answers
Answer: total net sales = $7950
Step-by-step explanation:
The formula for determining total net sales is expressed as
total net sales = Gross sales - (sales returns + allowances + discount)
Gross sales means total sales.
From the information given,
Gross sales = $9000
Discounts = $900
Returns = $150
Allowances = 0(this is because it was not given)
Therefore,
total net sales = 9000 - (900 + 150)
= 9000 - 1050
total net sales = $7950
Answer:
7950
Step-by-step explanation:
Suppose a car tire has a diameter of 32 inches. How many complete rotations will the tire make if it travels one mile
Answers
Answer: about 630.57 rotations per mile.
Step-by-step explanation: There are 1760 yards in one mile. 36 inches per yard. Convert miles to inches: 1760×36=63360
Figure the circumference of the tire: C=π×32 3.14×32=100.48=C
Divide the length of the mile by the circumference of the tire:. 63360/100.48 = 630.57 approximately.
A movie complex is showing the same movie in three theaters. In theater A, 72 of the 90 seats are taken. In theater B, 51 seats are taken and 9 seats are empty. In theater C, 28 of the 80 seats are empty. Which theater has the greatest percent of its seats taken?
Answers
Answer:
The answer is A
Step-by-step explanation:
hope this helps
what is 7.849+0.09? can you help me find the answer?
Answers
Answer:7.939
Step-by-step explanation:
25% equals what decimal
Answers
Answer:
0.25
Step-by-step explanation:
25% can be written as the decimal 0.25. The word 'percent' means 'per 100. ' So, 25 percent is the same as 25 out of 100.
Answer:
[tex]25\% = \frac{25}{100 } \\ \\ 25\% = 0.25[/tex]
how much will you have to invest to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
$7,185.50
$5,020.71
$1,016.90
$4,957.33
Answers
Answer:
You have to invest $5,020.71 to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
Step-by-step explanation:
Let the principal be x
Amount = $6000
Time = 4 years 3 months = [tex]4 years +\frac{3}{12} years = 4.25 years[/tex]
Rate of interest = [tex]4 \frac{1}{5}\% = \frac{21}{5}\%[/tex]
No. of compounds per year = 12
Formula:[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]6000=P(1+\frac{21}{500 \times 12})^{12 \times 4.25}[/tex]
[tex]\frac{6000}{(1+\frac{21}{500 \times 12})^{12 \times 4.25}}[/tex]=P
P=$5,020.71
Hence You have to invest $5,020.71 to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
A packet of 8 pens costs £1.84 how much does each pen cost
Answers
Answer:
23p
Step-by-step explanation:
Pens : Cost
8 : £1.84
divide each by 8
1 pen = £0.23 = 23p
Which shape is always a parallelogram?
A. A rectangle because it has 2 pairs of parallel sides.
B. A quadrilateral because it has 4 sides.
C. A trapezoid because it has 1 pair of parallel sides.
D. A hexagon because it has 3 pairs of parallel sides.
Answers
Answer:
the answer is A because it has 2 sides of parallel line
Step-by-step explanation:
The correct shape which is always a parallelogram is,
⇒ A rectangle because it has 2 pairs of parallel sides.
We have to given that,
To find shape which is always a parallelogram
Since, A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Hence, We can say that;
Rectangle shape is always a parallelogram.
Thus, The correct shape which is always a parallelogram is,
⇒ A rectangle because it has 2 pairs of parallel sides.
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please help me with this fast
Answers
Answer:
5
Step-by-step explanation:
A negative plus a negative equals a positive so the equation would be 4 1/3 + 2/3 and the sum is 5.
Hopes this helps :)
In a lab experiment, 590 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 24 hours. How many bacteria
would there be after 13 hours, to the nearest whole number?
Answers
Answer:
There would be 859 bacteria after 13 hours.
Step-by-step explanation:
The population of bacteria after t hours is given by the following equation:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
The number of bacteria is able to double every 24 hours.
This means that [tex]P(24) = 2P(0)[/tex]. So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]2P(0) = P(0)e^{24r}[/tex]
[tex]e^{24r} = 2[/tex]
[tex]\ln{e^{24r}} = \ln{2}[/tex]
[tex]24r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{24}[/tex]
[tex]r = 0.0289[/tex]
590 bacteria are placed in a petri dish.
This means that P(0) = 590. So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = 590e^{0.0289t}[/tex]
How many bacteria would there be after 13 hours, to the nearest whole number?
This is P(13).
[tex]P(t) = 590e^{0.0289t}[/tex]
[tex]P(13) = 590e^{0.0289*13} = 859[/tex]
There would be 859 bacteria after 13 hours.
Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why.
1. 15x4 - 6x + 3x2 - 1
II. 12x3 + 8x + 4
III. 285 + 8x2 + 10%
Which student's response is correct?
Answers
Answer:
Only II. is written in standard form
Step-by-step explanation:
The three polynomials given are:
I. [tex]15x^4 - 6x + 3x^2 - 1[/tex]
II. [tex]12x^3 + 8x + 4[/tex]
III. [tex]285 + 8x^2 + 10%[/tex]
A polynomial is said to be in standard form when the variables are written in terms of descending powers i.e. the term with the highest power first, followed by the next and so on.
Examining the three polynomials I, II and III, there is only one which follows this rule and that is:
II. [tex]12x^3 + 8x + 4[/tex]
The term with the highest power (3) came first, followed by the term with the next degree of power (1) and the last term with degree of power as 0.
Hence, only II. is written in standard form.
Only the second polynomial, 12x3 + 8x + 4, is in standard form because its terms are arranged in descending order of degrees. The first polynomial is not in standard form due to the incorrect order of terms by degree. The third expression contains a percentage sign (%) and wasn't written in order of descending degree, hence it doesn't qualify as a polynomial in standard form.
Explanation:In mathematics, a polynomial is said to be in standard form when its terms are written in descending order by degree. The degree of a term is the exponent used in the term. Let's evaluate each option:
15x4 - 6x + 3x2 - 1: This polynomial is not in standard form because the terms are not arranged in descending order of degrees. Properly ordered, it would read 15x4 + 3x2 - 6x - 1.12x3 + 8x + 4: This is in standard form because the terms are arranged in descending order of degrees from 3 to 0.285 + 8x2 + 10%: This is not a polynomial in the standard sense of the word due to the presence of the percentage sign (%). Also, it was not written in descending order of degrees.Learn more about Polynomials in Standard Form here:https://brainly.com/question/32213698
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What value of x will make parallelogram ABCD a rhombus?
x = ?
Answers
Answer:
x=34
Step-by-step explanation:
3x-12=90
3x-12+12=90+12
3x=102
3x/3 = 102/
x=34
Answer:
x = 34Step-by-step explanation:
From the picture we have
AD = CD = BC = AB
it's enough to say that this quadrangle is a rhombus.
The diagonals in each rhombus are perpendicular and divide to half.
Therefore we have the equation:
3x - 12 = 90 add 12 to both sides
3x - 12 + 12 = 90 + 12
3x = 102 divide both sides by 3
3x : 3 = 102 : 3
x = 34
Find m∠7 if m∠8 = 119°
m∠7 = ???
Answers
Answer:
119
Step-by-step explanation:
it will be the same as 8 because they are adjacent..
I got D is this correct?
Answers
Answer:no
Step-by-step explanation:
Answer:
C. x [tex]\geq[/tex] 0
Step-by-step explanation:
The answer is C, x is greater than or equal to zero, because that is the only answer that makes sense.
A) x can also be equal to 0, so this answer is wrong
B) x can't be -2, and it definitely can't be less than -2, so that's wrong.
D) Again, x can't be -2, or -1. It can't be any negative number because 4 * (a negative number) would put a negative sign under the square root. You can't take square roots of negative numbers.
Hope this is correct and that it helps you!
A total of 13.2 inches of snow fell during a snowstorm that lasted 5.5 hours. The same amount of snow fell each hour of the storm. How many inches of snow fell each hour? Enter your answer as a decimal in the box.
Answers
Answer:
2.4 inches per hour
Step-by-step explanation:
A total of 13.2 inches of snow fell during a snowstorm that lasted 5.5 hours and the same amount of snow fell each hour of the storm.
This means that there was a constant rate of snow fall.
To find how many inches of snow fell each hour, we divide the amount of snow fall by the amount of time that the snowstorm lasted.
That is:
[tex]R = \frac{13.2}{5.5}[/tex]
R = 2.4 inches per hour
This means that 2.4 inches of snow fell each hour during the snowstorm.
Answer:
2.4 inches
I did the quiz
What is the least common multiple of 7,13,14
Answers
Answer:
182
Step-by-step explanation:
You can start by realizing that 14 is 7*2, and that that is already a common multiple, meaning that you can forget about 7 entirely. Now, because 13 is prime, the least common multiple of 13 and 14 will just be 13*14=182. Hope this helps!
Answer:
182
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
The length of a rectangle is 5 inches more than the width. The area is 33 square inches. Find the length and width . Round to the nearest tenth if necessary.
Answers
Answer:
the length and width . Round to the nearest tenth are 8.8 inches and 3.8 inches respectively.
Step-by-step explanation:
The area A of a rectangle is the product of the length L and width W. This may be expressed mathematically as
A = L * W
As such, given that the length is 5 inches more than the width,
L = W + 5
33 = W(W + 5)
W² + 5W - 33 = 0
Using the formula method which states that
s = -b±√(b²-4ac)/2a
W = -5 ± √5² - 4(1)(-33)/2
= -5 ± 12.53/2
= 7.53/2 (since length cannot be negative)
= 3.755 inches
L = 3.755 + 5
= 8.755 inches
Help out please!!!!!!
Answers
Answer:
6.4
Step-by-step explanation:
A^2+B^2=C^2
(5*5)+(4*4)=C^2
25+16=[tex]C^{2}[/tex]
41=[tex]C^{2}[/tex]
[tex]\sqrt{41}[/tex]=[tex]\sqrt{C^{2} }[/tex]
c= 6.4
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Question 3 of 10
2 Points
What would be the most logical first step for solving this quadratic equation?
x2 + 2x-11 = 4
Answers
Answer:
Subtract 4 from both sides
Step-by-step explanation:
Ap ex
Consider this equation:
–2x – 4 + 5x = 8
Generate a plan to solve for the variable. Describe the steps that will be used.
Answers
Answer:
Step-by-step explanation:
Answer:
Solve for the (number or thing that changes), so you need to (separate far from others)/get x by itself
-2x - 4 + 5x = 8 First I want to combine like terms (-2x and 5x)
-4 + 3x = 8 (Add 4 on both sides)
3x = 12 Then divide 3 into both sides to get x by itself
x = 4
Combine like terms (add the 5x to the -2x to get 3x). Move the -4 to the other side to get 3x= 12. Divide both sides by 3 to get x=4. Apply the addition property of (a state where all things are equal), Apply the division property of (a state where all things are equal) to divide both sides by 3, Finally, check the solution by substituting 4 into the original equation.
*PLEASE MAKE TEXT INTO OWN WORDS IF POSSIBLE
3x^2-8x+4 pls factor step by step
Answers
144 students enter a spelling bee, but only 1/6 of the group will make into the semi-final round, and only 2 /3 that group will make into the final round. How many students will enter the final round of the spelling bee?
Answers
Answer:
16 students
Step-by-step explanation:
144 students enter a spelling bee contest.
Step 1
For the semi final round we are told that only 1/6 of the group will make it into that round.
This is calculated as
1/6 × 144/students = 24 students.
This means that only 24 students would make it into the semi final rounds.
Step 2
We are also told in the question that only 2/3 of THAT group would make it into the final round.
" THAT" group been referred to in the question means the number students that made it to the semi final round
This is calculated as
2/3 of that group( the group that made it to the semi finals)
= 2/3 × 24 students
= 16 students.
Therefore, the number of students that will enter the final round of the spelling bee is 16 students.
To calculate the number of students who will make it to the final round of the spelling bee, we first determine the semi-finalists by multiplying the total students by 1/6, and then the number of finalists by multiplying the semi-finalists by 2/3, resulting in 16 students.
Explanation:To solve this problem, we first need to determine the number of students who will make it into the semi-final round. Since only 1/6 of the total students will make it to the semi-final round, we can calculate that by multiplying the total students (144) by 1/6, which results in 24 students.
Next, we need to calculate the number of students that will make it into the final round from the semi-final round. This means we need to multiply the semi-finalists (24) by 2/3, which results in 16.
Therefore, 16 students will make it into the final round of the spelling bee.
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Which expressions are equivalent to -2(5x-3/4)? Check all that apply.
A. -2(5x)+(-2)(-3/4)
B. -10x-3/4
C. -10x+ 6/2
D. -10x+3/2
E. -10x-6/2
I WILL CHOOSE YOU FOR BRAINLIESS
Answers
Answer:
A
Step-by-step explanation:
-2(5x)+(-2)(-3/4) = -10x +6/4
-2(5x-3/4) = the same
The given expression is -2(5x-3/4). Which simplifies to -10x+6/4 or -10x+3/2
Answer A: -2(5x)+(-2)(3/4) simplifies to -10x+6/4 or -10x+3/2 which equals the expression given, so it is CORRECT.
Answer B: -10x-3/4 does NOT equal the expression given, so it is NOT correct.
Answer C: -10x+6/2 does NOT equal the expression given, so it is NOT correct.
Answer D: -10x+3/2 does equal the expression given, so it is CORRECT.
Answer E: -10x-6/2 does NOT equal the expression given, so it is NOT correct.
A & D are the correct answers. They equal the expression given.
A rectangular prism has a link of 8 cm in width of 2 cm in a height of 5 cm what is the service around the rectangular prism
Answers
Answer:
132 square centimeters
Step-by-step explanation:
The surface area of a rectangular prism can be calculated with the formula [tex]2lh+2lw+2hw[/tex] where l represents length, h represents height, and w represents width. In this case, the equation is [tex]2\cdot 2\cdot 8 + 2\cdot 2\cdot 5 + 2\cdot 8\cdot 5=132[/tex] square centimeters. Hope this helps!
Which formula is the correct formula to use when finding volume of a
cylinder?
Answers
Answer:
The last option.
Step-by-step explanation:
I WILL DO ANYTHING PLZ HELP MEE
Find the equation for the table.
Answers
Answer:
y = 5 * (1/2)^x
Step-by-step explanation:
This is an exponential function
y =ab^x
where a is the initial value ( where x = 0)
a = 5
y = 5 * b^x
Pick a point to determine b
(1,2.5)
2.5 = 5 * b^1
2.5 = 5 *b
Divide each side by 5
2.5/5 = b
b = 1/2
y = 5 * (1/2)^x