Final answer:
The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. They are continuous everywhere except where the denominator is zero.
Explanation:
The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. These functions are defined for all real numbers except when the denominator becomes zero. Therefore, they are continuous everywhere except where the denominator is zero.
For example, the cosine function, denoted as cos(x), is continuous for all real numbers. It has a periodic nature and oscillates between -1 and 1.
Similarly, the cosecant function, denoted as csc(x), is continuous everywhere except at the points where sin(x) is equal to zero. The secant function, denoted as sec(x), is continuous everywhere except at the points where cos(x) is equal to zero. The cotangent function, denoted as cot(x), is continuous everywhere except at the points where tan(x) is equal to zero.
You invested $2,300 in a stock. Your account now has a value of $2,643. Your percentage gain on the investment (rounded to the nearest percent) was:
a)0%
b)5%
c)10%
d)15%
Answer:
15%
Step-by-step explanation:
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Factor the polynomial 3x4 – 2x2 + 15x2 – 10 by grouping.
Which product is the factored form of the polynomial?
(–x2 – 5)(3x2 + 2)
(x2 – 2)(3x2 + 5)
(x2 + 5)(3x2 – 2)
(3x2 – 5)(x2 + 2)
Answer:
[tex](x^{2} + 5)(3x^{2} - 2)[/tex]
Step-by-step explanation:
The polynomial is first correctly stated as follows
[tex]3x^{4} - 2x^{2} + 15x^{2} - 10[/tex]
This is rearranged, grouped and solved as follows:
[tex]3x^{4} + 15x^{2} - 2x^{2} - 10[/tex]
[tex](3x^{4} + 15x^{2}) - (2x^{2} + 10)[/tex]
[tex]3x^{2} (x^{2} + 5) - 2(x^{2} + 5)[/tex]
Factorizing the common factors [tex](x^{2} + 5)[/tex], we have the product of the factored form of the polynomial as follows:
[tex](x^{2} + 5)(3x^{2} - 2)[/tex]
That is the third option in the question if rewritten in the correct form.
Use the law of cosines to find the value of cos. (see pic attached inside!!) Round the answer to two decimal places!
A. 0.84
B. 0.35
C. 0.23
D. 1.23
six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that exactly one girl and two boys will recite awards? express your answer as a percent
The probability that exactly one girl and two boys will receive awards is 75%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that there are:-
6 girls
4 boys
Probability of 1 girl being chosen: 1/6
Probability of 1 boy being chosen: 1/4
Probability of another boy being chosen: 1/3
1/6 = 0.17 x 100% = 17%
1/4 = 0.25 x 100% = 25%
1/3 = 0.33 x 100% = 33%
17% + 25% + 33% = 75%
Therefore the probability that exactly one girl and two boys will receive awards is 75%.
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how do you write (negative Infinity, 8)or (10, Infinity) as inequality?
Please I really don't get this. Can someone please help me?
There are ten shirts in your closet, four blue, three green, and three red. You randomly select a different shirt each day. You wear a blue shirt Monday, Tuesday, and Wednesday.
Answer:
It's a probability problem to find the odds of picking a green or red shirt out of the 10 shirts on Thursday, Friday and Saturday since you have randomly already know you have picked a blue shirt on the other days. Probability = Number favorable outcomes / total number of outcomes
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Step-by-step explanation:
a square with a side length of x+6 has the same perimeter as an equilateral triangle with a side length of 4x. what is the area of the square
Given that segments RS and RT are tangent to circle Q, find the length of RS.
As they both are tangents of the same circle, their lengths must be equal.
RS = RT
x/4 = x-6.3
x = 4x - 25.2
4x-x = 25.2
3x = 25.2
x = 8.4
As, RS = x/4, it will be equal to 8.4/4 = 2.1
SO, YOUR FINAL ANSWER IS RS = 2.1
To find the length of segment RS, we can use the tangent-radius theorem and the Pythagorean theorem. Segment RS is perpendicular to the radius of circle Q that passes through point S. By using the Pythagorean theorem, we can solve for the length of RS.
Explanation:The length of segment RS can be found using the tangent-radius theorem. According to this theorem, if a line is tangent to a circle at a certain point, then the line is perpendicular to the radius that passes through that point. Therefore, segment RS is perpendicular to the radius of circle Q that passes through point S.
Since RS is perpendicular to the radius, RS and the radius form a right triangle. The length of RS can be found using the Pythagorean theorem. Let's denote the length of the radius as r and the length of RS as x. The radius is the hypotenuse of the right triangle, so we have:
x^2 + RS^2 = r^2
Since RS is the only unknown, we can solve for it. Once we have the value of the radius, we can substitute it into the equation to find the length of RS.
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A(n) _____ is a segment that is formed by the intersection of two faces
Answer:
The answer is Edge. A segment that is formed by the intersection of two faces is called an EDGE.
Step-by-step explanation:
A segment that is formed by the intersection of two faces is called an EDGE.
An edge is defined as a type of line segment, that joins two vertices in a polygon, polyhedron etc. In a polytope, an edge is a line segment between faces.
Calculate the length of the circumference of a circle with diameter 6.2cm use pi = 3
The circumference of the circle with diameter 6.2 cm, using (pi) equal to 3, is calculated as 18.6 cm using the formula C = (pi)d.
The question asks to calculate the length of the circumference of a circle with a diameter of 6.2 cm, using an approximate value for (pi) as 3. To find the circumference of a circle, the formula C = (pi)d is used, where C is the circumference and d is the diameter. Since we are provided with the diameter (6.2 cm) and an approximate value for
(pi) as 3, the calculation is straightforward.
Using the formula,
C = (pi)dC = 3 * 6.2 cmC = 18.6 cmThus, the circumference of the circle is 18.6 cm.
Drag each equation to show if it could be a correct first step to solving the equation 2(x+7)=362(x+7)=36.
Translate this sentence into an equation.
The product of Raj's score and
6
is
66
.
Use the variable
r
to represent Raj's score.
Final answer:
The sentence 'The product of Raj's score and 6 is 66' translates to the equation 6 × r = 66. By dividing both sides by 6, we find that Raj's score r = 11.
Explanation:
To translate the sentence into an equation, we need to understand the mathematical operation described by the word 'product'.
The product refers to the result of multiplying two numbers.
In this sentence, the product of Raj's score, which we will represent with the variable r, and 6 is given to be 66.
Therefore, the equation representing this relationship is:
6 × r = 66
To solve for Raj's score, you would divide both sides of the equation by 6, which gives you:
r = 66 / 6
Therefore, Raj's score, r, is 11.
Translate the following statement into an inequality: Five less than a number is at least nine.
The given statement translates to the inequality x - 5 ≥ 9.
To do this, we first need to interpret ‘a number’ as a variable, which we can call x. ‘Five less than a number’ means we subtract five from our variable, expressed as x - 5. ‘At least nine’ indicates that the value should be greater than or equal to nine, which in inequality form is ( ≥ 9 ). Therefore, the complete inequality that represents the given statement is x - 5 ≥ 9.
List the fractors of 35 is this number prime or composite
Answer: Composite
Step-by-step explanation: To see if 35 is a prime number or a composite number, let's first start by finding the factors of 35.
To find the factors of 35, begin by dividing 35 by 1 which gives us 35. This means that 1 and 35 are factors.
Next, since 35 is not divisible by 2, 3, or 4, we divided 35 by 5 which gives us 7. This means that 5 and 7 are factors.
Next, since 35 is not divisible by 6, we divide 35 by 7 which gives us 5. Notice that 7 and 5 are repeat factors and once we hit repeat factors, this means that all other factors we try will repeat.
Therefore, the factors of 35 are 1, 5, 7, and 35.
Since 35 has more than two factors, it's called a composite number.
How many 1.4 meter sections of rope can be cut from a length of rope 6 meters long?
We can cut a total of 4 sections of 1.4 meters through 6-meter long rope.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Length of rope = 6 meter
Length of section = 1.4 meter
Number of sections = Length of rope ÷ Length of section
Number of sections = 6/1.4 = 4.28 since 0.28 part is not complete section so we will not consider it.
Hence "We can cut a total of 4 sections of 1.4 meters through 6-meter long rope".
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how do you write standard number 0.00073 in scientific notation?
5.7n + 4.1 = 2.96
What is n Im thinking -32
A flock of Canadian geese migrated 1623 miles in 28 days. What was the average rate at which these geese traveled in miles per day?
The graph shows how the distance an object traveled changed over time.
Between which two points was the object traveling at the greatest speed?
A.
between points C and D because that slope is the steepest
B.
between points A and B because that segment is the longest
C.
between points B and C because that segment is horizontal
D.
between points A and B because that slope is the steepest
The two points which shows the object traveling at the greatest speed is D. between points A and B because that slope is the steepest
How does this section show the greatest speed ?
The segment between points A and B has the steepest slope, indicating a rapid change in distance over a short period, which implies a higher speed.
This makes sense given the concept of the physics of motion, where a steeper slope on a distance-time graph represents a higher velocity or speed.
Between points C and D has the second greatest speed because it shows that as time went, distance was covered unlike between points B and C.
20,000 is what percent of 80,000
For what values of a and b is the following function is continuous at every x:
-7 x ≤ -3
f(X) = ax-b -3< x < 1
3 x ≥ 1
Find the values is a and b ix f(x) continuous at every x?
By solving a system of equations, we will see that the function is continuous for all values of x if:
a = 2.5b = -0.5.How to make the piecewise-function continuous for every x?Here we have the piecewise function:
f(x) = -7 if x ≤ -3
f(x) = a*x- b if -3 < x < 1
f(x) = 3 if 1 ≤ x
The piecewise function will be continuous only if the values at the limits where we have jumps (at x = -3 and x = 1) are the same in both pieces of the function.
This means that we must have:
f(-3) = -7 = a*(-3) - b
f(1) = 3 = a*1 - b
Then we have a system of equations:
-7 = -3a - b
3 = a - b
To solve this, first, we isolate one of the variables in one of the equations, I will isolate b in the second one to get:
b = a - 3
Now we can replace that in the other equation to get:
-7 = -3a - (a - 3)
Now we can solve this for a.
-7 = -4a + 3
-7 -3 = -4a
-10/-4 = a = 2.5
Then the value of a must be 2.5, to get the value of b we use:
b = a - 3 = 2.5 - 3 = -0.5
So the solution is a = 2.5, b = -0.5.
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Due to a leak, the amount of water in a pool is decreasing by 5858 gal every hour.
What is the total change in the number of gallons of water in the pool after 3434 h?
Enter your answer in the box as a simplified fraction.
Round 37.82 to the nearest tenths place.
Earl pours 1/3 of a bottle of juice into his glass. Roberto pours 1/3 of the remainder into his glass. What fraction of the bottle of juice is left?
An interior angle of a regular polygon has a measure of 120°. What type of polygon is it? decagon hexagon quadrilateral octagon
The answer is Hexagon
The correct answer is B. Hexagon
Explanation:
In geometry, a polygon refers to a figure with three or more sides and therefore at least three angles, this includes triangles, pentagons, octagons, etc. Additionally, polygons can include irregular or regular sides and angles.
In the case of hexagons, if a hexagon is regular, this includes six sides of the same length and six angles with the same measure. Moreover, each of the angles is120° considering the total of internal angles in a hexagon is always 720° and therefore 720° divided into six equal angles is equal to 120°.
Therefore, if an interior angle of a regular polygon (figure with equal sides and angles) has a measure of 120° the polygon is a hexagon because the only polygon that can have multiple sides and angles each with 120° and form a regular polygon is the hexagon.
If f(x) = 3x + 10 and g(x) = 2x – 4, find (f + g)(x).
A. (f + g)(x) = 3x – 2x + 14
B. (f + g)(x) = 3x + 2x + 6
C. (f + g)(x) = 5x + 6
D. (f + g)(x) = –3x – 2x – 14
Answer:
f(x)= 3x + 10 and g(x)= 2x - 4
(f+g)(x)= 3x + 10 + 2x - 4
3x + 2x + 6
5x + 6
b and c
Answer:
C. (f + g)(x) = 5x + 6.
Step-by-step explanation:
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In the situation, simple interest is calculated yearly. how much interest was earned? drag and drop the answer into the box. principal: $12,000; time: 3 years; interest rate: 15%; interest: ?
The amount of interest earned is $5,400
From the question,
We are to calculate the simple interest earned
Interest can be calculated by using the simple interest formula
I = PRT
Where I is the interest
P is the principal
R is the rate
T is the time
From the question
P = $12,000
R = 15%
T = 3 years
∴ Interest,
I = $12000 × 15% × 3
I = $12000 × 0.15 × 3
∴ I = $5400
Hence, the amount of interest earned is $5,400
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need help answer is not 3.14
The circumference, or perimeter, of a circle can be found by multiplying its diameter by 3.14. What is the circumference of a circle that has a diameter of inch?
Express your answer as a decimal.plz
The circumference of the circle with a diameter of inch is 3.14 inch.
Explanation:The circumference of a circle can be found by multiplying its diameter by π (pi). In this case, the diameter of the circle is given as inch. To find the circumference, we need to multiply the diameter by π.
Circumference = Diameter × π
Since the diameter is inch, the circumference of the circle is ( inch) × π = inch × π = 3.14 inch.
Nam has a beginning balance of $815 in her checking account. She writes a check for $210 and has a debit transaction of $525. What is her new balance?
$125
$80
$1550
$120
Answer:the answer is ($80)
Step-by-step explanation:i took the test on k12 online school
plz give me bianleast it helps oh lot thank you