Hello and Regards zoecenters91522.
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
Step-by-step explanation:The distance between two points is the measure of the length of the straight line that joins them. On a Cartesian plane, the distance between two points is calculated using the Euclidean distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of the sum of the squares of the differences of their coordinates:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
This formula can be used to calculate the distance between two points on any plane, such as a three-dimensional plane or Euclidean space of any dimension.
Now we locate the points of x and y.
x₁ = 15, y₁ = -17x₂ = -10, y₂ = -17We substitute the points in the formula and solve:
[tex]\huge \boxed{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex]\huge \boxed{d=\sqrt{(-10-15)^2+(-17-(-17))^2 } }[/tex]
[tex]\huge \boxed{d=\sqrt{(-25)^2+0^2}=\sqrt{625+0} }[/tex]
[tex]\huge \boxed{d=\sqrt{625}=25 \ units }[/tex]
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
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Multiply the complex’s numbers
(7-2i)(1+3i)
The multiplicatiοn οf the cοmplex number is 13+19i.
What is cοmplex number?Cοmplex numbers are the numbers that are stated in the fοrm οf a+ib where, a,b are real numbers and I is an imaginary number termed "iοta".
Cοmplex numbers allοw sοlutiοns tο all pοlynοmial equatiοns, even thοse that have nο sοlutiοns in real numbers. Mοre precisely, the fundamental theοrem οf algebra asserts that every nοn-cοnstant pοlynοmial equatiοn with real οr cοmplex cοefficients has a sοlutiοn which is a cοmplex number.
Here the given cοmplex number is ,
=> (7-2i)(1+3i)
Nοw simplifying the expression then,
=> [tex]7\times1+7\times3i-2i \times1 -2i \times3i[/tex]
=> 7+21i-2i-[tex]6i^2[/tex]
=> 7+19i -6(-1) [[tex]i^2=1[/tex]]
=> 7+19i+6
=> 13+19i
Hence the multiplication of cοmplex number is 13+19i.
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please show your work as well
By trigonometric functions, the missing sides of the right triangles are:
Case 7: AC = 9.725, BC = 10.071
Case 8: AB = 21.301, BC = 18.807
Case 9: BC = 4.585, AC = 8.999
Case 10: AB = 10.461, BC = 7.774
How to determine the missing sides in right triangles
In this problem we have four cases of right triangles, each of which has a known side and a known angle and we must determine all the missing lengths by trigonometric functions:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Where:
x - Leg adjacent to an angle.y - Leg opposite to an angle.r - Hypotenuse.θ - Angle, in degrees.Now we proceed to determine the values of the missing lengths:
Case 7
AC = 14 · sin 44°
AC = 9.725
BC = 14 · cos 44°
BC = 10.071
Case 8
AB = 10 / cos 62°
AB = 21.301
BC = 10 · tan 62°
BC = 18.807
Case 9
BC = 10.1 · sin 27°
BC = 4.585
AC = 10.1 · cos 27°
AC = 8.999
Case 10
AB = 7 / cos 48°
AB = 10.461
BC = 7 · tan 48°
BC = 7.774
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b. Find the quadratic equation whose roots are aß² and a²ß. If a and b
are the roots
of the quadratic equation x^2- 3x + 2 = 0
The quadratic equation is; x^2 -6x + 8 = 0
What is a quadratic equation?A quadratic equation is a mathematical equation of the form ax^2 + bx + c = 0, where x is the unknown variable, and a, b, and c are constants (numbers). The exponent of x in the equation is 2, which means it is a second-degree polynomial equation.
We know that the solution of x^2- 3x + 2 = 0 is x = 2 and x = 1 hence;
α = 2, β = 1
We have that;
αβ^2 = 2
α^2β = (2)^2(1) = 4
The equation would now be;
x^2 - (2 + 4)x - (2 * 4) = 0
x^2 -6x + 8 = 0
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Pack of card has 52 cards, how many cards in 36 packs?
Answer:
1872 cards
Step-by-step explanation:
1 cards=52
36×52
=1872 cards
Rafael wants to find the slope of the line
The correct formula for the slope will be:
m = (100 - 50)/(4 - 2) = 50/2 = 25 . Rafael took the reciprocal of the values.
Explain about the slope of the line?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Δy and Δx are the net changes in the y and x coordinates, respectively.
So,
m = Δy / Δx
Using the slope-intercept form, as illustrated below, we can quickly get the slope for just a given line:
Y = mx + c can be used to represent a line.
where the slope's numerical value is m, the x-coefficient.A line's slope and steepness are both referred to as its slope.For the stated question:
The slope calculated by Rachel is:
m = (4 - 2) / (100 - 50) = 2/50 = 1/25
Which is incorrect .
Thus, the correct formula for the slope will be:
m = (100 - 50)/(4 - 2) = 50/2 = 25
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Which expression is equivalent to 9(2x+5y)
Answer: 18x + 45y.
Step-by-step explanation:
Expanding the brackets, we get:
9(2x+5y) = 92x + 95y
Simplifying the products, we get:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
Answer:
18x+45y
Step-by-step explanation:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
Question 6 of 10
Fill in the blank to complete the following sentence.
If a polynomial has one root in the form a- √5, it has a second root in the
form of a√5.
Considering the complex-conjugate root theorem, the statement is given as follows:
If a polynomial has one root in the form a - √5, it has a second root in the
form of a + √5.
What is the complex-conjugate theorem?The complex conjugate theorem for rational roots states that if a polynomial with real coefficients has a complex root of the form a + bi (where a and b are real numbers and i is the imaginary unit), then its complex conjugate a - bi is also a root of the polynomial.
In the case of a rational root, we have that:
If [tex]a + \sqrt{b}[/tex] is a root, then the number [tex]a - \sqrt{b}[/tex] is also a root, which justifies the answer for this problem.
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Jake is traveling 12 mph in his boat. After 3 hours, how far will he have traveled?
Answer:
36 miles
Step-by-step explanation:
speed = distance/time
distance = speed × time
distance = 12 miles/hour × 3 hours
distance = 36 miles
A serving of Cereal A contains 4 more grams of carbohydrates than a serving of Cereal B. If you eat a serving of each cereal, you will consume 66 g of carbohydrates. Find the amount of carbohydrates in each cereal.
Answer:
Let's assume that a serving of Cereal B contains x grams of carbohydrates.
According to the problem, a serving of Cereal A contains 4 more grams of carbohydrates than Cereal B. So, the amount of carbohydrates in Cereal A is (x + 4) grams.
The total amount of carbohydrates consumed from both cereals is 66 grams:
x + (x + 4) = 66
Simplifying the equation:
2x + 4 = 66
Subtracting 4 from both sides:
2x = 62
Dividing by 2:
x = 31
So a serving of Cereal B contains 31 grams of carbohydrates.
And a serving of Cereal A contains 4 more grams:
31 + 4 = 35
Therefore, a serving of Cereal A contains 35 grams of carbohydrates.
Find the measure of line segment JK.
The measure of line segment JK using the Secant Theorem is found as 7 units.
Explain about the Secant Theorems?According to the intersecting secants theorem, the product of one whole secant segment but also its outer segment is equivalent to the product of the other whole secant segment as well as its external segment when two secants cross at an exterior point.
According to the Secant Theorem,
If two secants are drawn from an identical point through a circle, their products, A times their external segment and B times their external segment, are equal.
So, using Secant Theorem:
JK*JL = RM*RL
8* (2x + 7) = 24 * 7
Solving the equation:
x = 7
Thus, the measure of line segment JK using the Secant Theorem is found as 7 units.
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Find the value of an in the parallelogram shown to the right. Note that the figure is not drawn to scale.
59°
(2a+27)°
The value of a in the given parallelogram such that 2a + 27 and 59 are opposite angles is 16
Finding the value of a in the parallelogramGiven the attached parallelogram
Opposite angles in a parallelogram are equal in measure.
This property is known as the "Opposite Angles Property" or "Alternate Angles Property" of a parallelogram.
So, we have
2a + 27 = 59
Evaluating the like terms, we have
2a = 32
Divide both sides by 2
a = 16
Hence, the value of a is 16
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what is the debt to equity ratio for 2024
Answer:
75.6%
Step-by-step explanation:
Reducing Debt: 2024's debt to equity ratio has increased from 67.6% to 75.6% over the past 5 years. Debt Coverage: 2024's operating cash flow is negative, therefore debt is not well covered.
1. In the Khan academy video, the ratio of boys to girls is 2 : 3. What is the ratio of boys to girls if there are 40 students in the classroom?
Answer: ____
a) 8 : 12 b) 10 : 5 c) 20 : 40 d) 16 : 24
Answer:
16:24
Step-by-step explanation:
The ratio of boys to girls is 2 : 3
total of the ratio is 5
∴ fraction of the class are boys = 2/5
and the girls= 3/5
Ratio of boys =( 2/5)×40=16
Ratio of girls=3/5 ×40 =24
Using the substitution method to solve the following system .if the equations of the systems are dependent ,or if the system is inconsistent,so indicate.
y = 3x
x + y = 8
Answer:
[tex]x = 2 , y = 6[/tex]
Step-by-step explanation:
The substitution method suggests that you will "substitute" a portion of one given equation to another in the system of equation:
In this case, substitute 3x for y in the 2nd equation:
[tex]y = 3x\\x + y = 8\\\\x + (3x) = 8[/tex]
Simplify. Combine like terms. Like terms are terms with the same amount of the same variable.
[tex]x + 3x = 8\\4x = 8[/tex]
Next, isolate the variable, x. Divide 4 from both sides of the equation:
[tex]4x = 8\\\frac{4x}{4} = \frac{8}{4} \\x = \frac{8}{4}\\ x = 2[/tex]
Next, plug in 2 for x in one of the equations, and simplify to solve for y:
[tex]y = 3x\\y = 3(2)\\y = 6[/tex]
Check: Plug in 2 for x and 6 for y in the second equation:
[tex]x + y = 8\\(2) + (6) = 8\\8 = 8[/tex](True)
~
[tex]x = 2 , y = 6[/tex] is your answer.
~
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Solve the equation 4tan+5=0 on the interval[0,360 )
answer
306.87 degrees and 666.87 degrees.
steps
4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Equation with tangent function.
Title: Solving an equation involving tangent function
Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).
Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).
Numbered list:
Start with the equation 4tanθ+5=0.
Subtract 5 from both sides to get 4tanθ=-5.
Divide both sides by 4 to obtain tanθ=-5/4.
Take the arctangent (or inverse tangent) of both sides to find θ.
Specify the interval [0,360) when giving the solution.
Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.
One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).
To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.
Subtracting 5 from both sides gives us: 4tanθ = -5
Dividing both sides by 4: tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
Sure, here's just the math:
4tanθ + 5 = 0
Subtracting 5 from both sides:
4tanθ = -5
Dividing both sides by 4:
tanθ = -5/4
Taking the arctangent (or inverse tangent) of both sides:
θ = arctan(-5/4)
Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.
Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:
θ = -53.13 + 360 = 306.87 degrees
Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.
ChatGPT
Which expression is equivalent to 1/3b+2/3b-5/6(b+1)
the answer is (a) [tex]\frac{1}{6}b-\frac{5}{6}[/tex]
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
what are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
from the question:
In order to combine the two terms that have a 3b common denominator, we can first do so to simplify the statement 1/3b + 2/3b - 5/6(b+1):
1/3b + 2/3b = 3/3b = 1/b
We can now reintroduce this value into the first expression:
1/b - 5/6(b+1)
We can distribute the 5/6 term in order to further simplify this:
1/b - 5/6b - 5/6
Now that the first two terms share a common denominator of 6b, we may combine them:
6/6b - 5/6b - 5/6
Simplifying this gives us:
1/6b - 5/6
Therefore, the answer is (a) 1/6b - 5/6.
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Based on her past experiences, a homeowner estimates that appliances lose 27% of their
resale value each year. If her estimate is accurate, how much will an appliance currently
valued at $1,128 be worth in 10 years?
Step-by-step explanation:
If the LOSE 27% per year, they RETAIN 100- 27 = 73% (.73 in decimal) per year
after ten years :
$ 1128 ( .73)^10 = $48.48
Answer:
$48.48
Step-by-step explanation:
Using compound depreciation
time
amount × percentage^
10
1128 × 0.73^ =48.477
.2. The International calls tariffs of Telkom are given in the following table.
Number of minutes
3
5
9
Y
Costs
R4.95
R8.25
X
R28.05
The following table lists Telkom's rates for international calls. Number minutes needed for [tex]x[/tex] to be [tex]17[/tex]and [tex]y[/tex] to be [tex]14.85[/tex].
Do numbers have any symbolic significance?Many numbers have deeper symbolic connotations in addition to their spiritual significance, and it is crucial to grasp these meanings in order to comprehend how they influence other cultures' perceptions of the physical world.
What may seeing 333 represent for you personally?According to Wilder, any sequence of consecutive threes is probably a sign of good fortune or a shift in your job, achievement, aspirations, or emphasis. According to Wilder, the number 333 is frequently a signal that you should have faith in your ability to make the next move.
Let[tex]y=k*b[/tex]
When [tex]x=3, y=4.95, x=5, y=8.25[/tex]
[tex]4.95=3k+b[/tex]
[tex]8.25=5k+b[/tex]
[tex]k=1.65[/tex]
[tex]b=0[/tex]
[tex]y=1.65x[/tex]
when [tex]x=9[/tex]
[tex]y=1.65*9 = 14.85[/tex]
when [tex]y=28.05[/tex]
[tex]x=y/1.65=28.05/1.65=17[/tex]
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The complete and the correct form of question is:
The International calls tariffs of Telkom are given in the following table:
Number of minutes 3 5 9 y
Cost R4.95 R8.25 X R28.05
Determine the cost of 9 minute call
PLEASE HELP ME!!!!!!!!!!
Reflect △ABC across the y-axis
PLEASE LOOK AT THE PICTURE!!!!!!!
A: (4,-2)
B: (1,-1)
C: (1,-4)
Hope this helps! Just graph it.
6 In the diagram below, BPCR is a rhombus. P is (0, 6), C is (6, t) and B is (2, 0). The lines PR. and BC bisect at Q, PR = 2BC and PR = 8√2. Find: (a) the value of t and the coordinates of R, (b) the equation of PR, (c) the area of the rhombus.
The value of t is equal to 4.
The equation of PR is y = -x + 6.
The area of the rhombus is equal to 32 square units.
How to determine the value of t and the coordinates of R?Since BPCR is a rhombus and all the side lengths of a rhombus are always equal in length, we would use the distance formula to determine the length of BP as follows:
Distance BP = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance BP = √[(0 - 2)² + (6 - 0)²]
Distance BP = √[4 + 36]
Distance BP = √40 units.
Also, side length BP is equal to side length PC:
√40 = √[(t - 6)² + (6 - 0)²]
√40 = √[(t - 6)² + 36]
40 = (t - 6)² + 36
(t - 6)² = 4
t - 6 = ±2
t = 6 ± 2
t = 8 or t = 4.
Therefore, C should be located at (6, 4).
Since Q is the midpoint PR and BC, we know that B is shifted 2 units right and 6 units down from P. Therefore, point R is represented by R(8, -2).
In order to determine the equation of PR, we would use the point-slope form:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 6 = \frac{(-2-6)}{(8 - 0)}(x - 0)[/tex]
y - 6 = -1(x)
y = -x + 6
In Mathematics, the area of a rhombus is calculated by using this formula:
Area = 1/2(d₁ × d₂)
Where:
d₁ and d₂ represent the diagonals of a rhombus.
PR = 2BC
8√2 = 2BC
BC = (8√2)/2
BC = 4√2
Area of rhombus = 1/2(PR × BC)
Area of rhombus = 1/2(8√2 × 4√2)
Area of rhombus = 1/2(64)
Area of rhombus = 32 square units.
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Calculate the area of the trapezoid, which is not drawn to scale.
Answer:
38 in²
Step-by-step explanation:
We can solve for the area of this trapezoid by using the area formula:
[tex]A = \dfrac{b_1 + b_2}{2} \cdot h[/tex]
First, we need to identify the trapezoid's bases ([tex]b_1[/tex] and [tex]b_2[/tex]). We know that the bases of a trapezoid are parallel. Using this information, we can identify 8 in and 11 in as the bases.
Next, we need to identify the height ([tex]h[/tex]). We know that the height of a trapezoid is the length from [tex]b_1[/tex] and [tex]b_2[/tex] that is perpendicular (at a right angle) to both of the bases. We can identify this as 4 in because we can see that it adjoins at a right angle to both of them.
Finally, we can plug these values into the area formula and solve for A.
[tex]A = \dfrac{8 + 11}{2} \cdot 4[/tex]
[tex]A = \dfrac{19}{2} \cdot 4[/tex]
[tex]A = \dfrac{76}{2}[/tex]
[tex]\boxed{A = 38 \text{ in}^2}[/tex]
Rodolfo has two checks that he needs to deposit into his checking account.
One check is for $108.93, and the second check is for $372.47. He wants to receive $75 cash back from his deposit. What is Rodolfo's net deposit?
Answer:
Rodolfo has two checks, one for $108.93 and the other for $372.47. Let's add the amounts of the checks to get the total amount of the deposit:
$108.93 + $372.47 = $481.40
Next, Rodolfo wants to receive $75 cash back from his deposit. We need to subtract $75 from the total amount of the deposit to get the net deposit:
$481.40 - $75 = $406.40
Therefore, Rodolfo's net deposit is $406.40.
Step-by-step explanation:
Answer:
Step-by-step explanation:
To find Rodolfo's net deposit, we need to add the values of his two checks and subtract the amount of cash he wants to receive back:
Net deposit = (Value of Check 1) + (Value of Check 2) - (Amount of Cash Back)
Net deposit = $108.93 + $372.47 - $75
Net deposit = $406.40 - $75
Net deposit = $331.40
Therefore, Rodolfo's net deposit is $331.40.
A golf course rents golf clubs for $10 plus $4 for each hour the golf clubs are rented. An expression for the total cost of renting the golf clubs for h hours is 10 + 4h.
Complete the table by finding the total cost of renting the golf clubs for h hours.
To complete the table, we can use the expression 10 + 4h to calculate the total cost of renting the golf clubs for different values of h.
Table below:h Total cost
1 14
2 18
3 22
4 26
5 30
For example, if the golf clubs are rented for 1 hour, the total cost is $14 (10 + 4(1) = 14). If they are rented for 2 hours, the total cost is $18 (10 + 4(2) = 18), and so on.
What is the expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented?The expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented is 10 + 4h.
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solve for x.
find m∠HJB
you'll get 50 points!!!
A bag of 100 marbles contains an equal amount of marbles that are blue, green, red, yellow, and orange. If one marble is pulled at random from the bag, the probability that it is a green marble is
Workout AG in the cuboid below. (3d trig)
The length of the diagonal AG = 7.56 cm.
Finding diagonal of cuboid:A cuboid is a three-dimensional shape that is bounded by six rectangular faces. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices.
To find the Length of the side AG, find the length of AC by using the Pythagorean formula. Now using the trigonometric ratios formulas find the length of AG.
Here we have a cuboid
Where
AD = 23 cm
DC = 18 cm
∠GAC = 75°
From the right angle triangle, ADC
=> AC² = AD² + DC² [ Using the Pythagorean formula ]
=> AC² = (23)² + (18)²
=> AC² = 529 + 324
=> AC = √853 = 29.20
From the right angle triangle, AGC
=> Cos B = AC/AG
=> Cos 75° = 29.20/AG
=> AG = Cos 75° (29.20)
=> AG = (0.26)(29.20)
=> AG = 7.56
Therefore
The length of the diagonal AG = 7.56 cm.
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I need help please!!!
The amount that would be in the account after 20 years would be $33,277.48.
The doubling time of the emissions would be 23.45 years
The total emissions will be higher in 2030 than 2010 by 100.96%
How to find the amount after years of investment ?To find the amount in the account after 20 years, we can use the formula:
A(t) = P(1 + r)^t
Take the 12th root of both sides:
(1 + r) = 2^(1/12)
Now find r:
r = 2^(1/12) - 1 ≈ 0.05946
Now we can find the amount in the account after 20 years with the investment of $10,000:
A(20) = 10000(1 + 0.05946)^20
A(20) = $33,277.48
How to find the doubling time ?To find the doubling time for emissions, we can use the formula:
Doubling time = ln(2) / ln(1 + r)
Doubling time = ln(2) / ln(1 + 0.03)
Doubling time = 23.45 years
To find how much higher total emissions will be in 2030 than in 2010, we can use the exponential growth formula:
E(t) = E₀(1 + r)^t
We want to find the ratio of emissions in 2030 to emissions in 2010:
E(20) / E(0) = (1 + 0.03)^20
E(20) / E(0) ≈ 2.0096
Higher emissions = E(20) / E(0) - 1
Higher emissions ≈ 1.0096
So, total emissions will be approximately 100.96% higher in 2030 than in 2010.
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Simplify each expression to a single term: 5.5.1 cos² 19⁰-sin² 19° = 5.5.2 cos² 19° + sin² 19⁰ = 5.5.3 2 cos² 50° -1 =.... 5.5.4 1-2 sin² 50° = ........ 5.5.5 6cos² 2 -3= orpress cos169
Answer:
Step-by-step explanation:
5.5.1 cos² 19⁰ - sin² 19° = cos² 19° - (1 - cos² 19°) = 2cos² 19° - 1
5.5.2 cos² 19° + sin² 19⁰ = 1
5.5.3 2 cos² 50° -1 = cos 100° - 1
5.5.4 1-2 sin² 50° = cos² 50°
5.5.5 6cos² 2 -3 = 6cos²(180°-11°) -3 = 6cos²11° -3 = 6cos²(360°-349°) -3 = 6cos²349° - 3
Note: cos(360°-x) = cos x and cos(180°-x) = -cos x, so we can write cos169° = cos(180°-11°) = -cos11°.
A cylindrical tank is lying horizontally on the ground.
Diameter - 20ft
Length - 22ft
Depth of water in tank is 6ft.
1 gallon = 231 cubic inches.
A). How many gallons of water are in the tank?
B). How many more gallons of water will it take to fill the tank?
Answer:
I don't know
Step-by-step explanation:
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(CLASSKICK) HELP ASAP!!!
Answer:
94.3
Step-by-step explanation:
You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"
ProportionThe diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.
The solution is found by multiplying both sides by 82:
(x/82)·82 = (115/100)·82
x = 94.3
EquationThe question can also be written as a statement:
"what" is 115% of 82
When written as an equation, "is" means "equals", and "of" means "times":
what = 115% × 82
Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...
x = 115/100 × 82 = 1.15 × 82
All that remains is to evaluate this expression.
x = 1.15 × 82 = 94.3
So, the answer to the question is ...
94.3 is 115% of 82.