Answer:
Step-by-step explanation:
122121
How do you find the sine cosine and tangent of an acute angle?
The sine , cosine and tangent of an acute angle can be find by using:
Sin θ = Opposite side/HypotenuseCos θ = Adjacent/HypotenuseTan θ = Opposite/AdjacentAcute Angle:
Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.
Sine of an Acute Angle :
The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.
Cosine:
Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.
Tangent:
The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).
So the formula for tan x is:
tan x = sin x/cos x
tan x = opposite side/adjacent side
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what is the answer 6u+2(u-8) - 4
Answer:
8u - 20
Step-by-step explanation:
What are 5 ways to solve problems?
The 5 ways to solve problems are identifying the problem, generating different solutions, choosing one solution, implementing the chosen solution and evaluating the result.
A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.
There are 5 different steps to solving a problem
Step 1. Identify the Problem
Step 2. Generate potential solutions
Step 3. Choose one solution
Step 4. Implement the solution you’ve chosen
Step 5. Evaluate results
Sometimes it is required to start the process entirely over. To make the problem-solving process easier, it’s best to facilitate the solution as much as possible. Try to concentrate on the solution instead of the problem. Finally, be in the correct psyche to want to change. This contains having the right mindset language, both are positive and open-minded. With sufficient practice, any problem can be solved.
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I really need help on this. 22 points if you get it!!
The value of angle x in the triangle shown is 78°
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
A triangle is a polygon that has three sides and three angles. The sum of angles in a triangle is 180 degrees. Types of triangles are isosceles, scalene, equilateral
In the large triangle let the missing angle by y, hence:
y + 87 + 36 = 180 (sum of angle in a triangle)
y = 57°
In the triangle containing the angle 45, let the missing angle be z, hence:
z + y + 45 = 180 (angle in a triangle)
z + 57 + 45 = 180
z = 78°
x = z (corresponding angles are equal)
x = 78°
The value of x is 78°
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How do you multiply FG?
FG cannot be multiplied because it is not a numerical value.
Multiplication is a mathematical operation that involves multiplying two numerical values together to produce a single numerical result. In order for multiplication to be possible, both values must be numerical values. FG is not a numerical value, which means that it cannot be multiplied. In order for FG to be multiplied, it would need to be replaced with a numerical value, such as a number or an expression that can be evaluated to a number. Without a numerical value, multiplication is not possible. Multiplying numerical values is done by taking the product of the two values, meaning that the result of the multiplication is the sum of each value multiplied by itself the number of times the other value is. For example, if you were to multiply 3 and 4, the result would be 12 because 3 multiplied by itself 4 times is 12, and 4 multiplied by itself 3 times is also 12. Without numerical values, this operation cannot be performed.
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last month greg arrived late to work 3 out of 21 days his boss used this information to determine the probability of greg being late again. which pair of probabilites is correct
The probability of Greg being late again, along with the type of probability, is given as follows:
1/7, experimental probability.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
In the context of this problem, the outcomes are given as follows:
Desired: Greg being late, 3 times.Total outcomes: 21 times that Greg went to work.The probability of Greg being late is then calculated as follows:
3/21 = 1/7.
Which is an experimental probability, as the number of outcomes are taken from previous "experiments".
The other type of probability is theoretical, for example, a fair coin has a 50% chance of falling heads and 50% change of falling tails.
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Random students from a high school were surveyed to determine if there was enough interest to start a Ukulele Club.
Identify the population:
A. Students of high schools across the country
B. Students of the high school
C. Citizens of the city
D. Every citizen of the country
Answer:
b
Step-by-step explanation:
Answer:
B. Students of the high school
Step-by-step explanation:
It is high school because you just want to ask that area.
The pitchers for the home team had 12 strikeouts for 32 batters, while the pitchers for the visiting team had 15 strikeouts for 35 batters. Which pitching team had a greater fraction of strikeouts.(Hint: Just make the 12 for 32 and 15 for 35 into fractions and see which is greater or less than.)
Answer:
2958843/5 5/1000775747373838388484737372737375823The domain of y = √√√x-5-1 is
DONE
3 of 8
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10
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6
5
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The function domain is X≥5 Or in interval notation [5, ∞)
What is Domain definition?The domain of a function is the set of input or argument values for which the function is real and definedThe domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limitedIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the functionFind non-negative values for radicals x≥5solve x-5≥0:x≥5 function domain is X≥5 Or in interval notation [5, ∞)To learn more about Domain definition refers to:
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the scatter plot shows a regression line of units demanded and price. if the demand is for 35 units what would be the predicted price per unit?
A)$20
B)$23
C)$27
D)$32
According to the following graph, we have identified that if the demand is for 35 units then the predicted price per unit is $27.
The term graph in math is defined as pictorial representation of algebraic equation.
Here we have given the following graph and here we also know that the scatter plot shows a regression line of units demanded and price.
Here we need to know the definition of regression line, which means the relationship between two variables. And it is applied in scenarios where the change in the value of the independent variable causes changes in the value of the dependent variable.
Based on these definition, here we have the relationship between the units demanded and the price of those units.
Now, by looking into the given graph, we have identified that if the demand is for 35 units, then the units price is $27.
Therefore, option (c) is correct.
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HELPPP. I need help finding this answer
Answer:Don't know
Step-by-step explanation:
ESSENTIAL QUESTION CHECK-IN
17. Tell how you can determine whether a number is a solution of an
equation.
324 Unit 4
Answer:
Step-by-step explanation:
1. Substitute the number for the variable in the equation.
Circles centered at $A$ and $B$ each have radius 2, as shown. Point $O$ is the midpoint of $\overline{AB}$, and $OA
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers.
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Please help ASAP this is for a final test
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer: I'm sorry bro i don't know
Step-by-step explanation:
The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is 132 centimeters, find the value of the shortest of the four side lengths.
The value of the shortest of the four side lengths of the quadrilateral is 30 cm
What is the length of the shortest side of the quadrilateral?The perimeter of a quadrilateral is the sum of all the sides.
Perimeter of the Quadrilateral = 132 centimeters
Let
The shortest side = x
Since, the sides are consecutive even integers;
Second side = (x + 2)
Third side = (x + 4)
Fourth side = (x + 6)
Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side
132 = x + (x + 2) + (x + 4) + (x + 6)
132 = x + x + 2 + x + 4 + x + 6
132 = 4x + 12
132 - 12 = 4x
120 = 4x
divide both sides by 4
x = 120/4
x = 30 centimeters
Therefore,
Second side = (x + 2)
= 30 + 2
= 32 cm
Third side = (x + 4)
= 30 + 4
= 34 cm
Fourth side = (x + 6)
= 30 + 6
=36 cm
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Find the greatest common factor of $144$ and $405$.
Answer:The answer to your question is 9
Condition A a recangle with four right angles condition B: a square with one side measuring 5 inches conddion C: a rhombus with one angle measuring 43 condition D: a parallelogram with one angle measuring 32 condition E a parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches condition F: a rectangle with adjacent sides measuring 4 inches and 3 inches One Quadrilateral Many Quadrilaterals
The conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.
What is a quadrilateral?
A quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. Quadrilaterals always have a total internal angle of 360 degrees.
Given,
condition A : a rectangle with four right angles
condition B : a square with one side measuring 5 inches
condition C : a rhombus with one angle measuring 43°
condition D : a parallelogram with one angle measuring 32°
condition E : a parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches
condition F : a rectangle with adjacent sides measuring 4 inches and 3 inches.
Now we are asked to match the above conditions to one quadrilateral and many quadrilaterals groups according to the number of quadrilaterals that can be constructed using the given condition.
Condition A : Many Quadrilaterals
All the rectangles have four right angles in them. So many rectangles of different lengths can be formed.
Condition B : One Quadrilateral
The defining factor that make a square unique is the length of its side. All the sides of the square also has equal length. So only one square of 5 inches side can be made.
Condition C: Many Quadrilaterals
For a rhombus the opposite angles are equal and the sum of angles should be 360°. Even though the angles are fixed, this rhombus can have any side length.
Condition D: Many Quadrilaterals
As discussed for rhombus, even though the angles of the parallelogram is fixed, there can be many sides lengths.
Condition E: One Quadrilateral
In this case, side length as well as the angle of the parallelogram is given. So there can be only one parallelogram.
Condition F:One Quadrilateral
The side lengths are what make a rectangle one of its kind. So one one rectangle can be formed with lengths 4 inches and 3 inches.
Therefore conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.
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Please help!!! Very confused on my homework.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!
Step-by-step explanation:
we need to use both equations for the volumes.
the only variables in them are r1 and r2.
when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.
and then we can easily transform the equation into "r1 = ..." or "r2 = ..."
and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.
a.
the goal here is an equation in the form
"r1 = ..."
that means r1 is a function of r2.
36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =
= 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³
r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)
b.
the goal here is
"r2 = ..."
again
36×pi×r1² = 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
3×36 × r1² = 2 × r2³
3×18 × r1² = r2³
54 × r1² = r2³
[tex]r2 = \sqrt[3]{54 \times {r1}^{2} } = 3 \times \sqrt[3]{2 \times {r1}^{2} } [/tex]
c.
r2 is doubled.
so, we have to go back to our equation of a.
r1 = sqrt(1/54 × r2³).
when r2 is doubled, we get
r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =
= sqrt(8) × sqrt(1/54 × r2³)
so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.
How do you write 4 7/8 as a decimal
Answer:
4.88
Step-by-step explanation:
Turn 4 7/8 as an improper fraction Divide The FractionDone!Hops This Helps!
To convert 4 7/8 into a decimal, we first need to turn the mixed number into an improper fraction.
In order to turn the mixed number into an improper fraction, we need to multiply the whole number by the denominator and add it up with the numerator.
[tex]4\dfrac{7}{8}[/tex]
[tex]4\times8=32+7=39[/tex]
Now, put that sum over the denominator:
[tex]\dfrac{39}{8}[/tex] (improper)
Now, to turn the improper fraction into a decimal, we need to divide the numerator by the denominator:
[tex]39\div8[/tex]
[tex]=\fbox{4.875}[/tex] (final answer)
3 pounds of peanuts for 7.50. how much is one pound
Answer: Ok to solve this question you would have to do $7.50 divided by
3 and your answer should come out to be $2.5 or $2.50 per each pound.
Step-by-step explanation:
$7.50 divided by 3 = 2.5
and with money if you get a $2.5 it would be $2.50 because you have to add the zero to the end of it.
4x(3 +5) Please answer :(
Answer: 32x
Step-by-step explanation:
4x (3 + 5)
add 3 and
⇒ 4x (8)
⇒ 32x answer .
hope that helps...
Find the length of the third side. If necessary, round to the nearest tenth
Answer:
6.3
Step-by-step explanation:
This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C. A and B equal the legs, or the shorter sides.) So once you plug in the values, your equation should look like this:
3² + b² = 7²
Square each side, or in other words multiply it by itself.
9 + b² = 49
Subtract 9 from both sides.
b² = 40
Take the square root of 40 and your done!
b = 6.3
I hope this helped you! :)
A single-engine plane can travel up to 140 miles per hour. The total number of miles m is represented by the function m = 140h, where h is the number of hours traveled. Determine appropriate input values for this situation.
Answer: The input values for this function are the number of hours traveled, represented by the variable h. Therefore, appropriate input values for this function would be any positive number representing a number of hours traveled.
For example, some appropriate input values could be:
h = 1: This represents 1 hour of travel, or a total distance of 140 miles.
h = 2: This represents 2 hours of travel, or a total distance of 280 miles.
h = 3.5: This represents 3.5 hours of travel, or a total distance of 490 miles.
Note that the input values do not have to be whole numbers, they can be any positive number representing a number of hours traveled.
Step-by-step explanation:
Is 2025 a perfect square Yes or no?
EXPLANATION
2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.
Simplify the expression please!
Using the provided expression and the law of indices, The power get subtracted in division, The answer is [tex]6^{22}[/tex] .
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.
What do you mean by law of indices?The laws of indices, also known as the laws of exponents, are a set of rules that govern how exponents (or indices) are used in mathematical operations. These laws include:
a^m * a^n = a^(m+n) (product of powers)(a^m)^n = a^(m*n) (power of a power)a^m / a^n = a^(m-n) (quotient of powers)(a^m)^(-n) = a^(-m*n) (power of a reciprocal)These laws allow us to simplify expressions with exponents and make it easier to perform calculations involving them.
[tex]= \frac {6^{15}}{6^{-7}}\\= 6^{15-(-7)}\\= 6^{15+7}\\=6^{22}[/tex]
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What is the solution of 2x^2 3x 5 0?
Answer: The answer is 10x2
Step-by-step explanation:
if logx 27 +logy 4 =5 and log x 27 -logy 4=1 find x and y
Answer:
[tex](x,y)\rightarrow(3,2)[/tex]
Step-by-step explanation:
I assume you mean [tex]\log_x(27)+\log_y(4)=5[/tex] and [tex]\log_x(27)-\log_y(4)=1[/tex]:
[tex]\biggr(\log_x(27)+\log_y(4)\biggr)-\biggr(\log_x(27)-\log_y(4)\biggr)=5-1[/tex]
[tex]2\log_y(4)=4\\\log_y(4)=2\\4=y^2\\2=y[/tex]
[tex]\log_x(27)+\log_y(4)=5\\\log_x(27)+\log_2(4)=5\\\log_x(27)+2=5\\\log_x(27)=3\\27=x^3\\3=x[/tex]
What is 2(−2x+1)−5x+2= -23
Answer:
Step-by-step explanation:
To solve this equation, you will need to manipulate the equation in order to isolate the variable x on one side of the equation. Here is one way you could solve this equation:
Begin by distributing the 2 on the left side of the equation: 2(-2x+1) = -46 + 2x.
Next, distribute the -5 on the right side of the equation: 2(-2x+1) = -23 - 5x.
Combine like terms on the right side of the equation: 2(-2x+1) = -5x - 23.
Combine like terms on the left side of the equation: -4x + 2 = -5x - 23.
Add 4x to both sides of the equation to isolate the variable on one side: 2 = -x - 23.
Add 23 to both sides of the equation: 25 = -x.
Finally, divide both sides of the equation by -1 to solve for x: x = -25.
Therefore, the solution to the equation is x = -25.
Answer:
x=3
Step-by-step explanation:
2(−2x+1)−5x+2= -23
Distribute
-4x+2-5x+2=-23
Combine like terms
-9x+4=-23
Subtract both sides by 4
-9x=-27
Divide both sides by -9
x=3
Hope this helps :)
6) The area of a triangle is A = bh-2. If the base (b) is H untis and the
height (h) Is 7 units, what is the area of the triangle?
I
Answer:
The area of a triangle can be calculated using the formula A = 1/2 * b * h, where b is the base and h is the height of the triangle. In this case, if the base of the triangle is H units and the height is 7 units, the area of the triangle would be A = 1/2 * H * 7 = 3.5 * H.
Step-by-step explanation:
How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together
On solving the provided question, we can say that the permutation will bw , N = (4!)(5!)(3!)(3!)= 103,680
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
we can put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together will be , N = (4!)(5!)(3!)(3!)= 103,680
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