starting value 16 increases by 50% with each teem
suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is pi/3. what is the length of the third side of the triangle
The length of the third side of the triangle will be 2.65 units.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:
a² + b² – 2ab cos(C) = c²
A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.
Then the length of the third side of the triangle will be
c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)
c² = 4 + 9 – 12 x (1/2)
c² = 13 – 6
c² = 7
c = √7
c = 2.65 units
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Verify the identity. Show your work. cos(α - β) - cos(α + β) = 2 sin α sin β
In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
The value of the 3 in the ten thousands place is 30,000, while the value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number.
Explanation:The value of the 3 in the ten thousands place in 33,294 is 30,000. The value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number. In this case, the 3 in the ten thousands place is ten times greater than the 3 in the thousands place.
In a certain class 40% of students are girls and 20% of the girls wear glasses what percent of the children in the class a girl who wear glasses?
The percentage of the children in the class who is a girl and wears glasses is 8%.
Given that:
Total students in the class = 100%
Percentage of students in the class who are girls = 40%
Percentage of girls who wear glasses = 20%
It is required to find the percentage of students in the class who are girls wearing glasses.
This can be found as:
P = 40% × 20%
= 0.4 × 0.2
= 0.08
Now 0.08 in terms of percentage is 0.08 × 100 = 8%.
Hence the percentage of girls who wear glasses is 8%.
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Will someone please do number 8 for me ?
I NEED HELP PLEASE??!!!???
when is a rectangle a square?
a) when its sides are parallel
b) when its angles are right angles
c) when its sides are congruent
d) when its angles are convex angles
A rectangle becomes a square when all of its sides are congruent, which is the defining characteristic that differentiates it from a rectangle. While rectangles do share other attributes such as parallel sides, right angles, and convex angles, these do not specifically define a square.
A rectangle becomes a square when all of its sides are congruent. This by definition means that all four sides of the shape are of equal length. While rectangles do have parallel sides and right angles, these characteristics alone do not suffice to differentiate a square from a rectangle, as rectangles also have these attributes. In the case of convex angles, both squares and rectangles have angles that are convex, so this also cannot be used to distinguish a square from a rectangle.
To specifically address the options provided:
a) when its sides are parallel: This is true for both rectangles and squares, but it doesn't make a rectangle a square.b) when its angles are right angles: Again, both shapes share this characteristic so it doesn't define a square specifically.c) when its sides are congruent: This is the defining characteristic of a square compared to a rectangle.d) when its angles are convex angles: Both rectangles and squares have convex angles, so this does not define a square.Therefore, the most accurate answer is (c) when its sides are congruent.
A circle has a diameter of 9 inches. What is the approximate ratio of the circumference of the circle to its diameter?
A) 22/7
B)7/22
C)1/2
D)2/1
what is the perimeter of a right trianglr whose hypotenuse is the line segment A(-6,4) B(2,-1)
The legs of a right triangle are 13 and 22 inches long. Needa says that the hypotenuse is 17.7 inches long and Monifa says that it is 25.6 inches long. Is either of them correct? Explain
lindsey earn $70 for working 5 hours. how much does she earn for working 12 lawns?
Answer $ 168
as per the question,
money earned for working 5 hours = 70
money earned for working 1 hour = 70/5= 14
money earned for working 12 hours = 12 * 14
money earned for working 12 hours = $168
What is the equation of this circle in general form?
x² + y² + 8x + 10y + 25 = 0
x2+y2−8x−10y+25=0
x2+y2−8x−10y+37=0
x² + y² + 8x + 10y + 37 = 0
Tis the actual answer :)
find the surface area
twice a number x is at most -24. 2x ≥ -24
The value of x should be equal to and greater than -12.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
twice a number x is at most -24.
So, the mathematical expression is
2x ≥ -24
Now, divide both side by 2
2x / 2 ≥ -24 /2
x ≥ -12
So, the value of x should be equal to and greater than -12.
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Genna can build a cabinet in 4 hours. Claude can build a cabinet in only 3 hours. Which of the following can be used to determine the amount of time it would take for Genna and Claude to build a cabinet together? (2 point
he circle shown below has AB and BC as its tangents: AB and BC are two tangents to a circle which intersect outside the circle at a point B. If the measure of arc AC is 160°, what is the measure of angle ABC? (1 point) 80° 40° 60° 20°
Answer:
m∠ABC=20°
Step-by-step explanation:
Consider quadrilateral ABCO. The sum of the measures of all interior angles in quadrilateral ABCO is equal to 360°.
Lines BA and BC are tangent to the circle, then the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,
m∠BCO=90°;m∠BAO=90°.The measure of the angle AOC is 160° (because the measure of arc AC is 160°). So,
m∠ABC+m∠BCO+m∠BAO+m∠AOC=360°,
m∠ABC=360°-(m∠BCO+m∠BAO+m∠AOC)=360°-(90°+90°+160°)=20°.
simplify the expression given below
By what percent will a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%?
40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, numerator is decreased by 30% and its denominator is decreased by 50%.
Let x/y be the original fraction.
Then, the new fraction is (x-30% of x)/(y-50% of y)
= 0.7x/0.5y
Now, difference = 0.7x/0.5y-x/y
= 0.7x/0.5y - 0.5x/0.5y
= 0.2x/0.5y
Percentage increase = 0.2x/0.5y ÷ x/y
= 0.2/0.5 ×100
= 40%
Therefore, 40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
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Dana and her 4 friends are going on a camping trip. Dana wants to see how much fruit she can share so everyone will get the same amount of fruit. There are 5 apples, 10 oranges, 5 strawberries and 10 grapes. How much will each person get?
George does not like the fact that his neighborhood makes it mandatory to pay a yearly fee to use the pool. He conducts a survey of all the neighborhood families to help support his case that the yearly fee should be voluntary. The survey asks questions about pool usage and financial statistics of the families. Is this a valid survey? Why or why not?
round the following number to the nearest hundredth which one of the numbers is in the hundreds place and does it go up or down I don't know which number is the hundredths place
The lines shown below are parallel. If the green line has a slope of -2, what is the slope of the red line?
Find equations for the tangent plane and the normal line at point upper p 0(3 comma 5 comma 0) on the surface negative 7 cosine left parenthesis pi x right parenthesis plus 3 x squared y plus 5 e superscript xz baseline plus yz equals 147.
if an object is shot with an initial velocity , vo, in feet per second(ft/s) the velocity, v, in ft/s is given by the formula v=v0 -32t, where t is time in seconds. find the initial velocity of an object if the velocity after 3 seconds is 31 ft/s
To find the initial velocity, we rearrange the given velocity equation to solve for the initial velocity, then substitute the given values. The initial velocity is found to be 127 ft/s.
Explanation:The given formula for velocity is v = v0 - 32t, where 'v' is the velocity at a certain time 't', and 'v0' is the initial velocity. In this case, we're given that v is 31 ft/s after 3 seconds. To find the initial velocity 'v0', you need to rearrange the equation to solve for 'v0'. This gives:
v0 = v + 32t
Substituting the given values into the rearranged equation gives:
v0 = 31ft/s + 32(3s)
This simplifies to:
v0 = 31ft/s + 96ft/s = 127ft/s
So the initial velocity of the object is 127 ft/s.
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Does the graph represent a function that has an inverse function?
A. Yes
B. No
Answer: A. Yes.
Step-by-step explanation:
To find out if the function represented in the graph has an inverse function, you must apply the Horizontal Line Test, which is used to know if a function is a One-to-one function.
A one-to-one function is that function where each x value has an unique y value.
Therefore, if in the Horizontal Line Test, the horizonal intersects the graph of the function at only and only one point, then the function has an inverse function.
As you can see in the graph attached, the horizontal lines intersect the function at only one point, therefore, you can conclude that it is a One-to-one function and it has an inverse function.
TRUE. The graph represents a function that has an inverse function because it passes the horizontal line test.
Explanation:The graph represents a function that has an inverse function if and only if each horizontal line crosses the graph at most once. This is known as the horizontal line test. If a function passes the horizontal line test, then it has an inverse function. If it fails the horizontal line test, then it does not have an inverse function.
In this case, we can see that the graph passes the horizontal line test because each horizontal line intersects the graph at most once. Therefore, the graph represents a function that has an inverse function.
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find the value of the combination
The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviation of 5.3 lbs. what is the probability that for (a random sample of) 100 passengers … the total luggage weight is less than 2,100 lbs?
Answer:
0.9987
Step-by-step explanation:
Given that X, The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviation of 5.3 lbs.
For a sample of size 100, we have
n=100
Hence std deviation of sample = [tex]\frac{SD}{\sqrt{n} } =0.53[/tex]
To find the probability that X>2100/100 lbs
=P(X<21[tex]\frac{21-19.4}{0.53} =3.019[/tex]) =P(Z<3.019)
=0.5+0.4987
0.9987
Factorise x^2 + 3x -40
One number is 4 less than twice a second number. find a pair of such numbers so that their product is as small as possible.
Answer:
Numbers are -2 and 1.
Step-by-step explanation:
Let x be the second number,
⇒ First number = 4 less than twice a second number
= 2 × Second number - 4
= 2x - 4
Thus, the product of first and second number is,
[tex]f(x) = x(2x-4)[/tex]
[tex]\implies f(x) = 2x^2 - 4x[/tex]
Differentiating with respect to x,
[tex]f'(x) = 4x -4[/tex]
Again differentiating with respect to x,
[tex]f''(x) = 4[/tex]
Now, for maximum or minimum,
[tex]f'(x)=0[/tex]
[tex]\implies 4x - 4 = 0\implies 4x = 4\implies x = 1[/tex]
Since, for x = 1, f''(x) = Positive,
Therefore, the function f(x) is minimum for x = 1,
⇒ The product is smallest for x = 1,
Hence, the second number = x = 1,
And, first number = 2x - 4 = 2 - 4 = -2