Answer:
21
Step-by-step explanation:
a,a+2,..
4(a+2)=29+3a
4a+8=29+3a
4a-3a=29-8
a=21
What is the measure of AC?
Enter your answer in the box.
°
Image shows a circle with angle A B C inscribed in a circle. Angle B measures 4 x minus 5.5 degrees. Arc A C measures 3 x plus 9 degrees.
Answer:
In the circle, the measure of the arc AC is 21°.
Step-by-step explanation:
Concept: We can use the Inscribed Angle theorem to get the measure of AC.
Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.
Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
3x - 1.5 = 0.5(3x + 9)
6x - 3 = 3x + 9
3x = 12
x = 4
Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,
intercepted arc AC is 21°.
Hence the intercepted arc AC is 21°.
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6. Given that the term independent of x in the binomial expansion of (x²+p/x)^6 is 240,
(a) find the value of the positive constant p
By the binomial theorem,
[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]
where
[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]
is the so-called binomial coefficient.
The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have
[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]
but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]
Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
please help
Step-by-step explanation:
via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.
so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.
Andrea has 3 tiles. One is a regular octagon, one is a regular pentagon and one is a regular hexagon. Andrea thinks the 3 tiles will fit together perfectly, as shown in the diagram. Show calculations to prove that she is wrong.
From calculations, we can say that the given tiles will not fit together perfectly.
How to find the sum of interior angles of a Polygon?If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
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I need help lol xoxoxo
Estimate the solution to the following system of equations by graphing.
Type the expression that results from the following series of
steps:
Start with n, divide by m, then subtract p.
Answer:
(n/m) - p
Step-by-step explanation:
Image attached
MATH!!! find the surface area of the prism
the cost of 10 water bottles is $55. find the unit cost of the water bottle
Answer:
$5.50
Step-by-step explanation:
For one water bottle you divide the 55 dollars by 10
55/10= 5.5
Answer:
$5.50
Step-by-step explanation:
We must divide to solve so lets do that now :)
55/10 = 5.50
Each bottle will cost 5 dollars and 50 cents :)
Have an amazing day!!
Please rate and mark brainliest!!
What term does the formula sin A/a = sin B/b represent?
Answer:
Law of sines
Explanation:
The law of sines states that the ratios of the sines of angles and their opposite sides are equal for all angles inside a triangle.
Step-by-step explanation:
hope you can understand
The graph below shows the solution to which system of inequalities?
Answer:
C
Step-by-step explanation:
The horizontal line, y=2, is solid and shaded above, so it represents
[tex]y \geqslant 2[/tex]
The slanted line, y=x is dashed and shaded below, so it represents y<x.
Answer
Answer is A
Step-by-step explanation:
Quadratic Equation Question
Answer: 0.68 or 13.92
Step-by-step explanation:
If the height is 47 meters, then the height, h, is equal to 47.
[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]
Using the quadratic formula,
[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]
ignore the answer i clicked on, i did not mean to click it
Answer:
20√2Step-by-step explanation:
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
Diagonal = 5 * 2 = 10
P = 2√2 * 10
P = 20√2
On day 1, Perry shipped packages and tracked their weight to the nearest kilogram. The packages weighed 1, 8, 1, 12, 1, 11, 7, and 6 kilograms.
On day 2, Perry shipped 12 kilograms more weight than he did on day 1 while shipping the same number of packages.
What is the increase in the mean kilograms per package for the second day compared to the first?
Enter your answer in the box.
Answer:
1.5kg
Step-by-step explanation:
The mean for the packages on day 1 will be:
= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8
= 47/8
= 5.875
The mean for day 2 will be:
= (47 + 12)/8
= 59/8
= 7.375
The increase in mean:
= 7.375 - 5.875
= 1.5
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.
How to depict the information?From the information given about the probability, the goal here is to design a simulation for this situation.
In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.
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Please help me i would really appreciate it, worth 11 points
The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.
How to Evaluate a Function?We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:
h(t) = 0 (height of the ground is 0)t = seconds the waste takes to height the groundInitial height = 400 feetPlug in the values into the equation of the function
0 = -16t² + 400
Solve for t
0 - 400 = -16t²
-400 = -16t²
-400/-16 = t²
400/16 = t²
√(400/16) = t
20/4 = t
5 = t
t = 5
The number of seconds it takes is: 5 seconds.
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A man bought a car for Gh55,000.00 and sold it for Gh65,000.00. Find the percentage gain.
Answer:
18.18%
Step-by-step explanation:
(65000-55000)/55000×100
A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing
equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the
two pieces of equipment?
Answer:
First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
Step-by-step explanation:
This question deals with Slope of a line.
Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet
Thus, slope = 6/4 = 3/2 ≈ 1.5
For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet
Thus, slope= 10/6 = 5/3 ≈ 1.66
Thus,
Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3
Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
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Identify the height of a triangle in which b=12 m and A=(18x−6) m^2. SHOW YOUR WORK!!!
Answer:
[tex]3x-1[/tex]
Step-by-step explanation:
The formula to find the area of a triangle:
[tex]A = \frac{bh}{2}[/tex]
Here, [tex]A[/tex] is the area, [tex]b[/tex] is the base and [tex]h[/tex] is the height.
However, we are looking for height, so let's rearrange the equation for [tex]h[/tex]:
[tex]A = \frac{bh}{2}\\2A = bh\\h = \frac{2A}{b}[/tex]
Now we know the formula to find the height, let's do so:
[tex]h = \frac{2(18x-6)}{12}\\\\h = \frac{36x-12}{12}\\\\h = 3x - 1[/tex]
Therefore, our final answer is [tex]3x-1[/tex].
Use the law of cosines to find each missing side. Round to the nearest tenth
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
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in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning
The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.
What is the similarity law?It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Triangle ABC ~ EDC
Angle ACD = Angle BCE = 90 degree (vertically opposite angle)
Angle ACB = Angle DCE = 90 degree (vertically opposite angle)
BE ║ AD
Angle EBC = Angle CDA = 40 degree (alternative angles)
Triangle ABC ~ Triangle EDC
Angle ABC = Angle CDE
Angle BAC = Angle DEC
∴ AB ║ DE
Triangle ACD ~ Triangle ECB
Angle EBC = Angle CDA and
Angle BEC = Angle CAD
∴ Triangle ACD ~ Triangle ECB
Angle A + Angle E = 180 degree
∠x + 50 + 50 + ∠x = 180
∠x = 40
Angle CAD = 40 degree
We know,
Angle A = Angle E = Angle B = Angle D = 90 degree
So ABCD is a square
AB = ED = 12
AD = AB = BE = ED = 12
Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.
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Write the rationalized expression of:
Answer:
A
Step-by-step explanation:
First, simplify the numerator:
[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]
Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.
[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]
Finally, evaluate the denominator by multiplying them together.
[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]
Simplify:
[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]
And done! :)
im always having problems with this i need someone to explain please
For every meter there are 3.281 feet. The perimeter of the yard is 188ft. Divide 188 by 3.281 and you get 57.3 (rounded to 1dp). Round that up to the nearest meter and you get 58. So, Mr Smith needs 58 meters of fencing for his yard.
What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
Which inequality is shown in this graph?
OA. ys-3x+3
OB. y2-3x+3
OC. ys 3x+3
OD. y23x+3
Answer:
A
Step-by-step explanation:
The line is shaded below, so we can eliminate B and D.
Also, the line has negative slope, so this eliminates C.
The inequality of the graph is y ≤ -3x + 3.
The correct option is A.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
The inequality graph has two points on the line (0, 2) and (2, -3).
And the shaded region of the graph is left to the line made by points (0, 2) and (2, -3).
The line passing through the points (0,2) and (2,-3) can be written in a slope-intercept form as:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line is given by:
m = (y2 - y1) / (x2 - x1) = (-3 - 2) / (2 - 0) = -5/2
The y-intercept can be found by substituting the coordinates of either point into the equation:
y = mx + b
2 = (-5/2)(0) + b
b = 2
So the equation of the line is:
y = (-5/2)x + 2
The shaded region of the graph is to the left of this line. Since the line has a negative slope, any point below the line will satisfy the inequality y ≤ -3x + 3. Therefore, the correct answer is A.
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What is the answer to the question?
Answer:
See attached file for answers and explanation.
Step-by-step explanation:
See attached image.
Find the derivative of y = x^3/2.
Find the derivative of y = 1/x^3.
Find the derivative of y = 1/√x.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
properties to be used here :
[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]
[tex]\large \textsf{Question : 1} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\large \textsf{Question : 2} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\large \textsf{Question : 3} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
On Friday, a local hamburger shop sold a combined total 312 of hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
r,u,t,s are positive
RXS=15
SXT=3
TXV=7
RXV=??
Answer:
35
Step-by-step explanation:
R × S = 15 could be 5 × 3 = 15, 3 × 5 = 15
15 × 1 = 15, 1 × 15 = 15
S ×T =3 From our previous step we can see that S could be 1 or 3 or 5 or 15.
Given that S×T =3, will make sense that S is 1 or 3
If S is 1 then T is 3 and if S is 3 then T is 1, so multiplied will give 3.
T×V=7 From previous step we see that T could be 1 or 3.
Since T×V = 7 it will make sense that T is 1, and therefore V is 7.
T ×V = 7, S ×T =3, R × S = 15, R × V = ??
1 × 7 = 7, S ×1 = 3, R × 3 = 15, 5 × 7 = ??
3 ×1 = 3, 5 × 3 = 15, 5 × 7 = 35
Line I is a perpendicular bisector
Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.
What is the perpendicular bisector theorem?According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.
Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.
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