5. in the following figure, GE= r.
where ris the radius of the circle.
a) What is the nature of the triangle GEO? Justify your answer.
b) By calculating SEG in two different ways. using ares of the
Answer + Step-by-step explanation:
a) GE = r = GM
Then GEO is an isosceles triangle
b) since GEO is an isosceles triangle then :
m∠SEG = m∠GOM = measure of the arc GM (mGM) (result 1)
On the other hand :
m∠SEG = m∠SEG = (1/2)×(mAS - mGM) (it’s a formula) (result 2)
Now ,we equate (result 1) and (result 2) :
m∠SEG = mGM
m∠SEG = (1/2)×(mAS - mGM)
Then
mGM = (1/2)×(mAS - mGM)
c) mGM = (1/2)×(mAS - mGM)
⇔ 2mGM = mAS - mGM
⇔ 3mGM = mAS
⇔ 3m∠SEA = m∠SOA
Remember:
mGM = m∠GOM = m∠SEA
Which THREE statements would produce the truth value F when pis true and q is false?
The THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p
How to determine the statements with a false truth value?To do this, we simply analyze each option
The given parameters are:
p = true
q = false
(a) p → q
This means that:
If p then q
So, we have:
If true then false
The above statement would return false.
(b) ¬ p ∧ ¬ q
This means that:
If not p and not q
So, we have:
If not true and not false
i.e.
If false and true
The above statement would return false.
(c) p → ¬ q
This means that:
If p then not q
So, we have:
If true then not false
i.e.
If true then true
The above statement would return true.
(d) q ∨ ¬ p
This means that:
If q and not p
So, we have:
If false and not true
i.e.
If false and false
The above statement would return false.
Hence, the THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p
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A scientist is working with 12 meters of gold wire. How long is the wire in millimeters?
Answer:
12 meters = 12000 mmStep-by-step explanation:
A scientist is working with 12 meters of gold wire. How long is the wire in millimeters?
12 meters = 12000 mm
(1m = 1000 mm)
12 * 1000 = 12000
PLEASE HELP WILL GIVE BRAINLEST! What is the amplitude of the function graphed below?
Answer:
The amplitude is the highest point that the curve reached
Which is in your case = 2
Solve for x.
144°
18 degrees
30 degrees
48 degrees
120 degrees
Answer:
x = 18 °Step-by-step explanation:
you have a rotation angle of 360 °, take out the known values (360 ° -90 ° -144 ° = 126), 144 ° is part of a flat angle of 180 °, from 180 ° remove 144 and you have 36 °, they are opposite angles therefore the same. therefore 360 - 144 - 90 - 36 - 36 = 54.
54 is 3x, so x = 18 ° (54 : 3 = 18)
From 1984 to 1995 the winning scores for a golf tournament were 275,279,279,276,278,277,280,282,284and 270 Find the mean of the data is
Answer: The mean of the data is 278.
Step-by-step explanation:
To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.
275+279+279+276+278+277+280+282+284+270=2780
2780/10=278
Find the errors and solve the problem correctly!
Thanks
The sequence converges to 5 as n goes to ∞. We can prove this rigorously:
The claim is that, for [tex]n\in\Bbb N[/tex],
[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = 5[/tex]
By definition of the limit, this means for any ε > 0, there exists some N such that for any n larger than N, we have
[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| < \varepsilon[/tex]
In order to ensure this inequality, we work backwards to find N in terms of ε :
[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| = \left| \dfrac{5n-1 - 5(n+1)}{n+1} \right| = \dfrac4{|n+1|} < \varepsilon[/tex]
n is a natural number, so n + 1 > 0 and |n + 1| = n + 1. Then
[tex]\dfrac4{n+1} < \varepsilon \implies \dfrac{n+1}4 > \dfrac1\varepsilon \implies n+1 > \dfrac4\varepsilon \implies n > \dfrac4\varepsilon - 1[/tex]
Let N be the smallest natural number greater than or equal to 4/ε - 1, i.e.
[tex]N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]
Then the proof follows: suppose
[tex]n \ge N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]
Then
[tex]n \ge \left\lceil\dfrac4\varepsilon - 1\right\rceil \implies n > \dfrac4\varepsilon - 1 \\\\ \implies n+1 > \dfrac4\varepsilon \\\\ \implies \dfrac4{n+1} < \varepsilon \\\\\implies \left|\dfrac{5n-1}{n+1}-5\right| < \varepsilon[/tex]
as required.
Or we can avoid the rigor and use some facts we know about limits:
[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = \lim_{n\to\infty} \frac{5-\frac1n}{1+\frac1n} = 5[/tex]
since 1/n converges to 0 as n goes to ∞.
help with practice problem
Answer:
-5<x<-3
Step-by-step explanation:
Hope this helps! ;-)
GIVING BRAINLIEST!!!!!
Answer:
7x+2y=18
The first one
Step-by-step explanation:
The equation to be perpendicular switches they numbers before the x and y. Also plugging into a graphing calculator like desmos will show you
that
What is the volume of a cone with a height of 10.5 inches and a radius of 8 inches? cone v = 1 3 bh 1. rewrite the formula for the base area: v = 1 3 πr2h 2. substitute the values into the formula: v = 1 3 π(82)(10.5) 3.evaluate the power: v = 1 3 π(64)(10.5) 4.simplify using multiplication: v = 1 3 π(672) the cone has a volume of pi inches cubed.
The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³
What is the Volume of a Cone?Volume = 1/3πr²h
Given the parameters:
Height (h) = 10.5 in.Radius (r) = 8 in.Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)
Volume of the cone = 1/3π(64)(10.5)
Volume of the cone = 703.7 in.³
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Answer:
224Pi inches cubed
Step-by-step explanation:
Match the attributes to each three-dimensional shape that has the cross-section described.
Only consider cross-sections with whole number dimensions parallel to a side of one of the prisms or the base of the pyramid.
Quadrilateral A:
area of
16 square inches
Quadrilateral B:
perimeter of
24 inches
Quadrilateral C:
perimeter of
16 inches
The attributes to each three-dimensional shape that has the cross-section is 4,16 and 4.
What is a quadrilateral and parallelogram?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given;
Quadrilateral A: area of 16 square inches
Quadrilateral B: perimeter of 24 inches
Quadrilateral C: perimeter of 16 inches
Now,
Quadrilateral A:
a^2=16
a=4
Quadrilateral B;
4a=24
a=6
Quadrilateral C:
4a=16
a=4
Therefore, the answers of quadrilaterals will be 4,6 and 4.
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Luke bought 256 ounces of strawberries. he divided them evenly between 8 different pies.
Answer:
2 pounds.
Step-by-step explanation:
We have been given that Luke bought 256 ounces of strawberries. He divided them evenly between 8 different pies. We are asked to find the pounds of strawberries that Luke put on each pie.
First of all, we will convert 256 ounces into pounds.
We know that 1 pound equals 16 ounces. To convert 256 ounces into pounds, we need to divide 256 by 16.
[tex]256[/tex] [tex]ounces=\frac{256}{16}[/tex] [tex]pounds=16[/tex] [tex]pounds[/tex]
Now we will divide 16 pounds by 8 to find number of strawberries put on each pie.
[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=\frac{16}{8}[/tex]
[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=2[/tex]
Therefore, Luke put 2 pounds strawberries on each pie.
factor by grouping
NEED HELP ASAP
# after letters are the exponent
1: 28v+16v2-21v-12
2: 49x3-35x2+56x-40
3: 24r3-64r2-21r+56
Answer and step-by-step explanation:
[tex]28v^3 +16v^2-21v-12 =[/tex] collecting [tex]4v^2[/tex] in the first two terms and [tex]-3[/tex] in the last two:
[tex]4v^2(7v+4)-3(7v+4) =[/tex] collecting the bracket
[tex](7v+4)(4v^2-3)[/tex]
Bonus stage: if you are factoring over the real numbers and not over the rational, the second brackets is a difference of squares. Else, you stop here.
[tex](7v+4)(2v+\sqrt3)(2v-\sqrt3)[/tex]
NEXT!
[tex]49x^3-35x^2+56x-40=[/tex]As before, [tex]7x^2[/tex]in the first two, and [tex]8[/tex] in the last two:
[tex]7x^2(7x-5)-8(7x-5)[/tex] collecting the bracket again
[tex](7x-5)(7x^2-8) =[/tex]again, bonus step
[tex](7x-5)(\sqrt7 x +2\sqrt2) (\sqrt7x-2\sqrt2)[/tex]
FINALLY!
[tex]24r^3-64r^2-21r+56 =\\8r^2(3r-8) -7(3r-8)=\\(3r-8)(8r^2-7) =[/tex]Again, bonus step
[tex](3r-8)(2\sqrt2r+\sqrt7)(2\sqrt2r-\sqrt7)[/tex]
Since usually most courses talk about factorization of polynomials BEFORE talking about real numbers, I would stop at the third stage, skipping the fourth.
PLEASE HELP!!! 25 POINTS!!
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box.
Can somebody help me with this? Please and Thank you
[tex]\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x[/tex]
Solve the simultanious equations 2x+3y=13 4x-y=-2
6. The three side lengths of a triangle are given. Which triangle is a right triangle?
A. Triangle 1: 13, 6, 7
B. Triangle 2: 7, 8, 13
C. Triangle 3: 10, 11, 12
D. Triangle 4: 10, 9,8
Which summation formula represents the series below?
1 + 2 + 6 + 24
Answer:
First one is the answer of the question u asked
Answer:
Option a: ∑⁵(n−1)! is the correct answer.
n=²
Step-by-step explanation:
Option a: ∑n=25(n−1)
By substituting the values of n and expanding the summation, we have,
(2−1)!+(3−1)!+(4−1)!+(5−1)!
Subtracting, we have,
1!+2!+3!+4!
Expanding the factorial,
1+(2∗1)+(3∗2∗1)+(4∗3∗2∗1)
Simplifying, we get,
1+2+6+24
Thus, the summation ∑⁵ (n−1)! represents the
n=2
series 1+2+6+24
Hence, Option a is the correct answer.
find arc JK
BRAINLIEST,POINTS,THANKS AND RATING GIVEN!!!
A builder is developing a neighborhood of one-bedroom and two-bedroom houses. the builder wants to build 12 houses and can use as many as 88 total
windows. the one-bedroom houses need 6 windows and the two-bedroom houses need 9 windows.
part a
write and solve a system of equations to represent the situation. let 2 represent the number of one-bedroom houses. let y represent the number of two-
bedroom houses. round your answers to the nearest hundredth, if necessary.
Builder can build 7 one bedroom houses and 5 two bedroom houses.
What is consistent Equation?
A linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
Let x represents the number of one-bedroom houses and y represents the number of two bedroom houses.
According to Question,
Total number of houses is 12 i.e. x + y = 12..........(i)
Total we have 88 windows in which 6 windows can be use in one bedroom house and 9 windows can be used in two bedroom house so,
6x + 9y = 88 ..................(ii)
From Equation (i) and (ii), we get
x = 7 and y = 5
Thus, Builder can build 7 one bedroom houses and 5 two bedroom houses.
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ANSWER QUICK ILL GIVE BRAINLIEST
A researcher posts a radio advertisement offering $35 in exchange for participation in a short study. The researcher accepts the first eight people who respond to the advertisement. Which of the following statements is true about the sample? It is a valid sample because the first eight people were selected to participate. It is not a valid sample because it is not a random sample of the population. It is a valid sample because money was offered to participants. It is not a valid sample because it is only a short study.
Answer: Choice B
It is not a valid sample because it is not a random sample of the population.
Explanation:
The researcher should have randomly selected the participants, either by picking names out of a hat, using a random number table, or some kind of computer software to pick the names. Letting the first 8 people form the sample is very likely not representative of the population at large. We have a lot of bias here. Therefore, this is not a valid sample.
which of the tables represent a function?
(sorry for the bad photo)
15 points!
Answer:
Table B
Step-by-step explanation:
A function is present when x-value can only have a single y-value.
In Table A, the x-value 5 corresponds to 2 y-values : 3 and 2, hence it is not a function.In Table B, each x-value corresponds to a single y-value, hence it is a function.Write the verbal sentence as an algebraic equation.
The product of a three and a number plus five is 20.
Step-by-step explanation:
product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20
3×x +5=20
3x+5=20
Subtract 5 from both sides
3x+5-5=20-5
3x=15
3x/3=15/3
x=5
11z-6=16, then z=
First answer get to be brainliest!
- - -- - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]
11z-6=16, what is z?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
We need to make sure that all variables are on the left-hand side and the numbers are on the right-hand side.
Since we have a number on the left-hand side, we need to move it to the right-hand side with the opposite operation:-
11z=16+6
[tex]\it{11z=22}[/tex]
Divide by 11 on both sides:-
[tex]\it{z=2}[/tex]
We can check our solution by replacing z with 2 and seeing whether or not we end up with a true statement:-
[tex]\it{11(2)-6=16}[/tex]
[tex]\it{22-6=16}[/tex]
[tex]\it{16=16}[/tex]
So we conclude that our solution, z=2, is correct.
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:
z=2
Step-by-step explanation:
11(2)-6=16
22-6=16
approximately, how much air would be needed to fill a soccer ball with a radius of 15 centimeters ?
Answer:
about 2827cm^3
Step-by-step explanation:
you are looking for the area
4*pi*r^2
4*pi*15^15
pi*4*225
pi*900
2827.43
The point S is on the line AB so that lengths AS:SB are in the ration 3:2. If A = (21,3) and B = (6, 33) then find the co ordinate of S
From the section formula, it was found that the coordinate for the point S is (12,21).
Section Formula
The coordinates of the point S which divides the line AB into two sections can be found from the application of the Section Formula that is presented below:
[tex]S=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex], where
[tex]ratio=\frac{m}{n}[/tex]
[tex]x_1[/tex] and [tex]y_1[/tex] are coordinates of A
[tex]x_2[/tex] and [tex]y_2[/tex] are coordinates of B
Find the point SThe question gives r=[tex]\frac{3}{2}[/tex], A=(21,3) and B=(6,33). From the ratio, you can find m=3 and n=2.
Next step, applying the internal section formula. Then, you have:
[tex]S=(\frac{3*6+2*21}{3+2}, \frac{3*33+2*3}{3+2})\\ \\ S=(\frac{18+42}{5}, \frac{99+6}{5})\\ \\ S=(\frac{60}{5}, \frac{105}{5})\\ \\ S=(12, 21)[/tex]
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7(7-2 × 3) = ?
What is the answer?
A. 24
B. 7
C. 14
D. 26
Answer:
b) 7 option B 7 is the answer
Step-by-step explanation:
bidmas rule:
7-2×3
2×3= 6
7-6=1
7×1= 7
therefore the answer is 7.
Answer: The answer is [tex]B. 7[/tex]
Step-by-step explanation:
[tex]7(7-2[/tex] × [tex]3)[/tex]
Simplify the expression.
[tex]7-2= 5[/tex]
[tex]7[/tex] × [tex]3[/tex] = [tex]21[/tex]
[tex]21[/tex] ÷ [tex]3=7[/tex]
Help pls!!!!!!
A family sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2x8x9 inches costs $4.50. What is the difference in price per cubic inch?
Answer:
$0.01
Step-by-step explanation:
Family size rate (per cubic inch)
Volume of box = 3 x 9 x 12 = 324 in³Cost = $6Rate = 6/324 = 1/54 = $0.02 per cubic inchRegular size rate
Volume of box = 2 x 8 x 9 = 144 in³Cost = $4.50Rate = 4.50/144 = 1/32 = $0.03 per cubic inchDifference in price
$0.03 - $0.02$0.01Volume of family sized box
LBH3(9)(12)27(12)324in³Price per inch
6/324=0.02$/inVolume of regular size
2(8)(9)144in³Price per in
4.5/144=0.03$/inDifference:-
|0.02-0.03|=0.01$
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x 25x2 1
The integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]
How to evaluate the integral?The integral expression is given as:
[tex]\int {x(25x^2 + 1)} \, dx[/tex]
Start by expanding the bracket
[tex]\int {25x^3 + x} \, dx[/tex]
Next, we integrate each term in the expression
[tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]
Hence, the integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]
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Which is a stretch of an exponential decay function? f(x) = one-fifth (one-fifth) superscript x f(x) = one-fifth(5)x f(x) = 5one-fifth f(x) = 5(5)x
The exponential function that represents a stretch of a decay function is given as follows:
[tex]f(x) = \frac{5}{4}\left(\frac{4}{5}\right)^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.It represents a stretch if a > 1, and a decay function if b < 1. Researching the problem on the internet, the correct option is given as follows:
[tex]f(x) = \frac{5}{4}\left(\frac{4}{5}\right)^x[/tex]
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Answer:
the answer is C :)
Step-by-step explanation: