12. What is m∠GEA?

Answer:

[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]

Step-by-step explanation:

The formula of a midpoint:

[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]

We have the points

[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]

Substitute:

[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]

Answer:

The answer is (a/2,a/2)

Step-by-step explanation:

Fill in 2 then a

In conclusion (a/2,a/2)

Answer:

Correct Option is : StartFraction 1 Over m Superscript 8 EndFraction

Step-by-step explanation:

=> [tex]m^{-8} p^0[/tex]

According to law of exponents [tex]a^0 = 1[/tex]

=> [tex]m^{-8} (1)[/tex]

Using Law of exponents [tex]a^{-m} = \frac{1}{a^m}[/tex]

=> [tex]\frac{1}{m^8}[/tex]

The simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].

The question is not well formatted the question might be as follows:

Which is the simplified form of [tex]m^{-8}p^0[/tex]?

Exponents are numbers that say how many times a number is to be multiplied. For example, 2⁸ means 2 is multiplied 8 times.

[tex]m^{-8}p^0[/tex] = [tex]m^{-8}[/tex]  since, p⁰=1.

⇒[tex]m^{-8}[/tex] = [tex]\frac{1}{m^8}[/tex] .

Hence, the simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].

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Answer:

a = 0

Step-by-step explanation:

p(x) = ax²+x+1

Let x+1 = 0 => x = -1

Putting in the above polynomial

=> p(-1) = a(-1)^2+(-1)+1

By Remainder Theorem, Remainder will be zero

=> 0 = a(1) -1+1

=> 0 = a

OR

=> a = 0

Answer:

Step-by-step explanation:

Factors are what we can multiply to get the number.

x² + x + 1

Factor the polynomial.

x(x+1) + 1

ax² + x = x(x + 1)

ax² + x = x² + x

[tex]a=\frac{x^2 +x}{x^2 +x}[/tex]

a = 1

Answer:

y is the range

Step-by-step explanation:

the y is the range

x isthe domain

Answer:

Length of guy wire is 590.6 ft

Step-by-step explanation:

The complete question is

A radio transmission tower is  210  feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of  20°  with the ground. Give your answer to the nearest tenth of a foot.

height of tower = 210 ft

8 ft fro the top leaves 210 - 8 = 202 ft to the ground

This is an angle of elevation problem

the opposite is 202 ft

hypotenuse = ?

angle is  20°  

using sin ∅ = opp/hyp

sin  20°  = 202/hyp

0.342 = 202/hyp

hyp = 202/0.342 = 590.6 ft   this is the length of the guy wire

Answer:

264 degree angle

Step-by-step explanation:

Answer:

(A)

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B)

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Step-by-step explanation:

The given equation is

[tex]6x^2 - 13x + 5 = 0[/tex]

The solution is of the form as given by

[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]

(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.

The quadratic formula is given by

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

The equations of N, M and D are

[tex]N = -b[/tex]

[tex]D =b^2 -4ac[/tex]

[tex]M = 2a[/tex]

The values of a, b and c are

[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]

So,

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4

N = 13

D = 49

M = 12

[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]

[tex]$x=\frac{13\pm7}{12}$[/tex]

[tex]$ x=\frac{13+7}{12} $[/tex]  and [tex]$ x=\frac{13-7}{12} $[/tex]

[tex]$ x=\frac{20}{12} $[/tex]  and [tex]$ x=\frac{6}{12} $[/tex]

[tex]$ x=\frac{5}{3} $[/tex]  and [tex]$ x=\frac{1}{2} $[/tex]

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Answer:

49)   [tex]12\,b^4[/tex]

50)   [tex]200\,x^6[/tex]

Step-by-step explanation:

Use the properties of exponent to reduce this expressions:

a)  [tex]3\,b\,*\,4 \,b^3=(3\,*\,4)\,(b\,*\,b^3)=12\,b^{(1+3)}=12\,b^4[/tex]

b)  [tex]5\,x^2\,*\,8\,x\,5\,*\,x^3=(5\,*\,8\,*\,5)\,(x^2\,*\,x\,*\,x^3)=200\,x^{(2+1+3)}= 200\,x^6[/tex]

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

(f+g)(x)= 9x² + 9x

(f+g)(3) = 108

Step-by-step explanation:

f(x)=8x² +7x

g(x)= x² +2x

(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x

(f+g)(x)= 9x² + 9x

(f+g)(3)= 9*3² + 9*3 = 108

Answer:

A. Yes, the triangles are congruent by SAS.

Step-by-step explanation:

EF = FG and DF = FH-> Given

angle EFD = angle HFG -> Vertical angles are congruent

DE F = HGF -> SAS Triangle Congruence Theorem

We can prove  ∠DE F = ∠HGF by SAS congruency.

Hence option A is correct.

In the given triangle,

DE = GE

DF = FH

We know that,

SAS congruency stands for "Side-Angle-Side" congruence,

Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.

This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.

Since the triangles

DE,GE and DF, FH are the corresponding sides and

DE = GE

DF = FH

Since DEF and FHG are congruent.

Therefore,

∠DE F = ∠HGF

Hence proved.

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Answer:

[tex]Total\ Selection = 30\ ways[/tex]

Step-by-step explanation:

Given

Girls = 3

Boys = 5

Required

How many ways can 2 boys and girls be chosen?

The keyword in the question is chosen;

This implies combination and will be calculated as thus;

[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]

For Boys;

n = 5 and r = 2

[tex]Selection =\ ^5C_2[/tex]

[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]

[tex]Selection = \frac{5!}{3!2!}[/tex]

[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]

[tex]Selection = \frac{20}{2}[/tex]

[tex]Selection = 10[/tex]

For Girls;

n = 3 and r = 2

[tex]Selection =\ ^3C_2[/tex]

[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]

[tex]Selection = \frac{3!}{1!2!}[/tex]

[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]

[tex]Selection = \frac{3}{1}[/tex]

[tex]Selection = 3[/tex]

Total Selection is calculated as thus;

[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]

[tex]Total\ Selection = 10 * 3[/tex]

[tex]Total\ Selection = 30\ ways[/tex]

Answer:

Step-by-step explanation:

The data given are;

sample size n = 100

sample mean x = 3.1

standard deviation σ = 0.5

mean = 3

The value for Z can be determined by using the formula:

[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]

[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]

Z = 0.2

At 95% Confidence interval, level of significance ∝ = 0.05

From the z table ;P- value for the test statistics at ∝ = 0.05

P = 0.0228

We can see that the P-value is < ∝

Decision Rule:

Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝

Conclusion:

At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min

Answer:

$252

Step-by-step explanation:

This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.

Jan's " give away " = Ami + 36, Jan - 108, Toy + 72

Toy's " give away " = Ami + 72, Jan + 36, Toy - 108

Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.

144 + 72 + 36 = 252 dollars ( in total )

Answer:

answer is 252

Step-by-step explanation:

Good luck :)

Answer:

Step-by-step explanation:

Fog=2(g)+1

2(3x+2+4)+1

2{3x+6)+1

6x+12+1

=6x+13

Fog(-2)=6(-2)+13

-12+13

=1

Gof=3(f)+2+4

=3(2x+1)+6

6x+3+6

=6x+9

Gof(-2)=6(-2)+9

-12+9

=-3

Answer:  0 ft, maximum, 11.6 ft, 6.8 ft, 13.6 ft

Step-by-step explanation:

y = -0.25x² + 3.4x

   a= -0.25    b = 3.4    c = 0

"c" is the initial height = 0

"a" is negative ⇒ ∩-shaped parabola ⇒ vertex is a maximum

Axis of Symmetry (horizontal distance at maximum):

[tex]x=\dfrac{-b}{2a}=\dfrac{-(3.4)}{2(-0.25)}=\dfrac{-3.4}{-0.5}\quad = \large\boxed{6.8}[/tex]

Maximum: (heighth at maximum)

y = -0.25(6.8)² + 3.4(6.8)

   =    -11.56      +    23.12

   =  11.56

Zeros (when the ball is on the ground):

0 = -0.25x² + 3.4x

0 = x(-0.25x + 3.4)

0 = x                      0 = -0.25x + 3.4

                          -3.4 = -0.25x

                       [tex]\dfrac{-3.4}{-0.25}=x[/tex]

                          13.6 = x

x = 0 is where the ball started

x = 13.6 is where the ball landed

Answer:

Hey there!

This question is basically asking for the least common multiple, or LCM of the three numbers.

If it is a multiple of 10, it has to be a multiple of 5. Thus, the only thing we need to do now, is find the LCM of 10 and 7, which is 70.

Thus, your answer is 70.

Hope this helps :)

Answer:

I think it is 70.

Step-by-step explanation:

I think that is the Lowest common Multiple of 5, 7 and 10:

10 = 2*5

7 = 7

5 = 5

So the LCM is 2 * 5 * 7 = 70.

Answer: 4

Step-by-step explanation:

Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100.  Thus, 90/x = 70/100.

Hope it helps <3

Answer:

4

Step-by-step explanation:

90 is 70% of x.

90 = 70% × x

90 = 70/100x

Divide both sides by x.

90/x = 70/100

Answer:

49145 years

Step-by-step explanation:

In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.

Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?

In 10 years, the expectancy increased by 85/45 = 17/9

between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is  [tex]85*(\frac{85}{45})^{10} = 49145[/tex]  years

The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.

Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would  expectancy for women in 2100

Over a ten-year period, life expectancy rose by 85/45 = 17/9.

It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be

⇒ 85×(85/45)¹⁰

⇒ 85×(1.88)¹⁰

⇒ 49145 years

Hence, the life expectancy for women will be 49145 years

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Answer:

10 m

Step-by-step explanation:

Since all of the side lengths of a regular octagon are equal and there are 8 sides on an octagon, the answer would be 80 / 8 = 10 m.

Using concepts of percentage,

3 is 16.63% of 22.

22 is 13.41% of 164.

0.88 is 4% of 22.

8 is 22% of 36.36.

1.1 is 5% of 22.

A percentage is a number or ratio expressed as a fraction of 100.

Let 3 be x% of 22.

[tex]=\frac{x}{100} *22 = 3\\\\=x = \frac{3*100}{22} = 13.63%[/tex]

3 is 13.63% of 22.

Let 22 be y % of 164.

[tex]=\frac{y}{100} *164 = 22\\\\=y = \frac{22*100}{164} = 13.41%[/tex]

13.41% of 164 is 22.

4% of 22 = 0.88

[tex]\frac{4}{100}*22 = 0.88[/tex]

Let 8 is 22% of z.

[tex]\frac{22}{100}*z = 8\\ \\z = \frac{8*100}{22} = 36.36[/tex]

5% of 22 = 1.1

[tex]\frac{5}{100}*22 = 1.1[/tex]

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Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 9x

Base ( b ) = 10

Hypotenuse ( h ) = x + 10

Now, let's find the value of x

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plug the values

[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]

Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression

[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]

To raise a product to a power , raise each factor to that power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]

Evaluate the power

[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]

Cancel equal terms on both sides of the equation

[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]

Move x² to R.H.S and change its sign

[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]

Calculate

[tex]20x = 80 {x}^{2} [/tex]

Swap both sides of the equation and cancel both on both sides

[tex]80x = 20[/tex]

Divide both sides of the equation by 80

[tex] \frac{80x}{80} = \frac{20}{80} [/tex]

Calculate

[tex]x = \frac{20}{80} [/tex]

Reduce the numbers with 20

[tex]x = \frac{1}{4} [/tex]

The value of X is [tex] \frac{1}{4} [/tex]

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = [tex] \frac{1}{4} + 10[/tex]

Write all numerators above the common denominator

[tex] \frac{1 + 40}{4} [/tex]

Add the numbers

[tex] \frac{41}{4} [/tex]

[tex] = 10.25[/tex] inches

Hope this helps..

best regards!!

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie

Answer:

Hello! The answer will be below!

Step-by-step explanation:

The answer is 60, steps will be below....

Steps:

6 divided by 10

=0.6

And than we do (0.6 x 100)%

Which will give us 60%

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer: x= - 4/3 and x = 4/3

Step-by-step explanation:

(3x-4) times (3x+4) = 0

Answer:

(3, 1)

Step-by-step explanation:

Plug-in points and see which one works. (x, y). <=  means less than or equal to.

Answer:

D. (3,1) is the correct answer

Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]

here;

m = 5

n = 9

r = 0.5

Then:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]

For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,

the responses are;

(1) The number of terms are 9

(2) The value of the sum is approximately 0.374

The given geometric series is presented as follows;

3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³

(1) The number of terms in the series = 13 - 4 = 9

Therefore;

(2) The value of the sum can be found as follows;

The common ratio, r = 0.5

The sum of the first n terms of a geometric progression is presented as follows;

[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]

The sum of the first 4 terms are therefore;

[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]

The sum of the first 13 terms is found as follows;

[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]

Which gives;

The sum of the 5th to the 13th term = S₁₃ - S₄

Therefore;

[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]

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Answer:

AB =-4 24 25

-5 15 15

BC= -5

4

10

2BC = -10

8

20

THE Operation AB -2BC cannot be performed because the unequality of the arrays

Step-by-step explanation:

AB=first row (3*2)+(1/2*0)+(5*-2), (3*-4)+(1/2*2)+(5*7), (3*0),(1/2*0),(5*5)

Second row ((1*1)+(-1*0)+(3*-2),(1*-4)+(-1*2)+(3*7), (1*0)+(-1*0)+(3*5)

AB =-4 24 25

-5 15 15

BC =FIRST ROW (1*1)+(-4*2)+(0*0)

SECOND ROW (0*1)+(2*2)+(0*0)

THIRSD ROW (-2*2)+(7*2)+(5*0)

BC= -5

4

10

2BC = -10

8

20

THE Operation AB -2BC cannot be performed because the unequality of the arrays

Answer:

x < 4 or x = ( -∞, 4)

Step-by-step explanation:

or

[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]

Answer: 0.9964

Step-by-step explanation:

Consider,

P (disk failure) = 0.06

q = 0.06

p = 1- q

p = 1- 0.06,

p = 0.94

Step 2

Whereas p represents the probability that a disk does not fail. (i.e. working entire year).

a)

Step 3

a)

n = 2,

let x be a random variable for number...

Continuation in the attached document