m∠DFG=(2x+6)° and m∠EFG=(3x−11)°. Find the value of x.

The figure shows straight angle D F E that consists of two angles, D F G and E F G.

Answers

Answer 1

Answer:

x = 37

Step-by-step explanation:

A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.

2x + 6 + 3x - 11 = 180     Combine like terms

5x - 5 = 180                   Add 5 to both sides

5x = 185                         Divide by 5

x = 37

∠DFG = 80°

∠EFG = 100°


Related Questions

please help
PLEASE ​

Answers

Answer:

Step-by-step explanation:

4567890987654345678

The graph of a function f(x) is shown. What is the value of x where f(x) = -5? And f(0)?

Answers

Answer:

x = -3 when f(x) = -5

f(0) = 3

Step-by-step explanation:

When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.

If the number is in the parentheses of the function, they are giving you the x value. When x  = 0, y = 3

2
3
4
5
Which distance measures 7 units?
L
M
N
-8-7-6-5-4-3-2-1012
3
the distance between points L and M
the distance between points L and N
the distance between points M and N
the distance between points M and P
5 6 7 8
TIME REMAINING
56:41

Answers

Answer:

the distance between points M and P

Step-by-step explanation:

i did it

Jackson took 8 fewer pictures on Saturday than he did on Friday. If he took 11 pictures on Friday, how many pictures did he take on Saturday?

Answers

Friday =11

Saturday =?

But, we know that the pictures he took on Saturday are eight times fewer than those he took on Friday.

Saturday = 11-8

               = 3

∴ He took 3 pictures on Saturday.

       Hope this helps >3

Use the compound interest formulas A=P1+
r
nnt and A=Pert to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 7% if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded​ monthly; d. compounded continuously.

Answers

The accumulated value of an investment if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded​ monthly; d. compounded continuously is $30731.4 $ , $30785.98  $30823.14 , 30841.95

What is Interest ?

Interest is the amount received by a person as a result of investing certain amount of money for a certain period of time.

It is given that

Principal = $ 25000

Time = 3 years

Interest Rate = 7 %

The amount is given by

[tex]\rm A = P( 1+ \dfrac{r}{n}) ^{nt}[/tex]

Compounded semiannually

n = 2

Compounded Quarterly

n = 4

Compounded Monthly

n =12

Compounded Continuously

P = P₀ [tex]\rm e ^{rt}[/tex]

Therefore the accumulated value for

compounded Semiannually is

[tex]\rm A = 25000( 1+ \dfrac{7}{200}) ^{2*3}[/tex]

A = $30731.4

Compounded Quarterly

[tex]\rm A = 25000( 1+ \dfrac{7}{400}) ^{4*3}[/tex]

A = $30785.98

Compounded Monthly

[tex]\rm A = 25000( 1+ \dfrac{7}{1200}) ^{12*3}[/tex]

A = $30823.14

Compounded Continuously

[tex]\rm P = 25000 e ^{ 7 * 3 }[/tex]

P = $30841.95

Therefore the accumulated value of an investment if the money is

a. compounded​ semiannually; b. compounded​ quarterly; c. compounded​ monthly; d. compounded continuously is

$30731.4 $ , $30785.98  $30823.14 , 30841.95

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The circle above with center O has a circumference of 36. What is the length of minor arc AC? A) 9 B) 12 C) 18 D) 36

Answers

Answer:

A) 9

Step-by-step explanation:

⇒ Circumference of a Circle = 2πr

[tex]36=2\pi r[/tex]

[tex]r=\frac{36}{2} \pi[/tex]

[tex]r=\frac{18}{\pi }[/tex]

Length of arc = rθ

θ = angle AC = [tex]90^o[/tex]

Convert [tex]90^o[/tex] to radian

= [tex]\frac{90\pi }{180}[/tex]

= [tex]\frac{\pi }{2}[/tex]

length of arc = 18/π x π/2

= 9

All of the details to the question are in the picture that is attached in this question, please helpp

Answers

Answer:

10

Step-by-step explanation:

The arc length of the semicircle is

a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10

As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.

So,

(42/180)(5a+10)=a+442(5a+10)=180(a+4) [multiply both sides by 180]210a+420=180a+720 [distributive property]30a+420=720 [subtract 180a from both sides]30a=300 [subtract 420 from both sides]a=10 [divide both sides by 30]

Solve for x
3x² - 5x + 6 = 10 - 4x​

Answers

Answer: [tex]-1, \frac{4}{3}[/tex]

Step-by-step explanation:

[tex]3x^{2}-5x+6=10-4x\\\\3x^{2}-x-4=0\\ \\ (x+1)(3x-4)=0 \\ \\ x=\boxed{-1, \frac{4}{3}}[/tex]

Answer:

x = -1
x = 4/3

Step-by-step explanation:

Hello!

First, let's convert the equation into Standard Form: [tex]ax^2 + bx + c = 0[/tex]

[tex]3x^2 - 5x + 6 = 10 - 4x[/tex][tex]3x^2 - x - 4 = 0[/tex]

We can solve this by factoring the quadratic. We have to find two numbers that multiply to [tex]ac[/tex] but add up to [tex]b[/tex].

ac = -12b = -1

The two numbers would be -4 and 3. We can expand -x to -4x + 3x, and then factor by grouping.

Factor[tex]3x^2 - x - 4 = 0[/tex][tex]3x^2 +3x - 4x - 4 = 0[/tex][tex]3x(x + 1) - 4(x + 1) = 0[/tex][tex](3x - 4)(x + 1) = 0[/tex]

Use the Zero Product Property. Set each factor to zero and solve for x.

3x - 4 = 03x = 4x = 4/3

x + 1 = 0x = -1

The solutions to the quadratic are -1 and 4/3.

Timothy has a savings account that he started five years ago to begin saving for college. The
savings account has an interest rate of 3% and has earned $225 in interest since he began the
account. How much money did Timothy start the account with when he originally opened the
savings account?
A. $1500.00
B. $33.75
C. $7500.00
D. $3375.00
of $18

Answers

Answer:

A. $1500.00

Step-by-step explanation:

Assuming this is a simple interest savings account.

Simple interest formula

I = Prt

where:

I = total interestP = principal amountr = interest rate (in decimal form)t = time (in years)

Given:

I = $225r = 3% = 0.03t = 5 years

Substitute the given values into the formula and solve for P:

⇒ I = Prt

⇒ 225 = P(0.03 ×5)

⇒ 225 = P(0.15)

⇒ P = 225 ÷ 0.15

⇒ P = 1500

Therefore, Timothy started the account with $1500.00.

I=PRT/100P=100I/RTP=100(225)/5(3)P=22500/15P=$1500

Help please I'll mark you as brainlist if the answer is correct

if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p​

Answers

If (x + q) is factor of two polynomial [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex] than [tex]a = \frac{n - q}{m- p}[/tex].

x + a is factor of equations  [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex]

What is a polynomial equation?

Polynomial equation is equation of independent variables.


Putting it in both the equations

[tex]x^2+px+q=0[/tex]                          
[tex](-a)^2+p(-a)+q=0\\a^2-ap+q=0 ........(1)[/tex]  

[tex]x^2+mx=n = 0\\(-a)^2+m(-a)+n=0\\a^2-am+n=0 .....(2)[/tex]

subtracting (2) from (1)

[tex]-am+ap+n-q=0[/tex]
[tex]a=\frac{n-q}{m-p}[/tex]

Thus, the required expression is [tex]a=\frac{n-q}{m-p}[/tex].

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all natural numbers (N) are integers (Z), but not all integers are natural numbers true or false

Answers

True. All natural numbers N are integers Z, but not all integers are natural numbers.

Natural numbers:

Natural numbers starts from zero to infinity are all positive.All the natural numbers are whole numbers.It is denoted by NThe set of natural numbers are N = 1,2,3, ...

Integers:

Integers are the whole numbers that contain positive numbers, zero and negative numbersIt is denoted by ZThe set of integers are Z = ... ,-3,-2,-1,0,1,2,3, ...

Since natural numbers are all positive, N is positive integers but not all integers are natural numbers.

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what is the measure of easy interior angle of a regular octagon?

Answers

The sum of the interior angle is 1080 and each angle measure is 135 degrees.

What is a regular polygon?

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have an octagon

In an octagon the number of sides = 8

The sum of the angles in the octagon is given by:

= (n - 2)×180

n = 8

= (8 - 2)180

= 6×180

The sum of the interior angle = 1080

Each angle = 1080/8 = 135 degree

Thus, the sum of the interior angle is 1080 and each angle measure is 135 degrees.

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An equilateral triangle has the height BO= 80 cm. Considering, height BO splits the base (segment) AC into two equal segments of size x/2, find X.

Answers

Answer:

Given - an equilateral triangle

An equilateral triangle means all sides equal and all angle equal to 60°

In triangle BOA

sin 60° = OB/ AB

√3/2. = 80/AB

AB = 160√3/3

X = 160√3/3

find the gradient of the line joining the points (0,2) and (-2,-4)

Answers

Answer:

m = 3

Step-by-step explanation:

Gradient of a line is given by the formula

m= (y2-y1) /(x2-x1) which is change y divided by change in x

m = (-4-2)/(-2-0)

m = -6/-2

m = 3

Answer: the gradient is 3

Step-by-step explanation:

for a full explanation refer to the document and the ones written colorfully are the explanation. So, if you want just the workings they are the ones written in black.

and I drew an eye! Have a nice day!

5. In an arithmetic sequence, the fifth term is 44 and the ninth term is 80.(a) Find the common difference. (b) Find the first term. (c) Find the sum of the first 50 terms of the sequence.​

Answers

Step-by-step explanation:

first you should do is that find the common difference which is 9

Use substitution to solve the following system of equations

2x + 3y = 18 AND X = y - 6

Answers

Answer:

y=6,x=0

Step-by-step explanation:

here's an attachment with how to solve

a-3/7 devided by 3-a/21

Answers

The answer is pretty simple but I put it in a picture below

The davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length and width the same amount to increase the total area of the patio by 160 ft2. which quadratic equation best models the situation? a = lw (15)(12) (x)(x) = (15)(12) 160 (15x)(12x) = (15)(12) 160 2(15 x) 2(12 x) = (15)(12) 160 (15 x)(12 x) = (15)(12) 160

Answers

Answer:

160

Step-Step Explaining:

So I Know This ⏩ ⏩

please help! [4 x 3⁵ - 9 x (-7)] + 3³ (-4² +2²) - 11 Give your answer in simplest form.

Answers

Answer:

Please see the question below.

Step-by-step explanation:

In the expression "[4 x 3⁵ - 9 x (-7)]" I'm unclear if the "x" is a multiplication sign, or the variable x.  I'll assume it is the variable x in my answer.

4 x 3⁵ = 972x

- 9 x (-7) = 63x

3³ (-4² +2²)  = 27 (20) = 540

-11 = -11

========

Putting it all together:

972x + 63x + 540 -11

1035x + 529

Find the measure of the remote exterior angle. m∠x=(198−5n)°m∠y=(5n+37)°m∠z=(n+7)°

Answers

The value of the angle ∠x will be ∠x = 128°. Then the correct option is C.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle is given below.

The sum of the two interior angle is equal to the third exterior angle.

m∠x = (198 − 5n)°

m∠y = (5n + 37)°

m∠z = (n + 7)°

We know that

∠x = ∠y + ∠z

198 - 5n = 5n + 37 + n + 7

       11n = 154

          n = 14

Then the value of the angle ∠x will be

∠x = 198 – 5 × 14

∠x = 128°

Then the correct option is C.

The complete question is given below.

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A single die is rolled. How many ways can you roll a number that is prime,
followed by a number less than 6? (Remember that 1 is not a prime number.)

Answers

Answer:

3 different ways

Step-by-step explanation:

2, 3, and 5 are all prime numbers under 6

If the nth term of a sequence is 18-8n what is the 8th term

Answers

Answer:

[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]

Answer:

-46

Step-by-step explanation:

(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :)  )

We know that the nth term of the sequence is 18 - 8n

the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value}  )

  18 - 8n is sequence

  18 - 8(8) is 8th term

  18 - 64 is 8th term

 -46 is the 8th term

hope this helps!! :)

inequalities i need help question is in picture

Answers

Answer:

19-73 19-73 is fine thanks 70-65-46 024 465 8554 48-57

The driving distance between Manchester and London is 195 miles. Farid intends to travel from Manchester to London by coach. The coach will leave Manchester at 3.30pm.

Farid assumes that the coach will travel at an average speed of 50mph

A)Using his assumption, work out Faris's arrival time at London.

It actually turns out that the coach has a lower average speed.

B)Describe how this affects the arrival time

Answers

Answer:

7:24pm

Step-by-step explanation:

At 50 mph, it will take 195/50 = 3.9 hours to reach London

3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )

3:30 + 3:34 ==> 7:24

(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24

Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm

If the train is slower average speed, then the arrival time is delayed beyond 7:24pm

can someone please help mee i need the right answers please(30 points and i will give brainliest!!!)

Answers

Step-by-step explanation:

Funtion-A:

Given:

[tex]y = {x}^{2} - x - 6[/tex]

To find the x-intercepts set y to 0 and solve for x which is done below:

⇒x²-x-6=0⇒(x-3)(x+2)=0X=3 and -2

Therefore x-intercepts:(3,0),(-2,0)

To figure out the y-intercept , substitute 0 for x and simplify

⇒y=0²-0-6⇒y=-6

Hence, The y-intercept is (0,-6)

The vertex (0.5,-6.25)

(skipped the steps as you've already figured it out)

Function-B:

Likewise A:

X-intercepts:

⇒-x²+x+6=0⇒x²-x-6=0⇒x=3 and -2

Therefore,x-intercepts:(3,0),(-2,0)

Y-intercept:

⇒y=-0²+0+6

⇒y=6

Therefore, y-intercept (0,6)

The vertex:(0.5,6.25)

Inspection of the Parabolas:

The difference between the two parabolas is that The blue parabola is the result of reflection over x-axis of the red one.

Answer:

a.

The x-intercepts are 3 and -2

The y-intercept is -6

The vertex is (1/2 , -25/4)

b.

The two parabola are symmetric across the x-axis

Step-by-step explanation:

x² - x - 6

[tex]=x^{2}-2\times \frac{x}{2} +\frac{1}{4} -\frac{1}{4}-6[/tex]

[tex]=(x-\frac{1}{2} )^{2} -(\frac{1}{4}+6)[/tex]

[tex]=(x-\frac{1}{2} )^{2} -\frac{25}{4}[/tex]

The x-intercepts :

(x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² - 0 - 6 = -6

b.

we notice that :

-x² + x + 6 = -(x² - x - 6)

Then

-x² + x + 6

[tex]=-(x-\frac{1}{2} )^{2} +\frac{25}{4}[/tex]

The x-intercepts :

[tex]-(x-\frac{1}{2} )^{2} +\frac{25}{4}=0[/tex]

⇔ (x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² + 0 + 6 = 6

A 11 gram sample of a substance that’s used to treat thyroid disorders has a k- value of 0.125

Answers

The substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

What is exponential decay?

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.125t}[/tex]

Solving for t:

t = 5.54 ≈ 5.5 days

Thus, the substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125

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Simplify the expression
-17.8a-2.4a+25-19.5

Answers

Answer:

-20.2a+5.5

subtract the values with a in it and the ones without the a together.

Help asap show your work!

Answers

Answer:

x = 4

Step-by-step explanation:


someone help me get outta summer school slope? And y intercept?

Answers

Okay bud I’m not sure how about it or what if we are all the good ones you have that to me and my brother wants to go buy a new one and then go back to church class today or what do you want it to be in a big deal if we can get some stuff done then I’ll do the work I have for that you don’t want to me I don’t know how you want it I know but it’s like I don’t know why I’m not

Triangle BDC is isosceles.

Circle A is shown. Line segments A B, A C, and A D are radii. Lines connect each of the points on the circle to the other points to form a triangle. Sides C B and B D are congruent.

Which angle is congruent to ?

Answers

As per the question, the answer is ∠CAB is congruent to ∠BAD.

The isosceles triangle :

An isosceles triangle named BDC is positioned within a circle. The segments of the circle they pass through are congruent because the faces of the triangles BC and BD are congruent, or identical.

Due to the triangle's faces BC and BD being identical and congruent

BC=BD

Additionally, the segments of the circle it goes across are congruent.

In the case of ΔBAC & ΔBAD

AC=AD= the radius of the circle

AB=BA

Thus, BAC is consistent with BAD according to SSS guidelines.

As a result, the central angles of the sections are also congruent; hence, BAD and CAB are congruent.

As a result, ∠BAD is equivalent to ∠BAC OR ∠CAB.

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Answer:

B on edge

Step-by-step explanation:

CAD

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