The measures of the angles of a triangle are shown in the figure below. Solve for x.

Step-by-step explanation:

[tex](9x + 24) + 30x = 180[/tex]

[tex]39x + 24 = 180[/tex]

[tex]39x = 156[/tex]

[tex]x = 4[/tex]

Hence，we know

<DEC

[tex] = 9x + 24 = 9 \times 4 + 24 = 60[/tex]

<AEB=<DEC=60

Answer:

72 kg

Step-by-step explanation:

let weight of third person=x

62-55=x-62

7=x-65

x=7+65=72 kg

The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.

Current is the flow of electrons through a conductor when voltage is applied across the conductor.

Given the peak voltage of 18 V, hence:

[tex]V_{rms}=\frac{Peak\ value}{\sqrt{2} } =\frac{18}{\sqrt{2} } =12.73 V\\\\I_{rms}=\frac{V_{rms}}{resistance } =\frac{12.73}{4 } =3.18 A\\[/tex]

The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.

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The geometric sequence 128,32,8,2 has a common ratio

The recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128

The geometric sequence is given as:

128,32,8,2

Start by calculating the common ratio (r)

[tex]r = \frac{a_{n}}{a_{n-1}}[/tex]

Substitute 2 for n

[tex]r = \frac{a_2}{a_1}[/tex]

Substitute known values

[tex]r = \frac{128}{32}[/tex]

Evaluate the quotient

[tex]r = 4[/tex]

Substitute 4 for r in [tex]r = \frac{a_{n}}{a_{n-1}}[/tex]

[tex]4 = \frac{a_{n}}{a_{n-1}}[/tex]

Cross multiply

[tex]a_n = 4a_{n-1}[/tex]

Hence, the recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128

Read more about geometric sequence at:

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Answer:

I think the answer is 3x

Step-by-step explanation:

If i am wrong please correct me

The correct answer is 3x

So, the equation is [tex]18x^{3}+6x^{2} y-9x^{2} -3xy[/tex]

We need to find the GCF from the given equation  

[tex]3x(6x^{2} +2xy-3x-y)[/tex]

Hence, here we are getting the common factor as 3x

which the largest common factor in the given equation.

Learn more about Greatest common factor below.

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Answer:

D: 699

E: 582.5

F: 116.5

2. 1398

3. 13048

Step-by-step explanation:

Hope this helps!

Answer:

x=-3

y=-8

I answered your question in the photo sent.

Solution :-

Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.

And we know that vertically opposite angles measure same. Thus,

∠2 = 135°

And,

∠2 + ∠6 = 180° ( Co - interior angles sum up to 180° )

135° + ∠6 = 180°

∠6 = 180° - 135°

∠6 = 45°

Now,

we see that ∠6 and ∠5 are making a linear pair of angles, and we know that angles in a linear pair measure 180° Thus,

∠5 + 45° = 180°

∠5 = 180° - 45°

∠5 = 135°

Thus, the value of angle 5 is 135°

Hope that helps. :)

Answer:

200 meters2

Step-by-step explanation:

4 * 5 = 20

20 * 20 ÷ 2 = 200

Answer:

(a) 0 (b) 1^2

Step-by-step explanation:

photo number 1 is answer for question 2(a)

photo number 2 is answer for question 2(b)

Answer:

172 cm

Step-by-step explanation:

The total height of the first 7 people is the average of the 7 people multiplied by the number of people, which is 156 * 7 or 1092. Using the same method, the total height of the first 8 people is 158*8 or 1264. The eighth person must be 1264 - 1092 cm tall or 172 cm tall.  

Answer:

4%

Step-by-step explanation:

6000 x 100 / 5000 = 120

after 5 years the total interest is 20%

each year interest = 4%

( 4 x 5 =20 )

Answer:

30

Step-by-step explanation:

The distance between 2 points on a number line uses the following equation:

point2 - point1.

In this case we get 15 - (-15) which equals 30.

Answer:

See below ↓

Step-by-step explanation:

A) The Western Beach width decreases with increase in time whereas the Dune Beach width increases with increase in time.

B) Between Year 11 and Year 12

C) Find out the exact change in width per year for both beaches and plot them lines of change on a graph or as equations. Find where they intersect on the graph or solve the pair of equations to find out when they will both have the same width.

Answer:

Bottom Right graph

Step-by-step explanation:

The quation asks what slope of the graph represents how many people are served per hour. If 600 people are served in 10 hours, you divide 600 by 10 to see how many people are served per hour. In this case it is 60 people per hour. Then you find the graph that shows 60 more people served per hour. Hope this helps.

Answer:

Step-by-step explanation:

focus (1 , -7)  ⇒ a = 1  & b = -7

y = 1 ⇒ c = 1

Equation of parabola :

(x - a)² + (y - b)² = (y - c)²

(X - 1)² + (y + 7)² = (y - 1)²

Now, expand.

x² - 2x + 1 + y² + 2*7*y + 7² = y² - 2*y*1 + 1

x² - 2x + 1 + y² - 14y + 49 = y² - 2y +1

x² - 2x + 1 + y² - 14y +  49  - y² + 2y - 1 = 0

x² - 2x  + y² - y²   - 14y + 2y   + 1 + 49 - 1 = 0

x² - 2x  - 12y + 49 = 0

Answer:

[tex]\sf 2 \frac14 \ cups[/tex]

Step-by-step explanation:

Add the amounts together:

[tex]\sf \implies \dfrac24+1+\dfrac34[/tex]

Convert the whole number 1 into a fraction with denominator 4:

[tex]\sf \implies \dfrac24+\dfrac44+\dfrac34[/tex]

As all the denominators are the same, we can simply add the numerators:

[tex]\sf \implies \dfrac{2+4+3}4[/tex]

[tex]\sf \implies \dfrac94[/tex]

Finally, convert the improper fraction into a mixed number:

[tex]\sf \implies 2 \frac14 \ cups[/tex]

Add all

[tex]\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{2+3+4}{4}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{9}{4}[/tex]

[tex]\\ \rm\rightarrowtail 2\dfrac{1}{4}cups[/tex]

Answer:

x = 110 & y = 28

Step-by-step explanation:

The top and bottom lines are both intersected by a transversal. Because of this, we can say the 100-degree angle is equivalent to the (x-10) angle due to the Corresponding Angles Theorem.

If 100 = x -10 then you add 10 to both sides to get x = 110 degrees.

Then, using the Same Side Exterior Angles Postulate, you can conclude that the 100-angle and the (2y + 24) angle are supplementary, meaning they add up to 180 degrees.

So, 100 + (2y + 24) = 180.

Subtract 100 from both sides to get 2y + 24 = 80

Then subtract 24 from both sides to get 2y = 56

And divide both sides by 2 to get y = 28 degrees.

Answer:

Problem #6: 31.8

Step-by-step explanation: all you have to do is plug in 31 and 7 into the phythangorean therom equation so 31 squared + 7 squared and you will end up getting 1010 but then you have to find the square root of 1010 which equals 31.78049... so then you round your answer

Answer:

ONE “1”

Step by step:

Taking into account the definition of a system of equations, this nonlinear system of equations has one solution.

A system of equations is a set of two or more equations that share two or more unknowns. The solutions of a system of equations are all the values that are valid for all equations.

That is, to find the solution to a system of equations, you must find a value (or range of values) that satisfies all the equations in the system.

Graphically, the points where the graphs of the equations intersect will be the solutions to the system.

A system of equations with a linear equation and a quadratic equation can have two, one, or no solutions. To find its quantity, we must look for the intersection between both graphs:

If the graphs of the equations do not intersect, then there are no solutions for both equations. If the parabola and the line touch at a single point, then there is a solution for both equations. If the line intersects the parabola in two places, then there are two solutions to both equations.

In this case, you can see that the parabola and the line touch at a single point. Then there is a solution for both equations.

In summary, this nonlinear system of equations has one solution.

Answer:

The correct answers are B & E

Step-by-step explanation:

The cost of adult tickets: 15$ * 2= 30$

The cost of student tickets: 8$ * 20= 160$

=> All the tickets cost 30$ + 160$= 190$

=> Martin still needs 10$ more to buy all of the tickets

Answer:

D. Mr. Anderson can travel 99.28 miles.

Step-by-step explanation:

If Mr. Anderson has 4 gallons and each gallon moves him 24.82 miles you can multiply the number of miles per gallon by the gallon resulting in an equation that looks like 4*24.82=99.28.

Answer:

-8.9° C

Step-by-step explanation:

Question:

Doing a scientific experiment the temperature of a container decreased by 35.7° C at a constant rate over 8 1/2 hours.

What value represents the change in the temperature of the container each hour?

Answer:

-8.9° C

Answer:

PM is radius

NL is diameter

LM is chord

LJ is secant

NJ is tangent

N is point of tangency

P is center

Answer:

560

Step-by-step explanation:

To find the total combination you have to multiply the combination of entrees with combination of sides. U have to use the nCr equation to find these separate equations. n is number of items in total of the set and r is the number of items you want to choose from the set.

See the pic below for work

Answer: 120cm

Step-by-step explanation:

Multiply length x width x height

10 x 6 x 2 is equal to 120, so the volume is 120cm or centimetres.

Answer:

10cmx6cmx2cm

6x2=12

12×10=120cm

Answer:

C. 51

Step-by-step explanation:

For Square:

Length x Height

7 x 6 = 42

For Triangle:

Base x Height x 1/2

(6x3)1/2 = 9

42 + 9 = 51

Answer: im pretty sure its 29 degrees .

Step-by-step explanation: your welcome <3

Answer:

4x - 28

Step-by-step explanation:

[tex]-3(4x + 3) - (2x - 5) + 6(3x - 4)[/tex]

[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a-b\right)=-a+b[/tex]

[tex]-\left(2x-5\right)=-2x+5[/tex]

[tex]=-3\left(4x+3\right)-2x+5+6\left(3x-4\right)[/tex]

[tex]=-12x-9-2x+5+6\left(3x-4\right)[/tex]

[tex]=-12x-9-2x+5+18x-24[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=-12x-2x+18x-9+5-24[/tex]

[tex]\mathrm{Add\:the\:numbers:}\:-9+5-24=-28[/tex]

[tex]=-12x-2x+18x-28[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-12x-2x+18x=4x[/tex]

[tex]=4x-28[/tex]

~Learn with Lenvy~

Answer:

Step-by-step explanation:

A = [tex]\frac{b_{1} +b_{2} }{2}[/tex] × h

~~~~~~~~

[tex]b_{1}[/tex] = 15 in.

[tex]b_{2}[/tex] = 6 + 15 + 6 = 21 in.

h = 18 in.

A = [tex]\frac{15+21}{2}[/tex] × 18 = 324 in.²