simplify that equation

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

(x - 45) + (x - 12) = x

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x                             Remove parenthesis

2x - 57 = x                                       Combine like terms

2x = x + 57                                      Add 57 to both sides

x = 57                                             Subtract x from both sides

Finding m∠D:

x - 45 = ?

57 - 45 = 12º                                          

Finding m∠C:

x - 12 = ?

57 - 12 = 45º                                          

** (Checking x: 12 + 45 = 57) **

Finding m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Step-by-step explanation:

Given : The perimeter of a rectangle is 320 mm. If its length increases by 10 mm and its breadth decreases by 10 mm then it its area will be 32 less.

To find : Calculate the length and breadth of the original rectangle ?

Solution :

The area of the rectangle is [tex]A=L\times B[/tex]

Let the length of the rectangle be 'x'

The breadth of the rectangle be 'y'

The area is [tex]A=xy[/tex]

Now, length increases by 10 mm i.e. L=x+10

breadth decreases by 10 mm i.e. B=y-10

The new area is [tex]A_n=(x+10)(y-10)[/tex]

According to question,

[tex]A-A_n=32[/tex]

[tex]xy-(x+10)(y-10)=32[/tex] ......(1)

The perimeter of a rectangle is 320 mm.

i.e. [tex]P=2(L+B)[/tex]

[tex]320=2(x+y)[/tex]

[tex]x+y=160[/tex]

[tex]x=160-y[/tex] .....(2)

Substitute the value of y from eqn (2) in (1),

[tex]y(160-y)-(160-y+10)(y-10)=32[/tex]

[tex]160y-y^2-(170-y)(y-10)=32[/tex]

[tex]160y-y^2-(180y-1700-y^2)=32[/tex]

[tex]160y-y^2-180y+1700+y^2=32[/tex]

[tex]1700-20y=32[/tex]

[tex]20y=1732[/tex]

[tex]y=\frac{1732}{20}[/tex]

[tex]y=86.6[/tex]

Substitute in (2),

[tex]x=160-86.6[/tex]

[tex]x=73.4[/tex]

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Answer:

[tex]76\frac{7}{8}\ lb[/tex]

Step-by-step explanation:

we know that

One box of 12'' weighs 3 3/4 lb

so

To find out the weight of 20 1/2 boxes, multiply the weight of one box by the total number of boxes

[tex]3\frac{3}{4}(20\frac{1}{2})[/tex]

Convert mixed number to an improper fraction

[tex]3\frac{3}{4}\ lb=\frac{3*4+3}{4}=\frac{15}{4}\ lb[/tex]

[tex]20\frac{1}{2}\ boxes=\frac{20*2+1}{2}=\frac{41}{2}\ boxes[/tex]

substitute

[tex]\frac{15}{4}(\frac{41}{2})=\frac{615}{8}\ lb[/tex]

Convert to mixed number

[tex]\frac{615}{8}\ lb=\frac{608}{8}+\frac{7}{8}=76\frac{7}{8}\ lb[/tex]

Answer:

 What we are going to do for this case is find the cost for each case:

 Cost to run the car before the mechanic worked on it:

 Cost to run the car after the mechanic worked on it:

 The difference between both cases is:

 Answer:

 It cost to run the car after the mechanic worked on it 0.01 $ / mile less than before the mechanic worked on it.

Read more on Brainly.com - https://brainly.com/question/2528459#readmoreStep-by-step explanation:

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have the following equation:

[tex]6x + 5y = -5\\5y = -6x-5\\y = - \frac {6} {5} x- \frac {5} {5}\\y = - \frac {6} {5} -1[/tex]

Thus, the slope is: [tex]m = - \frac {6} {5}[/tex]

By definition, if two lines are parallel then their slopes are equal.

Thus, a line parallel to the given line will have a slope: [tex]m = - \frac {6} {5}.[/tex]Therefore, the equation will be of the form:

[tex]y = - \frac {6} {5} x + b[/tex]

We substitute the given point and find "b":

[tex]-4 = - \frac {6} {5} (5) + b\\-4 = -6 + b\\-4 + 6 = b\\b = 2[/tex]

Finally, the equation is:

[tex]y = - \frac {6} {5} x + 2[/tex]

Answer:

[tex]y = - \frac {6} {5} x + 2[/tex]

Answer:

A) Irrational

Step-by-step explanation:

The square root of 27 is an irrational number since it's not a rational number. We identify rational numbers because they can be expressed as fractions

If we take the value of [tex]\sqrt{27}[/tex] we get

5.1961524227066318805823390245176...

There is no way to transform that number into a fraction because

* It has no decimal limit

* It has no decimal pattern (or period)

Examples of rationals are

5.44444...

[tex]0.\overline{32}[/tex]

2.375

The last one has limited decimals, the first two have repetitive patterns or a period.

Answer:

7+7+7+6+4+2=33

Each friend will have to pay $11

Step-by-step explanation:

The question is incomplete. The complete question is attached below.

Answer:

(a). AB = 16.4 in

(b) BC = 11.5 in

Step-by-step explanation:

From the rectangle ABCD shown below,

AB is the base of rectangle and CB is the altitude of the rectangle.

Given:

AC = 20 in

(a)

From triangle ABC,

Applying cosine ratio for angle 35°, we get:

[tex]\cos(35)=\frac{AB}{AC}\\AB=AC\times \cos(35)\\AB=20\times \cos(35)=16.38\approx 16.4\ in[/tex]

Therefore, AB = 16.4 in

(b)

Applying sine ratio for angle 35°, we get:

[tex]\sin(35)=\frac{CB}{AC}\\CB=AC\times \sin(35)\\AB=20\times \sin(35)=11.47\approx 11.5\ in[/tex]

Therefore, CB = 11.5 in

Final answer:

Using the cosine function, the base AB of the rectangle is approximately 16.4 inches. Using the sine function, the altitude CB is approximately 11.5 inches, both rounded to the nearest tenth of an inch.

Explanation:

To find the base AB and the altitude CB of rectangle ABCD with a given diagonal AC of 20 inches and an angle of 35° with base AB, we can use trigonometric ratios.

First, we will use the cosine function, which relates the base of a right-angled triangle to the hypotenuse:

Next, we use the sine function, which relates the altitude to the hypotenuse:

Answer:

8:50 A.M

Step-by-step explanation:

You have to add all the numbers.

Example:

5+15+25=45

45 Minutes + 5 Minutes= 50 Minutes=

8:50 A.M

Answer: 8:55AM

Step-by-step explanation:

8:05 AM - 8:10 AM : gather the ingredients

8:10 AM - 8:25 AM: mix the ingredients

8:25 AM - 8:50 AM: bake the cake

5+15+25=45 minutes + 8:05 AM = 8:50 AM

Answer:

111.15754585272 or 2√3089

Step-by-step explanation:

Here I will show you two methods that you can use to simplify the square root of 12356. In other words, I will show you how to find the square root of 12356 in its simplest radical form using two different methods.

To be more specific, I have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√12356 = A√B

Greatest Perfect Square Factor Method

The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12356 to simplify the square root of 12356. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 12356. The factors of 12356 are 1, 2, 4, 3089, 6178, and 12356. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 12356 divided by the greatest perfect square from the list of all factors of 12356. We determined above that the greatest perfect square from the list of all factors of 12356 is 4. Furthermore, 12356 divided by 4 is 3089, therefore B equals 3089.

Now we have A and B and can get our answer to 12356 in its simplest radical form as follows:

√12356 = A√B

√12356 = 2√3089

Double Prime Factor Method

The Double Prime Factor Method uses the prime factors of 12356 to simplify the square root of 12356 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 12356 and then take the square root of that product. The prime factors that multiply together to make 12356 are 2 x 2 x 3089. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 12356 by the number (A) squared. 2 squared is 4 and 12356 divided by 4 is 3089. Therefore, B equals 3089.

Once again we have A and B and can get our answer to 12356 in its simplest radical form as follows:

√12356 = A√B

√12356 = 2√3089

Answer:

4 inches long

Step-by-step explanation:

2+1=3

6÷3=2

2×2=4

The length of a chameleon's tongue is 4 inches

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

We have been given that the ratio of the length of a chameleon's tongue to the length of its body is 2:1

Let the length of a chameleon's tongue is 2x and the length of its body is x

⇒ 2x + 1x = 3x

We have been given that a chameleon is 6 inches long

⇒ 3x = 6

⇒ x = 6/3

⇒ x = 2

Therefore, the length of a chameleon's tongue = 2(2) = 4 inches

Learn more about Arithmetic operations here:

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Answer:

f(a)=2a

Step-by-step explanation:

The formula of the expression -3a + 6b= a + 4b in terms of a will be f(a) = 2a.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression will be solved as below:-

-3a + 6b= a + 4b

-3a -a = -6b + 4b

-4a = -2b

b = 2a

f(a) = 2a

Therefore, the formula of the expression -3a + 6b= a + 4b in terms of a will be f(a) = 2a.

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Answer: 14

Step-by-step explanation: hope this helps u :)

Answer:

14 tons

Step-by-step explanation:

divide the mass value by 32000

448,000 divided by 32000 = 14 tons

Answer:

227/6

Step-by-step explanation:

454/12=227/6

Answer:

[tex]A_{21} = 6[/tex]

Step-by-step explanation:

We are given that  

[tex]A = \left [\begin{array}{cccc}10&4&11&12\\6&3&2&8\end{array}\right][/tex] and we have to find the value of [tex]A_{21}[/tex]

Now, the general term [tex]A_{mn}[/tex] denotes the term in the matrix whose position is mth row and nth column.  

So, [tex]A_{21}[/tex] denotes the term in matrix A whose position is 2nd row and 1st column.

Hence, the term is 6.

So, [tex]A_{21} = 6[/tex] (Answer)

Answer:

The  number of adults visiting the zoo =  51

The number of children visiting the zoo =  134

Step-by-step explanation:

Let us assume the number of adults  going to the zoo = m

Total number of people visiting the zoo = 185

SO, the number of children visiting the zoo = 185 - m

Now, the cost of 1 adult ticket = $15

So, the total cost of m adult tickets = m x ( cost of 1 adult ticket)

= m  x ( $15)  = 1 5 m

And, the cost of 1 children ticket = $6

So, the total cost of ( 185 - m) adult tickets

= ( 185 - m) x ( cost of 1 children ticket)   = (185 - m )  x ( $6)  = 6( 185 - m)

Also, the combined cost of all tickets  = $ 1569

⇒ The cost of ( Adult's tickets  + Children's Tickets)  = $1569

or,  15 m + 6( 185 - m)  = $1569

or, 15 m + 1110 - 6 m = 1569

or, 9 m =  459

⇒ m = 459/9 =  51 , or m = 51

Hence the  number of adults visiting the zoo = m = 51

The number of children visiting the zoo = 185 -m =  134

Answer:

(95/31, -118/31)

Step-by-step explanation:

-7x-8y=9

4x+9y=-22

----------------

4(-7x-8y)=4(9)

7(4x+9y)=7(-22)

-----------------------

-28x-32y=36

28x+63y=-154

-----------------------

31y=-118

y=-118/31

-7x-8(-118/31)=9

-7x+944/31=9

-7x=9-944/31

-7x=279/31-944/31

-7x=-665/31

7x=665/31

x=(665/31)/7

x=(665/31)(1/7)

x=665/217=95/31

x=95/31, y=-118/31

For this case we have a factorized quadratic equation. We equal each factor to zero and thus find the roots:

[tex]x + 5 = 0[/tex]

Subtracting 5 from both sides we have:

[tex]x = -5[/tex]

Thus, the first solution of the equation is:

[tex]x_ {1} = - 5[/tex]

On the other hand we have:

[tex]x-3 = 0[/tex]

Adding 3 to both sides:

[tex]x = 3[/tex]

Thus, the second solution of the equation is:

[tex]x_ {2} = 3[/tex]

Answer:

The solutions of the equation are:

[tex]x_ {1} = - 5\\x_ {2} = 3[/tex]

Answer:

144

Step-by-step explanation:

x^2+24x=17

b=24

(b/2)^2=(24/2)^2=12^2=144

Answer:

Half-life of uranium-238 [tex]18 \times 10^{3} \text { times greater }[/tex] that of uranium-234

Explanation:

Half time of uranium-238 = [tex]4.5\times 10^9[/tex]  years

Half time of Uranium-234 = [tex]2.5\times 10^5[/tex] years

To find how much times greater the half life of uranium-238 is from uranium-234

= [tex]\frac{\text { Half life of Uranium-238 }}{\text { Half time of Uranium - 234 }}[/tex]

=[tex]\frac{4.5 \times 10^{9}}{2.5 \times 10^{5}}[/tex]

=[tex]18 \times 10^{3} \text { times greater }[/tex]

Hence Uranium-238 is  [tex]18 \times 10^{3} \text { times greater }[/tex] than Uranium-234

Final answer:

The half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234, determined by dividing the half-lives.

Explanation:

The half-life of uranium-238 is 4.5x10⁹ years, and the half-life of uranium-234 is 2.5x10⁵ years. To determine how many times greater the half-life of uranium-238 is than that of uranium-234, we divide the half-life of uranium-238 by the half-life of uranium-234:

(4.5x10⁹ years) / (2.5x10⁵ years) = 4.5/2.5 x [tex]10^{9-5[/tex] = 1.8 x 10⁴

Therefore, the half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234.

The solution in slope-intercept form for:

y + 7 = -3(x - 1) is y = -3x - 4

3x + y = -4 is y = -3x - 4

We have been given two equations  

y + 7 = -3(x - 1) and 3x + y = -4

we have been asked to simplify these equations in slope intercept form.

The slope intercept form can be written as follows:

y = mx + b

Where, m is the slope of the line and b is the y-intercept.

The y-intercept of this line is the value of y at the point where the line crosses the y axis

Now, let us write the first equation in slope intercept form as follows:

y + 7 = -3(x - 1)

y + 7 = -3x + 3

y = -3x + 3 - 7

y = -3x - 4

The slope intercept form for the first equation is y = -3x - 4

Now, let us write the second equation in slope intercept form.

This can be done as follows:

3x + y = -4

y = -3x - 4

Therefore, the slope intercept form for the second line is y = -3x - 4

Answer:

[tex]\large\boxed{(x-3)^2+(y+7)^2=200\to(x-3)^2+(y+7)^2=(10\sqrt2)^2}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2-6x+14y=142[/tex]

We must use

[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]x^2-6x+y^2+14y=142\\\\x^2-2(x)(3)+y^2+2(y)(7)=142\qquad\text{add}\ 3^2\ \text{and}\ 7^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(3)+3^2}_{(a-b)^2=a^2-2ab+b^2}+\underbrace{y^2+2(y)(7)+7^2}_{(a+b)^2=a^2+2ab+b^2}=142+3^2+7^2\\\\(x-3)^2+(y+7)^2=142+9+49\\\\(x-3)^2+(y+7)^2=200\\\\(x-3)^2+(y+7)^2=(\sqrt{200})^2\\\\(x-3)^2+(y+7)^2=(\sqrt{100\cdot2})^2\\\\(x-3)^2+(y+7)^2=(10\sqrt2)^2[/tex]

[tex]center:(3,\ -7)\\radius:10\sqrt2[/tex]

Answer:

The correct answer is D. 15 squared centimeters.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Base one = 10 centimeters

Base two = 5 centimeters

Height = 2 centimeters

2. Let's find out the area of the trapezoid, using the following formula:

Area = 1/2 (Base one + Base two) * Height

Replacing with real values:

Area = 1/2 (10 + 5) * 2

Area = 1/2 (15 * 2) = 1/2 (30)

Area = 15 centimeters ²

The correct answer is D. 15 squared centimeters.

Note: Same answer provided to question 14021584, answered by me.

Final answer:

To evaluate -6(4 2/3), convert 4 2/3 to an improper fraction, then multiply it by -6 and simplify the result.

Explanation:

To evaluate the expression -6(4 2/3), we need to simplify the expression inside the parentheses first. 4 2/3 can be converted to an improper fraction as follows: (4 * 3 + 2) / 3 = 14 / 3. Then, we multiply -6 by 14/3 to get: -6 * 14/3 = -84/3. The final step is to simplify -84/3, which is -28.

Answer:

The x-intercept is (3,0).

The vertex of the function is (3,0).

Step-by-step explanation:

Given : Function [tex]g(x)=-5(x-3)^2[/tex]

To find : What are the x-intercept and vertex of this quadratic function?

Solution :

Function [tex]g(x)=-5(x-3)^2[/tex]

The x-intercept is when g(x)=0.

i.e.  [tex]-5(x-3)^2=0[/tex]

Divide by -5 both side,

[tex](x-3)^2=0[/tex]

Taking root both side,

[tex]x-3=0[/tex]

Add 3 both side,

[tex]x=3[/tex]

The x-intercept is (3,0).

The general vertex form of the quadratic function is [tex]y=a(x-h)^2+k[/tex]

where, (h,k) is the vertex

Compare the given function [tex]g(x)=-5(x-3)^2[/tex]

a=-5 , h=3 and k=0

The vertex of the function is (3,0).

The x-intercept and the vertex of the quadratic function g(x) = -5(x - 3)² are both (3, 0).

Step-by-Step Solution

Finding the x-intercept:

Therefore, the x-intercept is (3, 0).

Finding the Vertex:

Therefore, the vertex is (3, 0).

Answer:

x = (-4/3)

y = (-5)

Step-by-step explanation:

there ya go, I think this was the answer you were looking for. :)

Answer:

The rate of interest for compounded daily is 2.1 6

Step-by-step explanation:

Given as :

The principal investment = $ 98,000

The Time period for investment = 7 years

Let The rate of interest compounded daily = R %

The Amount at the end up = $ 114,000

From compounded method

Amount = Principal × [tex](1+\dfrac{rate}{365\times 100})^{365\times Time}[/tex]

Or, $ 114,000 = $ 98,000  × [tex](1+\dfrac{R}{365\times 100})^{365\times 7}[/tex]

Or, [tex]\frac{114000}{98000}[/tex] = [tex](1+\dfrac{R}{36500})^{2555}[/tex]

or, 1.16326 = [tex](1+\dfrac{R}{36500})^{2555}[/tex]

or, [tex](1.16326)^{\frac{1}{2555}}[/tex] = 1 + [tex]\frac{R}{36500}[/tex]

1.00005919 - 1 =  [tex]\frac{R}{36500}[/tex]

or, 0.00005919 =  [tex]\frac{R}{36500}[/tex]

∴ R =  0.00005919 × 365000 = 2.16

Hence the rate of interest for compounded daily is 2.1 6   Answer

Answer:

x = 7/3

Step-by-step explanation:

To find the of x, isolate it from the other numbers (moving everything to the other side)

What you do to one side, you must do to the other:

3x + 8 = 15

3x + 8 - 8 = 15 - 8  (subtract 8 on both sides to rid of the "+ 8")

3x = 7

3x/3 = 7/3   (divide by 3 on both sides to rid of the 3 attached to "x")

x = 7/3

Answer:

x=2.3

Step-by-step explanation:

15-8=7

Divide 3 on each side (3x=7)7 divided by 3 is 2.3

so X=2.3