Devon needs a wood board with an area of 516 square yard to complete a project. If the wood board is 13 yard wide, how long must the board be?

Answer:

x= 65 degrees

Step-by-step explanation:

If the triangles vertices are marked CDE (d as the right angle and c as the leftmost vertex) then:

Alternate interior angles

⇒m∠ACE=85 degrees

m∠ACD=25 and  m∠ACD+m∠DCE=m∠ACE=85 degrees

⇒ 25 + m∠DCE= 85 ⇒ m∠DCE=60 degrees

Since the sum of the angles in a triangle is 180 degrees

⇒ 60 + 90 + m∠DEC = 180 ⇒ m∠DEC= 30 degrees

Finally, since ∠BEC is supplementary to the given 85 degree angle

⇒ 30 + 85 + x = 180 ⇒ x=65

Answer:

[tex]\huge\boxed{x = 65 \ \text{degrees}}[/tex]

Step-by-step explanation:

We can use angle relationships to find the measure of [tex]x[/tex] here.

Let's assume that the triangle has the points ABC, where m∠a is the leftmost angle, m∠b is the right angle, and m∠c is the rightmost angle (I've labeled it in the attached picture).

We have to realize here that a and b are parallel lines. This means that the angles on one side will be equivalent to the other as long as the triangle in the center is symmetrical along both.

It's not. However, we can make it symmetrical by realizing that the 85° angle is the exact same as Line A AC. These are alternate interior angles, meaning their angle measurements will be the same. So Line A A C is also 85°.

Line A A C covers the area even in the triangle. Since we know the total measure and the measure outside the triangle, we can find the measure of m∠a.

[tex]25 + a = 85\\\\a = 85-25\\\\a = 60[/tex]

Now we know that m∠a is 60°. We also know that m∠b is a 90° angle. All triangle angles add up to 180°. Since we know two out of the three, let's find the measure of m∠c by adding up what we know and subtracting from 180.

[tex]60+90+c=180\\\\150+c=180\\\\c=180-150\\\\c=30[/tex]

Now that we know m∠c, we can note that the 85° angle, m∠a, and x are supplementary. This means their angle lengths add up to 180°. Since we know two out of the three, we can do a process similar to finding the missing triangle angle.

[tex]85+30+x=180\\\\115+x=180\\\\x=180-115\\\\x = 65[/tex]

Therefore, x is 65°.

Hope this helped!

Answer:

4/-3

Step-by-step explanation:

To find the slope

y2 - y1 / x2 - x1 =

12 - -4          16

---------- =     ----

1 - 13           -12

Simplify by dividing both parts by 4

4/-3 is your slope :)

Answer:

Step-by-step explanation:

I've answered this question already.

Answer:

18.3 ( when EPS is 45 cents), otherwise there is none of these

Step-by-step explanation:

PE = Current Price / EPS

current Price = $ 8.22 = 822 cents

EPS = .45 cents (?) ... is it 45 cents ?

if it is 45 cents : PE = 822 / 45 = 18.26 ≈ 18.3

The required PE ratio of the Zolt's is given as 18.3. Option A is correct.

Given that,
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

PE = Current Price: EPS
PE = Current Price / EPS

Current Price = $ 8.22 = 822 cents

EPS = 0.45 cents = 45 cents

it is 45 cents per PE
So Ratio = 822 / 45 = 18.3

Thus, the required PE ratio of the Zolt's is given as 18.3. Option A is correct.

Learn more about ratios here:

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Answer:

-2475

Step-by-step explanation:

Answer:

( f + g ) (x) = [tex] 2 x^{2}  + x - 4[/tex]

g(x) - f(x) = [tex] x^{2}  - 2 x - 4[/tex]

Step-by-step explanation:

( f + g ) (x) = f(x) + g(x)

                = [tex] 4 x - 4 + 2  x^{2}  - 2 x[/tex]

                = [tex] 2 x^{2} + x -4[/tex]

   2.  g(x) = [tex] x^{2}  + 1[/tex] and f(x) = 2 x + 5

g(x) - f(x) = [tex] x^{2}  + 1 - (2 x + 5)[/tex]

              = [tex] x^{2}  + 1 - 2 x - 5[/tex]

              = [tex] x^{2}  - 2 x - 4[/tex]

Answer:

1242

Step-by-step explanation:

[tex]1. \: 6(15 - 5 + 3)4 \times 4 - 6 \\ 2. \: 6(10 + 3)4 \times 4 - 6 \\ 3. \: 6(13)4 \times 4 - 6 \\ 4. \: 78 \times 4 \times 4 - 6 \\ 5. \: 312 \times 4 - 6 \\ 6. \: 1248 - 6 \\ 7. \: = 1242[/tex]

Answer:

y=-2x

Step-by-step explanation:

Answer:

y+2x=8

Step-by-step explanation:

when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope

Answer:

(-8 - 4)/(-4 - 0) = -12/-4= 3

y - 4 = 3(x - 0)

y - 4 = 3x - 0

y = 3x + 4

the answer is c

Answer:

The two numbers are

518

694

Step-by-step explanation:

As per requirements the two equations will be

X+Y=1212

X-Y=518

When we subtract these equations we get

X=1212-518

X=694

Now put the X value and find the Y value in any equation

X+Y= 1212

Y=1212-X

Where X = 694

Y=1212-694

Y=518

X=694 and Y=518

Answer:

answer is 865.

Step-by-step explanation:

865+347 is 1212 an the diff is 518.

and the largest number out of 865 and 347 is 865

Answer:

Adrian would make $196000 in his 26th year working.

Step-by-step explanation:

Adrian salary in first year = $66,000

As Adrian is expected to get raises of $5,000 every year going forward.

Here is the sequence of Adrian's raises:

5,000, 10000, 15000, 20000, 25000 .....

As the common difference between consecutive terms is constant.

d = 10000 -  5,000 = 5,000 ⇒ d = 15000 -  10000 = 5,000

So, Adrian's raises is in Arithmetic sequence.

a₁ = 5,000

n = 26

[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]

Put n = 26 to get the total amount of salary raises in Adrian's 26th year.

[tex]{\displaystyle \ a_{26}=5000+(26-1)5000}[/tex]

[tex]{\displaystyle \ a_{26}=5000+(25)5000}[/tex]

[tex]{\displaystyle \ a_{26}=5000+125000}[/tex]

[tex]{\displaystyle \ a_{26}=130000}[/tex]

Total raises amount after 26th year = $130000

Adding total raises after 26th year to the initial salary would let us figure out the total salary Adrian would make in his 26th year.

So,

Total Salary after 26th year = initial salary + total raises of 26 years

                                              = 66000 + 130000

                                              = $196000

So, Adrian would make $196000 in his 26th year working.

Keywords: arithmetic sequence, salary, raises, common difference

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Answer:

x= -12.6/7. you may try this

Good evening ,

Answer:

The solutions of the equation 7x(x+1.8)=0 are -1.8 and 0.

Step-by-step explanation:

7×(0)×[(0)+1.8] = 0×[1.8] = 0×1.8 = 0

7×(-1.8)×[(-1.8)+1.8] = 7×(-1.8)×[0] = 7×(-1.8)×0 = 0.

:)

Answer:

9/10 ( or 0.9)

Step-by-step explanation:

quotient of 3/4 and 5/6

= 3/4 ÷ 5/6

= 3/4 x 6/5

= 18/20

= 9/10 ( or 0.9)

Answer:

9/10

Step-by-step explanation:

Answer:

50 Minutes.

Step-by-step explanation:

The function c approximates the total number of calls made after m minutes since the start of the phone tree.

[tex]c(m)=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]

We need to find the number of minutes after which the total number of calls will 363.

Substitute c(m)=363 in the given function.

[tex]363=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]

Multiply 3/2 both sides.

[tex]363\times \frac{3}{2}=(3^{\frac{m}{10}}-1)[/tex]

[tex]242=3^{\frac{m}{10}}-1[/tex]

Add 1 on both sides.

[tex]243=3^{\frac{m}{10}}[/tex]

[tex]3^5=3^{\frac{m}{10}}[/tex]

On comparing both sides we get

[tex]5=\frac{m}{10}[/tex]

Multiply both sides by 10.

[tex]50=m[/tex]

Therefore, the total number of calls will 363 after 50 minutes since the start of the phone tree.

Answer:

50 minutes

Step-by-step explanation:

Answer:

The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we know that

A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.

we have

[tex]0.25[/tex]

Let

[tex]x=0.25[/tex]

Multiply by 100 both sides

[tex]100x=25[/tex]

Divide by 100 both sides

[tex]x=\frac{25}{100}[/tex]

Simplify

Divide by 25 both numerator and denominator

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

Answer:

2,1

Step-by-step explanation:

y=-3x+7

y=-3(2)+7

y=-6+7

y=1

so (2,1)

Answer:

The y-intercept of the line is 34.

Step-by-step explanation:

There are few points on the z-y plane through which a straight line passes.

The points are (-56,66), (-42,58) and (-28,50).

Now, take the first two points to get the equation of the straight line.

The equation is [tex]\frac{y - 58}{58 - 66} = \frac{z - (-42)}{-42 - (- 56)}[/tex]

⇒ [tex]\frac{y - 58}{- 8} = \frac{z + 42}{14}[/tex]

⇒ 14(y - 58) = - 8(z + 42)

⇒ [tex]y - 58 = - \frac{8}{14}z - 24[/tex]

⇒ [tex]y =  - \frac{8}{14}z + 34[/tex]

This equation is in slope-intercept form.

Hence, the y-intercept of the line is 34. (Answer)

Answer:

(3x − 4) (x + 2)

Step-by-step explanation:

3x² + 2x − 8

Factor using AC method.

3 × -8 = -24

Factors of -24 that add up to 2 are -4 and 6

Divide by 3 and reduce: -4/3 and 6/3 = 2/1

(3x − 4) (x + 2)

Answer:

∠A ≈ 19.47°

Step-by-step explanation:

As you know , the angle that tangent makes with the radius at the point of tangency is 90°.

∴∠OKA = 90°

As  AO = 15 and OK = 5 ,

[tex]sin(A) = \frac{OK}{AO}[/tex]

[tex]sin(A) = \frac{5}{15} [/tex]

[tex]sin(A) = \frac{1}{3} [/tex]

∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]

∠A ≈ 19.47°

Answer:

[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]

Step-by-step explanation:

This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.

[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]

In ΔAKO,

m∠AKO = 90°

Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.

AO = 15

OK = 5

[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]

[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]

[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]

To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator

value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°

Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]

(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°

Therefore m∠AKO = 90°)

Answer:

4

Step-by-step explanation:

Consecutive integers are  e.g.  1, 2, 3, 4, ...

So they are 1 units apart.

If we let one of the integers be "x", then the next consecutive one would be "x + 1".

x is the smaller

x + 1 is the larger

of the two...

Now,

The sum of smaller (x) and 2 TIMES larger (x + 1) is 14, so we can write:

[tex]x+2(x+1)=14[/tex]

We use algebra and solve for x:

[tex]x+2(x+1)=14\\x+2x+2=14\\3x=14-2\\3x=12\\x=4[/tex]

So, the two numbers is 4  &  5

smaller of the two numbers is "4"

To find the smaller of two consecutive integers where the sum of the smaller and two times the larger is 14, set up the equation x + 2(x + 1) = 14 and solve for x to find that the smaller integer is 4.

To find the smaller of two consecutive integers x, when the sum of the smaller and two times the larger is 14, we can set up a simple algebraic equation. Let x be the smaller integer; then the larger integer is x+1. The equation based on the given information is:

x + 2(x + 1) = 14

Now, let's solve for x:

Therefore, the smaller consecutive integer is 4.

Answer:

Width [tex]10y^6[/tex] units

Length [tex]7y^2+3[/tex] units

Step-by-step explanation:

The rectangle has an area of [tex]70y^8+30y^6.[/tex]

The width of the rectangle is equal to the greatest common monomial factor of [tex]70y^8[/tex] and [tex]30y^6.[/tex] Find this monomial factor:

[tex]70y^8=2\cdot 5\cdot 7\cdot y^8\\ \\30y^6=2\cdot 3\cdot 5\cdot y^6\\ \\GCF(70y^8,30y^6)=2\cdot 5\cdot y^6=10y^6[/tex]

Hence, the width of the rectangle is [tex]10y^6[/tex] units.

The area of the rectangle can be rewritten as

[tex]10y^6(7y^2+3).[/tex]

The area of the rectangle is the product of its width by its length, then the length of the rectangle is [tex]7y^2+3[/tex] units.

Answer:

  (x, y) = (-1.8, -1.4)

Step-by-step explanation:

Modern graphing calculators make it trivially simple to solve many problems by graphing. It has become my favorite method.

The graph shows the solution to be (x, y) = (-1.8, -1.4).

___

If you're graphing by hand, it is usually convenient to start with the y-intercepts, then draw the lines with the required slopes. These equations are written in slope-intercept form, making that approach relatively simple.

The first equation has a y-intercept of (0, 4) and a slope of 3. So, another point on the graph will be left 1 and down 3 (as opposed to right 1 and up 3). That point is (-1, 1).

The second equation has a y-intercept of (0, -5) and a slope of -2. So, another point on the graph of that will be left 1 and up 2, to (-1, -3)

Answer:

y-6=4(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=4(x-4)

Answer:

256a^20b^24

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.

HOPE THIS HELPED ;3

Answer:

5(4-1)

Step-by-step explanation:

5(4-1)

20-5

5x4= 20

5x1= 5

Answer:

The blue portion of the flag is actually 2/6 or 1/3 of the flag

Step-by-step explanation:

If you look at the size of the blue portion of the line it takes up twice the space as the white part. Imagine a small line drawn through the middle of the blue rectangle, now you can see that the flag is split up into 6 parts, rather then 5! Since we now have 2/6 of the flag being taken up by blue, that can be reduced down to 1/3 of the flag covered in blue.

Answer:

The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks .

Step-by-step explanation:

Given as :

The amount of money having with Ava at starting = $100

The money that Ava is saving each week = $5

The amount of money having with Addison at starting = $200

The money that Addison is saving each week = $4

Now, Let The numbers of weeks for which both Ava and Addison have same amount of money saved = n weeks

Now, According to question

The amount of money having with Ava at starting + (The money that Ava is saving each week × numbers of weeks) = The amount of money having with Addison at starting + (The money that Addison is saving each week × numbers of weeks)

Or, $100 + $5 × n = $200 + $4 × n

Or, $5 × n - $4 × n = $200 - $100

Or, n = 100

So,  The numbers of weeks for which both Ava and Addison have same amount of money saved = n = 100 weeks

Hence,The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks . Answer

Answer:

14:26, 21:39, 28:52, 35:65, 42:78, 41:91

Step-by-step explanation:

All of the above are equivalent ratios. These are only a few. More can be found by just simply multiplying 7 by any amount, and 13 by any amount.

Ratios that are equivalent to 7:13 from the given options are 21:39, 28:52, and 14:26. Option A, C, D is correct.

To find equivalent ratios, we need to multiply or divide both terms of the ratio by the same non-zero number. Let's go through the options provided:

Therefore, the equivalent ratios are 21:39, 28:52, and 14:26.

Hence, A. C. D is the correct option.

The complete question is:

Which are equivalent ratios to 7:13?

A) 21:39

B) 72:128

C) 28:52

D) 14:26

E) 36:48