A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L=3D+200 gives L as a function of D. The crew can work for at most 90 days. Identify the correct description of the values in both the domain and range of the function. Then, for each, find the most appropriate set of values. PLEASE PLEASE PLEASE HELP!!! I WILL GIVE BRAINLIEST!!!

Answer:

Always

Step-by-step explanation:

Coplanar lines are lines that intersect making intersecting lines always coplanar.

The value of the gauge car after 4 years will be $18195.25.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given,

Principle amount (P)  = $29000

Rate of decrement (R) = 11%

Time period(T) = 4 years

Percentage decrement over T time period is given by

Final amount = P[tex][1 - R/100]^{T}[/tex]

Final amount = 29000[tex][1 - 11/100]^{4}[/tex]

Final amount = 29000(0.89)⁴

Final amount = $18195.25.

Hence, The value of the gauge car after 4 years will be $18195.25.

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The value of the car after 4 years is $18195.24989.

Given,

Gage bought a new car for $29000 to use while he is away at college.

The car decreases in value by 11% annually.

We need to find what would the cars value after 4 years.

we have,

Cost of the car = $29000

The car decreases annually by = 11%

1st-year decrease.

$29000 x 11/100 = $3190

The cost of the car after 1st year = $29000 - $3190 = $25810

2nd-year decrease.

$25810 x 11/100 = $2839.1
The cost of the car after 2nd year = $25810 -  $2839.1 = $22970.9

3rd-year decrease.

$22970.9 x 11/100 = $2526.799

The cost of the car after 3rd year = $22970.9 - $2526.799 = $20444.101

4th-year decrease.

$20444.101 x 11/100 = $2248.85111

The cost of the car after 4th year = $20444.101 - $2248.85111 = $18195.24

Thus the value of the car after 4 years is $18195.24989.

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Answer:

11/6

Step-by-step explanation:

To find the improper fraction

Take the denominator times the whole number

6*1 = 6

Add the numerator

6+5 =11

Put this over the denominator

11/6

Answer:

[tex]\frac{11}{6}[/tex]

Step-by-step explanation:

What is 1 5/6 as an improper fraction?

If you wanna make 1 5/6 as a improper fraction, you must take the 5 from 1 5/6 and add it 6.

[tex]6+5=11[/tex]

[tex]\frac{11}{}[/tex]

Since the denominator is 6, you will put it down.

[tex]\frac{11}{6}[/tex]

So now you got your answer!

Hope this Helps!

Answer:

Step-by-step explanation:

R = 12 in

360°:30° = 12

so the area of the slice is ¹/₁₂ of whole pizza

A = ¹/₁₂•πR² = ¹/₁₂•π•12•12 = 12π in² ≈ 37.7 in²

Crust is the perimeter of pizza so crust of the slice is ¹/₁₂ of the perimeter:

L = ¹/₁₂•2πR = ¹/₁₂•2π•12 = 2π in ≈ 6.28 in

Greetings from Brasil...

We have 2 conditions:

1 - angles opposed by the vertex - the angles are equal

2 - supplementary angles - the sum of the two angles results in 180

2:

(4X + 15) and (5X + 30) are supplementary angles, so:

(4X + 15) + (5X + 30) = 180

9X = 180 - 15 - 30

9X = 135

1:

(3Y + 15) and (5X + 30) are angles opposed by the vertex, so they are equal

3Y + 15 = 5X + 30

3Y = 5X + 30 - 15

3Y = 5X + 15   above we have already calculated the value of X

3Y = 5.(15) + 15

3Y = 75 + 15

3Y = 90

Y = 90/3

Answer:

Slope-Intercept form: y=3x+7

Standard form: 3x-y=-7

Point-slope form: y-1=3(x+2)

Step-by-step explanation:

Slope-Intercept form:

First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).

So let's write those in our equation to find slope:

[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]

Therefore, our slope is 3.

Now let's write our linear equation with what we have already in slope-intercept form:

y=3x+b

Well, we still need to find the y-intercept, or "b".

Plug in one of your points for the x and y values of the equation.  We'll use the point (-2,1)

[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]

This means our y-intercept is 7.  Now we can write our equation in slope-intercept form completely:

y=3x+7

Standard form:

Now, let's find this equation is standard form.

Take your equation in slope-intercept form and write it out again:

[tex]y=3x+7[/tex]

Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:

[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]

The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:

[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]

Therefore, your equation in standad form is:

3x-y=-7

Point-Slope form:

The formula for point-slope form is y-y₁=m(x-x₁).  We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.

x₁ is -2 and y₁ is 1 and m is 3, so:

y-1=3(x-(-2)) or y-1=3(x+2)

That means our equation in point-slope form is:

y-1=3(x+2)

Answer:

on her first quiz

Step-by-step explanation:

27/30=

27÷30=

0.9=

09×100/100=

0.9×100%=

(0.9×100)% =

90%

Answer:

first quiz

Step-by-step explanation:

100 divided by 30 times 27<92%

Answer:

The area of the hubcap is 196π or 615.7521601

Step-by-step explanation:

You can use A=πr² to find the area of a circle. So that would mean that A equals 14². 14²=196. If the answer is in π form, then the answer is 196π. If not then its 196·π. 196·π=615.7521601

Hope that helps!

Answer:

The area of the hubcap is about 615.44 cm²

Step-by-step explanation:

A = πr²

 Use the formula.

A = π(14)²

 Substitute. Use 14 for r.

A ≈ 3.14 × 14²

 Substitute. Use 3.14 for π.

A ≈ 3.14 × 196 Evaluate the power.

A ≈ 615.44 Multiply.

Step-by-step explanation:

First factor out the negative sign from the expression and reorder the terms

That's

[tex] \frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) } [/tex]

Using trigonometric identities

That's

Rewrite the expression

That's

[tex]\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } } [/tex]

We have

Rewrite the second fraction

That's

Since they have the same denominator we can write the fraction as

[tex] - \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]

Using the identity

Rewrite the expression

We have

Using the trigonometric identity

Rewrite the expression

That's

Which is

Using the trigonometric identity

Rewrite the expression

That's

Simplify the expression using symmetry of trigonometric functions

That's

Remove the parenthesis

We have the final answer as

As proven

Hope this helps you

Answer:   see proof below

Step-by-step explanation:

Use the following identities:

[tex]\cot\alpha=\dfrac{1}{\tan\alpha}\\\\\\\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\cdot \tan\beta}{\tan\alpha-\tan\beta}[/tex]

Proof  LHS →  RHS

Given:                  [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\cot 6A-\cot 2A}[/tex]

Cot Identity:        [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}-\dfrac{1}{\tan 2A}}[/tex]

Simplify:              [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}\bigg(\dfrac{\tan 2A}{\tan 2A}\bigg)-\dfrac{1}{\tan 2A}\bigg({\dfrac{\tan 6A}{\tan 6A}\bigg)}}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{\tan 2A-\tan 6A}{\tan 6A\cdot \tan 2A}}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}[/tex]

                         [tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}\bigg(\dfrac{-1}{-1}\bigg)[/tex]

                        [tex]= \dfrac{1}{\tan 6A-\tan 2A}+\dfrac{\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]

                        [tex]= \dfrac{1+\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]

Sum Difference Identity:    cot(6A - 2A)

Simplify:                               cot 4A

cot 4A = cot 4A   [tex]\checkmark[/tex]

Answer:

A

Step-by-step explanation:

A

The mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality. which is the correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question

6x - 1 = -2x + 9

Addition property of equality

8x - 1 = 9

Subtraction property of equality

8x = 10

Division property of equality

x = 10/8

Simplification

x = 5/4

Thus, the mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality.

Hence, the correct answer would be option (A).

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Answer: Because division is the inverse of multiplication.

Step-by-step explanation:

By multiplying the equation 2x=20 by 1/2  you will be able to eliminate the x variable,

For example,

1/2 * 2x = 20*1/2  

 x=  10  

The same way if  you divide both sides of the equation 2x=20 by 2 you will be able to to eliminate the x variable.

For example

2x = 20  Divide both sides by 2

x= 10  

As you can see 2 is the division inverse of 1/2.

Answer:

10x²+3xy+6x-y²+3y

Step-by-step explanation:

(2x+y)(5x-y+3)  steps

2x(5x-y+3)=10x²-2xy+6x

y(5x-y+3)= 5xy-y²+3y

add: 10x²-2xy+6x+5xy-y²+3y

10x²+3xy+6x-y²+3y

Answer:

Orthogonal.

Step-by-step explanation:

Given:

u = <10, 0>

v = <0, -9>

In unit vector notation, the above vectors can be re-written as:

u = 10i + 0j

v = 0i - 9j

Now, note the following:

(i) two vectors, u and v, are parallel to each other if one is a scalar multiple of the other. i.e

u = kv

or

v = ku

for some nonzero value of a scalar k.

(ii) two vectors are orthogonal if their dot product gives zero. i.e

u . v = 0

Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.

(a) If parallel

u = k v

10i + 0j = k (0i - 9j)   ?

When k = 1, the above equation becomes

10i + 0j  ≠  0i - 9j

When k = 2,

10i + 0j ≠ 2(0i - 9j)

10i + 0j ≠ 0i - 18j

Since we cannot find any value of k for which u = kv or v = ku, then the two vectors are not parallel to each other.

(b) If Orthogonal

u.v = (10i + 0j) . (0i - 9j)  

[multiply the i components together, and add the result to the multiplication of the j components]

u.v = (10i * 0i) + (0j * 9j)

u.v = (0) + (0)

u.v = 0

Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.

Answer:

0.9

Step-by-step explanation:

Y = B0 + B1X

B1 is the slope an from the question the slope estimate is 0.5

S.E= standard error at 0.2

At 5percent Level of significance, the z value for the test is equal to 1.96

We are required to find out the largest value of b for which the null hypothesis would be accepted.

0.5 + 1.96 x 0.2

= 0.892

Approximately 0.9

Answer:

  y + (y+10) = 107.50

Step-by-step explanation:

Let y represent Terry's purchases. Then Tori's purchases are (y+10). The sum of their purchases is given by the equation ...

  y + (y+10) = 107.50

_____

Then y = 48.75 represents Terry's spending, while y+10 = 58.75 represents Tori's spending.

Answer:

A. Trapezoid

B. Isoclese triangle

c. Equilateral triangle

d. Kite

Answer:

A, Parallelogram (more specifically a trapezoid)

B. Isosceles Triangle

C. Equilateral Triangle

D. Kite

Answer:

Width = 40ft

Step-by-step explanation:

Area of a rectangle = Length x Width

=> 1600 = 40 x W

=> 1600 = 40W

=> 1600/40 = 40W/40

=> 40 = W

So, the width is 40 ft

Answer:

40 ft  is the correct answer

Answer:

20

Step-by-step explanation:

[tex] \frac{9}{g} + 2h + 5 \\ = \frac{9}{3} + 2 \times 6 + 5 \\ = 3 + 12 + 5 \\ = 20[/tex]

Answer:

The value of the 8 in the front is 800,000 and the value of the second is 80,000. The front value is ten times as big as the second value.

Step-by-step explanation:

Answer:

[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]

Step-by-step explanation:

Given

[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]

Required

Find an equivalent expression

[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]

Apply the following law of indices;

[tex]\frac{a^m}{a^n} a^{m-n}[/tex]

The expression becomes

[tex]125^{2-\frac{4}{3}}[/tex]

Solve the exponents

[tex]125^{\frac{6-4}{3}}[/tex]

[tex]125^{\frac{2}{3}}[/tex]

Express 125 as 5³

[tex]5^{3^*\frac{2}{3}}[/tex]

Solve the exponents

[tex]5^2[/tex]

[tex]25[/tex]

Hence;

[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]

Answer:

d

Step-by-step explanation:

i just took it! edgen

Answer:

Geetha is 32.5 years old

her daughter is 11.5 years old

Step-by-step explanation:

sum of their ages is 44 years

G + D = 44

in two years, Geetha's age is 3 times her daughters age. (to find present age, subtract 2)

G = 3D - 2

substitute

(3D - 2) + D = 44

combine like terms

4D - 2 = 46

4D = 46

D = 11.5

plug in D to either equation

G + (11.5) = 44

G = 32.5

G = 3(11.5) - 2

G = 32.5

Answer:

x = 8

Step-by-step explanation:

[tex] \triangle XYZ \sim\triangle PQR... (GIVEN) \\

\therefore \frac{XY}{PQ} = \frac{YZ}{QR}.. (csst) \\

\therefore \frac{20}{30}= \frac{x+6}{21}\\

\therefore \frac{2}{3}= \frac{x+6}{21}\\

\therefore \frac{2\times 21}{3}= {x+6}\\

\therefore 14= {x+6}\\

\therefore 14-6= {x}\\

\therefore 8= {x}\\

\huge \orange{\boxed {\therefore x = 8}} [/tex]

Answer:

x = - [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Given

5x - 2 = 25x + 14 ( subtract 25x from both sides )

- 20x - 2 = 14 ( add 2 to both sides )

- 20x = 16 ( divide both sides by - 20 )

x = [tex]\frac{16}{-20}[/tex] = - [tex]\frac{4}{5}[/tex]

Answer:

y = 8

Step-by-step explanation:

[tex] \frac{y}{4} = \frac{5 + 5}{5} \\ \\ \frac{y}{4} = \frac{10}{5} \\ \frac{y}{4} = 2 \\ y = 4 \times 2 \\ y = 8[/tex]

Answer:

4.5

Step-by-step explanation:

→ Set up the direct proportion equation

z = kx

→ Substitute in the values

12 = 3k

→ Divide both sides by 3 to isolate k

4 = k

→ Substitute the value of k back into the original direct proportion equation

z = 4x

→ Substitute the value of z in

18 = 4x

→ Divide both sides by 4 to isolate x

4.5 = x

Answer:

4.5

Step-by-step explanation:

Answer:

y= -1

Step-by-step Explanation:

3(5y +2)-y=2(y-3)

Distribute-  15y +6-y=2y -6

Combine variables-  15y-2y-y=-6-6

Add everything together-  12y= -12

Divide-  y= -1

Answer:

y = -1

Step-by-step explanation:

Step 1. Expand the brackets.

3(5y + 2) - y = 2(y - 3)

(3 x 5y) + (3 x 2) - y = (2 x y) - (2 x 3)

15y + 6 - y = 2y - 6

Step 2. Simplify the expanded brackets (not always necessary but is in this case).

15y + 6 - y = 15y - y + 6 = 14y + 6

So

14y + 6 = 2y - 6

Step 3. Solve the equation.

14y + 6 = 2y - 6

+ 6 to both sides

14y + 12 = 2y

- 14y from both sides

12 = -12y

÷ 12 on both sides

1 = -y

flip the negative

-1 = y

Step 3. Write your answer.

y = -1

Answer:

20 degrees.

Step-by-step explanation:

Since these triangles are similar, they will have congruent angles.

Since BAC is corrosponding to EDF, they will have the same angle measurment.

BAC = 20, so EDF = 20

Answer:

EDF = 20

Step-by-step explanation:

If the triangles are similar, the angle measurements have to be equal

<A = <D

<B = <E

<C = <F

Since BAC = 20,  <A = 20 that means D = 20

EDF = 20

Answer:

[tex] \frac{1}{5} ( - m - 4)[/tex]

Step-by-step explanation:

But method 1 best suits the question

Answer:

[tex] - \frac{1}{5} m - \frac{4}{5} [/tex]

Answer:

-1/5m    -4/5

Step-by-step explanation:

2/5 m -4/5 - 3/5 m

Combine like terms

2/5m - 3/5m    -4/5

-1/5m    -4/5

Answer:

X = 2000 / (75 + 150)

Step-by-step explanation:

Given the following :

Christine's typing rate = 75 words per minute

Paula's speed = 2 times Christine's speed

If 2000 words needs to be transcribed. The time taken in minute 'x' will be :

From the relation :

Time = distance / speed

Distance here is the number of words in the document

Christine's speed = 75 words per minute

Paula's speed = 150 words per minute

Combined speed per minute = 150 + 75 = 225 words per minute

Time taken (x) = 2000 / 225

X = 2000 / (75 + 150)