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The area of a rectangle is 35 yd?, and the length of the rectangle is 3 yd more than twice the width. Find the dimensions of the rectangle.
DO

Answer:

Let s = his speed on the outbound trip

Then s + 20 = his speed on the return trip

Let t = his travel time on the outbound trip

Then t - 10 = his travel time for the return trip

Given: d = 750

Since distance = speed x time, for the two trips we have

750 = s*t

750 = (s+20)(t-10)

Solve for t in the 1st equation, substitute in the 2nd:

750 = (s+20)(750/s-10)

Solve for s:

750 = 750 - 10s + 15000/s - 200

Simplify:

s^2 + 20s - 1500 = 0

Factor:

(s+50)(s-30) = 0

Take the positive solution, s = 30

So the rates are 30 kph and 50 kph

So

[tex]\\ \rm\Rrightarrow v=r\omega[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{v}{\omega}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\div\dfrac{34\pi}{3}=\dfrac{17\pi}{6}\times \dfrac{3}{34\pi}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{4}[/tex]

[tex]\\ \rm\Rrightarrow r=0.25ft[/tex]

Convert to ft

1 min=60s

Hence

So

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\times \dfrac{1}{680\pi}[[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{40}[/tex]

[tex]\\ \rm\Rrightarrow r=0.025in[/tex]

Convert to ft

None of the above

The radius of the smaller gear is 15 feet, Option C is correct.

Velocity is defined as the rate of change of distance of a body with respect to time

We can use the relationship between linear velocity and angular velocity for gears to solve this problem:

v = rω

where v is the linear velocity, r is the radius of the gear, and ω is the angular velocity.

We are given the linear velocity of the larger gear, which is 17π/6 inches per second.

v = 17π/6 inches per second

ω = (34π/3) / 60 radians per second

the radius of the smaller gear is:

r = v / ω

= (17π/6) / ((34π/3) / 60)

= 17π/6×60/(34π/3)

=17π/6×60×3/34π

= 1/6 ×60× 3/2

= 180/12

=15 feet

Hence,  the radius of the smaller gear is 15 feet.

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Answer:

68°

Step-by-step explanation:

triangle ODB is congruent to triangle FIL. Therefore, angle L is equal to angle B. So angle L is 68°

Answer:

a₁₂ = 106

Step-by-step explanation:

Given

Formula for nth term

Using that to expand a₆ and find d

Finding a₁₂

Answer:

[tex]a_{12}=106[/tex]

Step-by-step explanation:

Arithmetic sequence

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Given:

To find the common difference (d), substitute the given values into the general formula and solve:

[tex]\begin{aligned}\implies a_6=(-4)+(6-1)d & =46\\ 5d-4 & =46\\ 5d & = 50\\ d & =10\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}[/tex]

To find the 12th term, substitute n = 12 into the equation:

[tex]\implies a_{12}=10(12)-14=106[/tex]

Answer:

The answer is

→ [tex]3 \frac{1}{8}x + 9\frac{11}{14}[/tex]

Step-by-step explanation:

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Answer:

A, C, can't see full answers

Step-by-step explanation:

a. 15/3=5 plus 10 is 15

Answer:

rewrite f(g(-2))

plug in -2 in g(x)

g(x)=-2-3

g(x)=-5

now plug in -5 into f(x)

f(x)=-5^2

f(x)=25

25 is the answer

Answer:

-2x^3+6x^2

or simplified : -2x^2(x-3)

Step-by-step explanation:

Rewrite the statement as:

[tex]((x^2)(x-3))(-2)\\[/tex]

Distribute:

[tex](x^2*x-3*x^2)(-2)\\(-2)(x^3-3x^2)\\-2x^3+6x^2[/tex]

simplify by taking a common factor out, in this case, -2x^2:

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

Natalie Albert deposited checks totaling $1,735,97 into her savings account, she withdrew $100.00 while depositing some coins. If her total deposit was $1,668.71 then Natalie deposited $32.74 in coins.

Two or more expressions with an Equal sign is called as Equation.

Let's call the amount Natalie deposited in coins "x".

We know that her total deposit was $1,668.71,

so we can write an equation:

1,735.97 - 100.00 + x = 1,668.71

Simplifying, we get:

1,635.97 + x = 1,668.71

Subtracting 1,635.97 from both sides, we get:

x = 32.74

Therefore, Natalie deposited $32.74 in coins.

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Answer:

  $545

Step-by-step explanation:

Finding the price that maximizes profit requires several steps. We need the demand function that tells quantity sold in terms of selling price. With this, we can express the cost and revenue functions in terms of selling price. The profit will be the difference between revenue and cost.

__

The demand (q) is said to be a linear function of price (p). The equation for that can be written ...

  q(p) = (q2 -q1)/(p2 -p1)(p -p1) +q1 . . . . . for two points (p1, q1) and (p2, q2)

Using the given demand points, this can be ...

  q(p) = (1900 -2600)/(575 -470)(p -470) +2600

  q(p) = -20/3(p -470) +2600

  q(p) = -20/3p +5733 1/3

__

The cost function in terms of selling price can be found by substituting the q(p) equation for x in c(x). For the purpose of finding the maximum profit, we only need the marginal cost function:

  c(q(p))' = c'(q(p))·q'(p) = (608 -0.18(q(p)))·(-20/3) = (608 -0.18(-20/3p +5733 1/3))(-20/3)

  c'(p) = -8p +2826 2/3

__

As with cost, the function we need for finding the maximum profit is the marginal revenue function. Revenue is the product of price and demand, so the marginal revenue is ...

  r(p) = p·q(p)

  r'(p) = q(p) +p·q'(p) = (-20/3p +5733 1/3) +p(-20/3)

  r'(p) = -40/3p +5733 1/3

__

The maximum profit is found where the marginal profit is zero. In turn, that is found where the difference between marginal revenue and marginal cost is zero:

  P = R -C

  P'(p) = 0 = r'(p) -c'(p) = (-40/3p +5733 1/3) -(-8p +2826 2/3)

  0 = -16/3p +2906 2/3

  16p = 8720 . . . . . multiply by 3, add 16p

  p = 545 . . . . . . . price for maximum profit

The price per set that maximizes profit is $545.00.

Answer:

The first option is the best

Step-by-step explanation:

1       (1+ 07/4)^4 = 7.186 % annual

2      ( 1+.068/12)^12 = 7.0159 %   annual

3       7.1 %

4       (1 + .069/365)^365 = 7.143

Answer:

y^2 - 28/7

Step-by-step explanation:

Check the picture below, recall that the radius of a circle is always the same length in the circle.

Answer:

you can get 4 pieces

Step-by-step explanation:

2.5+2.5+2.5+2.5=10. or 2.5×4=10

Answer:

Yes

Step-by-step explanation:

The relation here is we see that the y value is 1 less than the x value.

So, the function can be written as :

Answer:

they all have a factor of 5

Step-by-step explanation:

Answer:

According to this problem, i would say the answer is c

Step-by-step explanation:

a variable examples are letters such as x, y, z, n

Answer:

Upward

Step-by-step explanation:

Upward the graph looks like the above picture.

Answer:

2 thirds, or 0.666666666667

Step-by-step explanation:

Answer: the answer is A or the 1st one

Step-by-step explanation:

Answer:

the answer is the frist one

Step-by-step explanation:

Answer:

Hope it helps................

Answer: 2,990 Is the amount of Bricks Marcus will use for the wall

Step-by-step explanation:

If the wall is 130 bricks high and 23 bricks across then all you have to do is 130 x 23 which gives you 2,990

but since the question asks for best estimate just choose the answer closest to 2,990 unles they have 2,990 as an answer

Hope this Helps!

Answer:

1 7/8 - 1 5/8 = 2/8.

Step-by-step explanation:

The amount of milk in cups that Samuel had after he made biscuits is 1/4 cups.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

Given that,

Amount of milk Samuel had = 1 7/8 cups

Amount of milk used to make biscuits = 1 5/8 cups

We have to find the amount of milk left after he made the biscuits.

This is found by subtracting the total amount of milk by the amount of milk used to make the biscuits.

Amount of milk left = 1 7/8 - 1 5/8

                                = 2/8

                                = 1/4 cups

Hence 1/4 cups of milk will be left.

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The lateral area of the prism is the area of the three rectangles in the middle of the net. (The two triangles are the bases of the prism, which don't count toward lateral area.) The total length of the three rectangular prism faces is (8 +15 +17) cm = 40 cm. The width of those rectangles is 9 cm. The lateral area will be the product of this length and width:

... lateral area = (40 cm)(9 cm) = 360 cm²

The area of the rectangle in terms of x is 2x² - 8

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

Given one side of the rectangle is 2x+4 and the perimeter is 6x+4

Let the other side be y.

We know that:

perimeter = 2 × (sum of two sides)

or, 6x + 4 =  2 (2x+4+y)

or,6x + 4 = 4x + 8 + 2y

or, 2x - 4 = 2 y

or, y = x - 2

Now area of the rectangle = product of sides =  (x - 2)(2x+4)

Area = 2x² - 4x + 4x - 8

or, Area = 2x² - 8

Hence the area of the rectangle in terms of x is  2x² - 8

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The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.

From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.

The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.

Therefore, the highest common factor is 16.

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Answer:

16

Step-by-step explanation:

to the right is P(z> Z)

so P(z>Z) = 0.9909

P(z< Z) = 1- 0.9909 = 0.0091

Closest values from a z-table

P(z< -2.37) = 0.00889 (-0.00011 away)

p(z< -2.36) = 0.00914 (+0.00014 away)

so the answer must be (c) since it is between -2.36 and -2.37

Answer:

Domain: allrealnumbers

Range: f(x) <= -8

Step-by-step explanation:

This equation shows that this shape is a parabola that is opening downwards (because of the negative in the -5/6)

This means it has a highest point. The x+2 means the curve is shifted/slid/tranlated to the right 2 units and the -8 at the end shows that it is slid/shifted/translated down 8 units. So the curve only exists starting from -8 and going down. That is the range f(x) <= -8

All upward and downward opening parabolas have a domain of all real numbers.

Let's see

[tex]\\ \rm\rightarrowtail y=\dfrac{-5}{6}(x+2)^2-8[/tex]

[tex]\\ \rm\rightarrowtail x\in R[/tex]

Domain is R

Now

[tex]\\ \rm\rightarrowtail y=\dfrac{-5(x+2)^2}{6}-8[/tex]

Vertex form of parabola:-

On comparing with this

Hence

Range :-

Answer:36

Step-by-step explanation:

x2 - 10x + 25 = 0 2x2 - 2x - 5 = 0 x2 - 16x = 36. This problem has been solved!