Explain how to estimate the quotient using compatible numbers. 27 2/3 divided by 3 9/10. Write a Sentence or two.

Answer:

7/2

Step-by-step explanation:

50 miles per hour  is the rate (speed) of the wind.

Step-by-step explanation:

Let consider the variable ‘x’ for speed of wind.  

Below we write two values of the speed of the airplane in the air in terms of ‘x’:

1. Subtract wind speed from airplane speed: 250 - x.

2. Add wind speed to the airplane speed against the wind: 150 + x.

And now, set these above two expressions equal to each other to find x (wind speed),

                                      250 – x = 150 + x

                                      2x = 100

                                     x = 50 miles per hour

12oz of the drink contains 159oz of calories.

A new energy drink advertises 106 calories for 8oz.

Based on the given conditions, formulate: 12*(106/8)

=12*(13.25)=159

Calories are in 12oz of the drink is 159oz

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Answer:

The value of x is 17°.

Step-by-step explanation:

The two exterior angles on the same side of the transversal are always supplementary.

Therefore, if the measure of two exterior angles on the same side of the transversal are 3x and 7x+10, then we can write  

3x + (7x + 10) = 180°

⇒ 10x = 180° - 10° = 170°

⇒ x = 17°  

Therefore, the value of x is 17°. (Answer)

Answer: 188 months

Step-by-step explanation:

Principal = $129 000

Payment = $1000

Mortgage % = 5.15

Since,

Number of Months = log (1+[rate/(Payment/Principal)-rate] / log (1 + rate)

Also,

rate = 5.15/1,200 = 0.004292

Number of Months = log (1 + [0.004292/(1,000/129000) -0.004292] / log(1+0.004292)

Number of Months = log ( 1 + 0.004292/ ((0.007752 -0.004292) / log (1.004292)

Number of Months = log ( 1 + (0.004292/0.00346))/ log (1.004292)

Number of Months = log (1 + 1.240) / log (1.004292)

Number of Months = log (2.240) / log (1.004292)

Number of Months = 0.3502 / 0.001860

Number of Months = 188.28 months

Approximation to whole month,

Number of months = 188 Months.

Answer:

Yes, No, Yes, No, No

Step-by-step explanation:

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Final answer:

Greg's unit rate is  [tex]1\frac{5}{7}[/tex]  walls per hour, which is found by dividing 1/7 of a wall by 1/12 of an hour. The correct answer is option C: [tex]1\frac{5}{7}[/tex].

Explanation:

If Greg can build 1/7 of a brick wall in 1/12 of an hour, we want to find his unit rate, which is the amount of wall he can build per hour. To find Greg's unit rate, we divide the fraction of the wall built by the fraction of the hour spent building it. This calculation gives us:

Unit rate = (1/7) ÷ (1/12) = (1×12)/(7×1) = 12/7 = [tex]1\frac{5}{7}[/tex] walls per hour.

Therefore, the correct option is C: [tex]1\frac{5}{7}[/tex].

Answer:

4w+3

Step-by-step explanation:

2/3(7w+4)-1/3(2w-1)

14/3w+8/3-2/3w+1/3

14/3w-2/3w+8/3+1/3

12/3w+9/3

4w+3

Answer:

Step-by-step explanation:

(-5,-8), (-7,3)

midpoint = (x₁+x₂/2, y₁+y₂/2)

        = ( -5+-7/2 , -8+3/2) = (-5-7/2,-8+3/2)

       = (-12/2, -5/2) = (-6,-5/2)

Answer:

The amount to be pay for coat is $128.70.

Step-by-step explanation:

Given:

The sales tax rate is 7.25% in California.

The cost for a coat in Los angeles is $120.00.

Now, to find amount to be paid.

Sales tax = 7.25%.

Cost = $120.00.

So, amount to be paid = $120 + 7.25% of $120.00.

[tex]=120+\frac{7.25}{100} \times 120.[/tex]

[tex]=120+\frac{870}{100}.[/tex]

[tex]=120+8.70[/tex]

[tex]=\$128.70[/tex]

Therefore, the amount to be pay for coat is $128.70.

Answer:

x = 1

Step-by-step explanation:

Given

- | x + 2 | + 1 = 4x - 6 ( subtract 1 from both sides )

- | x + 2 | = 4x - 7 ( multiply both sides by - 1 )

| x + 2 | = - 4x + 7

The absolute value always returns a positive value, but the expression inside can be positive or negative, thus

x + 2 = - 4x + 7 ( add 4x to both sides )

5x + 2 = 7 ( subtract 2 from both sides )

5x = 5 ( divide both sides by 5 )

x = 1

OR

- (x + 2) = - 4x + 7, that is

- x - 2 = - 4x + 7 ( add 4x to both sides )

3x - 2 = 7 ( add 2 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check substitute these values into both sides of the equation and if both sides are equal then they are the solutions.

x = 1 : - |1 + 2| + 1 = - | 3 | + 1 = - 3 + 1 = - 2

right side = 4(1) - 6 = 4 - 6 = - 2 ← True

x = 3 : - |3 + 2| + 1 = - |5| + 1 = - 5 + 1 = - 4

right side = 4(3) - 6 = 12 - 6 = 6 ← False

Thus x = 3 is an extraneous solution and

x = 1 is the solution

Answer:

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x+2|=\left\{\begin{array}{ccc}x+2&for&x+2\geq0\to x\geq-2\\-(x+2)&for&x<-2\end{array}\right[/tex]

[tex](1)\ x<-2\\\\-\bigg(-(x+2)\bigg)+1=4x-6\\\\+(x+2)+1=4x-6\qquad\text{combine like terms}\\\\x+(2+1)=4x-6\\\\x+3=4x-6\qquad\text{subtract 3 from both sides}\\\\x+3-3=4x-6-3\\\\x=4x-9\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\x-4x=4x-4x-9\\\\-3x=-9\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-9}{-3}\\\\x=3\notin(1)[/tex]

[tex](2)\ x\geq-2\\\\-(x+2)+1=4x-6\\\\-x-2+1=4x-6\\\\-x+(-2+1)=4x-6\\\\-x-1=4x-6\qquad\text{add 1 to both sides}\\\\-x-1+1=4x-6+1\\\\-x=4x-5\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x-4x=4x-4x-5\\\\-5x=-5\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-5}{-5}\\\\x=1\in(2)[/tex]

Answer:

53

Step-by-step explanation:

Answer:

The value of x is 2[tex]\sqrt{29}[/tex] .

Step-by-step explanation:

Given as :

The area of Trapezoid = x² unit²

The measure of base 1 = [tex]b_1[/tex] = - 19 unit

The measure of base 2 = [tex]b_2[/tex] = 10 unit

The height of the mid segment = 8 unit

Now, From the Area of Trapezoid

i.e Area = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height

Or, x² = [tex]\dfrac{1}{2}[/tex] × (19 + 10) × 8

Or,  x² = [tex]\dfrac{8}{2}[/tex] × (29)

Or, x² = 4 × (29)

Or,  x² = 116

∴ x = [tex]\sqrt{116}[/tex]

I.e x = 2[tex]\sqrt{29}[/tex]

Hence, The value of x is 2[tex]\sqrt{29}[/tex] . Answer

Final answer:

Using the properties of a trapezoid's midsegment being the average length of the bases, the equation (10 + (x² - 19))/2 = 8 was solved to find that x equals 5.

Explanation:

The question revolves around the properties of a trapezoid and its midsegment. In a trapezoid, the midsegment (also called the median) is the segment that joins the midpoints of the non-parallel sides and is parallel to both bases.

The length of the midsegment is the average of the length of the two bases, which can be expressed as (base1 + base2) / 2.

Given that the midsegment is 8 units long, and one base is given as 10 units, let the other base be expressed as x² − 19 units. The formula for the midsegment becomes:

(10 + (x² − 19))/2 = 8

Now we solve for x:

10 + x² − 19 = 16

x² − 9 = 16

x² = 25

x = ± 5

Since the measure of a base cannot be negative, the positive root is the realistic solution:

x = 5

Answer: $10272.17

Step-by-step explanation: Please see attachment for explanation

Answer:

[tex]\$10272.17[/tex]

Step-by-step explanation:

Since it is compounded continuously, we will use:

[tex]A=A_0 \cdot e^{k t}[/tex]

[tex]A_0[/tex] is the amount invested.

[tex]k[/tex] is the rate.

[tex]t[/tex] is the number of years you let the money sit.

[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.

(Note:

I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)

[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]

[tex]A=5000 \cdot e^{0.72}[/tex]

[tex]A=5000 \cdot 2.0544332[/tex] (approximated)

[tex]A=10272.16605[/tex] (approximated)

To the nearest cent this is [tex]\$10272.17[/tex].

Answer:

False

Step-by-step explanation:

Answer:

11.25 pi

Step-by-step explanation:

Pi is 180 degrees, a circle is 360 degrees, 9/10's of 180 is 162, and divide that by the full 360 which is .45. Then, multiply that by 25 and you have 11.25 pi is the area of that sector.

Answer:

JKL and ABC

DEF and GHI

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

so

In this problem

1) triangles JKL and ABC are similar

because

[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]

substitute the given values

[tex]\frac{10}{20} =\frac{7}{14}[/tex]

Simplify

[tex]\frac{1}{2} =\frac{1}{2}[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

2) triangles DEF and GHI are similar

because

[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]

substitute the given values

[tex]\frac{15}{10} =\frac{12}{8}[/tex]

Simplify

[tex]1.5=1.5[/tex]  ---> is true

therefore

The ratio of the corresponding sides is proportional

That means----> The triangles are similar

The pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

Corresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.

Thus, triangles KJL and ABC are similar triangles because:

BC/KL = AC/JL = 2

Also, triangles DEF and GHI are similar triangles because:

GI/DF = HI/EF = 1.5

Therefore, the pairs of triangles that are similar to each other are:

B. ΔDEF ~ ΔGHI

E. ΔJKL ~ ΔABC

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Answer:

50/50 chance

Step-by-step explanation:

Answer: Classical Probability (also know as priori or theoretical probability)

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).  If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.

[tex]f(1)=-2(1)^2+4(1)+1[/tex]

so f(1) = 3.  Your choice is (1, 3)

The solution is (1, 3) where the vertex of the function located.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have

given that,

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1.

now, we have to find the vertex of the function.

If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).

 If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.

now, putting the value of x as 1 ,

so, we get,

f(1) = –2(1)^2 + 4*1+ 1

    =-2 + 4 +1

    =3

so f(1) = 3.  

The solution is (1, 3).

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Answer:

Part A) The vertex is the point (22,100) see the explanation

Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation

Part C) The y-intercept is the point (0,-384) see the explanation

Step-by-step explanation:

Let

x ----> the number of cups of coffee sold

f(x) ---> the amount of profit

we have

[tex]f(x)=-x^{2} +44x-384[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Part A) Determine the vertex. What does this calculation mean in the context of the problem?

Convert the quadratic equation in vertex form

Factor -1

[tex]f(x)=-(x^{2}-44x)-384[/tex]

Complete the square

[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]

[tex]f(x)=-(x^{2}-44x+484)+100[/tex]

Rewrite as perfect squares

[tex]f(x)=-(x-22)^{2}+100[/tex]

The vertex is the point (22,100)

That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22  

Part B)  Determine the x-intercepts. What do these values mean in the context of the problem?  

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

so

we have

[tex]f(x)=-(x-22)^{2}+100[/tex]

For f(x)=0

[tex]0=-(x-22)^{2}+100[/tex]

solve for x

[tex](x-22)^{2}=100[/tex]

take square root both sides

[tex](x-22)=\pm10[/tex]

[tex]x=22\pm10[/tex]

so

[tex]x=22+10=32[/tex]

[tex]x=22-10=12[/tex]

The x-intercepts are the points (12,0) and (32,0)

That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero

Part C) Determine the y-intercept. What does this value mean in the context of the problem?

we know that

The y-intercept is the value of the function  when the value of x is equal to zero

so

For x=0

[tex]f(x)=-x^{2} +44x-384[/tex]

substitute the value of x

[tex]f(x)=-(0)^{2} +44(0)-384[/tex]

[tex]f(x)=-384[/tex]

The y-intercept is the point (0,-384)

That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)

Answer: 639.14

Step-by-step explanation:

Answer:

y=9

Step-by-step explanation:

substitution x=2 in equation

y= 3^2

y=9

Final answer:

To evaluate y=3^x for x=2, substitute x=2 into the expression y=3^x to find that y=9.

Explanation:

The given expression is y = 3^x. To evaluate y for x = 2, substitute x = 2 into the expression:

y = 3^2

y = 9

Therefore, y = 9 when x = 2.

Answer:

Step-by-step explanation:

This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.

I hope this helps!

- sincerelynini

Answer:

Yes.

Step-by-step explanation:

There is 3 feet in every yard. So LeBron has 18ft of cable.

The company picnic cost $ 1300 for 80 employees

Solution:

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

[tex]cost \propto \text{ number of employees attending picnic }[/tex]

[tex]c \propto n\\\\c = kn[/tex]

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

[tex]487.50 = k(30)\\\\k = \frac{487.50}{30} = 16.25[/tex]

How much does a company picnic cost for 80 employees?

Substitute n = 80 and k = 16.25 in eqn 1

[tex]c = 16.25(80) = 1300[/tex]

Thus $ 1300 is the cost for 80 employees

Answer:

$1,300.00

Step-by-step explanation:

Answer:

Step-by-step explanation:

 13x+2y=1

+ 5x-2y=-19

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

18x=18

x=1

5x1-2y=-19

5-2y=-19

-2y=-19-5

-2y=14

-y=7

y=-7

x=1

y=-7

To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].

To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.

First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:

[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]

This simplifies to:

[tex]\[ 13x + 5x = -18 \][/tex]

[tex]\[ 18x = -18 \][/tex]

Now, divide both sides by 18:

[tex]\[ x = \frac{-18}{18} \][/tex]

[tex]\[ x = -1 \][/tex]

Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:

[tex]\[ 13(-1) + 2y = 1 \][/tex]

[tex]\[ -13 + 2y = 1 \][/tex]

Add 13 to both sides:

[tex]\[ 2y = 1 + 13 \][/tex]

[tex]\[ 2y = 14 \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{14}{2} \][/tex]

[tex]\[ y = 7 \][/tex]

So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].

Answer: 2.12

Step-by-step explanation: Divide by 94 on both sides to get X by itself

Answer:

4

Step-by-step explanation:

3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.

Answer:

Step-by-step explanation:

3x=5x -8​

3x - 5x = - 8

-2x = -8

x = -8/-2

x = 4

Answer:

9 pounds of flour

Step-by-step explanation:

mix together

Answer:

1 year

Step-by-step explanation:

Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.

In this problem, "m" is the rate of growth in inches per year.

"b" is the starting height.

let "x" be the number of years

let "y" be the height in inches

Tree A: y = 8x + 3

Tree B: y = 9x + 2

Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.

8x + 3 = 9x + 2

8x + 3 - 3 = 9x + 2 - 3      Subtract 3 from both sides

8x = 9x - 1

8x - 9x = 9x - 9x - 1     Subract 9x form both sides

-x = -1       Divide both sides by -1 to isolate

x = 1         Number of years for the trees to be the same height

Therefore it will take 1 year for the trees to be the same height.

If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.

y = 8x + 3

y = 8(1) + 3

y = 11     Number of inches when trees are the same height