Simplify (x^3 + 2x^2 - x) + (4x^3 + x^2 + x)

Step-by-step explanation:

2 objects and their shadows create 2 similar right-angled triangles.

that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.

so,

122 × f = 2

f = 2/122 = 1/61

therefore, Ryan is

305 × f = 305 × 1/61 = 5 ft

tall.

If the Statue of Liberty is 305 feet tall, Ryan is 5 feet tall.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.

Given that,

The length of shadow of Statue of Liberty = 122 foot.

The length of shadow of Ryan = 2 foot.

Also, the height of Statue of Liberty = 305 feet.

Let the height of Ryan = x

To find the value of x,

Use ratio and proportion method,

122 / 305 = 2 / x

x = 2 x 305 / 122

x = 305 / 61

x = 5

The height of Ryan is 5 feet.

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Answer:

Below

Step-by-step explanation:

Formula for an arithmetic sequence is an = 4n - 5

First 4 terms are

-1, 3, 7, 11.

10th term = 4(10) - 5

= 35.

The total snowfall throughout the day is the expected value of the distribution.

The estimated total snowfall during the day is 30 inches

Start by calculating the average rate of snow collected on that day.

[tex]Rate = \frac{0 + 1.5 + 2.5 + 2.0 +1.0 +0.5}{6}[/tex]

This gives

[tex]Rate = \frac{7.5}{6}[/tex]

Divide 7.5 by 6

[tex]Rate = 1.25[/tex]

There are 24 hours in a day.

So, the total snowfall is:

[tex]Total = Rate \times Hours[/tex]

This gives

[tex]Total = 1.25 \times 24[/tex]

Multiply

[tex]Total = 30[/tex]

Hence, the estimated total snowfall during the day is 30 inches

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Answer:

  √26 ≈ 5.10 units

Step-by-step explanation:

The midpoint to which the median is drawn is ...

  M = (B +C)/2

  M = ((-3, 3) +(5,1))/2 = (-3+5, 3+1)/2 = (2, 4)/2 = (1, 2)

The distance between the first vertex and this point is given by the distance formula.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((2 -1)^2 +(7 -2)^2) = √(1^2 +5^2) = √26 ≈ 5.0990 ≈ 5.10

The length of the median is √26 units.

Answer:

a) Draw a line horizontally on 4 on the y axis

b)x=2,y=3

1) Move all terms to one side.

[tex]34x+24x^{2} -35-57y=0[/tex]

2) Use Quadratic Formula.

[tex]x=\frac{-34+2\sqrt{1368y+1129} }{48} ,\frac{-34-2\sqrt{1368y+1129} }{48}[/tex]

3) Simplify solutions.

[tex]x=-\frac{17-\sqrt{1368y+1129} }{24} ,-\frac{17+\sqrt{1368y+1129} }{24}[/tex]

Step-by-step explanation:

The x-intercept is the value of x when y is 0

So you need to substitute:

0 = 4x + 7

-7 = 4x

-7/4 = x

(-7/4,0)

Similarly, the y-intercept is the value of y when x is 0

So:

y = 4x + 7

y = 4(0) + 7

y = 7

(0,7)

Answer:

240

Step-by-step explanation:

36+4=40

40x6=240

Answer:

Step-by-step explanation:

None

The hint is in the slopes which is the number in front of x. Both equations have a slope of 1/2

The y intercepts are different (4 for the top one 2 for the bottom one). That tells you that you have two lines and not one of top of the other. These two lines never meet, because the slopes are the same. Therefore there are no values that both lines have in common.

That makes the answer none.

Answer:

[tex]7x(4x-1)[/tex]

Step-by-step explanation:

First, find the largest integer that divides evenly into both numbers. In this case, 28 and 7 are both divisible by 7.

Next, find the highest degree of the variable that divides evenly into both. Here, that's just x. I'll show another example of that below.

Multiply those together, and you get 7x. That is what we need to factor out. Divide by that factor while multiplying by that factor at the same time to keep the value of the expression equal:

[tex]28x^2-7x\\\\7x(\frac{28x^2}{7x}-\frac{7x}{7x})\\\\7x(4x-1)[/tex]

Another example of what I said above would be this:

Take 4x + 2. The largest integer that divides these is 2, and the highest degree of x that divides them is 0. That is an x⁰, and that is equal to 1. Multiply those, and you just get 2.

[tex]4x+2\\\\2(\frac{4x}{2}+\frac{2}{2})\\\\2(2x+1)[/tex]

Answer:

A line parallel to this one would have a slope of 3. where m is the slope and b is the y intercept. In this case, the equation y=3x+5 is already in slope intercept form, which means the slope is 3. Parellel lines have the same slope, so any other line with slope 3 is parallel to this line.

I think that's the answer

Answer: y = -3x - 3

Step-by-step explanation:

If you are looking for a line that is parallel, then it must have the same gradient

Therefore;

y= -3x +c

And because it passes through (0,3), substitute in the values to find c

3 = -3 x 0 + c

c = 3

So the equations would be y = -3x -3

[tex]\mathfrak{( \frac { 6 x } { y } ) ( \frac { y } { 3 x - 3 } ) } [/tex]

[tex]\mathfrak{ \frac{6xy}{y\left(3x-3\right)} } [/tex]

[tex]\mathfrak{ \frac{6x}{3x-3} } [/tex][tex]\mathfrak{ \frac{6x}{3\left(x-1\right)} } [/tex]

[tex]=\boxed{\mathfrak{\frac{2x}{x-1} } }[/tex]

☆ Option 3 is correct.

[tex]\mathbb{MIREU} [/tex]

Answer:

Perimeter= 40

Area= 120.71

Step-by-step explanation:

Answer: 5, 7/2

Step-by-step explanation:

2x − 4y = -4

3x + 2y = 22

divide both sides of the equation by 2

 x − 2y = -2

3x + 2y = 22

Eliminate one variable by adding the equation;  sum the equations vertically to eliminate at least one variable

4x=20

Divides both sides by 4

x=5

Substitute  the given value of x into the equation 2x-4y = -4

2*5-4y =-4

solve the equation for y

y=7/2

If the given equations are indeed

[tex]\begin{cases}x-\frac4{5y} = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]

we can solve by substitution. Solve the second equation for x :

[tex]-14x - 4y = -46[/tex]

[tex]\implies 7x + 2y = 23[/tex]

[tex]\implies7x = 23 - 2y[/tex]

[tex]\implies x = (23 - 2y)/7[/tex]

Substitute this into the first equation and solve for y :

[tex]\dfrac{23-2y}7 - \dfrac4{5y} = 9\dfrac45[/tex]

On the right side, write the mixed number as an improper fraction:

[tex]9 + \dfrac45 = \dfrac{45}5 + \dfrac45 = \dfrac{45+4}5 = \dfrac{49}5[/tex]

[tex]\implies \dfrac{23-2y}7 - \dfrac4{5y} = \dfrac{49}5[/tex]

Multiply both sides of this equation by 35y (the LCM of the denominator of all three fractions)

[tex]35y \times \dfrac{23-2y}7 - 35y \times \dfrac4{5y} = 35y \times \dfrac{49}5[/tex]

[tex]5y\times(23-2y) - 7\times4 = 7y \times 49[/tex]

[tex]115y - 10y^2 - 28 = 343y[/tex]

[tex]10y^2 + 228y + 28 = 0[/tex]

[tex]5y^2 + 114y + 14 = 0[/tex]

To solve the quadratic, I'll complete the square :

[tex]5\left(y^2 + \dfrac{114}5y\right) + 14 = 0[/tex]

[tex]5\left(\left(y + \dfrac{57}5\right)^2 - \left(\dfrac{57}5\right)^2 \right) + 14 = 0[/tex]

[tex]5\left(y + \dfrac{57}5\right)^2 - \dfrac{57^2}5 + 14 = 0[/tex]

[tex]5\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}5[/tex]

This system has no real solutions since the square of any real number must be positive.

If we allow complex numbers, we can continue solving to end up with two complex solutions for y,

[tex]\left(y + \dfrac{57}5\right)^2 = -\dfrac{3179}{25}[/tex]

[tex]y + \dfrac{57}5 = \pm i \sqrt{\dfrac{3179}{25}}[/tex]

[tex]y = -\dfrac{57}5 \pm i\dfrac{17\sqrt{11}}5[/tex]

and we can go on to solve for x.

Hence my comment; I suspect you meant to write the system

[tex]\begin{cases}x-\frac45 y = 9\frac45 \\ -14x - 4y = -46\end{cases}[/tex]

because its solution is far simpler. Multiplying through the first equation by 5 gives

[tex]5\times x - 5 \times \dfrac45 y = 5 \times 9\dfrac45[/tex]

[tex]\implies 5x - 4y = 49[/tex]

(since we know 9 + 4/5 = 49/5)

Meanwhile, multiplying through the second equation by -1 gives

[tex]-1 \times (-14x) + (-1) \times (-4y) = -1 \times (-46)[/tex]

[tex]\implies 14x + 4y = 46[/tex]

So if we combine the two equations, we can eliminate y and solve for x :

[tex](5x - 4y) + (14x + 4y) = 49 + 46[/tex]

[tex]\implies 19x = 95[/tex]

[tex]\implies \boxed{x = 5}[/tex]

and solving for y gives

[tex]14x + 4y = 46[/tex]

[tex]\implies 70 + 4y = 46[/tex]

[tex]\implies 4y = -24[/tex]

[tex]\implies \boxed{y = -6}[/tex]

b:375:75=5 or 370:100=3.75 but it doesn't make sence B=5

Answer:

300

Step-by-step explanation:

Answer:

14, 4

Step-by-step explanation:

First things first, we can name out pairs with the ratio of 7:2.

7, 2

14, 4

21, 6

We can then test these pairs out with the first condition and find the answer.

The least common multiple has to be 28:

LCM(7, 2) = 14

LCM(14, 4) = 28

Ah, ha! We can see that the least common multiple of 14 and 4 is 28.

The only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"

This question bothers on place values.

Given the decimal value 89.033, the place value of the blue 3 on the left is the hundredth place (1/100) while the place value of the orange 3 is in the thousandth place(1/1000).

We need to check which of the statement is correct.

For the first option, the blue 3 on the left is 300 times the value of the orange 3 on the right;

Since 0.01≠0.3, hence the first option is wrong

For the second option, the blue 3 on the left is 100 times the value of the orange 3 on the right;

0.01≠0.1, hence the second option is wrong.

The blue 3 on the left is equivalent to the orange 3 on the right is also wrong since they are positioned in a different place

The orange 3 on the right is 1/10 of the value of the blue 3 on the left, is expressed as;

Hence the only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"

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Answer:

2

Step-by-step explanation:

if the angle of the two triangles are the same,

6 is 2/3 of nine

Therefore,

2/3x3=2

The function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]

The table is represented as:

Years  - Values

1          -  $104,271. 02

2         -  $107,399. 15

Appreciation and depreciation are often represented using exponential function as follows:

[tex]f(x) = ab^x[/tex]

At year 1, we have:

[tex]104271. 02 = ab^1[/tex]

[tex]104271. 02 = ab[/tex]

At year 2, we have:

[tex]107399. 15 = ab^2[/tex]

Divide both equations

[tex]\frac{107399.15}{104271.02} = \frac{ab^2}{ab}[/tex]

[tex]1.03 = b[/tex]

Rewrite as:

[tex]b = 1.03[/tex]

He bought the real estate for $101,234.

So, we have:

[tex]a = 101234\\[/tex]

Substitute values for (a) and (b) in [tex]f(x) = ab^x[/tex]

[tex]f(x) = 101234(1.03)^x[/tex]

Replace x with t

[tex]f(t) = 101234(1.03)^t[/tex]

Hence. the function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]

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Answer:

×=40

Step-by-step explanation:

The total value of all the angles on any line is 180

so x+(4x-20)=180

40+(4×40-20)=180

Answer:

40°

Step-by-step explanation:

The sum of angles x and (4x - 20) is 180°

x + (4x - 20) = 180

5x = 200

x = 40°

Answer:

14.5

Step-by-step explanation:

AB is halfway between MN and PO. this means it would be the distance halfway between 9 units (length of MN) and 20 units (length of PO). to find this, find the average of 20 and 9. 20+9= 29. 29/2= 14.5