Find the solution for 16-x=x+10

Equivalent expressions to given expression are:

A : -8+19-3x

C : -11x+19

Step-by-step explanation:

Given

[tex]-5+4(-2x+6)-3x[/tex]

We will simplify the given expression to find the equivalent expressions

[tex]-5+4(-2x+6)-3x\\= -5-8x+24-3x\\= -8x+19-3x\\=-11x+19[/tex]

by observing the simplification we can see that the equivalent expressions are:

A : -8+19-3x

C : -11x+19

Keywords: Polynomials, Expressions

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Answer:

The solution of x for the slope intercept is 2 .

Step-by-step explanation:

Given expression as :

- 9 = - 2 ( x + 3 ) + 1

Or. - 9 = - 2×( x + 3 ) + 1

or, - 9 = - 2 x - 6 + 1

or, - 9 = - 2 x - 5

or, - 9 + 5 = - 2 x

or , - 4 = - 2 x

∴  x = [tex]\frac{-4}{-2}[/tex]

I.e x = 2

Hence the solution of x for the slope intercept is 2 . Answer

Answer:

2x (x-3)

Step-by-step explanation:

Answer:

2x(x - 3).

Step-by-step explanation:

2x is common so if we divide 2x^2 - 6x by 2x we get x - 3 and the factors are:

2x(x - 3).

Answer:

B) maximum value at 39.

Step-by-step explanation:

maximum value at 39

First, set the expression equal to 0.

−x2 − 10x + 14 = 0

Complete the square.

−x2 − 10x = −14

−(x2 + 10x) = −14

−(x2 + 10x + 25) = −39

−(x + 5)2 + 39= 0.

Therefore, the maximum value is 39.

Answer:

D. 18 : 1

Step-by-step explanation:

Students : teachers and aides

450 : 25

Treat it like a fraction. 450 over 25 simplifies to 18 over 1 because 450/25=18 and 25/25=1.

Therefore, the ratio is 18 : 1

Answer: 18:1

Step-by-step explanation:

450 students : 25 teachers

18 students : 1 teachers

450/25= 18

Answer:

Yes, it's an arithmetic sequence.

Step-by-step explanation:

Each term in this sequence is 4 more than the previous term.  Therefore we have an arithmetic sequence.

Answer: 13/100

Step-by-step explanation:

any number with 100 as it denominator and that is less than 100 is it's self but move the decimal back for how many place values it have.

for example:

1/100=  .1

99/100= .99

The decimal 0.13 is equivalent to the fraction 13/100, as the number has two decimal places, and the fraction's denominator is set to 100.

The decimal 0.13 can be expressed as a fraction where the denominator is a power of 10 equivalent to the number of decimal places. To convert 0.13 to a fraction, you consider that there are two decimal places, so you use 100 as the denominator. Therefore, 0.13 as a fraction is 13 over 100, which can be written as 13/100.

This is because to convert a decimal to a fraction, you write down the numbers to the right of the decimal point as the numerator and a power of 10 that corresponds to the number of decimal places as the denominator. In the case of 0.13, since there are two decimal places, the power of 10 used is 102, which is 100.

Answer:

None

Step-by-step explanation:

Note that we have 6x on both sides here.  If we subtract 6x from both sides, the equation becomes -6 = +15, which is never true.

Thus, this equation has NO SOLUTION.

The two equations that can be used to relate the distance from the focus and the directrix to any point on the parabola are x² = 4py and y = (x-k)² + h.

To correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola, we can use the following two equations:

Where p is the distance from the focus to the directrix, (h,k) is the vertex of the parabola, and the equation x² = 4py represents a parabola with its axis parallel to the y-axis, and y = (x-k)² + h represents a parabola with its axis parallel to the x-axis.

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The following system of equations represents the given statement;

x = y+z

y = 2z

10x+15y+40z = 600

They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.

Step-by-step explanation:

Let,

Small pizza = x

Medium Pizza = y

Large Pizza = z

Cost of one small pizza = $10

Cost of one medium pizza = $15

Cost of one large pizza = $40

According to given statement;

They usually sells as many small pizzas as medium and large pizzas combined.

x = y+z  

The number of medium pizzas sold is usually twice as many as large ones.

y = 2z

How many of each pizza must they sell to get $600.

10x+15y+40z = 600

The following system of equations represents the given statement;

x = y+z    Eqn 1

y = 2z      Eqn 2

10x+15y+40z = 600    Eqn 3

Putting value of x and y from Eqn 1 and 2 in Eqn 3;

[tex]10(y+z)+15(2z)+40z=600\\[/tex]

We know that y=2z from Eqn 2,

[tex]10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600[/tex]

Dividing both sides by 100;

[tex]\frac{100z}{100}=\frac{600}{100}\\z=6[/tex]

Putting z=6 in Eqn 2;

[tex]y=2(6)\\y=12[/tex]

Putting value of y and z in Eqn 1;

[tex]x=12+6\\x=18[/tex]

They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.

Keywords: linear equations, substitution method

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Answer:

The percentage change of vacationers is 33.3 %

Step-by-step explanation:

Given as :

The old value of the vacationers = $ 1500

The new value of the vacationers = $ 2000

Let the percentage variation = x %

Or, x % increase = [tex]\dfrac{\tyextrm new value - \textrm old value}{\textrm old value}[/tex] × 100

Or,  x % increase = [tex]\dfrac{\tyextrm $ 2000 - \textrm $ 1500}{\textrm $ 1500}[/tex] × 100

Or, x % increase = [tex]\frac{500}{1500}[/tex] × 100

Or, x % increase = [tex]\frac{1}{3}[/tex] × 100

Or, x % increase = [tex]\frac{100}{3}[/tex]

∴  x  = 33.3 %

So, The percentage increase change is 33.3 %

Hence The percentage change of vacationers is 33.3 %   Answer

Answer:

A

Step-by-step explanation:

25.00-3.75 is 21.25. divide that by 1.25 to get exactly 17.

Answer:A

Step-by-step explanation:

Answer:

Option C) y = -2x - 6

Step-by-step explanation:

The correct question is

In the xy coordinate plane the slope of line p is 1/2 and its x-intercept is -3. Find the equation of a line that is perpendicular to p and intersects p at is x-intercept.

step 1

Find the slope of a line that is perpendicular to p

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=\frac{1}{2}[/tex] ----> slope of line p

substitute

[tex](\frac{1}{2})*m_2=-1[/tex]

[tex]m_2=-2[/tex] ----> slope of the line perpendicular to p

step 2

Find the equation of the line  that is perpendicular to p and intersects p at is x-intercept

we have

[tex]m=-2[/tex]

[tex]point\ (-3,0)[/tex]

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-0=-2(x+3)[/tex]

[tex]y=-2x-6[/tex]

Answer:

48.72%

Step-by-step explanation:

(18794.10-9638)/18794.10*100 = 9156.1/18794.10*100 = 48.72%

Answer:

Exact form: 8/5

Answer:

10s^2-15s+20

Step-by-step explanation:

because 5(2s^2)=10s^2, 5(-3s)=-15s, and 5(4)=20

hope it helps:)

Answer:102−15+20

Step-by-step explanation:that’s that answer because I just did the question on imagine math

Answer:

The fraction of Megan's blue stickers are 1/6.

Step-by-step explanation:

Given:

Megan has 12 star sticker. 1/2 of her stickers are yellow, 1/3 are green, and the rest are blue.

Now, to find the fraction of stickers which are blue.

Total number of stickers  =  12.

Number of red stickers are = [tex]12\times \frac{1}{2}[/tex]

                                              = [tex]6 stickers[/tex]

Number of green stickers are = [tex]12\times \frac{1}{3}[/tex]

                                                  = [tex]4 stickers[/tex]    

Number of blue stickers are = [tex]12-(6+4)[/tex]

                                               = [tex]12-10=2 stickers[/tex]

Now, to get the fraction of stickers we divide the number of blue stickers by the total number of stickers:

Fraction of blue stickers = [tex]2\div 12[/tex]

                                         = [tex]\frac{1}{6}[/tex]

Therefore, the fraction of Megan's blue stickers are 1/6.

Answer:

Step-by-step explanation:

Area of pool:

Area of walkway:

If the areas are equal, then:

Final answer:

To find the value of x when the area of the walkway equals the area of the pool, set up an equation and solve for x. The value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.

Explanation:

To find the value of x when the area of the walkway equals the area of the pool, we need to set up an equation. The area of the pool is the length multiplied by the width, which is 6 meters multiplied by 4 meters, or 24 square meters. The area of the walkway is the total area of the larger rectangle minus the area of the pool.

The total area of the larger rectangle is the length plus twice the width, all multiplied by the width. So, the area of the walkway is x(6 + 2x - 4). Setting the area of the walkway equal to the area of the pool gives us the equation: x(6 + 2x - 4) = 24.

To solve this equation, we can first simplify it by distributing the x through the parentheses: 6x + 2x^2 - 4x = 24. Combining like terms, we have 2x^2 + 2x - 24 = 0. To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us 2(x + 6)(x - 2) = 0. So either (x + 6) = 0 or (x - 2) = 0. Solving for x, we find that x = -6 or x = 2.

Since we are dealing with width, the negative solution x = -6 is not applicable. Therefore, the value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.

Answer:

equation: y=35x+1200

a) the rate of change is 35.

b) 1200.

c) The Independent Variable is amount of students per year.

d) The Dependent Variable is the year

I'm not sure about the dependent varaliable, so don't take my word.

a) The rate of change is 35 students per year.

b) The initial value is 1200 students.

c) The independent variable is "x," which represents the number of years since 2000.

d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.

Identifing The Variables.

Set up an equation to represent the enrollment of the school each year after 2000.

We can use the form of a linear equation, where "y" represents the enrollment in a given year (after 2000), and "x" represents the number of years since 2000.

a) Rate of Change (Slope):

The rate of change, which represents how much the enrollment increases each year, is 35 students per year.

b) Initial Value (y-intercept):

In the year 2000, the enrollment was 1200 students.

Therefore, initial value (the value of "y" when "x" is 0) is 1200.

c) Independent Variable: The independent variable, "x," represents the number of years since 2000.

d) Dependent Variable: The dependent variable, "y," represents the enrollment of the school each year after 2000.

We can write the equation:

y = 35x + 1200

a) The rate of change is 35 students per year.

b) The initial value is 1200 students.

c) The independent variable is "x," which represents the number of years since 2000.

d) The dependent variable is "y," which represents the enrollment of the school each year after 2000.

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Answer:

4/3*100^3*π

Step-by-step explanation:

V = 4/3*π*r^3

= 4/3*π*100^3

≈ 4.18879*10^6

Answer:

Step-by-step explanation:

If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like

[tex]y=\frac{K}{x^{2} }[/tex]

Where [tex]K[/tex] is the constant of propotionality.

Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]

[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]

Replacing this constant, the expression between variables is

[tex]y=\frac{4}{x^{2} }[/tex]

Which is the answer to a).

Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be

[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]

Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]

In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.

In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.

To express y in terms of x, we can rearrange the equation as y = k/(x^2).

To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).

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Answer:

4

Step-by-step explanation:

Gave a picture to explain

Answer: I can confirm x=4

Step-by-step explanation:

Answer:

34/35=0.9714285

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3 - 2 = 1

3 + 2 =5

5 x 1 =5

The Fendley family is planning a vacation, and they are trying to choose which resort they will stay in. Mrs. Fendley has created the table below showing their four options. They want to spend no more than $250 per night for the resort. Which resorts will fit into their budget? Select two that apply.

Resort Amount Charged

A $550 for 2 nights

B $694 for 3 nights

C $1028 for 4 nights

D $1153 for 5 nights

A no

Resort A $275 per night

B maybe

Resort B $231.33 per night

C no

Resort C $257 per night

D maybe

Resort D $230.60 per night

the answer is b or d you choose which one you would like to choose

Answer:

x = -12

Step-by-step explanation:

Remember that ax + bx = (a+b)x

-10x + 9x = 12

Add -10x and 9x together

(-10 + 9)x = 12

-x = 12  (-1x is written as -x, just as 1x is written as x)

÷ -1 both sides

x = -12

I hope this helps. Happy studying. :)

-10x+9x= -1x

-1x=12 -1 divided by 12 equals -12 Therefore x = -12

Answer:

[tex]f(x)=(2x+1)(2x-1)[/tex].

Step-by-step explanation:

We want to convert the function into the form that let's us easily find the x-intercept, and it would be for the form [tex](ax+b)(cx+d)[/tex] because then we can find the x-intercept in the following manner:

[tex](ax+b)(cx+d)=0[/tex]

[tex]x=-b/a[/tex]

[tex]x=-d/c[/tex]

We factor our function [tex]f(x)=4x^2-1[/tex] and get

[tex]\boxed{f(x)=(2x+1)(2x-1)}[/tex]

Now this form let's us easily find the x-intercepts:

[tex]x=-1/2[/tex]

[tex]x=1/2[/tex]

and so we pick the second choice: f(x)=(2x+1)(2x-1).

Answer:

b

Step-by-step explanation:

Answer:

a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.

b. 25 more trees are to be planted per acre to maximize the total yield.

Step-by-step explanation:

If the no. of trees per acre is doubled then it will be equal to,

[tex]100 \times 2[/tex]

= 200

So, the no. of trees per acre is increased by (200 - 100) = 100

hence, the average yield per tree will be,

(150 - 100) = 50 in that case.

Hence, the total yield will be,

[tex]50 \times 200[/tex]

= 10,000 apples per acre

Now , if x trees are planted, the total no. of apples produced per acre will be,

[tex](150 - x) \times (100 + x)[/tex]

= [tex]15000 + 50x - x^{2}[/tex]

= f(x) [say]

So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)

= 50 - 2x---(1)

taking f'(x) = 0 , we get,

50 - 2x = 0

⇒ x = 25 --------------(2)

Again,

[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25

=  -2 (<0)

So, f(x) attains it's maximum value at x = 25

Hence,

25 more trees are to be planted per acre to maximize the total yield.