Write each expression as a difference.
a+5

p(1) = 1

Let p(x) = x2 + bx = c

then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c

Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)

= -2b/c2+bc+c = f(a,b) (say)

For critical points,

∂f/∂c = 0 and ∂f/∂b = 0

= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0

= b(2c+b+1) =0  

= b= 0 or b= - (1+2c)  = -(2c(c+1))/c2+bc+c = 0

If c=0 , b= -1  => c= 0 or c=-1

If c = -1 ,b = 1

thus we have the following possibility for (b,c)

(0,0) , (0,-1) , (-1,0) ,(1,-1).

At (0,0) f(0,0) = not defined

(0,-1) f(0,-1) = 0

(1,-1) f(1,-1) = 2

(-1,0) is not possible.

p(x) = (x2 +x-1)² + (x2 +x-1) -1

= p(1) = (1+1-1)² + (1+1-1) -1

= 1

Hence, p(1) = 1

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47% of those who received a certificate were men

It is given that in an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

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Each girl contributed 10.50gh

Each boy contributed 20.50gh

These are further explained and computed below:

The measure of central tendency being tested here is the mean, in other words, the resulting average when the total amount contributed by girls or boys is divided by the number of girls or boys.

The fact that 68 of the 80 students are girls means that the remaining 12 students are boys because 80 minus 68 gives 12.

each girl's contribution=total girls' contribution/number of girls

each girl's contribution=714/68

each girl's contribution=10.50gh

Total boys' contribution=total contribution-total girls' contribution

Total boys' contribution=960-714

Total boys' contribution=246

each boy's contribution=Total boys' contribution/number of boys

each boy's contribution=246/12

each boy's contribution=20.50gh

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Each girl contributed 10.5gh and each boy contributed 20.5gh

The given parameters are:

Total amount = 960gh

Number of students = 80

Amount contributed by girls = 714gh

Number of girls = 68

The amount contributed by each girl is:

Girl = Amount contributed by girls/Number of girls

This gives

Girl = 714gh/68

Evaluate

Girl = 10.5gh

The amount contributed by each boy is:

Boy = (Total - Amount contributed by girls)/(Total students - Number of girls)

This gives

Boy = (960gh - 714gh)/(80 -68)

Boy = 246gh/12

Evaluate

Boy = 20.5gh

Hence, each girl contributed 10.5gh and each boy contributed 20.5gh

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Thee linear equation which contains the points (-2,5) and (4,1) is [tex]4x+6y-22=0[/tex]

Graph The points which is in the equation (-2,5) and (4,1).

Equation is basically a relationship between two or more variables and it is usually in equal to form. It is equated to find the value of variables. We can also make graphs of different equations. Linear equation is a equation whose graph looks like straight line means values comes from a relationship. It not necessarily means parallel to any axis.

The linear equation can be found by:

[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )* (x-x_{1} )[/tex] where the coordinates are [tex](x_{1},y_{1}), (x_{2},y_{2})[/tex]

[tex](y-5)=(1-5)/(4+2)*(x+2)[/tex]

[tex](y-5)=-4/6 *(x+2)[/tex]

[tex]6y-30=-4x-8[/tex]

[tex]y=(22-4x)/6[/tex]

Hence the equation which has points (-2,5)(4,1) is [tex]4x+6y-22=0[/tex]

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The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)

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The product of all the values of a, such that f(a)=f(2a) is -1/2

Given the function below;

f(x)=1/x + x

f(a) = 1/a + a

f(2a) = 1/2a  + 2a

If f(a) = f(2a), hence;

1/a + a = 1/2a + 2a

Collect the like terms

1/a - 1/2a = 2a - a

2-1/2a = a

1/2a = a

Cross multiply

2a² = 1

a² = 1/2

a = ±√1/2

The values of a are √1/2 and -√1/2

Product = -√1/2 * √1/2

Product = -1/2

Hence the product of all the values of a, such that f(a)=f(2a) is -1/2

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = - 4 ( subtract 3x from both sides )

2y = - 3x - 4 ( divide terms by 2 )

y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - [tex]\frac{3}{2}[/tex] x + 5 ← equation of parallel line

Answer:

C

Step-by-step explanation:

the solution is at the point of intersection of the 2 lines.

the lines intersect at (1, 4 ) , then

solution to the system of equations is (1, 4 )

Answer:

A. 8x+5y

Step-by-step explanation:

First day: 3x+2y

Second day: 5x+3y

Add both expressions together.

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

= 3x+2y+5x+3y=8x+5y

Hope this helps!

If not, I am sorry.

Answer:

y^-1 = 3x - 6

Step-by-step explanation:

f(x) = 1/3x + 2

The inverse function is where we swap out y for x and x for y. f(x) represents y, so we will be replacing it with x. Then, we solve and get a new equation for the inverse of y.

x = 1/3y + 2 (subtract 2 from both sides)

x - 2 = 1/3y (multiply by 3 on both sides)

y^-1 = 3x - 6

Brainliest, please :)

Answer:

f(x) = 3x- 2

Step-by-step explanation:

The easiest way to find the inverse of a function is to replace y with x and rearrange the equation.

x = 1/3y + 2

-2            -2

______________

x-2 * 3  = 1/3y * 3

y = 3x-2

Answer:

≥ and ≤ will both be solid dots, as it includes the number

x ≥ -7 is everything greater than -7; x ≤ 4 is everything less than 4.

to include both, you'd click -7, drag right, and stop at 4

The value of x in the triangle is (d) 7

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

[tex]\sin(45) = \frac{x}{7\sqrt 2}[/tex]

Evaluate sin(45)

[tex]\frac 1{\sqrt 2} = \frac{x}{7\sqrt 2}[/tex]

Solve for x

[tex]x = \frac{7\sqrt 2}{\sqrt 2}[/tex]

Divide

x = 7

Hence, the value of x in the triangle is (d) 7

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The graph of the system can be seen below, there we can see that the solution is (-2, 3).

To do so, we just need to graph both equations on the same coordinate axis and see where the graphs intercept.

The interceptions will be the solutions of the system of equations.

Here we have the system:

y = (-1/2)*x + 2

3x + y = -3

The graph can be seen below, where the green line is the first equation, and the blue line is the second equation.

On the graph, you can see that the lines intersect at the point (-2, 3), so that is the solution of the system.

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Answer:

slope intercept is used when you are given a point (most likely a y intercept) on the graph and a slope. The point slope is a larger formula that is used when you are given a slope and the coordinates of a point.

Step-by-step explanation:

slope intercept : y=mx+b

point slope : y-y1= m(x-x1)

Answer:

Hi  sorry if the reply is late! The answer is

OPTION (B)m∠AVC+m∠CVB=m∠AVB

Step-by-step explanation:

Given: It is given that a point C is inside ∠AVB and ∠AVC=39° and ∠CVB=23°.

From the figure, we can see that C is inside ∠AVB, therefore ∠AVB is divided into two parts that is ∠AVC and ∠CVB, thus

m∠AVC+m∠CVB=c

⇒39°+23°=62°

Answer:

p=4

Step-by-step explanation:

plug x=-1 into the polynomial with the unknown

(-1)³+p(-1)+(-1)+6=0

-1-p-1+6=0

-p+4=0

p=4

Answer:

Your answer is 6x

Step-by-step explanation:

Given,

          length(l)     = 3x

          breadth(b) = 2x

          area of a rectangle(A) = ?

Now,

A = l*b

A = 3x*2x

A = 6x    ans.

Hope its helpful!

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Answer:

6 x^2

Step-by-step explanation:

Area =  Length * Breadth  

         =   3x   * 2x     =     6x^2  

Answer: 797 feet 3 inches

Step-by-step explanation:

[tex]\frac{3}{4} *1063=\frac{3189}{4} =797.25[/tex]

The error is present in second step when cancelling numerator and denominator and the solution of the expression [tex](1+1/x)/(1-1/x^{2} )[/tex] is [tex]x/x-1[/tex].

Given Expression [tex](1+1/x)/(1-1/x^{2} )[/tex] and incorrect solution. and we need to identify the error and solve the expression correctly.

The expression is [tex](1+1/x)/(1-1/x^{2} )[/tex]

In the solution given the second step of cancelling 1's in numerator and denominator is wrong.

The solution which is correct is as under:

[tex](1+1/x)/(1-1/x^{2} )[/tex]

firstly take LCM in numerator and denominator

=[tex](x+1)/x/(x^{2} -1)/x^{2}[/tex]

Now we can write the expression properly.

=[tex](x+1)*x^{2} /(x^{2} -1)*x[/tex]

Power of [tex]x^{2}[/tex] to be deducted from x

=[tex](x+1)*x/(x^{2} -1)[/tex]

Now [tex]x^{2} -1[/tex] can be written as (x+1)(x-1)

=[tex](x+1)*x/(x+1)(x-1)[/tex]

(x+1) will be deducted now from numerator and denominator.

=x/(x-1)

Hence the solution of the given expression is x/(x-1).

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The answer to this question is x/x₋1

Given the expression is 1₊1/x /1₋1/x²

Take the LCM of the denominators

we get, x₊1/x / x²₋1/x²

Now multiply the expression

=x₊1/x × x²/x²₋1

=(x₊1) x²/ x(x²₋1)

(x²₋1) is in the form of (a²₋b²)=(a₊b)(a₋b)

Therefore, (x₊1)x²/x(x₋1)(x₊1)

After cancelling like terms we get the answer as:

x/(x₋1)

Hence we get the simplification answer as x/(x₋1).

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a) Solve the first equation for [tex]x[/tex].

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

Substitute this into the second equation and solve for [tex]y[/tex].

[tex]2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}[/tex]

Solve for [tex]x[/tex].

[tex]x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}[/tex]

b) Eliminate [tex]y[/tex] by combining the two equations in appropriate parts, namely

[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3)[/tex]

and solve for [tex]x[/tex].

[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}[/tex]

Solve for [tex]y[/tex].

[tex]2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}[/tex]

Answer:

x = 12.0 cm

Step-by-step explanation:

If we draw a line parallel to the 12 cm line right below the line x, a right-angled triangle is formed, with x as the hypotenuse and the shortest side equal to (8 - 7 = ) 1 cm.

∴ x² = 12² + 1²

⇒ x = [tex]\sqrt{12^2 + 1^2}[/tex]

⇒ x = [tex]\sqrt{144 + 1}[/tex]

⇒ x = [tex]\sqrt{145}[/tex]

⇒ x = 12.0 cm   [3 s.f.]

Answer:

12.0 cm

Step-by-step explanation:

See attached image for steps.  Take the figure and convert it into a rectangle and right triangle by drawing a single line.  The Pythagorean  Theorem can then be used.

Answer:

6 years

Step-by-step explanation:

So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.

So the father can be represented as: y=x+38

The sons can be represented as: y = x+13 and y=x+5

The daughter can be represented as: y=x+8

So adding up all his children you get:

(x+13)+(x+5)+(x+8)

This gives you the equation:

3x+26

Now set this equal to the father's age to solve for x (in this context it's years)

3x+26=x+38

Subtract from both sides

2x+26=38

Subtract 26 from both sides

2x=12

Divide both sides by 2

x=6

So in 6 years the father will be the same age as his children put together

The correct option is the last one. h is negative and k is positive.

For the absolute value function:

g(x) = |x - h| + k

We know that the vertex is on the point (h, k).

On the graph, we can see that the vertex is on the point (-2, 1), then we have:

h = -2

k = 1

So the sign of h is negative and the sign of k is positive. The correct option is the last one.

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Answer:

the answer is provided down below

Step-by-step explanation:

steps

9 - ( 1 3 x 3 x3)

36 - (3 x 2 x2x3)

81 -( 3 x 3 x 3 x 3)

144 - ( 2 x 3 x 3 x 2 x 2 x 2 x 2)

225 - ( 5 x 5 x 3 x 3)

576 -( 2 x 2 x 2 x 2 x 2 x 2 x 3 x3)

625 - ( 5 x 5 x 5 x5 )

2401 - ( 7 x 7 x 7 x 7)

The minimum number of shirt they will sell to make the given profit is 192 shirts

Inequalities are equations not separated by an equal sign.

If a cheerleading team plans to sell t-shirts as a fundraiser and the teams goal is to make profit of at least $1248 with each t-shirt sold at $6.50, then the equation required is;

6.50t ≥ 1246

Divide both sides by 6.50

6.50t/6.50 ≥1246/6.5

t ≥ 192

Hence the minimum number of shirt they will sell to make the given profit is 192 shirts

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Answer:

y=17.2x²-226.3x+2184.5

Answer:

LA = 624 cm²

Step-by-step explanation:

h² = 5² + 12²

h = 13

LA = 4 × bh/2

LA = 4 × (24 cm)(13 cm)/2

LA = (48 cm)(13 cm)

LA = 624 cm²

Answer:

The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].

Step-by-step explanation:

[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]