PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Answer: $0.12 per pound

Step-by-step explanation:

divide $360.00 by 3, then divide it by 1000, because 1000 lbs is 1 ton

Final answer:

To calculate the price per pound of dirt, divide the total cost of $360.00 by the total weight of 6000 pounds, resulting in a cost of $0.06 per pound.

Explanation:

The student asked how much it would cost per pound if 3 tons of dirt cost $360.00. First, it's essential to know how many pounds are in a ton. There are 2000 pounds in one ton. So for 3 tons, there would be 6000 pounds (3 tons x 2000 pounds/ton).

Next, to find the price per pound, you would divide the total cost by the total weight in pounds. That's $360.00 divided by 6000 pounds, which equals $0.06 per pound.

Therefore, the price per pound of dirt is $0.06.

let's use those two endpoints in the line of (-5 , 2) and (5 , -1)

[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-2}{5-(-5)}\implies \cfrac{-3}{5+5}\implies -\cfrac{3}{10}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{3}{10}[x-(-5)]\implies y-2=-\cfrac{3}{10}(x+5) \\\\\\ y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2\implies y=-\cfrac{3}{10}x+\cfrac{1}{2}[/tex]

Answer:

y=-(3/10)x+(1/2)

Step-by-step explanation:

Let

A(-5,2),B(5,-1)

step 1

Find the slope m

m=(-1-2)/(5+5)

m=-3/10

step 2

Find the equation of the line into slope point form

we have

m=-3/10

point A(-5,2)

y-2=(-3/10)(x+5) ----> equation of the line into slope point form

Convert to slope intercept form -----> isolate the variable y

y=-(3/10)x-(15/10)+2

y=-(3/10)x+(5/10)

simplify

y=-(3/10)x+(1/2)

Sorry this took awhile.

So for Friday, it would be $550

Saturday, $895

Sunday, 1,095

So the total is $2540 if you add the numbers up. Hope this helps!

Answer:

Step-by-step explanation:

We have given:

√2x+3 - √x+1  = 1

First of all isolate the square root of the left hand side:

√2x+3 = √x+1 +1

Now take square on both sides.

(√2x+3)^2 = (√x+1 +1)^2

Open the R.H.S by squaring formula.

∴(a+b)^2 = a^2+2ab+b^2

2x+3 = (√x+1)^2 + 2(√x+1)(1)+(1)^2

2x+3 = x+1 +2√x+1 +1

2x+3 = x+2 +2√x+1

Combine the like terms:

2x-x+3-2 = 2√x+1

x+1 = 2√x+1

Take square on both sides

(x+1)^2 = (2√x+1)^2

x²+2x+1 = 4x+4

x²+2x-4x+1-4 = 0

x²-2x-3 = 0

Now solve the quadratic equation:

a = 1 , b= -2 , c = -3

x = -b+/-√b²-4ac/2a

x = -(-2)+/-√(-2)² - 4(1)(-3) / 2(1)

x = 2 +/- √4+12 / 2

x = 2+/- √16/2

x = 2+/- 4 /2

x = 2+4/2     , x = 2-4/2

x = 6/2      , x = -2/2

x = 3      , x = -1

The solutions we get is (3, -1).

Answer:

Quadratic Equation:  x²-2x-3 = 0

Solutions (Next Question): (3, -1)

Step-by-step explanation:

Absor201 is correct! (look at the BOLDED text in their answer)

ANSWER

p

[tex]{f}^{ - 1} (x) = 3x + 4[/tex]

EXPLANATION

The line r has equation,

[tex]f(x) = \frac{x - 4}{3} [/tex]

The line that represents

[tex] {f}^{ - 1} [/tex]

is p.

To find the equation of p, we let

[tex]y = \frac{x - 4}{3} [/tex]

We now interchange x and y.

[tex]x= \frac{y - 4}{3} [/tex]

We solve for y,

[tex]3x=y - 4[/tex]

[tex]y = 3x + 4[/tex]

Therefore

[tex] {f}^{ - 1} (x) = 3x + 4[/tex]

Subtract the monthly fee from the total, then divide by the price of each session.

125 - 15 = 110

110 / 13.75 = 8

She got 8 sessions.

Answer:

A = 42 cm^2

Step-by-step explanation:

To find the area of a rectangle , multiply the length and the width

A = lw

A = 7cm * 6 cm

A = 42 cm^2

Replace x in the equation with the x value from the ordered pair and see if the y value meets the inequality.

y ≤ 2(-9) -7

y ≤ -18 - 7

y ≤ -25

The y value in the ordered pair is 1, so replace y with 1 and see if the inequality is true:

1 ≤ -25

1 is a positive value and the equation equals a negative value, so this is not true, because 1 is greater than -25.

Answer:

Step-by-step explanation:

y=kx

4=k(-2)

k=-2

y=-2x

when x=30

y=-2*30=-60

Answer:

100

Step-by-step explanation:

1=ad=100

and I need more characters so don't mind me.

Answer:

The correct option is 3. The measure of arc AD is 100°

Step-by-step explanation:

Given information: BD is a diameter, ∠1 = 100°  and arc BC=30°.

The central angle of an arc is the measure of arc.

From the given figure it is clear that the central angle of arc AD is equal to the angle 1.

[tex]Arc(AD)=\angle 1[/tex]

It is given that ∠1 = 100°

[tex]Arc(AD)=100^{\circ}[/tex]

The measure of arc AD is 100°, therefore the correct option is 3.

Answer:

66

Step-by-step explanation:

cos 0=20/50

The approximate measure of the angle formed by the top of the slide and the vertical support is approximately 21.8 degrees.

In trigonometry, the tangent function can help us find the angle in a right-angled triangle. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case, the side opposite the angle is the height of the slide (20 feet), and the adjacent side is the length of the slide (50 feet).

Now, we can use the tangent function to find the angle (θ):

tan(θ) = Opposite / Adjacent

tan(θ) = 20 feet / 50 feet

tan(θ) = 0.4

To find the value of θ, we can take the inverse tangent (also known as arctan or tan⁻¹) of 0.4:

θ ≈ arctan(0.4) ≈ 21.8 degrees

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Answer:

The correct option is 4.

Step-by-step explanation:

If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.

In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.

In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.

[tex]\frac{1}{1}\neq \frac{1}{2}[/tex]

The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.

Therefore the correct option is 4.

Answer:

There is no dilation transforming triangle I into triangle II.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

When the leading coefficient (the coefficient of the x² term) is 1, we can complete the square by taking the b coefficient (coefficient of the x term), dividing it by 2, squaring the result, and adding it to both sides.

b = -6

b/2 = -3

(b/2)² = 9

Add 9 to both sides to make the left side a perfect-square trinomial.

To form a perfect square trinomial from the equation x²-6x, add 9 to both sides. This is achieved by halving the coefficient of x and squaring the result.

Amira can make the left side of the equation, x² - 6x, a perfect-square trinomial by adding 9 to both sides. The process for this involves completing the square. Half of the coefficient of x, which is -6, is -3. Squaring -3 gives 9. Therefore, Amira should add 9 to both sides of the equation to get x² - 6x + 9 = 1 + 9, simplifying to (x-3)² = 10. This results in a perfect-square trinomial on the left.

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Answer:

s = 4

Step-by-step explanation:

Solve for s:

8 s - 10 = 34 - 3 s

Add 3 s to both sides:

8 s + 3 s - 10 = (3 s - 3 s) + 34

3 s - 3 s = 0:

8 s + 3 s - 10 = 34

8 s + 3 s = 11 s:

11 s - 10 = 34

Add 10 to both sides:

11 s + (10 - 10) = 10 + 34

10 - 10 = 0:

11 s = 34 + 10

34 + 10 = 44:

11 s = 44

Divide both sides of 11 s = 44 by 11:

(11 s)/11 = 44/11

11/11 = 1:

s = 44/11

The gcd of 44 and 11 is 11, so 44/11 = (11×4)/(11×1) = 11/11×4 = 4:

Answer:  s = 4

Answer:

49

Step-by-step explanation:

y = -x² - 10x + 24

For a parabola ax² + bx + c, the vertex is at x = -b/(2a).

In this case, a = -1 and b = -10.  So:

x = -(-10) / (2 * -1)

x = -5

The y coordinate is:

y = -(-5)² - 10(-5) + 24

y = -25 + 50 + 24

y = 49

Answer:

Problem:

Solve x+y=7;x+2y=11

Steps:

I will try to solve your system of equations.

x+y=7;x+2y=11

Step: Solvex+y=7for x:

x+y+−y=7+−y(Add -y to both sides)

x=−y+7

Step: Substitute−y+7forxinx+2y=11:

x+2y=11

−y+7+2y=11

y+7=11(Simplify both sides of the equation)

y+7+−7=11+−7(Add -7 to both sides)

y=4

Step: Substitute4foryinx=−y+7:

x=−y+7

x=−4+7

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=4

ANSWER

[tex]y= log_{x}(p)[/tex]

EXPLANATION

The given expression is

[tex] {x}^{y} = p[/tex]

We take logarithm of both sides to base x.

[tex] log_{x}( {x}^{y} ) = log_{x}(p) [/tex]

Apply the power rule of logarithms to get:

[tex]ylog_{x}( {x}) = log_{x}(p)[/tex]

Logarithm of the base is 1.

This implies that,

[tex]y( 1) = log_{x}(p)[/tex]

[tex]y= log_{x}(p)[/tex]

It’s c which is 28 degree Celsius

The value of x will be equal to 28. The correct option is C.

'The intersecting chords theorem is a statement that describes a relation of the four-line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.'

According to the given problem,

Given,

We know, according to intersecting chords theorem,

⇒ x = [tex]\dfrac{CD + AB}{2}[/tex]

⇒ x = [tex]\dfrac{56}{2}[/tex]

⇒ x = 28

Hence, we can conclude, that the value of x is 28.

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6 adults and 11 children.

In order to solve this problem we going to use linear equations.

A group of 17 people went to the concert. There are adults and children in that group x + y = 17 where x are adults and y are children. That group pay $57.50 for tickets, if tickets cost $5.00 for adults and $2.50 for children, then 5.00x + 2.50y = 57.50.

x + y = 17 ---------->  y = 17 - x

Substituting the value of y in the equation 5.00x + 2.50y = 57.50:

5.00x + 2.50(17 - x) = 57.50 solving

x = 6

Substituting x = 6 in the equation x + y = 17

6 + y = 17 solving

y = 11

From a group of 17 people who went to the concert 6 are adults and 11 are children.

Answer:

Option B) y=4/5x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have that

case A) y=x+4/5

The line does not passes through the origin, is not a proportional relationship

case B) y=(4/5)x

The line passes through the origin ---->represents a proportional relationship

The slope m is equal to the constant of proportionality k

The slope m=4/5

therefore

The line  y=4/5x

Represents a proportional relationship that has a constant of proportionality equal to 4/5

case C) xy=4/5

Represent an inverse variation is not a proportional relationship

case D) x+y=(4/5)

The line does not passes through the origin, is not a proportional relationship

Answer:

The Answer is B.

Step-by-step explanation:

Trust me .

Answer:

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Step-by-step explanation:

The terms of the sequence are:

[tex]5,-1,-7,-13,-19[/tex]

The first term of this sequence is [tex]f(1)=5[/tex].

There is a constant difference among the terms.

This constant difference can determined by subtracting a previous term from a subsequent term.

[tex]d=-1-5=-6[/tex]

The general term of this arithmetic sequence is given  recursively by [tex]f(n)=f(n-1)+d[/tex]

We substitute the necessary values to obtain:

[tex]f(n)=f(n-1)+-6[/tex]

Or

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Answer:

C

Step-by-step explanation:

Answer:

Part A)AT=16x^2

Part B)AT=4b^2 +12x^2

Step-by-step explanation:

Part A:

length of each side of square in tile=x

length of each small base side of trapezoid in tile=x

length of each large base side of trapezoid in tile=2x

height of each trapezoid in tile=x

Area of each square in tile= x^2

Area of each trapezoid in tile= x(x+2x)/2

                                               = (3x^2)/2

area of squares inside tile= 4(x^2)

area of trapezoids inside tile= 8[(3x^2)/2]

Area of tile, AT= area of squares inside tile+area of trapezoids in tile

AT= 4(x^2) + 8[(3x^2)/2]

     = 4x^2 + 12x^2

      = 16x^2

Part B)

if If the tile is a square with a length of b centimeters then AT

= 4b^2 +12x^2 !

Answer:

The employers pay their employees based on hourly rates, commission and salary.

Step-by-step explanation:

The employees get their pay based on hourly rates that can range from a minimum hourly rate of say $12 per hour to any maximum figure like $40 per hour.

The final salary is based on the numbers of hours worked multiplied by the hourly rate.

Secondly, the pays are also commission based. That is your base salary plus the commission.

The salary is typical in management positions. These are not hourly based but a lump sum pay.

So, the correct answers are : commission, hourly pay and salary.

Answer:

commission

hourly pay

salary

Step-by-step explanation:

PLATO USERS

Answer:

B. Systematic Random Sampling

Step-by-step explanation:

The process of systemic random sampling involves randomly selecting the starting point but the succeeding points will be based on the interval in between each point. The interval is computed by dividing the population by the sample size.

Answer:

B. Systematic Random Sampling

Step-by-step explanation:

none that i can explain

The answer is:

The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.

To solve the problem, we need to evaluate both variables for the given values:

[tex]x=-2[/tex]

and

[tex]y=4[/tex]

So, we are given the expression:

[tex]-6x^{3}-y^{2}-3xy[/tex]

Then, evaluating the given values for both variables, we have:

[tex]-6*(-2)^{3}-(4)^{2}-3*(-2)*(4)=(-6*-8)-(16)+24=48-16+24=56[/tex]

Hence, we have that the answer is:

The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.

Have a nice day!

Answer:

The value of given expression = 56

Step-by-step explanation:

It is given an expression in variable x and y

-6x³ - y² - 3xy

To find the value of given expression

Let expression be,

-6x³ - y² - 3xy

When x = -2 and y =4

-6x³ - y² - 3xy = -6(-2)³ - 4² - (3 * -2 * 4)

 = -6*-8 - 16 + 24

 = 48 - 16 + 24

 = 56

Therefore the value of given expression is 56

Answer:

Option B. [tex]11.78\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3} \pi r^{2}h[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3} \pi (1.5)^{2}(5)[/tex]

[tex]V=3.75\pi\ in^{3}[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]V=3.75(3.14)=11.78\ in^{3}[/tex]

1. The angles DCA and BCA are the same.

2. Angles DCA and BCA are not supplementary. Since the both of them add up to 90° (we know that angle c is equal to 90° because in a right square all angles are 90°) the angles would be complementary, not supplementary. Supplementary angles add up to 180°

The angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.

A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.

Given that, ABCD is a square.

Here, a straight line from point A to C.

1) AC is diagonal, ∠DCA and ∠BCA are equal.

2) ∠DCA and ∠BCA are equal and added to 90°.

Therefore, the angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.

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Answer: Inconsistent.

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Solve for y from each equation:

Equation 1:

[tex]-\frac{1}{2} x = -6 - y\\\\y-\frac{1}{2} x = -6\\\\y=\frac{1}{2} x-6[/tex]

Equation 2:

[tex]3+y= \frac{1}{2} x + 4\\\\y= \frac{1}{2} x + 4-3\\\\y= \frac{1}{2} x+1[/tex]

A system of equations can be classified by its number of solutions.

You can observe that the slopes of both equations are the same but the y-intercepts are different, then these lines are parallel, which means that they do not intersect.

By definition, when to lines are parallel there is NO SOLUTION and the system is classified as "Inconsistent".

let's bear in mind that the cylinder and the cone both have the same volume of 112 cm³, and the same radius, but different heights.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=112\\ h=7 \end{cases}\implies 112=\pi r^2(7)\implies \cfrac{112}{7\pi }=r^2\implies \cfrac{16}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{16}{\pi }}=r\implies \cfrac{\sqrt{16}}{\sqrt{\pi }}=r\implies \cfrac{4}{\sqrt{\pi }}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \qquad \begin{cases} r=\frac{4}{\sqrt{\pi }}\\ V=112 \end{cases}\implies 112=\cfrac{\pi \left( \frac{4}{\sqrt{\pi }} \right)^2(h)}{3} \\\\\\ 336=\pi \left( \cfrac{4^2}{(\sqrt{\pi })^2} \right)h\implies 336=\pi \cdot \cfrac{16h}{\pi }\implies 336=16h \\\\\\ \cfrac{336}{16}=h\implies \blacktriangleright 21=h \blacktriangleleft[/tex]

Calculate the radius of the cup using its volume and height. Determine the cone's height by applying the cup's height to the volume formula for a cone after elimination.

The volume of the cup:

The formula for the volume of a cylinder: V = πr²h.

The formula for the volume of a cone: V = (π/3)r²h.

(πr²h)cylinder = ((π/3)r²h)cone

Since the cone has the same radius as the cylindrical cup and given h = 7 cm

Finding the height of the cone by eliminating:

[tex]h_{cylinder}[/tex] = [tex]h_{cone}[/tex]×(1/3)

[tex]h_{cone}[/tex] = 3 × 7 = 21

Therefore, height of cone is 21 cm.

Answer:

Step-by-step explanation:

Instead of x substitute (x + 4) to f(x) = x² - 12

f(x + 4) = (x + 4)² - 12        use (a + b)² = a² + 2ab + b²

f(x + 4) = x² + 2(x)(4) + 4² - 12

f(x + 4) = x² + 8x + 16 - 12

f(x + 4) = x² + 8x + 4