The function P(x) = 3x2 + 4x + 5,is dilated by the function I(x) = P(2x). Write the new function I(x).

Answer:

The x-intercept are (-7 , 0) and (5 , 0)

Step-by-step explanation:

* Lets revise the general form of the equation of the parabola

- The general form of the equation of the parabola is:

  y = ax² + bx + c , a , b , c are constant

- The y-intercept is c, because the parabola intersect the y-axis at

  point (0 , c)

- The x-coordinate of the vertex point is -b/2a

* Now lets solve the problem

∵ The general form of the equation of the parabola is y = ax² + bx + c

∵ The y-intercept is -105

∴ c = -105

∴ y = ax² + bx - 105

∵ The vertex point is (-1 , -108)

∴ The x-coordinate of the vertex of the parabola = -1

∵ The x-coordinate of the vertex of the parabola = -b/a

∴ -b/2a = -1 ⇒ using cross multiplication

∴ -b = -2a ⇒ multiply two sides by -1

∴ b = 2a

- Substitute the value of b in the equation

∴ y = ax² + 2ax - 105

- Substitute the value of x , y in the equation by the coordinates of

 the vertex point

∵ The vertex point lies on the parabola

∴ put x = -1 and y = -108

∴ -108 = a(-1)² + 2a(-1) - 105

∴ -108 = a - 2a - 105 ⇒ add the like term

∴ -108 = -a - 105 ⇒ add 105 to both sides

∴ -3 = -a ⇒ multiply both sides by -1

∴ a = 3

- Substitute the value of a in the equation

∵ y = ax² + 2ax - 105

∴ y = 3x² + 2(3)x - 105

∴ y = 3x² + 6x - 105

- To find the x-intercept put y = 0

∴ 3x² + 6x - 105 = 0

- All the terms have 3 as a common factor

∴ divide all the terms by 3

∴ x² + 2x - 35 = 0

- Now factorize it into two factors

∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the

  2nd bracket

∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the    

  2nd bracket

∵ x × - 5 = -5x ⇒ means

∵ x × 7 = 7x ⇒ extremes

∵ 7x - 5x = 2x ⇒ the middle term

∴ (x - 5)(x + 7) = 0

- Equate each bracket by 0

∴ x - 5 = 0 ⇒ add 5 to both sides

∴ x = 5

OR

∴ x + 7 = 0 ⇒ subtract 7 from both sides

∴ x = -7

∴ The x-intercept are -7 , 5

* The x-intercept are (-7 , 0) and (5 , 0)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have a square in the base and four triangles on the lateral surface.

The formula of an area of a square:

[tex]A_{\square}=s^2[/tex]

s - side

We have s = 9mm. Susbtitute:

[tex]A_{\square}=9^2=81\ mm^2[/tex]

The formula of an area of a triangle:

[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 9 mm and h = 12 mm. Substitute:

[tex]A_{\triangle}=\dfrac{(9)(12)}{2}=54\ mm^2[/tex]

The Surface Area:

[tex]S.A.=A_{\square}+4A_{\triangle}[/tex]

Substitute:

[tex]S.A.=81+4(54)=297\ mm^2[/tex]

Answer:

278

Step-by-step explanation:

The 0.3 in the highlighted cell mean 30% ordered dessert but no appetizer.

The correct option is (D).

The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values.

As, the number is in the column with no appetizer and row with dessert

So, 0.3 = 0.3*100/100

= 30/100

= 30% ordered dessert but no appetizer.

Hence, 30% ordered dessert but no appetizer.

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Answer:

  64 : 27

Step-by-step explanation:

When using scale factors

Length = scale factor

Area = scale factor squared

Volume = scale factor cubed

The ratio is 4:3

The ratio of the volume is 4^3 : 3^3

                                            64 : 27

Answer:

The length of AB is [tex]\sqrt{74}\ units[/tex]

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(2,-6)\\B(7,1)[/tex]  

substitute

[tex]d=\sqrt{(1+6)^{2}+(7-2)^{2}}[/tex]

[tex]d=\sqrt{(7)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{49+25}[/tex]

[tex]AB=\sqrt{74}\ units[/tex]

Answer:

hyperbola

Step-by-step explanation:

hyperbola

Ax^2+By^2+Cx+Dy+E=0

A=B you probably have a circle

A and B have same sign but A isn't B you probably have an ellipse

A and B are opposite in sign you probably have an hyperbola

If either A or B=0 (but not both) then you have a parabola

ANSWER

Hyperbola

EXPLANATION

The given conic has equation:

[tex] {x}^{2} - {y}^{2} = 16[/tex]

We divide through by 16.

[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = \frac{16}{16} [/tex]

We simplify the right hand side to get

[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{16} = 1[/tex]

Or

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

This is a hyperbola, that has its vertex at the origin because the quadratic terms have different signs. One is positive and the other is negative.

Answer:

Step-by-step explanation:

I don't think it really does grow by a constant rate. As he puts money in, the amount he puts in becomes less significant to the total.

Suppose he starts at 100 dollars.

After week one, he puts in 100 + 15 = 115 dollars.

The 15 dollars represents an increase of  15/100

After the second week, he puts in another 15 dollars. He has 115 in there already.

(15/115) * 100% = 13.04%

After the third week, he puts in another 15 dollars. (15/130 ) * 100% = 11.53

And so one

Answer:

40 - x² = 0

x² = 40

x = ±√40 = ±√4√10 = ±2√10

Answer:

The mean of pictures is 2

Step-by-step explanation:

To find the mean we add up all the pictures then divide it by the amount of newspapers, there are 10 and 5 newspapers. 10/5=2.

Answer:

Option A.12 square units

Step-by-step explanation:

Let

[tex]A(-2,2), B(1,2), C(0,-6)[/tex]

Plot the vertices

see the attached figure

we know that

The area of triangle is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

[tex]b=AB=(1-(-2))=3\ units[/tex]

[tex]h=(2-(-6))=8\ units[/tex]

substitute

[tex]A=\frac{1}{2}(3)(8)[/tex]

[tex]A=12\ units^{2}[/tex]

Answer:

Step-by-step explanation:

A. 12

Answer:

[tex]\displaystyle y' = -4e^{-4x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = e^{-4x}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The derivative of y = e^-4x is -4e^-4x.

To find the derivative of y = e-4x, we can use the power rule for derivatives. The power rule states that if we have a function of the form y = axb, then the derivative is given by dy/dx = abxb-1. Applying this rule to the given function, we have dy/dx = -4e-4x. Therefore, the derivative of y = e-4x is -4e-4x.

Answer:

10b + 2

Step-by-step explanation:

To simplify this expression. 10b + 7 - 3 - 2​ use the sample you demonstrated above to simplify it

10b + 7 -3 -2

combine the like terms

10b + 7 - 5

10b + 2

The expression 10b + 7 - 3 - 2, when simplified by grouping and adding or subtracting like terms, becomes 10b + 2.

To simplify an expression, like the one you've given which is 10b + 7 - 3 - 2,  it is necessary to group like terms and combine them.

First, let's combine like terms. In this case, you only have a single term with a variable:

10b (which we will leave as is since there are no other terms with 'b' in them)

Then, you have constants (numbers without variables) 7, -3, and -2. We can combine these by adding or subtracting them: 7 - 3 - 2 = 2

So your simplified expression becomes: 10b + 2

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Answer:

5 1/8 - 2 7/8 =

3 -6/8 =

2 2/8 =

2 1/4 =

2.25

Step-by-step explanation:

Answer:

Constant of variation (k) = -18

Step-by-step explanation:

We are given that y varies inversely as x and we are to find the constant of variation (lets assume its [tex] k [/tex] if [tex] y = 2 [/tex] and [tex] x = - 9 [/tex].

[tex] y [/tex] ∝ [tex] \frac { 1 } { x } [/tex]

Changing this inverse proportionality to equality to get:

[tex] y = \frac { k } { x } [/tex]

Substituting the given values:

[tex] 2 = \frac { k } { -9 } [/tex]

[tex]k=-9 \times 2[/tex]

k = -18

Answer:

Up to 39 shortbread cookies.

Step-by-step explanation:

Start by considering: how many cookies can Ramon make if

Assume that flour runs out before the other two ingredients. How many cookies can Ramon make?

It takes 1 1/2 = 3/2 cups of flour to bake fifteen cookies. 5 cups of flour is available. How many batches of fifteen cookies will that 5 cups of flour make?

[tex]\displaystyle \frac{5}{3/2}\right = \frac{10}{3}[/tex].

That's

[tex]\displaystyle 5\times \frac{10}{3} = 50\;\text{cookies}[/tex].

Similarly, assume that sugar runs out before the other two ingredients. How many cookies can Ramon make?

It takes one cup of sugar to bake fifteen cookies. 4 cups of sugar is available. That 4 cups of sugar will make up to four batches of fifteen cookies. That's 60 cookies.

Assume that butter runs out before the other two ingredient. How many cookies can Ramon make?

It takes 1 1/4 = 5/4 cups of butter to bake fifteen cookies. 13/4 cups of butter is available. That 13/4 cups of butter will make up to 13/5 batches of fifteen cookies. That's

[tex]\displaystyle 15 \times \frac{13}{5} = 39\;\text{cookies}[/tex].

These three numbers differ. How many cookies will these materials actually make? The ingredient that will make the smallest number of cookies will run out before other ingredients. In this case, butter runs out first. These materials will make up to 39 shortbread cookies.

Answer:

He shrunk .6 cm each year

Step-by-step explanation:

To find the decrease per year, we take the total decrease and divide by the number of years

2.4 cm/ 4 years

.6 cm/ year

He shrunk .6 cm each year

Answer:

Step-by-step explanation:

[tex]y=-\dfrac{3}{4}x+3\ and\ y=-12\\\\\text{Substitute the value of y to the first equation:}\\\\-12=-\dfrac{3}{4}x+3\qquad\text{multiply both sides by 4}\\\\-48=-3x+12\qquad\text{subtract 12 from both sides}\\\\-60=-3x\qquad\text{divide both sides  by (-3)}\\\\20=x\to x=20[/tex]

Answer:

x = 20, y = -12

Step-by-step explanation:

y= -3/4x+3 and y=-12

x = 20, y = -12

Answer:

[tex]\large\boxed{a)\ 21,\ 24,\ 29}\\\boxed{b)\ \text{five terms}}[/tex]

Step-by-step explanation:

[tex]a_n=n^2+20\\\\a)\\\\\text{Substitute}\ n=1,\ n=2\ \text{and}\ n=3\ \text{to the }\ a_n:\\\\a_1=1^2+20=1+20=21\\\\a_2=2^2+20=4+20=24\\\\a_3=3^2+20=9+20=29[/tex]

[tex]b)\\\\\text{You have to solve the inequality:}\\\\n^2+20<50\qquad\text{subtract 20 from both sides}\\\\n^2<30\to n<\sqrt{30}\to n\leq5\\\\a_1,\ a_2,\ a_3,\ a_4\ \text{and}\ a_5\ \text{are less than 50.}[/tex]

a) The first three terms of the sequence are 21, 24 and 29.

b) The no. of terms less than 50 are 6.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, The nth term of a sequence is n² + 20.

The first three terms we'll get by replacing 1, 2, and 3 in place of n.

The first term is (1)² + 20 = 21.

The second term is (2)² + 20 = 24.

The third term is (3)² + 20 = 29.

No. of terms that are less than 50 are

n² + 20 < 50.

n² < 30.

n < ± √30.

n < 6 approx.

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Answer: second option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]

Answer:

The correct answer is second option

6√2

Step-by-step explanation:

From the figure we can see a right angled triangle, with angles 45°, 45° and 90°

The height of triangle is 6 units

Points to remember

If the angles of a right angled triangle are  45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2

To find the value of x

From the figure we can see that, the angles are  45°, 45° and 90°

Therefore the two sides are equal and one side is x

The equal side is 6 units

Therefore 6 : 6 : x = 6 : 6 : 6√2

The value of x = 6√2

The second option is the correct answer.

Answer:

Half gallon

Step-by-step explanation:

at the least expensive price per ounce (60 cents), half gallon is the answer.

Answer:

34.54

Step-by-step explanation:

C= 2pir

11/2= 5.5

5.5* pi=17.27

17.27*2=34.54

Answer:

The circumference of the circle is [tex]\pi * 11[/tex] inches, which is about [tex]34.54[/tex] inches.

Step-by-step explanation:

The circumference of a circle when you only have the diameter ([tex]11[/tex] inches in this case) can be calculated with the formula [tex]C=\pi d[/tex] where [tex]C[/tex] represents the circumference and [tex]d[/tex] represents the diameter.

Plug in the value for the diameter, which is [tex]11[/tex] inches, to get [tex]C=\pi * 11[/tex].

[tex]\pi * 11[/tex] inches is the final exact answer, but you can estimate the answer by replacing [tex]\pi[/tex] with [tex]3.14[/tex] to get [tex]C=3.14 * 11[/tex].

This can be simplified to get [tex]C=34.54[/tex], but this is only an estimate.

Answer:

-10.6

Step-by-step explanation:

-3|z| + 2(a + y) =

= -3|-4.2| + 2(-2 + 3)

= -3(4.2) + 2(1)

= -12.6 + 2

= -10.6

Answer:

I have not the slightest clue but there's an app called cam calc and I swear its the best

Answer:

-2!

Step-by-step explanation:

im just finished this exact test and i swear thats the right answer!!

Answer:

[tex]A=24\ un^2.[/tex]

Step-by-step explanation:

Plot points A(0,0), B(6,0), C(2,4) and D(8,4) on the coordinate plane (see attached diagram). The segment CE is the height of the parallelogram ABDC.

The area of the parallelogram is

[tex]A=\text{Base}\cdot \text{Height}[/tex]

Base= AB

Height =CE

So,

[tex]AB=\sqrt{(6-0)^2+(0-0)^2}=\sqrt{36+0}=\sqrt{36}=6\\ \\CE=\sqrt{(2-2)^2+(4-0)^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]

Hence, the area of the parallelogram is

I'll tell you how to do it for any polygon in the cartesian plane with the vertices listed in order.

First we have to list the vertices in order so each pair is a side:

(0,0) (6,0) (8,4) (2,4)

Now for each side (a,b)(c,d) we calculate the cross product ad-bc

(0,0)(6,0)   0(0)-0(6)=0

(6,0)(8,4)   6(4)-0(8)=24

(8,4)(2,4)   8(4)-4(2) = 24

(2,4)(0,0)   2(0)-4(0)=0

We add up the cross products, and take half the absolute value of the sum for the area:

Area = (1/2) | 0 + 24 + 24 + 0 | = 24

Answer: 24

Answer:

y=50

Step-by-step explanation:

Since the y value doesn't change and it is a line

y=50

Answer:

[tex]y= 0x + 50[/tex]

Step-by-step explanation:

Since, the slope intercept form of a line is,

y = mx + c,

Where, m is the slope of the line.

Also, the equation of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Thus, the equation of the line passes through (-25, 50) and (25, 50) is,

[tex]y-50= \frac{50-50}{25+25}(x+25)[/tex]

[tex]y-50=0[/tex]

[tex]\implies y = 0x + 50[/tex]

Which is the required equation.

Answer:

[tex]m + \frac{1}{3} [/tex]

Step-by-step explanation:

[tex]1. \: 1 - \frac{2}{3}+m \\ 2. \: m + (1 - \frac{2}{3}) \\ m + \frac{1}{3} [/tex]

Answer:

29/6

Step-by-step explanation:

1+ -2/3 - (-m)

1 - 2/3 + m

1/3 + m

Let m = 9/2

1/3 +9/2

Get a common denominator of 6

1/3 *2/2 = 2/6

9/2 *3/3 = 27/6

2/6 + 27/6

29/6

Answer:

A or (2x+1)/(x-1)

Step-by-step explanation:

Let's simplify the top of the fraction first.

1. Simplify the numerator.

2x^2 -7x-4=(2x+1)(x-4)

2. Simplify the denominator.

x^2-5x+4=(x-4)(x-1)

Now we have:

((2x+1)(x-4))/((x-4)(x-1))

We see that there is an (x-4) both on the numerator and denominator.

We can remove (x-4) by division.

Doing that, we have:

(2x+1)/(x-1) or A

Answer:

[tex]4x(2x + 3)[/tex]

Step-by-step explanation:

We have the expression

[tex]8x^2 + 12x[/tex]

and we must factor it

Note that the expression has no independent term

Then we can factor the expression by taking the variable 4x as a common factor

[tex]8x^2 + 12x[/tex]

[tex]4x(2x + 3)[/tex]

Finally the factored form of [tex]8x^2 + 12x[/tex] is [tex]4x(2x + 3)[/tex]

Answer: 4x(2x+3).

Step-by-step explanation: To factor a number means to break it up into numbers that can be multiplied together to get the original number. In the given problem, we can factorize the expression by taking out a common factor, in this case 4x:

[tex]8x^{2} +12x=[/tex]

[tex]4x(2x+3)[/tex]

as we can see, if we multiply 4x*(2x+3) we obtain the original expression.