Consider the function y= x^2 +4x-4.
a) what is the vertex of this function? Show your work.
b) what is the equation of the axis of symmetry? Explain how you know.
c) What is the y- intercept?
d) Graph the line of symmetry. Plot the vertex and the point containing the y-intercept. Then plot another point on the graph and use the plotted points and the axis of symmetry to plot two more points. Draw the graph of the function through the points.

We have

[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{x-2}=x^3+4x^2+x-6[/tex]

The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that [tex]x=-2[/tex] is a root, since [tex](-2)^3+4(-2)^2+(-2)-6=0[/tex], so [tex]x+2[/tex] is also a factor and we have

[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3[/tex]

Finally, we can factorize the remaining quotient easily:

[tex]x^2+2x-3=(x+3)(x-1)[/tex]

so the other factors are [tex]x+2[/tex], [tex]x+3[/tex], and [tex]x-1[/tex].

Answer:3.758

Step-by-step explanation:

Sin70= m/4

m= 4*sin70

m = 3.758

Answer:

[tex]f(x) = \frac{1}{16}x^2[/tex]

Step-by-step explanation:

If the graph of the function [tex]y=f(hx)[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If [tex]0 <h <1[/tex] the graph is stretched horizontally  by a factor [tex]\frac{1}{h}[/tex]

If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]

In this problem we have the parent function [tex]y=x^2[/tex] And we know that it stretches horizontally by a factor of 4

Therefore

[tex]0 <h <1[/tex]  and [tex]h=\frac{1}{4}[/tex]

The transformation is:

[tex]y=f(\frac{1}{4}x)[/tex]

And the function is:

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

Answer:

I believe I would be the last one D

Answer:

Last choice

Step-by-step explanation:

He spins the spinner and can get Red, White, or Blue.

For each of those three outcomes, the coin can land on Heads or Tails.

The sample space has the following 6 possible outcomes.

Red, Heads

Red, Tails

White, Heads

White, Tails

Blue, Heads

Blue, Tails

The answer is the last choice.

Answer;

63.20 / .045 = $2.84

Answer:

63.20 / .045 = $2.84

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

-7+12x^4-5y^8+x

Terms:

1: -7

2: 12x^4

3: 5y^8

4: x

These are all different terms so there are 4

Answer:

x² + 7x + 12

Step-by-step explanation:

The area of a rectangle = length × width

here length = x + 4 and width = x + 3, hence

A = (x + 4)(x + 3)

Each term in the second parenthesis is multiplied by each term in the first parenthesis.

A = x(x + 3) + 4(x + 3) ← distribute each parenthesis

A = x² + 3x + 4x + 12 ← collect like terms

A = x² + 7x + 12 ← in standard form

Answer:

( A )

Step-by-step explanation:

If two lines are parallel, then the slope of both lines SHOULD be the same.

Answer:

4.  30

5.  108

Step-by-step explanation:

4.  There are 2 styles, 3 sizes and 5 colors

2 * 3 * 5 = 20

There are 30 different bikes

5. There are 4 appetizers, 9 entrees, and 3 desserts

4*9*3 = 108

We can order 108 different combinations

If this helps you please mark brainliest. As it helps me out.

Output = Input - 2

Input = Output + 2

So

-3 - 2 = -5

And

-1 - 2 = -3

And

0 - 2 = -2

Hope this helps!

Answer:

4.225 L

Step-by-step explanation:

The box has a height of 21 cm.  After the box is filled to 18 cm, there's 3 cm left of space.  The volume of this space is:

V = lwh

V = (25 cm) (37 cm) (3 cm)

V = 2775 cm³

1 cm³ is the same as 1 mL, so the volume of the space is 2775 mL.

1 L is 1000 mL, so this volume is 2.775 L.

7 L of water is then poured in.  The box can hold 2.775 L.  The rest overflows.  The overflow volume is:

7 L - 2.775 L = 4.225 L

Final answer:

The volume of water that overflows from the container after pouring an additional 7 liters is 4,225 mL or 4.225 liters.

Explanation:

The question involves calculating the volume of water that overflows from a rectangular container when additional water is poured in. The existing water depth, dimensions of the container, and the volume of the additional water are given. We know that 1 cm³ of water is equivalent to 1 mL, and there are 1000 mL in 1L.

The initial water volume in the container is the product of the length, width, and depth filled with water. Thus, the initial volume is:

25 cm (length) × 37 cm (width) × 18 cm (depth) = 16,650 cm³ (or mL)

When an additional 7 liters (which is 7,000 mL) of water is added to the container, the total volume of water becomes:

The full capacity of the container is calculated by multiplying its length, width, and height:

By subtracting the full capacity from the total volume after pouring:

We find that 4,225 mL (or 4.225 liters) of water overflows.

Answer:

5/2 or 5:2

Step-by-step explanation:

Answer:

6*5=30 to 2*6=12

Step-by-step explanation:

6:5 and 2:6 for smaller hexagon

Final answer:

To simplify the expression, distribute the -1.01 across the parentheses, combine like terms, and the simplified result is 14.652c - 21.22b. Given values for a, b, and c are not needed.

Explanation:

To simplify the algebraic expression 9.4c - 1.01∙(22b - 5.2c) + b, we first distribute the -1.01 across the parentheses, and then combine like terms.

Step-by-Step Explanation:

Distribute -1.01 to each term inside the parentheses: -1.01 * 22b = -22.22b, and -1.01 * (-5.2c) = 5.252c.

Combine the distributed terms with the original expression: 9.4c - 22.22b + 5.252c + b.

Combine like terms: (9.4c + 5.252c) + (b - 22.22b).

Adding c terms together gives 14.652c, and combining b terms gives -21.22b(because 1b - 22.22b equals -21.22b)

The simplified expression is now 14.652c - 21.22b.

Note: The given values a = 1, b = 0.0211, and c = -0.0211 are not relevant to the simplification process.

Answer:

A reflection across the x-axis.

Step-by-step explanation:

A reflection across the x-axis changes the signs of the y-coordinates like it does in the problem. (3, 2) becomes (3, -2) and (2, -3) becomes (2, 3).

I hope this helps!

ANSWER

Reflection in the x-axis

EXPLANATION

The given line segment has endpoints at (3,2) and (2,-3).

After this point are reflected the image points are:

(3,-2) and (2,3)

We can observe that the y-coordinates were negated to obtain the image points hence the mapping for the reflection is;

[tex](x,y)\to(x,-y)[/tex]

This is a reflection in the x-axis.

Answer:

f(x) = 10 [ (x + 4)^2 = -6 ]

Step-by-step explanation:

Please use " ^ " to indicate exponentation.  Thanks.

Also, please share the possible answer choices.  "Select the best answer from the choices provided."

Start with f(x) = 10x^2 + 80x + 220 = 0

Factor out the 10 to simplify this "completing the square."

f(x) =  10(x^2 + 8x + 22) = 0

Complete the square of x^2 + 8x + 22 only, for now.

Identify the coefficient of the x term.  It is 8.  Take half of that (it is 4) and square your result:  16

Now add 16 to x^2 + 8x  and then subtract 16 from that sum:

x^2 + 8x + 16 - 16 + 22 = 0, or

x^2 + 8x + 16      + 6     = 0

Rewrite x^2 + 8x + 16  as (x + 4)^2

and then the whole expression x^2 + 8x + 16 - 16 + 22 as (x + 4)^2 = -6

Finally, rewrite this as

f(x) = 10 [ (x + 4)^2 = -6 ] which is the desired form of the original equation.

Answer:

The answer is

[tex](x+4)^2=-6[/tex]

Step-by-step explanation:

Follow the steps below.

1) Take common factor 10

[tex]10(x^2 + 8x + 22) = 0[/tex]

2) For an equation of the form [tex]ax ^ 2 + bx + c[/tex]

Calculate [tex](\frac{b}{2})^2[/tex]

In this case the equation is [tex]x^2 + 8x + 22= 0[/tex]

[tex]a=1\\b=8\\c =22\\\\(\frac{b}{2})^2 = (\frac{8}{2})^2 = 16[/tex]

3) Add 16 on both sides of equality

[tex]10(x^2 + 8x + 16) +220= 16*10[/tex]

4) Factor the expression into parentheses and simplify

[tex]10(x+4)^2 +220= 16*10[/tex]

[tex]10(x+4)^2= 16*10-220[/tex]

[tex]10(x+4)^2 =-60[/tex]

[tex](x+4)^2 =-6[/tex]

Answer:

the answer is A I'm 80% sure

Answer:

8 or 8.5

Step-by-step explanation:

27 divided by 2 = 13.5

13.5 take away 5 = 8.5

The age of Jari now if the age after 5 years doubles is 11.

Given that:

Five years after jari's age now doubles, he will be 27.

Let x be the age of Jari now.

An equation can be formed with the given information.

When the age doubles, the age is 2x.

Five years after this age can be written as 2x + 5.

Now, it is given that this age is 27.

So,

2x + 5 = 27

Subtract both sides by 5.

2x = 27 - 5

2x = 22

Divide both sides by 2.

x = 22/2 = 11

Hence Jari is now 11 years old.

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Answer: is A

Step-by-step explanation: so I did 1×3/12+1×4/12 (3+4)/12 =7/12

Answer:

D. 7/36 pounds

Step-by-step explanation:

Combine the two using like terms so 1/3 and 1/4 = 4/12 and 3/12 so 4+3=7 so 7/12.

Next you divide by 3. To do this, find a larger denominator with a number that can be divided by 3.

7/12 to 14/24 and 21/36. 21 can be divided by 3.

Divide 21/36 by 3 and get 7/36. This can not be simplified any further.

Therefore your answer is D. 7/36.

Hope I helped!

Answer:

400mL/3l

Is the correct answer

Step-by-step explanation:

To find the quotient of 6 liters by 27 liters and 600 milliliters, convert both to milliliters and divide. The quotient is approximately 0.21739.

To find the quotient of 6 liters (L) divided by 27 liters and 600 milliliters (mL), we first need to convert the amounts to the same unit. Since there are 1,000 milliliters in a liter, we can convert 27 liters into milliliters:

27 L × 1,000 mL/L = 27,000 mL

Now we add the 600 mL:

27,000 mL + 600 mL = 27,600 mL

Rewrite the problem with both measurements in milliliters:

6,000 mL / 27,600 mL

We now divide 6,000 by 27,600:

6,000 mL / 27,600 mL = 0.21739 (rounded to five decimal places)

So, the quotient is approximately 0.21739.

Answer:

About 609,000 Cowboy stadiums could fit inside of Mount Everest

Step-by-step explanation:

we have

The estimate volume of Mount Everest is at around [tex]2,413\ km^{3}[/tex]

The Dallas Cowboys Stadium has a volume of [tex]140,000,000\ ft^{3}[/tex]

step 1

Convert ft³ to km³

we know that

1 km=3,280.84 ft

so

[tex]140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}[/tex]

step 2

To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium

[tex]2,413/0.003964=608,729[/tex]

Round to the nearest Thousands

[tex]608,729=609,000[/tex]

The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium

To estimate how many Dallas Cowboys stadiums could fit inside Mount Everest, we converted the volume of the stadium to cubic kilometers and then divided Mount Everest's volume by this number, resulting in approximately 608,845 stadiums.

Calculating the Volume of Mount Everest Compared to the Dallas Cowboys Stadium

To estimate how many Dallas Cowboys stadiums could fit inside of Mount Everest, we need to convert the volume of both structures to the same units and then perform a division.

We have the volume of Mount Everest as approximately 2,413 cubic kilometers. To convert the volume of the Dallas Cowboys Stadium from cubic feet to cubic kilometers, we use the conversion factor of 1 cubic kilometer equals 35.3147 million cubic feet:

Cowboys Stadium volume in cubic kilometers = 140 million cubic feet × (1 cubic kilometer / 35.3147 million cubic feet) = 3.9642 × 10-3 cubic kilometers.

Now, we can find how many Cowboys stadiums fit into Mount Everest:

Mount Everest volume / Cowboys Stadium volume = 2,413 cubic kilometers / 3.9642 × 10-3 cubic kilometers ≈ 608,845.

Therefore, approximately 608,845 Dallas Cowboys stadiums could fit inside of Mount Everest's volume.

To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵), align the exponents and then subtract the base numbers, resulting in (8.855 × 10⁶) expressed in scientific notation.

To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵) and express the result in scientific notation, we will align the exponents and then subtract the base numbers. Since the exponents are not the same, we need to adjust the smaller exponent to match the larger one.

First, we rewrite (2.25 × 10⁵) with a base of 10⁶, which becomes (0.225 × 10⁶). Now we can subtract:

(9.08 × 10⁶) - (0.225 × 10⁶) = (9.08 - 0.225) × 10⁶

Performing the subtraction, we get:

(8.855 × 10⁶)

If 1 cm represents 117 Km.

Then, 85.26 cm represents 117×85.26=9975.42 Km

therefore, the given places are 9975.42 Km apart from eachother.

The distance between Washington, D.C., and Baghdad, Iraq, are approximately 9,764.82 km apart in real life.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

We are given that;

11cm=117km

Distance of baghdad and iraq= 85.26cm

Now,

If the scale on a map is 1 cm for every 117 km and Washington, D.C., and Baghdad, Iraq, are 85.26 cm apart on the map, then we can use the scale to find the actual distance between the two cities.

We can set up a proportion to solve for the actual distance:

1 cm / 117 km = 85.26 cm / x

To solve for x, we can cross-multiply:

1 * x = 117 * 85.26

x = 9,764.82 km

Therefore, by the scale factor the answer will be 9,764.82 km.

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Answer: 8x - 11

Step-by-step explanation:

(5x-28)+(2x+11)+(x+5)

combine like terms 5x, 2x, x = 8x

combine all regular numbers -28, 11, 5 = -11

So the answer is : 8x-11

18j + 32w = $19.92

14j + 26w = $15.76

HAVE A GREAT DAY MA DUDE!

The system of equations that represent the costs of a juice box j and a bottle of water w are :

18j + 32w = 19.92 ....(1)

14j + 26w = 15.76 ....(2)

As per the given information, Consider that the cost of a juice box be represented by j and the cost of a bottle of water be represented by w.

The teacher who purchased 18 juice boxes and 32 bottles of water spent $19.92, we can write the equation as follows:

18j + 32w = 19.92

Similarly, the other teacher who purchased 14 juice boxes and 26 bottles of water spent $15.76, we can write the equation as :

14j + 26w = 15.76

Hence, the system of equations is:

18j + 32w = 19.92 ....(1)

14j + 26w = 15.76 ....(2)

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Answer:

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

Step-by-step explanation:

[tex]\frac{15x^3 (y-z)^2}{10x^{-2}(y^2-z^2)}[/tex] We need to solve this equation.

We know (x^2-y^2) = (x-y) (x+y)

Using the above formula, and taking 5 common:

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

Answer:

23.5

Step-by-step explanation:

x = 4 ; y = 5

x² + y³ = 4² + 5³ = 16 + 125 = 141

2 + x = 2 + 4 = 6

141 ÷ 6 = 23.5

PLEASE DO RATE ME AS BRAINLIEST UWU

Answer:

x² + y³ = 4² + 5³

= 16+ 125

= 141

2 + x =

2 + 4 = 6

your answer is

141 / 6 = 23.5

Step-by-step explanation:

Answer:

amount invested in mutual fund B; $4,800

amount invested in mutual fund A; $8,200

Step-by-step explanation:

Let the amount invested in mutual fund B be x. Then the amount invested in fund A would be;

(13000-x)

The loss emanating from fund B would be;

3.5% of x

=(3.5/100)*x

=0.035x

The profit resulting from investment in fund A would be;

6% of (13000-x)

= (6/100)*(13000-x)

=0.06(13000-x)

=780-0.06x

The total profit earned from funds A and B in terms of x will be;

780 - 0.06x + (-0.035x)

=780 - 0.095x

The total profit earned was 324, thus;

780 - 0.095x = 324

solving for x;

780 - 324 = 0.095x

456 = 0.095x

x = 4800

Then the amount invested in fund A would be;

13000 - 4800 = 8200

Answer:

16pi

Step-by-step explanation:

A=(pi)r^2

A=(pi) 4^2

A=16pi

Answer:

[tex]\large\boxed{1.\overline{21}=\dfrac{40}{33}}[/tex]

Step-by-step explanation:

[tex]x=1.\overline{21}\\\\x=1.212121...\qquad\text{multiply both sides by 100}\\\\100x=121.212121...\\\\\text{subtract x from 100x}\\\\100x-x=121.212121...-1.212121...\\\\99x=120\qquad\text{divide both sides by 99}\\\\x=\dfrac{120}{99}\\\\x=\dfrac{120:3}{99:3}\\\\x=\dfrac{40}{33}[/tex]

Answer:

Step-by-step explanation:

You have to start by taking away $55 from the 2300. The 55 does not get exchanged.

2300 - 55 = 2245

1 US dollar = 12.6577 pesos

2245 US dollars = x                             Cross multiply

x = 12.6577 * 2245

x = 28416.54 pesos. (rounded to 2 places)

Answer:

$28,416.54 Mexican pesos

Step-by-step explanation:

That $2,300 will be divided into two parts:  1) $55 fee and 2) equivalent amount in Mexican pesos:

The amount exchanged into pesos is $2,300 - $55, or $2,245.

Converting this into pesos:

$2,245      12.6577 Mex pesos

------------ * ------------------------------- = $28,416.54 Mexican pesos

     1                          $1