Form the perfect square trinomial in the process of completing the square. What is the value of c?

x²+3x+c=7/4+c

C = ?

Could you explain?

No "spam" answers, please!

Thank you!

Check the picture below.

so the parabola looks more or less like so, bearing in mind that the directrix is a horizontal line, thusu the parabola is a vertical one, so the squared variable is the "x".

The vertex is always half-way between the focus point and the directrix, as you see there, and the distance from the vertex to the focus is "p" distance, since the parabola is opening downwards, "p" is negative, in this case -2.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=(x-0)^2\implies -8y=x^2\implies y=-\cfrac{1}{8}x^2[/tex]

To find the standard form of the parabola with a focus at (0, -2) and a directrix at y = 2, the process involves identifying the vertex, determining direction, and substituting into the general equation to get x² = -8y.

To find the standard form of the equation of a parabola with a focus at (0, -2) and a directrix at y = 2, we start by identifying key properties of parabolas. The vertex of the parabola is midway between the focus and the directrix. Here, the distance between the focus and the directrix is 4, so the vertex is 2 units away from each, placing it at (0, 0) as the directrix and focus are symmetrically placed above and below the x-axis.

The general equation for a parabola opening upwards or downwards is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola, and p is the distance from the vertex to the focus (positive if the parabola opens upwards, negative if downwards). Given the focus (0, -2) and the vertex (0, 0), p = -2, indicating the parabola opens downwards. Applying these values to the general equation yields: x² = -8y, which is the standard form of the equation for the described parabola.

Answer:

29

Step-by-step explanation:

Since they have given you x = 4, simply sub it into the equation,

(4)^2 + 3(4) - 7 + 8

=  29

Answer:

29

Step-by-step explanation:

Substitute 4 for x into the expression x^2+3x−7+8 and then simplify using the order of operations.

4^2+3(4)−7+8

16+12−7+8

29

Multiply the total amount by the percentage.

250 mL x 0.65 = 162.5

The answer is 162.5 mL

Answer:

Step-by-step explanation:

Find two rows in the table that have the same values in the f(x) and g(x) columns.

Answer:

[tex]\large\boxed{12.25=\dfrac{49}{4}}[/tex]

Step-by-step explanation:

[tex]12.\underbrace{25}_{2}=\dfrac{1225}{1\underbrace{00}_2}=\dfrac{1225:25}{100:25}=\dfrac{49}{4}\\\\12.25=12+0.25=12+\dfrac{25}{100}=12+\dfrac{25:25}{100:25}=12+\dfrac{1}{4}\\\\=\dfrac{12\cdot4}{4}+\dfrac{1}{4}=\dfrac{48+1}{4}=\dfrac{49}{4}[/tex]

Answer:

the answer is 20P4 = 4845

Step-by-step explanation:

Answer:

There are 20 ways to pick the first book, 19 ways for the second

Step-by-step explanation:

If order of the 4 books does not matter then

₂₀C₄ = 20! / (20-4)!4! = 20!/(16!*4!) = 4845 ways

Answer:

Probably because learning to do polynomials by hand boosts understanding of the topic and improves general algebraic solving ability,both of which are required in further topics like advanced calculus and algebra

Learning polynomial division by hand is crucial for understanding concepts, enhancing problem-solving skills, and fostering critical thinking in mathematics.

The importance of learning polynomial division by hand despite the availability of computer algebra systems lies in developing a deep understanding of the underlying concepts, fostering problem-solving skills, and enabling visualization of geometric interpretations.

By manually carrying out mathematical operations, students can better grasp the logic behind the processes, which aids in building a strong foundation for more complex mathematical tasks.

Furthermore, mastering hand calculations equips students with the ability to perform quick mental math, apply critical thinking skills, and comprehend the practical applications of the mathematical concepts.

Answer:

b

Step-by-step explanation:

hope this helps

Answer:

  D.  64 and 81

Step-by-step explanation:

The best benchmarks are the ones that are the closest to the value you want the root of. Perfect squares in that neighborhood are ...

The closest are 64 and 81.

The area of deltoid is defined by formula:

[tex]A=\dfrac{e\cdot f}{2}[/tex]

Where e and f are diagonals.

If you were to double the size of either one. Let's say f. You would result with:

[tex]A=\dfrac{e\cdot2f}{2}=e\cdot f[/tex]

Which means if either of diagonals double in length the area of deltoid will be twice as big as it was before.

Hope this helps.

r3t40

the kite, which looks more like a rhombus but being called a kite, will look like the one in the picture below.

now, as you see in the picture, the kite is really 4 congruent triangles, each with a base of 2.5 and a height of 5, so their area is

[tex]\bf \stackrel{\textit{area of one triangle}}{\cfrac{1}{2}(2.5)(5)}\implies 6.25\qquad \qquad \stackrel{\textit{area of all four triangles}}{4\left[ \cfrac{1}{2}(2.5)(5) \right]}\implies 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doubling the base or height}}{4\left[ \cfrac{1}{2}(2.5)(5)\underline{(2)} \right]}\implies \stackrel{\textit{the area is twice as much as the original}}{\underline{(2)}~~\left[ 4\left[ \cfrac{1}{2}(2.5)(5) \right] \right]}[/tex]

Answer:

The perimeter is [tex]P=73.12\ cm[/tex]

Step-by-step explanation:

we know that

The perimeter of the figure is equal to the circumference of a semicircle

plus the perimeter of a square minus the diameter of the circle

so

[tex]P=\pi r+4(b)-D[/tex]

we have

[tex]r=8\ cm[/tex]

[tex]b=16\ cm[/tex]

[tex]D=16\ cm[/tex]

The diameter of the circle is equal to the length side of the square

substitute

[tex]P=(3.14)(8)+4(16)-16[/tex]

[tex]P=25.12+64-16[/tex]

[tex]P=73.12\ cm[/tex]

Answer:

p(-5)=-11,987

p(3)=-227

Step-by-step explanation:

To find the value of the function p(-5) just substitute x=-5 into the function expression instead of x:

[tex]p(-5)=2\cdot (-5)^5-9\cdot (-5)^4-2\cdot (-5)^2+12\cdot (-5)-2=\\ \\=-6,250-5,625-50-60-2=-11,987[/tex]

To find the value of the function p(3) just substitute x=3 into the function expression instead of x:

[tex]p(3)=2\cdot 3^5-9\cdot 3^4-2\cdot 3^2+12\cdot 3-2=\\ \\=486-729-18+36-2=-227[/tex]

Answer with Step-by-step explanation:

We are given a function:

[tex]p(x) = 2x^5-9x^4-2x^2+12x-2[/tex]

We have to find the value of p(-5) and p(3)

[tex]p(-5) = 2\times (-5)^5-9\times (-5)^4-2\times (-5)^2+12\times (-5)-2\\\\=-6250-5625-50-60-2\\\\=-11987[/tex]

[tex]p(3) = 2\times 3^5-9\times 3^4-2\times 3^2+12\times 3-2\\\\=486-729-18+36-2\\\\=-227[/tex]

Hence, p(-5)= -11987

and p(3)= -227

Answer: 3/5 probability of choosing a number LESS THAN 8

Answer:

  x = 9

Step-by-step explanation:

Adjacent angles A and D are supplementary:

  (30 +5x)° +(15 +10x)° = 180°

  15x +45 = 180 . . . . . collect terms, divide by °

  15x = 135 . . . . . . . . . subtract 45

  135/15 = x = 9 . . . . . divide by the coefficient of x

The value of x is 9.

Answer: 720 mph or 12 miles a minute

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

(I actually have the problem in front of me, and I think you switched the minute and hour hands on the clock)

Adel

left at 5:30 and arrived at 8:30. That’s 3 hours, which is 180 minutes. 180/180 = 1 mile per minute

60 minutes in an hour

60*1 = 60 mph

Answer: The slope of the line is: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The slope can be calculated with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

You need to choose two points of the line. You can pick the point (6,2) and the point (-6,-6)

You can identify that:

[tex]y_2=-6\\y_1=2\\x_2=-6\\x_1=6[/tex]

Now, you must substitute these values into the formula:

[tex]m=\frac{-6-2}{-6-6}[/tex]

With this procedure you get that the the slope of the line on the graph is:

[tex]m=\frac{-8}{-12}[/tex]

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

The new triangle produced is an exact remake of the first one. The angles or size does not change between the two. Thus, this transformation is an Isometry.

Answer:

The right answer is B: The probability is equal to p%.

Step-by-step explanation:

Answer:

  3

Step-by-step explanation:

You know that ...

  1000 = 10³

when you take the logarithm to base 10, you get

  log₁₀(1000) = 3

Step-by-step explanation:

Waves have the form:

y = A sin (2π/T x + φ) + B

where A is the amplitude (the distance from the center of the wave to the max or min),

T is the period (time it takes for one cycle),

φ is the phase shift (moves the wave left or right),

and B is the offset (moves the wave up or down).

This can also be written with cosine.

Here, we have d = 6 cos(π/2 t).

The amplitude is A = 6, so the maximum distance from the equilibrium position is 6 units.

The period is:

2π / T = π/2

T = 4

So the period is 4 seconds.

Answer:

Step-by-step explanation:

The distance from Q to S is 2 - (-14), or 16.

We start at point Q.  Note how 3 and 5 add  up to 8, which allows us to write:

R = Q + (3/8)(16), or R = -14 + 6, or R = -8.

From R to S it is (5/8)(16), or 10 units.

The directed line segment is partitioned into segments of lengths 6 and 10, whose combined length is 16, as expected.

Answer:

14/5 or A

Step-by-step explanation:

I just took this assignment.

Answer:

  7 days

Step-by-step explanation:

At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.

"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.

_____

We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)

Answer:

  8.  1483.33

  9.  21 months

Step-by-step explanation:

8. Morgan's income after taxes is 55000/12 = 4583.33 per month. The amount  available after expenses is 4583.33 -3100.00 = 1483.33 per month.

Morgan is able to put $1483.33 per month into savings.

__

9. If Morgan is able to save $1483.33 per month, it will take her ...

  $30,000/$1483.33 ≈ 20.2

months to save $30,000. After 20 months, she won't have quite enough, so it will take her one more month to save the desired amount.

It will take Morgan about 21 months to save $30,000.

_

If you like, you can write an equation for "m", the number of months it will take Morgan to save 30,000:

  1483.33×m = 30,000

  m = 30,000/1483.33 ≈ 20.2 . . . . . . divide by the coefficient of m

Answer:

The answer is D (line symmetry and rotational symmetry; 180o; order 2.

Step-by-step explanation:

You can fold the figure in half and it would be the same on both sides.  The figure also has rotational symmetry because if you rotate the figure 180 degrees about the center, then it basically maps itself, or in other words, its the same.  So the ANSWER IS D

line symmetry and rotational symmetry; 180 degree; order 2. Correct option is D.

The figure described exhibits characteristics of both reflectional and rotational symmetry. Firstly, it possesses reflectional symmetry because you can fold it in half, and both sides of the fold will be identical, essentially mirroring each other. This demonstrates that the figure can be divided into two equal parts that are reflections of each other along the fold line.

Furthermore, the figure displays rotational symmetry, specifically a 180-degree rotational symmetry. When you rotate it by 180 degrees about its center, the figure aligns with itself, showing that it remains unchanged upon this rotation. This means that you can rotate the figure halfway, and it will still appear identical.

So, the correct answer is not just "D," but rather a more comprehensive explanation of the figure's symmetrical properties, encompassing both reflectional and rotational symmetry.

to know more about rotational symmetry;

https://brainly.com/question/13268751

#SPJ3

Answer:

35 combinations

Step-by-step explanation:

You have to use the formula for finding combinations in probability.  It looks like this:

₇C₃ = [tex]\frac{7!}{3!(7-3)!}[/tex]

so that gives you

₇C₃ = [tex]\frac{7*6*5*4!}{3*2*1*4!}[/tex]

The 4 factorials cancel each other out, and when you do the math, you get 210/6.  That divides evenly into 35.  So there are 35 combinations.

Answer:

The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k

Step-by-step explanation:

* Lets revise how to solve the problem

- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and

 point (x , y , z) divides the segment externally at ratio m1 :m2, then

 [tex]x=\frac{m_{1}x_{2}-m_{2}x_{1}}{m_{1} -m_{2}},y=\frac{m_{1}y_{2}-m_{2}y_{1}}{m_{1}-m_{2}},z=\frac{m_{1}z_{2}-m_{2}z_{1}}{m_{1}-m_{2}}[/tex]

* Lets solve the problem

∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)

∵ Point C lies on line AB such that AC : BC=3 : 2

∵ From the ratio AC = 3/2 AB

∴ C divides AB externally

- Lets use the rule above to find the coordinates of C

- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)

 and AC : AB is m1 : m2

∴ x1 = 3 , x2 = 1

∴ y1 = 1 , y2 = -5

∴ z1 = 2 , z2 = 4

∴ m1 = 3 , m2 = 2

- By using the rule above

∴ [tex]x=\frac{3(1)-2(3)}{3-2}=\frac{3-6}{1}=\frac{-3}{1}=-3[/tex]

∴ [tex]y=\frac{3(-5)-2(1)}{3-2}=\frac{x=-15-2}{1}=\frac{-17}{1}=-17[/tex]

∴ [tex]z=\frac{3(4)-2(2)}{3-2}=\frac{12-4}{1}=\frac{8}{1}=8[/tex]

∴ The coordinates fo point c are (-3 , -17 , 8)

* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k

Answer:

576 cuboids

Step-by-step explanation:

Let

x -----> the length side of the cube

n -----> number of cuboids that are needed

we know that

The volume of the cuboid is equal to

[tex]V=(2)(3)(4)=24\ cm^{3}[/tex]

The volume of the cube is equal to

[tex]V=x^{3}[/tex]

Find the number of cuboids that are needed

[tex](n)24=x^{3}}[/tex]

n*24 must be a perfect cube

so

The minimum value that satisfied n to make n*24 a perfect cube is n=576

[tex]576*24=13,824=24^{3}[/tex]

Answer:

576 Cuboids

Step-by-step explanation:

The first equation can be further simplified so first do that by subtracting 15 to both sides

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

y - 3x = -5

We know from the second equation that y is 6 - 4x so in the equation y - 3x = -5 plug in 6 - 4x for y

(6 - 4x) - 3x = -5

6 - 4x - 3x = -5

Combine like terms

6 - 7x = -5

(6 - 6) - 7x = -5 - 6

-7x = -11

Isolate x

-7x/-7 = -11/-7

x = 11/7

To solve for y plug in 11/7 in for x in the equation 6 - 4x = y

6 - 4(11/7) =y

6 - 44/7 = y

y = -2/7

so...

(11/7 , -2/7)

Hope this helped!

~Just a girl in love with Shawn Mendes

1.) Solving for X problem 1#

y-3x+15=10

-3x+15-15=10-15-y

-3x=-y-5

-3x/-3=-y-5/3

x=(-y-5)/3

2.) Solving for Y problem 1#

y-3x+15=10

y-3x+3x+15-15=10-15+3x

y=3x-5

1.) Solving for X problem 2#

6-4x=y

-4x+6-6=y-6

-4x/4=y-6/4

x=(y-6)/4

2.) Solving for Y problem 2#

6-4x=y

y=-4x+6

Answer:

Explanation:

The area of the octagon may be calculated as the difference of the area of the original square and the area of the four corners cut off.

1) Area of the square.

The original square's side length is the same wide of the formed octagon: 10 cm.

So, the area of such square is: (10 cm)² = 100 cm².

2) Area of the four corners cut off.

Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.

The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).

Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².

Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².

3) Area of the octagon:

And that is the answer: 92 cm².