Express x^2+4x-7 in the form (x+a)^2-b where a and b are integers

Answer:

In Quadrant I or III

Step-by-step explanation:

We know if the sign was not showing closed inequality facing other way

xy < 0 would be in the 2nd or 4th quadrant.

If xy = 0  then either xy or both are on the x or y axis

But if xy>0 then they are in quadrant I or III

If xy>0, then the points of P(x,y) lies in Quadrant I and III

According to the given condition;

This means that the product of x and y is a positive number.

Hence, either both x and y-coordinates are positive or are both negative

Hence, only points in the Quadrant I have positive x and y coordinates Or Quadrant III in which case all x and y values are negative.

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Answer:

2/7

Step-by-step explanation:

Since 4 out of 14 times it landed on blue, it must have a 4/14 experimental probability of 4/14 for landing on blue.  4/14 simplifies to 2/7.

Answer:

2,4,5

Step-by-step explanation:

Do not repeat numbers, u need to put them in order from least to greatest, and range is for the y

To write the equation, we need the slope and y-intercept.

Remember that slope is the same as rate of change

or the change in y over the change in x.

Start by setting up a table with x and y values

which I have provided below.

Filling out our table, our given points are (10, 50) and (25, 20).

In the y column, we can see that the value of y

goes from 50 to 20 so it decreases by -30.

This means that the change in y is -30.

In the x column, we can see that the value of x goes from 10 to 25

so it increases by 15 which means that the change in x is 15.

So the rate of change is -30/15 which simplifies to -2.

To find b, we can use any ordered pair

in our table as the values for x and y.

Let's use the first ordered pair.

So we have 50 = -2(10) + b.

Solving from here, we get 50 = -20 + b.

Now add 20 to both sides to get 70 = b.

So if our slope is -2 and our y-intercept is 70,

we can substitute these values into our formula.

This gives us y = -2x + 70.

Answer:

B

Step-by-step explanation:

Replace x with a number and solve for y. Plot the points out on a graph.

See the attached picture.

Rotate the image.

Answer:

f(3π/4) = -π

A = π

b = 2

Step-by-step explanation:

Given that the function follows the form: f(x) = A sin(bx), then f(0) = 0. Given that the period is π, then at x = π/4 the function reaches a maimum, at x = π/2, f(x) = 0, and at x = 3π/4, f(x) reaches a minimum, which have to be π*(-1) = -π

Given the general equation: f(x) = A sin(bx), its period is calculated as:

period = 2π/b

which is equal to π, then:

2π/b = π

b = 2

Replacing x = π/4 into the equation of the function, we get:

A sin(2(π/4)) = π

A sin(π/2) = π

A = π

Answer:

[tex]4.5 \: miles[/tex]

Step-by-step explanation:

[tex]3 \: miles \: in \: 28 \: minutes.[/tex]

[tex]x \: miles \: in \: 42 \: minutes.[/tex]

[tex]28x=42 \times 3[/tex]

[tex]28x=126[/tex]

[tex]\frac{28x}{28}=\frac{126}{28}[/tex]

[tex]x=\frac{9}{2}[/tex]

Answer:

[tex]4.5 \: \: miles \\ [/tex]

Step-by-step explanation:

[tex]3 \: \: miles = 28 \: \: min \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \: \: \: = 42 \: min[/tex]

use cross multiplication

[tex]42 \times 3 = 28 \times x \\ 12 6 = 28x \\ \frac{126}{28} = \frac{28x}{28} \\ x = 4.5 \: \: miles[/tex]

Answer:

[tex]xy=30-109i+30i^2[/tex]

Step-by-step explanation:

If x=(10-3i) and y=(3-10i), then xy=

[tex](10-3i)(3-10i)=[/tex]

Using the FOIL method:

First: [tex]30[/tex]

Outer: [tex]-100i[/tex]

Inner: [tex]-9i[/tex]

Last: [tex]30i^2[/tex]

[tex]30-100i-9i+30i^2=\\30-109i+30i^2[/tex]

[tex]xy=30-109i+30i^2[/tex]

Answer:

At least 11: x≥11  ; At most 11:x≤11 ; More than11: x>11 ; Fewer than 11: x<11; Strictly between 3 and 11 : 3 < x < 11  ; Between 3 and 11: 3≤x≤11  ; Inclusive no more than 3: x≤3

Step-by-step explanation:

At least means that the number can't be lower than 11 (11 included)

At least means that the number can't be higher than 11 (11 included)

More means that the number must be higher than 11 ( 11 not included)

Fewer than means that the number must be lower than 11 ( 11 not included)

"Strictly between" means excluding the endpoints

Including endpoints.

Inclusive includes number 3 (less or equal)

Feel free to ask for more if needed or if you did not understand something.  

Answer:

D

Step-by-step explanation:

we can set up the equation as 15x = 15x^2

factoring we get

15x(x-1) = 0

So the solutions are when x are 0 and 1

this gives the coordinates

(0,0) and (1,15)

Answer:

Answer is 16 ft.

The answer is rounded to the nearest tenth place.

Step-by-step explanation:

[tex]given \: that \: \\ diameter \: of \: circle \: = 5 \: ft \\ then \: radius \: = \frac{5}{2} \: ft \\ we \: know \: that \\ circumferece = 2\pi \: r \\ on \: substiuting \: r= \frac{5}{2} \: ft \ \\ in \: formula \\ circumferece = 2\pi \times \frac{5}{2} \\ = 5\pi \\ substiuting \: \pi = 3.14 \\ = 5(3.14) \\ = 15.7079 \\ = 15.708 \\ when \: it \: is \: rounded \: off \: to \: nearest \: tenth \\ we \: get \: 16 \: ft\: as \: the \: answer.[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

The circumference of the circle having a diameter of 5 ft will be 15.7 ft.

The easiest way to find the perimeter for any shape is to add up the lengths of all the sides, but a circle only has one side, so that isn't possible. If you don't know its circumference, you also don't know the length of that side.

Fortunately, we can use a formula that uses other properties of a circle to find its circumference. In fact, there are two different formulas for circumference we can use and they look like this:

C = 2πr

Here the diameter of the giver circle is 5 ft so the radii will be 2.5 ft

By putting the value of radius in the formula we get

[tex]C=2\pi r[/tex]

[tex]C=2\pi \times 2.5=15.7\ ft[/tex]

Hence the circumference of the circle having a diameter of 5 ft will be 15.7 ft.

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Answer:

7.07

Step-by-step explanation:

f(x) = 2(x)^2 + 5 sqrt(x+2)

Let x= 0

f(x) = 2(0)^2 + 5 sqrt(0+2)

      = 2*0 + 5 sqrt(2)

      = 0  + 5 sqrt(2)

     = 5 sqrt(2)

     = 7.07106

To the nearest hundredth

    = 7.07

Answer:

Even

Step-by-step explanation:

If z-2 is an odd integer, that means z itself is an odd integer because very other integer is odd. Next, an odd integer + 1 is always an even integer. Therefore, z + 1 is an even integer.

Answer:

The answer is option (B).

Answer:

x=36

Step-by-step explanation:

3x+2x=180 (because they're supplementary angles)

5x=180

x=36

Answer:

$350 (profit)

Step-by-step explanation:

add the expenses together and subtract the product from the revenue

9,000 + 200 = 9,200

9,550 - 9,200 = 350

Answer:

The numbers are 7 and 42

Step-by-step explanation:

Let x and y be the numbers

x = 6y

x-y = 35

Substitute the first equation into the second equation

6y -y = 35

Combine like terms

5y = 35

Divide by 5

5y/5 = 35/5

y = 7

Now find x

x = 6*y

x = 6*7

x = 42

Answer:

The two numbers are 42 and 7.

Step-by-step explanation:

6x-x=35

5x=35

x=7

6(7)=42

7=7

Answer:

To me the triangles in #6 appear to be the same shape as the first triangle in #7(EFG) with different lengths on the sides. But not much else is the same. I mean they are all triangles but the shape of the second triangle in #7(XYZ) isn't the same as either of the triangles in #6.

I hope that made sense to you!

Hope this helped! Have a great day! :)

Answer:

40cm^2

Step-by-step explanation:

A=a+b/2×h

A=6+10/2*5

A=16cm/2*5cm

A=8cm*5cm

A=40cm^2

Answer:

150 degrees

Step-by-step explanation:

90+30=120.

Since angle afc is bisected by line bf, that means that the angles formed equal each other. Since the total angle measurement is 180 degrees, we do 180-120=60. 60/2=30. 120+30=150 degrees.

Could you show the given circle please?

Answer: The answer is C.

Step-by-step explanation: I just did it

Answer:

its 60-10+x why, because she bought the dress with $60 and she received $10 dollars back. We don't know the variable.

The point which is farthest from the origin is required.

The point which is the greatest distance from the origin is [tex](4,5)[/tex]

The distance of a point from origin is given by

[tex]d=\sqrt{x^2+y^2}[/tex]

[tex](1,6)[/tex]

[tex]d=\sqrt{1^2+6^2}\\\Rightarrow d=\sqrt{37}\ \text{units}[/tex]

[tex](2,6)[/tex]

[tex]d=\sqrt{2^2+6^2}\\\Rightarrow d=\sqrt{40}\ \text{units}[/tex]

[tex](4,5)[/tex]

[tex]d=\sqrt{4^2+5^2}\\\Rightarrow d=\sqrt{41}\ \text{units}[/tex]

[tex](5,1)[/tex]

[tex]d=\sqrt{5^2+1^2}\\\Rightarrow d=\sqrt{26}\ \text{units}[/tex]

The largest number is [tex]\sqrt{41}[/tex]

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Answer:

h=14

Step-by-step explanation:

3/4*1/4=3/16

21/32/(3/16)=14

Answer:

h=25

Step-by-step explanation:

Answer:

254 square inches

Step-by-step explanation:

A=pi*r^2

A=pi*(d/2)^2

A=3.14*(18/2)^2

A=3.14*(9)^2

A=3.14*81

A=254.34 in^2

So, rounded no the nearest whole, the answer is 254 in^2

Which is option 2 or B

Answer:

use the indices formula

Answer:

[tex]3\sqrt{5}.[/tex]

Step-by-step explanation:

It is given that the initial point of [tex]\vec{a}[/tex] is (-2,4) and terminal point is (-5,-2). So, [tex]\vec{a}[/tex] is defined as

[tex]\vec{a}=(-5-(-2))\hat{i}+(-2-4)\hat{j}[/tex]

[tex]\vec{a}=(-5+2)\hat{i}+(-2-4)\hat{j}[/tex]  

[tex]\vec{a}=-3\hat{i}-6\hat{j}[/tex]

The magnitude of [tex]\vec{v}=a\hat{i}+b\hat{j}[/tex] is

[tex]|\vec{v}|=\sqrt{a^2+b^2}[/tex]

The magnitude of [tex]\vec{a}[/tex] is

[tex]|\vec{a}|=\sqrt{(-3)^2+(-6)^2}[/tex]

[tex]|\vec{a}|=\sqrt{9+36}[/tex]

[tex]|\vec{a}|=\sqrt{45}[/tex]

[tex]|\vec{a}|=3\sqrt{5}[/tex]

Modulus of magnitude is

[tex]||\vec{a}||=|3\sqrt{5}|=3\sqrt{5}[/tex]

So, the magnitude of [tex]\vec{a}[/tex] is [tex]3\sqrt{5}.[/tex]

Answer:

Step-by-step explanation:

[tex]\sum\limits_{k=1}^{5}6\left(4\right)^{k-1}=6\left(4\right)^{1-1}+6\left(4\right)^{2-1}+6\left(4\right)^{3-1}+6\left(4\right)^{4-1}+6\left(4\right)^{5-1}=\\\\\\=6\cdot4^0+6\cdot4^1+6\cdot4^2+6\cdot4^3+6\cdot4^4=6+24+96+384+1536=\\\\=2,046[/tex]

or:

is geometric series:  [tex]S_n=\dfrac{a_1(1-q^n)}{1-q}[/tex]

[tex]a_n=a_1\cdot q^{n-1}\quad\implies\quad\begin{cases}a_1=6\\q=4\\n=5\end{cases}[/tex]

so:

[tex]\sum\limits_{k=1}^{5}6\left(4\right)^{k-1}=S_5=\dfrac{6(1-4^5)}{1-4}=\dfrac{6(1-1,024)}{-3}=-2(-1,023)=2,046[/tex]

Answer:

B

Step-by-step explanation:

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