4x-16=2x+6

Find x please i really need this lol

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0\hspace{5em}\textit{we also know that} \begin{cases} x=-4\\ y=1 \end{cases} \\\\\\ 1=a(-4-0)^2 + 0\implies 1=16a\implies \cfrac{1}{16}=a~\hfill \boxed{y=\cfrac{1}{16}x^2}[/tex]

Answer:

[tex] {12}^{2} - {10}^{2} = 44 \\ \sqrt{44} = 2 \sqrt{11} [/tex]

If you have problems in mathematics you can text me if you want

After converting the given differential equation into first order we will get it as [tex]\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]

The equation dy/dx =f (x,y) with two variables x and y with its function f(x,y) specified on a region in the xy-plane defines a first-order differential equation. There are no higher-order derivatives since it only contains the one derivative, dy/dx, making it a first-order equation.

The given differential equation is

[tex]\left(1-x^2\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0----(i)[/tex] with y_1=x [tex]\Rightarrow & y^{\prime \prime}-\frac{2 x}{1-x^2} y^{\prime}+\frac{2}{1-x^2} y=0\end{aligned}$$[/tex]

Equation (1) is in the form of

[tex]$$y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0$$[/tex]

where [tex]$p(x)=\frac{-2 x}{1-x^2}, \quad q(x)=\frac{2}{1-x^2}$[/tex]

As we know that if y_1 is given, we can find y_2 as:

y_2=4y_1, where u is a function of x and can be determined by

[tex]$U=\int \frac{e^{-\int p d x}}{y_1^2} d x$[/tex]

[tex]=\int \frac{e^{-\int \frac{-2 x}{1-x^2}} d x}{x^2} d x\\=\int \frac{e^{-\ln \left|1-x^2\right|}}{x^2} d x\\=\int \frac{1}{x^2\left(1-x^2\right)} d x\\=\int \frac{\left(1-x^2\right)+x^2}{x^2\left(1-x^2\right)} d x\\=\int\left(\frac{1}{x^2}+\frac{1}{1-x^2}\right) d x[/tex]

[tex]$$\begin{aligned}& =\int \frac{1}{x^2} d x+\int \frac{1}{1-x^2} d x \\& =-\frac{1}{x}+\int \frac{1}{1-x^2} d x\end{aligned}$$[/tex]

Now, [tex]$\int \frac{1}{1-x^2} d x=\int f(x) d x$[/tex] (say)

Where, [tex]$f(x)=\frac{1}{1-x^2}=\frac{1}{(1+x)(1-x)}$[/tex]

[tex]=\frac{A}{1+\eta}+\frac{B}{1-x} \\[/tex]

1=A(1-x)+B(1+x)

Putting x = 1, we will get B = 1/2

x = -1, we will get it as: A = 1/2

[tex]\therefore \int \frac{1}{1-x^2} d x=\int \frac{1 / 2}{1+n} d x+\int \frac{1 / 2}{1-x} d x[/tex]

[tex]=\frac{1}{2} \ln |1+x|-\frac{1}{2} \ln |1-x|\\=\ln \sqrt{1+x}-\ln \sqrt{1-x}\\\\=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)\\\Rightarrow \int \frac{1}{1-x^2} d x=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)[/tex]

Hence [tex]$u=-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)$[/tex]

[tex]\Rightarrow y_2=u \cdot y_1=x\left[-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)=x \ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)-1\right.\\\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]

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Answer:

There are many possible arrays that could be used to model a rectangular quilt with 24 paper squares. Here are a few examples:

A 3x8 array could be created by gluing the paper squares into a rectangle that is 3 squares wide and 8 squares long. This could be represented by the equation 3x8 = 24.

A 4x6 array could be created by gluing the paper squares into a rectangle that is 4 squares wide and 6 squares long. This could be represented by the equation 4x6 = 24.

A 6x4 array could be created by gluing the paper squares into a rectangle that is 6 squares wide and 4 squares long. This could be represented by the equation 6x4 = 24.

A 8x3 array could be created by gluing the paper squares into a rectangle that is 8 squares wide and 3 squares long. This could be represented by the equation 8x3 = 24.

These are just a few examples, but there are many other possible arrays that could be created with 24 paper squares. Some other examples might include a 2x12 array, a 6x4 array, or even a 1x24 array. The key is to find combinations of width and length that will multiply together to equal 24.

Step-by-step explanation:

The applicants that would have to apply in order to meet the target is 52. Option 4 is correct.

We have to define x as the applications to meet target

The number of persons to hire is 30

10 percent do not meet requirements. Hence 90 meets the requirements. 90% of x

= 0.9X

12% fail the pre screening stage. Hence 88% have passed it. This would be 88% of 0.9x. = 0.792x

23% Did not come for the interview, hence 77% showed up. This would be 0.77*0.792x = 0.60984x

then 5% are said to have failed the background test. This means that 95% passed the test.

0.95 * 0.60984x = 0.579348X

We have to equate this to 30 in order to get the value of x

0.579348X = 30

divide through by 0.579348

X = 30 / 0.579348

X = 51.78

X ~ 52

The number of applicants is 52

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Answer:

x = -19/7 z

z = -7/19 x

Lets solve for x in 21x + 39z = (7x+z):

Step 1: Add -7x to both sides.

21x+39z+−7x=7x+z+−7x

14x+39z=z

Step 2: Add -39z to both sides.

14x+39z+−39z=z+−39z

14x=−38z

Step 3: Divide both sides by 14.

14x/14 = −38z/14

x = −19/7 z

Lets solve for z in 21x 39z = (7z+z):

Step 1: Add -z to both sides.

21x+39z+−z=7x+z+−z

21x+38z=7x

Step 2: Add -21x to both sides.

21x+38z+−21x=7x+−21x

38z=−14x

Step 3: Divide both sides by 38.

38z/38 = −14x/38

z = −7/19 x

Hope this helps!!

Answer:

D [tex]\sqrt{3}[/tex]

Step-by-step explanation:

tan60 is the same for all values when you plug it into a calculator you will get [tex]\sqrt{3}[/tex]

The area of the large rectangle shown in the image is (2 + 3 + 4)a unit square

An equation is an expression that shows the relationship between two or more numbers.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a rectangle is the product of its length and width. It is given by the equation:

Area of a rectangle = length * width

From the diagram:

Width = a; length = 2 + 3 + 4

Area = length * width

Substituting the terms into the equation:

Area = (2 + 3 + 4)a

Further simplification gives:

Area = 2a + 3a + 4a

The area of the rectangle is 2a + 3a + 4a

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The domain of the function [tex]f(x) =log x[/tex] is (0, ∞) which means the given function is defined for all the values greater than 0.

The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.

Given function can also be written as   [tex]y=log_{10}x[/tex]

                                                             ⇒ [tex]10^{y}=x[/tex]

This means the domain of  [tex]logx[/tex]  is the set of all values that [tex]10^{y}[/tex] can be.Since 10 is a positive integer which means its power with any number will always be positive.Therefore domain of function [tex]logx[/tex] will always be positive.

                                     ∴ Domain of function = (0, ∞)

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According to the question, Triangles are said to be in SSS (Side-Side-Side) congruence if their third sides are the same length as the third sides of another triangle.

One of the following conditions must be satisfied for two triangles to be considered congruent: There is equality between all three pairs of corresponding sides. Two matching side pairs have identical angles between them, as well as equal sides between them. The corresponding sides between two sets of corresponding angles and their two pairs are equal.

If both of a triangle's three sides and three angles are equal in any orientation, the two triangles are said to be congruent.

When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical.

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Analyzing the provided total storage for the CD and amount of pictures stored in it, Using simple difference , The answer is 581.28 megabytes.

Storage refers to the process of preserving data in a computer or other electronic device for later retrieval. This can include both short-term storage, such as in RAM, and long-term storage, such as on a hard drive or in the cloud. Data can be stored in various formats, including text, images, videos, and audio. Storage devices come in different forms including internal storage, external storage, removable storage, and cloud storage.

The term "difference" in mathematics can refer to a few different concepts, depending on the context. In subtraction, the difference between two numbers is the result of subtracting one number from the other. For example, the difference between 8 and 3 is 8 - 3 = 5. In set theory, the difference between two sets is a new set that contains all the elements that are in the first set, but not in the second set. In geometry, the difference between two shapes is the area left over when one shape is subtracted from the other.

total = 700 MB

used by pictures = 53 * 2.24 = 118.72 MB

Space left = 700 - 118.72 = 581.28 MB

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Answer:

143 degrees, 37 degrees

Step-by-step explanation:

Let's say the angle is x and the supplementary angle is x-106:

x + (x-106) = 180  ==> supplementary angles add up to 180 degrees

x + x - 106 = 180

2x - 106 = 180

2x = 286 ==> isolate x by adding 106 to both sides

x = 143 ==> divide 2 on both sides

x-106=

143-106 = 37

Answer: 143 degrees, 37 degrees

The required measures of the angles of parallelogram ABCD as are follows m∠A = 66°,  m∠B = 114°, and m∠C = 66°.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given parallelogram ABCD,

m∠D = 114°

In a parallelogram, the opposite angles are congruent, so m∠A is congruent to m∠C. This means that m∠A and m∠C have the same measure.

If m∠D = 114°, then m∠A must be equal to 180° - 114° = 66°, since the measures of the adjacent angles of a parallelogram add up to 180°.

So, m∠A = m∠C = 66°

So, m∠B = 114°

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The student is not correct when he forms a triangle with side lengths 3 ,5 ,9 inches.

A triangle contains of  3 sides and 3 angles

The Triangle Inequality Theorem, which asserts that the total of any two sides must be greater than the third side, must be followed in order to determine whether a collection of integers is a legitimate measure of a triangle's sides.

as per the details stated above

Let a is 3 inches , b is 5 inches c is 9 inches

According to the triangle Inequality theorem

a + b > c

that is 8>9

which is incorrect

a + c > b

that is 12 > 5

which is correct

b + c > a

14 > 3

which is correct

as the theorem it does not satisfy one case so we can say that it will form a triangle

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No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle.

No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle. This theorem is based on the idea that the longer side of a triangle must always be opposite the largest angle. Therefore, the longest side of the triangle must be less than the sum of the other two sides. Essentially, this means that in order for a triangle to be formed with side lengths of 3 in, 5 in, and 9 in as the student suggests, the longest side must be less than 8 in, which is not possible. Therefore, the student is incorrect, and it is impossible to form a triangle with the side lengths they have provided.

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The value of Differential Equation will be [tex]y_1=c_1 e^{-x}+c_2 e^{-2 x}+\sin (2 x)+3 \cos (2 x)[/tex]

[tex]$$\begin{aligned}& y^{\prime \prime}+3 y^{\prime}+2 y=-20 \sin (2 x) \\& \frac{d^2}{d x^2} y+3 \frac{d}{d x} y+2 y=-20 \sin (2 x)\end{aligned}$$[/tex]

A second order linear, non-homogeneous ODE has the form of ay"+b y'+cy=g(x).

General Solution can be written as y=y_h+y_p y_h is the solution to the homogenous ODE

a(x) y"+b(x) y'+c(x) y=0

Y_p is the particular solution to any function that Satisfies the non-homogenous equation.

Finding. y_n by solving

[tex]\frac{d^2}{d x^2}(y)+3 \frac{d}{d x}(y)+2 y=0 . \quad y=e^{y-t} .[/tex]

We can rewrite it as:

[tex]\frac{d^2}{d x^2}\left(\left(e^{x x}\right)\right)+3 \frac{d}{d x}\left(e^{y x}\right)+2 e^{y x}=0 \quad y=e^{y x}[/tex]

We will get it after solving as:

[tex]$\frac{d^2}{d x^2}\left(e^{8 x}\right)$[/tex] apply for chain role

we get [tex]$\Rightarrow r^2 e^{r x}$[/tex]

[tex]$$\begin{aligned}& \quad \frac{d}{d x}\left(e^{r x}\right) \Rightarrow \text { we get }=e^{r x} r \text { sob } \\& \therefore \quad r^2 e^{r x}+3 e^{r x} r+2 e^{r x}=0 .\end{aligned}$$[/tex]

Factor [tex]$e^{r x}\left(r^2+3 y+2\right)=0$[/tex]

By solving this we get r=-1, fr=-2

For two real roots [tex]$r_1 \neq r_2$[/tex].

The general solution will be:

[tex]$$y=c_1 e_2^{-x}+c_2 e^{-2 x}$$[/tex]

Similarly, further solving, we wll get: [tex]\frac{d^2}{d x}(y)+3 \frac{d}{d x}(y)+2 y=-20 \sin (2 x)[/tex]

We will get it as:

y=sin (2 x)+3 cos (2 x)

[tex]y_1=c_1 e^{-x}+c_2 e^{-2 x}+\sin (2 x)+3 \cos (2 x)[/tex]

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The correct question should be:

Find a particular solution of the following differential equations:

y" + 3y + 2y = –20 sin(2x)

The sum of the infinite series is approximately 0.6740, calculated to four decimal places.

The sum of the series can be approximated by adding up the first few terms.

1/4 + (-1/16) + (1/384) + (-1/18432) + (1/798336)

= 0.673975

Therefore, the sum of the series is approximately 0.6740, calculated to four decimal places.

The sum of the infinite series can be approximated by adding up the first few terms. The series is of the form (−1)^n/4^n n! with n = 1,2,3,4,… The first term is 1/4, which is the sum when n=1. The second term is then (-1/16), which is the sum when n=2. This pattern continues, with the next terms being 1/384 and -1/18432, respectively. After adding up the first five terms, we get a sum of 0.673975. Therefore, the sum of the series is approximately 0.6740, calculated to four decimal places.

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The value of x ≈ 8.0 rounded to the nearest tenth.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

In the right-triangle,

The cosine ratio,

cos37° = perpendicular / hypotenuse

cos37° = x / 10

Using cross multiplication,

10 × cos37° = x,

x = 0.7986 × 10

x = 7.986

x ≈ 8.0 rounded to the nearest tenth.

Therefore, x ≈ 8.0 rounded to the nearest tenth.

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Answer:

A quadrilateral is a parallelogram if and only if opposite angles are equal.

So, to make the quadrilateral a parallelogram, we can set the following equalities:

(4x + 13) deg = (5x - 12) deg

(4y + 7) deg = (3x - 8) deg

Solving the first equation,

4x + 13 = 5x - 12

x = -5

Solving the second equation,

4y + 7 = 3(-5) - 8

4y + 7 = -17

4y = -24

y = -6

So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6

The range of the function g(x) = √-(x2 + 4) is |x| ≥ 2

Range of the function g of x is equal to negative square root of the quantity x squared plus 4.

The range of the function g(x) = √-(x2 + 4) can be determined by solving the inequality g(x) ≤ 0.

To solve the inequality, we need to first simplify the expression by squaring both sides:

(√-(x2 + 4))2 ≤ 0

-x2 - 4 ≤ 0

-x2 ≤ 4

x2 ≥ -4

Now, we can take the square root of both sides to get the final expression:

|x| ≥ √-4

|x| ≥ 2

Therefore, the range of the function g(x) = √-(x2 + 4) is |x| ≥ 2.

We can also express this range in interval notation as [2, ∞).

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The range of given function is (-∞ ,-2] . Range is calculated  using the concept of Maximum and minimum value of the function.here maximum value is -2 and minimum value is –∞.

In this question, we have asked about a range of an function so let's try to understand what is range of an function.

The set of numbers that a function can produce is known as its range. With all potential x-values plugged into the function, it is the set of y-values that results. The domain is the set of feasible x-values. If you're interested in learning how to determine a function's range.

The collection of each function's results.

You say:

range, function, and domain

Example: The range is 1,4,9,... when the function f(x) = x^2 is given the values x = 1,2,3,...

Given function in this question is f(x) = [tex]-\sqrt{x^2+4}[/tex] .

This is a negative sqaure root function . here let's try to understand properties of square root function.

The square root symbol √ is used in the square root function (which is read as "square root of"). A integer "y" such that y^2 = x is said to be a number "x's square root.

For calculating range we have to find what is the minimum value of function and what is the maximum value of function.

we know sqaure root function always gives positive value.

negative square root function will give negative value.

Minimum value is –∞.

For maximum value x = 0 f(x) = [tex]-\sqrt{4}[/tex]  = -2

So the range of given function is (-∞ ,-2].

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Answer:

  (b)  15 over 56 times a squared

Step-by-step explanation:

You want the product of (5/8a) and (3/7a).

The commutative and associative properties of multiplication help you find this product:

  [tex]\dfrac{5}{8}a\,\times\,\dfrac{3}{7}a = \left(\dfrac{5}{8}\cdot\dfrac{3}{7}\right)\times (a\cdot a)=\dfrac{5\cdot3}{8\cdot7}a^2=\boxed{\dfrac{15}{56}a^2}[/tex]

The value that shows the occupancy for the cobalt ion is -1. Option B

We know that the electrons can be found in the orbitals that are contained in the atom. The d orbital diagram is the image that shows the occupancies of the d orbital of the atom. This is the number of the electrons that can be found in a particular orbital.

Let us note that the elements that have a d level that is not completely occupied as said to be the transition elements. As such the transition elements are the elements that have d orbitals that are incompletely filled.

We have a transition metal complex here and the number or the magnitude of the charge that is carried by the complex is what has been designated as n in the image that has been attached here.

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Answer:

Step-by-step explanation:

it looks like squirt

so 33 = y

Answer:

Yes, t=9 is a solution to the inequality t ≤ 10. When t is equal to 9, the inequality is satisfied because 9 is less than or equal to 10.

Step-by-step explanation:

Answer:

I thing yes! because ≤ means less than or equal to, which 9 is less than 10.

Step-by-step explanation:

Hope it helps!

[tex]f^{-1}{x} = \sqrt{(x+4)} + 1[/tex], is the inverse function of f(x) = (x-1)² - 4

What is an inverse of a function?

In mathematics, an inverse function is a function that undoes the effects of another function. Given a function f(x), the inverse function of f(x) is denoted as f^-1(x) or as f^1(x). The inverse function f^-1(x) satisfies the condition that f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain of the function.

To find the inverse of a function, one common way is to algebraically manipulate the function and the relationship between the function and its inverse.

To identify the inverse of the function f(x)=(x-1)^2-4, we can start by swapping x and y in the original function:

y = (x-1)^2-4

Then we need to solve for x:

x = (y+4)^0.5 + 1

To check that this is indeed the inverse function, you can substitute x = (y+4)^0.5 + 1 into f(x) and check that you get back y:

f((y+4)^0.5 + 1) = (((y+4)^0.5 + 1)-1)^2-4 = y

Hence, [tex]f^{-1}{x} = \sqrt{(x+4)} + 1[/tex], is the inverse function of f(x) = (x-1)² - 4.

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There are 18 hours would the server have to work to earn $135 in tips.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A restaurant server averages $30 in tips for a 4 hour shift.

Now,

Since, A restaurant server averages $30 in tips for a 4 hour shift.

Hence, The time for a restaurant server averages in tips $1 = 4/30

So, The time for a restaurant server averages in tips $135 = 4/30 × 135

                                                                                        = 18 hour

Thus, The time for a restaurant server averages in tips $135= 18 hours

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Considering the graph of g(x) which is a transformation of the graph of

f(x) = 3ˣ, the equation for g(x) is

g(x) = 3ˣ ⁺ ¹- 2

Translation say x units to the left is represented by positive x units while to the right is represented by negative x values. the left and right translation is restricted to the x values.

Translation say x units up is represented by positive x units while to the down is represented by negative x values. the top and down translation is restricted to the y values or the function itself.

The transformation of f(x) = 3ˣ include

translation 1 unit to the left = x + 1 putting to the equation yields 3ˣ ⁺ ¹

translation 2 units to the down = "the equation itself" - 1 putting to the equation yields 3ˣ ⁺ ¹- 2

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Answer:

b = 138⁰ (Being alternate angles)

Answer:

b

production of pancakes depends on batter

Answer:

b, because they are asking how much batter(b) they will need to make pancakes(p), which the dependent variable is what happens as a result of the independent variable, which in this case it is, b, or the batter to make the pancakes, so the dependent variable would be b.

Step-by-step explanation:

Hope it helps!

Answer: Don't use this if it is a test!

Step-by-step explanation:

Hello! An equation for this to represent the number of dogs that are not yellow is 12 dogs - yellow dogs = dogs that are not yellow.  Make an expression out of this with numbers and variables! I hope this helps you!