Solve 4a^4 - 8a^2+4 = 0 for a and list all of the solutions. Explain how you got your answer.

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

Suppose vector "a" is given and we want to determine an expression to produce vector "b". To do this, we need to find two vectors, "c" and "d", such that:

a = c + d

where c and d are the vectors that when added together produce vector a. The expression to produce vector b can then be represented as:

b = d - c

The expression can be determined by first finding the components of vector a, and then using these components to determine the components of vectors c and d. For example, if vector a is represented as:

a = <a1, a2, a3>

We can set c and d equal to:

c = <a1/2, a2/2, a3/2>

d = <a1/2, a2/2, a3/2>

So, the expression to produce vector b can be represented as:

b = d - c = <a1/2, a2/2, a3/2> - <a1/2, a2/2, a3/2> = <0, 0, 0>

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

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Let's say vector a is represented by the expression (a1, a2), and vector b is represented by the expression (b1, b2).

Then, the expression for the resultant vector (c1, c2) can be calculated as follows:

c1 = a1 + b1

c2 = a2 + b2

So the expression for the resultant vector is (a1 + b1, a2 + b2).

To determine an expression that produces vector b from vector a, you would need to know the relationship between the two vectors. If vector b is a scalar multiple of vector a, the expression for vector b can be represented as:

b = k * a

Where "k" is the scalar factor. If vector b is a vector that is in the opposite direction of vector a, the expression for vector b can be represented as:

b = -1 * a

In this case, the scalar factor is -1.

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Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

(y+2)/(x+5)=-6/5

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

The value of variable, x when f(x) = 4 according to the given function expression; f(x) = -x + 3 is; -1.

It follows from the task content that the value of x is to be determined according to the given function expression; f (x) = -x + 3.

Hence, when f (x) = 4, the resulting expression is;

4 = -x + 3

Hence, to determine the value of x, we must solve for x as follows;

4 - 3 = -x

1 = -x

x = -1.

Ultimately, the value of x for which the function instance f(x) = 4 is; x = -1.

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Answer:

39 miles

Step-by-step explanation:

We can start by using algebra to represent the problem in equation form. Let j be the number of miles Jacob ran.

From the information given, we know that:
Adam ran 21.5 miles less than Jacob.
Adam ran 17.5 miles.

We can use these two pieces of information to set up the following equation:
j = 17.5 + 21.5

Now we can solve for j by adding 21.5 to both sides:
j = 39

So Jacob ran 39 miles.

Answer: A. 9/19

Step-by-step explanation:

20 + 18(amount of cookies) = 38

there are 18 chocolate chip cookies, so it's an 18/38 chance it's a chocolate chip cookie that broke, but 18/38 can be simplified.

18 divided by 2 is 9 and 38 divided by 2 is 19

so 9/19

We would expect about 80 seventh-graders to attend after-school programs.

To estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:

28 out of 140 respondents attend after-school programs, which is a proportion of

= 28 / 140

= 0.2.

We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:

400 * 0.2 = 80

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The value of x using Pythagoras theorem is x = √30.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

⇒ 5² + base² = 8²

⇒ 25 + base² = 64

⇒ base = √64 - 25
⇒ base = √39

In the other triangle,

x² + 3² = 39

⇒ x² = 39 - 9

⇒ x = √30

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The factors for the expression (3x+7)(3x-7)

squared the given 9x² = 3x 49 = 7 if the operation in the first unfactor form is negative the factored form's operation will be positive and negative,  = (3x+7)(3x-7)

The factored form occurs when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form may be restated in standard form.

Several strategies may be used to derive the factored form of a quadratic equation Ax2+Bx+C=0 , A x 2 + B x + C = 0.

Factored form assists us in determining the function's x-intercepts or zeros.

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Answer:

An increase of 20

Step-by-step explanation:

-20 + 20 = 0

The change in temperature in degrees Fahrenheit required is A = 20°F

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The current temperature is -20°F, and we want to know how much it needs to increase to reach 0°F.

On simplifying the equation , we get

We can calculate this by finding the difference between the two temperatures:

0°F - (-20°F) = 0°F + 20°F = 20°F

Hence , the temperature needs to increase by 20°F to reach 0°F

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Correct answer:

(-1, 8)

(-2, 6)

(1, 4)

Answer:

Correct choices are:

(-1, 8)

(1, 4)

which would correspond to the second and fourth entries of your options

Step-by-step explanation:

Best way to solve this problem is to plug in x and y values for each ordered pair and see if these values result in a consistent equation. It is impossible to solve the equation since there are two unknowns and only one equation

Here is each ordered pair and resulting y value when x value is plugged in

(-1, 2) ==> y = 2, x = -1
6 - 2(-1) = 6 + 2 = 8
This is not equal to the given value of y =2. So incorrect

(-1, 8)
We figured out from above that when x = -1, y = 8 so this is a correct choice

(-2, 6) ==> x = -2, y = 6

6 - 2(-2) = 6 + 4 = 10
Does not match y-value; incorrect

(1, 4) ==> x = 1, y = 4

6 - 2(1) = 6 - 2 = 4

This matches the given value of y so correct choice

The value of g(2) = 36 for the given function.

The given function g is defined by,

[tex]g(x) = 4(3)^{x}[/tex]

Now to find the value of g(2), put x = 2 in the given function we get,

g(2) = 4(3)²

g(2) = 4 × 3 × 3

g(2) = 36

Therefore, the value of g(2) = 36 for the given function.

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Answer:

no, x = -6y+30 is the right answer

Step-by-step explanation:

The required slope of the curve at the designated point P is 1/4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the curve at point p is given as
= rise/run

From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4

Thus, the required slope of the curve at the designated point P is 1/4.

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Step-by-step explanation:

-8(-5/8x + y = -1/4)

5x - 8y = 2 is the standard form

The value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

Since ZU and ZV is equal to 8, then QR is equal to ST and the radii ZY and ZW bisect ST and QR respectively.

we shall solve for x in the circle as follows:

QR = ST

4x - 5 = 7

4x = 7 + 5 {add 5 to both sides}

4x = 12

x = 12/4 {divide through by 4}

x = 3

The length VS = 7/2

VS = 3.5

Therefore, the value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

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The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is equal to Avogadro's number.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there is A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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Answer:  u = sr/qut

Step-by-step explanation:

Given the equation sr = qut, we can solve for u by isolating it on one side of the equation. To do this, we divide both sides by qut. This gives us sr/qut = u. This means that u can be represented in terms of q, r, s, and t as sr/qut. This is the final result.

.........

Given the equation sr = qut, we can solve for u in terms of q, r, s, and t by isolating u on one side of the equation.

To do this, we can divide both sides of the equation by (qut)

sr/qut = u

Then we have u = sr/qut

So, u is expressed in terms of q, r, s, and t as u = sr/qut

Answer:

-26

Step-by-step explanation

1) substitute -2 for X

4(-2)(2)-3(-2)-16

2) solve

-8(2)+6-16

-16+6-16

-10-16

-26

The value of function at x= -2 is f(-2) is 54.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 4x² - 3x - 16.

Now, to find the value of f(-2) put the value of x= -2.

so, f(-2)= 4(-2)² - 3(-2) - 16

= 4(16) + 6 - 16

= 64 -10

= 54

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The equation you provided is a linear equation that can be solved by isolating the variable y on one side of the equation. To find the solution for y, we need to follow these steps

First, we will simplify the equation by combining like terms: 2.8y + 0.2y = 5y – 14 + 6 3y = 5y – 8

Next, we need to get y alone on one side of the equation by subtracting 3y from both sides: 0 = 2y - 8

We will add 8 to both sides of the equation: 8 = 2y

Finally, we will divide both sides of the equation by 2 to find the solution for y: y = 4

So the solution for the linear equation 2.8y + 6 + 0.2y = 5y – 14 is y=4.

It's worth mentioning that this is the only solution that this equation has since it's a linear equation which has only one answer.

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Answer:

$41.04

Step-by-step explanation:

set up a proportions equation:

[tex]\frac{18.20}{2\frac{1}{3}} =\frac{x}{5\frac{1}{4}}[/tex]

cross multiply and solve for x. this gives you:

x = 41.04

hope this helped, good luck!

The measure of angle C is 47.86⁰

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

C,U and B are the angles and the  c,u and b are the sides opposite to the angles  C,U and B  respectively.

Law of cosines:

c² = u² + b² - 2ub cos C

58²=78²+48² - 2(78)(48) cos C

3364=6084+2304-7488 cos C

3364 = 8388-7488 cos C

=> 7488 cos C = 8388 - 3364 = 5024

=>  cos C = 5024 /7488 = 0.6709

=> C = arccos(0.6709) = 47.86⁰

So,  the measure of angle C is 47.86⁰

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The volume of cylinder = 15,869.56 mm.

The formula for determining a cylinder's volume is the base area times the height. Volume of a cylinder is r2h cubic units.

To calculate a box's volume, you need to know its height, width, and depth. The volume can be calculated by multiplying these three dimensions.

Assume for the moment that the spherical discs are stacked h levels high. The volume of the cylinder will now be calculated by multiplying the discs' base areas by their heights, "h". Therefore, r2h is used to represent the volume of a cylinder with base radius r and height h. The amount of material required to fill an object can be calculated using the volume of the object.

We know that the volume of cylinder = πr²h

Given,

height = 14 mm

radius = 19 mm

V = π × 19 × 19 × 14

⇒  V = 15,869.56 mm

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The Chang family has been traveling for 18 hours, thus, t-value is 18.

A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.

D(t) = 2,280 - 60t

D(t) = 1,200; find t.

D(t) = 2,280 - 60t

1200 = 2280 - 60t

From both sides of the equation, deduct 2280.

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

multiplied by -60 on both sides

- 1080 / -60 = - 60t / -60

18 = t

t = 18

The Chang family had travelled for 18 hours, according to this.

The Chang family has been traveling for 18 hours, t = 18.

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The complete question is,

Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?

A.t = 20; the Chang family has been traveling for 20 hours.

B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.

The Chang family has been traveling for 18 hours, thus c. t = 18.

The Chang family must go home for an additional 18 hours using the formula D. t = 18.

The pair of expressions 4p + 3c and (c +2p)(2) are not equivalent because they aren't equal.

This is referred to as the expressions that work the same even though they look different.

we were given: 4p + 3c and (c +2p)(2)

: 4p + 3c = (c +2p)(2)

: 4p + 3c = 2c + 4p

They are not equal thereby making them not to be equivalent.

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The full question:

determine whether each pair of expressions are equivalent 4p + 3c and (c +2p)(2)

Four rules of multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

As given in the question,

Four rules of the multiplication are given by :

1. Zero × any number = 0

0 × a = 0 , a ∈ R.

Example : 0 × 5 = 0

2. One  × any number = Number itself.

1 × a = a  , a ∈ R.

Example : 1 × 5 = 5

3. Multiply two numbers with same sign gives positive negative.

-a × -a = + a , +a × +a = + a,  , a ∈ R.

Example : -2× -2 = 4

3 × 3 = 9

4. Multiplication of two numbers in any order does not affect the result.

a × b = b × a, a and b ∈ R.

Example : 2 × 3 = 3 × 2

Therefore, the four rules of the multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

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Gross income means all income you receive in the form of money, goods, property, and services that isn't exempt from tax.

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Answer:

x = - [tex]\frac{6}{5}[/tex] , x = - 1

Step-by-step explanation:

(x + 1)(5x + 6) = 0 ← in standard form

equate each factor to zero and solve for x

5x + 6 = 0 ( subtract 6 from both sides )

5x = - 6 ( divide both sides by 5 )

x = - [tex]\frac{6}{5}[/tex]

or

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

Answer:

the b part

Step-by-step explanation:

Answer: The y-intercept of y=mx+b is B

Step-by-step explanation:

1. Y is the y-variable

2. Mx is the slope

3. B is the y-intercept.