Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.

As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.

There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.

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Answer:

Answer:

Weight of each large box: 18.25kg

Weight of each small box: 13.25kg

Step-by-step explanation:

For this question, we have two unknowns, but we can solve them as we are given two equations.

If we use the variables 'L' for Large and 'S' for small, we  an write out the information given to us as equations:

3L + 5S = 121

6L + 2S = 136

Now we can solve these simultaneous equations by multiplying one of them by a constant so that one of the variable co-efficients are the same so we can cancel them. We can see here that we can easily double the first equation which would result in both having 6L:

2(3L + 5S) = 2(121)

=> 6L+10S=242

Now that we have one term which is the same, we can subtract one equation from the other:

  6L+ 10S = 242

- (6L + 2S = 136)

------------------------

=>0L + 8S = 106

Now we can solve for S:

8S/8 = 106/8

S = 13.25

And use this value of S to solve for L:

3L + 5(13.25) = 121

3L + 66.25 = 121

3L + 66.25 - 66.25 = 121 - 66.25

3L = 54.75

3L/3 = 54.75/3

L = 18.25

Hope this helped!

Answer:

The table represents a function and the slope is -1/2

Step-by-step explanation:

Here, we want to know if the given table is a function

For a relation to be a function, no two y values have same x value

however, 2 x values can have same y value

Looking at the table, we can conclude that what we have is a function

To find the slope, we select any two points and apply the slope formula

m = (y2-y1)/(x2-x1)

(x1,y1) = (6,-2)

(x2,y2) = (-2,2)

m = (2 -(-2))/(-2-6) = 4/-8 = -1/2

Answer:

Step-by-step explanation:

Standard for of quadratic equation:

We have

Sum of the roots

Product of the roots

We have:

The square of the above is:

Substitute known values and solve for c:

Answer:

c = 3.09375

Step-by-step explanation:

Factored form of a quadratic equation

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

Given quadratic:

[tex]2x^2-5x+c=0[/tex]

Therefore, the leading coefficient is:

[tex]\implies a=2[/tex]

Substitute the value of a into the formula:

[tex]\implies y=2(x-r_1)(x-r_2)[/tex]

Expand:

[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]

Compare the coefficients of x:

[tex]\implies -(2r_2+2r_1)=-5[/tex]

[tex]\implies 2r_2+2r_1=5[/tex]

[tex]\implies r_2+r_1=2.5[/tex]

If the difference between the roots is 0.25 then:

[tex]\implies r_2-r_1=0.25[/tex]

Add the two root equations to eliminate r₁:

[tex]\implies 2r_2=2.75[/tex]

[tex]\implies r_2=1.375[/tex]

Substitute the found value of r₂ into one of the root equations and solve for r₁:

[tex]\implies 1.375-r_1=0.25[/tex]

[tex]\implies r_1=1.375-0.25[/tex]

[tex]\implies r_1=1.125[/tex]

As c = 2r₁r₂ then:

[tex]\implies c=2(1.125)(1.375)[/tex]

[tex]\implies c=3.09375[/tex]

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Answer:

60

Step-by-step explanation:

Answer:

$2,611.21

Step-by-step explanation:

A = P(1 + r/n)^nt

A = 1500(1 + 0.057/1)¹⁰

A = 1500(1.057)¹⁰

A = 1500(1.740803988528..)

A = 2611.205982792..

A ≈ $2,611.21

______________________

Where A is the total amount including interest, P is the initial amount or principle, r is the rate, n is how many times it is compounded per year, and t is the time in years.

Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .

Examples of negation are ,

Logical operations are performed to check the trueness of an expression.

These are generally Boolean expressions or algebraic functions.

A negation of a basic assertion is made by  inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.

Under negation, what was true becomes false and the vice - versa.

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There are seven zeroes  located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).

Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.

Let P=1/(2^5.5^8)

Multiplying and dividing the numerator by 2^3

P= 2^3/(2^5.5^8.2^3)

P=8/(2^8.5^8)

P=8/10^8

P=0.00000008

The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.

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The required simplified expression as a monomial is given as -12[z⁶].

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,

Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]

Thus, the required simplified expression as a monomial is given as -12[z⁶].

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Answer:

Percent is 40%

the decimal is .40

Step-by-step explanation:

1/5 = 20%/.20

So if 1/5 is 20% 2/5 should just have 20% more resolving in 40% or .40

Answer:

x = 11

m∠A = 44°

Step-by-step explanation:

Complimentary angles total 90

(2x + 22) + 46 = 90

Subtract 46 from both sides

2x + 22 = 44

Subtract 22 from both sides

2x = 22

Divide both sides by 2

x = 11

------------------------

m∠A = 2x + 22

m∠A = 2(11) + 22

m∠A = 44°

Answer:

x = 11

∡A = 44°

Step-by-step explanation:

2x+22 + 46 = 90

2x + 68 = 90

2x = 22

x = 11

∡A = 2(11)+22 = 44°

Answer:

SaS

Step-by-step explanation:

Answer:

NEED:

WANT:

Step-by-step explanation:

Right on Plato! <3

Have a wonderful day!

The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.

The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.

On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.

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Answer:

70

Step-by-step explanation:

The formula for this question is

60/100 * x = 42

Look carefully at how this is written. You have so many pets (x) in the shop.

60 % of them are dogs. But that 60% we are told is also how many animals are dogs and that is 42.

So you have two facts meaning the same thing.

Multiply the equation by 100

100 * 60/100 *x = 42 * 100

60x = 4200    

Divide by 60

x = 4200/60

x = 70

The total number of animals was 70

Answer:

62>j

Step-by-step explanation:

mrk me brainliest plz

Answer:

Step-by-step explanation:

Aquí,

[tex] \sqrt{94} [/tex]

= 9.69......

= 9.7(aproximado)

Answer:

[tex](x+5)^2+(y+8)^2=6217[/tex]

Step-by-step explanation:

Hi there!

Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and r is the radius

1) Plug the center of the circle into the equation

Center: (-5,-8)

[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2[/tex]

2) Determine r²

Plug in the given point (16,68)

[tex](x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2[/tex]

Therefore, r² is equal to 6217. Plug this back into [tex](x+5)^2+(y+8)^2=r^2[/tex]:

[tex](x+5)^2+(y+8)^2=6217[/tex]

I hope this helps!

Answer:

1.028 × 10⁹

= 1028000000

Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.

A contingency table is a matrix-form table that shows how often different combinations of variables appear.

It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.

They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.

A contingency table gives you an idea of how two variables relate to each other.

It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.

Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.

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Complete question:

The degrees of freedom for a contingency table with 10 rows and 11 columns are:

A. 100

B. 110

C. 21

D. 90

The Equation of line F is y= -9/2x  + 59/2.

The Equation of line G  is y = 1/10 x .

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

For Line F:

slope = -9 /2

and, Equation of line F as

y - (-2) = -9/2 (x -(7))

y + 2= -9/2( x- 7)

y = -9/2x + 63/2 -2

y= -9/2x  + 59/2

For Line G:

Slope = (0 -(1))/ ( 0-(10))

slope = 1/10

and, Equation of line G as

y - (1) = 1/10 (x -10)

y-1 = 1/10 x - 1

y = 1/10 x

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The domain and range of the function on the graph are:

Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).

To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.

The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:

D: [-2, 1)

For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:

R: [0, 4]

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Answer:

since speed is miles per hour it would be s=1/1/2 so it would be 2mph

Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.

Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:

length of wood per birdhouse x number of birdhouses = total length of wood

So, in this case, we can substitute the given values in the formula:

58 yards x 12 birdhouses = 696 yards

This means Meri needs 696 yards of wood to make 12 birdhouses.

This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.

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substitute the place of the X

Answer:

11p+3q

Step-by-step explanation:

Answer: 135 boys

Step-by-step explanation:

Multiply 3*45 since you know the number of boys is 3 times more than the number of girls.