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Simplify the expression (6^2)4.

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

Katie is studying the polynomial  and determines the polynomial has three real roots. Do you agree or disagree with Katie's statement? Explain your reasoning.

the complete question is

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.

Write properties of function:

x intercept/zero: [tex]x_{1}[/tex] = 3/2 ; [tex]x_{2}[/tex] = 4 ; [tex]x_{3}[/tex] = -[tex]\sqrt{3}[/tex] ;  [tex]x_{4}[/tex] = [tex]\sqrt{3}[/tex]

Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots.  you  disagree with Katies statement because the function has four real roots

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The quadratic function in the standard form containing the point (-7, 5) and vertex (1, 9) is y = (-1/16)(x - 1)² + 9.

The vertex form of a quadratic function with vertex (h, k) is written as

y = a(x - h)² + k, where (x, y) denotes a point on the parabola. Real integers a, h, and k are also included.

Given:

Point (x, y) = (-7, 5)  

Vertex (h,k) = (1, 9)

The general equation of quadratic function in vertex form is:

 y = a(x - h)² + k

To solve for a, substitute the given point (x,y) = (-7,5) into the equation.

5 = a(-7 - 1)² + 9

a(-8)² = -4

a = -4 /64

a = -1/16

Therefore, the required quadratic function is,

 y = (-1/16)(x - 1)² + 9

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The equation that can be used to get the number of men if the total number of people who attended was 2400 is x + 3x + x + 240 = 2400.

It should be noted that from the information given, in the health camp the number of children was three times the number of men and the number of men was 240 less than the number of women.

Number of men = x

Number of children = 3x

Number of women = x + 240

Total number of people = 2400

The appropriate equation will be:

x + 3x + x + 240 = 2400

5x + 240 = 2400

Collect like terms

5x = 2400 - 240

5x = 2160

Divide

x = 2160 / 5

x =432

Therefore, the total number of men is 432 men.

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Considering that a transversal line cuts two parallel lines, the relations between the angles are given as follows:

1. Corresponding angles.

2. Alternate exterior angles.

3. Consecutive interior angles.

Angles 1 and 3 are corresponding angles, as they are both at the same position relative to their lines, j for angle 1 and m for angle 3, being cut by the transversal line t.

Angles 4 and 8 are alternate exterior angles, as:

Inverse positions in both senses, left/right and up/down, hence alternate exterior angles.

Angles 2 and 3 form a supplementary pair inside the same region, between the two lines being cut by the transversal, hence they are consecutive interior angles.

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The equation h>= 11/2 feet represents the required height of an individual to ride the roller coaster.

Your height = 5 1/3 feet tall

Required height in feet to ride a roller coaster = at least 5 1/2 feet

When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions.

Let h represent the height

h>= 5 1/2

Converting into an improper fraction

h>= 11/2 feet

Your height in improper fraction = 16/3 feet

Comparing the required height and your height we find that

Required height>Your height

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Answer:

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. 

Answer:

x=10

Step-by-step explanation:

48=6x-12

60=6x

x=10

Answer: y=-4x+30

Step-by-step explanation: put into point slope form y-y1=m(x-x1). M is out slope with the given point (7,2) 7 is out x and 2 is our y. Give us y-2=-4(x-7) once done distribute yo get y-2=-4x+28. Add the 2 from the left to the right. to get y=-4x+30

7-(-4) is 4 units from 7 in the negative direction. See the explanation and the linear scale attached.

The direction being referred to is the direction of the number on a numerical scale or Linear Scale.

In the attached linear scale, we can see that the arrow stops at 11. This is arrived at by expanding the bracket:

7 - (-4)

the subtraction signs cancel out each other creating a positive sign. Hence we have:

7 + 4

= 11.

Hence, 11 is 4 units away from 7 in the negative direction. That is going toward zero is negative or a reduction hence, to get to 7 you need to go toward the negative section of the scale.

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Answer: 9,800

Step-by-step explanation:

She should save 9,800 yearly.

2/10 = 20/100 ; 20%

20% = 0.2

0.2 x 49,000

(which is 20% of 49,000)

= $9,800

Answer:

3 Feet

Step-by-step explanation:

Issac's Kitchen Area - 54 sqft

Issac's Pantry Area - 54/9 = 6 sqft (His pantry is 9x smaller than his kitchen)

[tex]area = length * width[/tex]

Here we have the total area and the width, so we can substitute for finding the length:

[tex]6 = length * 2\\ \\ = > \frac{6}{2} = length\\ \\ = > length = 3[/tex]

Hence is pantry is 3 feet long.

Answer:

Step-by-step explanation:The walker family uses 45 pounds of crisped rice cereal per year. 1.55 pounds  they save by buying the 18-oz. box for $3.50 rather than the 12-oz. box for $2.75  by using unitary method.

What is called pound?

A pound is a unit of weight used mainly in Britain, America, and other countries where English is spoken. One pound is equal to around 0.454 kilograms. A pound of something is a quantity of it that weighs one pound.

For this, we get the unit price per ounce of each.

3.50/ 18 = 0.1944 unit

2.75 / 12 = 0.229 unit

The walker family uses 45 pounds of crisped rice cereal per year 45 ×0.1944=8.74845 ×0.229= 10.305.

Thus ,they save 10.305 - 8.75 = 1.55

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3x+x+(x+12)=152

<AOD =<COB(VERTICAL OPPOSITE ANGLES)

[tex]5x+12=152\\5x=152-12\\5x=140\\\frac{5x}{5} =\frac{140}{5} \\x=28[/tex]

x=28°

be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT

i.e <COE,<EOF AND <FOB

It should be no mystery that amounts deposited get added to bank balance, and amounts withdrawn by any means get subtracted. Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal.

Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal. The debit card withdrawal differs from a check in the check register in that there is no check number (and frequently no transaction number) connected to it.

initial transaction

$100 is deposited to open the account. The starting balance is that sum.

two-way transaction

You must calculate the tax on the purchases for this issue. Normally, the store would take care of that for you, and you would write a check to cover the debt. The sum owed in this case is...

Rounding up from $43.82 to 45.5728 is 45.57.

Instead of calculating the tax individually and then adding it to the original amount, it is more convenient to use a multiplier to determine the amount with tax. You should be aware that the purchase price multiplied by 100% plus 4% equals 104%, or 1.04 times the price.

As a withdrawal, this $45.57 is deducted from the prior transaction's $100 total, resulting in a new balance of $54.43.

third action

This is a straightforward withdrawal, therefore $46.43 is obtained by deducting the sum from the prior balance.

As previously said, there is no transaction number connected to this. It can occasionally be helpful to keep track of which debit card is being used if you have several debit cards that are taking money out of the account. The final four digits of the card number are used to identify transactions on my bank statement.

Fourth action

You must calculate the payroll deposit amount for this problem. That would typically be handled for you by your employer, along with any deductions for taxes, insurance, union dues, or employee purchases. The sum deposited in this case is...

Hourly rate times 40 equals $9.75, which equals $390.

The previous value is increased by this deposit, making the new balance $436.43.

In most cases, the coupon is applied to transactions including coupons before the tax is calculated. The fact that the purchase amounts are combined should be obvious. (You can calculate the total when there are numerous items at the same price using repeated addition or multiplication; most people find multiplication to be simpler.)

The purchase from the bike shop is arguably the most difficult. The total of the values in brackets is...

$180.00 + 14.95 + 8.95 = 203.90

Then, the 15% discount is applied.

Rounding up to 30.59 from 0.15 x $203.90 = 30.585

Taking this out of the previous amount* yields (before taxes)...

$203.90 -30.59 = $173.31

The amount subject to tax can then be calculated using the same multiplier described above:

Round to $180.24 using the formula: amount with tax = $173.31 x 1.04 = $180.24

* Talk about the 15% discount

As with additional tax, you can calculate the discount using a multiplier:

100% - 15% = 85% . . . 0.85 times as much

The result of applying this multiplier to the number 203.90 is 173.315, which is typically rounded up to 173.32. But this figure results from a discount that is rounded to the nearest half cent (30.585). The discounted amount, 173.315, is rounded down to 173.31 if the discount is rounded up. The intricacy of applying a multiplier to discounts is there.

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Answer: the second one

Step-by-step explanation:

commutative is like

A+b=b+A

So 4+(-6)=-6+4

Which is like 4-6=-6+4

Answer:

[tex]g(x)=2x+3[/tex]

Step-by-step explanation:

[tex]g(x)=\frac{1}{2}(4x+6)=2x+3[/tex]

The relationship will be a solid line .

How to find the relationship between the given amounts?

Given:

The amount of one lunch =$4

The amount of the school lunch card=$100

Let, the amount remaining on the card= b

Let the number of lunches to buy  = a

The equation is given by,

b = 100 - 4a

When 1 lunch is bought ,a= 1 ;

b= 100 - 4(1) = 96

When 2 lunches are bought ,a= 2;

b= 100 - 4 (2)= 92

When 3 lunches are bought ,a= 3;

b= 100 - 4 (3)= 88

When 4 lunches are bought ,a= 4;

b= 100 - 4 (4)= 84

Since ,the decrease is gradual and same, the relationship will be a solid line.

The complete question is:

What is the relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card. Is the relationship a solid line or a set on unconnected points?

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In order to solve this quadratic equation by completing the square, let's analyse the coefficient b by comparing the equation with the standard form:

We have b = -12. In order to be a perfect square, the coefficient c needs to be (-12/2)^2 = (-6)^2 = 36

We already have 30, so we just need to add 6:

Answer:

I think your answer is correct

Step-by-step explanation:

You did that right. You moved the point from zero to negative one, then you raised it to negative two. Good job.

For the function x³ - 6x² + 11x - 6, we have that:

a) The x-intercepts are: x = 1, x = 2, x = 3.

b) The y-intercept is of y = -6, while the end behavior is that it decreases to the left and increases to the right.

The function is given as follows:

f(x) =  x³ - 6x² + 11x - 6

x - 3 is a factor of the function, meaning that x = 3 is a x-intercept and the function can be written as follows:

x³ - 6x² + 11x - 6 = (x - 3)(ax² + bx + c)

Then we have to build a system of equations to find the coefficients as follows:

x³ - 6x² + 11x - 6 = ax³ + (b - 3a)x² + (c - 3b)x - 3c.

Then the coefficients are given as follows:

Then the factor is given by:

x² - 3x + 2.

Hence the other intercepts of the polynomial are found when:

x² - 3x + 2 = 0

(x - 2)(x - 1) = 0.

x - 2 = 0 -> x = 2.

x - 1 = 0 -> x = 1.

The y-intercept is the value of f(x) when x = 0, that is, f(0), hence:

f(0) = 0³ - 6(0)² + 11(0) - 6 = -6.

For the end behavior, we need to find the limits as x goes to infinity, hence:

When the limit goes to infinity, we consider only the term with the highest exponent of the polynomial.

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Answer:

Number

Step-by-step explanation:

48 divided by 100 equals .48

Answer:

d

Step-by-step explanation:

Pythagorean theorem : a2 + b2 = c2

Here, ‘a’ is the vertical side i.e. wall

‘b’ is the base side i.e. bottom = 5 m

‘c’ is the hypotenuse i.e. the ladder = 10 m

If b = 5 m, c = 10 m

Then, a2 = c2 - b2 = (10 x 10) - (5 x 5) = 75

a = √75 = 8.66 m

The the top of the ladder is at 8.66 m.

86 = 1p + 5n

n = p + 4

86 = 1p + 5(p + 4)

86 = 1p + 5p + 20

66 = 6p; p = 11

86 = 1(11) + 5n

86 = 11 + 5n

75 = 5n; 15 = n

11 pennies, 15 nickels

11(1) + 15(15) = 11 + 75 = 86

Answer: x= -5

Step-by-step explanation: Zero is x

f(-5)= -15 +7= -8

f(-5)= -1 - 7 = -8

Answer is -8

Based on the given parameters, the amount of the investment after 4 years is $1030

The given parameters about the compound interest are

Principal Amount, P = $1000

Interest Rate, R = 0.85%

Time, t = 4

Number of times, n = 1 i.e. annually

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

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

Substitute the known values in the above equation

A = 1000 * (1 + 0.85%/1)^(1 * 4)

Express 0.85% as decimal

A = 1000 * (1 + 0.0085/1)^(1 * 4)

Evaluate the sum

A = 1000 * (1.0085/1)^(1 * 4)

Evaluate the exponent

A = 1000 * 1.03

Evaluate the product

A = 1030

Hence, the value of the investment is $1030

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The linear equation that models the water left in the bathtub is g = 32 - 4t.

The first step is to determine the rate of drainage of the bathtub. The rate of drainage is the ratio of the change in water to the change in time.

Rate of drainage = change in water levels in the bathtub / change in time

(20 - 36) / (7 - 3)

-16 / 4 = -4

The second step is to determine the amount of water in the bathtub before it started draining

Initial amount of water in the bathtub = 20 + (4 x 3) = 32 gallons

The form of the linear equation that can be used to determine the amount of water left in the tank is:

Water in the bathtub = initial amount of water - (rate of drainage x number of minutes)

g = 32 - 4t

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Using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

So, liters of water when mixed with 10 lemon juice:

Solve, the expression as follows:

Therefore, using mathematical operations, (D) 6⅔ of water should be mixed with 10 lemon juice.

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The correct question is given below;
Four liters of water are mixed with 6 juiced lemons to make lemonade. how many liters of water should be mixed with 10 juicer lemons to obtain the same result? (pls kinda show work)

A) 4 2/3

B) 5 1/3

C) 6 1/3

D) 6 2/3

E) 8 1/3

Answer:

=2s−4

Step-by-step explanation:

−4s−3+6s−1

=−4s+−3+6s+−1

Combine Like Terms:

=−4s+−3+6s+−1

=(−4s+6s)+(−3+−1)

=2s+−4

Answer:

=2s−4