Find the area of 9.5 and 4.1

Answer: q²x² - p³x + 3pqx + q = 0

Step-by-step explanation:

Since a and B are the roots of x² - px + q = 0, then x = a and x = B

⇒ (x - a)(x - B) = 0

⇒ x² - ax - Bx + aB = 0

⇒ x² - (a + B)x + aB = 0

Comparing this to the given equation of x² - px + q = 0, we discover that

Next, given the roots for the new equation as [tex]x = \dfrac{a}{B^2} \quad\text{and}\quad\ x=\dfrac{B}{a^2}[/tex]

⇒ [tex]\bigg(x - \dfrac{a}{B^2}\bigg)\bigg(x-\dfrac{B}{a^2}\bigg)=0[/tex]

⇒ (B²x - a)(a²x - B) = 0

⇒ a²B²x² - a³x - B³x + aB = 0

⇒ a²B²x² - (a³ + B³)x + aB = 0

Let's look at each term individually:

1st term: a²B²x² = (aB)²x²   = q²x²  (since q = aB)

2nd term: (a³ + B³)x  cubic formula can be used

             = [(a + B)(a² - aB + B²)]x

              = [(a + B)(a² + (2aB - 3aB) + B²)]x

              = [(a + B)(a² + 2aB + B² - 3aB)]x

              = [(a + B)(a + B)² - 3aB)]x

              = [(   p   )(  p²     -  3 q      )]x      since p = a + B and q = aB

              = (p³ - 3pq)x       distributed "p" into p² - 3q

              = p³x - 3pqx       distributed "x" into p³ - 3pq

3rd term: aB = q       since q = aB  

Put it all together:

   q²x² - (p³x - 3pqx) + q = 0

⇒ q²x² - p³x + 3pqx + q = 0

Immediately, we can factor an x out of each term to simplify the polynomial.

x(x^2 + 2x - 24)

In doing this, we know the first zero will be x = 0.

Using the AC method, we can find the next two zeros.

x(x - 4)(x + 6)

The zeros of the polynomial function f(x) = x^3 + 2x^2 -24x are x = -6, 0, and 4.

The question requires finding the zeros of the polynomial function f(x) = x^3 + 2x^2 -24x. The zeros of this function can be found by setting the function equal to zero and solving for x. So, we have 0 = x^3 + 2x^2 - 24x. All terms have an 'x', so we can factor out 'x' to give: 0 = x (x^2 + 2x - 24). The quadratic formula (which is used for expressions of the form ax^2 + bx + c = 0) to solve x^2 + 2x - 24 = 0, we get x = -6 and x = 4. Therefore, the zeros of the function are x = -6, 0, and 4.

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[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\\boxed{15^{\frac{1}{3}}=\sqrt[3]{15}}[/tex]

Radical form is the form of a equation in which the number or variable is written under some power of the root. The 15 to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].

15 to the 1/3 power is the 1/3 power of the number fifteen and it can be expressed as,

[tex]=(15)^{\dfrac{1}{3}[/tex]

This number has to be written in the radical form.

Radical form is the form of a equation in which the number or variable is written under some power of the root.

When a fractional exponents of the number is given the numerator becomes the power and the denominator becomes the root. Let [tex]x^{\dfrac{a}{b}[/tex] is a number with fractional exponents where a and b are the real and positive integer, then a becomes the power and the b becomes the root of the number x.

[tex]x^{\dfrac{a}{b} }=\sqrt[b]{x^a}[/tex]

For the given number,

[tex]=(15)^{\dfrac{1}{3}}=\sqrt[3]{15}[/tex]

Hence the 15  to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].

Learn more about the radical form here;

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Answer:

54

Step-by-step explanation:

to evaluate substitute b = 18 into 3b

3b = 3 × 18 = 54

[ Answer ]

54

[ Explanation ]

B = 18

Substitue B for 18

3 * 18

= 54

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Answer:

a) 6.73104 x 10⁵

b) about 480 times larger

Step-by-step explanation:

a) 673,104 people in scientific notation is 6.73104 x 10⁵

b)325.7 million is the same as 325700000 = 3.257 x 10⁸

so (3.257 x 10⁸) divided by (6.73104 x 10⁵) ≈ 0.48 x 10³

480 times larger

To find the real zeros of the given function, set it equal to zero and solve the resulting equation.

The real zeros of the function F(x) = x^3 + 4x^2 + x - 6 are the values of x that make the function equal to zero.

Answer:

640 kilocalories are there in this 2-cup serving.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

As per the given statement: There are 1600 kilocalories in 5 cups of dog food that mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food.

Let x kilocalories are there in 2-cup serving.

then, by definition of proportion;

[tex]\frac{1600}{5} =\frac{x}{2}[/tex]

Multiply both sides by 2 we get;

[tex]x = \frac{1600}{5} \times 2[/tex]

Simplify:

[tex]x = 320 \times 2 = 640 kilocalories[/tex]

Therefore, 640 kilocalories are there in this 2-cup serving.

Answer:

centre = (3, 9 )

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 3)² + (y - 9)² = 16 is in this form

with centre = (3, 9) and r = [tex]\sqrt{16}[/tex] = 4

Answer:

(3,9) -apex!!!!!!

Step-by-step explanation:

Answer:

Step-by-step explanation: 20 percent

:)

Answer:

1.77 to nearest hundredth

Step-by-step explanation:

Z-score = (score - mean)  / standard deviation

98 is the highest score and its z-score is (98- 81.5) / 9.3

= 1.7742

Answer: 1.77

Step-by-step explanation:

Given : The test grades of a science class are given.

78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89

The grades are normally distributed with a mean [tex]\mu= 81.5[/tex] and a standard deviation [tex]\sigma=9.3[/tex] .

let x be any random variable represents the test grades of a science class.

Formula for z-score:-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

The highest score= 98

Then , the z-score of the highest grade in the test will be :-

[tex]z=\dfrac{98-81.5}{9.3}=1.77419354839\approx1.77[/tex]

Hence, the z-score of the highest grade in the test =1.77

Answer: 25%

Step-by-step explanation:

Hi, if you buy 2 sweaters at full price (100%)

$48 x 2 = $96

"Buy one get one 1/2 off sale"´price

48 + (48/2) = 48 +24 = $72

So, the normal price for both sweaters (96) multiplied by a percentage is equal to the "buy one get one 1/2 off sale” price.

96 x =72

x =72/96 = 0.75  

Multiplying by 100 to obtain the percentage form

0.75 =75%

So, the sale price is %75 of the full price.

To obtain the percent discount.

100%-75% = 25%

This rounded number has three zeros. The number 38,469 rounded to the nearest thousand is 38,000.

To find the number of zeros in 38,469 when rounded to the nearest thousand, we first need to round the number appropriately. We look at the hundreds place (the third digit from the right), which is '4'. Since 4 is less than 5, we do not round up.

Answer:

x=9

Step-by-step explanation:

2x+3y =36

We know y =6, so we can substitute this into the equation

2x+ 3(6) = 36

2x+18 = 36

Subtract 18 from each side

2x+18-18 = 36-18

2x =18

Divide each side by 2

2x/2 =18/2

x=9

I really like that you put the answer out there for other people. that's pretty cool! B) 9

Given : (5b - 9) - 3(8 - 26)

⇒ (5b - 9) - 3(-18)

⇒ (5b - 9) + 54

⇒ 5b - 9 + 54

⇒ 5b + 45

Answer:

i think its 5b + 45

Step-by-step explanation:

im not 100% sure what your asking for but i just distributed the -3 to the 8 and -26 and got 5b -9 -24 + 78. then i combined the like terms to get 5b + 45.

hope this helps !!

Answer:

Brand A = 21 heart-rate watches.

Brand B = 13 heart-rate watches.

Step-by-step explanation:

Let A be the number of Brand A heart watches and B be the number of Brand B heart watches.

We have been given that a nonprofit community health organization purchased 34 ​heart-rate watches for use at a wellness center.

We can represent this information in an equation as:

[tex]A+B=34...(1)[/tex]

We have been given that in a certain​ year, brand A of​ heart-rate watch cost ​$39.99 and brand B cost ​$59.99 and the organization spent ​$1619.66 for the​ watches.

We can represent this information in an equation as:

[tex]39.99*A+59.99*B=1619.66...(2)[/tex]

We will use substitution method to solve our system of equations.

From equation (1) we will get,

[tex]A=34-B[/tex]

Substituting [tex]A=34-B[/tex] in equation(2) we will get,

[tex]39.99*(34-B)+59.99*B=1619.66[/tex]

[tex]1359.66-39.99*B+59.99*B=1619.66[/tex]

[tex]-39.99*B+59.99*B=1619.66-1359.66[/tex]

[tex]20*B=260[/tex]

[tex]B=\frac{260}{20}[/tex]

[tex]B=13[/tex]

Therefore, the organisation purchased 13 heart-rate watches of brand B.

Now let us substitute B=13 in equation (1).

[tex]A+13=34[/tex]

[tex]A+13-13=34-13[/tex]

[tex]A=21[/tex]

Therefore, the organisation purchased 21 heart-rate watches of brand A.

Answer:

42:53 would be the answer

Step-by-step explanation:

In a ski club fundraiser, the ratio of Italian hoagies sold to the total number of hoagies sold, when the numbers of Italian and roast beef hoagies are 42 and 53 respectively, is 42:95.

The student is asking for the ratio of Italian hoagies sold to the total number of hoagies sold at a ski club fundraiser. To calculate this ratio, one must add the number of Italian hoagies to the number of roast beef hoagies to determine the total hoagies sold. In this case, 42 Italian hoagies were sold, and 53 roast beef hoagies were sold, yielding a total of 95 hoagies sold. Thus, the ratio of Italian hoagies sold to total hoagies sold is 42:95. In ratio terms, this expresses that for every 42 Italian hoagies sold, there were 95 total hoagies sold.

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Answer:

y-4 = 3 (x-2)

Step-by-step explanation:

To find the slope of a line

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

slope = (1-4)/(2-3)

         = -3/-1

         =3

Now we use the point slope form for a line

y-y1 = m(x-x1)

y-4 = 3 (x-2)

Answer:

y-4 = 3 (x-2)

y=-3x+10

ΔABC and ΔCBD are similar. Therefore we have the proportion:

[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\\\AB=6;\ BC=x;\ BD=2[/tex]

Substitute:

[tex]\dfrac{6}{x}=\dfrac{x}{2}[/tex]    cross multiply

[tex](x)(x)=(6)(2)\\\\x^2=12\to x=\sqrt{12}\\\\x=\sqrt{4\cdot3}\\\\x=\sqrt4\cdot\sqrt3\\\\\boxed{x=2\sqrt3}[/tex]

The value of x can be any real number because raising 1 to any exponent will always result in 1.

The question needs us to solve for x in the equation [tex](6 to the 0 power)^x[/tex]= 1. We know that any non-zero number raised to the 0 power is 1 (e.g.,[tex]10^0[/tex] = 1). Thus, 6 to the 0 power is 1 regardless of the value of 6. From this, we have[tex]1^x[/tex], which is still 1 for any value of x because 1 raised to any power is always 1. Hence, the equation remains true for any real number value of x.

Answer:

slope = -1/2

Step-by-step explanation:

The formula for slope is (y2-y1)/ (x2-x1)

          m = (10-14)/(5--3)

            = (-4)/(5+3)

            = -4/8

           = -1/2

The values less than 6,766 are one fourth x 6,766 and one half x 6,766 (A and C options are correct)

Numbers, symbols and operators (such as and times) grouped together that show the value of something.

Given is an expression, 6,766

The values less than 6,766 are,

i) 1/4x6,766 = 1691.5

1691.5 < 6,766

ii) 1/2x6,766 = 3383

3383 < 6,766

Hence, one fourth x 6,766 and one half x 6,766 are correct answers.

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Answer:

1 and 3/4 days are equal to 42 hours

Step-by-step explanation:

42 hours = (42 hours) (1 day / 24 hours)

42 hours = 42/24 days

Simplyfing the fraction: Dividing the numerator and denominator by 6:

42 hours = (42/6) /  (24/6) days

42 hours = 7/4 days

42 hours = (4+3)/4 days

42 hours = (4/4+3/4) days

42 hours = 1 3/4 days

To determine how many days are equal to 42 hours, you divide 42 by 24 which results in 1.75. Therefore, 42 hours is equivalent to 1 and 3/4 days.

In this mathematics problem, we are asked to convert 42 hours into a measurement of days. To begin with, we know that 1 day equals 24 hours. Therefore, to convert 42 hours into days we will divide 42 by 24.

The result of this division is 1.75. In terms of a day fraction, this value represents 1 and 3/4 days. As such, we can say that 42 hours is equivalent to 1 and 3/4 days.

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Answer:

p=1.2

Step-by-step explanation:

Additive inverse of any number means a number which can be added to the original number to get

Two numbers are said to be additive inverse of each other if sum of both numbers is 0. For example if 5 is the given number then -5 will be it's additive inverse. So to find additive inverse, we basically change the sign of number.

Given number p is additive inverse off -1.2 so p must be 1.2.

Sum will obviously be 0.

So to graph them on number line, we make a point at -1.2, 1.2 and at 0 for their sum.

Answer:P=1.2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

If on USA TEST PREP it is D

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

Firstly, the cost for renting the bike needs to be subtracted from the total amount:

79 - 15 = 64

Now this can be divided by 8 to find the hours:

64 ÷ 8 = 8

So he paid for 8 hours.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = [tex]\frac{1}{2}[/tex], hence

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (4, 9) into the partial equation

9 = 2 + c ⇒ c = 9 - 2 = 7

y = [tex]\frac{1}{2}[/tex] x + 7 ← equation in slope-intercept form

Answer:

Is it 15?

Step-by-step explanation:

Since it is asking for the sites, aren't you just supposed to count the dots...?

Answer:

15

Step-by-step explanation:

The question is asking how many sites are shown in this data set. So, on the side of the rectangle, it says "Number of Sites" & the dots represent the number of sites. So, there are 15.

Sorry if I'm incorrect...

You would need 12 gallons of paint A. You can find this answer by finding what 60% of 20 is, and do that by multiplying 20 • (0.6). This is what gives you 12. Following that, you’ll need 3 gallons of C, and 5 gallons of B.

[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]

Answer:

(x+5) is the final answer.

Step-by-step explanation:

We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]

Then select correct choice or choices from the given options.

[tex]2x^4+22x^3+60x^2[/tex]

[tex]=2x^2(x^2+11x+30)[/tex]

[tex]=2x^2(x^2+6x+5x+30)[/tex]

[tex]=2x^2(x(x+6)+5(x+6))[/tex]

[tex]=2x^2((x+5)(x+6))[/tex]

[tex]=2x^2(x+5)(x+6)[/tex]

From above factors, we see that only (x+5) is correct.

Hence (x+5) is the final answer.