What is the volume of the cone, rounded to the nearest cubic inch?

Answer:

x - 3

Step-by-step explanation:

Given

[tex]\frac{x^2-9}{x+3}[/tex]

Note that x² - 9 is a difference of squares and factors as

x² - 9 = (x + 3)(x - 3), thus

[tex]\frac{(x+3)(x-3)}{x+3}[/tex]

Cancel the x+ 3 factor on the numerator/ denominator leaving

x - 3 ← in simplified form

The simplified form of the given rational expression x²-9/x+3, provided x is not equal to -3, is x-3.

The given rational expression is x²-9/x+3. To simplify this expression, we can recognize that the numerator (x^2-9) is a difference of squares. In fact, we can rewrite the expression as (x+3)(x-3)/(x+3). As long as x doesn't equal -3 (to prevent division by zero), we can simplify the expression by canceling out the common factor of 'x+3' in both the numerator and denominator. Therefore, the simplified form of the rational expression is x-3 when x does not equal -3.

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Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}t_1=375\\t_{n}=5t_{n-1}\end{array}\right}[/tex]

Step-by-step explanation:

[tex]t_n=75(5^n)\\\\t_{n+1}=75(5^{n+1})\\\\\text{The common ratio:}\ r=\dfrac{t_{n+1}}{t_n}\\\\\text{Substitute:}\\\\r=\dfrac{75(5^{n+1})}{75(5^n)}\qquad\text{cancel 75 and use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\r=5^{n+1-n}=5^1=5\\\\\text{Calculate}\ t_1.\ \text{Put}\ n=1\ \text{to}\ t_n:\\\\t_1=75(5^1)=75(5)=375\\\\\text{The recursive formula of a geometric sequence:}\\\\t_1\\t_n=(t_{n-1})(r)[/tex]

Answer:

t1=375, tn = 5tn-1, where n EN and >1

Step-by-step explanation:

USA test prep said so

Answer: view image. its a proof (in red)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

$733.33

Step-by-step explanation:

The question is on finding the principal value

Formulae for simple interest

S.I= P×R/100×T where P is the invested amount of money, R is interest rate and T is time in years

Given that;

Simple interest=$77 , R=7% and T=1.5 years then

S.I= P×R/100×T...................substituting the values given

77=P×7/100 × 1.5

77=P×0.105

77/0.105 =P

$733.33=P

Answer:

m= 1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

-4-(-7) / 6-(-3)

3/ 9

1/3

Answer:

[tex]x=-15[/tex]

Step-by-step explanation:

[tex]8x+10-2x=4(x-5) \\ \\ 6x+10=4x-20 \\ \\ 2x=-30 \\ \\ x=-15[/tex]

x = -15

First, distribute the 4 to the x - 5 to get 8x + 10 - 2x = 4x - 20.

Now, subtract 4x and 10 from each side to get 4x - 2x = -30

Simplify the subtraction to get 2x = -30.

Divide both sides by 2 to get a final answer of x = -15.

Answer:

£37.80

Step-by-step explanation:

To find the sale price of a jacket during a 30% off sale, first subtract 0.30 from 1.00, obtaining 0.70, and then multiply the regular price (£54) by 0.70:

0.70(£54) = £37.80

The sale price of the jacket after a 30% discount is applied to the original price of £54 is £37.80.

The student's question is about calculating the sale price of a jacket after a discount of 30% is applied to the normal price of £54. This is a typical percentage problem that can be solved using the following steps:

To calculate the discount amount: 30% of £54 = 0.30 × £54 = £16.20.

Then, subtract the discount amount from the original price: £54 - £16.20 = £37.80.

Therefore, the sale price of the jacket is £37.80.

Answer:

[tex]9 \cdot 10^6[/tex]

Step-by-step explanation:

A phone number contains 7 digits. How many different numbers can be made using the digits 0–9 if the first digit is not 0 and all of the digits can be repeated

In 7 digit phone number, the first number cannot be 0

So only 1  to 9 are used to get the first digit. 9 numbers can be used

other digits can use number from 0 to 9. 10 number can be used

So possible numbers can be made is

[tex]9 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10[/tex]

[tex]9 \cdot 10^6[/tex]

The correct option is C.[tex]\ 9 \times 10^6[/tex]

To solve the problem of finding how many different [tex]7[/tex]-digit phone numbers can be made using the digits [tex]0–9[/tex], with the first digit not being 0 and digits allowed to repeat, we can follow these steps:

1. First Digit Choices

The first digit has 9 possible choices ([tex]1[/tex] through [tex]9[/tex]) since it cannot be 0.

2. Remaining Digits Choices

Each of the remaining [tex]6[/tex] digits can be any of the [tex]10[/tex] digits ([tex]0[/tex] through [tex]9[/tex]).

So, the total number of different [tex]7[/tex]-digit phone numbers can be calculated by multiplying the number of choices for each digit:

[tex]\[9 \text{ choices for the first digit} \times 10 \text{ choices for each of the remaining 6 digits}\][/tex]

This can be represented mathematically as:

[tex]\[9 \times 10^6\][/tex]

Calculating [tex]\(10^6\)[/tex]

[tex]\[10^6 = 1,000,000\][/tex]

So,

[tex]\[9 \times 1,000,000 = 9,000,000\][/tex]

3/6 because there are 6 sides and there are 3 numbers that you want to roll. They are even numbers so if you want to roll half of the numbers but not the other half well you have 3/6

Answer:

C. 26

Step-by-step explanation:

The question is on finding determinant of 3×3 matrix

General formulae is given by

if we have matrix (a  b  c)

                             (d  e  f)  

                              (g  h  i ) then the determinant will be given by

a× D( e f) - b × D (d f)  + c× D ( d e)

       (h  i)              (g i)              (g  h)

where D is the determinant

Evaluate

(a  b  c)     (-4  3  3)

(d  e  f)  =  (3  0  2)  = -4 ×D(0 2)  - 3×D (3 2) + 3×D (3 0)

 (g  h  i )     (3  1   1)                (1   1)           (3  1)           (3  1)

= -4 × {(I×0)-(1×2)} -3 {(3×1)-(3×2)} + 3 { (1×3)-(3×0)}

= -4 ×{-2} - 3×{-3} +3× {3}

=8+9+9= 26

first off let's convert the mixed fraction to improper fraction, and then do the division, since it was divided among all 6, he and 5 friends.

[tex]\bf \stackrel{mixed}{4\frac{4}{5}}\implies \cfrac{4\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{24}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{24}{5}\div 6\implies \cfrac{24}{5}\div \cfrac{6}{1}\implies \cfrac{24}{5}\cdot \cfrac{1}{6}\implies \cfrac{24}{6}\cdot \cfrac{1}{5}\implies \cfrac{4}{1}\cdot \cfrac{1}{5}\implies \cfrac{4}{5}[/tex]

Answer:

0.8 or 4/5

Step-by-step explanation:

4/5=.8 4.8/6=.8

Answer:

a = 15

b = 7

c = 4

Step-by-step explanation:

Given in the question an expression [tex]\sqrt[4]{15}^{7}[/tex]

This expression can be written as [tex]15^{\frac{7}{4} }[/tex]

As we know that roots are most often written using a radical sign, like this, [tex]\sqrt[n]{x}[/tex] But there is another way to represent the taking of a root.

You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. For example, [tex]\sqrt[n]{x}[/tex] can be written as [tex]x^{\frac{1}{n} }[/tex]

Secondly two powers having same base can be multiply

[tex]x^{n}(^{m})=x^{nm}[/tex]

Multiplying two negative numbers would always give you a positive product

Example 1) -2 * -1 = 2

Example 2) -5 * -4 = 20

Example 3) -10 * -3 = 30

3.25 • p = t

Or

p = t/3.25

Hope this helps!

The time it takes to print a number of photos can be shown as a proportionality relationship p = (78/24) * t, with p being the number of photos printed and t being time in seconds.

The relationship between the time (t) needed to print pictures and the number of pictures (p) printed by a photo printer can be represented by a simple proportionality relationship. This means that we can express this relationship as a rate. In this case, the printer prints 78 pictures in 24 seconds, so we can write the relationship as:

p / t =78/24

Or in other words:

p = (78/24) * t

This equation suggests that for any given unit of time t, you simply multiply t by the rate (78/24) to find the number of pictures p that can be printed in that time.

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Answer:

D

Step-by-step explanation:

Distribute the negative 1 in the second group.

[tex]5k^4*-1=-5k^4 \\ 5k^3*-1=-5k^3 \\ -k*-1=k[/tex]

Now add by combining like terms.

[tex]3k^4-5k^4=-2k^4 \\ -2k^3-5k^3=-7k^3 \\ k+k=2k[/tex]

[tex]-2k^4-7k^3+2k[/tex]

Answer:

Option B) Between 2 & 3 full pitchers

Step-by-step explanation:

Note  In this problem the volume of the pitcher is 1/3 gallon instead of 3 1/3 gallon

The options of the questions are

A) Between 1 & 2 full pitchers

B) Between 2 & 3 full pitchers

C) About 1/2 of a full pitcher

D) About 1/4 of a full pitcher

so

we know that

To find the number of water pitchers Jason will need to fill the water jug, we will divide the amount of water needed to fill the jug by amount of water in the pitcher

[tex](3/4)/(1/3)=9/4\ water\ pitchers[/tex]

Convert to mixed number

[tex]9/4\ water\ pitchers=(8/4)+(1/4)=2(1/4)\ water\ pitchers[/tex]

therefore

Is Between 2 & 3 full pitchers  

Despite having a 3 1/3 gallon pitcher, Jason will only need 3/4 gallon of water to fill his 3/4 gallon jug. The size of the pitcher doesn't matter, only the size of the jug.

Considering that Jason is seeking to fill a 3/4 gallon water jug with a 3 1/3 gallon pitcher, it is evident that the entire capacity of the pitcher will not be required. To determine precisely the volume of water required, we examine the jug's capacity. Given that the jug has a maximum volume of 3/4 gallon, that is the exact volume of water Jason will require to fill it. Regardless of the pitcher's volume, it's the jug's capacity, which is 3/4 gallon, that establishes the quantity of water needed. Consequently, 3/4 gallon is the volume of water he needs to fill the jug.

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Answer:

[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]

Step-by-step explanation:

[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]

The answer is B. I just answered this question earlier!

Answer:

i need the ansrew too

Step-by-step explanation:

hehe

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = -1/4 and the point (4, 5). Substitute:

[tex]y-5=-\dfrac{1}{4}(x-4)[/tex]

Answer: Option D

[tex]f(x)=(x+3)^2 -k[/tex]

Step-by-step explanation:

For a quadratic function of the form

[tex]ax ^ 2 + bx + c[/tex]

The x coordinate of the vertice is:

[tex]x =-\frac{b}{2a}[/tex]

In this case the function is:

[tex]f(x)=x^2+6x-2\\\\[/tex]

So

[tex]a=1\\b=6\\c=-2[/tex]

The x coordinate of the vertice is:

[tex]x=-\frac{6}{2*1}\\\\x=-3[/tex]

The y coordinate of the vertice is:

[tex]f(-3) = (-3)^2 +6(-3) -2\\\\f(-3)=-11[/tex]

The vertice is: (-3, -11)

The form e vertice for a quadratic equation is:

[tex]f(x)=(x-h)^2 +k[/tex]

Where

the x coordinate of the vertice is h and the y coordinate of the vertice is k.

Then h=-3 and k =-11

Finally the equation [tex]f(x)=x^2+6x-2\\\\[/tex] in vertex form is:

[tex]f(x)=(x+3)^2 -k[/tex]

Answer:

The correct answer option is D. f(x) = (x + 3)² - 11.

Step-by-step explanation:

We know that the standard form of a quadratic function is given by:

y = ax² + bx + c

The vertex form of a parabola is given by

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b / 2a and k = f(h)

In the given equation f(x) = x² + 6x - 2

a = 1, b = 6 and c = -2

Finding h:

h = -6 / (2 × 1)

h = -6/2

h = -3

Finding k:

k = 1(-3)² + 6(-3) + 3

k = 9 - 18 - 2

k = -11

Therefore, the given quadratic function in vertex form: f(x) = (x + 3)² - 11

Answer:

all real numbers

Step-by-step explanation:

Answer:

(B) 132 in²

Step-by-step explanation:

Top Length = 3 + 8 + 3 = 14 in

Bottom Length = 8 in

Area of the trapezoid

= 1/2 (14 + 8) x 12

= 1/2 (22) (12)

= 132 in²

Answer:

B

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases.

here h = 12, a = AB = 8 and b = DC = 3+ 8 + 3 = 14

A = [tex]\frac{1}{2}[/tex] × 12 × (8 + 14) = 6 × 22 = 132 in² → B

The answer is 1/2.

2r = d.

Hope this helps!

A Radius Of The Circle Is Always Half The Diameter. This Means That The Radius Is Half Way Across A Circle.

Answer:

5/48

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

Answer:

B. y+13=5(x+2)

Step-by-step explanation:

I personally do y=_+_(x-_) when solving these equations

Plug in -2 the x coordinate for (x- (-2) to be (x+3)

Plug in -13 for the y intercept.

5 from 5x is the slope.

Thus y=-13+5(x+3)

Then just move 13 to the other side

Answer:

8.

Step-by-step explanation:

In all of the steps to solve this specific question, x is a variable to represent the other factor, that we are trying to find out the answer to, and our equation that we need to set up for this problem, is -9 times x equals -72, because -9 multiplied by the other factor that we are trying to solve for, which is x in this case, should equal -72. So then, to completely finish simplifying this equation, we need to divide -9 from both sides, so we can get our variable x, that we are trying to get the answer for, by itself. Then finally, you get x equal to 8, as our final, simplified answer. These are all of the steps to completely get the correct answer to your question.

Hope this helps!!!

Kyle.

Answer:

The last option (62 degrees)

Step-by-step explanation:

Angle F is the same measure as angle E, just like angle D is the same measure as G.

The measure of angle ∠E will be 62°. Then the correct option is D.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

DEFG is an isosceles trapezoid.

Then the angle ∠E and ∠F will be congruent.

∠E = ∠F

∠E = 62°

Then the correct option is D.

More about the trapezium link is given below.

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Answer:

(-6, -36)

Step-by-step explanation:

The vertex [tex](h,k)[/tex] of a function of the form [tex]f(x)=ax^2+bx+c[/tex] is given by the formula:

[tex]h=\frac{-b}{2a}[/tex]

[tex]k=f(h)[/tex] in other words, we find h and then evaluate function at h to find k.

We know from our function that [tex]a=1[/tex], [tex]b=12[/tex].

Replacing values

[tex]h=\frac{-12}{2(1)}[/tex]

[tex]h=-\frac{12}{2}[/tex]

[tex]h=-6[/tex]

Now we can evaluate our function at -6 to find k:

[tex]k=f(h)=f(-6)[/tex]

[tex]k=(-6)^2+12(-6)[/tex]

[tex]k=36-72[/tex]

[tex]k=-36[/tex]

We can conclude that the vertex (h, k) of our function is (-6, -36)

Answer:

(-6,-36)

Step-by-step explanation:

The given function is

[tex]f(x)=x^2+12x[/tex]

We complete the square to write this function in the vertex form.

Add and subtract the square of half the coefficient of x.

[tex]f(x)=x^2+12x+6^2-6^2[/tex]

[tex]f(x)=x^2+12x+36-36[/tex]

The first three terms is now a perfect square trionomial

[tex]f(x)=(x+6)^2-36[/tex]

Or

[tex]f(x)=(x--6)^2-36[/tex]

The function is now in the form:

[tex]f(x)=a(x-h)^2+k[/tex]

where h=-6 and k=-36

The vertex is therefore (h,k)=(-6,-36)

Answer:

Do you need work shown?

Step-by-step explanation:

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