An infinite geometric series converges if the common ratio is

Answer:  [tex]5x-5 \ge 0[/tex]

This is the same as [tex]x-1 \ge 0[/tex]

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Explanation:

We have [tex]f(x) = \sqrt{5x-5}+1[/tex]

The stuff under the square root (this stuff is called the radicand) is what we'll focus on (the +1 at the end does not affect the domain at all). We want this to be 0 or larger. This is to avoid applying the square root to negative values, which leads to complications.

So 5x-5 must be 0 or larger meaning we write [tex]5x-5 \ge 0[/tex]

Optionally we can divide all three terms (5x, -5 and 0) by 5 to go from [tex]5x-5 \ge 0[/tex] to [tex]x-1 \ge 0[/tex]

If you wanted to solve for x, you would get [tex]x \ge 1[/tex] to set up the domain. Meaning that x = 1 is the smallest x value you can plug into the function. The x value can be anything larger than 1 as well.

Answer:

not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem to see if it is a right triangle

a^2 + b^2 = c^2

15^2 + 12^2 = 21^2

225 + 144 = 441

369 = 441

This is not true so it is not a right triangle

Answer:

Step-by-step explanation:

A triangle is a right angled triangle if sum of squares of two sides is equal to the square of third side.

12²+15²=144+225=369

21²=441

so a²+b²≠c²

it is not a right angled triangle.

Answer:

5.64mm

Step-by-step explanation:

book's thickness=page thickness*number on page

book's thickness=282 pages*0.02mm

book's thickness=5.64mm

Answer:

Current price $50eax135hats= $6750

Step-by-step explanation:

If he sells the hats at $52 he sells 3 less hats so $52x132=$6864

if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc

$56 x 126=$7056

Answer:

40 apples

Step-by-step explanation:

2 apples= [tex]\frac{1}{5}[/tex] grams

x apples= 4 grams

 8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40

Answer:

40

Step-by-step explanation:

edu instruction correct

Answer:

664 minutes

Step-by-step explanation:

34 + 49 = 83

83 minutes a day

83 x 8 = 664

Answer:223

Step-by-step explanation:

Answer:

G = 66.0

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan theta = opp/ adj

tan G = 9/4

take the inverse tan of each side

tan ^ -1 ( tan G) = tan^-1( 9/4)

G = 66.03751103

To the nearest tenth

G = 66.0

Answer:

B. Better measure of spread: the standard deviation

D. Better measure of center: the median

Step-by-step explanation:

The mean is the average of a data set.

The median value is best for measuring the center value because median measures the middle value of a set of data.

The IQR only measures the inner range of a data set.

The standard deviation is best for measuring the spread because standard deviation measures the spread of data distribution.

486 ÷ 108

4.5 x 100

450 were there last year

Answer:

Step-by-step explanation:

Let the original number of students be x

Since the number of students increased by 8% we add 8% to 100% making it 108%

108% of the original number of students gave us 486

So we have

108% of x = 486

108 / 100 × x = 486

Multiply through by 100

108x = 48600

Divide both sides by 108

x = 450

So the number of students in the school last year was 450

Hope this helps you

Answer:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)

The given equation is not written in quadratic form. To rewrite the equation:

To overcome this difficulty, follow these mathematical steps:

[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]

Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.

Part 2: Using the quadratic formula

The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].

Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]

Substitute these values into the quadratic formula and solve for x.

[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]

Part 3: Solving for x with the values from the quadratic formula

Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.

This equation will have two zeros/roots to solve for by setting x equal to zero.

Operation 1: Addition

[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]

Operation 2: Subtraction

[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]

Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Answer:

yes you're right it is 14 + 28p = 315

Answer:

C

Step-by-step explanation:

I had this question edge 2021

Answer:

3 gallons of gas are still remaining in the tank

Step-by-step explanation:

Royston's car had 15 1/5 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and he refueled the car with 5 3/5 gallons. If the car consumed 17 4/5 gallons of gas during the trip, there are still ____________ gallons of gas remaining in the tank?

Given:

Initial gallons of gas=15 1/5

Refueled gallons of gas= 5 3/5

Used gallons of gas=17 4/5=89/5

Total gallons of gas available=

Initial + Refueled

=15 1/5 + 5 3/5

=76/5 + 28/5

=76+28/5

=104/5 gallons

Equivalent to

=20 4/5 gallons

Total remaining gallons of gas= Total gallons of gas available - Total gallons of gas used

=104/5 -89/5

= 104-89/5

=15/5

=3 gallons

Answer:

3 gallons

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

1/2 * 600 = 300

There are 300 times would you predict getting an even number.

We have to given that,

The probability of spinning an even number is 1/2.

And, you spin 600 times.

Hence, Number of times would you predict getting an even number is,

⇒ 1/2 of 600

⇒ 1/2 × 600

⇒ 600 / 2

⇒ 300

Therefore, There are 300 times would you predict getting an even number.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ6

Answer:

see explanation

Step-by-step explanation:

Under a rotation ( clockwise or anticlockwise ) about the origin of 180°

a point (x, y ) → (- y, - x ), thus

A(5, 3 ) → A'(- 3, - 5 )

B(8, 10 ) → B'(- 10, - 8 )

C(11, 3 ) → C'(- 3, - 11 )

Answer:

t = log(2)/0.12  years (exact value)

= 5.776 years (to three decimal places)

Step-by-step explanation:

The future value of an amount P at continuous interest rate i% for t years can be calculated using the continuous interest formula:

FV = Pe^((i)t)

where e is the Euler's constant = 2.7182818284....

We're given

10000 = 5000 e^((0.12)t)

simplify

2 = e^(0.12t)   ........................ see below

[ please compare if this is the same as the one shown in the original question, the formula posted as  "2 = e 120" does not look right, probably because of typographical difficulties, then answer if the equation given in the question can be used to solve the problem]

take (natural) log using the power property of logarithms

log(2) = 0.12t log(e)

using natural log, log(e) = 1

log(2) = 0.12t

simplify

t = log(2)/0.12  years (exact value)

To obtain the time (in years)

t = log(2)/0.12 = 0.6931/0.12 = 5.7762 years

Check using the rule of 72 (approximate)

72/12(%) = 6,

Since continuous interest accumulates interest faster, so 5.8 years sound reasonable.

Answer:

slope = 1/4

Step-by-step explanation:

If a equation is in form of y = mx + c

them m is the slope of line.

____________________________________________

Let Y(d) be the distance ran by Alexandria on dth day

Y(0) = 2

she adds 1/4 miles each day then

Y(1) = 2 + 1/4

Y(2) = 2 + 1/4 +1/4 = 2 +1/4(2)

Y(3) = 2 + 1/4 +1/4 +1/4= 2 +1/4(3)

.

.

.

.

similarly

in d days she can run 2 miles + 1/4*d miles

thus, we have

Y(d) = 2 + 1/4(d)

it can be also solved

Thus we see that it is a linear relationship y = 2 + 1/4(d)

which is in the form of y = mx + c

comparing mx to 1/4 d

we have m = 1/4

thus,

slope of this linear relationship is 1/4

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

Answer:

[tex]\boxed{\sf \ \ YES \ \ }[/tex]

Step-by-step explanation:

Hello

let's say that the price of the book was x

the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x

and this is $72 so we can write that

0.8*x=72

and then divide by 0.8 both parts

x = 72/0.8=90

So the list price value of the book is $90

and we can verify as 90 - 20%*90 = 90 - 18 = 72

Hope this helps

Answer:

[tex]\sqrt[3]{88c^{2} }[/tex]

Step-by-step explanation:

If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.

So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.

[tex]\sqrt[3]{88c^{2} }[/tex].

Hope this helped! (By the way, this was my 100th answer!)

Answer:

Step-by-step explanation:

[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]

[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]

Answer:

0.0278 is the probability

Step-by-step explanation:

Okay, here we want to find the probability of 5 successes

The best way to go about this is by using the Bernoulli trial

So is p = probability of success = 0.51

Then q = probability of failure = 1-0.51 = 0.49

Mathematically, the Bernoulli approximation for k = 5 out of n = 18 is set up as follows;

P(k = 5) = nCk • p^k • q^(n-k)

P(k = 5) = 18C5 * 0.51^5 * 0.49^13

P(k = 5) = 0.027751047366 which is 0.0278 to 4 decimal places

Answer:

4 triangles and 1 square

Step-by-step explanation:

If we are to make a net of this pyramid, we'd have a net that has 4 triangles, and 1 square.

The base of the pyramid has 4 sides of equal length of 5 in each. A polygon that has 4 right angles and 4 sides that are of equal sizes or lengths is said to be a square.

Therefore, the net of the figure above is made up of 4 triangles and 1 square.

Answer:  4 triangles and 1 square

Step-by-step explanation

Answer:

The quotient is 2x^2+4x+11

Step-by-step explanation:

Answer:

where's the graph??? .......

Answer:

80%

Step-by-step explanation:

The basic idea of this problem is to convert [tex]\frac{44}{55}[/tex] into a percentage.  [tex]\frac{44}{55}[/tex]  can be simplified to [tex]\frac{4}{5}[/tex] which is also 80%.

Answer:

Step-by-step explanation:

44 out of 55

divide :44/55=0.8

to convert it to decimal  you multiply by 100 and put percentage next to it

0.8*100=80

%80

Answer:

Hey mate, here is your answer!

Step-by-step explanation:

let x be the #

x/3-11=38

x-11(3)=38(3)

x-33=114

x=114+33

x=147

Answer:

(3+2x)4  = 16x4+96x3+216x2+216x+81

Step-by-step explanation:

Answer:

(3+2x)^4

(3)^4+4(3)³(2x)¹+6(3)²(2x)²+4(3)¹(2x)³+(2x)⁴

81+216x¹+216x²+96x³+16x⁴

Answer:

a=-5

Step-by-step explanation:

When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.

Answer:

a = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)

m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )

- 2(a + 3) = 4 ( divide both sides by - 2 )

a + 3 = - 2 ( subtract 3 from both sides )

a = - 5

Answer:

[tex]\boxed{y=|\frac{1}{2}x - \frac{3}{2}|+3}[/tex]

Step-by-step explanation:

The translation is a horizontal translation.

The graph is translated 1 unit to the left. So the value of x is added by 1.

[tex]f(x+1)[/tex]

[tex]y=|\frac{1}{2} (x+1)-2|+3[/tex]

[tex]y=|\frac{1}{2}x + \frac{1}{2} -2|+3[/tex]

[tex]y=|\frac{1}{2}x + - \frac{3}{2}|+3[/tex]

Answer:

30 mph

Step-by-step explanation:

let s represent speed and h represent rebound.

Given that s is proportional to h then the equation relating them is

s = kh ← k is the constant of proportion

To find k use the condition s = 20, h = 10, then

20 = 10k ( divide both sides by 10 )

2 = k

s = 2h ← equation of proportionality

When h = 15 , then

s = 2 × 15 = 30 mph