Solve this please! And if you can tell me how and why

Answer:  [tex]5x-5 \ge 0[/tex]

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

========================================================

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:

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:

[tex]c = \frac{2}{5} t[/tex], if the number of texts is 4, then the cost is $1.60.

Step-by-step explanation:

If 2 texts costs $5, then each text costs $[tex]\frac{2}{5}[/tex].

So, we can setup the equation to  [tex]c = \frac{2}{5} t[/tex].

If the number of texts is 4, we can substitute that into our equation.

[tex]c = \frac{2}{5} \cdot 4[/tex]

[tex]c = \frac{8}{5}[/tex]

[tex]c = 1.60[/tex]

Hope this helped!

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:

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:

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.

Answer:

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

Step-by-step explanation:

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:

664 minutes

Step-by-step explanation:

34 + 49 = 83

83 minutes a day

83 x 8 = 664

Answer:223

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The inscribed angle's arc measures 36°, and central angle's arc measures 72°.

Answer:

the answer is B

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:

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:

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:

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

Answer:

both the equation and it's inverse are functions

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:

[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: 0

Step-by-step explanation:

The given equation: [tex]6a^2+5a+4=3[/tex]

Subtract 3 from both the sides, we get

[tex]6a^2+5a+1=0[/tex]

Now , we can split 5a as 2a+3a and [tex]2a\times 3a = 6a^2[/tex]

So, [tex]6a^2+5a+1=0\Rightarrow\ 6a^2+2a+3a+1=0[/tex]

[tex]\Rightarrow\ 2a(3a+1)+(3a+1)=0\\\\\Rightarrow\ (3a+1)(2a+1)=0\\\\\Rightarrow\ (3a+1)=0\text{ or }(2a+1)=0\\\\\Rightarrow\ a=-\dfrac{1}{3}\text{ or }a=-\dfrac{1}{2}[/tex]

At [tex]a=-\dfrac{1}{3}[/tex]

[tex]2a+1=2(-\dfrac{1}{3})+1=-\dfrac{2}{3}+1=\dfrac{-2+3}{3}=\dfrac{1}3{}[/tex]

At [tex]a=-\dfrac{1}{2}[/tex]

[tex]2a+1=2(-\dfrac{1}{2})+1=-1+1=0[/tex]

Since, [tex]0< \dfrac{1}{3}[/tex]

Hence, the possible value of 2a+1 is 0.

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.

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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

cos (x - π/3) = cos (π/2)

Then we need x - π/3 = π/2

Solving the equation:

x - π/3 = π/2

x = π/2 + π/3

x = 5π/6

Work Shown:

4*1000 = 4000 = 4 thousand

3*100 = 300 = 3 hundred

6 * (1/100) = 0.06 = 6 hundredths

7 * (1/1000) = 0.007 = 7 thousandths

add up the results

4000 + 300 + 0.06 + 0.007 = 4300.067

The expression (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000) in simplified as the decimal number 4,300.067.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000)

Simplify the expression, then we have

⇒ 4,000 + 300 + 0.06 + 0.007

⇒ 4,300.067

The expression (4 x 1,000) + (3 x 100) + (6 x 1 / 100) + (7 x 1 / 1000) in simplified as the decimal number 4,300.067.

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Answer:

[tex]x = 4 - \frac{4}{3}y[/tex]

Step-by-step explanation:

If we have the equation [tex]3x = 12-4y[/tex], we can simplify this equation down.

Divide both sides by 3:

[tex]x = 4 - \frac{4}{3}y[/tex] .

Hope this helped!

Answer:

X = 4 minus four-thirds y

Step-by-step explanation:

Well to solve for x we single it out.

3x = 12 - 4y

Divide 3 by everything,

x = 4 - 4/3y

Thus,

X = 4 minus four-thirds y.

I do hope this helps :)

Temos ai um retangulo. Para usa area, basta multiplicar a medidas - que no caso sao 2,3m e 1,46m

Area Comodo = 2,3 x 1,46

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:

(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

The value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  2x² - 5

g(x) = x² - 4x - 8

(f - g)(x) = f(x) - g(x)

= (2x² - 5) - (x² - 4x - 8)

= 2x² - 5 - x² + 4x + 8

= x² + 4x + 3

(f - g)(x) = x² + 4x + 3

Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

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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

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