A taxi cab company charges a flat rate of $2.00 per trip plus $0.25 per mile of the trip. If m is the number of miles traveled on a particular trip, interpret the following expressions: a) 0.25m b) 2.00 + 0.25m

Answer:

1. (x+9)^2 = 89

2. (Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Step-by-step explanation:

x^2 - 6 = 2 - 18x

1) rewrite the equation by completing the square

x^2 - 6 = 2 - 18x

x^2 + 18x = 2+6

x^2 + 18x = 8

Find the half of the coefficient of x and square it

18x

Half=9

Square half=(9)^2

=81

Add 81 to both sides

x^2 + 18x = 8

x^2 + 18x + 81 = 8 + 81

x^2 + 18x + 81 = 89

(x+9)^2 = 89

Check:

(x+9)(x+9)=89

x^2 + 9x + 9x + 81=89

x^2 + 18x +81 =89

2) (x+9)^2 = 89

√(x+9)^2 = √89

x+9=√89

x=√89 - 9

It can be rewritten as

x= -9 ± √89

(Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Answer:

c=13.42

Step-by-step explanation:

[tex]A^2+B^2=C^2\\6^2+14^2=C^2\\C^2=144+36\\C^2=180\\\sqrt{c^2}=\sqrt{180} \\c=13.42[/tex]

Answer:

x = 19

Step-by-step explanation:

The angles of a triangle add to 180

U and S are equal since they are the base angles  and UT and ST are equal

S + T + U = 180

x + 26 + 90 + x+26 = 180

Combine like terms

2x +142 = 180

Subtract 142 from each side

2x = 38

Divide each side by 2

2x/2 = 38/2

x = 19

Answer:

19

Step-by-step explanation:

x+26+x+26+90 = 180

2x + 52 = 90

2x = 38

x = 19

Answer:

18x^3+1

Step-by-step explanation:

since g(x)=√2x^3 and f(x)=9x^2+1 then

f(g(x))= 9(g(x))^2 +1 = 9(√2x^3)^2 +1 = 18x^3+1

this represents the amount of money Sonia earns baking loaves in x hours

The equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex], and it represents the amount of money Sonia makes when she bakes for x hours

The functions are given as:

[tex]f(x) = 9x^2 + 1[/tex]

[tex]g(x) = \sqrt{2x^3}[/tex]

Recall that:

[tex]f(x) = 9x^2 + 1[/tex]

Substitute g(x) for x

[tex]f(g(x)) = 9(g(x))^2 + 1[/tex]

Substitute [tex]g(x) = \sqrt{2x^3}[/tex]

[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Hence, the equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

Answer:

7

Step-by-step explanation:

the median is the middle value of the list. first off, write the list of numbers in ascending order (small to big)

3, 4, 4, 5, 7, 7, 8, 10, 10, 10

since there are 10 values, there are two middle numbers which are 7 and 7. since they are both 7, the median is 7

Answer:

The regular bottle holds 9 fl oz less

Step-by-step explanation:

Given

Family Size =  12 fl oz

Required

Determine the size held less by the regular bottle

From the question, we have that the regular bottle holds 75% less;

[tex]Regular\ Size = 75\% * Family\ Size[/tex]

Substitute 12 fl oz for Family Size

[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]

Convert percentage to fraction

[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]

[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]

[tex]Regular\ Size = 9\ fl\ oz[/tex]

Hence, the regular bottle holds 9 fl oz less

Answer:

D(-2,5;1); C(-1,1); E(0.5,3).

Step-by-step explanation:

Imagine that there is a line AB, it is divided into 4 equal parts. If there are 4 parts, There are 4+1=5 points. That's obvious that if parts are equal , the third point is on the middle of the line AB, suppose it is the point C

xc= (xa+xb)/2

xc=( -4+2)/2= -1

yc= (-3+5)/2=1

(-1,1)

There are to unknown points D (between A and C), and E (between C and B). D is on the middle of AC .

Xd= (-4-1)/2=-2.5

yd= (-3+1)/2=-1

(-2,5;1)

E is on the middle of CB

xe= (-1+2)/2= 0.5

ye=(1+5)/2=3

(0.5, 3)

Hey there! I'm happy to help!

Let's write this equation out.

2/3+1/3x=2x

We want to get all of the variables on the left side and all the numbers on the right side so we can see what number x is equal to. First, Let's subtract 2/x from both sides.

2/3+1/3x-2x=0

We subtract 2/3 from both sides.

1/3x-2x=-2/3

We combine our x values.

-5/3x=-2/3

We divide both sides by -5/3.

x=-5

Have a wonderful day and keep on learning! :D

Answer:

Let's call the length of the field "l", and the width of the field "w".

If the area of the field is 72 square meters, then we have:

l x w = 72

And if the length is 6 meters longer than the width, we have:

l = w+6

So looking at the first equation (l x w = 72), we can substitute the l for a w+6.

And we obtain:

(w+6) x (w) = 72

Which simplifies to w^2 + 6w = 72.

This quadratic equation is pretty easy to solve, you just need to factor it.

w^2 + 6w - 72 = 0

(w-6)(w+12)

This leaves the roots of the  quadratic equation to be 6 and -12, but in this case, a width of -12 wouldn't make sense.

So, the width of the rectangular field is 6, and the length of the field is 12.

Let me know if this helps!

Answer:

we assume one side is x and other side must be x+6 and when we multiple it together we can find x²+6x =72

Step-by-step explanation:

one side is 6 and. other is 12 so the lenght= 12 the width=6

Answer:

B 2x - 31 = -2x - 31 have exactly one solution

Step-by-step explanation:

Which of the following equations have exactly one solution?

Choose all answers that apply:

A 2x - 31 = 2x - 31

B 2x - 31 = -2x - 31

C 2x + 31 = 2x - 31

D 2x - 2 = 2x - 31

A. 2x - 31 = 2x - 31

2x-31=2x-31

Collect like terms

2x-2x= -31+31

0=0

Infinite number of solutions

B 2x - 31 = -2x - 31

2x - 31 = -2x - 31

Collect like terms

2x+2x=-31+31

4x=0

x=0

One solution

C 2x + 31 = 2x - 31

2x + 31 = 2x - 31

Collect like terms

2x-2x= -31-31

0= -62

No solution

D 2x - 2 = 2x - 31

2x - 2 = 2x - 31

Collect like terms

2x-2x= -31+2

0= -29

No solution

Answer:

please send the whole question.

actually the value of f(x) is missing

Answer:

C

Step-by-step explanation:

The end of a slinky is moved vertically up and down to simulate a wave.

Answer:

Step-by-step explanation:

[tex]\frac{9}{11}=0 .818181....[/tex]

     __  

= 0.81

Answer:

The correct option is;

D) Jan. 1

Step-by-step explanation:

The given information are;

The date at which drinking a glass of cola a day of cola began = Dec 3

The days in which to drink cols = Every day of the week except Saturday and Sunday

The number of glasses of drinking cola = 22

In the fires week, number of days in which to drink cola = Tuesday, Wednesday, Thursday, and Friday which is 4 days

On the week commencing Dec 9, 5 glasses drank

On the week commencing Dec 16, 5 glasses drank

On the week commencing Dec 23, 5 glasses drank

On the week commencing Dec 30, 3 glasses drank

Therefore on the week commencing Dec 30, cola was drank on the 30th, 31st and the 22nd glass was drank on Jan. 1

The correct option is Jan. 1.

Answer:

8, 19

Step-by-step explanation:

let group 1 have x students and group 2 have y students

x + y = 27

but group 2 has 2x + 3 students

the sum of students from both groups is 27

x + 2x + 3 = 27

3x + 3 = 27

3x = 24

x = 8

y = 2x + 3

y = 19

Answer:

Amount after 8 month (A) = $3775 (Approx)

Step-by-step explanation:

Given:

Amount invested (P) = $3,700

Rate of interest (r) = 3% = 0.03 / 12 = 0.0025 monthly

Number of month (n) = 8 month

Find:

Amount after 8 month (A)

Computation:

[tex]A=P(1+r)^n\\\\ A=3700(1+0.0025)^8\\\\A=3700(1.02017588)\\\\ A = 3774.650676[/tex]

Amount after 8 month (A) = $3775 (Approx)

Answer:

See below

Step-by-step explanation:

2^(10)= 2x...x2 how many times  =  10 times 2

15^(57)= 15x...x15 how many times  = 57 times 15

(-4)x...x(-4) 7 times =  (-4)^(7)

(1.5)x...x(1.5) 12 times = (1.5)^(12)

Answer:

m=-2 c=3

Step-by-step explanation:

y=mx+c

rearrange

-mx-c+y=0

original

y=2x-3

Answer:

[tex]9\ days[/tex]

Step-by-step explanation:

[tex]We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\[/tex]

[tex]Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ \frac{1}{n}th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.[/tex]

[tex]Here,\\In\ 1\ day,\\A\ would\ cover\ \frac{1}{15}th\ of\ the\ work.\\B\ would\ cover\ \frac{1}{12}th\ of\ the\ work.\\C\ would\ cover\ \frac{1}{20}th\ of\ the\ work.[/tex]

[tex]Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*\frac{1}{5}=\frac{2}{5}[/tex]

[tex]Hence,\\The\ portion\ of\ the\ total\ work\ left=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\\So,\\Since\ A\ has\ to\ complete\ \frac{3}{5}th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ \frac{3}{5}th\ of\ the\ entire\ work=15*\frac{3}{5}=9\ days[/tex]

Answer:

9 days

Step-by-step explanation:

A does in 15days, so A in 1day does 1/15part

B does in 12days, so B in 1day does 1/12part

C does in 20days, so C in 1day does 1/20part

So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.

Now A in 1/15 part takes 1day

So, in 3/5 part 15×3/5 = 9 days.

Answer:

9

Step-by-step explanation:

When given two points (x₁, y₁) and (x₂, y₂) on a plane, the Formula for the distance between the points is calculated as:

D= √(x₂ - x₁)² +(y₂ - y₁)²

In the question, we are given Point P is located at (2,-3), and point Q is located at (-4,4).

P(2, -3) , Q(-4, 4)

D = √(-4 - 2)² +(4 -(-3))²

D = √(-6)² + (7)²

D =√36 + 49

D = √85

D = 9.2195444573

Approximately to the nearest whole number, the distance between points P and Q is 9

Answer:

A

Step-by-step explanation:

The solution to a system of equations is the point of intersection of the 2 lines.

The lines intersect at (6, 9 ) ← solution

Answer:

A(6, 9)

Step-by-step explanation:

The intersecting points of the two lines gives the solution of the equation.

Answer:

58

Step-by-step explanation:

Hello, let's note the two digits a and b. the first number 'ab' can be written as 10a +b. For instance if this is 24 it can be written 20 + 4.

If the digits are interchanged the number become 'ba' so 10b + a

We can say that 10a + b + 10b + a = 143

11(a+b)=143

We divide by 13 both sides and we take

a+b = 143/11 = 13

and we know that the digits differ by 3 so b = a + 3

then a + b = a + 3 + a = 2a + 3 = 13

so 2a = 10 and then a = 5

Finally, b = 5+3=8 so the number is 58.

And we can verify that 58 + 85 = 143.

Thanks

Answer:

❍ According to Question now,

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

➥ x = 5

Therefore,

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

Answer:

Domain : any real number

Range : y ≥0

Step-by-step explanation:

The domain is the values that x can be

X can be any real number

The range is the values the y can be

Y can be zero or any positive value since y = x^2

Domain : any real number

Range : y ≥0

Answer:

[tex]\boxed{\sf Option \ A}[/tex]

Step-by-step explanation:

[tex]y=x^2[/tex]

[tex]\sf The \ domain \ of \ a \ function \ is \ all \ possible \ values \ for \ x.[/tex]

[tex]\sf There \ are \ no \ restrictions \ on \ the \ value \ of \ x.[/tex]

[tex]\sf The \ domain \ is \ all \ real \ numbers.[/tex]

[tex]\sf The \ range \ of \ a \ function \ is \ all \ possible \ values \ for \ y.[/tex]

[tex]\sf When \ a \ number \ is \ squared \ the \ result \ is \ always \ greater \ than \ or \ equal \ to \ 0.[/tex]

[tex]\sf The \ range \ is \ \{y:y\geq 0\}[/tex]

Answer:

The graph will shift 9 units to the right

Sorry about my hand writing

Answer: It moves 9 units to the right

Step-by-step explanation:

It moves 9 units to the right is because if it's inside parentheses it moves right/left instead of up/down. I also talked to my Algebra Teacher about it and got it right in the final test.

Answer:

2 x^2 sqrt(13)

Step-by-step explanation:

sqrt( 52x^4)

sqrt( 4*13 * x^2 * x^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt( 4)*sqrt(13) *sqrt( x^2) *sqrt( x^2)

2 sqrt(13) x*x

2 x^2 sqrt(13)

52|2

26|2

13|13

1

[tex]\sqrt{52x^4}=\sqrt{2^2\cdot13\cdot(x^2)^2}=2x^2\sqrt{13}[/tex]

the product of -9/17 and it's reciprocal will be 1

Answer:

63/8

Step-by-step explanation:

3 1/2 = 7/2

4 1/3 = 13/3

[tex] \frac{ \frac{7}{2} + 7 }{ \frac{13}{3} - 3} [/tex]

[tex] = \frac{ \frac{21}{7} }{ \frac{4}{3} } [/tex]

[tex] = \frac{63}{8} [/tex]

Answer:

x = 5

Step-by-step explanation:

The measure of an arc equals the measure of the central angle that intercepts it.

The measure of an arc intercepted by a diameter is 180 deg.

m(arc)EH = 180

m(arc)EF + m(arc)FG + m(arc)GH = m(arc)EH

10x + 8 + 67 + 11x = 180

21x + 75 = 180

21x = 105

x = 5

Answer:

The number is n-0.75

Step-by-step explanation:

Here in this question, we are interested in giving a number which is 75% of 1 less than a number n.

The first thing we do here is to calculate the value of 75% of 1.

That would be;

75/100 * 1 = 0.75

So this value less than n will be;

n- 0.75

Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)

Answer:

C) 6x³ - 24x² + 9x + 30

Step-by-step explanation:

(3x - 6)(2x² - 4x - 5)

3x • 2x² = 6x³

3x • -4x = -12x²

3x • -5 = -15x

-6 • 2x² = -12x²

-6 • -4x = 24x

-6 • -5 = 30

Combine terms.

6x³ - 12x² - 15x - 12x² + 24x + 30

Combine like terms.

6x³ - 24x² + 9x + 30

Learn with another example:

https://brainly.com/question/28001380