a) Model this situation with a linear system:
To rent a car, a person is charged a daily rate and a fee for each kilometre driven. When Chena
rented a car for 6 days and drove 320 km, the charge was $286.00. When she rented the same car
for 10 days and drove 900 km, the charge was $605.00.
b) Determine the daily rate and the fee for each kilometre driven.

Answer:

option 3 : (2x - 7 )

Step-by-step explanation:

ax + bx = x(a+ b)

a(x+ y) + b(x+y) = (x+y)(a+b)

[tex](3x - 8 ) ( 2x + 5) - (x + 1)(2x + 5)\\\\(2x+5)[ (3x - 8) - (x+1) ][/tex]      [ (2x + 5) is common is both terms ]

[tex](2x+ 5)(3x -8 -x + 1)\\\\(2x+ 5)(2x - 7)[/tex]

Therefore , the binomial is ( 2x - 7)

Answer:

33.89

Step-by-step explanation:

the side lengths are the distances between the corner points of the triangle.

P and Q have the same x value, and they therefore create a side parallel to the y-axis. and it is easy to find the length of this side : it is just the difference of the y values.

PQ = 6 - (-6) = 6 + 6 = 12

QR and RP are trickier.

we need Pythagoras to calculate the length of the direct connection between these points as the Hypotenuse of the right triangles with the differences in x and in y values as the other sides.

QR :

QR² = (-3 - 6)² + (-6 - -2)² = (-9)² + (-4)² = 81 + 16 = 97

QR = sqrt(97) ≈ 9.848857802

RP :

RP² = (6 - -3)² + (-2 - 6)² = 9² + (-8)² = 81 + 64 = 145

RP = sqrt(145) ≈ 12.04159458

the perimeter/circumference of the triangle is the sum of all 3 sides

= 12 + sqrt(97) + sqrt(145) ≈ 33.89

Answer:

Step-by-step explanation:

angle 2 is also 60 degree (being vertically opposite angles)

angle 3 is also 60 degree (being corresponding angles)

angle 4 is also 60 degree (being corresponding angles ) . sice angle 2 is 60 degree and relation between  angle 2 and 4 is corresponding angle , angle 4 will also be 60 degree.

Answer:

TH is an element on the sample space for first rolling a die and then tossing a coin. A coin has both heads and tails.

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

The elements can be any of the elements in the sample space.

It is the total number of possible outcomes from a given set.

We have,

The sample space for rolling a number cube and then tossing a coin consists of all possible outcomes from rolling the number cube and tossing the coin.

Each outcome is a pair consisting of a number from 1 to 6 (the possible outcome from rolling the number cube) and a head or tail (the possible outcome from tossing the coin).

Therefore, an element in the sample space can be represented as an ordered pair (n, h/t), where n is the number rolled on the number cube and h/t is the outcome of the coin toss (either head or tail).

So,

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

For example, (3, H), (6, T), (1, H), and (4, T) are all elements in the sample space.

Thus,

The sample space for rolling a number cube and then tossing a coin is:

{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}

Learn more about sample space here:

https://brainly.com/question/24273864

#SPJ7

A)

Replace the letters in the given equation with the corresponding values given in the problem:

A = 10,000 x 2.718^(0.05 x 2)

A = 11,051.59 , rounded to nearest dollar = $11,052

B)20,000 = 10000 x 2.718^(0.05 x t)

Divide both sides by 10,000:

2 = 2.718^(0.05 x t)

Apply exponent rules:

0.05tln(2.718) = 2

Solve for t:

t = ln(2) / 0.05ln(2.718)

t = 13.86 years, rounded to nearest year = 14 years.

Answer:

Step-by-step explanation:

Using [tex]A=Pe^{rt[/tex] as instructed, our equation looks like this:

[tex]A=10,000e^{(.05)(2)}[/tex] which simplifies a bit to

[tex]A=10,000e^{.1[/tex] which simplifies a bit more to

A = 10,000(1.10517) so

A = 11,051.71  Easy. Now onto the second part: solving for the number of years it takes for the investment to double. Setting A equal to 20,000 since 20,000 is 10,000 doubled:

[tex]20,000=10,000e^{.05t[/tex]  Begin by dividing both sides by 10,000 to get

[tex]2=e^{.05t[/tex] and take the natural log of both sides to get that exponent down out front, keeping in mind that the natural log will "undo" the e, leaving us with:

ln(2) = .05t and

t = 14 years (that's 13.8 rounded up to the nearest year)

Step-by-step explanation:

BE/BC=BD/BA

tHE TWO SIMILAR TRIANGLES ARE BED AND BC. tHE PROPORTION ABOVE REPRESENTS USE OF THE TWO SIMILAR TRIANGLES.

4/(4 + 10) = 5/(5+X) Cross Multiply

4(5+x) = 5(4+10)m

20 +4x=20 +50 subtract 20 from both sides

4x = 50 divide by 4

x =12.5

Answer:

Step-by-step explanation:

[tex]A) 5.3*10^{4}+4.7*10^{4}= (5.3 + 4.7)*10^{4}=10*10^{4}=10^{5}\\\\\\B) 3.7*10^{6} - 3.3*10^{6}=(3.7-3.3)*10^{6}=0.4*10^{6}=4.0*10^{-1}*10^{6}=4.0*10^{6-1}=4.0*10^{5}\\\\\\C) 4.8*10^{-3}+6.3^{-2}=4.8*10^{-2}*10^{-1}+6.3*10^{-2}\\\\=(4.8*10^{-1} +6.3)*10^{-2}\\\\=(0.48+6.3)*10^{-2}\\\\=6.78*10^{-2}\\\\\\D)6.6*10^{-5}-6.1*10^{-4}=6.6*10^{-1}*10^{-4}-6.1*10^{-4}\\\\=(6.6*10^{-1}-6.1)*10^{-4}\\\\=(0.66-6.1)*10^{-4}\\\\= (-5.44)*10^{-4}[/tex]

Answer:

D. - 3 ≤ x < 1

Step-by-step explanation:

The numerator cannot be the square root of a neg. no.

So, x + 3 ≥ 0 or x ≥ -3

The denominator cannot be a neg. no. or 0.

So, 1 - x > 0

1 > x or x < 1

So, altogether - 3 ≤ x < 1

Therefore, D is the correct answer.

HOPE IT MAY HELP YOU

PLEASE MARK AS BRAINLIST

Answer:

i think its A but im not sure its correct

Step-by-step explanation:

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4} +\frac{1}{6} +\frac{1}{3}[/tex]

4 = 2 × 2 × 1

6 = 2 × 3 × 1

3 = 3 × 1

GCF = 1

4 × 6 × 3 = 72

[tex]\frac{18}{72} +\frac{12}{72} +\frac{24}{72}[/tex]

[tex]\frac{18+12+24}{72}[/tex]

[tex]\frac{54}{72}[/tex]

54 = 2 × 3 × 3 × 3

72 = 2 × 2 × 2 × 3 × 3

GCF = 2 × 3 × 3

GCF = 18

[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{Looking for your LCD (Least Common Denominator) of each fraction}\downarrow\\\\\\\mathsf{\dfrac{1}{4}=\dfrac{3}{12}}\\\\\\\mathsf{\dfrac{1}{6}=\dfrac{2}{12}}\\\\\\\mathsf{\dfrac{1}{3}=\dfrac{4}{12}}\\\\\\\\\\\large\textsf{The LCD is \underline{12}}[/tex]

[tex]\mathsf{\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{3}}[/tex]

[tex]\mathsf{= \ \dfrac{1\times3}{4\times3}+\dfrac{1\times2}{6\times2}+\dfrac{1\times4}{3\times4}}[/tex]

[tex]\large\textsf{Solving for the numerators (TOP numbers)}\downarrow\\\\\mathsf{1\times3=\boxed{\bf 3}}\\\\\mathsf{1\times2=\boxed{\bf 2}}\\\\\mathsf{1\times4=\boxed{\bf 4}}[/tex]

[tex]\large\textsf{Solving for the denominators (BOTTOM numbers)}\downarrow\\\\\mathsf{4\times3=\boxed{\bf 12}}\\\\\mathsf{6\times2=\boxed{\bf 12}}\\\\\mathsf{3\times4=\boxed{\bf 12}}[/tex]

[tex]\mathsf{=\ \dfrac{3+2+4}{12}}[/tex]

[tex]\large\textsf{Solving for your numerator (TOP number) }\downarrow\\\\\\\mathsf{3+2+4}\\\\\mathsf{= 5+4}\\\\\mathsf{= \boxed{\large\textsf{\bf 9}}}[/tex]

[tex]\mathsf{=\ \dfrac{9}{12}}[/tex]

[tex]\mathsf{\dfrac{9\div3}{12\div3}}\\\\\\\\\mathsf{9\div3= \boxed{\large\textsf{\bf 3}}}\\\\\mathsf{12\div3=\boxed{\large\textsf{\bf 4}}}[/tex]

[tex]\mathsf{= \dfrac{3}{4}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\boxed{\mathsf{\bold{ \dfrac{9}{12}\ or\ \dfrac{3}{4}}\ either\ of\ those\ fractions\ should\ work\ because}}}}\\\boxed{\boxed{\large\textsf{they are equal to each other!}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

If that answer doesn't work, then try 29 without the percent sign.

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

Explanation:

We know with absolute certainty that the person ordered a hot drink, due to the "given".

This means we only focus on the values in the first row.

There are 5+48+22 = 75 hot drinks ordered. Of that total, 22 hot drinks are large.

The probability of getting a large drink, given it was a hot beverage, is 22/75 = 0.2933 approximately.

This converts to 29.33% and that rounds to 29%

Answer:

[tex]f(x) = 5x -11[/tex]  and  [tex]g(x) = \frac{x + 11}{5}[/tex]

Step-by-step explanation:

Required

The inverse pairs

Solving (a):

[tex]f(x) = 5x -11[/tex]    [tex]g(x) = \frac{x + 11}{5}[/tex]

Calculate the inverse of f(x)

[tex]f(x) = 5x -11[/tex]

Replace f(x) with y

[tex]y = 5x - 11[/tex]

Swap x and y

[tex]x = 5y - 11[/tex]

Solve for y

[tex]5y = x + 11[/tex]

[tex]y = \frac{x + 11}{5}[/tex]

So, we have:

[tex]g(x) = \frac{x + 11}{5}[/tex]

Hence, f(x) and g(x) in (a) are inverse functions

Others are not

Step-by-step explanation:

Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.

Answer:

Multiple of 3 from -3 to 15 are:-

3, 6, 9, 12 , 15

hope it is helpful to you ☺️

Answer:

13

Step-by-step explanation:

-2x + 6 = -20

Step 1 subtract 6 from both sides

6 - 6 cancels out

-20 - 6 = -26

We now have -2x = -26

Step 2 divide both sides by -2

-2x/-2 = x

-26/-2 = 13

We're left with x = 13

Answer: Choice E. 4/sqrt(7)

This is the same as writing [tex]\frac{4}{\sqrt{7}}[/tex]

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

Explanation:

0.75 = 3/4

Recall that cosine is the ratio of adjacent over hypotenuse.

That means if cos(theta) = 3/4, then the adjacent is 3 units and the hypotenuse is 4 units.

Through the pythagorean theorem, we would then find that

a^2+b^2 = c^2

a = sqrt(c^2 - b^2)

a = sqrt(4^2 - 3^2)

a = sqrt(7)

This is the opposite side of reference angle theta.

From here, we can say

csc(angle) = hypotenuse/opposite

csc(theta) = 4/sqrt(7)

which points to choice E as the final answer.

Answer:

The probability is 32/81

Step-by-step explanation:

We know that:

The probability that the team wins is p = 2/3

Then the probability of not winning is q = 1 - p = 1 - 2/3 = 1/3

The team plays 4 matches.

We want to find the probability that the team wins 1 more than half of the number of matches played.

So if there are 4 matches, the half is 2 matches

one more than half is then 3 matches.

Let's assume that the team wins the first 3 matches, and does not win the last match.

match one, the team wins with prob: P₁ = 2/3

match two, the team wins with prob: P₂ = 2/3

match three, the team wins with prob: P₃ = 2/3

match four, the team wins with prob: P₄ = 1/3

The joint probability is the product of all the individual probabilities:

P = (2/3)*(2/3)*(2/3)*(1/3)

Now we must also considerate the permutations, we have the cases:

the team does not win the fourth match

the team does not win the third match

the team does not win the second match

the team does not win the first match

So we have just four permutations, then the total probability is:

probability = 4*P = 4*(2/3)*(2/3)*(2/3)*(1/3) = 4*(8/81) = (32/81)

Answer:

0.075 metre

2000 mm

500 cm

0.001 gram

1.5 × 10-6 kilogram

86400 second

18000 second

Step-by-step explanation:

hope it helps

Answer:

a) 0.075 m

b) 2000 mm

c) 500 cm

d) ?

e) 0.0015 kg

f) 86400 seconds

g) 18000 seconds

Answer:

D i think

Step-by-step explanation:

its just a guess

Answer:

-18 =x

Step-by-step explanation:

-3/4 = x/24

Using cross products

-3*24 = 4*x

-72 = 4x

Divide each side by 4

-72/4 = 4x/4

-18 =x

Answer:

B. -18

Step-by-step explanation:

solve the proportion using cross multiplication

swap the side

divide both side by 4

B neither perpendicular nor parallel

Answer:

B

Step-by-step explanation:

B. neither perpendicular nor parallel

because, the line are not crossing nor are they aside from each other.

Answer:

this means she ate an average of 30 raisins each day

so she ate 30 on the third day

so the amount she ate each day is like this

1. 16

2. 23

3. 30

4. 37

5. 44

16 + 23 +30 +37 +44=150

Answer:

a. 30 b. 16

Step-by-step explanation:

n=number of days

a1= raisins she at on 1st day

d=increase per day

n(a1+an)/2

5(a1+a1+d(n-1))/2=150

5(2a1+4d)=300

d=7, 10a1+20(7)=300

a1+14=30

a1=16

a. a1+2d 16+14=30 b. 16

Answer:

(2w+2)(w+8) ≤ 100

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Draw the number line like in the picture.

Step-by-step explanation:

√5 is about 2.236, meaning it's kind of close to 2.25.

√7 is about 2.646, meaning it's very close to 2.625.

Responder:

m = 7; n = - 3

Explicação passo a passo:

Dada a equação:

m − 3n = 16m + 5n = −8

Resolvendo a equação:

m − 3n = 16 - - - (1)

m + 5n = - 8 - - - (2)

Subtraia 1 de 2

m - m - 3n - 5n = 16 - - 8

-3n - 5n = 16 + 8

-8n = 24

n = 24 / - 8

n = - 3

Coloque n = - 3 em (1)

m − 3n = 16

m - 3 (-3) = 16

m + 9 = 16

m = 16 - 9

m = 7

Answer:

8

Step-by-step explanation:

Answer:

[tex]{ \tt{GH =GI - HI }} \\ = 9 - 1 \\ GH = 8[/tex]