Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write a system of linear inequalities to represent this situation.

(I did not mean to select one)

Answer:

y = -3/2 x.

Step-by-step explanation:

y = kx where k is a constant.

6 = -4k

k = 6/-4 =  -3/2

So the equation is y = -3/2 x.

Answer:

  yes

Step-by-step explanation:

The ratio between the present value and the future value will be the same for any present or future date, provided that the discount/interest rate is the same in each case.

Alternative cash flows projected to the same date will have the same ratio, regardless of the chosen date — again, provided that the discount/interest rate is the same in each case.

Answer:

x = 3

Step-by-step explanation:

[tex]\\4x^2-2x=30\\\\x=3\\4(3)^2-2(3)=30\\4(9) - 6 =30\\36 - 6 = 30\\30 = 30 \\\\x=4\\4(4)^2-2(4)=30\\4(16) - 8 =30\\64 - 8 = 30\\56\neq 30[/tex]

56  is not equal to 30

Answer:

20/13

Step-by-step explanation:

(12/13)/(3/5)=

(12/13)(5/3)=

20/13

so the right ans is of option C

Answer:

36

Step-by-step explanation:

This questions tests for the fundamentals of counting.

Let's say event [tex]x_i[/tex] can be done in X ways and event [tex]y_i[/tex] can be done in Y ways, therefore the total number of ways [tex]x_i[/tex] and [tex]y_i[/tex] can be done is given as [tex]xy[/tex].

Applying this counting principle in our case, the total different sandwiches is obtained as the product of the individual sandwich types.

[tex]Total=s\times m\times b\\=3\times 4 \times 3\\=36[/tex]

36 different sandwiches can be made.

Answer:81

Step-by-step explanation:

3x3x3x3

Answer:81

Step-by-step explanation:

3.3.3.3=81

Answer:

Column 1:

Positive infinity

Negative infinity

Column 2:

Negative infinity

Positive infinity

Answer:

3x + 3y

Step-by-step explanation:

X + 2X = 3X

Y + 2Y = 3Y

In this expression, we can combine the like terms to simplify it.

To simplify the expression x + 2x + y + 2y, we can combine the like terms. Like terms are terms that have the same variables raised to the same power. In this case, the terms 2x and x are like terms because they both have the variable x raised to the power of 1. Similarly, the terms 2y and y are like terms because they both have the variable y raised to the power of 1.

So, when we combine the like terms, the expression becomes 3x + 3y.

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Answer:

20+4+0.02

Step-by-step explanation:

The height of a puffin in expanded form is [tex]\(2 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2}\) cm[/tex].

To write the height of a puffin, which is 24.02 cm, in expanded form, we need to express each digit as a product of the digit and its corresponding power of 10. Starting with the leftmost digit:

- The first digit is 2, and it is in the tens place, so it is [tex]\(2 \times 10^1\)[/tex].

- The second digit is 4, and it is in the ones place, so it is [tex]\(4 \times 10^0\)[/tex] (since any number to the power of 0 is 1).

- The third digit is 0, and it is in the tenths place, so it is [tex]\(0 \times 10^{-1}\)[/tex]. Since it is multiplied by 0, this term contributes nothing to the total and can be omitted.

- The fourth digit is 2, and it is in the hundredths place, so it is [tex]\(2 \times 10^{-2}\)[/tex].

Putting it all together, we get the expanded form as:

[tex]\(2 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2}\) cm.[/tex]

Answer:

option 3

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex], that is

[tex]\frac{20}{sin30}[/tex] = [tex]\frac{CA}{sin45}[/tex] ( cross- multiply )

CA × sin30° = 20 × sin45° ( divide both sides by sin30° )

CA = [tex]\frac{20sin45}{sin30}[/tex] → (3)

Answer:

Area of trapezoid = 32√3

Step-by-step explanation:

Using Pythagoras theorem

8² = (4√3)² + x²

64 = 48 + x²

x² = 64 - 48

x² = 16

x = √16

x = 4

Area of trapezoid = ½(a + b) h

Where a = 10 - 4 = 6

b = 10

h = 4√3

Area of trapezoid = ½(6 + 10) × 4√3

= ½ × 16 × 4√3

= 8 × 4√3

= 32√3

h = -16t^2 + 64t

When the ball reaches the ground, h will equal zero.

0 = -16t^2 + 64t

16t^2 = 64t

16t = 64

t = 4 seconds

Answer:

the first answer the other person put is the correct one

Step-by-step explanation:

just Dubble checked it

Answer:

No

Step-by-step explanation:

Because in a function for every one x there is one y.

Answer:

YES.

Step-by-step explanation:

f(x) = 3x^2.

This is a parabola which opens upwards ( roughly U shaped) so it will pass the vertical line test and is a function.

Answer:

17 nights.

Step-by-step explanation:

The total length of the scarf that should be knitting = 34 cm

Sarah has already knit 17 centimeters of a scarf.

So, the remaining = 34 - 17 = 17 cm

Sarah can knit 1 centimeter each night.

So, the number of nights will Sarah have to spend knitting = 17/1 = 17 nights.

Step-by-step explanation:

Let ABCD be a rhombus. So, AC (AC = 14 cm) and BD (BD=48 cm) will be its diagonals. Let us assume that diagonals are intersecting at point O.

Since, diagonals of a rhombus are perpendicular bisector.

[tex] \because \: OA = \frac{1}{2} \times AC \\ \\

\therefore \: OA = \frac{1}{2} \times 14

\\ \\ \huge \red{ \boxed{\therefore \: OA = 7 \: cm}} \\ \\ \because \: OB = \frac{1}{2} \times BD \\ \\ \therefore \: OB = \frac{1}{2} \times 48 \\ \\ \huge \red{ \boxed{\therefore \: OB = 24 \: cm}} \\ \\ In \: \triangle OAB, \: \: \angle AOB=90° \\ \therefore \: by \: Pythagoras \: Theorem \\ AB= \sqrt{OA^2 +OB^2 } \\ = \sqrt{7^2 +24^2 } \\ = \sqrt{49+576 } \\ = \sqrt{625 } \\ \huge \orange{ \boxed{\ \therefore \:AB= 25 \: cm.}}[/tex]

Hence, length of a side (or all) is 25 cm.

Final answer:

To find the length of a side of a rhombus with diagonals measuring 14 cm and 48 cm, one can use Pythagoras' theorem on the right-angled triangles formed by half the diagonals. The length of the side of the rhombus is calculated to be 25 cm.

Explanation:

The question involves finding the length of a side of a rhombus given the lengths of its diagonals. According to the properties of a rhombus, the diagonals bisect each other at right angles. In this case, the diagonals are 14 cm and 48 cm long. Therefore, we have two right-angled triangles formed by the diagonals, with each triangle having legs of 7 cm (half of 14 cm) and 24 cm (half of 48 cm).

To find the length of a side of the rhombus, we can use Pythagoras' theorem, which states that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

Applying Pythagoras' theorem:

Let the length of each side of the rhombus be s.

Use the right-angled triangle with sides 7 cm and 24 cm to solve for s (hypotenuse).

Calculate s² = 7² + 24².

So, s² = 49 + 576.

s² = 625.

Therefore, s = [tex]\sqrt{625}[/tex] = 25 cm.

Hence, the length of a side of the rhombus is 25 cm.

Answer:

1/5

Step-by-step explanation:

Answer:

[tex]\frac{1}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}[/tex]÷[tex]\frac{3}{1}[/tex]

[tex]\frac{1}{5}[/tex]·[tex]\frac{1}{3}[/tex]

[tex]\frac{1}{15}[/tex]

24h=d.

if you multiply 24 by the number of hours than you will get the distance.

if you traveled for 2hours than you would have traveled 48miles because if you multiply 24 by 2 you get 48.

In the equation 24 is distance traveled in 1 hour.

Answer:

24h=d

Step-by-step explanation:

0=0

2=48

4=96

7=168

its just multiples of 24 :)

Answer:

-c +2

Step-by-step explanation:

-1(c-2)

Distribute

-1*c -1*(-2)

-c +2

Step-by-step explanation:

Let the measure of required angle be x degree

[tex] \therefore \tan \: x = \frac{33}{56} \\ \\ \therefore \tan \: x = 0.589285714 \\ \\ \therefore \: x = {\tan}^{ - 1} (0.589285714) \\ \\ \therefore \: x = {\tan}^{ - 1} ( \tan \: 30.510237394 \degree) \\ \\ \huge \red{ \boxed{\therefore \: x = 31\degree}}[/tex]

Thus, first option is the correct answer.

Answer:

The probability that he chooses a yellow ball is 5/14. If he removes all the orange balls, the probability that he will choose a red ball is 2/10.

Step-by-step explanation:

Simple logic.

Answer:

Step-by-step explanation:

Let r and m represent the registration fee and the monthly fee, respectively. We are told that the charges are ...

  370 = r + 4m

  530 = r + 6m

This is your system of equations.

__

Subtract the first equation from the second to start the solution.

  (530) -(370) = (r +6m) -(r +4m)

  160 = 2m . . . . . . simplify

  80 = m . . . . . . . . divide by 2

Using this value in the first equation, we find ...

  370 = r + 4(80)

  50 = r . . . . . . . . . . . . subtract 320

The registration fee is $50; the monthly fee is $80.

Answer:

8a -4b

Step-by-step explanation:

3a+2b+5a-6b

Combine like terms

3a+5a = 8a

2b-6b = -4b

Add them back together

8a -4b

Answer:

[tex]8a - 4b[/tex]

Step-by-step explanation:

Step 1:  Combine like terms

[tex]3a + 2b + 5a - 6b[/tex]

[tex](3a + 5a) + (2b - 6b)[/tex]

[tex]8a - 4b[/tex]

Answer:  [tex]8a - 4b[/tex]

There is 20% error in zookeeper's calculations.

Step-by-step explanation:

Given,

Approx weight of newborn lion = Approx value =2.8 pounds

Exact weight of newborn lion = Exact value = 3.5 pounds

Percent error = [tex]\frac{|approx-exact|}{exact}*100[/tex]

Percent error = [tex]\frac{|2.8-3.5|}{3.5}*100\\[/tex]

Percent error = [tex]\frac{|-0.7|}{3.5}*100[/tex]

Percent error = [tex]\frac{70}{3.5}[/tex]

Percent error = 20%

There is 20% error in zookeeper's calculations.

Final answer:

To find the zookeeper's percent error, subtract the predicted weight from the actual weight to find the absolute error, divide by the actual weight, multiply by 100, and round to the nearest percent. The percent error in predicting the weight of the newborn lion is 20 percent.

Explanation:

To calculate the zookeeper's percent error in predicting the weight of a newborn lion, we follow these steps:

Round to the nearest percent.

The zookeeper predicted the weight would be 2.8 pounds, but the actual weight was 3.5 pounds. So the absolute error is:

|Predicted Weight - Actual Weight| = |2.8 pounds - 3.5 pounds| = 0.7 pounds

Then, divide the absolute error by the actual weight:

0.7 pounds / 3.5 pounds = 0.2

Multiply by 100 to convert to a percentage:

0.2 × 100 = 20%

Since we round to the nearest percent, the zookeeper's percent error is 20 percent.

Answer:

$215.73

Step-by-step explanation:

take $7.99 and multiply it by 27 to get $215.73

following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Step-by-step explanation:

Here we have , following expression to evaluate . 1/3(9 - 18x) + 1/4(8x - 12 or , [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] :

⇒ [tex]\frac{1}{3}(9 - 18x) + \frac{1}{4}(8x - 12)[/tex]

⇒ [tex]\frac{1(4)}{3(4)}(9 - 18x) + \frac{1(3)}{4(3)}(8x - 12)[/tex]

⇒ [tex]\frac{(9 - 18x)(4)}{3(4)} + \frac{(8x - 12)(3)}{4(3)}[/tex]           { Making denominator of both terms same ! }

⇒ [tex]\frac{(9 - 18x)(4)+(8x - 12)(3)}{12}[/tex]

⇒ [tex]\frac{9(4) - 18(4)x+8(3)x - 12(3)}{12}[/tex]

⇒ [tex]\frac{36- 72x+24x - 36}{12}[/tex]

⇒ [tex]\frac{ -48x}{12}[/tex]           { Simplifying even further }

⇒ [tex]-4x[/tex]

Therefore , following expression  [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to  [tex]-4x[/tex] . Kindly match with your options!

Final answer:

The equivalent expression for 1/3(9 - 18x) + 1/4(8x - 12) is -4x.

Explanation:

The given expression is 1/3(9 - 18x) + 1/4(8x - 12).

We need to distribute the fractions across the terms inside the parentheses:

Therefore, the equivalent expression is -4x.

Answer:

2

Step-by-step explanation:

8+6+4+2+1 =21

Total 21 dots/observations

Centre at 11th dot which corresponds to 2

Number of Laps Around a Track. A dot plot going from 1 to 5, 1 has 8 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot,  the center is 2.

The location is sometimes alluded to as the data collection's "core." The two metrics that are most frequently used to identify the "center" of both the data are the mean (average) and the median. To find the weighted mean of 50 people, add up all 50 weights once more and divide by 50.

Order the data and locate the number that divides the information into two equal portions to determine the median weight of both the 50 individuals. Because it is unaffected by the specific numerical values of the outliers, the median is typically a better indicator of the center if there are extreme values or outliers. The most popular way to measure the center is with the mean.

8+6+4+2+1 =21

21 dots/observations

Centre at 11th dot which corresponds to 2

Therefore, the center is 2.

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Answer:

Vertical angles

Step-by-step explanation:

Two non-adjacent angles formed by the intersection of two lines are called vertical angles.

C. Is your answer

y=−52+8x