What is the unit price of 12 gallons of gasoline that costs $39.48?

Step-by-step explanation:

Go and learn numbers , it will be 1 2 3 4 5

Answer:

2nd statement

Step-by-step explanation:

it is

The equation of the function in the form y=mx+b is y = 110x-2020

The standard equation of a line is expressed as:

y = mx + b

where:

m is the rate of change or slope

b is the intecept

Using the coordinate points

Determine the slope

m = 550/5

m = 110

For the intercept

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

Hence the equation of the function in the form y=mx+b is y = 110x-2020

Learn more on rate of change here: https://brainly.com/question/8728504

The area of the garden enclosed by the fencing is

A(x, y) = xy

and is constrained by its perimeter,

P = x + 2y = 200

Solve for x in the constraint equation:

x = 200 - 2y

Substitute this into the area function to get a function of one variable:

A(200 - 2y, y) = A(y) = 200y - 2y²

Differentiate A with respect to y :

dA/dy = 200 - 4y

Find the critical points of A :

200 - 4y = 0   ⇒   4y = 200   ⇒   y = 50

Compute the second derivative of A:

d²A/dy² = -4 < 0

Since the second derivative is always negative, the critical point is a local maximum.

If y = 50, then x = 200 - 2•50 = 100. So the farmer can maximize the garden area by building a (100 ft) × (50 ft) fence.

Answer:

[tex]\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10[/tex]

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                           [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                 [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                     [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                   [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                               [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: https://brainly.com/question/26401241

Learn more about calculus: https://brainly.com/question/20197752

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

No there is no solution

Step-by-step explanation:

X cannot be found no matter how you try to solve the simultaneous equation so therefore y can also not be found.

Answer:

i)  Using log law:  [tex]\log_aa=1[/tex]

[tex]\implies \log_55+1=1+1=2[/tex]

ii) [tex]\log \left(\dfrac{15}{8}\right)+4 \log 2-\log 3[/tex]

Using log law [tex]a \log b=\log b^a[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 2^4-\log 3[/tex]

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 16-\log 3[/tex]

Using log law [tex]\log a-\log b=\log (\frac{a}{b})[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log\left(\dfrac{16}{3}\right)[/tex]

Using log law  [tex]\log a+\log b=\log(ab)[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\cdot \dfrac{16}{3}\right)[/tex]

[tex]\implies \log 10[/tex]

Using log law:  [tex]\log_aa=1[/tex]

[tex]\implies \log_{10} 10=1[/tex]

iii) Take log of base 10:

[tex]\log_{10}(\sqrt{8.357}\times0.895^2)[/tex]

[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]

Log tables

The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.

The mantissa is found using the log tables and is always prefixed by a decimal point.

The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number

Use the log tables to find [tex]\log_{10}(8.357)[/tex]:

8.357 = 8.357 × 10⁰

⇒ characteristic = 0

log table:  row 83, column 5 ⇒ mantissa 9217

(as there is a 4th digit) Mean difference 7 = 4

mantissa + mean difference = 9217 + 4 = 9221 ⇒ 0.9221

characteristic + mantissa = 0 + 0.9221 = 0.9221

Therefore, [tex]\log_{10}(8.357)=0.9221[/tex]

Use the log tables to find [tex]\log_{10}(0.895)[/tex]:

[tex]0.895 = 8.95\times 10^{-1}[/tex]

⇒ characteristic = -1

log table: row 89, column 5 ⇒ mantissa 9518⇒ 0.9518

characteristic  + mantissa = -1 + 0.9518= -0.0482

Therefore, [tex]\log_{10}(0.895)=-0.0482[/tex]

Therefore,

[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]

[tex]\implies \dfrac12 \cdot 0.9221+2\cdot-0.0482[/tex]

[tex]\implies 0.36465[/tex]

Therefore,

[tex]\log_{10}(\sqrt{8.357}\times0.895^2)=0.36465[/tex]

Using [tex]\log_ab=c \implies a^c=b[/tex]

[tex]\implies \sqrt{8.357}\times0.895^2=10^{0.36465}[/tex]

[tex]\implies \sqrt{8.357}\times0.895^2=2.3155[/tex]

Answer:

Step-by-step explanation:

Given two points, the equation for the line can be found by starting with determining the slope. Then the point-slope form can be used to find the equation. That form can be rearranged to give the slope-intercept form (or any other form you may desire.)

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -(-4))/(-1 -7) = 7/-8 = -7/8

Then the point-slope form using the first point is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y +4 = -7/8(x -7) . . . . . line with slope -7/8 through (7, -4)

__

Eliminating parentheses, and subtracting 4 gives the slope-intercept equation:

  y +4 = -7/8x +49/8 . . . eliminate parentheses

  y = -7/8x +17/8 . . . . . subtract 4; slope-intercept equation

_____

The attached graph shows both forms of the equation draw the same line.

the answer is 15!

Hope this helps!

¤ Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

Have a great day !!

Answer:

if this is high school i cant do it

Answer:

d) 4w - 2

Step-by-step explanation:

(7w-5) and (-3w+3)

(7w-5) + (-3w+3)

1(7w-5) + 1(-3w+3)

7w - 5 - 3w + 3

Combine like terms:

7w - 5 - 3w + 3

7w - 3w - 5 + 3

4w - 2

Hope this helps!

Answer:

Step-by-step explanation:

10+5=15 1/9 goes into 15 about twice so it goes to plus 1

so about without solving is 16 1/15

Answer:

It is 3

•°•°•°

Math is poop

Answer:

r = 3

Step-by-step explanation:

50 % =20 Learners

100%= x

x=100/50

=2

=2×20

=40 learners

was this helpful?

Answer: 4 year difference

Step-by-step explanation: 4 year difference

Answer:

12 oz bottle

Step-by-step explanation:

See attached image.

Step-by-step explanation:

hope you have got the answer in the attachment.

Answer:

There are 3 feet in a yard, so divide 34 by 3, which is 11 with a remainder of 1, the remainder 1 is the remaining foot, so 34 feet is 11 yards and 1 foot.

Step-by-step explanation:

answer:

67.5

Explanation:

Let the triangle be ΔABC and angles be ∠A,∠B,∠C

Now, we know that all the 3 angles of a triangle sum up to be 180° from the Triangle Sum Property.

:.∠A + ∠B + ∠C = 180

:.3x+3x+2x=180 [3:3:2]

:.8x = 180

:.x = 180/8

:.x = 22.5°

:.

/_A=3x=3(22.5)=67.5°

/_B=3x=3(22.5)=67.5°

/_C=2x=2(22.5)=45°

Hey there!

12: 1, 2, 3, 4, 6, & 12

30: 1, 2, 3, 5, 6, 10, 15, & 30

75: 1, 3, 5, 15, 25, & 75

LIKE TERMS: 1 and 3

GCF: 3

Therefore, your answer is: 3

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Since the variable type of writing utensil assumes labels and not numbers, it is classified as qualitative.

In this problem, the type of writing utensil has 4 labels: regular pencil, mechanical pencil, pen, whatever.

Hence, since the variable assumes labels and not numbers, it is classified as qualitative.

More can be learned about quantitative and qualitative variables at https://brainly.com/question/20598475

Answer:

1122.63ft

Step-by-step explanation:

Let, AB be the height of the monument, BC=789ft be the length of the monument ∠BAC=35.1° be the angle of elevation.

Now,

[tex]tanA=\frac{789ft}{AB} \\\\tan35.1=\frac{789ft}{AB} \\\\AB=\frac{789ft}{0.7028} \\\\AB=1122.63ft[/tex]

Hope this is correct.

Answer:

3/10

Step-by-step explanation:

There are 10 students

5 of them voted either Los Angeles or New York

That means ignore (screw) the other 5 people

If 2/10 students chose Los Angeles,

that is 2/5 because the others didn't choose those cities that are part of the equation (nobody asked about the other people)

So if 5 people chose two groups of cities, and two people chose one city, that meant 3 chose the other

3/10 (remember its out of all of them) Students Voted for New York

Hope this helps :)

-jp524