Help. The graph shows the system of equations below.
2x -3y = -6
y = - 1/3x -4

Answer:

so 1/3 must be subtracted from the sum of 1/4 and 1/6 to have an average of 1/12 of all the two fractions.

Step-by-step explanation:

let the fraction be x

(1/4 + 1/6)-x =  1/12

or, 10/24 - x = 1/12

or, 5/12-1/12 = x

so, x = 4/12 = 1/3

Split up the integral:

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]

For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get

[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]

and

[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]

Then

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]

Answer:

Step-by-step explanation:

Let the quadratic function be

y=a(x+4)²-1

∵(-7,8) lies on it.

8=a(-7+4)²-1

8+1=a(-3)²

9a=9

a=9/9=1

so quadratic function  is

f(x)=1(x+4)²-1

or

f(x)=x²+8x+16-1

so quadratic function is

f(x)=x²+8x+15

Step-by-step explanation:

At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.

Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.

Then that's your answer.

9514 1404 393

Answer:

  544 square units

Step-by-step explanation:

The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...

  A = 1/2bh . . . . area of a triangle with base b and height h

  A = LW . . . . . are of a rectangle of length L and width W

__

  SA = 2(1/2)(12)(8) + (10 +10 +12)(14)

  SA = 96 +448 = 544 . . . square units

Answer:

a) 3.19

b) 3.29

c) 96.81

Step-by-step explanation:

Question a:

Levere's: 10.63s

Ross: 10.98s

10.98 - 10.63 = 0.35s shorter than 10.98s, so:

0.35*100%/10.98 = 3.19% shorter.

Question b:

35s longer than 10.63s, so:

0.35*100%/10.63 = 3.29% longer.

Question c:

3.19% shorter, so 100 - 3.19 = 96.81% of Ross.

9514 1404 393

Answer:

Step-by-step explanation:

"No more than 21" means "less than or equal to 21." The total of flowers Lydia has listed is ...

  8 + 2 + t + 3 + p = 13 +p +t

Lydia wants this less than or equal to 21, so the appropriate inequality is ...

  13 +p +t ≤ 21

__

Subtracting 13 from both sides gives us a relation that helps us better see the possible values of p and t.

  p +t ≤ 8

Then suitable numbers of peonies and tulips will numbers that total 8 or less. Of the choices listed, ones that match that requirement are ...

  2 tulips and 3 peonies

  5 tulips and 3 peonies

Answer:

10

Step-by-step explanation:

Answer:

Two tailed test

Test statistic = 3.20

Pvalue = 0.001

H1 : p ≠ 0.91

Step-by-step explanation:

Given :

Test of p=0.91 vs p≠0.91

The use if not equal to ≠ sign in the null means we have a tow tailed test, which means a difference exists in the proportion which could be lesser or greater than the stated population proportion.

The test statistic :

This is the Z value from the table given = 3.20

The Pvalue = 0.001

Since Pvalue < α ;Reject H0

So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.

22 hours x $8.50 = $187

Subtract that from the cost of the computer:

899-187 = $712

She needs $712 more.

Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75

Divide what she needs by amount per shift:

712 / 46.75 = 15.22 shifts

She needs to work 16 more shifts.

Answer:

Induction produces an electromagnetic field in a coil to transfer energy to a work piece to be heated. When the electrical current passes along a wire, a magnetic field is produced around that wire

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

How many Senior tickets sold ?

0

Find how many adult tickets were sold than child tickets ?

5

Step-by-step explanation:

Answer:

:];];]

u know

meeeeeeeeeeeeeeeeeeeeeeeeeeeee

brainlistttt

cutie

k?

Step-by-step explanation:

Answer:

1,032,564 tickets

Step-by-step explanation:

Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:

86,047(12)

= 1,032,564

So, if every game sells out, 1,032,564 tickets will be sold.

Answer:

By multiplying 88.92 from 21.33 we get 1896.6636.

Answer:

1896.6636

Step-by-step explanation:

Hope this helps

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Take note of the inequality symbol. It is < (not ≤), so the "equal to" case is not included. That means the line 3x+4y=-16 is not part of the solution set. That boundary line is graphed as a dashed line.

Take note of where the variables are in relation to the inequality symbol. Both are on the "less than" side, so the shading of the graph will be where the values of x and y are less than those on the boundary line. The boundary line has a negative slope, so the values less than those on the boundary are to the left and below the line.

Plot the dashed boundary line 3x +4y = -16, or y = -3/4x -4, and shade the area below and to its left.

Step-by-step explanation:

| - 5 | + | - 4 |

5 + 4

= 9

| - 6| - 4

6 - 4

2

I hope this answers your question.

Answer:

1. No 2. No 3. Yes 4. Yes

Step-by-step explanation:

Compare the value of each digit from the leftmost digit.

Answer:

$3.20

Step-by-step explanation:

Divide the number 16 (as in the cost per Jacket) by 5. (The amount of shirts you could buy with $16)

Then once you have divided 16 by 5, your answer should be 3.2, so the cost of one shirt is $3.20

Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).

Use the concept of the rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given that,

Rectangle dimensions: 2 feet by 8 feet

And here are the options provided:

A) 4 feet by 16 feet

B) 6 feet by 12 feet

C) 12 feet by 32 feet

D) 22 feet by 28 feet

To determine if two rectangles are similar,

Compare their corresponding side lengths.

In this case,

A rectangle with dimensions 2 feet by 8 feet.

After simplifying it we can write 1:4

Let's check each option to see if it matches the similarity:

A) 4 feet by 16 feet:

The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,

Which simplifies to 1:4 as well.

So, option A is similar to the given rectangle.

B) 6 feet by 12 feet:

The given rectangle has side lengths of 6:12,

Which simplifies to 1:2.

So, option B is not similar to the given rectangle.

C) 12 feet by 32 feet:

The given rectangle has side lengths of 12:32,

Which simplifies to 3:8.

So, option C is not similar to the given rectangle.

D) 22 feet by 28 feet:

The given rectangle has side lengths of 22:28,

Which simplifies to 11:14.

So, option D is not similar to the given rectangle.

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Answer:

The number of flowers on the plant

Step-by-step explanation:

Answer:

C: Number of flowers on the plant

Step-by-step explanation:

i got it right on my test

Answer: [tex]\dfrac{11}{9}I[/tex]

Step-by-step explanation:

Given

There is [tex]l[/tex] liter of pure alcohol

Suppose [tex]x[/tex] liters of water is added

After addition of water, alcohol becomes 45% in concentration

[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]

Thus,  [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.

Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:

(1 - cos(x)) y' - y sin(x) = 0

==>   (1 - cos(x)) y' = y sin(x)

==>   y'/y = sin(x)/(1 - cos(x))

==>   dy/y = sin(x)/(1 - cos(x)) dx

Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.

∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx

∫ dy/y = ∫ du/u

ln|y| = ln|u| + C

exp(ln|y|) = exp(ln|u| + C )

exp(ln|y|) = exp(ln|u|) exp(C )

y = Cu

y = C (1 - cos(x))

Answer: (d)

Step-by-step explanation:

Given

There are six flavors of ice-cream that is chocolate, vanilla, strawberry, birthday cake, rocky road, and butter pecan

First ice-cream can be tasted in 6 different ways

Second can be in 5 ways

similarly, remaining in 4, 3, 2 and 1 ways

Total no of ways are  [tex]6\times5\times 4\times 3\times 2\times 1=720\ \text{ways}[/tex]

Option (d) is correct.

Answer:  [tex]9\sqrt{3}[/tex]

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

Explanation:

For any 30-60-90 triangle, the short leg is always half the hypotenuse.

This makes the short leg to be 18/2 = 9 units long.

We then multiply this by [tex]\sqrt{3}[/tex] to get the length of the long leg.

[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\text{long leg} =9\sqrt{3}[/tex]

Or you could use the pythagorean theorem to solve [tex]x^2+9^2 = 18^2[/tex] and you should get [tex]x = \sqrt{243} = 9\sqrt{3}[/tex]

Answer:

[tex]x=2\\y=3[/tex]

Step-by-step explanation:

Solve by substitution method

[tex]y=4x-5\\y=3x-3[/tex]

First, solve [tex]y=4x-5[/tex] for [tex]y[/tex]:

Substitute [tex]4x-5[/tex] for [tex]y[/tex] in [tex]y=3x-3[/tex]

[tex]y=3x-3[/tex]

[tex]4x-5=3x-3[/tex]

[tex]4x-3x=5-3[/tex]

[tex]x=2[/tex]

Now that we have the value of x

substitute [tex]2[/tex] for [tex]x[/tex] in [tex]y=4x-5[/tex]

[tex]y=4x-5[/tex]

[tex]y=4(2)-5[/tex]

[tex]y=8-5[/tex]

[tex]y=3[/tex]

∴ The value of [tex]x[/tex] is [tex]2[/tex] and the value of [tex]y[/tex] is [tex]3[/tex]

9514 1404 393

Answer:

  (b) 7x + 2y = 1

Step-by-step explanation:

You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)

  7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does

The equation is ...

  7x +2y = 1

__

Additional comment

The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.

Answer:

b

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = base x height

A = 39 x 20

A = 780

Step 2: Find the area of the semi-circles

---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.

A = pi x r^2

A = pi x 10^2

A = 100pi = 314

Step 3: Find the area of the figure

Area = area of the rectangle - area of the semi-circles

A = 780 - 314

A = 466 cm^2

Hope this helps!

Answer:

466 cm^2

Step-by-step explanation:

This one is done basically the same as the other.

Rectangle = 20 x 39

Circle = (3.14) x 10^2

Rectangle = 780

Circle = 314

rectangle - circle

780 - 314 = 466

Answer:

E

Step-by-step explanation:

The percentage of the whole week that Adam spends in sleeping is 33%.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

According to the give question.

Adams sleeps for nine hours each night, five nights a week.

⇒ Number of hours he sleep for five nights = 5 × 9 = 45 hours

Also, 11 hours for two nights a week.

So, the total number of hours Adam sleeps in a week = 45 + 11 = 56 hours

And, total number of hours in a week = 24 × 7 = 168

Therefore,

The percentage of the whole week that Adam spends in sleeping

= (total number of hours Adam sleep in a week/Total numbers of hour in a week) × 100

[tex]=\frac{56}{168}[/tex] × 100

= 33.33%

= 33%

Hence, the percentage of the whole week that Adam spends in sleeping is 33%.

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