Find the antiderivative of the function. f(x)=10x+3

Answer: side AB is 5.7 units

Step-by-step explanation:

If you look at the congruence marks on the angles, you can see that side AB and side KL correspond. Since we know KL is 5.7, AB must be 5.7 as well. :)

Answer:

  58.0°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides of a right triangle and trig functions of the acute angles.

Here, the hypotenuse of the triangle is given (17 cm), as is the side adjacent to angle x (9 cm). This suggests using the relation ...

  Cos = Adjacent/Hypotenuse

  cos(x) = (9 cm)/(17 cm) = 9/17

The angle for this cosine value is found using the inverse trig function.

  x = arccos(9/17)

  x ≈ 58.034°

Rounded to the nearest tenth, the angle is ...

  x = 58.0°

__

Additional comment

Of course, the angle y is the complement of this:

  y = 32.0°

I disagree with the student's claim. The number of decimal places in the product may not always be the same as the total number of decimal places in the factors.

In multiplication, the total number of decimal places in the product is determined by adding the decimal places in the factors. For example, if we multiply 2.5 by 0.3, both factors have one decimal place. When we multiply them, the product is 0.75, which also has one decimal place. In this case, the student's claim holds true.

However, in other operations like division or addition/subtraction, the number of decimal places in the product can differ from the total number of decimal places in the factors.

For instance, when we divide 2.5 by 3, the quotient is 0.83333333..., which has an infinite number of decimal places. Here, the product has more decimal places than the total number of decimal places in the factors.

Therefore, the number of decimal places in the product is not always the same as the total number of decimal places in the factors, and it depends on the specific mathematical operation being performed.

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Answer:

x = 4

Step-by-step explanation:

2(x + 8) = x + 20

2x + 16 = x + 20

-x           -x

x + 16 = 20

   -16     -16

x = 4

Answer:

x=4

Step-by-step explanation:

2x  + 16 = x + 20

-x           -x

1x + 16 = 20

   - 16 = -16

1x = 4

1      1 = 4    (x=4)

Answer: 2.5

Step-by-step explanation: 40 divided by 4 = 10  1.4 x 10 = 2.5

Answer:

2.5

Step-by-step explanation:

1/4 is equal to 0.25, So if it's 0.25 for 4 servings, the ratio is 0.25:4. You can the divide 40 by 4 and get 10. You can now take that ten and multiply it by 0.25 to get 2.5 or 2 and 1/2

The profit to be made when she sells the house is $103,800.

The first step is to determine the value of Tammy's house in 13 years. The formula to be used is:

$184,000 x (1.035)^13 = $287,767.92

Profit = value of the house in 13 years - cost of the house

$287,767.92 - $184,000 = 103,767 = $103,800

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Therefore , the solution of the given problem of standard deviation comes out to be  the width of the confidence interval for a making a mark parameter decreases.

Variance is measured in statistics using variance. The average variation between the data and the mean is calculated by taking the square root of that value. By comparing each value to the mean, it incorporates all data points in its computations, in contrast to some other quantitative measures of variability. Variations may occur due to internal or external factors, and they may include things like unintentional errors, exaggerated expectations, and changing commercial or economic conditions.

Here,

The standard error and margin of error drop when the sample size rises, keeping all other factors constant.

As a result, the width of the confidence interval for a making a mark parameter decreases.

Thus, The width of an error range for a papulation characteristic will increase as sample size rises, keeping all other factors constant.

Therefore , the solution of the given problem of standard deviation comes out to be  the width of the confidence interval for a making a mark parameter decreases.

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Volume is the amount of space in an object. The fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

First, we calculate the volume of the cube.

\(Volume = Length^3\)

From the figure, we have:

\(Length = r\sqrt 2\)

So:

\(V_1 = (r\sqrt2)^3\)

\(V_1 = (2\sqrt2)r^3\)

Next, the volume of the cylinder

\(Volume=\pi r^2h\)

So, we have:

\(V_2 = \pi r^2 (2r + 4)\)

The fraction (n) occupied by the cube is:

\(n = \frac{V_1}{V_2}\)

So, we have:

\(n = \frac{(2\sqrt2)r^3}{\pi r^2(2r + 4)}\)

Factor out 2 in the denominator

\(n = \frac{(2\sqrt2)r^3}{2\pi r^2(r + 2)}\)

Cancel out common terms

\(n = \frac{r\sqrt2}{\pi(r + 2)}\)

Hence, the fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

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Answer:

$97.524

Step-by-step explanation:

The height of the building is 71 meters.

We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:

(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

2.8 / 1.49 = (height of building) / 37.5

To find the height of the building, we can cross-multiply and solve for it:

(2.8 * 37.5) / 1.49 = height of building

Calculating the expression on the right side:

(2.8 * 37.5) / 1.49 ≈ 70.7013

Rounding to the nearest meter, the height of the building is approximately 71 meters.

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Answer:

Step-by-step explanation:

You want to know the dimensions of a rectangular building that has a perimeter of 2516 feet and is 194 feet longer than wide.

Let w represent the width of the building. Then w+194 is the length, and the perimeter is ...

  P = 2(L +W)

  2516 = 2((w+194) +w)

  2516 = 4w +388 . . . . simplify

  2128 = 4w . . . . . . . subtract 388

  532 = w . . . . . . . divide by 4

  w+194 = 726 . . . . . length

The building is 532 feet wide and 726 feet long.

Answer:

B

Step-by-step explanation:

From supplementary angles, y = 180 - 52 - 59 = 69. From sum of angles in a triangle, x = 180 - 63 - 69 = 48.

Answer:

x = 48

Step-by-step explanation:

First find y

52+y+59 = 180 since they from a straight line

y = 180-59-52

y = 69

Then we know the angles of a triangle add to 180

x+y+63 = 180

x+69+63 = 180

x = 180-69-63

x =48

Answer: Where is the question.

Step-by-step explanation: Where is the question.

The image of the line v = 4u under G is given by the equation y = 2.5u + 120 in slope-intercept form.

To obtain the image of the line v = 4u under the map G(u, v) = (2u + 0.5u + 120), we need to substitute the expression for v in terms of u into the equation of G.

We have; v = 4u, we substitute this into G(u, v):

G(u, 4u) = (2u + 0.5u + 120)

Now, simplify the expression:

G(u, 4u) = (2.5u + 120)

The resulting expression is (2.5u + 120) for the image of the line v = 4u under G.

To express this in slope-intercept form (y = mx + b), we can rewrite it as:

y = 2.5u + 120

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Answer:

19

Step-by-step explanation:

The answer is 19 because your basically just multiplying it until you get to 10.

Answer:

11.8

Step-by-step explanation:

First 4 matches: 4 x 16

                         = 64

Next 6 games: 9 x 6

                       = 54

Average = Total points / Games

Total = 64 + 54

         = 118

Average = 118/10

              = 11.8

              = 12 (2 sf)

As given by the question

(17)

There are given that the equation

Now,

From the general solution for the given equation

Then,

Solve above solution

So, divide by 3 on both side of the equation

Hence, the value of the given equation is shown below:

The value of x in the right triangle is  4√2 units.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, the triangles are similar. Let's use this similarity to find the value of x in the triangles.

Hence, using proportion,

x / 8 = 4 / x

cross multiply

x² = 8 × 4

x² = 32

square root both sides of the equation

x = √32

x = √16 × 2

x = 4√2 units

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Answer:

57 meters

Step-by-step explanation:

just know it- not really right just wanted points

Answer:

Thats the answer r=-7/6

Step-by-step explaintion

r=-7/6

The approximate value of x₂(0.2) is -1.2897 (approx) Answer: -1.290 (approx)

Given ODE is:-x₂(1) 1.5x (1)² - 0.5x, (1)³x,(0) (H *** (*) - (-)where a = 28

We need to use Euler's method with step size 0.1 to fill in the following table. t x, (1) 0 0.1 0.2

The step size is 0.1.

The interval from 0 to 0.1 is, thus, the first step.t = 0x, (1) = 0.0H = 0.1H***= 0.5 * H=0.05x,(2) = x,(1) + H*** f(t, x,(1))

where f(t, x) = -x₂(1) 1.5x (1)² - 0.5x, (1)³x,(0) (H *** (*) - (-)

Substituting x,(1) = 0, t = 0 and H = 0.1,x,(2) = 0.0 + 0.05[-x₂(1) 1.5x (1)² - 0.5x, (1)³x,(0) (H *** (*) - (-)

where a = 28x,(2) = 0 + 0.05[- x₂(1) 1.5 (0)² - 0.5(0)³28 **(*) - (-)]x,(2) = 0 - 0.05[0 - 0 + 28]x,(2) = -1.4t x, (1) x,(2)0.1 -1.4H = 0.1H***= 0.5 * H=0.05x,(3) = x,(2) + H*** f(t, x,(2))x,(3) = -1.4 + 0.05[-x₂(1) 1.5x (1)² - 0.5x, (1)³x,(0) (H *** (*) - (-)]

where a = 28, x,(1) = 0t = 0.1, H = 0.1x,(3) = -1.4 + 0.05[-x₂(1) 1.5 (0.1)² - 0.5(0)³28 **(*) - (-)]x,(3) = -1.4 + 0.05[- 1.5(0.01) - 0 + 28]x,(3) = -1.3695t x, (1) x,(2) x,(3)0.1 -1.4 -1.3695H = 0.1H***= 0.5 * H=0.05x,(4) = x,(3) + H*** f(t, x,(3))x,(4) = -1.3695 + 0.05[-x₂(1) 1.5x (1)² - 0.5x, (1)³x,(0) (H *** (*) - (-)]

where a = 28, x,(1) = 0t = 0.2, H = 0.1x,(4) = -1.3695 + 0.05[-x₂(1) 1.5 (0.2)² - 0.5(0)³28 **(*) - (-)]x,(4) = -1.3695 + 0.05[- 1.5(0.04) - 0 + 28]x,(4) = -1.2897

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Even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

Let R be a relation that is reflexive and transitive. We want to prove that R2 = R for any relation R with these two properties.

To prove this, we need to show that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R.

First, let's consider (a, b) ∈ R2. By definition, (a, b) ∈ R2 means that there exists an element c such that (a, c) ∈ R and (c, b) ∈ R.

Since R is reflexive, we know that (a, a) ∈ R and (b, b) ∈ R.

By the transitivity of R, if (a, c) ∈ R and (c, b) ∈ R, then (a, b) ∈ R.

Therefore, (a, b) ∈ R2 implies (a, b) ∈ R.

Now, let's consider (a, b) ∈ R. Since R is reflexive, we have (a, a) ∈ R and (b, b) ∈ R.

By the definition of R2, (a, a) ∈ R2 and (b, b) ∈ R2.

Since R is transitive, if (a, a) ∈ R2 and (a, b) ∈ R2, then (a, b) ∈ R2.

Therefore, (a, b) ∈ R implies (a, b) ∈ R2.

We have shown that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R. Hence, R2 = R.

If the relation R is anti-reflexive, it is not necessarily true that R2 is anti-reflexive.

To understand why, let's consider an example. Let R be a relation defined on the set of integers such that R contains the ordered pairs (a, b) where a < b.

In this case, R is anti-reflexive because for any integer a, (a, a) is not in R.

Now, let's consider R2. R2 is the composition of R with itself. If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R2.

In our example, if we take a = 1, b = 2, and c = 3, we have (1, 2) ∈ R and (2, 3) ∈ R. Therefore, (1, 3) ∈ R2.

However, (1, 1) is not in R2 because (1, 1) is not in R. Therefore, R2 is not anti-reflexive in this case.

This example demonstrates that even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

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Jonathan and Seth both had a time per lap of 2 minutes, which means they swam at the same rate.

To determine who swam at the same rate, we need to calculate the time per lap for each swimmer. This can be done by dividing the time by the number of laps.

Jonathan: 4 ÷ 2 = 2 minutes per lap

Julian: 1 ÷ 1 = 1 minute per lap

Seth: 6 ÷ 3 = 2 minutes per lap

Bennett: 21 ÷ 7 = 3 minutes per lap

Taylor: 7 ÷ 4 = 1.75 minutes per lap

From the calculations, we can see that Jonathan and Seth both had a time per lap of 2 minutes, which means they swam at the same rate.

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This expression represents the Boolean function G in its full SOP form, where each term represents a combination of inputs that results in a logical 1 output.

To convert the given Boolean function G(x, y, z) = x + ÿz into its full SOP (Sum of Products) form, we first need to apply De Morgan's law to the complement of z. The complement of z, ÿz, can be represented as ¬z or z'.

So, the function G(x, y, z) = x + ÿz can be rewritten as G(x, y, z) = x + ¬z.

Next, we need to expand the function into its full SOP form. The full SOP form represents the function as a sum of all possible product terms. In this case, since we have two variables (x and z), there will be a total of four possible product terms: (x' ˣ y' ˣ z'), (x' ˣ y' ˣ z), (x ˣ y' ˣ z'), and (x ˣ y' ˣ z).

Therefore, the full SOP form of the function G(x, y, z) = x + ÿz is:

G(x, y, z) = (x' ˣ y' ˣ z') + (x' ˣ y' ˣ z) + (x ˣ y' ˣ z') + (x ˣ y' ˣ z).

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Let A(2,0),B(0,92)

Let A(2,0),B(0,92)and let mid-point be C(1,3p)

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31We need to show that line 5x+3y+2=0 passes through point (−1,3p)

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31We need to show that line 5x+3y+2=0 passes through point (−1,3p)Point =(−1,3p)=(−1,3×31)=(−1,1)

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31We need to show that line 5x+3y+2=0 passes through point (−1,3p)Point =(−1,3p)=(−1,3×31)=(−1,1)Putting (−1,1) in line

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31We need to show that line 5x+3y+2=0 passes through point (−1,3p)Point =(−1,3p)=(−1,3×31)=(−1,1)Putting (−1,1) in line5x+3y+2=0

Let A(2,0),B(0,92)and let mid-point be C(1,3p)Finding coordinates of C(1,3p)=⎝⎜⎜⎛22+0,20+92⎠⎟⎟⎞⇒(1,3p)=(1,91)Comparing y-coordinate3p=91∴p=31We need to show that line 5x+3y+2=0 passes through point (−1,3p)Point =(−1,3p)=(−1,3×31)=(−1,1)Putting (−1,1) in line5x+3y+2=0⇒5(−1)+3(1)+2=0

Answer:

A. 7 divided by 2

Step-by-step explanation:

The computation is shown below;

\(= 6\frac{3}{4} \div 1 \frac{2}{3} \\\\= \frac{27}{4} \div \frac{5}{3}\\\\= \frac{27}{4} \times \frac{3}{5}\\\\= \frac{27\times 3}{4\times 5} \\\\= \frac{81}{20} \\\\= 4 \frac{1}{20}\)

It could be 4.05

So according to the given options, the option 1 is chosen at is closed to 4.05

Hence, the option A is correct

Answer: 120!

Step-by-step explanation:

6 + 6 = 12

12 x 10 = 120

If the sum is twice the sum of 6 you would add 6 twice and then you would multiply 12 times 10.

Hope i helped! <333

Answer:

Great question!!

Step-by-step explanation:

I don't have an answer for you, although, I'm sure that you will figure it out on your own, or god forbid, ask/email your teacher and/or peer!

Answer:

30tan59°

Step-by-step explanation:

from the diagram, the opposite, is the side of the triangle to angle is facing, which is h ft. and the adjacent is 30ft.

therefore, using SOHCAHTOA, we know that to get he value of h, we have that tan 59°=h/30, which gives the answer

The volume of the cylinder after the prism is cut out is 593 cm^3.

To calculate the volume of the cylinder after the prism is cut out, we need to first determine the volume of the prism that will be removed. This can be found by multiplying the length, width, and height of the prism. Once we have this value, we can subtract it from the original volume of the cylinder.

For example, if the cylinder has a radius of 5 cm and a height of 10 cm, and the prism to be removed has a length of 6 cm, a width of 4 cm, and a height of 8 cm, we can calculate the volume of the prism as follows:

Volume of prism = length x width x height
Volume of prism = 6 cm x 4 cm x 8 cm
Volume of prism = 192 cm^3

To find the volume of the cylinder after the prism is cut out, we simply subtract the volume of the prism from the original volume of the cylinder:

Volume of cylinder = pi x radius^2 x height
Volume of cylinder = 3.14 x 5^2 x 10
Volume of cylinder = 785 cm^3

Volume of cylinder after prism is cut out = 785 cm^3 - 192 cm^3
Volume of cylinder after prism is cut out = 593 cm^3

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Answer: 64

Explanation: All of the numbers are quite close to one another. The number farthest apart from them all would be 64 with a difference of 15. Also, it's visibly shown how there are the 20s, 30s, and 40s, but it skips quickly to the 60s.

I hope this helped!

Good luck <3