Given: F(x) = 3x and G(x) = x 2 + 1 Find (F + G)(x).

 3x³ + 1
 x² + 3x + 1
3x² + 1

Answer:

x  = 3

Step-by-step explanation:

Given in the question an equation,

[tex]2lne^{ln5x}=2ln15[/tex]

Step 1

[tex]e^{lnx}=x[/tex]

so,

[tex]2ln(5x)=2ln15[/tex]

Step 2

cancel 2 on both sides of the equation

[tex]ln{5x}=ln15[/tex]

Step 3

[tex]ln{5x}-ln15=0[/tex]

[tex]ln\frac{5x}{15}=0[/tex]

Step 4

[tex]ln\frac{x}{3}=0[/tex]

Step 5

[tex]e^{ln\frac{x}{3}}=e^{0}[/tex]

Step 6

x/3 = 1

x = 3(1)

x = 3

Answer:

Step-by-step explanation:

Formula

a^2 + b^2 = c^2

Givens

a = x

b = 20.2

c = 14.7 + x

Solution

x^2 + 20.2^2 = (14.7 + x)^2                       Expand the brackets

x^2 + 408.04 = 14.7^2 + 29.4x + x^2       Cancel the x^2

408.04 = 216.9 + 29.4x                            Subtract 216.9 from both sides.

191.98 = 29.4x                                           Divide by 29.4

6.52993 = x                                               Answer.

6.5 to the nearest tenth.

Answer:

x = 6.5 cm

Step-by-step explanation:

The tangent to the circle forms a right angle with the radius x

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

The hypotenuse is (x + 14.7) ← opposite the right angle, hence

(x + 14.7)² = x² + 20.2² ← expand parenthesis on left side

x² + 29.4x + 216.09 = x² + 408.04 ( subtract x² from both sides )

29.4x + 216.09 = 408.04 ( subtract 216.09 from both sides )

29.4x = 191.95 ( divide both sides by 29.4 )

x ≈ 6.5 cm

Answer:

d. arc BCE

Step-by-step explanation:

BE is a diameter which means it cuts the circle in half therefore arc BCE is a semicircle

Answer:

e). 4

Step-by-step explanation:

45-45-90

x-x-xsquare root of 2

Final answer:

The measure of the leg of a 45-45-90 right triangle with a hypotenuse of 4√2 is 4 units.

Explanation:

The question asks for the measure of the leg of a 45-45-90 right triangle given that the hypotenuse is 4√2. In a 45-45-90 right triangle, both legs are of equal length and the hypotenuse is √2 times the length of a leg. Using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a2 + b2), we can find the length of a leg when the hypotenuse is known.

Let the length of each leg be 'a'. Since the hypotenuse is 4√2, the equation according to the Pythagorean Theorem would be a2 + a2 = (4√2)2. This simplifies to 2a2 = 32, so a2 = 16, and thus a = √16. Therefore, each leg measures 4 units.

Answer: 7.5 hours

Step-by-step explanation:

750/50=15 to see how many times he climbed 15 feet

15 times 30=450 (total minutes)

450/60=7.5 hours

Answer:7.5

Step-by-step explanation:

450/60

Answer:

12.3

Step-by-step explanation:

cos(35) = y/15

y = 15 * cos(35) = 12.3

Answer:

y = 12.3 cm

Step-by-step explanation:

Since the triangle is right with hypotenuse 15, use the cosine ratio to solve for y, that is

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]

Multiply both sides by 15

15 × cos35° = y, hence

y ≈ 12.3

Answer:

The surface area of the sphere is [tex]529\pi\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=23/2=11.5\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]SA=4\pi (11.5)^{2}[/tex]

[tex]SA=529\pi\ ft^{2}[/tex]

Answer:

12612837.8375

Step-by-step explanation:

first you have to multiply 5.015 x 10 and you get 50.15 the put that to the power of 3 and then multiply the total by 100.

Answer:

# The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² - 36y + 9y² = 0

# The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Step-by-step explanation:

* Lets revise the general form and the standard form of the ellipse

- The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0

- The standard form is (x - h)²/a² + (y - k)²/b² = 1

* Lets solve the problem

# x²/3² + (y - 2)²/2² = 1

∵ x²/9 + (y - 2)²/4 = 1 ⇒ multiply both sides by 9 × 4 (36)

∴ 4x² + 9(y - 2)² = 36 ⇒ open the bracket power 2

∴ 4x² + 9(y² - 4y + 4) = 36 ⇒ multiply the bracket by 9

∴ 4x² + 9y² - 36y + 36 = 36 ⇒ subtract 36 from both sides

∴ 4x² - 36y + 9y² = 0

* The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² + 9y² - 36y = 0

# (x + 7)²/7² + y²/6² = 1

∵ (x + 7)²/49 + y²/36 = 1 ⇒ multiply both sides by 49 × 36 (1764)

∴ 36(x + 7)² + 49y² = 1764 ⇒ open the bracket power 2

∴ 36(x² + 14x + 49) + 49y² = 1764 ⇒ multiply the bracket by 36

∴ 36x² + 504x + 1764 + 49y² = 1764 ⇒ subtract 1764 from both sides

∴ 36x² + 504x + 49y² = 0

* The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# x²/6² + (y + 4)²/4² = 1

∵ x²/36 + (y + 4)²/16 = 1 ⇒ multiply both sides by 36 × 16 (576)

∴ 16x² + 36(y + 4)² = 576 ⇒ open the bracket power 2

∴ 16x² + 36(y² + 8y + 16) = 576 ⇒ multiply the bracket by 36

∴ 16x² + 36y² + 288y + 576 = 576 ⇒ subtract 576 from both sides

∴ 16x² + 288y + 36y² = 0

* The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# (x - 3)²/3² + y²/5² = 1

∵ (x - 3)²/9 + y²/25 = 1 ⇒ multiply both sides by 9 × 25 (225)

∴ 25(x - 3)² + 9y² = 225 ⇒ open the bracket power 2

∴ 25(x² - 6x + 9) + 9y² = 225 ⇒ multiply the bracket by 25

∴ 25x² - 150x + 225 + 9y² = 225 ⇒ subtract 225 from both sides

∴ 25x² - 150x + 9y² = 0

* The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Answer:In Plato this is the correct answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is not biased.  It doesn't push the participants to answer one way or another.

However, the sample is biased.  It does not represent the population.

The first and fourth options are correct.

Hello there! Here are your answers:

Does Kerri's dot plot match the data in the tally table? No.

Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.

The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):

5 - classmates spent 3 hours at the park

3 - classmates spent 4 hours at the park

6- classmates spent 5 hours at the park

4 - classmates spent 6 hours at the park

I hope this was helpful and let me know if you need more help! :) Have a great day! :)

Answer:

the other guy is right

Step-by-step explanation:

-~- boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii laggy

Answer:

the correct answer would be c, g(x)=2^x+2

Step-by-step explanation:

We can eliminate the first and the last option because the line is going upwards, not downwards(it would if it was negative or had the negative sign in front). We can cross out the second option because if it was 2^x+3, then it would be crossing (0,4) on the y-axis. Therefore the correct option is C, since it crosses right at (0,3).

hope this helps :)

Answer:

We have 8 cups of orange juice

Step-by-step explanation:

orange juice:  water:  total

1                     : 3         : 4

Multiply everything by x

1x                 3x             4x

We have 32 cups total

4x = 32

Divide each sice by 4

4x/4 = 32/4

x = 8

We have 8 cups of orange juice

3*8 = 24

We have 24 cups of water

The ratio of orange juice to water in the punch is 1:3, which means that for every single cup of orange juice, there are 3 cups of water. To find out how many cups of orange juice were used to make 32 cups of punch, we find out what 1 part out of the total 4 parts is, which is 32 ÷ 4 = 8. Therefore, James used 8 cups of orange juice for the punch.

The subject of the question is Mathematics and it pertains to the concept of ratios in particular. The ratio of orange juice concentrate to water is given as 1:3. This means that for every 1 cup of orange juice, James uses 3 cups of water. So, the total parts in the punch are 1 (for orange juice) + 3 (for water) = 4 parts.

However, James made 32 cups of punch. Hence, to find out how many cups of orange juice he used, we need to find out what 1 part out of the total 4 parts is. To do this, you divide the total punch made (32 cups) by the number of total parts (4).

Therefore, 32 cups divided by 4 equals 8 cups. Hence, James used 8 cups of orange juice to make the punch.

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Answer:

  1.3×10⁻² = 0.013

Step-by-step explanation:

The "E" stands for "×10^", so 1.3E-2 means 1.3×10^-2.

Of course 10^-2 = 1/10^2 = 1/100 = 0.01, so

  1.3E-2 = 1.3×10^-2 = 1.3×0.01 = 0.013

_____

This notation was used by early computers to print results where the character set was limited and superscripts could not be printed.

A = 1/2aP

P = number of sides x length of each side

P = 8 x 5.8

P = 46.4

A= 1/2 x 7 x 46.4

A = 162.4

Answer:

Find the GCF

Step-by-step explanation:

When multiplying the following polynomials:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5)

1.     First we need to use the distributive property:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 2x^3 * 9x^2  - 2x^3 * 4x  + 2x^3 * 5 + 2x^2 * 9x^2 - 2x^2 * 4x + 2x^2 * 5 - 3x * 9x^2 + 3x * 4x - 3x * 5.

2.   Second, we need to use the multiplication property of exponents:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 - 8x^4 + 10x^3 + 18x^4 - 8x^3 + 10x^2 - 27x^3 + 12x^2 - 15x.

3. We need to combine like terms:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 +10x^4 -25x^3 + 22x^2 - 15x.

We don't need to find the GCF.

Answer:

  1. predicted attendance: 141.35

  2. residual: 18.65

Step-by-step explanation:

1. Predicted attendance is ...

  y = -5.9·5 +170.85 = 141.35

__

2. As the problem statement tells you, ...

  actual value - predicted value = residual

  160 - 141.35 = 18.65 . . . the residual

A statistical question is a question asked with the goal of collecting data. You could rewrite the question so that it says something like, “How old were you when..” That way the responses will vary and you would be able to graph and compare them.

The statistical question of the given statement is How old were you then.

Hence, the statistical question of the given statement is How old were you then.

Learn more about the statistical question, refer to:

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Sphere = 4PiRsquared

Radius = 13

13 x 13 = 169

169 x 4= 676 Pi

5e surface is 676Pi

Answer:

The correct answer is option B.   676π units²

Step-by-step explanation:

Formula:-

The surface area of a sphere = 4πr²

Where r is the radius of sphere

To find the surface area of given sphere

Here r = 13 units

Surface area = 4πr²

 = 4 * π * 13²

 = 4 * π * 169 = 676π units²

Therefore the  correct answer is option A.   676 units²

Answer:

Option A, 7 and Option B, -2

(7,0) and (-2,0)

Step-by-step explanation:

Given in the question a function f(x) = (x+2)(x-7)

Step 1

Expand the function (x+2)(x-7)

x(x-7)+2(x-7)

x² - 7x + 2x - 14

x² - 5x - 14

Step 2

To find the x-intercepts we will substitute y with 0

y = x² - 5x - 14

0 = x² - 5x - 14

(x-7)(x+2) = 0

x = 7

x = -2

Answer:

The x-intercepts would be 7 and -2.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

A plane is a flat, infinite 2D surface, so when we say two things are coplanar, they can all fit on a single plane. In this case, all three lines a, b, c, and d lie on the same 2D surface, so we'd consider them coplanar. True.

Answer:

yes

Step-by-step explanation:

Answer:

"Membership decreased by an average of 6,600 people per year from year 3 to year 5"

Step-by-step explanation:

To get average rate of change from year 3 to year 5, we need to divide the change from year 3 to 5 by 2 (because from year 3 to 5 is 2 years).

THe change is:

83.6 - 96.8 = -13.2

We divide by 2 to get per year average rate of change:

-13.2 / 2 = -6.6

In thousands, that is 6600 decrease.

2nd answer choice is right.

Answer: [tex]3\sqrt{2}\ m[/tex]

Step-by-step explanation:

The perimeter of a square is:

[tex]P=4s[/tex]

Where "s" is the lenght of a side of the square.

Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:

[tex]s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m[/tex]

You can calculate the length of the diagonal with this formual:

[tex]d=s\sqrt{2}[/tex]

Where "s" is the lenght of a side of the square.

Substituting the value of "s" into the formula  [tex]d=s\sqrt{2}[/tex], you get that the lenght of the diagonal of this square is:

[tex]d=3\sqrt{2}\ m[/tex]

Answer:

D

Explanation:

A is the same thing as the statement, only that it says if the polygon is convex. Same thing for B. C could've worked if it said exterior instead of interior. D is basically the converse of the statement.

A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

Each interior angle of a convex polygon is less than 180° while in the case of the concave polygon at least one angle is more than 180°.

In the diagram attached,

We can see in the case of a convex polygon if we join any two vertices, a line segment joining two vertices never passes through the exterior or interior of the polygon.

In the case of a concave polygon, at least a line segment joining two vertices passes through the exterior of a polygon.

Therefore, A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

To get more about polygons visit:

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Answer:

C

Step-by-step explanation:

Draw in <QOS. That's the central angle. It is also 60 degrees.

<R  which has Q and S as its end points, = 1/2 the central angle (always) so <R = 30 degrees.

C

The area of a triangle is half the multiplication of the base and the height.

So, if the smaller triangle has height 6 cm and base 2 cm, its are is

[tex]\dfrac{6\times 2}{2}=6[/tex]

Similarly, if the height of the larger triangle is 9 cm, and its base is 3 cm, its area is

[tex]\dfrac{9\times 3}{2}=\dfrac{27}{2}[/tex]

So, the total area is

[tex]6+\dfrac{27}{2} = \dfrac{12}{2}+\dfrac{27}{2}=\dfrac{39}{2}[/tex]

The total area of the two triangles that need to be painted is 19.5 cm².

The total area of the two triangles that need to be painted can be found by adding the area of the smaller triangle and the area of the larger triangle. The formula to calculate the area of a triangle is:

Area = (base * height) / 2

For the smaller triangle, the base is 2 cm and the height is 6 cm. Substituting these values into the formula, we get:

Area of smaller triangle = (2 cm * 6 cm) / 2 = 6 cm²

For the larger triangle, the base is 3 cm and the height is 9 cm. Substituting these values into the formula, we get:

Area of larger triangle = (3 cm * 9 cm) / 2 = 13.5 cm²

To find the total area, we add the areas of the two triangles:

Total area = area of smaller triangle + area of larger triangle = 6 cm² + 13.5 cm² = 19.5 cm²

Answer:

(a, 0)

Step-by-step explanation:

As S is on the x-axis, its y-coordinate will be zero.

And since this is a right trapezoid, ∠QPS and ∠PSR are right angles, so S and R will have the same x-coordinate, which is a.

Therefore, the coordinate of Point S is (a, 0)

Answer: 120

Step-by-step explanation:

Answer:

The profit will be [tex]\$22.31[/tex]

Step-by-step explanation:

we know that

To find the profit subtract the cost of the case of bottled water from the sell of all the bottles of water  

Let

x-----> the profit

[tex]x=36*0.75-4.69=\$22.31[/tex]