f(x)=x^2+6x find f(3)

Answer:

Yes, the tank is more than half full of gasoline after 3.5 hours.

Step-by-step explanation:

To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!

The percentage of the cookies were gingerbread is 60%.

Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"

Here, Difference =55-22

=3

Percentage =33/55 ×100

= 0.6 ×10

= 60%

Therefore, the percentage of the cookies were gingerbread is 60%.

Answer:

Step-by-step explanation:

 cccccc

Answer:

1440

Step-by-step explanation:

"Percent" means "out of 100"

5 "percent" means 5 out of 100

[tex]\frac{5}{100} =\frac{72}{x}[/tex]

We need to find the number that when multiplied by 5, equals 72.

72 / 5 = 14.4

Now, we need to multiply 100 by 14.4 to "scale" proportionately.

100 * 14.4 = 1440

We can check our work:

1440 * (0.05) = 72

The volume of the pyramid, in cubic meters, given the length of each side and the height, is 2, 592, 100 meters ³

The Volume of a pyramid can be found by the formula :

= ( Base length x Base width x Height ) / 3

Base length = 230 meters

Base width = 230 meters as this is a square base

Height = 147 meters

The volume is therefore:

= ( 230 x 230 x 147 ) / 3

= 2, 592, 100 meters ³

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First, we need to find the number of students that are freshmen: 3400 students x 3/8 = 1050 students

Next, we need to find the number of students that are in favor of forming a track team: 3/5 of the freshmen are in favor = 3/5 * 1050 = 630 students

To find the number of non-freshmen students: 3400 students - 1050 students = 2350 students

Now we need to find the number of non-freshmen students in favor of forming a track team: 1/5 of the non-freshmen students are in favor = 1/5 * 2350 = 470 students

Finally, to find the number of students opposed to the idea we need to subtract the number of students in favor from the total number of students: 3400 students - (630 students + 470 students) = 3400 - 1100 = 2300 students

So there are 2300 students at Central High School that are opposed to the idea of forming a track team.

The area of a rectangle ABCD is 60 square inches and the area of triangle ACD is 30 square inches.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

In the given rectangle ABCD, AD= 5 in. and DC=12 in.

a) Now, area of rectangle ABCD =DC×AD

= 12×5

= 60 square inches

b) By joining vertices A and C, we get triangle ACD.

c) Now, the area of triangle ADC is

Area =1/2 ×Base×Height

= 1/2 ×12×5

= 30 square inches

Therefore, the area of a rectangle ABCD is 60 square inches.

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1. The length of the sides of the two smaller squares are 3 and 4

2. Area of 4 triangles and middles square = 25

3. Area of the big square = 5

The dimensions of the the triangle and the square are

length of square = 1

base = 3

height = 4

Area of the triangle

= 1/2 base * height

= 0.5 * 3 * 4

= 6

For four triangles

= 4 * 6

= 24

Area of small square

= 1 * 1

= 1

summation of the areas

= 24 + 1

= 25

Solving for side of the big square from the area

= √25

= 5

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Answer:

y = -8/3x + 8/3

Step-by-step explanation:

(-2, 8) and (1, 0)

m = 0-8/1+2

m = -8/3

y = -8/3x + b

0 = -8/3(1) + b

0 = -8/3 + b

b = 8/3

y = -8/3x + 8/3

Answer:

x=7

Step-by-step explanation:

hope this helps :)

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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Answer:

To compare the length of the plankton to the length of the jellyfish, we can express the length of the plankton as a percentage of the length of the jellyfish.

First, we need to convert the length of the jellyfish from inches to centimeters so that we can compare the two measurements in the same unit.

12 inches = 12*2.54 = 30.48 cm

Next, we divide the length of the plankton by the length of the jellyfish and multiply by 100 to get the percentage.

0.08 inches / 30.48 cm * 100 = 0.00262 * 100 = 0.262%

So, the length of the plankton is 0.262% of the length of the jellyfish.

volume of cone is  =1/3 x³.

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.

here, given that,

The base diameter and the height of a cone are both equal to x units.

Volume =  ⅓ r²h

              =1/3 x²x

              =1/3 x³

Hence, volume of cone is  =1/3 x³.

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Answer:

3186.25

Step-by-step explanation:

318,625*10 = 3186.25

The value of the equation g ( x ) = -x + 4 , when g ( x ) = 0 , is x = 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

g ( x ) = -x + 4   be equation (1)

On simplifying the equation , we get

when g ( x ) = 0

Substitute the values in the equation , we get

0 = -x + 4

Adding x on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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There are 23% more 41+ year olds have a preference for Enterprise Content Management in comparison to 18-25 year olds

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We are given that the table shows the Technology career types for different ages groups.

The 41+ year olds have a preference for Enterprise Content Management = 3215

The percent become

3215 / (3215 + 4673 + 5822) x 100

3215 / (3215 + 4673 + 5822) x 100

3215 / 13710 x 100

23.45

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Answer: (0,0) (4, -3) (8, -6)

Step-by-step explanation:

It is correct.

Answer: 5

Step-by-step explanation:

A triangle's area is half of a squares, so we can treat this as a square for now. It says the area is 20 units squared, and if we convert this to the area of the square, it is 40 units. 40/8 is 5, and so 5 is the length of x

The value of the inequalities will be:

a. x > 6

b. x ≤ 24

c. x ≥ 6

d. x < 6

e. x ≥ 24

It should be noted that inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x + 28 > 34

Collect the like terms

x > 34 - 28

x > 6

x/2 ≤ 12

Cross multiply

x ≤ 12 × 2

x ≤ 24.

7x ≥ 42

Divide

x ≥ 42/7

x ≥ 6

x - 2 < 4

x < 4 + 2

x < 6.

3x ≥ 72

Divide

x ≥ 72/3

x ≥ 24

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The description does NOT guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

A quadrilateral is a four-sided polygon. It is a closed geometric figure with four straight sides and four angles and A rectangle is a four-sided shape with two pairs of parallel, perpendicular sides. Its opposite sides are equal in length and also opposite angles are equal in measurement.

Therefore, the correct answer is as identified. It can be concluded that the one that does not guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other

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On solving the provided question we can say that -  Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

On solving the provided question, we can say that the value of x = 5√3

values of x and y

Pythagorean theorem,

The trigonometric ratio: soh-cah-toa, and

According to the given question:

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]

Pythagorean Theorem

[tex]5²+x²=10²\\x²=100−25=75\\[/tex]

x=√75=√3×25=5√3

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Answer:

$25,900 initially

$8,128 after 11 years

Step-by-step explanation:

One thing to note, is I'm assuming you meant: [tex]v(t)=25,900(0.90)^t[/tex] and not  [tex]v(t)=25,900(0.90)^2[/tex], otherwise that would just be a constant function and not an exponential function.

There are a couple key features of exponential functions we can derive from simply analyzing the equation.

For now I will be using the form: [tex]y=a(b)^x\text{ where b} > 0, \text{b}\ne 1[/tex]

The y-intercept, is just the "a" value, which is because the y-intercept is simply when x=0, and if we raise a number to the power of zero, we get one (excluding zero as a base), so we get the form: [tex]y=a[/tex], so "a" is our y-intercept.

there's actually two type of exponential functions: exponential growth and exponential decay.

Exponential Decay:

Exponential decay, as the name implies, is when a function is decaying or decreasing. This occurs when [tex]0 < b < 1[/tex].

The decay rate can be represented as "r" in decimal form, where: [tex]b=1-r[/tex].

The reason for this is because "1" can be thought of as 100% and "r" is r%, so you're taking away r% or decaying the value by r%, also known as a decay rate.

Exponential Growth:

Exponential growth as the name implies, is when a function is growing or increasing. This occurs when b > 1

The growth rate can be represented as "r" in decimal form where: [tex]b=1+r[/tex]

The reason for this is similar to decay rate except instead of taking away r% or decaying, it's "giving r%" or growing.

The question doesn't actually require finding exponential growth or decay, but it's still an important key feature.

In this case, we really just need to find the y-intercept and plug in t=11.

The y-intercept in many graphs, not just exponential graphs, represents some sort of initial value, which in this case, is the initial value of the car. As stated above, this y-intercept is just the value in front, which is 25,900.

As for the value after 11 years, we simply need to plug in t=11 to get the following: [tex]v(11)=25,900(0.90)^{11}[/tex], from here we can use a calculator to simplify this: [tex]v(11)\approx25,900(0.31381059609)\approx 8,127.694438731[/tex], which rounds to 8,128

The measure of ∠A is 123 degrees.

The angle made between the radius and the tangent at the point of contact on a circle is 90°.  

Therefore,

∠D = 90 degrees

∠E = 90 degrees

The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees.  Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.

Hence,

90 + 90 + 2x + 7 + 5x - 2 = 360

180 + 7x + 5 = 360

7x = 360 - 180 - 5

7x = 180 - 5

7x = 175

x = 175 / 7

x = 25

Therefore,

∠A = 5(25) - 2 = 125 - 2 = 123 degrees.

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Answer:

Below

Step-by-step explanation:

(25380 - 18000) / 18000     * 100% =

7380/18000 * 100 = 41 % increase

Answer:

2,506

Step-by-step explanation:

1/5/2023

7:37PM

Answer:

the nearest thousandth is 241.006.

The required least number is n - p and the highest number is p - n.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

here,
The given numbers that are to be plotted on the number line are,
n - p, n + p, p -n

Since on the number line n comes former and p comes later it tends that p > n.

So the least number would be n - p because it will be negative,
And the height number would be p - n because
n is negative and in the operation, it becomes more than n + p.

Thus, the required least number is n - p and the highest number is p - n.

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The compound interest rate is 3.9%.

We know that when we talk about the compound interest, we mean the kind of interest that is going to accrue both on the principal and on the interest.

In this case we know that;

A = P(1 + r)^n

A = amount

P = principal

r = rate

n = number of years

710.89  = 658.20(1 + r)^2

710.89/658.20 = (1 + r)^2

1.08 = (1 + r)^2

ln(1.08) =ln (1 + r)^2

0.077 = 2ln(1 + r)

0.077/2 = ln(1 + r)

ln(1 + r) = 0.0385

1 + r = 1.039

r = 1.039 - 1

r = 0.039

r = 3.9%

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