What is the value of 238 - 3x^2 when x=4??

Answer with Step-by-step explanation:

Area of octagon=2(1+√2)a²

Where a is the length of the side of the octagon

Area=35 cm²

Let a' be the length of side of new octagon

a'=5a

Area=2(1+√2)a'²

       =25×2(1+√2)a²

       =25×35 cm²

       = 875 cm²

Hence, correct option is:

B. 875 cm²

The inverse of the function will be, ⁣[tex]\rm y=\frac{1}{4} x-2[/tex]. Option A is correct. The function is obtained by rearranging the equation.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The given function is;

[tex]\rm f(x) = 4x + 8 \\\\ y=4x+8 \\\\[/tex]

After rearranging the equation, we get;

[tex]\rm x=4y+8 \\\\ y= \frac{1}{4} (x-8)\\\\ y=\frac{x}{4} -2\\\\ y=\frac{1}{4} x-2[/tex]

The inverse of the function will be, ⁣[tex]\rm y=\frac{1}{4} x-2[/tex].

Hence, option A is correct.

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[tex] |\Omega|=52\\
|A|=\underbrace{13}_{\text{clubs}}+\underbrace{4}_{\text{jacks}}-\underbrace{1}_{\text{jack of clubs}}=16\\\\
P(A)=\dfrac{16}{52}=\dfrac{4}{13}\approx31\% [/tex]

Answer:

A. 4/13

Step-by-step explanation:

4/13 in percent is 30%(30.7692308 percent)

For Plato Users

Answer:5

Step-by-step explanation:

The correct answer is 2.48*10^12.

Answer:

its actually a

Step-by-step explanation:

The graph of the ordered pairs is a straight line graph with x,y values (-2, -6), (1, 6), and (2,10).

What are ordered pairs.

In geometry, Ordered pairs are the values of x and y on the coordinate plane. They are called ordered pairs because they are usually arrange in (x,y) axis.

For a linear equation, the graph is a straight line graph. From the information given:

y = 4x + 2

The points x-axis {-2, 1, 2} are marked on the graph and the corresponding y-values are {-6, 6, 10} respectively.

The value of c that makes x² + 10x + c a perfect square trinomial is c = 25.

Given the equation in the question:

x² + 10x + c

A perfect square trinomial is of the form (ax² + bx + c), and it can be factored into (px + q)², where p and q are constants.

To find the value of c such that x² + 10x + c is a perfect square trinomial, we need to factor it as (px + q)².

Note that, the coefficient of x in the given trinomial is 10, so 2pq must equal 10.

Also, the coefficient of x² is 1, so p² must equal 1.

Hence, we have:

2pq = 10

p² = 1

From equation (2), we know that p could be either 1 or -1, after taking the square of both sides:

If p = 1, from equation (1) we have:

2pq = 10

2(1)q = 10

2q = 10

q = 10/2

q = 5

So, if p = 1 and q = 5, the perfect square trinomial is (x + 5)².

Let's expand to check:

(x + 5)² = x² + 10x + 25

Therefore, the value of c is 25.

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The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle  justifies how the area of a sector of a circle is derived

The explanation that justifies how the area of a sector of a circle is derived is:

"The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle."

This method involves finding the fraction of the circle that the sector represents by dividing the central angle of the sector by 360 degrees. Then, multiply this fraction by the area of the whole circle to get the area of the sector.

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Answer: B ) [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given: The number of students in junior class n(S)= 50

The number of students take only Latin n(L-F)= 15

The number of students take only French n(F-L)=25

The number of students take both = n(F∩L)=10

The number of students take Latin n(L)=n(L-F)+n(F∩L)=15+10=25

Therefore, the probability that the student takes Latin is given by :-

[tex]\text{Probability(Latin)}=\frac{\text{number of students take latin}}{\text{Total students}}\\\\=\frac{25}{50}=\frac{1}{2}[/tex]

The quotients are different because the order matters in division. When 3 is divided by 1/5 it becomes a multiplication problem with reciprocal of 1/5, yielding 15. However, when 1/5 is divided by 3, it becomes multiplication with reciprocal of 3 and yields 1/15.

The reason that the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three is due to how division works in mathematics. To put it simply, the order of numbers in a division operation matters; it is not commutative like addition or multiplication.

When you divide 3 by 1/5, you're essentially asking, 'how many times does 1/5 fit into 3?'. Here, you're dealing with fractions and whole numbers. To perform the division, we multiply 3 by the reciprocal of 1/5, which is 5. The answer is 3 * 5 = 15.

But, when you divide 1/5 by 3, you're asking 'how many times does 3 fit into 1/5?'. Here, you need to multiply 1/5 by the reciprocal of 3, which is 1/3. The calculation is (1/5) * (1/3) = 1/15.

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Final answer:

Intellectual property rights such as patents and copyrights incentivize creative work by providing creators a temporary monopoly, allowing them to recover development costs and potentially make a profit without immediate competition.

Explanation:

Two intellectual property rights are patents and copyrights. A patent gives the inventor the exclusive legal right to make, use, or sell an invention for a limited time, usually for 20 years, and a copyright provides the author exclusive legal rights over their creative works.

Intellectual property rights offer creators monopoly profits during this protected period, acting as significant incentives for the production of creative work.

This exclusive period allows researchers and companies to recover the costs associated with research and development. Without these protections, there would be little to no incentive to invest in creating new works if they could quickly be replicated without any benefit to the creator.

Let's assume

Randy's speed =x mph

we have

Andy’s speed was slower than Randy’s by 15 miles per hour

so,

Andy's speed =x-15

Randy drove 540 miles

so, we can find time taken by Randy

time = distance / speed

so, we get

[tex]t_R=\frac{540}{x}[/tex]

we can find time taken by Andy

time = distance / speed

so, we get

[tex]t_A=\frac{135}{x-15}[/tex]

Randy drove 540 miles in three times the time it took Andy to travel 135 miles

so,

[tex]t_R=3t_A[/tex]

we can plug it

[tex]\frac{540}{x}=3*\frac{135}{x-15}[/tex]

now, we can solve for x

[tex]540\left(x-15\right)=405x[/tex]

[tex]135x=8100[/tex]

[tex]x=60[/tex]

so,

Calculation of rate:

Randy's speed is 60 mph

Andy's speed =x-15

Andy's speed =60-15=45mph

Calculation of time:

Randy's time is

[tex]t_R=\frac{540}{x}[/tex]

[tex]t_R=\frac{540}{60}[/tex]

[tex]t_R=9 hours[/tex]

Andy's time is

[tex]t_A=\frac{135}{x-15}[/tex]

[tex]t_A=\frac{135}{60-15}[/tex]

[tex]t_A=3 hours [/tex]

The four astronomical bodies represents here are A represents Universe, B represents Galaxy, C represents Solar System, and D represents Mars.

The hierarchical level D is different from the rest is because Mars is a planet and unlike all other astronomical bodies it does not hold other astronomical bodies with in it.

"Astronomical bodies are objects in space like sun, moon, planets, and stars. They form a part of the vast universe we live in and are very far from Earth."

"The universe includes all space, time, and their objects that also includes planets, stars, galaxies, and other forms of matter and energy."

"Galaxy is a vast collection of dust, gas, billions of stars with their solar systems that are all held together by gravity."

"Solar System is a gravitationally bound system of eight planets, their moons in orbit round the sun with small bodies like comets, meteoroids, and asteroids."

"Mars is the fourth planet from the sun and the second smallest planet in the Solar System."

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Since there is a decrease in quantity and supply the answer would be Consumer reports indicate that the sunglasses break easily.

Answer "A" is definitely wrong

The volume of a right circular cone with height 7h and base radius 3r is ⅔ 9r² h.

The volume of a right circular cone can be calculated using the formula V = ⅔ ² h, where r is the radius of the base and h is the height of the cone.

Plugging in the values, we have V = ⅔ (3r)² (7h) = ⅔ 9r² h.

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Final answer:

To solve the sigma notation problem, we individually calculate each term for n from 1 to 5 and sum them up, resulting in a total value of 33. Thus, the correct answer is C.33.

Explanation:

The problem involves evaluating a series using sigma notation. Specifically, we're looking at the summation of 3 × (-2)n-1, with n going from 1 to 5.

To find the solution, we need to calculate each term separately for each value of n, and then sum all of the calculated terms together.

Adding these values together: 3 - 6 + 12 - 24 + 48 = 33.

So the correct answer to the summation is 33, which corresponds to choice C.

Answer:  The answer is given below.

Step-by-step explanation: The given circles are:

Circle 1: centre (2, 3) and radius 4  

Circle 2: centre (2, 3) and radius 12.

The equations of circle 1 and circle 2 are respectively given as :

[tex](x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.[/tex]

These two circles are drawn on the graph as shown in the attached figure.

We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor

[tex]S=\dfrac{12}{4}=3.[/tex]

Thus, the two circles are similar.

Answer:

the sum will be degree 5

the maximum number of terms of the sum is 6

Step-by-step explanation:

Answer:

B) 5

Step-by-step explanation:

The probability of picking yellow first is  

x

12

. The probability of picking yellow second is  

x-1

11

. This will give a solution of  

x (x-1)

132

.  

5

33

is equivalent to  

20

132

. 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5 yellow marbles in the bag.