Find the product of (3x + 7y)2. 9x2 − 42xy + 49y2 9x2 − 49y2 9x2 + 49y2 9x2 + 42xy + 49y2
Answer:
[tex]9x^{2}+42xy+49y^{2}[/tex]
Step-by-step explanation:
we know that
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]
In this problem we have
[tex](3x+7y)^{2}[/tex]
so
[tex]a=3x[/tex]
[tex]b=7y[/tex]
substitute
[tex](3x+7y)^{2}=(3x)^{2}+2(3x)(7y)+(7y)^{2}[/tex]
[tex]=9x^{2}+42xy+49y^{2}[/tex]
55% decrease followed by a 25% increase
Which of the following is true about the age of rock layers and the age of the Earth? A. All rock layers are older than the Earth. B. The Earth is older than any rock layer. C. The bottom layer in a sequence of rock layers is older than the Earth. D. The top layer in a sequence of rock layers is older than the Earth.
The Earth is older than any rock layer. This fact is determined through the use of principles like the law of superposition and radioactive dating methods, such as uranium-lead dating. The oldest rocks on Earth have been dated to be almost 4.4 billion years old, whereas the Earth itself is estimated to be around 4.5 billion years.
Explanation:This is based on geological principles and radioactive dating methodologies. One of the foundational principles in geology is the law of superposition, which states that in an undisturbed sequence of rock layers, each layer is younger than the one below it.
The age of Earth is estimated to be around 4.5 billion years. We can deduce this from radioactive dating methods, such as uranium-lead dating. In this method, the oldest rocks on Earth, known as the Jack Hills zircons from Australia, have been dated at almost 4.4 billion years old.
Given these findings, it is understood that no existing rock layer can be older than the Earth itself.
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B. The Earth is older than any rock layer.
The Law of Superposition states that in an undeformed sequence of sedimentary rocks, the bottom layer is the oldest and the top layer is the youngest. Applying this principle to the Earth's rock layers, we can conclude that the Earth is older than any rock layer as the layers closer to the surface are younger compared to those at the bottom.
The general term for the sequence 2, 4, 8, 16, 32, . . . is
We are given
sequence is 2 , 4 , 8 ,16 , 32 , .....
Firstly , we will check whether it is geometric sequence
Checking geometric sequence:
We will find common ratio between successive terms
and then we check whether they are equal
r1=(second term)/(first term)
[tex] r_1=\frac{4}{2}=2 [/tex]
r2=(third term)/(second term)
[tex] r_2=\frac{8}{4}=2 [/tex]
r3=(fourth term)/(third term)
[tex] r_3=\frac{16}{8}=2 [/tex]
r4=(fifth term)/(fourth term)
[tex] r_4=\frac{32}{16}=2 [/tex]
we can see that all four ratios are same
[tex] r_1=r_2=r_3=r_4=2 [/tex]
so, this is geometric sequence
Calculation of general term:
We got
common ratio is
[tex] r=2 [/tex]
Let's assume
number of terms is n
first term is 2
[tex] a_1=2 [/tex]
now, we can use formula
[tex] a_n=a_1 (r)^{n-1} [/tex]
we can plug values
and we get
[tex] a_n=2(2)^{n-1} [/tex]
[tex] a_n=2^1(2)^{n-1} [/tex]
[tex] a_n=(2)^{n-1+1} [/tex]
[tex] a_n=(2)^{n} [/tex]..................Answer
Answer:
a1: 2 r1: 2
Step-by-step explanation
just did it on edge :)
the answer for the second part is the 1st and 4th formulas
A Glass paperweight has the shape of a triangular prism. The bases are equilateral triangles with side lengths of 4 inches and a height of 3.5 inches. The height of the prism is 5 inches. find the lateral area and the total surface area of the paperwork.
The lateral area of the triangular prism is 21 square inches and the total surface area is 35 square inches.
Explanation:
To find the lateral area of the triangular prism, we need to calculate the area of all three sides excluding the bases. Since the bases are equilateral triangles with side lengths of 4 inches, the area of each base is ½ × base length × height = ½ × 4 × 3.5 = 7 square inches. The lateral area is the sum of the areas of the three sides, which is 3 × 7 = 21 square inches.
The total surface area of the prism includes the bases as well. So we need to calculate the area of the two triangular bases and add it to the lateral area. The total surface area is 2 (area of base) + lateral area = 2 × 7 + 21 = 35 square inches.
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The lateral area of the triangular prism is 60 square inches, and the total surface area is 74 square inches.
To find the lateral area and total surface area of a triangular prism:
Step 1: Calculate the Area of One Triangular Base
The base is an equilateral triangle with sides of 4 inches and a height of 3.5 inches. The area of an equilateral triangle is calculated using the formula:[tex]Area = \frac{1}{2}*base*height[/tex]
So the area is:[tex]Area = \frac{1}{2} *4\ in*3.5\ in = 7\ square\ inches[/tex]
Step 2: Calculate the Perimeter of the Base
The perimeter of the base is:Perimeter = 3 * side length = 3 * 4 in = 12 inches
Step 3: Calculate the Lateral Area
The lateral area of a prism is given by:Lateral Area = Perimeter * height of the prism
Therefore, the lateral area is:Lateral Area = 12 in * 5 in = 60 square inches
Step 4: Calculate the Total Surface Area
The total surface area is the sum of the lateral area and the areas of the two triangular bases:Total Surface Area = Lateral Area + 2 * Area of one baseTotal Surface Area = 60 square inches + 2 * 7 square inches = 74 square inchesThus, the lateral area and total surface area are 60 square inches and 74 square inches.
18 out of 24 of Emils CDs are country music 5 out of 8 of Imanis CDs are country music. Which is a true statement A Half of each CD coleection consists of country music B less than half od ech CD collection consists of country music E Emil has a greater fraction of country music than Imani
D imani has greater fractionof country music than Emil which one is true A B C or D
Suppose all left-handed people are excluded from a sample. What is this an example of?
A. Selection bias
B. Response bias
C. Nonresponse bias
D. Nonselection bias
Answer: A . selection bias
Step-by-step explanation:
If two prisms have the same volume, do they always, sometimes, or never have the same surface area
Answer:
sometimes
Step-by-step explanation:
Two prisms with the same volume sometimes have the same surface area, but not always, because surface area depends on the dimensions of all prism faces. Different shapes with the same volume, such as a sphere, a cube, and a cylinder, can have significantly different surface areas, especially if their proportions change.
Explanation:If two prisms have the same volume, they do sometimes have the same surface area, but not always. The volume of a prism is determined by the area of the base multiplied by the height, but the surface area includes the areas of all the faces of the prism.
Therefore, two prisms can have the same volume, but if their dimensions—base areas and heights—are different, their surface areas can be very different as well. This holds true for other geometric shapes as well.
Example with Different ShapesFor instance, consider a sphere, a cube, and a cylinder that all have the same volume. According to the formula for a sphere, sphere: volume = 4/3 (pi) (r)³; surface area = 4 (pi) (r)², for a cube, cube: volume = (s)³; surface area = 6 (s)², and for a cylinder, cylinder: volume = height (pi) (r)²; surface area = 2 (pi) (r) (height) + 2 (pi) (r)². Even if all these shapes have a volume set at 1 unit cubed, their surface areas can vary significantly.
Furthermore, changing the shape's proportions while keeping the volume constant (such as elongating a cylinder or a cube) generally increases the surface area.
This is showcased in data where cylinders and cubes shapes elongated in length or width have different surface areas but maintain the same volume.
^^I have no idea what this is, means or is asking so help please, thanks!
Mike’s current restaurant measures 60 feet by 30 feet. Due to increase in the number of customers, he wants to rent a bigger restaurant. The dimensions of the bigger restaurant will be related by a scale factor of 2. What is the difference in area between Mike's new restaurant and his current restaurant, in square feet?
Order the sides or angles of the triangle from least to greatest
HELP ME!
The Pythagorean Theorem and Distance Formula are both used to find distances on the coordinate plane. Explain when it is appropriate to use each method.
if the measure of AB is 8 find the length of the radius of C
Help ASAP
Nina is participating in a swim-a-thon to raise money for a charity. For every lap that Nina swims, her grandmother has promised to donate $2.50. If Nina swims 18 laps, how much will her grandmother donate?
A.$45.00
B.$20.50
C.$18.00
D.$7.20
the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to return to earth? round your answer to the nearest tenth of a second. show all your work.
The rocket takes approximately 8.6 seconds to return to earth.
Explanation:To calculate the time it takes for the rocket to return to earth, we need to consider the projectile motion in the vertical direction. The initial vertical velocity of the rocket is 42 m/s. We can use the equation for vertical displacement to find the time:
Δy = v0yt + (1/2)gt²
Since the rocket returns to the same altitude, the displacement is 0. Therefore, we have:
0 = (42)t + (1/2)(-9.8)t²
Simplifying this equation and solving for t, we find that it takes approximately 8.6 seconds for the rocket to return to earth.
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Jane biked 34 miles in 2 hours. At this rate, how far could she bike in 5 hours?
13.6 mi
37 mi
76 mi
85 mi
Solve the equation 2^(3−2) +4=16.
Please show all work.
Two sides of a right triangle measure 7 units and 3 units. What is the area of the square that shares a side with the third side of the triangle?
We can use the Pythagorean theorem to find the length of the third sides.
c²=a²+b²
Where c is the longest (unkwon ) side, a and b are the remaining sides. So,
c²=7²+3²
= 49+9
= 58
So, c=√58
So, the length of the third side or the side length of square is √58.
So, the area of the shaded region (square)= c²
=(√58)²
=58
So, the area of the square is 58 units².
Answer: 58 units squared
Step-by-step explanation:
In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 288π cm².
What is the value of x?
HELP QUICK PLEASE!!!!
explain in a short paragraph how the figure below shows this is a right angle, by the converse of the phythagorean theorem
Joelle plans to sell two types of balloons at her charity event: 171717‑inch latex balloons that require 222 cubic feet (\text{ft}^3)(ft 3 )left parenthesis, f, t, start superscript, 3, end superscript, right parenthesis of helium and 181818‑inch mylar balloons that require only 0.5 \,\text{ft}^30.5ft 3 0, point, 5, space, f, t, start superscript, 3, end superscript. She only has access to 1{,}000 \,\text{ft}^31,000ft 3 1, comma, 000, space, f, t, start superscript, 3, end superscript of helium, 15\%15%15, percent of which will be unused due to pressure loss in the tanks. She wants to have at least 500500500 balloons for sale in total. For the number of latex balloons, LLL, and number of mylar balloons, MMM, which of the following systems of inequalities best represents this situation? Choose 1 answer:
Which mathematical property is demonstrated? 40 • (25 • 74) = (40 • 25) • 74
A. commutative property of addition
B. associative property of multiplication
C. associative property of addition
D. commutative property of multiplication
Answer:
d
Step-by-step explanation:
hope it helps
4/7x = 64
Answer for x
x = 112
This is because
4/7x = 647/4 x 4/7 = 64/1 x 7/4
1x= 448/4
x = 112How many triangles can be constructed with angles measuring 120°, 40°, and 10°?
A. One
B. None
C. More than one
What’s the first 200 digits of pie?????????
Please help ‼️ I’m doing functions
How do you find the area of a rectangular prism?
The equation d=60t gives the distance d (in miles) a car travels after t hours. Identify the independent and dependent variables.
The required d is the dependent variable and t is the independent variable.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values.
In the equation, d=60t, t is the independent variable and d is the dependent variable. The value of d depends on the value of t, which is the amount of time the car travels, and hence is the independent variable.
Thus, d is the dependent variable and t is the independent variable.
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You are working as an office apprentice for the bksb Newcastle Arena. The arena is deciding what events to book for next year. Examine the market research below and answer the questions that follow. Look at the bar chart below.
*What music genre is the 26 to 36 age group’s favorite?
*How many people from the 37 to 47 age group like ‘other’ music?
*Which three genres has the most fans?
Answer:
What music genre is the 26 to 36 age group’s favorite? It's pop
How many people from the 37 to 47 age group like ‘other’ music? 20 people
Which three genres has the most fans? "Pop", "Rock" and "Dance"
Step-by-step explanation:
What music genre is the 26 to 36 age group’s favorite?
The colors indicate the different age ranges. So first you must locate the color belonging to the range of 26 to 36 years, which is gray.
Now, you place that color in the graph and to determine which genre of music is the favorite in that age, you must place the genre with more people aged between 26 and 36. That reads on the “y” axis, which in the graph is seen as "the tallest gray rectangle". Once this is located, you read on the "x" axis the genre to which it belongs. This results in the music genre "pop"
How many people from the 37 to 47 age group like ‘other’ music?
For this case, as in the previous case, you first locate the color belonging to the age range of 37 to 47, which is the color yellow.
But now you must first place that color on the "x" axis, which is the one corresponding to the music genre. In this case you locate the genre "others". Then with the yellow color you read the number of people on the "y" axis.
Note that the numbers marked are every 100, but that between each number there are 5 divisions. This means that the scale is 20 people (obtained as 100 divided by 5)
The color belonging to the age range of 37 to 47 in the genus "others" reaches the first division. This means that the number of people who like this genre is 20.
Which three genres has the most fans?
In this case you should pay attention to which genders ("x" axis) have the greatest number of people ("y" axis), regardless of age. Observing "the longest colored rectangles", which indicate that more people like the genre, and reading the axis of music genres, you can see that the three genres that have more fans are "Pop", "Rock" and "Dance"
Use the distributive property to simplify the expression (12 + 10x) 1/2
Answer:
2(5x + 6)
Step-by-step explanation:
i think you need to rearrange 12 + 10x which that is also 2(5x + 6) ?
sorry if i didn't explain well
Answer:
i Don’t understand
Step-by-step explanation:
pls give me brainliest for the love of god