Answer: theres a website called weegy did you try that?
If the sum of first 7 terms of an A.P is 49 and the sum of first 17 terms is 289 find the sum of first 30 term
Sum of first 7 terms of an AP = 49.
Sum of first 17 terms = 289
Find:the sum of first 30 term
Solution:We know that,
Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]
Hence,
→ 7/2 * [ 2a + (7 - 1)d ] = 49
→ 2a + 6d = 49 * 2/7
→ 2( a + 3d ) = 14
→ a + 3d = 14/2
→ a + 3d = 7 -- equation (1)
Similarly,
→ 17/2 * [ 2a + 16d ] = 289
→ 17/2 * 2 * (a + 8d) = 289
→ a + 8d = 289 * 2/17 * 1/2
→ a + 8d = 17 -- equation (2)
Subtract equation (1) from (2).
→ a + 8d - (a + 3d) = 17 - 7
→ a + 8d - a - 3d = 10
→ 5d = 10
→ d = 10/5
→ d = 2
Substitute the value of d in equation (1).
→ a + 3 * 2 = 7
→ a = 7 - 6
→ a = 1
Now,
Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]
→ S(30) = 15 (2 + 58)
→ S(30) = 15 * 60
→ S(30) = 900
Therefore, the sum of first 30 terms of the given AP is 900.
I hope it will help you.
Regards.
answer refer in pic siso
Enter the correct answer in the box.
What is the factored form of this expression?
64x^3 - 125
Write all factors in standard form.
9514 1404 393
Answer:
(4x -5)(16x² +20x +25)
Step-by-step explanation:
The factoring of the difference of cubes has a standard form:
a³ -b³ = (a -b)(a² +ab +b²)
Here, your knowledge of the cubes of small integers tells you that ...
64 = 4³
125 = 5³
So, in the above, we have ...
a = 4x, b = 5
and the factored form is ...
(4x -5)(16x² +20x +25)
plz help me!! Polynomial Long Division (Level 2)
x^3 + 3x^2 + 16x + 48
Answer:
(x2 +16)⋅(x+3)
Step-by-step explanation:
Can someone help me create a slope story???
Answer:
I was walking home which I had to go up a hill I wanted to stop by the gas station which was a small hill upwords went back down that hill and the big hill to reach home.
Step-by-step explanation:
y axs = elavation
x axs = time
Hope that helped a little I need to do my hw but seen you needed help sorry if I did not help :(
Brooke purchased 16 boxes of a popular novel to sell at her bookstore. If each box weighs 29.5 pounds, what is the total weight of all of the boxes of books? A. 483.8 pounds B. 456 pounds C. 472 pounds D. 488 pounds
Answer:
C. 472
Step-by-step explanation:
16x29.5=472
You are given a fraction in simplest form. The numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal. Which numbers from 1 to 10 could be the denominator?
When the denominator is
_______, ________, ________, or ________ the result will be a repeating decimal.
Please explain your answer.
Answer:
.
Step-by-step explanation:
the mass of the moon
Answer:
The answer is 10^24kg. 0.07346.
The graph below shows a proportional relationship between xxx and yyy.
What is the constant of proportionality,
x
y
start fraction, y, divided by, x, end fraction ?
0.50
Step-by-step explanation:
Its right <3
In the graph the constant of proportionality is 0.5
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The constant of proportionality is the ratio between two directly proportional quantities.
Two quantities are directly proportional when they increase and decrease at the same rate.
The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
From the given graph let us take one point (1, 0.5)
k=0.5/1
Constant of proportionality is 0.5
Hence, in the graph the constant of proportionality is 0.5
To learn more on Graph click:
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What is the slope of 4x + 3y = −24?
Answer:
slope is 4/3x
Step-by-step explanation:
How much is 37 1/2 percent of 48.72?
Answer:
18.27
Step-by-step explanation:
18.27
Answer: 18.28125
Step-by-step explanation:
Convert 37.5% to a decimal:
0.375
Multiply 48.72 by the decimal:
48.72(0.375)
18.28125
This can be rounded to 18.28 if you need.
Hope this helps!
Rhode Island has a population of about 60,000 8th graders in the state. New Jersey has a total of 920,000 8th graders. Calculate the difference in Rhode Island and New Jersey's state's population of 8th graders. Express your final answer in scientific notation.
Answer:
8.6 × 10^5
Step-by-step explanation:
New Jersey 8th graders = 920,000
Rhode island 8th graders = 60,000
Difference in Rhode island 8th graders and New Jersey 8th graders population
= 920,000 - 60,000
= 860,000
Answer in scientific notation
860,000
The decimal point will move 5 places in
= 8.6 × 10^5
Find the value of x
A-6
B- 4
C- 11
D- 5
Answer:
b.11
Step-by-step explanation:
3x+2+70=9x+6
put your like terms on one side:
9x-3x=70+2-6
6x=66
divide both sides by 6
x=11
Goran took 3 hours to clean the bathroom. Then he took 2 hours to clean the kitchen. How much total time did Goran take to clean the two rooms?
Write your answer as a mixed number in simplest form.
Answer:
5
Step-by-step explanation:
To the nearest tenth, how many inches equal 12.55 centimeters? (1 in. = 2.54 cm)
Answer:
5.1
Step-by-step explanation:
all you do is divide 12.55 by 2.54
Answer:
5 inches.
Step-by-step explanation:
If each inch is 2.54, you basically have to divide 12.55 divided by 2.54. Which would equal 4.94094488189. That would round to 5, which means approximately, it equals 5 inches.
Sorry if this is incorrect, but I do believe it is correct, have a good day!
The formula for the circumference, C, of a circle with radius r is given.
C=2pi
Amanda made a circular toy hoop using a plastic tube. The circumference of the hoop is 125.6 inches. What is the radius of the hoop? Use 3.14 for pi.
A.
80 inches
B.
10 inches
C.
20 inches
D.
40 inches
What is the equation of the line ? and how do i know ?
Answer:
The equation of the line is y=-16x+7
Step-by-step explanation:
I am not totally sure if that is what you meant by the equation of the line but that is my answer. I can change it if you are more specific.
Anyways, you need to find the slope because you already know the y-intercept, 7.
Slope=rise/run between two pretty points( A point that lines up on the grid)
So you must go from the bottom point and count how ever many are separating the two points. It turned out to be 16 and since the line is going down it is a negative. You then plug the numbers into the slope intercept form and that is your answer.
Find the slope of the line
Answer:
Slope= -5/3
Step-by-step explanation:
Item 3 Find the distance from point $A$ to $\overleftrightarrow{XZ}$ . Round your answer to the nearest tenth. Triangle X Z A and line X Z are plotted on a coordinate plane. The x-axis ranges from negative 5 to 5, in increments of 1. The y-axis is ranges from negative 5 to 5, in increments of 1. Point X is at ordered pair negative 4 comma negative 3, point Y is at ordered pair 2 comma negative 1.5, point A is at ordered pair 3 comma 3 and point Z is at ordered pair 4 comma negative 1. Angle A Z X is marked with a right angle.
Answer:
3.2
Step-by-step explanation:
Given the coordinates
X(4, -3)
Y(2, 1.5)
A(3, 3)
Z(4,-1)
We are to find the distance from point A to XZ
First let us get the coordinate XZ
According to vector notation XZ = Z-X
XZ = (4,-1)-(4,-3)
XZ = [(4-4),-1-(-3)]
XZ = (0, 2)
Next is to find the distance from A(3, 3) to XZ(0,2) using the formula for calculating the distance between two points.
D = √(x2-x1)²+(y2-y1)²
x1 = 3, y1 = 3, x2 = 0, y2 = 2
D = √(0-3)²+(2-3)²
D = √9+1
D = √10
D = 3.16
Hence the distance from point A to XZ to nearest tenth is 3.2
Can someone help me please? Im really confused
Answer:
141 degrees i think
Step-by-step explanation:
Tickets to a movie cost $11 for adults and $7 for students. A group of friends purchased 8 tickets
for $76. Write a system of equations to represent the situation. How many adult tickets and
student tickets were purchased
PLEASE HELP ME
Answer:
5 Adult tickets were purchased and 3 student tickets were purchased.
Step-by-step explanation:
5 Adult tickets were purchased and 3 student tickets were purchased.
Step-by-step explanation:
Write the problem as an equation like this
11x+7x=76
Now make an equation for the number of purchased tickets. Let x be adult and y be students.
x+y=8
Rewrite x + y = 8 as y = -x +8
Substitute y = -x + 8 into the first equation for y.
11x+7(-x+8)=76
11x+(-7x)+56=76
solve for 11x+(-7x)
4x+56+76
subtract 56 from both sides
4x=20
Divide both sides by 4
X=5
x + y = 8
5 + y = 8
y = 3
5 Adult tickets were purchased and 3 student tickets were purchased.
5 adult tickets and 3 student tickets were purchased.
What are system equations?
A finite set of simultaneous equations are called system equations.
Let, they purchased x tickets for adults and y tickets for students.
Therefore, system equations are:
x + y = 8 ----- equation 1
11x + 7y = 76----- equation 2
From equation 1, we get: x = (8 - y)
Now, substituting the value of x in equation 2, we get:
11 × (8 - y) + 7y = 76
⇒ 88 - 11y + 7y = 76
⇒ 88 - 76 = 4y
⇒ 4y = 12
⇒ y = 3.
Therefore, putting the value of y in equation 2, we get: x = (8 - 3) = 5.
Hence, 5 adult tickets and 3 student tickets were purchased.
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Apply a 90 degree rotation to the point (1, 2)
Answer:
(-1,2)
Step-by-step explanation:
90 degree rotation from (a,b) is (-a,b)
Is it always true that dilations of a triangle are congruent to the original triangle
Answer:
A dilation is a transformation that changes the size but not the shape of a figure. Therefore, the image created by the dilation is not congruent to the pre-image, the original figure; it is similar. ... The scale factor of a dilation is the ratio of a length in the image to the corresponding length in the pre-image.
Step-by-step explanation:
hope this helps ig
An ornament shaped like a sphere has a radius of 2.3 inches which measurement is closest to the volume of the ornament in cubic inches
Answer:
50.97in^3Step-by-step explanation:
Volume of a sphere
The expression for the volume of a sphere is given as
V=4/3πr^3
Given that the radius is 2.3in
Substitute r= 2.3 in the expression to find the volume of the sphere
V=4/3*3.142*(2.3)^3
V=4/3*3.142*(12.167)
V=4/3*38.23
V=152.9/3
V=50.97in^3
Therefore the volume of the ornament is 50.97in^3
The radius of a circle is 2 feet longer than the radius of another circle. What is the
radius of each if their areas differ by 241 square feet?
Answer:
Step-by-step explanation:
ario made a deposit in an account that earns annual interest. His account balance, in dollars, after t years is represented by the expression 400⋅1.05t . Yvonne made a deposit in an account that earns annual interest. Her account balance, in dollars, after t years is represented by the expression 300⋅1.06t . Which statement describes the situation correctly? A. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent more annual interest than Mario’s account. B. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent less annual interest than Yvonne’s account. C. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent less annual interest than Mario’s account. D. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent more annual interest than Yvonne’s account.
Answer:
nothing at all.
Step-by-step explanation:
HELP!!!
This is a geometry question!
Please give reasoning with your answer!
I can and will mark a "real" answer brainliest!
Answer:
see below
Step-by-step explanation:
shape LNMP is :
translated as 0,-7 flip of mirrored along y-axis reflected imaged is ABCD as givenA rectangle has an area of 2,340 sq ft and a width of 45 ft. What is its length ? What is the perimeter
Answer:
length is 52 ft
perimeter is 194
Step-by-step explanation:
2340/45 = 52
2(52+45) = 194
Marissa is choosing a four-digit PIN for her ATM card. The first digit must be a digit from 1 through 9. For the other three digits, she can choose any combination of digits 0 through 9, but may not repeat a digit. Which shows part of the sample space for Marissa's PIN?
Answer:
2345, 2034, 2134
Step-by-step explanation:
From the choices available the only options that would samples would be 2345, 2034, 2134. These three samples meet all of the requirements of the ATM cards pin system. Each of them starts with a 2 which is between 1 and 9. The last 3 digits of each of these samples are between 0 and 9 and are also not repeated from any of the other digits in the pin. All of the other options available either start with a 0 or have at least one repeating digit in its pin code.
What is the area of this polygon?
Pleasee help mee
I will mark brainliest!
Answer:
60 squared inches.
Step-by-step explanation:
You can break this polygon into two parts. The rectangle part of the polygon is 55 squared inches. The triangle part is 5 squared inches.
The rectangle:
[tex]5(11)=55[/tex]
The triangle:
[tex]2(5)=10\\10/2=5[/tex]
Therefore, the whole polygon is 60 squared inches.
Like what the other one said, and thank you so much for the points.