Given:
[tex]x = 1, y = 7,z = 15[/tex]
A number is added to x, y, and z yields consecutive terms of a geometric sequence.
To find:
The number which is added to x, y, and z, then find the first three terms in the geometric sequence.
Solution:
Let the unknown number be k.
After adding k to x, y, and z, we get
[tex]x = 1+k, y = 7+k,z = 15+k[/tex]
These are the consecutive terms of a geometric sequence. So,
[tex](7+k)^2=(1+k)(15+k)[/tex]
[tex]49+14k+k^2=15+k+15k+k^2[/tex]
[tex]49+14k=15+16k[/tex]
Isolate the variable terms.
[tex]49-15=16k-14k[/tex]
[tex]34=2k[/tex]
[tex]\dfrac{34}{2}=k[/tex]
[tex]17=k[/tex]
The unknown number is 17.
Now,
[tex]x=1+k[/tex]
[tex]x=1+17[/tex]
[tex]x=18[/tex]
Similarly,
[tex]y=7+k[/tex]
[tex]y=7+17[/tex]
[tex]y=24[/tex]
And
[tex]z=15+k[/tex]
[tex]z=15+17[/tex]
[tex]z=32[/tex]
Therefore, the three terms in the geometric sequence are 18, 24, 32.
Find the percent of change of 2/5 to 1/3?
HELPPPPPPPPPPPP MEHHHHHHHHHHHHHHHHHHHHHHHHH PLZZZZZZZZZZZZZZZZ GRADES GO OUT TOMMORROW AND I NEED THIS SO I CAN GET MY GRADE UP FROM A D+ PLZZZZZZZZ MY PARENTS WILL MURDER ME
Answer:
Fair well i hope you lived a good life
Step-by-step explanation:
A cone has a height of 10 meters and a diameter of 20 meters. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth
Answer: 235.5 cm³
Step-by-step explanation: Volume of a cylinder is the area of the circular base times the height of the cylinder:
V = π r² h
Given r = 5 cm and h = 3 cm:
V = (3.14) (5 cm)² (3 cm)
V = 235.5 cm³
f(x) = -2x + 9 What is f(2h) ?
Answer:
f(2h) = -4h + 9
Step-by-step explanation:
Jacob: Start with the given function f(x) = -2x + 9 and replace 'x' with 2h:
f(x) = -2x + 9 becomes:
f(2h) = -2(2h) + 9, or
f(2h) = -4h + 9
Answer:
-4h + 9
Step-by-step explanation:
f(x) = -2x + 9
f(2h) = -2(2h) + 9
f(2h) = -4h + 9
ASAP!!! and no links please 25 points!!!!!
The radius of a can of soda is 0.75 inches. Find the area of the top of the can. Round to the nearest hundredth.
(Values only! No units!)
Answer:
2.36
Step-by-step explanation:
Multiply the radius (0.75) with the value of pi (3.14.....)
0.75 x pi = area
area = 2.35619449019
ROUNDED TO HUNDREDTHS = 2.36
hope this helps :)
HELPP ME PLEASEEE!!!!!
don’t answer just for points. i’ll report you.
Answer:
-2
15 - (-2) = 17
a = -2
Answer:
A= -2
Step-by-step explanation:
15-a=17
+a +a
15=17+a
-17 -17
-2=a
2) 24, 12, 10, 15, 10, 22, 12 mean: _________ median: _________ mode: ________ range: ________
A fine fabric was selling for $10.50 per half yard. Joni bought 2 1/3 yards. How much did he spend? Brainliest for correct answer.
Answer:
$49 is spended by him.
solution given:
rate=for $10.50 per half yard=$10.50/0.5=$21 per yard
area=2 1/3=7/3yards
now
total cost =rate× area =$21×7/3=$49
What is the surface area of this design?
PLEASE HELP ASAP!!
SO you would have to first have the surface area of the cube which is 25 for each side so 25 x 6 = 150
Then you find the surface area for the other sides and It is 4 x 5 divided by two for each triangle on the side, so that would be 20 and you multiply then 6.4 x 5 to equal 32 for the rectangle. The last part is the bottom and it is 4 x 5 again which is 20 so then you add them all up but im not sure.
Use the recursive relationship to complete the next two rows of Pascal's triangle. Row 5: 1 _ _ _ _ 1 Row 6: 1 _ _ _ _ _ 1
Answer:
1 5 10 10 5 1 Row 5
1 6 15 20 15 6 1 Row 6
Recursive relationship:
Each row has number of positions = row number + 1. The Row 0 is always 1.
The first and last number in each row is 1, the number in the second position and the penultimate corresponds to the number of the row. The middle numbers correspond to the sum of the two numbers in the top row. The resulting number from the addition is located in the middle of the numbers added in the next row.
Step-by-step explanation:
The pascal's triangle
* Row 0 = 1
* Row 1 = 1 1
1 Row 0
1 1 Row 1
Since there are only two positions, the first and last are 1.
*Row 2 = 1 _ 1
1 Row 0
1 1 Row 1
1 2 1 Row 2
2 is the sum of 1 + 1 and we place it in the next row between the added numbers 1 and 1.
* Row 3 = 1 _ _ 1
1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3
1 + 2 = 3 (the row number and the and adding the numbers from the previous row)
* Row 4 = 1 _ _ _ 1
1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3
1 4 6 4 1 Row 4
1 + 3 = 4 (the row number)
3 +3 = 6
* Row 5 = 1 _ _ _ _ 1
1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3
1 4 6 4 1 Row 4
1 5 10 10 5 1 Row 5
1 + 4 = 5
4 + 6 = 10
* Row 6 = 1 _ _ _ _ _ 1
1 Row 0
1 1 Row 1
1 2 1 Row 2
1 3 3 1 Row 3
1 4 6 4 1 Row 4
1 5 10 10 5 1 Row 5
1 6 15 20 15 6 1 Row 6
1 + 5 = 6
5 + 10 = 15
10 + 10 = 20
How do I solve this ?
Answer:
16
Step-by-step explanation:
because it's g of 7 use the third equation.
(7+1)(7-5) = 8x2 = 16
what is the answer?????
Answer:
40 meter (4000 centimeters)
Step-by-step explanation:
bro just do 4 x 10 = 40 x 100 = 4000
Give me Brainllest
(5x - 7y + 8) + (-y + 6 - 4x) + (9 - 3x + 8y)
Place the quadratic y=2x^2+24x+79 into vertex form by using the method of completing the square and then state the coordinates of its vertex.
Answer:
[tex]y=2(x+6)^2+7[/tex]
[tex](-6,7)[/tex]
Step-by-step explanation:
[tex]y=2x^2+24x+79[/tex]
Completing the square is a process of converting a quadratic equation in standard form into vertex form.
The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.
[tex]y=(2x^2+24x)+79[/tex]
Factor out the coefficient of the quadratic term,
[tex]y=2(x^2+12x)+79[/tex]
Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.
[tex]y=2(x^2+12x+36-36)+79[/tex]
Simplify,
[tex]y=2(x^2+12x+36)+79+(2)(-36)[/tex]
[tex]y=2(x+6)^2+79-72[/tex]
[tex]y=2(x+6)^2+7[/tex]
The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.
[tex](-6,7)[/tex]
If a=10 and b=3 , find the value of x .
Answer:
7
Step-by-step explanation:
10-3=7
. Evaluate the following: |15 - 47] + 9 - (-2)(-4) - 17|
Answer:
48
Step-by-step explanation:
Since there is an absolute value, the answer must be positive. Multiply 2 by 8 since two negatives equal a positive. So, |15-47 + 9 - 8 -17|. Then add and subtract to get the answer. -32 + 9 - 8 -17 = -48. |-48| = 48
Answer: 50
Step-by-step explanation:
did i do this right “what % of 369 is 26” i got 7.04 so is that the rounded answer (hundredths place) or just 7.0=7?
Answer:
26 is 7.05% or 7.04% of 369.
Step-by-step explanation:
Now 7.04% of 369 is actually 25.9776.
and 7.04% is 26.01452.
But if you round both 25.9776 and 26.01452 you get 26
So, technically you are correct.
Hope this helps! :)
What 6 over 4 simplified
Triangle ABC is a right triangle. The length of one leg is 30 cm and the hypotenuse is 78 cm. What is the length of the other leg?
Answer:
72
Step-by-step explanation:
there is 180 degrees in a triangle
In ΔRST, s = 70 inches, t = 46 inches and ∠R=109°. Find ∠T, to the nearest degree.
Answer:
T = \cos^{-1}(0.890172999145)\approx 27.105\approx 27^{\circ}
T=cos
−1
(0.890172999145)≈27.105≈27
∘
Step-by-step explanation:
Use the distributive property to write an expression that is equivalent to 6(w - 4)
Answer:
6w-24
Step-by-step explanation:
You would distribute 6 into the parentheses, which would turn (w-4) to 6w-24
Answer:
(w - 4)6
Step-by-step explanation:
its the same exact thing but if you're looking for the simplified version then it's 6w-24
HELP ASAP
Which number is IRRATIONAL?
A)
64
B)
V81
C)
96
D)
144
Answer:
All are rational numbers
Step-by-step explanation:
irrational numbers can't be expressed as a fraction.
96 is an irrational numbers
If 1/2 gallon of paint covers 1/8 of a wall, then how many quarts of paint are needed for the entire wall?
Answer:
4
Step-by-step explanation:
i need help with this no link pls
Answer:
1. x = 36 equation is x + 2x + 9 = 117, then solve for x
2. x = 50 equation is x + x + 12 = 112, then solve for x
Step-by-step explanation:
Graph the equation y=-x^2-12x-35y=−x 2−12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
please help and explain I'm very confused and I have no idea what to do.
The graph of y=-x^2-12x-35 is attached and it has x intercepts at x=-7 and x=-5 and vertex is at (6, -107).
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
To graph the equation y=-x^2-12x-35, we can start by finding the x-intercepts (or roots) and the vertex of the parabola.
To find the x-intercepts, we can set y=0 and solve for x:
0 = -x² - 12x - 35
Using the quadratic formula, we get:
x=-b±√b²-4ac/2a
x=12±√144-140/2(-1)
x=12±√144-140/(-2)
x=12±2/(-2)
The x-intercepts are approximately x=-7 and x=-5
To find the vertex, we can use the formula x=-b/2a to get the x-coordinate, and then substitute it into the equation to get the y-coordinate:
x = -b / 2a = -(-12) / 2(-1) = 6
y = -x² - 12x - 35 = -(6)^2 - 12(6) - 35 = -107
So the vertex is at (6, -107).
Hence, the graph of y=-x^2-12x-35 is attached and it has x intercepts at x=-7 and x=-5 and vertex is at (6, -107).
To learn more on Quadratic equation click:
https://brainly.com/question/17177510
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)) What is 538 rounded to the nearest ten? 500 535 ))
Step-by-step explanation:
540 because it I think or 535 but I I think it's 540
Helppppppp I’ll give you 10 pointssss plzzz
PLEASE GIVE RIGHT ANSWER Triangle EFG has coordinates E (0, 0), F (0, 2), and G (3, 0). If ΔEFG ≅ ΔXYZ, what is the measure of XY? 1.5 units 2 units 3 units 3.5 units
Answer:
2 units
Step-by-step explanation:
Congruent triangles are those triangles, which have same shape & size (same side & angle size).
If ΔEFG ≅ ΔXYZ. And, E (0, 0), F (0, 2), and G (3, 0)
So, length EF = length XY.
Length of E (0,0) & F (0,2) is 2 units
As triangles are congruent, EF = XY
Hence, measure of XY = 2 units
Answer:
2 units
Step-by-step explanation:
Write two numbers that have the given absolute value.
22
Answer:
22 and -22
Step-by-step explanation:
Absolute value means the distance of a number from zero
Which of the following statements about parallelograms are true?
Select all that apply. (You should have more than one answer choice selected.)
a
all angles of a parallelogram add up to 360 degrees
b
all sides of a parallelogram are parallel
c
all parallelograms are rectangles
d
opposite angles of a parallelogram are congruent
e
opposite sides of a parallelogram are congruent
f
all rectangles are parallelograms
Answer:
a,d,e,f
Step-by-step explanation:
