Given:
4, x, y, 108 are the consecutive terms of a G.P.
To find:
The x and y.
Solution:
The nth term of a G.P. is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Let us consider 4, x, y, 108 are the first 4 terms of the G.P. Here 4 is the first term of the given G.P.
Suppose r the common ratio, then 4th term of the given G.P. is:
[tex]a_4=4(r)^{4-1}[/tex]
[tex]a_4=4(r)^{3}[/tex]
The 4th term of the G.P. is 108.
[tex]4(r)^{3}=108[/tex]
[tex]r^{3}=\dfrac{108}{4}[/tex]
[tex]r^{3}=27[/tex]
[tex]r^{3}=3^3[/tex]
On comparing both sides, we get
[tex]r=3[/tex]
The common ratio is 3.
The second term of the given G.P. is:
[tex]x=4r[/tex]
[tex]x=4(3)[/tex]
[tex]x=12[/tex]
The third term of the given G.P. is:
[tex]y=xr[/tex]
[tex]y=12(3)[/tex]
[tex]y=36[/tex]
Therefore, the value x is 12 and the value of y is 36.
Find the slope of the line that passes through (4, 10) and (1, 11).
Answer:
-1/3
Step-by-step explanation:
Kate has a coin collection. She keeps 7 of the coins in a box, which is only 5% of her entire collection. What is the total number of coins in Kate's coin collection?
Answer:
140
Step-by-step explanation:
7/.05 -140
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
Solve equation2/3*2/3*2/3*2/3=
Answer:
16/81
Step-by-step explanation:
Same as (2/3)^4
Benjamin and Felix are 35 miles apart. At 3:00pm they start jogging towards each other. Benjamin jogs at a pace of 16 minutes per mile. Felix jogs at a pace of 10 minutes per mile. how many miles will Benjamin jog in 45 minutes
Using division operation, since Benjamin jogs at a pace of 16 minutes per mile, in 45 minutes he will jog 2.8 miles.
What is the division operation?The division operation is one of the basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient (the result).
The distance between Benjamin and Felix = 35 miles
Benjamin's jogging pace or speed = 16 minutes per mile
Felix's jogging pace or speed = 10 minutes per mile
The number of miles that Benjamin can jog in 45 minutes = Time/Speed
= 2.8125 miles (45/16)
Thus, Benjamin will jog 2.8 miles in 45 minutes.
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Sharon created a rectangular prism with cubes that have a side length of 1 inch. The prism is shown below.
What is the volume of Sharon’s prism? A. 18 cubic inches B. 27 cubic inches C. 36 cubic inches D. 54 cubic inches
Answer:
6 x 2 x 3 = 36
Step-by-step explanation:
C is answer :)
Answer:
lets look at the width and the height and the length!
your width is: 6
your height is: 2
your length is: 3
Now lets multiply all given lengths to find the volume!
6 x 2 x 3 = 36 cubic inches!
The product of all of the solutions of (4x + 2k)(2 -5x ) = 0 is (−15). Find k.
Answer:
k = 75------------------------------
Given equation:
(4x + 2k)(2 - 5x) = 0Its solutions are:
4x + 2k = 0 and 2 - 5x = 04x = - 2k and 2 = 5xx = - 0.5k and x = 0.4The product of the solutions is -15:
- 0.5k * 0.4 = - 15- 0.2k = - 15k = - 15/- 0.2k = 753x • 3y + 8 when x = 3, y = 2
Answer:
62
Step-by-step explanation:
Substitute x by 3 and y by 2
3*3*3*2+8=62
question 12 to find the shaded portion
12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,
= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].
= [8×8 - 4×4] cm².
= 64 - 16 cm².
= 48 cm².
10. Similarly the figure in (10) is twice the area of the two trapezoids.
11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.
12. The total area is the sum of the areas of the trapezoid and the parallelogram.
13. The larger figure is a rectangle with a right-angle triangle on top.
We have to subtract two rectangles from this to obtain the area of the shaded region.
14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.
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Write an equation in standard form of the line that passes through the point and has the
given slope.(-2, 4); m = -6
O None of the other answers are correct
Oy - 6x = 8
O 6x + y = -8
Oy - 6x = -8
O 6x - y = 8
Answer:
6x + y = -8
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
m = -6
So
[tex]y = -6x + b[/tex]
(-2, 4)
This means that when [tex]x = -2, y = 4[/tex]. We use this to find b.
[tex]y = -6x + b[/tex]
[tex]4 = -6(-2) + b[/tex]
[tex]b = 4 - 12 = -8[/tex]
So
[tex]y = -6x + -8[/tex]
[tex]6x + y = -8[/tex]
44x46 ayuda plssss speak spanish plssssss
Answer:2024
Step-by-step explanation: 44x46
If point C is between points A and B, AB=43, AC= -12x -9, BC = 24x + , what is the value of X? please help
Answer:
equation: 43+(-12x-9)+24x=X
Step-by-step explanation:
This line plot shows how many miles Monique rode her bike this week.
Answer:
151
Step-by-step explanation:
Answer:
152 miles
Step-by-step explanation:
There are 2 Xs above 20 1/2, so she rode that distance twice. There are 3 Xs above 22 1/2, so she rode that distance three times. The other distances with Xs she only did once. We add up the distances for each X to get the total:
20.5 + 20.5 + 21.5 + 22 + 22.5 + 22.5 + 22.5 = 152 miles
Helpp me pleasee! No fake people or responses
Answer:
The first statement and the 3rd statement are true. :)
For future reference, cosine is ratio of the adjacent side to the hypotenuse
Pls help! Step by step
Answer:
x = 55
Step-by-step explanation:
Since the sides of the shape are parallel, AngleC and AngleD will add up to 180° (see "parallel lines cut by a transversal" or maybe you have learned a big pile of parallelogram theorems)
Use this relationship to set up an equation.
2x + 20 + 50 = 180
combine like terms
2x + 70 = 180
subtract 70
2x = 110
divide by 2
x = 110/2
x = 55
x is 55
Answer:
The value of x is 55°
Step-by-step explanation:
GivienTwo adjacent angles of a parallelogram are (2x + 20)° and 50° respectivelySince we know that opposite angles of a parallelogram are equal
m∠C = m∠B = (2x + 20)°m∠D = m∠A = 50°The sum of any two adjacent angles is supplementary. This means, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180.
So,
∠C + ∠D = 180°
(2x + 20)° + 50° = 180°
2x + 70° = 180°
2x + 70° - 70° = 180° - 70°
2x = 110°
2x/2 = 110°
x = 55°
Thus, The value of x is 55°
Use the distributive property to write an equivalent expression.
16+32
Hint: find the gcf.
Answer:
2( 4+4) = 16
Step-by-step explanation:
The gcf of 16+32 is 16
I WILL GIVE BRAINLIST
The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Use 3.14 for 10,
Round to the nearest whole number,
14 in
14 in.
15 in
Suom
Save and Exit
thandro
Write an expression for "b divided by 6."
Please help solve the equation using cos(no links)
Answer:
cos 52 = 11/alpha ---> alpha = 11/cos52 = 17.9
Select all the values of r that make the inequality r>4.6 true.
A. 4.60
B. 5.05
C. 3.7
D. 4.9
E. 4.08
Rosa sold lemonade at a baseball game. She sold 101 cups for $2.00 each.
She spent $40.50 on supplies. How much money did she make?
Answer: it’s 161.50
An appliance store sells 373 vacuum
cleaners in the month of August. If it
sells 300 more vacuum cleaners in the
next month, how many vacuum
cleaners does it sell in September?
The sum of three consecutive even numbers is 312. What is the value of the
smallest number?
Answer: 102
Step-by-step explanation:
Let the numbers be a, a+2 and a+4. Since the sum of three consecutive even numbers is 312, this will be:
a + a+2 + a+4 = 312
3a + 6 = 312
3a = 312 - 6
3a = 306
a= 306/3
a = 102
Therefore, the smallest number is 102.
Other numbers are 104 and 106.
please help me with this
Answer:
.38 or 38%
Step-by-step explanation:
I divided 44 by 116 then rounded
Answer: 38% of boys play an instrument.
Step-by-step explanation:
They are asking for the percentage of boys that play an instrument.
44 ÷ 116 = 0.379310...
Round to the nearest hundredth
0.38
Find the percentage
0.38 × 100 = 38 or 38%
find the eighth term of the sequence 1/3, -1, 3, -9, ..
Answer:
-729
Step-by-step explanation:
sequence is to multiply by -3 to get next term
To plan for retirement, Deandre deposits $ 318 each quarter in an annuity that pays 7.6 %% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 27 years, Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the Bst of financial formalas
Answer: 1040
Step-by-step explanation:
just took 65 and mutiply 65$
Plzz help me well mark brainliest if you are correct!!..
Answer:
I usually turn the fractions into a decimal. So it would turn into
.666 < x< .777
When you turn your answers into fractions, the only one that fits is C which is 3/4 or .75
Step-by-step explanation:
What is equivalent to " two more than three times a number is seven
Answer:
if it’s asking for a numerical answer it would be 1.67
(Rounded to the nearest two)
Step-by-step explanation:
What is the domain of f(x)=[1/2]*
Here we need to find the domain of the given function.
We will see that the domain is the set of all real numbers.
The first thing we need to do is to define the domain of a function.
For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.
Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.
Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.
Particularly, in our function: f(x) = (1/2)^x
We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).
Concluding, because there is no problem with any real value, we can see that the domain is the set of all real numbers
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A company bought New Year's greeting cards to send to its valued customers. Sixty of the cards they sent cost $2.30 each. Thirty of the cards cost $2.75 each The remaining 34 cards cost $1.95 each. What was the total amount spent on these cards?
Answer:
$287.82
Step-by-step explanation:
60 * 2.30 = 138
30 * 2.75 = 82.5
34 * 1.98 = 67.32
138 + 82.5 + 67.32 = 287.82