Answer:
[B] $6.88
Step-by-step explanation:
what is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?
Answer:
12.496
Step-by-step explanation:
a=10 (first term)
r= 1/5 (common ratio)
sum of first five terms
[tex] s_{5} = \frac{a( 1 - {r}^{n} ) }{1- r} [/tex]
=10{1-⅕⁵} ÷ 1-⅕
=10{1 - 1/3125} ÷ 4/5
=10{3124/3125} ÷ 4/5
=9.9968÷0.8
=12.496.
OR
a+ar+ar²+ar³+ar⁴
=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)
=10+2+0.4+0.08+0.016
=12+0.48+0.016
=12.496
Instructions: Find the measure of the indicated angle to the nearest
degree.
12
?
36
?
=
To find the indicated angle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the adjacent side and the hypotenuse. Therefore, we should use cosine to solve.
cos(x) = 12/36
x = cos^-1(12/36)
x = 71 degrees
Hope this helps!
Calculate the axis of symmetry in the equation Y = (x+1) (x-4)
Come on anyone please helppppppp.
Answer:
Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points
x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation
y=(x+1)(x-4)
=x^2-3x-4
a is 1,b is -3 and c is -4
x= -(-3)/2(1)
=1.5
and y=x^2-3x-4
=1.5^2-3(1.5)-4
= -6.25
therefore the axis of symmetry is (1.5,-6.25)
I hope this helps
342225 square root by division method pls give the steps
Answer:
185 is the square root of 34225
Step-by-step explanation:
hope you understood!!
After draining 8 gallons from a tub of water
, there were still 12 gallons left
How many gallons of water were in the tub to start?
Answer: 20
Step-by-step explanation:
X - 8 = 12
+ 8 +8
X = 20
20 gallons were in the tub to start with
A bag of M&M's contained 13 red, 15 yellow,
44 brown, 12 orange, and 9 green candies.
What percent of the M&M's were yellow?
Answer:
16%
Step-by-step explanation:
Use the percentage formula:
P × V1 = V2
Example:
EX: P × 30 = 1.5
P =
1.5
30
= 0.05 × 100 = 5%
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
please show steps!!
Answer:
x = 0, π/3, 2π/3, π, 4π/3, 5π/3
Step-by-step explanation:
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
x
The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
so, we get,
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
Hence, The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3.
To learn more on simplification click:
brainly.com/question/28996879
#SPJ2
The graph of $y = ax^2 + bx + c$ is shown below. Find $a \cdot b \cdot c$. (The distance between the grid lines is one unit.)
Answer:
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Step-by-step explanation:
Vertex is the minimum or maximum point of parabola
Vertex of parabola is (h,k)
Therefore, from given graph (-3,-2) is the lowest point.
Vertex of parabola is at (-3,-2).
Standard equation of parabola
[tex]y-k=a(x-h)^2[/tex]
Substitute the values
[tex]y-(-2)=a(x-(-3))^2=a(x+3)^2[/tex]
[tex]y+2=a(x+3)^2[/tex]
(-1,0) lies on the parabola.
Therefore, it satisfied the equation of parabola.
[tex]0+2=a(-1+3)^2=4a[/tex]
[tex]a=2/4=1/2[/tex]
Now, using the value of a
[tex]y+2=1/2(x+3)^2=1/2(x^2+6x+9)[/tex]
[tex]y+2=\frac{1}{2}x^2+3x+\frac{9}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9}{2}-2[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9-4}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{5}{2}[/tex]
By comparing with
[tex]y=ax^2+bx+c[/tex]
We get
[tex]a=\frac{1}{2}, b=3, c=5/2[/tex]
[tex]a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}[/tex]
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
If the ratio of plums to peaches to kiwis is 10:4:5, how many plums are there if the total number of fruits is 190?
Answer:
The answer is 100:40:50
Answer:
131 plums
Step-by-step explanation:
The fraction of plums = 10/(10+4.5)
= 10/14.5
= 100/145
So the required number of plums = 100 * 190 /145
= 131.
Write 42 as a product of primes use index notation
HELP PLEASE HURRY
THANKS
Answer:
Step-by-step explanation:
How much water should be added to 90ml of 45 percent acid solution to dilute it to 25 percent acid solution
Answer:
72 ml
Step-by-step explanation:
Let
x = amount of water that should be added
45% acid solution = 45/100 = 0.45
25% acid solution = 25/100 = 0.25
The equation is
90(0.45) = 0.25(x + 90)
40.5 = 0.25x + 22.5
40.5 - 22.5 = 0.25x
18 = 0.25x
Divide both sides by 0.25
x = 18/0.25
= 72
x = 72 ml
Which angles are supplementary to each other?
• Angle 7 and Angle 3
• Angle 9 and Angle 12
• Angle 6 and Angle 12
• Angle 12 and Angle 10
Answer:
∠9 and ∠12
Step-by-step explanation:
Supplementary angles are two angles that add up to 180. Looking at all the answer choices, A, C, and D have either Big-Big angle or Small-Small angle. What we need is Big-Small angle that is next to eachother, which is ∠9 and ∠12.
Hope this helped.
(Also sorry!)
What is the following product?
Answer:
D
Step-by-step explanation:
(5√2 - 4√3)^2 =
50 + 48 - 40√6 = 98 - 40√6
Determine which theorm should be user , and find AB
Step-by-step explanation:
perpendicular bisector
AB= 17
Which of the following statements is false?
A and B
I hoped it helped you
Select the correct location in the expression.
Consider this expression.
4x^4-6x^3+6x+3/x-3
Which term in the quotient of this expression contains an error?
Answer:
78
Correct term:60
Step-by-step explanation:
We are given that
[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]
The quotient of this expression is given by
[tex]4x^3+6x^2+18x+78+\frac{183}{x-3}[/tex]
We have to find the term in this expression which contains an error.
[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]
The quotient of this expression is given by
[tex]=4x^3+6x^2+18x+60[/tex]
[tex]Dividend=Divisor\times quotient+ remainder[/tex]
Using the formula
[tex]4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}[/tex]
We can see that in the given expression there is 60 in place of 78.
The error in the expression of quotient is 78.
Correct term is 60.
Help ASAP please Nd thanks
Answer:
D
Step-by-step explanation:
(4x)²=x+15
A student measures the length of a football field and reports it to be 294 feet long. The actual length of the field is 300 feet. What is the percentage error in the student's measurement
Answer:
Percentage error in the student measurement = 2%
Step-by-step explanation:
Percentage error = (change in length) / actual length × 100
Approximate length =294 feet
Actual length = 300 feet
Percentage error = (change in length) / actual length × 100
= (300 feet - 294 feet) / 300 feet × 100
= 6/300 × 100
= 0.02 × 100
= 2%
Percentage error in the student measurement = 2%
Can anyone help me ? I just need the numbers
Answer:
(-6, 0) and (0, 1.5)
Step-by-step explanation:
The equation of the line in pint slope form is expressed as;
y-y0= m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given
m = 1/4
(x0, y0) = (6,3)
Substitute into the formula;
y - 3 = 1/4(x-6)
4(y-3) = x - 6
4y - 12 = x-6
4y - x = -6+12
4y - x = 6
x = 4y - 6
To get the points to plot, we will find the x and y-intercept of the resulting expression.
For the x-intercept,
at y = 0
x = 4(0) - 6
x = -6
Hence the x-intercept is at (-6, 0)
For the y-intercept,
at x = 0
0 = 4y - 6
4y = 6
y = 6/4
y = 3/2
y = 1.5
Hence the y-intercept is at (0, 1.5)
Hence the required points to plot to get the required line are (-6, 0) and (0, 1.5)
Given TVW,MZV = 90°, TV = 14, and VW= 9,
which of the following choices is used to find mZW?
here's the answer to your question
Which of the following functions represent exponential decay?
An exponential decay function goes down to the right, like in the picture attached.
An exponential function follows this format: [tex]y=ab^x[/tex], where b is less than 1 and more than 0. b is more than 0 but less than 1 in function A.
what is the answer to 4 (2/5) /6
Answer:
= 4/15
Step-by-step explanation:
=4 . 2/5 /6
= 4/15
Answer:
0.26
Step-by-step explanation:
4 (2/5) /6
2/5 = 0.4
4 × 0.4 = 1.6
1.6 / 6 = 0.26
The answer is 0.26
13 A cylindrical iron rod 8 cm high and 6 cm in diameter stands in a cylindrical tin 12 cm in diameter. See Fig. 15.22. Water is poured into the tin until its depth is 8 cm. How far would the level drop when the rod is removed?
Answer:
2cm
Step-by-step explanation:
The volume of water displaced by the rod is
v = πr^2 h = π * 3^2 * 8 = 72π cm^3
The drop in water level is the rod volume divided by the cross-section area of the tin, or
72π/(π*6^2) = 2 cm
Write an equation that represents the line.
Use exact numbers.
Answer:
y = 4/5x - 18/5
Step-by-step explanation:
y = mx + b
m = 4/5
(2, -2)
-2 = 8/5 + b
b = -10/5 - 8/5 = -18/5
y = 4/5x - 18/5
Instructions: Find the measure of the indicated angle to the nearest
degree.
?
?
3
7
?
Answer:
x = 23
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan ? = 3/7
Taking the inverse tan of each side
tan ^-1 ( tan ?) = tan ^-1 (3/7)
?=23.19859
To the nearest degree
x = 23
Five students are asked to randomly select and name a polygon from the group shown below. what is the probability that the first two student choose the triangle and quadrilateral, in that order
Answer:
is it 2/5 I could be wrong
Pl ease H e l p I'm literally desperate-
If f(x) = 4x - 5 and g(x) = 7x -3, Show all steps & work. Find:
(f + g) (x)
and
(f * g) (x)
Answer:
f+g = 11x-8
f*g = 28x^2 - 47x+15
Step-by-step explanation:
f(x) = 4x - 5 and g(x) = 7x -3
(f+g)(x) = 4x - 5 + 7x -3
Combine like terms
= 4x+7x -5-3
= 11x-8
(f * g) (x) = ( 4x - 5) (7x -3)
FOIL
= 4x*7x + 4x(-3) + (-5)(7x) + (-5)(-3)
=28x^2 -12x-35x+15
Combine like terms
=28x^2 - 47x+15
Step-by-step explanation:
Step 1: Find (f + g)(x)
The definition of (f + g)(x) is f(x) + g(x). Basically add the two functions together.
[tex]f(x) + g(x)[/tex]
[tex](4x - 5) + (7x - 3)[/tex]
[tex]11x - 8[/tex]
Answer: [tex]11x - 8[/tex]
Step 2: Find (f * g)(x)
The definition of (f * g)(x) is f(x) * g(x). Basically multiply the two functions together.
[tex]f(x) * g(x)[/tex]
[tex](4x - 5) * (7x - 3)[/tex]
[tex](4x * 7x) + (4x * -3) + (-5 * 7x) + (-5 * -3)[/tex]
[tex](28x^{2}) + (-12x) + (-35x) + (15)[/tex]
[tex]28x^{2} - 47x + 15[/tex]
Answer: [tex]28x^{2} - 47x + 15[/tex]
How to find the measure of n
Answer:
6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we use Euclidian theorem to find n
n^2 = 6*18
n^2 = 108
n = 6[tex]\sqrt{3}[/tex]
A civil servant had a salary of Rs 9600. Tax up to Rs 85000 per year would be exempted. If he paid Rs 4530 as a tax, how much percent of tax was imposed?
Answer:
4%
Step-by-step explanation:
Yearly salary = 9600 * 12 = Rs. 115200
Tax = Rs . 4530
[tex]Tax \ percent = \frac{4530}{115200}*100[/tex]
= 3.93 = 4%
