Answer:
[tex]\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n[/tex] - n-th term
[tex]a_1[/tex] - first term
[tex]r[/tex] - common ratio
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]
We have
[tex]a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...[/tex]
The common ratio:
[tex]r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}[/tex]
It's not a geometric sequence.If [tex]a_3=-\dfrac{1}{16}[/tex] then the common ratio is [tex]r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}[/tex]
Put to the explicit formula:
[tex]a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}[/tex]
Put [tex]a_n=\dfrac{1}{1024}[/tex] and solve for n :
[tex]-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1[/tex]
[tex]\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6[/tex]
find the missing number so that it has no solution. __x-8-9x=-4x+8
Answer:
The missing number (i.e. the coefficient of x) is 5.
Step-by-step explanation:
5x - 8 - 9x = -4x + 8
-4x - 8 = -4x + 8
-8 ≠ 8
evaluate the expression xy for x = 6 and y = 3
Plug in values.
xy=
6(3) =
18 = Answer
how do i solve this using elimination
Answer:
The value of x=6 and y=4.
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
4x - 3y = 12 → (1)
x + 2y = 14 → (2)
Multiplying (2) by - 4 and adding to (1) will eliminate the y- term
- 4x - 8y = - 56 → (3)
Add (1) and (3) term by term
(4x - 4x) + (- 3y - 8y) = (12 - 56) ← simplify
- 11y = - 44 ( divide both sides by - 11 )
y = 4
Substitute y = 4 into either (1) or (2)
(2 ) : x + 8 = 14 ( subtract 8 from both sides )
x = 6
Solution is (6, 4 )
If f(x) = -4x2 - 6x-1 and g(x) = – x2 - 5x + 3, find (f+ g)(x).
Answer:
- 5x² - 11x + 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= - 4x² - 6x - 1 + (- x² - 5x + 3)
= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms
= - 5x² - 11x + 2
Answer:
-5x^2 -11x +2
Step-by-step explanation:
f(x) = -4x^2 - 6x-1
g(x) = – x^2 - 5x + 3,
Add them together
f(x) = -4x^2 - 6x-1
+ g(x) = – x^2 - 5x + 3,
-----------------------------------
-5x^2 -11x +2
HELP ASAP
What is the area of triangle DEF?
A)294 square centimeters
B)490 square centimeters
C)588 square centimeters
D)735 square centimeters
Answer:
The correct answer will be "588 square centimeters"
Step-by-step explanation:
The answer would be 588 squared cm because the area of a triangle is 1/2(base*height).
and The base is 42 cm and the height is 28 cm.
588 square centimeters is the correct answer !
Answer:
C) 588
Step-by-step explanation:
A= 1/2 b*h
First you need to find the base and height
Which is 42 and 28
42*28=1176
1176/2= 588
how do you round the answer to the nearest hundredth by doing 1062.98 * 0.092
Answer:
97.79
Step-by-step explanation:
1062.98 * 0.092 = 97.79416
To the nearest hundredth would be to the second 9. Since 4 is less than 5 just drop the 4 and anything after it.
If h(x)=4x^2-16 we’re shifted 7 units to the right and 3 units down what would the new equation be
Answer:
4(x-7)^2 - 19
Step-by-step explanation:
Shifting 7 units to the right: 4(x-7)^2 - 16.
3 units down: 4(x-7)^2 - 16 - 3, or 4(x-7)^2 - 19
Vertical angles are supplementary, true or false?
Answer:
False
Step-by-step explanation:
Vertical angles are a pair of opposite angles created by intersecting lines. The Vertical Angles Theorem states that if two angles are vertical, then they are congruent.
Answer:
False.
Step-by-step explanation:
Supplementary angles always equal up to 180 degrees.
The distance Din miles from an observer to the horizon over flat land or water can be estimated using the formula D-123/
where h is the height in feet of the point of observation. How far is the horizon for aperson whose eyes are 6 feet above the
ground?
a about 5.91 mi
c. about 3.01 mi
b. about 2.73 mi
d. about 7.64 mi
translate each phrase into an algebraic expression the quotation of 30 and three times a number
Answer:
[tex]\frac{30}{3x}[/tex]
Step-by-step explanation:
Let
x ----> the number
we know that
The phrase " The quotient of 30 and three times a number" is equal to divide the number 30 by the number x multiplied by 3
so
The algebraic expression is equal to
[tex]\frac{30}{3x}[/tex]
quadratic function (f)x=2x^2+8x-7
Answer:
See attached images
Step-by-step explanation:
The expression of your question is
f(x) = 2x^2+8x-7
A full analysis of the function is shown in the images below
Factor completely and then place the factors in the proper location on the grid a^2-a-20
Answer:
[tex](x-5)(x+4)[/tex]
Step-by-step explanation:
We have the following quadratic equation
[tex]a^2-a-20[/tex]
The factored expression will have the following form
[tex](x+b)(x+c)[/tex]
Where b and c are two real numbers which when added together result in -1, and multiplying them results in -20
[tex]b*c=-20\\b+c=-1[/tex]
You can verify that the numbers that meet this condition are:
-5 and 4
Then the factors are:
[tex](x-5)(x+4)[/tex]
Can someone please help me out ?
Answer:
The Answer is 9
Step-by-step explanation:
To find the answer you divide 63 by 7.
[tex]7m=63\\m=9[/tex]
Compare the three functions.
f(x) = 10x
x y
0 0
1 10
2 20
g(x) = 5x
x y
0 1
1 5
2 25
h(x) = 4x2 + 5x
x y
0 0
1 9
2 26
Select the true statement.
A.
As x approaches positive infinity, the quadratic function will exceed both the linear and exponential functions.
B.
As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions.
C.
As x approaches positive infinity, the linear function will exceed both the quadratic and exponential functions.
D.
As x approaches positive infinity, it cannot be determined which function will exceed the other two.
Answer:
B.
As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions. TRUE (Exponential functions increase faster than linear or quadratic)
Step-by-step explanation:
We can easily solve this problem if we plot each graph by using a graphing calculator or any plotting tool.
1st function
f(x) = 10x
2nd function
g(x) = 5^x
3rd function
h(x) = 4x^2 + 5x
Please, see attached graph.
A.
As x approaches positive infinity, the quadratic function will exceed both the linear and exponential functions. FALSE
B.
As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions. TRUE (Exponential functions increase faster than linear or quadratic)
C.
As x approaches positive infinity, the linear function will exceed both the quadratic and exponential functions.FALSE
D.
As x approaches positive infinity, it cannot be determined which function will exceed the other two.FALSE
Answer:
b
Step-by-step explanation:
just look up
Traveling at an average speed of 50 miles per hour, the trip from point A to point B takes 2 hours. Traveling at an average speed of 40 miles per hour, the same trip takes 2.5 hours.If time, y, varies inversely with speed, x, how long will the trip take traveling at 45 miles per hour?
Answer:
[tex]2\frac{2}{9} hrs[/tex]
Step-by-step explanation:
At a speed of 50m/h time taken is 2hours
At a speed of 45m/h time take is 2.5 hours
You can find the distance between A and B
Distance=speed × time
[tex]D=50*2=100\\[/tex]
But time y varies inversely with speed x , hence
[tex]y=\frac{k}{x}[/tex]
where k is a constant of proportionality and D is distance.
To find k
[tex]2=\frac{k}{50} \\\\2*50=k\\\\100=k\\\\y=\frac{100}{x}[/tex]
where y is time and x is speed
Given
x=45m/h you should find time y. Apply the expression above
[tex]y=\frac{100}{x} \\\\\\y=\frac{100}{45} =\frac{20}{9} =2\frac{2}{9} hrs[/tex]
Collin did the work to see if 10 is a solution to the equation r/4=2.4
Answer:
ill just cut to the chase it is c
Step-by-step explanation:
Answer:
b.Yes, because if you substitute 10 for r in the equation and simplify, you find that the equation is true.
Step-by-step explanation:
did the test
A warehouse is for rent downtown. The rate is $15 per square foot per month. Space measures 40 ft x 22 ft. How much will it cost to rent this warehouse for a year?
Answer:
[tex]\$158,400[/tex]
Step-by-step explanation:
step 1
Find the area of the warehouse
[tex]A=(40)(22)=880\ ft^{2}[/tex]
step 2
Remember that one year is equal to 12 months
step 3
Find the cost to rent the warehouse for a year
Multiply the area by $15 per square foot per month and then multiply by 12 months
so
[tex]880(15)(12)=\$158,400[/tex]
Answer:
158,400
Step-by-step explanation:
How many solutions does this linear system have?
y = 2x-5
_8x - 4y = -20
one solution: (-2.5, 0)
one solution: (2.5, 0)
Ono solution
O infinite number of solutions
Answer: C is correct, No solution
Step-by-step explanation:
Let’s simplify the second equation,
8x-4y=-20
We can divide the whole equation by 4...
8x/4-4y/4=-20/4
Which becomes....
2x-y=-5
Now let’s move things around to see if it’s the same equation as the one on top...
-y=-2x-5
y=2x+5
Now we need to solve the systems...
y=2x-5
y=2x+5
Since their slopes are both 2 and their y-intercepts are not identical, the answer is no solution. The two lines will continue on without ever crossing because they have the same slope.
The solution set for the given system of linear equations is -
(2.5, 0).
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to find the number of solutions that the given linear system of equations have -
y = 2x - 5
- 8x - 4y = -20
We will solve the given system of equations using the method of substitution. We can write -
y = 2x - 5
- 8x - 4y = - 20
- 8x + 20 = 4y
y = - 2x + 5
Now -
2x - 5 = - 2x + 5
4x = 10
x = 2.5
and -
y = 2 x 2.5 - 5
y = 0
Therefore, the solution set for the given system of linear equations is -
(2.5, 0).
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The slope of the line below is -2. Use the coordinates of the labeled point to
find a point-slope equation of the line.
•
4
-6)
Answer: y= -2x+2
Step-by-step explanation: y-y₁=m(x-x₁)
y-(-6)= -2(x-4)
y+6=-2x+8
y=-2x+8-6
y= -2x+2
Answer:
y + 6 = -2(x - 4)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope m = -2 and the point (4, -6). Substitute:
[tex]y-(-6)=-2(x-4)\\\\y+6=-2(x-4)[/tex]
Find the value of x in each case. Give reasons to justify your solutions!
answer ASAP
Answer:
x = 19
Step-by-step explanation:
YZ || XW, so ∠Y = ∠W
if ∠Y = ∠W, then ∠W = 2x
since the sum of the angles of a triangle is 180 degrees:
(3x-5) + 2x + 90 = 180
x = 19
simplify the expresion 8w+5r-t+9r
To simplify an expression you need to combine like terms.
In the given equation, there are two like terms, 5r and 9r.
There is a plus sing in front of each one, so add those together: 5r + 9r = 14r
There are no ther like terms so the simplified expresssion becomes:
8w + 14r - t
What is the radius of a circle whose equation is x2 + y2 – 10x + 6y + 18 = 0? units
Answer:15
Step-by-step explanation:
Answer: The radius of the given circle is 4 units.
Step-by-step explanation: We are given to find the radius of the circle with the following equation :
[tex]x^2+y^2-10x+6y+18=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2-10x+6y+18=0\\\\\Rightarrow (x^2-10x+25)+(y^2+6y+9)-25-9+18=0\\\\\Rightarrow (x-5)^2+(y+3)^2-16=0\\\\\Rightarrow (x-5)^2+(y-(-3))^2=4^2.[/tex]
Comparing it with the standard equation, the radius of the circle is given by
[tex]r=4.[/tex]
Thus, the radius of the given circle is 4 units.
What is the inverse of the function f(x) = 2x + 1?
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{2}x-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x+1\to y=2x+1\\\\\text{exchange x to y and vice versa:}\\\\x=2y+1\\\\\text{solve for y:}\\\\2y+1=x\qquad\text{subtract 1 from both sides}\\\\2y=x-1\qquad\text{divide both sides by 2}\\\\y=\dfrac{x-1}{2}=\dfrac{1}{2}x-\dfrac{1}{2}[/tex]
3 +0.5(4a + 8) = 9 – 2a
Answer:
0.5
Step-by-step explanation:
The required simplified value of a is 1/2 .
Given that,
3 +0.5(4a + 8) = 9 – 2a
The simplified value of a is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3 +0.5(4a + 8) = 9 – 2a
3 + 0.5*4a + 0.5*8 =9 - 2a
3 + 2a + 4 = 9 - 2a
7 - 9 = - 4a
a = 1 / 2
Thus, the required simplified value of a is 1/2.
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If
[tex]f(x) = \frac{(3 + x)}{x - 3} [/tex]
what is
[tex]f(a + 2)[/tex]
?
a)
[tex] \frac{3 + f(a + 2)}{f(a) - 1} [/tex]
b)
[tex] \frac{(5 + a)}{(a - 1)} [/tex]
c)
[tex] \frac{(3 + a)}{(a - 3)} + 2[/tex]
Answer:
Option B: [tex]\frac{5+a}{a-1}[/tex]
Step-by-step explanation:
Given function is:
[tex]f(x) = \frac{3+x}{x-3}[/tex]
In order to find f(a+2), we have to put a=2 in place of x in the function
So,
[tex]f(a+2) = \frac{3 + (a+2)}{(a+2)-3}\\ =\frac{3+a+2}{a+2-3}\\ = \frac{5+a}{a-1}[/tex]
Hence, we can see that option b is correct ..
The ratio of AB to BC is _______.
A) 3/1
B) 1/3
C) 2/3
D) 3/2
B 1/3
Ratio of AB:BC
3 : 9
1 : 3
Solve for x: -6 < x-1 < 9
Answer:
- 5 < x < 10
Step-by-step explanation:
Given
- 6 < x - 1 < 9 ( add 1 to each of the 3 intervals )
- 5 < x < 10
The value of x ranges from -5 to 10 as this inequality - 5 < x < 10.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given inequality is -6 < x-1 < 9. The value of x will be calculated as,
x- 1 < 9
x < 10
x- 1 > -6
x > 1 - 6
x > -5
Therefore, the value of x ranges from -5 to 10 as this inequality - 5 < x < 10.
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15p!!what is the percent of change from 12 to 19? round to the nearest percent!
Answer:
58%
Step-by-step explanation:
The change between 12 to 19 is 7
The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%
7/12*100
=58.3333333%
=58%(rounded to nearest percent)
58% increase
Percent change = 19 - 1212 × 100 = 58.333333333333 % (increase) Where: 12 and 19 is the new value. In this case we have % of increase because the new value is greater than the old value.
What is percentage change?Percent change differs by the percent increase or percent decrease of the sense that we could see both directions of the change. For example, the percent increase calculator calculates amount of increase, in which we shall say, "x percent increase".
The change between 12 to 19 is 7
The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%
7/12*100
=58.3333333%
=58%(rounded to nearest percent)
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Solve P = 2l + 2w for l.
Answer:
l = [tex]\frac{P}{2}[/tex] - w
Step-by-step explanation:
P = 2l + 2w
2l = P - 2w
l = [tex]\frac{P}{2}[/tex] - w
What is the slope of the line represented by the values in the table?
(10,14) (2,-2)
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (10, 14) and (x₂, y₂ ) = (2, - 2)
m = [tex]\frac{-2-14}{2-10}[/tex] = [tex]\frac{-16}{-8}[/tex] = 2
Answer:
slope =2
Step-by-step explanation:
To find the slope, we use the formula
m = (y2-y1)/(x2-x1)
= (-2-14)/(2-10)
= -16/-8
=2