Answer:
[tex]a_{n}[/tex] = 4n - 11
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = - 3 - (- 7) = 1 - (- 3) = 5 - 1 = 4
and a₁ = - 7, hence
[tex]a_{n}[/tex] = - 7 + 4(n - 1) = - 7 + 4n - 4 = 4n - 11
The explicit formula for the arithmetic sequence -7,-3,1,5 is an = -7 + (n-1)(4), where n is the position of the term in the sequence.
The student is asking for the explicit formula of the sequence -7,-3,1,5. This is an arithmetic sequence, where each term increases by a constant difference. The common difference (d) can be found by subtracting any term from the following term; for instance, -3 - (-7) = 4. To find the explicit formula, we'll denote the first term of the sequence as a1 which is -7. The explicit formula for an arithmetic sequence is an = a1 + (n-1)d. Substituting our values in, we get an = -7 + (n-1)(4).
Carly's age is 3 more than twice her sister's age, s. Which of the following expressions represents Carly's age?
Answer:
c = 2s + 3
Step-by-step explanation:
Let c be Carly's age.
Carly is 3 more . . . than twice her sister's age.
We can translate "twice her sister's age" into 2s.
Carly is 3 more than 2s.
We can translate this into:
Carly is 3 + 2s.
c = 2s + 3
Carly's age, given that it's three more than twice her sister's age, can be expressed with the mathematical expression 2s + 3. This translates the stated relationship into an algebraic context.
Explanation:The question is asking for an expression that represents Carly's age in relation to her sister's age. Given that Carly's age is three more than twice the age of her sister, we can express Carly's age (C) as 2s + 3, where s is her sister's age.
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which point on the number line represent the product of (-4)(-2)(-1)
-4 times -2 equals 8.
8 times -1 equals -8.
Therefore, the point on your number line that is on -8 is your answer!
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box.
Answer:
x ≈ 56.7°
Step-by-step explanation:
Since the triangle is right use the sine ratio to solve for x
sin x° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence
x = [tex]sin^{-1}[/tex] ( [tex]\frac{66}{79}[/tex] ) ≈ 56.7°
Answer:
x = 56.7
Step-by-step explanation:
which graph represents the function f(x)=4[x]?
Check the picture below.
bearing in mind that ⌈some expression⌉ means "ceil" or the ceil() function, which means any number in between one integer and the next, "ceils" or gets bumped up to the next integer.
namely for example, for y = ⌈x⌉ will yield
y(0.5) = 1
y(0.7) = 1
y(0.0000001) = 1
y(3.0000001) = 4
y(-2.000001) = -2
y(-5.00001) = -5
and so on
the same is true btw for the y = ⌊x⌋ or the "floor" floor() function, but it "floors" or drops down instead.
y(0.5) = 0
y(3.9999999) = 3
y(-5.0000001) = -6
and so on.
in this case is y = 4⌈x⌉, so any values in between each integer for "x" gets bumped up.
The graph which represents the given function is first graph.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given a function,
f(x)=4[x]
The step function [x] is defined as the piecewise constant function which has a countable or finite number of pieces.
Here a step function is multiplied to 4.
The correct graph which represents the step function is first graph.
Hence the correct option is A.
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Which expression is not equal is NOT equal to the volume of the prism
A) 5+4+2
B) 5×(4×2)
C) (5×4)×2
D) 5×4+5×4
Use vertical multiplication to find the product of
vertical multiplication [tex]x^{2} -x +1\\x.x^{2} -2x-2[/tex]
is C.[tex]x^{2} -x^4-x^3-4x^{2} -2[/tex]
Vertical multiplication
Vertical Multiplication. Set up the vertical multiplication by stacking the factors vertically and lining up the digits by place value. Although multiplication is commutative (order is not important) we want to place the number with more digits on top.
What does vertically mean in math?The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down. They are also called vertically opposite angles.
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Solve the following inequality-3.55g<-28.4
Answer:
B (the second graph)
Step-by-step explanation:
3.55g<-28.4
Divide each side by 3.55
3.55g/3.55<-28.4/3.55
g < -8
This would be an open circle at 8 (because g is less than not less than or equal to) and it goes to the left ( since g is less than)
PLZ HURRY IT'S URGENT!
Mr. Caldwell has 28 students in his class and 12 of them are boys. What is the ratio of girls to boys? A. 4 : 7 B. 3 : 4 C. 4 : 3 D. 7 : 4
Answer:
C
Step-by-step explanation:
Girls - 28-12 = 16
16:12 = 4:3 - so answer choice C
We know that out of the 28 students 12 of them are boys. To find how many girls there are subtract 12 from 28
28 - 12 = 16
That means that there are 16 girls in the class
Now you need a ratio of girls : boys so...
16 : 12
This can be further simplified to the following...
4 : 3 (C)
This means that for every four girls there are 3 boys
Hope this helped!
~Just a girl in love with Shawn Mendes
18) Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
2x = 5y2 - 3
x-axis, y-axis, origin
origin only
x-axis only
y-axis only
Answer:
x-axis only.
Step-by-step explanation:
2x = 5y2 - 3
Convert to vertex form:
x = 5/2 y^2 - 3/2
This is a parabola with axis of symmetry y = 0. The vertex is at (-3/2, 0) and it opens to the right.
The axis of symmetry is the x-axis ( y = 0).
The equation 2x = 5y2 - 3 is only symmetric with respect to the x-axis but not the y-axis or the origin.
Explanation:To test an equation for symmetry with respect to the x-axis, you would replace 'y' with '-y' and see if the equation remains the same. For symmetry with respect to the y-axis, you'd replace 'x' with '-x'. For origin symmetry, you would replace 'x' with '-x' and 'y' with '-y'
Applying this to your equation, 2x = 5y2 - 3:
If we replace 'y' with '-y', we get 2x = 5(-y)2 - 3. On simplifying, this reverts back to the original equation, so the graph of this equation is symmetric with respect the x-axis. Replacing 'x' with '-x', we don't get the original equation back, hence it is not symmetric about the y-axis. Replacing both 'x' with '-x' and 'y' with '-y', we don't get the original equation. Therefore, the graph of the equation is not symmetric about the origin.Learn more about Symmetry of equations here:
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mark needs to make $5, for every $2 he spends for his business to succeed. if mark spends $32, how much money will he make?
1) $95
2) $80
3) $160
.The binomial (a + 5) is a factor of a2 + 7a + 10. What is the other factor?
a2 + 7a + 10 = (a + 5)(a +
)
Answer:
(a+2) Is your answer
Step-by-step explanation:
You could try synthetic division, but it's pretty complicated (not to mention for much harder problems), so you should try factoring this. What two numbers multiply up to 10 and add up to 7? Using trial and error, we would find these two numbers to be 2 and 5. Therefore, it factors into (a+5)(a+2).
Answer:
2
Step-by-step explanation:
sin θ > 0 and tan θ < 0 then:
Answer:
last choice
Step-by-step explanation:
sin(theta) is positive
tan(theta)=sin(theta)/cos(theta) is negative
If sin(theta) is positive and tan(theta) is negative, then cos(theta) is negative because +/-=-
So we are looking for the quadrant where sine is positive and cosine is negative or when x is negative and y is positive.
This is in quadrant 2 so our angle theta is between 90 and 180 degrees.
The cost of 2 bottles of water and 3 bags of pretzels is $7.05. The cost of a bag of pretzels is $1.35. Write a system of
equations to represent this situation. Solve and explain what the answer means.
(SHOW WORK)
Step-by-step explanation:
let w be the cost of a bottle of water and p be the cost of a bag of pretzels
"2 bottles of water and 3 bags of pretzels is $7.05" can be written as
2w + 3p = 7.05 ------------- eq.1
"The cost of a bag of pretzels is $1.35" can be written as
p = 1.35 ------------- eq 2
Together, eq 1 and eq 2 make up your system of equations
To solve, take eq 2 and substitute this value int eq 1
2w + 3 (1.35) = 7.05
2w + 4.05 = 7.05
2w = 7.05 - 4.05
2w = 3
w = 1.5
Hence the cost of a bottle of water is $1.50
Answer: the cost of one bottle of water is $1.5 and the cost of one bag of pretzels is $1.35.
Step-by-step explanation: Let's call "b" the cost of a bottle of water and "p" the cost of a bag of pretzels, in the first equation of the system, we need to express the total prize of 2 bottles of water and 3 bags of pretzels, so it would be:
2b+3p=$7.05
The second equation will express the cost of a bag of pretzels:
p=$1.35
Now, to solve the system we replace the second equation into the first one:
2b+3($1.35)=$7.05
2b=$7.05-$4.05
2b=$3
b=$1.5
So the cost of one bottle of water is $1.5 and the cost of one bag of pretzels is $1.35.
From 12:00 midnight to 6:00am, the
temperature decreased by 12°C. If the original temperature was 12°C, which expression can be used to represent this situation? Plz show work.
A. 12-12
B. 12 + 12
C. 12- (-12)
D. -12 + (-12)
Answer:
A. 12-12
Step-by-step explanation:
Becuase if the temperature was originally 12°C then it decreases by 12° then it will be 12-12
Answer:
A.) 12 - 12.
Step-by-step explanation:
Given : From 12:00 midnight to 6:00 am, the temperature decreased by 12°C. If the original temperature was 12°C.
To find : which expression can be used to represent this situation.
Solution : We have given
At 12 : 00 midnight temperature = 12 °C.
At 6 : 00 am temperature decreased by 12 °C.
So, Final temperature = 12 °C - 12 °C.
Therefore, A.) 12 - 12.
Graph 2x -2= -4 and solve
Answer:
x=-1
Step-by-step explanation:
2x -2= -4
2x = -2
x = -1
Answer:
-1
Step-by-step explanation:
Which of the following is a polynomial?
Answer:
Option A and C are correct
Step-by-step explanation:
A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.
A. 4x^2+9x+12 is a polynomial
B. 3-√2x is not a polynomial
C. 15x^4 is a polynomial
D. 6x^2+2/x is not a polynomial
So, Option A and C are correct.
Answer: Option A and Option C
Step-by-step explanation:
Polynomials always have the following form:
[tex]ax ^ n + bx ^{n-1} + cx^{n-2} +...+ d[/tex]
Where a, b, c, and d are constant and are real numbers
The exponents of the variable x are always greater than or equal to zero.
Then identify among the options the expressions that have these characteristics
The answer are:
Option A.
[tex]4x^2 +9x+12[/tex]
Option C.
[tex]15x^4[/tex]
3x - 2y when x = 2 and y = 10
Answer:
the answer is -14
Step-by-step explanation:
3x - 2y
3(2)-2(10)
6-20
6+-20
-14
The value of 3x - 2y when x = 2 and y = 10 is -14
Step-by-step explanation:
Substitute x = 2 and y = 10 into the expression 3x - 2y.Calculate 3(2) - 2(10) to find the value.3(2) - 2(10) = 6 - 20 = -14. Therefore, 3x - 2y equals -14 when x = 2 and y = 10.The midpoint of A (-4, 2) and B(8,5) is
(2, 7/2)
(-6, 3/2)
(4, 7/2)
Answer:
A. (2,7/2)
Step-by-step explanation:
The midpoint formula is (x1+x2/2 , y1+y2/2).
So just plug the numbers into that formula and you get the answer.
Landry is building a rectangular flower garden. He wants the garden to be 3 feet longer than it is wide. He wants to buy a birdbath to put in the flower bed and after adding it he wants to have 35 square feet of space for planting. The cost of the birdbath will be $18 per square foot of the area of its base. He also needs to buy soil to cover the entire flower bed, including the space where the birdbath will be. The soil will cost $5 per square foot. He plans to spend a total of $150 on the soil and the birdbath. If x represents the width of the flower bed and y represents the area of the base of the birdbath, then which of the following systems of equations can be used to determine the length and width of the flower bed and the area of the base of the birdbath?
Answer:
Step-by-step explanation:
To create a system of equations, write an equation to model each condition that must be satisfied in the given situation.
It is given that x represents the width of the flower bed and that y represents the area of the base of the birdbath.
Write an equation to represent the condition regarding the planting area in the flower bed. It is given that there is 35 square feet of planting area. The flower bed is 3 feet longer than the width.
x(x+3) - y = 35
Write an equation to represent the condition regarding the cost of the soil and the birdbath. The question gives that the soil will cost $5 per square foot and the birdbath will cost $18 per square foot of the base.
5x(x+3)+18y=150
Combining both of the equations gives the following system of equations.
x(x+3)-y=35
5x(x+3)+18y=150
Assume x > 0 and y 0.
algebra II engenuity
Answer:
Third Option
Step-by-step explanation:
Given expression is:
[tex]\sqrt{\frac{55x^7y^6}{11x^11y^8}}[/tex]
Simplifying
[tex]=\sqrt{\frac{11*5*x^7*y^6}{11*x^11*y^8}}\\=\sqrt{\frac{5*x^7*y^6}{x^11*y^8}}\\Combining\ exponents\ with\ same\ base\\=\sqrt{\frac{5}{11*x^{(11-7)}*y^{(8-6)}}}\\=\sqrt{\frac{5}{x^{4}*y^{2}}}\\Applying\ radical\\=\frac{5^{\frac{1}{2}}}{x^{(4*\frac{1}{2})}*y^{(2*\frac{1}{2})}}}\\=\frac{\sqrt{5}}{x^2y}[/tex]
As 5 cannot be taken out of the square root, it will remain inside the square root.
Hence, Third option is the correct answer ..
What is the area of the parallelogram?
The area of a parallelogram is the base times the height.
Area = 14 x 8 = 112 square inches.
inter
A population of fish stats at 8,000 and decreases by 6% per year. What would the population of fish be after 10 years? Use 4 -
Answer:
4309
Step-by-step explanation:
initial 8000
1st year 8000(1-.06)=8000(.94)
2nd year 8000(.94)^2
...
10 year 8000(.94)^10 approx 4309
If (x) = 5х – 2 and g(x) = 2х+1, find (f-g)(x).
ОА. 7х- з
ОВ. 7x-1
Ос. 3 – 3х
OD. 3х- з
SUBMIT
PREVIOUS
Answer:
D. 3x - 3Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=5x-2,\ g(x)=2x+1\\\\\text{Substitute:}\\\\(f-g)(x)=(5x-2)-(2x+1)\\\\=5x-2-2x-1\qquad\text{combine like terms}\\\\=(5x-2x)+(-2-1)\\\\=3x-3[/tex]
find the exact value of cos(sin^-1(-5/13))
bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.
[tex]\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}[/tex]
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}[/tex]
le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.
What’s this answer helppp♀️♀️
Step-by-step explanation:
formula of square= width x length
width = length
each sides = √ 64
= 8 cm
area of the rectangle = 1 & 1/2 x 64
= 96 cm²
formula for area of rectangle = " square
8 x length = 96 cm²
length= 96/8
= 12 cm
perimeter= 4 (8 + 12 + 12)
= 128 cm
*multiple with 4 cuz issa cross (??) i hope you get what i mean(??)
correct me if i'm wrong i'm learning too
A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?
0.5
1 1.5 2 2.5
3 3.5 4 4.5 5 5.5 6 6.5
Answer:
Step-by-step explanation:
The correct answer is the second one. The function g(x) is increasing "faster" than f(x), and this is true of exponential functions in general. This should make sense if you're familiar with the concept of limits at infinity.
Ana drinks chocolate milk out of glasses that each hold 1/8 fraction of a liter. She has
7/10 of chocolate milk in her refrigerator.
Answer:
5.6
Step-by-step explanation:
If there is 70 percent of chocolate milk in the fridge and she holds 0.125 in each canister and divide and get 5.6 then turn that back into a fraction which should be easy.
Ana can fill exactly 5 full glasses of chocolate milk with her 7/10 of a liter, as each glass holds 1/8 of a liter. The calculation involves simple fraction division and the realization that 56/10 simplifies to 5 3/5, indicating the number of full glasses.
The question is about determining how many glasses of chocolate milk Ana can fill from the amount she has in her refrigerator. Since each glass holds 1/8 of a liter and Ana has 7/10 of a liter of chocolate milk, we need to calculate how many 1/8 liter portions make up 7/10 of a liter. To find this, we can set up a division:
[tex]\(\frac{7/10}{1/8}\)[/tex].
To divide fractions, we multiply by the reciprocal of the divisor:
[tex]\(\frac{7/10}{1} \times \frac{8}{1}\) = \(\frac{56}{10}\).[/tex]
Now we simplify the resulting fraction:
[tex]\(\frac{56}{10}\)[/tex] simplifies to [tex]\(5 \frac{3}{5}\)[/tex].
So, Ana can fill 5 full glasses of chocolate milk and will have some milk left over.
Which shape(s) have an angle that is acute?
Hello! My name is Zalgo and I am here to help you out on this marvelous day! The answer to your question is the 3rd choice;triangle. A triangle has 3 points to it's shape. If you look at the angel of the points, they are a bit small and are extremely pointed.
I hope this answer helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me Brainliest? I'd greatly appreciate it! Thank you! XP)
One cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used. Write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.
The equations are as follows where x represents the number of minutes the cell phone is used.
For plan one: Total cost = $20 + $0.15x
For plan two: Total cost = $35 + $0.10x
For both the costs to be the same, we need to use the cell phone for
300 minutes.
What are equations?Equations are relations showing the value of one quantity related to another quantity when it can change. The changing value is the variable.
How do we solve the given question?We are informed that one cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used.
We are asked to write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.
Let the number of minutes the cell phone is used be x minutes.
Now we solve for equations for both plans in the following way:-
Plan one:
Charges $20 per month plus $0.15 per minute used.
When the use is for x minutes, the additional charge = $0.15*x = $0.15x
∴ Total cost = Fixed cost + Additional cost
or, Total cost = $20 + $0.15x.
Plan two:
Charges $35 per month plus $0.10 per minute used.
When the use is for x minutes, the additional charge = $0.10*x = $0.10x
∴ Total cost = Fixed cost + Additional cost
or, Total cost = $35 + $0.10x.
We are asked to find the number of minutes used so that the costs in both the plans are equal. To find this we equate the equation of total costs in both the cases to get:
$20 + $0.15x = $35 + $0.10x.
Subtracting ($20 + $0.10x) from both sides of the equation, we get
$20 + $0.15x - ($20 + $0.10x) = $35 + $0.10x - ($20 + $0.10x).
or, $20 + $0.15x - $20 - $0.10x = $35 + $0.10x - $20 - $0.10x.
or, $0.05x = $15
Dividing both sides of the equation by $0.05, we get
$0.05x/$0.05 = $10/$0.05
or, x = 300.
∴ We must talk for 300 minutes for both the plans to cost the same to us.
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add 1/7 + -1/7 your answer should be reduced to its smallest form and should not be an improper fraction
Answer: 0 is the answer, the 1/7 and -1/7 cancel each other out. Leaving zero as the answer!