Using sequences concepts, it is found that:
The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with [tex]a_n = 150(0.75)^{n-1}[/tex].What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a(n) = a(0) + nd[/tex]
The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:
a(0) = 15, d = 2.5.
Hence the equation is:
a(n) = 15 + 2.5n.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:
[tex]a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75[/tex]
Hence the equation is given by:
[tex]a_n = 150(0.75)^{n-1}[/tex]
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Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y? y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5. y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
Answer:
This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is the equation for this situation?
It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:
y = x + 5.5
The possible values are
x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Step-by-step explanation:
This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
For the given expression
y = x + 5.5
The possible values are
x = It is expected x is equal to 0 or greater to it
since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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In the diagram Below
Answer:
∠UTC = 55°∠UCD = 70°∠BCT = 55°Step-by-step explanation:
In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.
__
UTC∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair
∠UTC = 180° -125° = 55°
__
UCD∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair
∠UCD = 180° -110° = 70°
__
BCT∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles
Solve the compound inequality for x and identify the graph of its solution.
x+7> 3 and x-5≤-1
OA. Solution: x<-4 or x ≥ 4
++
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
--
-5-4-3 -2 -1 0 1 2 3 4
OC. Solution: x>-4 and x≤ 4
+
H
-5 -4 -3 -2 -1 0 1
2
4 5
OD. Solution: x2-4 and x < 4
44
-5-4-3 -2 -1 0 1 2 3 4 5
3
5
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
Let's solve the compound inequality step by step:
x + 7 > 3
Subtract 7 from both sides to isolate x:
x > 3 - 7
x > -4
and, we have,
x - 5 ≤ -1
Add 5 to both sides to isolate x:
x ≤ -1 + 5
x ≤ 4
Now, we have two inequalities for x:
x > -4
x ≤ 4
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.
The correct representation is:
OC. Solution: x > -4 and x ≤ 4
Graph:
-5 -4 -3 -2 -1 0 1 2 3 4 5
+---|---|---|---|---|---|---|---|---|---+
-4 0 4
The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.
The shaded area between -4 and 4 represents the solution to the compound inequality.
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what does X equal to in this equation
Answer:
17
Step-by-step explanation:
5x+5x+10=180
10x=170
x=17
Answer:
Answer is 17
Step-by-step explanation:
It is done in this step
5x +5x+10=180
10x=170
x=17
Please help! Evaluate the following expression:
4+ (8x √9) ÷ (2+4)
A. 6
B. 28/6
C. 8
D. 15/6
Answer:
the answer to the question is C) 8
Which expression can be used to find the difference of the polynomials? (10m – 6) – (7m – 4) [10m (–7m)] [(–6) 4] (10m 7m) [(–6) (–4)] [(–10m) (–7m)] (6 4) [10m (–7m)] [6 (–4)]
The expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]
Difference of polynomials
A polynomial is a function that has a leading degree of 3 and above.
Given the expression below
(10m – 6) – (7m – 4)
Expand
10m - 6 - 7m + 4
Collect the like terms
10m - 7m - 6 + 4
Simplify
3m -2
Hence the expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]
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Help me solve the inequality: 2x- 3<2x+2 <3x +5
Answer:
[tex]x > - 3[/tex]
I hope this is helpful
Find the equation of the line through point (4,−7) and parallel to =−2/3+3/2 Use a forward slash (i.e. "/") for fractions (e.g. 1/2
Answer:
y=-2/3x-13/3
Step-by-step explanation:
parralel line have the same gradient
y=mx+c is the general straight line equation
m represents the gradient
if the equation is y=-2/3x+3/2
m=-2/3
the coordinates (4,-7)
x=4
y=-7
substitute into equation
-7=-2/3×4+c
-7=-8/3+c
c=-7+8/3
c=-13/3
so the equation is :
y=-2/3x-13/3
what is the vertex of the graph of y = -4x(x + 2)^2 + 5
Answer:
The vertex is the point of coordinates (-2 , 5)
Step-by-step explanation:
we notice that the equation of the parabola is given in vertex form :
y = -4(x + 2)² + 5
then
y = -4(x − (-2))² + 5
Therefore
The vertex of the graph is the point (-2 , 5)
Need help urgently please
Which expression is equivalent to \frac{r^9}{r^3}
Answer: [tex]\frac{r^9}{r^3} = r^{9-3} = r^6[/tex]
We subtract the exponents when dividing terms with the same base.
The general rule is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]
Hii!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
r^6
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
To simplify this we need to use the division property of exponents:
[tex]\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}[/tex]. So if we divide two numbers with the same base, we subtract their exponents.
Let's apply this rule here.
[tex]\twoheadrightarrow\sf r^9\div r^3[/tex].
[tex]\bullet[/tex] Since these two numbers have the same base, we subtract their exponents
[tex]\twoheadrightarrow\sf r^6[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
1. What is the sum? 7/2+(-3/5)
4I3
10
21
10
10
Answer:
29/10
Step-by-step explanation:
7/2+(-3/5)
7/2-3/5
35/10-6/10
29/10
What is the domain of the function y=3 In x graphed below?
Answer:
x>0
Step-by-step explanation:
points exist on the right of the graph so the domain is x>0
4. Which of the following uses the reciprocal property to rewrite
We can actually deduce here the one that uses the reciprocal property to rewrite [tex]\frac{x}{6} = \frac{28}{3\\}[/tex] is: C. [tex]\frac{6}{x} = \frac{3}{28}[/tex].
What is reciprocal?A reciprocal of a number is defined as the number that when it is multiplied by the number, the result is 1. Thus, we deduce here that the product of a number and its reciprocal gives one.
Thus: x/6 x 6/x = 1
Also, if 28/3 x 3/28 = 1
Thus, we see that they use the reciprocal property.
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what is the gradient if y=-x+3
Answer:
Slope = - 1
Step-by-step explanation:
The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex] is the intercept on [tex]y[/tex] axis.
Hence, in [tex]y=-x+3[/tex] , slope is -1 and intercept on [tex]y[/tex] axis is 3.
The graph of g(x) shown below resembles the graph of f(x) = 2*, but it has
been reflected over the x-axis. Which is the equation of g(x)?
A. g(x)=2x-1
OB. g(x)=2*+1
OC. g(x) = -2*
OD. g(x)=2x-1
The graph which resembles the graph of f(x)=[tex]2^{x}[/tex] but is reflected over the x-axis is g(x)=[tex]2^{x} +1[/tex]
Given Function f(x)=[tex]2^{x}[/tex].
We have to generate a function whose graph is similiar to the given function and is reflected over the x axis.
If we take first function g(x)=2x-1
put the value of x=-1 then the value of function g(x)=2*(-1)-1=-2-1=-3 means the value of y in this function will be negative means the graph will be under x-axis.
Taking second function g(x)=[tex]2^{x} +1[/tex]
for all the negative values of x it posses a positive value of y so the graph will be over the x axis.
Taking third function g(x)=-[tex]2^{x}[/tex]
In the above function for each value of x the function possess a negative value so the graph will be under x axis.
Taking fourth function g(x)=2x-1
For all values of x less than 1 the function becomes negative which takes graph below the x axis. First graph is for [tex]2^{x}[/tex] and the second is for [tex]2^{x} +1[/tex]
Hence the graph similar to [tex]2^{x}[/tex] and reflected over x axis is g(x)=[tex]2^{x} +1[/tex].
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Solve -5<4x+3<_<7
Not really sure how to solve, line under greater than sign
The solution to the complex inequality as in the task content is; -2 < x <= 1.
What is the solution of the inequality?The inequality in discuss is; -5<4x+3 <= 7.
Hence, solving the inequalities separately; we have;
-5 < 4x +3
-8 < 4x
-2 < x
Also; 4x+3 <= 7
4x <= 4
x <= 1.
Ultimately, the solution to the inequalities is;
-2 < x <= 1.
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It was reported that uninsured drivers caused 1 in 20 accidents. About 682,494 car crashes were reported. About how many of these drivers were uninsured?
How many more unit tiles must be added to the
function f(x)=x²-6x+1 in order to complete the square?
A 1
B 6
C 8
D 9
Question 13 * A farmer can plant 45 kg of peanuts on 4,000 square metres of land. Which of the following represents the number of peanuts (x) he could plant on 8,500 square metres of land? C. 45 4000 8500 45 8500 1 4000 45 1 8500 4000 Question 13 * A farmer can plant 45 kg of peanuts on 4,000 square metres of land . Which of the following represents the number of peanuts ( x ) he could plant on 8,500 square metres of land ? C. 45 4000 8500 45 8500 1 4000 45 1 8500 4000
The number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg
What is unitary method?"It is a method of finding the value of a single unit, and based on that value we can find the required value."
For given question,
A farmer can plant 45 kg of peanuts on 4,000 square meters of land.
Using unitary method,
[tex]\frac{4000}{45}\\\\=88.8888 \\\\\approx 88.89[/tex]
This means, a farmer can plant 1 kg of peanuts on 88.89 square meters of land.
We need to find the number of peanuts ( x ) he could plant on 8,500 square meters of land.
Here, 1 kg = 88.89 square meters
x kg = 8500 square meters
[tex]\Rightarrow x=\frac{8500}{88.89}\\\\ \Rightarrow x = 95.6~kg[/tex]
Therefore, the number of peanuts ( x ) he could plant on 8,500 square meters of land = 95.6 kg
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3/2 x 7/2= 2^x
A. X= 1
B. X= 3
C. X= 5
D. X= 8
Simplify the following expression 7a + 5b - 2a + b
Answer:
5a + 6bStep-by-step explanation:
Simplify the following expression:
Simplify the following expression:
7a + 5b - 2a + b =
5a + 6b
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8x and y = 2x + 2 intersect are the solutions of the equation 8x = 2x + 2. (4 points)
Part B: Make tables to find the solution to 8x = 2x + 2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 8x = 2x + 2 graphically? (2 points)
Quickly please! Thank you.
The point of intersection of two given equations is (0.333, 2.667).
Given that, equation with two variables are y = 8x and y = 2x + 2.
The given equations will intersect at some point where y is the same for both equations.
When you replace y in y = 2x + 2 with y = 8x, we get 8x = 2x + 2.
So, the solution of 8x = 2x+2 will satisfy both equations.
Now, we need to find the solutions to take the integer values of x between -3 and 3.
That is,
x = -3 , then 8(-3) = 2(-3) +2⇒-24 = -6+2
⇒-12 = -4 False.
similarly, for x = -2
8(-2) = 2(-2)+2
⇒-16 = -2 False
For, x = -1
8(-1) = 2(-1)+2
⇒-8= 0 False
For, x = 0
8(0) = 2(0)+2
⇒0= 2 False
For, x = 1
8(1) = 2(1)+2
⇒8= 4 False
For, x = 2
8(2) = 2(2)+2
⇒16 = 6 False
For, x = 3
8(3) = 2(3)+2
⇒24 = 8 False
Therefore, there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.
The equations can be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.
The point of intersection is the values of the variables which satisfy both equations at a particular point.
Hence, you can see the graph as shown below, the point of intersection is (0.333, 2.667).
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Which solid is a Platonic solid?
Please hurry!!!
Answer:
The five Platonic solids (regular polyhedra) are the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. In other words the second one.
We only have cows and ducks in our garden and know that the animals in the garden have 20 legs and 14 eyes. How many cows and ducks do we have
The number of cows and ducks in the garden are 3 and 4 respectively.
Solve the system of linear equationsLet the numbers of cows be x and the number of ducks is y.
Total number of legs=20
Total number of eyes=14
Linear equation for the total number of legs in the garden,
4x+2y=20 -(1)
Linear equation for the total number of eyes in the garden,
2x+2y=14 -(2)
Solve the system of the two linear equations to find the values of x and y.
Subtract equation (1) from equation (2), and we get,
2x=6
[tex]x=\frac{6}{2}\\[/tex]
x=3
Substitute the value of x in equation (1), and we get,
4(3)+2y=20
12+2y=20
2y=20-12
2y=8
[tex]y=\frac{8}{2}\\[/tex]
y=4
Number of cows=3
Number of ducks=4
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two negative integers have the sum of -12 and the product of 11 what are the integers
Answer:
-1 and -11
Step-by-step explanation:
"sum" means we're adding.
-1 + -11 = - 12
"product" means we're multiplying.
-1 × -11 = 11
prove that x-y = √(x+y)^2-4xy?
Proved Below
[tex]\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}[/tex]
[tex]\Longrightarrow x-y = \sqrt{(x-y)^2}[/tex]
[tex]\Longrightarrow x-y =x-y[/tex]
Let's check
x-y=√(x+y)²-4xy
Solve RHS
√(x+y)²-4xy√x²+2xy+y²-4xy√x²+y²-2xy√(x-y)²x-yHence proved
sin(90° - x) = sqrt3/2
Solve for X
picture below
how do you solve this pls
Step-by-step explanation:
The equation of a exponential function is
[tex]a \times (b) {}^{x} [/tex]
where a is the y value of the y intercept, b is the constant rate of change.
Here the y intercept is (0,4), the y value of the y intercept is 4.
So a=4
The graph passes through point (1,2) so
[tex]h(x) = 4 \times b {}^{x} [/tex]
Plug in 1 for x, 2 for h(x)
[tex]2 = 4 \times {b}^{1} [/tex]
Anything to the first power is itself so
[tex]2 = 4 \times b[/tex]
Isolate b.
[tex] \frac{1}{2} = b[/tex]
So our function is
[tex]4 \times ( \frac{1}{2} ) {}^{x} [/tex]
Answer:
[tex]h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]
Step-by-step explanation:
Exponential Function
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.x is the independent variable.y is the dependent variable.From inspection of the given diagram, the defined points on the curve are:
(0, 4)(1, 2)As one of the defined points is the y-intercept (0, 4) then:
[tex]\implies a=4[/tex]
Substitute the found value of a and the point (1, 2) into the general form of an exponential function and solve for b:
[tex]\begin{aligned}h(x)=ab^x & \\\implies h(1)=4b^1 & = 2\\4b & = 2\\b & = \dfrac{2}{4}\\b & =\dfrac{1}{2} \end{aligned}[/tex]
Finally, substitute the found values of a and b into the general formula to complete the equation for the function h(x):
[tex]\implies h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]
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