The common difference of the arithmetic sequence is found as -10.
What is defined by the term arithmetic sequence?The arithmetic sequence is indeed the sequence in which the common differences between any 2 successive terms remains constant. Let us review what a sequence is.We have two formulas for arithmetic sequences.The formula for determining the nth term in an arithmetic sequence.The formula for calculating the sum of an arithmetic sequence's first n termsFor the given question;
The arithmetic sequence is given as;
28, 14,....
Where 28 is the first term; a₁ = 24.
14 is the second term; a₂ = 14.
Then the common difference 'd' is calculated as;
d = a₂ - a₁
put the values.
d = 14 - 24
d = - 10
Thus, the common difference of the arithmetic sequence is found as -10.
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What is the value of s?S 120°
At first let us draw a sketch to show the position of the given angle
Please help me with this graph.
Answer:
f(x) = 1/4(x + 4)(x - 2)²Step-by-step explanation:
Let's analyze the graph.
We observe that:
It is an increasing function, so leading coefficient is positive,It has one x-intercept (- 4, 0), It has one touching point at x-axis (2, 0), so it has at least multiplicity of 2,It has a y-intercept (0, 4), It has a local maximum (- 2, 8).Based on our observations, the least degree polynomial function will have the form of:
f(x) = a(x + 4)(x - 2)²To find the value of a we'll use the y-intercept:
4 = a(0 + 4)(0 - 2)²4 = a*16a = 4/16a = 1/4Let's prove it with local maximum:
8 = 1/4(- 2 + 4)(-2 - 2)²8 = 1/4*2*168 = 8So the function is:
f(x) = 1/4(x + 4)(x - 2)²If y(x) = 4x, what is x when y(x) = 4?
2
1
4
0
Answer:
It should be 1. If y(x)= 4 then x should equal 1. This way we get 4=4 which is true.
Step-by-step explanation:
4x1 = 4, so if you substitute 1 for x in your equation you get 4.
Solve the following inequality algebraically. [tex] |x - 5| \leqslant 8[/tex]
The inequality to solve is:
[tex]|x-5|\leq8[/tex]Whenever we have absolute value inequality, we solve it in:
[tex]\begin{gathered} |x|Thus, we can write the problem as:[tex]-8\leq x-5\leq8[/tex]Now, solving it:
[tex]\begin{gathered} -8+5\leq x-5+5\leq8+5 \\ -3\leq x\leq13 \end{gathered}[/tex]Ben is a pool technician who is preparing a client's pool for the winter by draining the water. For each hour that he drains the pool, the volume of the water in the pool decreases by approximately how many gallons?
The volume of the water in the pool decreases by 7200 gallons an hour, considering the slope of the linear function.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function are described as follows:
m is the slope of the function, representing the rate of change of the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis, which in contexts such as this problem, that does not work with negative numbers, is the initial value of the function.From the given graph, two points are given as follows:
(2,8640) and (4,7200).
Given two points, the slope is given by change in y divided by change in x, hence:
m = (7200 - 8640)/(4 - 2) = -720 gallons an hour.
Missing informationThe graph of the function is given by the image at the end of the answer.
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4 x + 2 + x = Blank x – 19
[tex]x = \frac{5 +\sqrt{109} }{2} \text{ or }\\\\ x = \frac{5-\sqrt{109} }{2}[/tex]
How to find x?
4 x + 2 + x = ___ x – 19
⇒ 4 x + 2 + x = x(x) – 19
⇒ 5x+ 2 = [tex]x^{2}[/tex] - 19
⇒ 5x +2 - [tex]x^{2}[/tex] + 19 = 0
⇒ 5x - [tex]x^{2}[/tex] + 21 =0
⇒ -[tex]x^{2}[/tex] + 5x + 21 = 0
[tex]x^{2}[/tex] - 5x - 21 = 0 ----(1)
(1) is of the form [tex]ax^{2} +bx+c=0[/tex]
In (1) a = 1, b = - 5 , c = -21
Applying quadratic formula,
[tex]x = \frac{-b\pm\sqrt{b^{2} -4ac } }{2a} \\\\x = \frac{-(-5)\pm\sqrt{(-5)^{2} -4(-21)} }{2(1)} \\\\x = \frac{(5)\pm\sqrt{25 +84} }{2}\\\\x = \frac{5\pm\sqrt{109} }{2}\\\\x = \frac{5 +\sqrt{109} }{2} \text{ or } \frac{5-\sqrt{109} }{2}[/tex]
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The image of point (4,4)under a translation is (6,0). Find the coordinates of the image of the point (1,-4) under the same translation
The coordinates of the point's image (1,-4) under the same translation are (2, 0)
What is translation?A translation is a geometric transformation that moves all points of a figure, shape, or space by the same amount in the same direction. A translation can also be thought of as adding a constant vector to each point or shifting the coordinate system's origin. A translation is a type of transformation that involves sliding each point in a figure the same distance in the same direction. A translation is a transformation that moves every point in a figure in the same direction by the same amount. For example, this transformation shifts the parallelogram 5 units to the right and 3 units up. It is written as ( x , y ) → ( x + 5 , y + 3 ) .
Therefore,
The coordinates of the point's image (1,-4) under the same translation are (2, 0)
The x coordinate increased by 1, and the y coordinate increased by 4.
Now, do these same transformations to the other point, (1, -4)
x coordinate: 1 + 1 = 2
y coordinate: -4 + 4 = 0
So, the new point is (2, 0)
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Marlee's job pays her $13.80 per hour plus overtime pay for any additional hours worked above her normal 40 hour work week. Last week, Marlee worked for 68 hours. For each hour of overtime Marlee works,
she earns____.
Her gross pay for the week was____.
Answer:
938.4 normal time
Step-by-step explanation:
13.8 times 68.also what is overtime pay that no answer
Answer: $20.7 per hour of overtime
$1131.6 gross pay for the week
Step-by-step explanation: traditional overtime pay is 1.5 times regular pay meaning that she earns 13.8•1.5 for her overtime
multiply 13.8 times her regular 40 hour work week plus 28 hours of overtime pay
(13.8•40)+(13.8•1.5)•(hours of overtime)=gross pay
this is all subjective depending on your states overtime laws and if they count overtime as double for hours worked in excess of 48 hours in a week.
I would look at your states overtime laws and work on a conclusion.
if this is the case then the answer would be
(13.8•40)+(20.7•8)+(27.6•20)=gross pay
plsss help meeeeeee
Answer:
The angle measures are
x + (x + 30) + 2x = 180
x = 37.5
Step-by-step explanation:
x + (x + 30) + 2x = 180. (combine x and 2x)
3x + (x + 30) = 180. (combine 3x and x, 30 cant combine)
4x + 30 = 180. (subtract 30 from both)
4x = 150. (divide both sides by 4)
x = 37.5
Tell which equation you would use to solve for one of the variables when solving the system by substitution. Explain your reasoning.
Number 7 2x + 3y =5
4x - y =3
Number 8
2/3x + 5y = -1
x + 6y = 0
Number 9
2x + 10y = 14
5x - 9y = 1
Answer:
ANSWER FOR QUESTION 7
X=1,Y=1
Step-by-step explanation:
2x+3y=5.
4x-y=3.
In this question, we simply find the value of y from equation 2 because by doing this there will be no term in the denominator so it quiet be easy for us.
y= -3+4x(4x-3) put in eq 1
2x+3(4x-3)=5
2x+12x-9=5
14x=14
divide 14 into both sides
x=1.
put in eq 1 or eq 2 to find the value of y Answer will be the same.
let's put in eq 1
2(1)+3y=5
3y=3
divide 3 into both sides
y=1.
Same for question 8 and 9.
Find the values of x and y
-57 + 57 I really need the answer
Answer:
The answer is 0
Step-by-step explanation:
-57 cancels out 57 making it 0.
if you add a ten thousands digit that is 3 times the thousands digit to the number 3,721, what is the new number
Answer:
the answer is 93,721
if liz has 5 ken dolls how many barbie dolls would she have?
12.36 foreign-language study. choose a student in a u.s. public high school at random and ask if he or she is studying a language other than english. here is the distribution of results: language spanish french german all others none probability 0.30 0.08 0.02 0.03 0.57 explain why this is a legitimate probability model. what is the probability that a randomly chosen student is studying a language other than english? what is the probability that a randomly chosen student is studying french, german, or spanish?
The probability that a randomly chosen student is studying a language other than English is 0.43.
The probability that a randomly chosen student is studying french, german, or Spanish is 0.4.
This is a legitimate probability model since the random variable as well as the probability distribution function otherwise known as pdf has been provided in the question.
From the question, we can obtain the pdf as follows;
Language: Spanish French German All others None
Probability: 0.30 0.08 0.02 0.03 0.57
The probability that a randomly chosen student is studying a language other than English is 1 - 0.57 = 0.43.
The probability that a randomly chosen student is studying french, german, or Spanish is the sum of the individual probabilities of french german, and Spanish which is equal to
0.30 + 0.08 + 0.02 = 0.4.
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Work out the value of (√99 - √11)²
Answer: 44
Step-by-step explanation:
(√99 - √11)²
simplify the expression
(3√11 - √11)^2
collect like terms
(2√11)^2
use the properties of exponents
4 x 11
answer: 44
Select the best way to solve for the distance between the points (2, -1) and (6, 6
The best way to find the distance between the points (2,-1) and (6,6) is by using the distance formula.
The distance between the two points (2,-1) and (6,6) is 8.062 units (approximately).
Distance formula
The distance formula, is the algebraic expression that gives the distances between pairs of points in their coordinates.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:-
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
It is derived from the Pythagoras theorem.
We have,
[tex](x_1,y_1)[/tex] = (2,-1)
[tex](x_2,y_2)[/tex] = (6,6)
We have to find the distance between the two points (2,-1) and (6,6).
Hence, distance between the two points (2,-1) and (6,6) is given by:-
[tex]\sqrt{(6-2)^2+(6-(-1))^2}=\sqrt{4^2+7^2}=\sqrt{16+49}=\sqrt{65}[/tex] ≈ 8.062 units.
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Question 10 of 10
Which value of x is in the domain of f(x) = √x – 11?
-
A. X=0
B. x= -4
C. x= 13
D. x = 10
Answer:
C: x = 13
Step-by-step explanation:
It looks like the question is f(x) = sqrt(x - 11)
DOMAIN
The domain of a function refers to values of x that the function can graph and give a definite y value for. Functions can graph x values that do not result in undefined or complex numbers.
If that is the case then x would have to be greater than or equal to 11 because you can not get the square root of negative numbers unless you want to deal with complex numbers.
13 - 11 >= 0 so it is the answer.
What must be added to -9.46 to yield 7.489?
Let the number to be added = x
so the equation will be
-9.46+x=7.489
x=7.489+9.46
as the sign changes on the other side of the equals sign
x=16.949
To check: -9.46+16.949
=7.486
So the number to be added is 16.949
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Use the graph to find the value of f (x) when x = 1 for the function f (x) = -x2 - 4.
Answer: The value of f (1) is -6
Step-by-step explanation:
Substitute the 1 into the equation: f (1) = -(1)2 - 4
f (1) = -2 - 4
f (1) = -6
before launching its latest line of health drinks, a beverage manufacturer provided free samples of the health drinks to a large and culturally diverse set of families. it then conducted a survey with mostly open-ended questions where the participants were asked about their first impressions about the drinks. this is an example of research. question 10 options: 1) qualitative 2) analytical 3) quantitative 4) laboratory 5) statistical
Before the launching its latest line of health drinks, a beverage manufacturer provided free samples of the health drinks to a large and culturally diverse set of families. This is a qualitative research.
What is a Qualitative research?Qualitative research is the study of the nature of phenomena and is particularly effective for clarifying why something is (or is not) seen, assessing complicated multi-component interventions, and focusing on intervention improvement.
Data from first-hand observation, interviews, questionnaires, focus groups, participant-observation, recordings recorded in natural settings, documents, case studies, and artifacts are used in qualitative research. The information is mostly non-numerical.
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10
√
6
÷
2
√
2
I’m having trouble with this question..please could someone help
The radical expression 10√6 ÷ 2√2 has a value of 5√3, when evaluated
How to evaluate the expression?The expression is given as
10√6 ÷ 2√2
The above expression is a radical expression
So, we have
(10√6 ÷ 2√2) = (10 ÷ 2) x (√6 ÷ √2)
Evaluate the quotient of 10 and 2
So, we have
(10√6 ÷ 2√2) = 5 x (√6 ÷ √2)
Rewrite the expression as
(10√6 ÷ 2√2) = 5 x √(6 ÷ 2)
Evaluate the quotient of 6 and 2
(10√6 ÷ 2√2) = 5 x √3
This gives
(10√6 ÷ 2√2) = 5√3
Hence, the value of the expression is 5√3
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7. Copy and complete to factorise the expression.
3x2+5x-2=(3x___)(x___)
Answer:
(3x - 1)(x + 2).
Step-by-step explanation:
3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x(x + 2) - 1(x + 2)
= (3x - 1)(x + 2).
is the number of birds in different regions discrete or continuous
The number of birds in different regions is a discrete variable.
What is Discrete data?Discrete data can only have certain values. There may be an endless number of those values, but each one is distinct, with no grey space in between. Discrete data can be numerical, such as the number of apples, or categorical, such as red or blue, male or female, or good or bad.
The discrete variable is the number of birds.
This variable is not continuous in this case because we count the number of birds rather than measure them.
The continuous variables are measured rather than counted. For example, weight, height, and so on.
As a result, the quantity of birds in various places is a discrete variable.
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(03.01 LC)
A theater company charges $5.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets? (1 point)
Answer: 5.50 (c + a)
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
From the blue pre-image to the pink image, what was the transformation that occured?
From the blue pre-image to the pink image. The transformation that occured is
(a) Reflection (x,y) → (x, -y)
Define reflection.
A flip is a term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line through which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure.
A line of reflection is required to perform a geometry reflection; the resulting orientation of the two figures is the opposite. The figures' corresponding parts are spaced at the same distance apart from the reflection axis. Ordered pair rules are reflected along the x-axis at (x, -y), the y-axis at (-x, y), and the line at y=x.
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Find the distance of the line segment formed by (-3, 4) and (-2, 3)
[tex]\sqrt{2}[/tex] units
The line segment formed by joining (-3, 4) and (-2, 3) , the distance of line segment is [tex]\sqrt{2}[/tex] units
Solution:A line segment is defined as the area between two distinct points on a line. A line segment is a section of a line that connects two points. A line has no endpoints and extends in both directions indefinitely, whereas a line segment has two fixed or definite endpoints.when the coordinates of the two endpoints are given, the length of a line segment In this case, we employ the distance formula,D = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Given two points , (-3 , 4) and (-2 , 3)
to find the distance formula is ,
distance = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
by substituting the values,
d = [tex]\sqrt{(-2 - (-3)^{2} + (3 - 4)^{2} }[/tex]
d = [tex]\sqrt{(-2 + 3)^{2} + (-1)^{2} }[/tex]
d = [tex]\sqrt{1^{2} + (-1)^{2} }[/tex]
d = [tex]\sqrt{2}[/tex] units.
So the distance of line segment formed by joining (-3, 4) and (-2, 3) is
[tex]\sqrt{2}[/tex] units.
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The graph represents a quadratic function. Write an equation of the function in standard form
The quadratic quadratic equation represented in the graph has the equation y = 2x² + 7x + 4 .
The values of x that satisfy the equation are the roots or zeros of the expressions on the left side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double origin if there is only one solution. One real double root, two complex solutions that are complicated conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options. A quadratic equation will always have two roots if complex roots are taken into account; a double root counts as two. A quadratic equation can be factored into an equivalent equation.The graph of the function which is quadratic can be represented by the equation in the standard form of
y=ax²+bx+c
The graph passes through the points (-4,0) , (-0.5,0) and (0,4)
Putting the values in the equation we get:
0 = 16a - 4b + c
4 = c
0 = 0.25 a +0.5b + c
Solving the equations we get :
16 a - 4 b = -4
0.25a -0.5 b = -4
a =2 and b = 7
The required quadratic equation is y = 2x² + 7x + 4
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The numbers 15 and 35 have been
written as the product of their prime
factors.
15
3 × 5
35 = 5 x 7
=
Which of the following represents the
lowest common multiple (LCM) of 15 and
35?
2×3×5
2×5×7
3x5x5×7 3x5x7
LCM of 15 and 35 = 105
3x5x7 = 105
Answer:
3x5x7
True or False? A circle could be circumscribed about the quadrilateral below.B68"O A. True90"O B. False90°112"D
hello
the answer to this question is false
