Pam needs to save $905 per year for seven years to have enough for her first year with the help of her two grandfathers.
How Much Money Must Be Saved Every Year?Pam needs to save $903 each year to have enough for her first year of college tuition with the help of her two grandfathers.
To calculate this, we first need to add up the total amount of money Pam's two grandfathers are offering to contribute:
Grandfather 1: $6321
Grandfather 2: $6321
Total Contribution: $12642
We then subtract this total contribution from the total cost of tuition for the first year:
Tuition: $6321
Total Contribution: -$12642
Total Amount Needed: $6321
Finally, we divide this total amount needed by the number of years Pam has to save:
Total Amount Needed: $6321
Years: 7
Amount Needed to Save Each Year: $903
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A power company serves 17,000
customer's homes in a town. The
population of the town is decreasing by
about 3% every year. Which function
would represent the number of
homes,"H", the company will serve after
"n" years.
Answer:
2nd
Step-by-step explanation:
p=17000
r = -0.03
Hn)= p×(1+r)^n
H(n)= 17000(1+-0.03)^n
What is 2.66666666667 as a fraction?
The fraction 2.666666666667 equals [tex]\frac{8}{3}[/tex] .
A fraction is used to represent a portion/part of something larger. It symbolises the equal parts of the whole. A fraction is comprised of two components the numerator and the denominator. The top number is referred to as that of the numerator, and the bottom number is known as the denominator. The denominator specifies the total number of equal parts in a whole, whereas the numerator describes the number of equal parts taken.
2.666667 to fraction conversion:1. Assume that x = 2.666667 (1)
2. Six is the repeating digit.
To the left of the decimal point, put the repeating digit.
In this instance, multiply the decimal point by 10 to move it one place to the right.
Thus,
(x = 2.666667) * 10
Equation 10x = 26.66667 (2)
4. Take Eq. (1) away from Eq (2)
10x - x = 26.66667 - 2.666667
9x = 24
9 divided by both sides
x = [tex]\frac{24}{9}[/tex] or [tex]\frac{8}{3}[/tex]
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What are the factors of x³ 4x² 11x 30?
( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts.
what are roots in a equation ?The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts. These are all used across mathematics and have the same meaning as the zero concept. As a result, when a function y= or f(x)= is supplied, the zeros of the function are function values where y=0 or f(x)=0 f (x) = 0.
here ,
Since the sum of the coefficients is not zero , 1 is not a root
let x = -2
= -8 + 16 + 22 - 30 = 0
= -2 is a factor
dividing [tex]x^{3} + 4x^{2} -11x -30[/tex] by ( x + 2)
quotient = [tex]x^{2} + 2x -15[/tex]
= [tex]x^{2} +5x - 3x -15 =0[/tex]
= x(x + 5) - 3 ( x+ 5 ) =0
= ( x -3 ) ( x + 5 ) =0
other factors are ( x -3 ) and ( x+5 )
So , ( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .
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Find the values of X and y in the diagram.
Are the whole numbers closed under division justify with example?
The division of the whole numbers is not closed under property as the division of whole number is not always a whole number.
A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation then we say that the set is “closed under the operation.” The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division that is a ÷ b is not always a whole number.
For example, 5 and 8 are whole numbers, but 5÷8 is not a whole number.
Therefore, closure property does not exist for division of whole numbers.
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What is a function example equation?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Example of Function is f(x) = 2x + 5.
What is a function ?A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable).
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Based on Elements
One One FunctionMany One FunctionOnto FunctionOne One and Onto FunctionInto FunctionConstant FunctionBased on Equation
Identity FunctionLinear FunctionQuadratic FunctionCubic FunctionPolynomial FunctionsBased on the Range
Modulus FunctionRational FunctionSignum FunctionEven and Odd FunctionsPeriodic FunctionsGreatest Integer FunctionInverse FunctionComposite FunctionsBased on the Domain
Algebraic FunctionsTrigonometric FunctionsLogarithmic FunctionsExample of Function is f(x) = 2x + 5.
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The formula for the area of a trapezoid is A = ½h(b₁ + b₂), where h is the height
and b₁ and b2 are the two bases. Rewrite the formula to solve for h in terms of A, b₁
and b₂.
Step-by-step explanation:
that means that we need to transform the equation so that we get a form
h = ...
A = ½h(b1 + b2) | multiply both sides by 2
2A = h(b1 + b2) | divide both sides by (b1 + b2)
2A/(b1 + b2) = h
that's it.
Write two inequalities to compare a and b how do you know?
To compare two numbers, a, and b, we can write two inequalities:
a < b when a is less than b
a > b when a is greater than b.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We may write two inequalities to compare two numbers, a and b:
a < b
a > b
If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.
We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.
For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.
On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.
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Remember, jed's height is within 3 inches of pablo's height. Describe the solutions in words. Jed can be 67 inches or shorter. At least 67 inches, but at most 73 inches. 73 inches or taller. 67 inches or shorter, or 73 inches or taller.
at least 67 inches, but at most 73 inches if Jed can be 67 inches or
shorter
The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
67 ≤ x ≤ 73 are the solutions to the absolute value inequality |x − 70| ≤ 3
the complete question is
What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3.
Answer: 67 ≤ x ≤ 73
Remember, Jed's height is within 3 inches of Pablo's height.
Describe the solutions in words.
Jed can be
67 inches or shorter.
at least 67 inches, but at most 73 inches.
73 inches or taller.
67 inches or shorter, or 73 inches or taller.
Just found out it's the 2nd choice.
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Answer:
B: at least 67 inches, but at most 73 inches.
Step-by-step explanation:
What does congruent mean square?
Answer:
All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.
hope this helps
mark me brainliest
Step-by-step explanation:
Create a formula without a function that adds 14 days to the date the client was last contacted.
The Excel formula to enter in cell H4 is = (G4 + 14)
Excel formulas are expressions used to perform computation.
To determine the formula:
From the question,
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Excel formulas begin with the equality (=) sign
So, we have:
= (G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
Complete question:
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
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Excel formulas are expressions used to perform computation.
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
The graph below represents the number of miles, y, that the satellite Space Explorer
flies in a hours. Find the rate of change.
Miles
90,000
85,000
80,000
75,000
70,000
65,000
60,000
55,000
50,000
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
Answer:
0
Space Explorer
Seve
(10,10000)
(5.5000)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Hours
miles per hour
Submit Answer
Answer:
1000
Step-by-step explanation:
answer is 1000 miles per hour
shawna reads a study about exercise that includes the following scatterplot. which answer choice correctly indicates the explanatory variable and the response variable? a.) explanatory variable: exercise response variable: calories burned per minute b.) explanatory variable: weight response variable: exercise c.) explanatory variable: weight response variable: calories burned per minute d.) explanatory variable: calories burned per minute response variable: weight
Shawna finds The correct answer as "explanatory variable: weight response variable: calories burned per minute."
In this scatterplot, the explanatory variable is the weight of the individuals and the response variable is the number of calories burned per minute. The explanatory variable is the variable that is being manipulated or tested in the study, while the response variable is the variable that is being measured or observed.
In this case, the study is examining the relationship between weight and calories burned per minute, with weight being the explanatory variable and calories burned per minute being the response variable. The other answer choices do not correctly identify the explanatory and response variables in the scatterplot.
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Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the result of that transformation into the box under it.
Answer:
g(x) = f(x) + 4 → Graph #5
h(x) = f(x + 4) → Graph #6
k(x) = f(x) - 4 → Graph #4
m(x) = f(x - 4) → Graph #3
Step-by-step explanation:
g(x) = f(x) + 4 → Graph #5
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.
⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).
h(x) = f(x + 4) → Graph #6
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.
⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).
k(x) = f(x) - 4 → Graph #4
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.
⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)
m(x) = f(x - 4) → Graph #3
⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.
⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).
How do you solve two parallel lines crossed by a transversal?
When two lines are crossed by a transversal, a number of angle pairs are formed. The sum of the measures of these angle pairs can be used to solve for unknown angles in the diagram.
Here are some of the angle pair relationships that hold for two lines crossed by a transversal:
Alternate Interior Angles: Alternate interior angles are pairs of angles on opposite sides of the transversal, but inside the two lines. These angles are congruent (have the same measure).Alternate Exterior Angles: Alternate exterior angles are pairs of angles on opposite sides of the transversal, but outside the two lines. These angles are congruent.Corresponding Angles: Corresponding angles are pairs of angles on the same side of the transversal, but on opposite sides of the two lines. These angles are congruent.Using these relationships, you can set up equations to solve for unknown angles in the diagram. For example, if you are trying to find the measure of angle A, you might use the fact that corresponding angles are congruent to set up the equation "m<A = m<D". Then, you can use other angle pairs to find the measures of the other angles, and solve the system of equations to find the measure of angle A.
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Someone please help!! (screenshot attached)
The number of CDs that can be bought are { 5, 4, 3, 2, 1 }.
What is an inequality ?
A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality emerges from an imbalance.
Given, No. of CDs = x
A CD costs $11 and He has total $60.
So, According to the question,
No. of CDs × Cost of each CD ≤ 60
x × 11 ≤ 60
11x ≤ 60
x ≤ 60/11
Since the number of CDs can't be in fraction and The maximum CDs can be bought is 5.
So, The possible No. of CDs that can be purchased are { 5, 4, 3, 2, 1 }
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(b)
(i) Factorise 1000x³-y³ completely.
(ii) Hence, without using a calculator, show that 124 is a factor of 992.
Answer:
i. (10-y)(100x^2 +10xy + y^2)
ii. See the explanation
Step-by-step explanation:
i. 1000x³-y³ =
10³x³ - y³ =
(10x)³ - y³ = ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)
(10-y)((10x)^2 +10xy + y^2) =
(10-y)(10^2 * x^2 +10xy + y^2) = ==> simplify
(10-y)(100x^2 +10xy + y^2)
ii. 992/124=
(992-192)/(124-24)=
800/100 = 8
As a result, 8*124=992.
Hence, 124 (and 8) is a factor of 992
using the standard From of the quadratic Function y=-3x²-12x-9
The standard From of the quadratic Function is (−2,3).
What is the standard From?y=-3x²-12x-9
Find the given parabola's characteristics.
To continue, tap...
Opens down in the direction of ( 2, 3), with
( -2, 35 /12) as the focus.
x = 2 is the symmetry axis.
The directrix is y = 37 /12
By entering a few x values into the equation, you may get the associated y values. You should choose the x values close to the vertex.
To continue, tap...
x y − 4 − 9 − 3 0 − 2 3 − 1 0 0 − 9
Using the chosen points and the parabola's attributes, draw the curve.
Opens downward in direction
Focus: ( 2, 35 12) Vertex: ( 2, 3)
x = 2 is the symmetry axis.
The following directrix: y = 37 12 x y 4 9 3 0 2 3 1 0 0 9.
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I need help describing this, I forgot how to find all of it
The (a) Hole in the expression is x, (b) The vertical assumption is -10 and (c) the horizontal assumption is that the denominator is greater than the numerator.
How to find Hole, vertical and horizontal assumptions?You should know that a hole occurs if there is a common term between the the numeration and the denominator when factorized, For vertical assumption, the denominator must be equal to zero and horizontal assumption, numerator will be equal to denominator
The given expression is:
[tex]\frac{x^{2}-2x }{x^{3}-9x^{2} -10x }[/tex]
The Hole is
Factorize the numerator= x²-2x
x is common in the expression
x(x-2)
Factorize the denominator= x³-9x²-10x
x(x²-9x-10)
= [x²-10x+x-10]
x[(x²-10x)+(x-10)]
Simplify further to get
x[x(x-10)+1(x-10)]
=x[(x+1)(x-10)]
Combine numerator and denominator to see the hole
[tex]\frac{x(x-2)}{x(x+1)(x-10)}[/tex]
From the expression the hole is x
b. vertical assumption
The denominator =0
x³+9x²-10x=0
Differentiate to have
dy/dx= 3x²-18x-10
2nd order derivative is
d2y/d2x=6x-18
Applying limit as x approaches 0
6x-10
Therefore x=-10
c. horizontal assumption the numerator is less than the denominator
x²-2x<x³-9x²-10x
In conclusion, the Hole in the expression is x, The vertical assumption is -10 and the horizontal assumption is that the denominator is greater than the numerator.
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What kind of sequence is 6 12 24?
As there is a common ratio between each term so this is a geometric sequence.
How geometric sequence is applied in real life?The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.
What is the important property of geometric sequence?In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.
Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.
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keegan bought 5 T-shirts and 2 pairs of shoets for $49.50. Each pair of shorts, s, cost twice as much as each T-shirt, t.
Part A
Which system ot equations can vevused to find the price of the shorts and t-shirts?
(use attachment)
Part B
how much did keegan pay for each t-shirt and each pair of shorts?
Part A
Adding the costs, [tex]2s+5t=49.50[/tex].
Since a pair of shorts costs twice as much as a T-shirt, [tex]s=2t[/tex].
The correct answer is option 3.
Part B
[tex]2(2t)+5t=49.50 \\ \\ 9t=49.50 \\ \\ \boxed{t=5.50} \imploes \boxed{s=11}[/tex]
The ratio in the table for ditance covered in meter to time taken in hour i contant. Let d = ditance covered in 15 hr. Let t = time taken to cover 8 m. Which table how the correct value for t and d? A. B. C. D
The table that shows the correct t and d values is
Distance Covered (m) Time Taken (hr)
8 6
32 15
How to determine the correct values for t and d
The table of values is given as:
Distance Covered (m) Time Taken (hr)
8 6
16 12
32 15
48 18
The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours
When these values are extracted, we have:
Distance Covered (m) Time Taken (hr)
8 6
32 15
The above represents the table that shows the correct t and d values
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What is the nth root theorem?
Answer:
The nth root theorem is a mathematical principle that states that, for any positive integer, it will have n nth roots!
An nth root of x is equivalent to saying [tex]\sqrt[n]{x}[/tex]. To elaborate, if you want to know how many 2nd roots that 1 has, through this theorem you will know it has 2 of these roots (-1 and 1). This applies for all numbers!
hope this helps :)
does someone mind helping me with this? Thank you!
Answer:
[tex]y = 2x - 3[/tex]
Step-by-step explanation:
❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
⭐What does "opposite reciprocal" mean?
Opposite reciprocal: the slope of the perpendicular line is the reciprocal of the slope of the line it is perpendicular to and it has the opposite sign of the slope of the line it is perpendicular to.⭐What is slope-intercept form?
One way to write the equation of a line[tex]y = mx + b[/tex]m = the slopeb = the y-interceptWe can find the equation of the perpendicular line by:
Substituting the slope of the perpendicular line into the point-slope form equation using the opposite reciprocalSubstituting the given coordinate into the point-slope form equation to solve for b1. Substituting the slope into the point-slope form equation:
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
The slope of the line the perpendicular like is perpendicular to is [tex]\frac{-1}{2}[/tex].
Therefore, the slope of the perpendicular line is [tex]2[/tex]
Substitute the slope into the point-slope form equation.
[tex]y = 2x + b[/tex]
Now, all we have to do is solve for b.
2. Substituting the given coordinate into the point-slope form equation:
We are given the coordinate (6,9).
[tex]y = 2x + b[/tex]
[tex]9 = 2(6) + b[/tex]
[tex]9 = 12 + b[/tex][tex]-3 = b[/tex]
Substitute "b" into the point-slope form equation.
[tex]y = 2x + 3[/tex]
• Question 2
In the graph of an inequality, the region below the dashed horizor
What inequality does the graph represent?
The linear inequality represented by the graph is given as follows:
y < 1/4x + 2.
How to define the inequality?The dashed line is a linear function, hence the slope-intercept format of the inequality is given as follows:
y < mx + b.
(the sign is < because the line is dashed and not solid).
In which the coefficients are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value of y when the graph of the linear function crosses the y-axis.The line crosses the y-axis at y = 2, hence the intercept b is given as follows:
b = 2.
When x = -8, y = 0, thus when x increases by 8, y increases by 2, meaning that the slope is given as follows:
m = 2/8
m = 1/4.
Thus the inequality is given as follows:
y < 1/4x + 2.
Missing InformationThe graph of the linear inequality is given by the image shown at the end of the answer.
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your class collected more than 410 cans of food for th eannual food drive in the first week, 185 cans were collected.how many cans c of food were colected in the second week?
The number of cans collected in the second week would be 225 cans.
A can of food is a container that holds a prepared food product, such as vegetables, fruits, beans, or soups. Canned foods are shelf-stable, meaning they can be stored for long periods of time without spoiling. They are often used as a convenient and easy-to-store source of food, especially in emergency situations.
To find out how many cans of food were collected in the second week, you need to subtract the number of cans collected in the first week from the total number of cans collected. In this case, the number of cans collected in the second week would be:
410 cans - 185 cans = <<410-185=225>>225 cans.
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How to find the height of a pyramid using Pythagorean Theorem?
The Pythagorean Theorem states that because a pyramid's height, slant height, and apothem form a right triangle with slant height as its longest side: (apothem)² + (height)² = (slant height)².
Define the term pyramid?A pyramid is a three shape having a base that is a polygon and triangular sides that come together at the apex, which is located directly just above center of the base.
The distance here between center of the base as well as the apex of a pyramid is its height. The distance between the apex and one of the base's sides is its slant height. The distance between both the center of the base and one of the base's sides is its apothem.Let's start by taking a look at a pyramid with both the height, slant height, the apothem shown in order to demonstrate how to use the Pythagorean Theorem to get a pyramid's height.
a² + b² = c².
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40 POINTS!
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
A. (6, 0)
B. (0, 5)
C. (1, 4)
D. (1, 5)
The best estimate of the solution to the system of equations will be (1, 4). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
2x + 3y = 12 ...1
4x + 2y = 10 ...2
Divide the equation 2 by 2, then we have
2x + y = 5 ...3
Subtract equation 3 from equation 2, then we have
2x + 3y - 2x - y = 12 - 5
2y = 7
y = 3.5
y ≈ 4
Then the value of 'x' is calculated as,
2x + 3.5 = 5
2x = 1.5
x = 0.75
x ≈ 1
The best gauge of the answer for the arrangement of conditions will be (1, 4). Then, at that point, the right choice is C.
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What form is used to inform the SSS of your illness or injury?
A sickness Notification Form is used to inform the SSS loan of your illness or injury.
The sickness benefit, according to SSS President and Chief Executive Officer Aurora C. Ignacio, is a daily cash payment made for each day a member is unable to work as a result of illness or accident.
In order to be eligible for the program, a member must have made at least three monthly contributions in the twelve months prior to the semester of illness or injury, be confined for at least four days in a hospital or at home, have used all of their current company sick days for the current year, and have informed their employer of their illness or injury.
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Which expression is equivalent to 18-(8* q) ? .
A (8q) - 18
B (18 - q) * 8
C (18 - 8) * c
D 18 - (0 * 8)
Answer:
the way you typed that is kinda confusing but the answer is
[tex]18 - 8q[/tex]