The investment amount at 9% rate is $12500 and the investment
amount at 2% rate is $15500
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let x be the amount invested at 9% rate.
And (28000−x) be the amount invested at 2% rate.
The total annual income is $1435
Let us find the amount invested at 9% rate:
x9%+2%(28000−x)=1435
9%+2%(28000−x)=1435
0.09x+0.02(28000−x)=1435
0.09x+560−0.02x=1435
0.09x−0.02x=1435−560
0.07x=875
x=875/0.07
x=12500
Let us find the investment amount at 2% rate:
⇒28000−x
⇒28000−12500
⇒15500
Therefore, the investment amount at 9% rate is $12500 and the investment amount at 2% rate is $15500.
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Simplify, if possible.
8ab² +3ab+2a-3b+5
A. The expression is in its simplest form.
B. -10ab² +5
2
C. 8ab² + 2ab +5
D.
8ab²-3ab+5
Please select the best answer from the choices provided
Answer:
A. The expression is in its simplest form.
Step-by-step explanation:
Answer:
i tried this i think the answer is 11a plus 2a subract3b ppus 5
If f(x) is a decreasing function, which of the following statements must be true? Select all that apply.
(Assume that f(x) is always decreasing.)
a) f(5)−f(1) / 5−1 > 0
b) f(5)−f(1) / 5−1 < 0
c) For some value of x≠5, f(x)=f(5)
d) f(5) < f(1)
e) f(5) > f(1)
The two true statements are:
b) (f(5)−f(1)) / (5−1) < 0
d) f(5) < f(1)
Which of the following statements must be true?
We know that f(x) is a decreasing function, this means that, as x increases, the value of f(x) decreases.
So, if there are two values in the domain a and b, such that a < b, we will have that:
f(a) > f(b).
Then the statement:
[ f(5) - f(1)]/(5 - 1) < 0
Is true, because f(1) is larger than f(5).
Which means that statement d ( f(5) < f(1)) is also true.
Then the two correct options are b and d.
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what’s the answer to this question
A jewelry maker incurs costs for a necklace according to the equation shown below.
C(x) = 30x + 1692
The revenue function for the necklaces is given below.
R(x) = 77x
How many necklaces must be sold to break even?
necklaces
11. Represent and Connect After a recycling
awareness program, the number of tons of
recyclable material taken to the landfill is
reduced by 13 tons per month. Represent
the total change in the tons of recyclable
material taken to the landfill after
10
7 months resulting from the awareness
program. Show your work.
The total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
In this question, we have been given after a recycling awareness program, the number of tons of recyclable material taken to the landfill is reduced by 13 tons per month.
We need to represent the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program.
Given that reduction in materials = 13 7/10 tons per month
We rewrite the improper fraction 13 7/10 as a proper fraction.
13 7/10 = 137/10
Monthly reduction = 137/10 tons
After 7 months : (7 × 137/10)
= 959/10 tons
= 95.9 tons
Change in amount of material taken to the land fill:
Initial amount - amount after 7 months
If initial amount be x, then the change in amount = (x - 95.9) tons
So, we get an expression (x - 95.9)
Therefore, the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
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If l = √m-5 and m = 4n²-3, what is l when n = 2? What is n when l = 4?
what of disibility rules?
given g(x) is ...............
Answer:
-40
Step-by-step explanation:
It states with g(-2) that x = -2, so we can plug -2 for x.
g(x) = 3x^3 - 2x^2 + 4x
g(x) = 3(-2)^3 - 2(-2)^2 + 4(-2)
g(x) = 3(-8) - 2(4) + 4(-2)
g(x) = -24 - 8 - 8
g(x) = -40
1. Which of the following is a linear inequality in two variables? A. 3a-2b = 6 C. 3x ≤ 10 B. 3c+16 < -10 D. 3x + 4y ≥ 10
Answer:
D
Step-by-step explanation:
a linear expression in two variables has the form ax + by
an inequality uses the symbols < , > , ≤ , ≥
the only expression in this form is
3x + 4y ≥ 10
Using company C’s phone plan, the cost of an overseas phone call is a $0.80 connection fee plus 23 cents per minute. If the total cost of the call is 7.93, how long is the phone call?
Answer: 31 Minutes
Step-by-step explanation:
Minus 0.80 from 7.93, and then divide 7.13 by 0.23 and you get 31
Can y’all help me please??
Answer: 29/21
Quotient: 1
Reminder: 8
Step-by-step explanation:
Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.
Use the 1st digit 2 from dividend 29
21 & 29 squared root
Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.
1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.
Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answer:
Step-by-step explanation:
1/|2x - 9|≤5
How to solve the inequality
Answer:
5<x<7
Step-by-step explanation:
Hey there !
firstly, in inequality; we must know that we should put the x alone.
so, in order to put the x alone; we should do the following process,
1</2x-9/<5
here,
adding +9 in all sides, we get;
=1+9<2x-9+9<5+9
=10<2x<14
dividing it by 2;we get
=10/2<2x/2<14/2
=5<x<7
This is the following answer. hope it helps!
Thank you!
Use Order of Operations
mot to solve.
14+7 x 54 ÷6-7
Choose the estimate closest to the length of a woman's hand : 30 cm, 200mm, or 20 mm. Which is the correct answer?
Answer:
200mm
Step-by-step explanation:
200mm can be rewritten as 20 cm
a womans hand is on average 17.3 cm
this is the closest estimate out of the three
Which of the following best represents the
rate of change of this function?
A -1/2
B 1/2
C 2
D -2
Answer:
Step-by-step explanation:
Need more clarification! Which function?
How many times larger is (1.064 x 101) than (7 x 10−1)?
0.152
15.2
6.58
7.448
Answer:
is 15.2
Step-by-step explanation:
find the coordinates of pint P along the directed line segment AB so that AP to PB is the give ratio 2 to 6
Coordinates of P is 8
Since 3+2 = 5, we are dividing line segment AB into 5 congruent parts with point P 3/5 of the way from A to B.
x-coordinate of P = x-coordinate of A + (3/5)(change in x from A to B) = -4 + (3/5)(20) = 8
y-coordinate of P = y-coordinate of A + (3/5)(change in y from A to B) = 8 + (3/5)(-10) = 2
P = (8,2)
In each axis, find the distance from A to B, apply the ratio to get the distance from A to P, and add that value to A.
Note the ratio: We are given the ratio of AP to PB as 3/2. This means that the ratio of AP to AB is 3/5
Here is is for the X-axis:
AB = 20
AP = 20 *3/5 = 12
So P = -4 + 12 = 8
It is one of the branches of geometry where the position of a point is defined using coordinates.
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
It is used to divide any line into two parts, in m:n ratio
The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).
The four quadrants along with their respective values are represented in the graph below-
Quadrant 1 : (+x, +y)
Quadrant 2 : (-x, +y)
Quadrant 3 : (-x, -y)
Quadrant 4 : (+x, -y)
The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.
How To Find Coordinates of a Point on Graph With Examples
A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.
Coordinates Definition
A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.
The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:
x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.
y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.
Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).
Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).
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please answer as soon as possible
Three angles add up to 180 degrees, angle one has a measure of 4x+8, angle two has a measure of 8x+3 and angle three has a measure of 9x+3.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Answer:
39.60°
Step-by-step explanation:
The sum of three angles is 180 degrees.
Show this as equation and solve for x:
4x + 8 + 8x + 3 + 9x + 3 = 18021x + 14 = 18021x = 166x = 166/21x = 7.90 (rounded)Angle one is:
4*7.90 + 8 = 39.60Find x
A. 2.6
B 3.1
C 2.9
D 4
Answer:x=
Step-by-step explanation:
need the domain and range!
Answer: Domain: [-1, 1]
Range: [-2, 3]
Step-by-step explanation:
Domain: The x-values go from -1 to 1 with x=-1 and x=1 included.
Range: The range starts at the vertex of the function which is y=-2 and goes up to y=3 where the graph is cut off by 2 points on y=3.
A factory bottles 360 bottles of juice in 5 minutes. Find the factory’s unit rate of bottles per minute.
Answer:
72
Step-by-step explanation:
let's begin by restating what we already know,
360 bottles of juice in 5 minutes
for goodness's sake let's abbreviate this
360 boj in 5 mins
RATIO TIME!
360 : 5
pay attention how I put the BOJ (bottles of juice) first and the time last
now to find how many boj per min. we will say
[tex]\frac{1}{5} (360: 5)[/tex]
72:1
so, we now know that the factory of juice produces 72 bottles of juices per minute ( that's ALOT of juices per minute imo)
^_^ hope this helps, happy learning
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
A) Find an equation in the form
y=mx+b
where
x
is the number of monthly minutes used and
y
is the total monthly of the Ringular plan.
The equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
How to represent a linear equation?The customer uses 500 minutes, the monthly cost will be $132. If the customer uses 700 minutes, the monthly cost will be $172.
Using linear equation in slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence,
x = the number of monthly minutes used
y = the total monthly of the Ringular plan
Therefore, the equation in slope intercept form can be represented as follows:
(500, 132)(700, 172)
let's find the slope,
m = 172 - 132 / 700 - 500
m = 40 / 200
m = 4 / 20
m = 1 / 5
Hence,
y = 1 / 5x + b
using (500, 132) let's find the y-intercept
132 = 1 / 5 (500) + b
132 = 100 + b
b = 132 - 100
b = 32
Therefore, the equation in the form y = mx + b is as follows:
y = 1 / 5 x + 32
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Bill is buying several bottles of pop for a party. They each cost the same amount.
If Bill can buy 4 bottles for $7.16, how many bottles could he buy for $10.74?
Answer:
6
Step-by-step explanation:
First, divide 7.16 by 4 to find the price of one bottle, which is 1.79. Then, divide 10.74 by 1.79 to get 6.
5. Estimate:
$53
X 4
+what do I add
Math
11. Find the solution of the following system of equations using substitution:
2x + 7y = 5
y = x + 2
Answer:
(x,y) = (-1,1)
Step-by-step explanation:
step 1
subsitute the given value of y into the equation
2x+7(x+2)=5
step 2
solve for x
x= -1
step 3
subsitute the value of x in to the second equation
y= -1+2
step 4
solve for y
y=1
step 5
check if there true by putting the value of x and y back in to the equation.
then configure x and y into an ordered pair.
(x,y)=(-1,1)
I hope this helped!
Simplify.
(y^5)^3
Write your answer without parentheses.
Answer:
[tex]\boxed{\sf y^{15}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf (\:y^5\:)^3[/tex]When any expression is given in the format [tex]\sf (\ a^b \ )^c[/tex] then [tex]\sf a^{bc}[/tex].
[tex]\sf \rightarrow y^{5(3)}[/tex]simplify
[tex]\sf \rightarrow y^{15}[/tex]PLEASE HELP ME FIGURE THIS OUT
Cycling.
The graph below shows the ages of the top five male finishers in the Mt. Washington Auto Road Bicycle Hillclimb each year from 2017 through 2021.
1. Write the relation of this situation as a set of ordered pairs in terms of (age, finishing place).
2. Identify the domain and range of the relation.
3. Do the ordered pairs represent a function? Explain.
Answer:From the given table, we have that:
1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
What is the relation of this situation?
To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:
(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
What are the domain and the range?
The domain of a relation is the set that contains all possible input values for the values, that is, the values of x.
The range of a relation is the set that contains all possible output values for the values, that is, the values of y.
Hence, for the given relation:
The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
When does a relation represents a function?
A relation represents a function if each value of the input is mapped to only one value of the output.
For this problem, we have that:
There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
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Step-by-step explanation:
Identify all the pairs of parallel sides of each figure.
Answer:
2 on the 1st, 1 on the second, 3 on the third, 1 on the fourth
Between what two integers does square root of -80 lies
Answer: 8 and 9
Step-by-step explanation:
square root of - 80 is 8.94427191 so 8 and 9 is the integers around it.
Simplify to create an equivalent expression.
\qquad{2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)2, left parenthesis, 3, y, plus, 6, right parenthesis, minus, 3, left parenthesis, minus, 4, minus, y, right parenthesis
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
9y9y9, y
(Choice B)
B
5y+245y+245, y, plus, 24
(Choice C)
C
9y-249y−249, y, minus, 24
(Choice D)
D
9y+249y+24
The generated equivalent expression is 9y + 24. So, the correct answer is option D.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied on it. The operation can be addition, subtraction, multiplication and division.
Simplifying to generate an equivalent expression
The given expression is 2(3y + 6) - 3(- 4 - y)
= 2(3y + 6) + 3(4 + y)
= 6y + 12 + 12 + 3y
= 6y + 3y + 24
= 9y + 24
Hence, the generated equivalent expression is 9y + 24.
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