8x + 5y ≥ 50
This is from the inequality 16x + 10y ≥ 100.
The other three inequalities are:
x + y ≤ 8
x ≥ 1
y ≥ 3
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Total number of students = 100
Type A minibus = x
Type B minibus = y
Number of students type A carry = 16
Number of student type B carry = 10
We can write an inequality from the above situation as,
16x + 10y ≥ 100
Taking out the common factor.
2 (8x + 5y) ≥ 2 x 50
8x + 5y ≥ 50
The school wishes to use no more than eight minibusses.
This can be written as
x + y ≤ 8
The school wishes to use at least one type A minibus.
This can be written as
x ≥ 1
The school wishes to use at least three type B minibusses.
This can be written as
y ≥ 3
Thus,
8x + 5y ≥ 50
This is from the inequality 16x + 10y ≥ 100.
The other three inequalities are:
x + y ≤ 8
x ≥ 1
y ≥ 3
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Richard’s cumulative gpa for 3 semesters was 2. 0 for 42 credits. His fourth semester gpa was 4. 0 for 14 course units. What is richard’s cumulative gpa for all 4 semesters?.
Richard earned a cumulative GPA of 2.5 in all four semesters.
Here, we know that the cumulative GPA for the first 3 semesters is 2.0
He had earned 42 credits in total in all three semesters.
Cumulative GPA = Total points earned/credits rewarded
Hence,
Total points earned in 3 semestes= 2 X 42
= 84 points
In the fourth semester,
he had earned 14 credits with a GPA of 4.0
Hence total points earned = 4 X 14
= 56 points
Therefore, total points earned in all four semesters = 84 + 56 points
140 points
Total credits = 14 + 42
= 56
Hence, the cumulative GPA of all 4 semesters
= 140/56
= 2.5 points.
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A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.4% What will the account balance be after 10 years
The account balance after 10 years is $7200.
How to calculate the interest?It should be noted that simple interest is calculated as:
= (Principal × Rate × Time) / 100
= ($3000 × 1.4 × 10) / 100
= $4200
The total amount that will be in the account will be:
= Principal + Interest
= $3000 + $4200
= $7200
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What is 19% of 40? ??
Answer: 7.6
Step-by-step explanation:
19÷100×40 which will give you 7.6
Determine the value of x and the indicated angle measure.
I understand the concept of solving for x usually and solving the missing angle but I could use some help with this one. I'm stuck!
Please and thanks! ^_^
The value of x for the given triangle is 4.5
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of all three angles of a triangle is always 180°
In the given triangle ABC,
∠A=(9x+16)°, ∠B=(6x+15)°
And the extrior angle ∠C=(19x+3)°
Use the external angle property,
The sum of two interior angles is equal to an exterior angle.
Therefor,
∠C=∠A+∠B
(19x+3)°=(9x+16)°+(6x+5)°
19x+3=15x+21
4x=18
x=4.5
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A salesman bought a computer from a manufacturer. The salesman then sold the computer for $15600 making a loss of 25%. What amount did the salesman pay the manufacturer for the computer?
The amount that the salesman pay the manufacturer for the computer is $20800.
How to calculate the value?From the information, the salesman sold the computer for $15600 making a loss of 25%.
The amount that the salesman pay the manufacturer for the computer will be illustrated thus:
Since a 25% loss was made, the cost price will be: = 100% + 25% = 75%
Therefore, the cost price will be:
= Sales price / 125%
= $15600 / 0.75
= $20800
The amount is $20800.
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A regular pentagon with sides of 7 cm. What is the area of this pentagon?
The area of the regular pentagon with sides of 7 cm is 84.30 cm²
How to calculate the area of a regular pentagon?
The area of a regular pentagon can be determined if the side length (s) is given. The formula used for calculating the area of a regular pentagon is:
[tex]A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}[/tex]
Given: side length (s) = 7 cm
Area (A) = 1/4×√( 5(5+2√5) ×7² = 84.30 cm²
Therefore, the area of the pentagon is 84.30 cm²
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Can someone please help me!!
Please I need help please
Serenity invested $16,000 in an account paying an interest rate of 4. 5% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?.
The amount of money that would be in the account after 9 years, giving the interest rate and the amount invested is $23, 777.52
How to find the amount in future?The amount in the account after 9 years is called the future value of the amount that Serenity invested.
To find this future value, you use the future value formula which is:
= Amount invested x ( 1 + interest rate) ^ number of years
The amount in the account after 9 years would therefore be:
= 16, 000 x ( 1 + 4.5%) ⁹
= $23777.52224662808994653125
= $23, 777.52
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note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the expression in factored form? 9x^2-4
Answer: (3x-2)(3x+2)
I knew the answer it was just hard to explain all of it. Sorry if this doesn't help
The diagonal of a square is x units. What is the area of the square in terms of x?
The area of the square is (x²/2) square units.
We are given a square. The length of the diagonal of the square is x units. We have to find the area of the square in terms of "x".
Let the side of the square be denoted by the variable "s". We will use the Pythagorean theorem to find the length of the side of the square.
s² + s² = x²
2s² = x²
s² = x²/2
s = √(x²/2)
s = (x/√2)
The area of the square is given by the square of the side length. Let the area of the square be denoted by the variable "A".
A = s²
A = (x/√2)²
A = x²/2
Hence, the area of the square is (x²/2) square units.
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alex and ben go to a cafe with some friends.
alex buys 4 cups of coffee and 3 cups of tea. he paid a total of £6.95.
Ben buys 5 cups of coffee and 2 cups of tea. He pays a total of £7.20.
work out the total cost of each cup of coffee in the cost of each cup of tea
Answer:
Step-by-step explanation:
Assume the cost for a cup of coffee is x and the cost for a cup of tea is y.
For Alex: 4x+3y=6.95
For Ben 5x+2y=7.20
Then multiply Alex's cost by 2 and Ben's by 3 to cancel y.
8x+6y=13.90
15x+6y=21.60
Equation 2 minus equation 1 would be
15x+6y-(8x+6y)=15x+6y-8x-6y=7x
21.60-13.90=7.70
7x=7.70
Then x=1.10 and plugging it one of the equations,
y= 0.85
A cup of coffee costs 1.10 pounds and A cup of tea is 0.85 pounds
:)
The table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
A) Write an equation that models the amount of storage as a function of the number of songs
B) Interpret the slope and t-intercept of the line of fit
pls include work
a) An equation that models the amount of storage as a function of the number of songs is y = -0.005x + 16
b) Slope of the equation is -0.005 and the intercept of the equation is 16
Slope intercept form
Slope intercept form presents the graph of a straight line and is represented in the form of
y = mx + c.
where
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Given,
Here we have the table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
Now, we have to find the following:
a) Equation of the table
b) Slope and intercept.
In order to find the equation, we have to identify the slope an intercept of the table.
So, to find that we have to take two points from the table.
Then the selected points are
(0, 16), (242, 14.8)
By using these point we have to calculate the slope as,
m = (14.8 - 16) / (242 - 0)
m = -1.2/242
m = -0.005
Now, the intercept is calculated by using the point (0, 16) and the slope -0.005, then we get,
16 = -0.005(0) + c
c = 16
Therefore, the equation is y = -0.005x + 16.
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write a coordinate rule for the composition.blue quadrilateral w x y z and green quadrilateral s t u v are graphed on a coordinate plane. quadrilateral w x y z has vertex w at ordered pair negative 1 comma negative 2, vertex x at ordered pair negative 2 comma 0, vertex y at ordered pair 1 comma 2, and vertex z at ordered pair 1 comma negative 1. quadrilateral s t u v has vertex s at ordered pair negative 2 comma negative 4, vertex t at ordered pair negative 2 comma 2, vertex u at ordered pair 2 comma 4 and vertex v at ordered pair 4 comma 0.$\left(x,\ y\right)\rightarrow$ ( , )skip to navigation
Coordinate rule for the composition is w(-1,-2) → s(-1-1,-2-4) → s(-2,-4) , x(-2,0) → t(-2+0,0+2) → t(-2,2), y(1,2) → u(1+1,2+2) → u(2,4) , z(1,-1) → v(1+3,-1+1) → v(4,0).
Given:
w x y x has vertices w(-1,-2) , x(-2,0), y(1,2) and z(1,-1).
s t u v has vertices s(-2,-4) , t(-2,2) , u(2,4) and v(4,0).
The coordinate rule for transformation is:
w(-1,-2) → s(-1-1,-2-4) → s(-2,-4)
x(-2,0) → t(-2+0,0+2) → t(-2,2)
y(1,2) → u(1+1,2+2) → u(2,4)
z(1,-1) → v(1+3,-1+1) → v(4,0)
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6. Jung purchased several video games priced at $29.95 each and paid $5.95 for express shipping. His total purchase was $185.65. How many video games did he purchase?
Answer:
6 video games
Step-by-step explanation:
We can solve this question with an algebraic equation.
29.95x + 5.95 = 185.65
29.95x + 5.95 - 5.95 = 185.65 - 5.95
29.95x ÷ 29.95 = 179.7 ÷ 29.95
x = 6
math homework similar shapes pls help
Answer: Both p and q are 8cm long.
Step-by-step explanation:
BE created a similar triangle that is exactly half of the larger triangle.
So if BE is 4 and AE is 8 then we know that CD is 8 and AD is 16.
However we only need segment q which is half of AD so the answer is:
p=8 and q=8
;)
Find the measure of each missing angle. a || b
Answer:
though the answers are scattered but I worked them all , just patiently study it.
Factor each sum or difference of cubes
a) 8-1/8a^3
b) 1/64m^3+1000
c) 125a^3-64b^3
d) 1/27x^3+1/125y^3
Write each polynomial as the square of a binomial as an expression opposite to the square of a binomial
e) 0.25x^2-0.6xy+0.36y^2
f) -a^2+0.6a-0.09
g) 9/16a^4+a^3+4/9a^2
The following are the answers:
a) 7 / (2a)³
b) 1/(4m)³ + 10³
c) (5a)³ - (4b)³
d) 1/(3x)³ + 1/(5y)³
e) (0.5x - 0.6y)²
f) (-a - 0.3)²
g) ((3/4)²a² + (2/3)²a)²
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
a)
(8 - 1) / 8a^3
= 7 / (2a)³
b)
1/64m^3 + 1000
= 1/(4m)³ + 10³
c)
125a^3 - 64b^3
= (5a)³ - (4b)³
d)
1/27x^3 + 1/125y^3
= 1/(3x)³ + 1/(5y)³
Now,
Polynomial is an expression of writing with more than one term.
We will write it in the form of:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
e)
0.25x^2 - 0.6xy + 0.36y^2
= (0.5x)² - 2 x 0.5 x 0.6 + (0.6y)²
= (0.5x - 0.6y)²
f)
-a^2 + 0.6a - 0.09
-a² - 2 x (-a) x 0.3 - (0.3)²
= (-a - 0.3)²
g)
9/16a^4 + a^3 + 4/9a^2
((3/4)²a²)² + 2 x (3/4)²a² x (2/3)²a + ((2/3)²a)²
= ((3/4)²a² + (2/3)²a)²
Thus,
The following are the answers:
a) 7 / (2a)³
b) 1/(4m)³ + 10³
c) (5a)³ - (4b)³
d) 1/(3x)³ + 1/(5y)³
e) (0.5x - 0.6y)²
f) (-a - 0.3)²
g) ((3/4)²a² + (2/3)²a)²
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What is 1/2 of 17 by estimating each product
the goal of the least-squares regression is to compute a line that
Answer: you did not put in the full equation but i got this right out of the box.
ˉx 28
r 0.82
Which expreion are equivalent to
−
90
−
60
w
−90−60wminu, 90, minu, 60, w?
Chooe 3 anwer:
Chooe 3 anwer:
(Choice A, Checked)
A
−
30
(
3
2
w
)
−30(32w)minu, 30, left parenthei, 3, plu, 2, w, right parenthei
(Choice B)
B
(
−
9
−
6
w
)
⋅
10
(−9−6w)⋅10left parenthei, minu, 9, minu, 6, w, right parenthei, dot, 10
(Choice C)
C
−
3
(
30
−
20
w
)
−3(30−20w)minu, 3, left parenthei, 30, minu, 20, w, right parenthei
(Choice D)
D
(
6
4
w
)
×
15
(64w)×15left parenthei, 6, plu, 4, w, right parenthei, time, 15
(Choice E)
E
−
20
(
4. 5
3
w
)
−20(4. 53w)minu, 20, left parenthei, 4, point, 5, plu, 3, w, right parenthei
The expression equivalent to the expression -90 - 60w is -30(3 + 2w), (-9 - 6w)10 and -20(4.5 + 3w)
We need to find the expressions that are equivalent to given expression
We solve the expression and check,
A) -30(3 + 2w)
-90 - 60w
Yes it is equivalent.
B) (-9 - 6w)10
-90 - 60w
Yes it is equivalent.
C) -3(30 - 20w)
-90 + 60w
No it is not equivalent.
D)(6 + 4w)15
90 + 60w
No it is not equivalent.
E) -20(4.5 + 3w)
-90 - 60w
Yes it is equivalent.
Therefore, The expression equivalent to the expression -90 - 60w is -30(3 + 2w), (-9 - 6w)10 and -20(4.5 + 3w)
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I need to know (basically what the picture shows)
Answer:
Step-by-step explanation:
Hi, you are studying trigonometry :P nice
conterminal means stopping at the same place, right? sooo what is the same place for 659° compared to our only once around the circle of 360° since 720° is twice around a circle our 659° is less than that so just subtract 360° from 659° to get the co-terminal angle.
659-360=299°
299° is the co-terminal angle
270 is the line between the 3rd and 4th quadrant, so this is definitely in the 4th quadrant.
let's just count backwards (CW) from zero degrees till we get to our 299° angle going in the forward (CCW) direction. so 299-360= -61°
the reference angle is 61°
Does all of this make sense? :/
Each time that Daniel runs an obstacle course, he can run it 2 seconds faster than the last time.
He ran the course in 57 seconds the first time. How fast will he run the course the seventh time?
OA. 43 seconds
B. 45 seconds
O C. 47 seconds
OD. 55 seconds
Please help me with my math homework
Given system has no solution.
The correct answer is an option (D)
In this question, we have been given the graph of system of equations.
The solution of given system is the point of intersection of all lines.
We can observe that the graph of any two lines intersected at points (2, -1), (-2, 3) and (0, 3)
But there is no common point of intersection for given system.
This means, the system has no solution.
Therefore, the given system has no solution.
The correct answer is an option (D)
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Write an equation to determine the number of friends (x) at Jack's party.
Answer:
x = 48/3
when Jack got 50 chocolates and has left 2, then Jack gave away 50-2=48 chocolates. When each friend got 3 chocolates, the number of friends x is equal to 48 divided by 3.
A square with perimeter p has sides of length
p
4
. The playground at DeVille Elementary School is square-shaped, and has a perimeter of 600 feet.
What is the length of each side of the playground?
The length of each side of the playground is 150 feet.
Calculating the length of a square-shaped playgroundFrom the question, we are to determine the length of each side of the playground.
From the given information,
The perimeter of a square is given by the formula,
P = 4l
Where P is the perimeter of the square
and l is the length of a side of the square
"The playground at DeVille Elementary School is square-shaped, and has a perimeter of 600 feet."
That is,
P = 600 feet
Now, we will determine the value of l
Substitute the value of P into the equation
P = 4l
600 = 4l
Divide both sides by 4
600/4 = 4l/4
150 = l
Therefore,
l = 150 feet
Hence, the length is 150 feet
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alexander has 418 songs on his MP3 player. he divides the songs into 11 equal groups. About how many songs are in each group. (round the numbers)
Answer:
38 songs in each group.
Step-by-step explanation:
Alexander has 418 songs on his MP3 player. he divides the songs into 11 equal groups. About how many songs are in each group. (round the numbers)
418/11 = 38 songs in each group.
Write the point-slope form of the equation of the line through the given points:
1) through: (5, 4) and (-2, 5)
2) through: (4, -5) and (0, 2)
3) through: (0, 4) and (2, 1)
The equation of the line in point slope form is as follows:
y - 4 = - 1 / 7(x - 5)y + 5 = - 7 / 4(x - 4)y - 4 = - 3 / 2(x - 0)How to represent linear equation in slope intercept form?Linear equation can be represented in different form such as point slope form, slope intercept form, standard form and general form.
Therefore, equation in point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopeTherefore, let's find the point slope form of the lines.
1) through: (5, 4) and (-2, 5)
m = 5 - 4 / -2 - 5
m = 1 /- 7 = - 1 / 7
Therefore,
y - 4 = - 1 / 7(x - 5)
2) through: (4, -5) and (0, 2)
m = 2 + 5 / 0 - 4
m = 7 / -4 = - 7 / 4
Therefore,
y + 5 = - 7 / 4(x - 4)
3) through: (0, 4) and (2, 1)
m = 1 - 4 / 2 - 0
m = - 3/ 2
Therefore,
y - 4 = - 3 / 2(x - 0)
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Evaluate 9/g + 2h + 5
Evaluated expression of the given mathematical expression is (9+2gh+5g)/g.
Given the mathematical expression is 9/g + 2h + 5.
So, now the LCM (g,1,1) = g
So evaluating the given expression we get,
9/g + 2h + 5 = (9+2gh+5g)/g
Hence the evaluated expression is (9+2gh+5g)/g .
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What’s the equation of the function?
Hi again! The equation to the function would be..
y = 1/2x + 1 (assuming that the initial value is one)