Answer:
a = (c - by) / x
Step-by-step explanation:
ax + by = c
ax = c - by
a = (c - by) / x
Bloomington University charges $53,730 for tuition. If they raise their tuition by 8% each
year, how much will tuition be in 2 years?
If necessary, round your answer to the nearest cent.
$
E
Two friends, Bo and Daniel, had just bought their first cars. The equation y = 31.5x
represents the number of miles, y, that Daniel can drive his car for every x gallons of
gas. Bo uses 9 gallons of gas to drive 256.5 miles in his car.
By using a linear equation, it is obtained that
Distance farther Daniel's car travel in 1 gallon of gas than Bo's car =
3 miles
What is linear equation?
At first, it is important to know about equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The equation y = 31.5x represents the number of miles, y, that Daniel can drive his car for every x gallons of gas
Distance driven by Daniel in 1 gallon of gas = [tex]31.5 \times 1 = 31.5 \ miles[/tex]
Bo uses 9 gallons of gas to drive 256.5 miles in his car.
Bo uses 1 gallon of gas to drive [tex]\frac{256.5}{9}[/tex] miles in his car.
Bo uses 1 gallon of gas to drive 28.5 miles in his car.
Distance farther Daniel's car travel in 1 gallon of gas than Bo's car =
31.5 - 28.5 = 3 miles
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Complete Question
The complete question has been attached here.
5x - 4 ≥ 4x + 3 or 9 + 4x2-1 + 9x
Answer:
9x3
Step-by-step explanation:
x+9
/4
9x=8
x=2
+2=4
x=1+4234
Find the inequality represented by the graph
The inequality represented by the graph is y ≥ -x + 2
How to find the inequality the graph representsA graph is a pictorial representation of data and the graph presented represents inequality data
The graph shows a linear function written in the form
y = mx +c
where slope, m calculated as
c = intercept
x = input variables
y = output variables
calculation of slope
The points used for the slope is gotten from the graph as (0. 2) (1, 1)
m = (y₂ -y₁) / (x₂ - x₁)
substituting the values
= ( 2 - 1 ) / ( 0 - 1 )
= 1 / -1
= -1
y intercept, c this is a point where the graph cuts the y axis
c = 2
The graph contains a solid line as result there will be "equal to" attached to the inequality symbol usedshading above the line means greater thanThe two points result greater than or equal to written with the symbol ≥
hence the equation is
y ≥ -x + 2
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helen buys two pineapples she pays with a £5 note and gets £3.60 change work out the cost of one pineapple
Answer:
Each pineapple costs £0.70.
Step-by-step explanation:
Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.
Helen's total cost would be: P*C = total cost.
The total cost is the difference between £5 and £3.60, which is £1.40.
We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:
P*C = total cost
2*C = £1.40
C = £0.70
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio
She needs to make 35 litres of punch for a party.
How much of each ingredient does she need?
Fruit juice
7 litres
Lemonade =
28 litres
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade.
How much xtra punch can she make?
litres
To make the second batch of punch go further Josie
adds 2 more litres of lemonade.
What is the ratio of fruit juice to
lemonade in the second batch?
Let the lemonade and fruit be Mixed in x ratio.
[tex]\therefore[/tex] Total mixture of fruit punch [tex]= 1\times x \ + \ 3\times x = 4x[/tex]
She needs to make 35 liters of punch.
Requirement of ingredients :
Fruit juice to be added [tex]= \frac{x}{4x} \times 35 = 8.75[/tex] liters of fruit juice
If 8.75 liters of fruit juice is to be added,
then,
lemonade required[tex]=35\ litres - 8.75\ litres = 26.25\ litres .[/tex]
Now ,
According to question she wants to make more fruit punch,
so , given that she had 2 liters of fruit juice.
Here ,
⇒x become 2.
⇒Lemonade required =[tex]2\times x[/tex]
⇒Lemonade required = [tex]2\times3 = 6\ liters[/tex]
There total fruit punch = [tex]6 + 3=9\ liters[/tex]
[tex]\therefore\\[/tex] ratio of fruit juice to lemonade in the second batch = 6:9 = 2:3.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
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Write an expression to represent:
8 less than the product of 2 and x.
Answer:
(2x)-8 is the correct answer
Step-by-step explanation:
Hope this helps
What fraction of their goal did the sixth graders reach after day 2? day 4? day 6? day 8? day 10?
The fractions of sixth graders that reached their goal after each day are given as follows:
Day 2: 1/4.Day 4: 1/3.Day 6: 1/2.Day 8: 2/3.Day 10: 3/4.What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
In which the technical terms related to x and y are as follows:
x, which is the top term of the fraction, is the numerator.y, which is the bottom term of the fraction, is the denominator.The fraction can be represented by bars, in which:
The number of painted bars is the numerator.The total number of bars is the denominator.As shown by the image at the end of the answer, the fractions are given as follows:
Day 2: 1 out of 4 bars painted, hence the fraction is of 1/4.Day 4: 1 out of 3 bars painted, hence the fraction is of 1/3.Day 6: 1 out of 2 bars painted, hence the fraction is of 1/2.Day 8: 2 out of 3 bars painted, hence the fraction is of 2/3.Day 10: 3 out of 4 bars painted, hence the fraction is of 3/4.Missing InformationThe image is given at the end of the answer.
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In the diagram below, GH is parallel to DE. If FH is 5 more than GF, DF:
and FE = 48, find the length of GF. Figures are not necessarily drawn to scal
State your answer in simplest radical form, if necessary.
Answer: GF =
The length of side GF from the similar triangles shown is GF = √10 units
What is an equation?A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.
If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.
In a similar triangle, DE = GF, Hence:
GF/DF = GH/DE
GF / 5 = 2 / GF
GF² = 10
GF = √10
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I'm not sure I need help.
Answer:
A
Step-by-step explanation:
It is perpendicular because it forms a right angle with the second line
(6,10)
(a,8)
(4,b)
(2,2)
What are the values of a and b?
a=
b=
Answer:
Step-by-step explanation:
Put the value of a in equation 2. b² = 6² + a². b² = 36 + (81 / 4 ). b = √(225 / 4). b = 15 / 2. Therefore, the value of a and b will be 9.
please help. To convert to degrees Fahrenheit, use the formula F=95C+32, where C is the degrees in Celsius. Which is the first step to solve for Celsius if the temperature is 70 °F?
If you translate the square root parent function up three units, and reflect it across the x-axis, what is the equation of the new function?
The equation the function after the transformation is (c) g(x) = -√x - 3
How to determine the transformation of the function?The equation of the function is given as
f(x) = √x ---- i.e the square root parent function
The sequence of transformations is given as follows:-
Translate up by 3 unitsReflection across the x-axisWhen the above transformations are combined, we have:
Translate up by 3 units: g(x) = f(x) + 3
Reflection across the x-axis: g(x) = -(f(x) + 3)
So, we have
g(x) = -(√x + 3)
Expand
g(x) = -√x - 3
Hence, the function g(x) is (c) g(x) = -√x - 3
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2) What is the slope of the line from the following table? (Please show your work)
Answer:
pick any two points
im going to chose (1,3) and (3,7)
so the equation y2-y1/x2-x1
1 = x1
3=y1
3=x2
7=y2
so 7-3/3-1 is 4/2
which is 2
factorise completely: 9+35x-4x^2
Answer:
- (4x+1) (x-9)
Step-by-step explanation:
-4x^2+35x+9
Factor out the 1:
-(4x^2-35x-9)
Factor:
-(4x+1)(x-9)
Plot these points of graph f(x)= -(x-5)^2+5 that correspond to x-values 3 and 4. Plot the vertex and reflections of these points in axis
Answer:
On the attached graph
Step-by-step explanation:
See attached graph
Why is every rhombus a parallelogram but not every parallelogram is a rhombus? Why is every square a rectangle but not every rectangle is a square? Why is every square a rhombus but not every rhombus
square?
A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
We need to identify the properties of the given figure in order to answer why one figure can not be the other one:
A rhombus has all sides equal as well as parallel but all angles might not be right angles.
A square has all four sides equal and has 4 right angles.
A rectangle has equal opposite sides and 4 right angles.
A parallelogram has opposite parallel sides.
Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
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A board game is played by moving a counter S space forward at a time, where S is determined by the following rule: A fair six-sided dice is thrown once. S is half the number shown on the dice if that number is even; otherwise S is twice the number shown on the dice.
1. Write out a table showing the possible value of S and their possibilities.
2. Find the probability that, in a single turn, a player moves their counter forward more than 2 spaces.
The table showing the possible value of S and their possibilities is attached below,
The probability that a player moves their counter forward more than 2 spaces is 0.5.
The Probability is the ratio of favorable outcomes to total number of outcomes. The probability of an event must be less than 1 as the sum of all probabilities of events is equal to 1.
Here, If the number on the dice is even, S is half that number; if it is not even, S is double that amount. The table showing the possible value of S and their possibilities is attached below,
Now, finding the probability that a player moves their counter forward more than 2 spaces,
As seen from the table, the number of favorable outcomes where the player moves the counter more than 2 spaces is 3.
The total number of outcomes is 6. so, the probability will be,
Probability [tex]=\frac{3}{6}[/tex]
[tex]=\frac{1}{2} \\\\=0.5[/tex]
Hence, the probability that a player moves their counter forward more than 2 spaces is 0.5.
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There are 16 questions on a test. Karen got 4 wrong. What percent did she get right?
Hola, me ayudan a despejar X - 8 = -2
Answer:
x=6
Step-by-step explanation:
x-8=-2
x=-2+8
x=6
Answer:
x = 6
Step-by-step explanation:
x - 8 = -2
x - 8 + 8 = -2 + 8
x + 0 = 6
x = 6
Check:
6 - 8 = -2
Suppose g(x) = f(x + 2) - 3. Which statement best compares the graph of g(x)
with the graph of f(x)?
• A. The graph of g(x) is shifted 2 units left and 3 units up.
• B. The graph of g(x) is shifted 2 units right and 3 units down. 3
• C. The graph of g(x) is shifted 2 units right and 3 units
up.
• D. The graph of g(x) is shifted 2 units left and 3 units down.
We deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x). The best choice is C.
Describe a graph.A diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
Right-shift a function
Inside the function's argument, subtract. For instance, is essentially moved b units to the right.
You go to the right while subtracting from the parameter of the function.
Accordingly, f(x) is moved two units to the right in g(x) = f(x - 2).
also to advance a function
Outside of the function, add. For instance, is essentially shifted up units.
G(x) = f(x - 2) + 3 hence says that f(x) is shifted up by 3 units.
Overall, then, using two transformations, we deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit upswing in the graph of g(x).
Therefore, choice C is right.
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Find the value of x. 50 points
Answer:
x = 53°
Step-by-step explanation:
Forming the equation,
→ x + (2x + 21°) = 180°
Now the value of x will be,
→ x + (2x + 21°) = 180°
→ 3x = 180° - 21°
→ x = 159°/3
→ [ x = 53° ]
Hence, the value of x is 53°.
one serving of wheat square cereal has 11 grams of fiber, which is 32% of the recommended daily amount. what is the total recommended daily amount of fiber? round your answer to the nearest tenth if necessary.
Using the principle of proportional relationship, the total recommended daily amount of fiber is 34.4 grams
Let x be the recommended daily amount ( in grams ) of the fiber,
So, 32% of x = [tex]\frac{32}{100}x[/tex] = 0.32x
According to the question,
11 grams is 32% of the recommended daily amount of fiber,
That is, 0.32x = 11
x = 11/0.32 = 34.4 grams
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i need solving this problem
The percentage statement 28 is 35% of 80 is written in the form
a/b = p/100 as 28/80 = 35/100.
Explain the term percentages?A ratio or value that can be stated as a fraction over 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its total and then multiply it by 100.The proportion usually applies to a component per hundred. Per 100 refers to what the word percent means.For the given question.
The statement defining the percentage is ;
28 is 35% of 80.
This can be written as;
35% of 80 = 28
Solve percentage.
35×80/100 = 28
35/100 = 28/80
Or,
28/80 = 35/100
This is the form
a/b = p/100
a = 28
b = 80
p = 35
Thus, the percentage statement 28 is 35% of 80 is written in the form
a/b = p/100 as 28/80 = 35/100.
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while eating out, mike and joe each tipped their server 22 dollars. mike tipped 10\% of his bill and joe tipped 20\ % of his bill. what was the difference, in dollars between their bills?
Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.
Let be Mike's bill and be Joe's bill.
(10/100) *m = 2
M = 20
(20/200 )*j = 2
J = 10
So the desired difference is
m-j = 20 – 10
= 10
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P=2l+2w. Solve the formula for w in terms of P and l
The formula for w in terms of p and l is w = (p - 2l)/2
What is an expression?Numbers, symbols and operators grouped together that show the value of something.
Given that, an expression p = 2l + 2w
Solving for w, we get,
w = (p - 2l)/2
Hence, The formula for w in terms of p and l is w = (p - 2l)/2
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The difference between five-halves of a number
and 17 is 48.
The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
What are algebraic expressions ?An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.
CalculationWords can be expressed algebraically.
The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
Let the number be x.
Five-halves of x is: 5/2x
So the difference between and 17 is:
5/2x - 17 = 48 or 17 - 5/2x = 48
Combine both expressions
[tex]| 17 - \frac{5}{2}x|[/tex] = 48
Hence, the required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
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If your weekly salary is $1,015.00, how much do you have left each week after you pay for the following? Rent - $443.50 Cable TV -$23.99 Electricity - $45.62 Groceries - $124.87 ?
(need explanation.)
P(A and B)
P(B)
Find P (Junior | Girl) Hint:
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5
7 12
Junior 2
3 5
Senior 1 4 5
12 18
[?]
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
As given in the question,
From the given table we have,
Total number of girls and boys in the class = 30
Total number of boys in class = 12
Total number of girls in class = 18
As per given Hint: P(A/B) = P(A and B) / P(B)
A is the Junior
B is the girl
Probability as per given condition is:
P(Junior / Girl) = P(Junior and girl) / P(girl)
= (3/30) / (18/30)
= 3/18
= 1/6 ( lowest term of fraction)
Therefore, probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
The complete question is:
Find P(Junior / Girl) Hint: P(A/B) = P(A and B) / P(B) .
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1 4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
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There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, what is the probability that everyone in the group is a girl
There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30
It is given that,
Total number of students = 10
Number of boys = 6
Number of girls = 4
Total number of ways to select 3 students from 10 students.
10C3= 10!/ 3!7!= 120
Total number of ways to select 3 students from 4 girls
4C3 = 4!/ 3!=4
The probability that everyone in the group is a girls is
P = 4/120
= 1/30
Hence , the probability that everyone in the group is a girl is 1/30
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