Step-by-step explanation:
Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?
nickels = n
dimes = d
We use:
d + n = 65
0.10d + 0.05n = 5.10
solve for d:
d + n = 65
d + n - n = 65 - n
d = 65 - n
substitute in for the second equation: d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n= -1.4
n = 28
so there are 28 nickels
Now, solve for d: when n = 28
d + n = 65
d + 28 = 65
d = 37
so there are 37 dimes
Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of nickels would be n
Let the number of dimes would be d
As per the given question,
d + n = 65 ....(i)
0.10d + 0.05n = 5.10 ....(ii)
From equation (i),
d + n = 65
d + n - n = 65 - n
d = 65 - n
Substitute in for the equation(ii): d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n = -1.4
n = 28
This means there are 28 nickels
Substitute the value of n = 28 in the equation (i),
d + n = 65
d + 28 = 65
d = 37
So there are 37 dimes
Thus, Jim has 28 nickels and 37 dimes in his pocket.
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Can someone help me thank you
The fraction in their simplest form will be:
9. 12/15 = 4/5
10. 6/8 = 3/4
11. 25 / 100 = 1/4
12. 5 / 40 = 1/8
13. 7/77 = 1 / 11
14. 4 / 36 = 1/9
15. 18/20 = 9/10
16. 100/1000 = 1/10
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
It should be noted that in order to divide a fraction in their simplest form, the equivalent numbers must be used.
For example, 100/1000 will be:
(100 ÷ 100) / (1000 ÷ 100)
= 1 / 10
25 / 100 has a common factor of 25 as.this gives 1/4.
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NEED HELP ASAP!! ( NEED DONE WITHIN THREE MINS OF POSTING)
Answer: i am not positive but i think 2.5 on x and 9, and 27 on y
Step-by-step explanation: just want to help asap
Helppp pls …………………….
Answer:
B
Step-by-step explanation:
the two angles lies on the same lines and they have the same vertex
What is the reason for each step in the solution of the inequality?
−2(x+3)−4>4x+30
Select the reason for each step from the drop-down menus.
The missing reasons used in solving the given inequality are;
Reason 2; Subtraction property
Reason 3; Subtraction property of order
Reason 5; Division property of order.
How to solve Inequality problems?
There are different properties of algebra such as distributive property, commutative property, associative property, addition property, division property e.t.c
We are given the inequality as;
−2(x + 3) − 4 > 4x + 30
Step 1;
-2x - 6 - 4 > 4x + 30
Reason 1; Distributive property
Step 2; -2x - 10 > 4x + 30
Reason 2; Subtraction property
Step 3; -6x - 10 > 30
Reason 3; Subtraction property of order
Step 4; 6x > 40
Reason 4; Addition property of order
Step 5; x < -20/3
Reason 5; Division property of order.
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solve the absolute value inequality.
|-3x|-7≥ 11
Answer:
x ≥ 6
Step-by-step explanation:
|-3x| - 7 ≥ 11 The absolute value of -3x is 3x
3x - 7 ≥ 11 Cancel the 7 by adding it on both sides
3x ≥ 18 To get x by itself divide 3 on both sides
x ≥ 6
Anna Marie goes to dinner at a restaurant where the sale tax on meals is 9%. she leaves a tip that is 175% of the amount of sales tax. if her total bill is $45 what was the cost of her meal and what percent tip did she leave
Answer: $78.75
Step-by-step explanation:
You have to multiply the price by tax and add
If 5/11 of the class are girls, what is the ratio of girls to boys?
Answer:
5:6
Step-by-step explanation:
The entire class is 11/11.
Girls: 5/11 of the class.
Boys: 11/11 - 5/11 = 6/11
Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6
Answer: 5:6
Andrea puts 100 g weight on a pan balance how many 10 g weights does she need to balance the scale?
answer:
10
step-by-step explanation:
easy: 100 ÷ 10 = 10. you need 10
explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:
100 = 10x. solve by dividing each side by 10.
10 = x. verify by doing 10 x 10 = 100
Alton estimated that 230 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error. 13% 15% 30% 86%
The percent of error is 15%. The correct option is B.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Alton estimated that 230 people attended the band concert.
The actual count for attendance was 200 people.
To find the percent of error:
230 - 200 / 200
= 30 / 200
= 0.15
0.15 decimal to the percentage is 15%.
Therefore, the error is 15%
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Sketch the graph of each line
The straight line y = x -1 is shown figure
Sketching graph of a line:
To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.
Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.
After calculating the coordinates, use the resultant points to plot the line as a graph.
Here we have a line
y = x -1
To sketch the graph we need to make a value table as given below
First take x values as, -1, 0, 1 from that find the values of y
At x = -1 => y = -1 - 1 = -2
At x = 0 => y = 0 - 1 = -1
At x = 1 => y = 1 - 1 = 0
From the above calculations, the value table is
x -1 0 1
y -2 -1 0
Use the above value and Sketch the graph
[ the resultant graph is shown below ]
The straight line y = x -1 is shown figure
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mr colton needs 4.62 cups of flour to make 3 pound of dough.How many cups does she need to make 2 pounds of dough
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10
Let the number of cups be represented by x.
This will be expressed as:
2/3 = x/4.62
Cross multiply
3x = 2 × 4.62
3x = 9.24
Divide
x = 9.24 / 3
x = 3.08
Therefore, 3.08 cups are needed.
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Answer:
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
Step-by-step explanation:
Select the correct answer A developer buys an empty lot to build a small house. What is the area of the lot?
A. 323 yd²
B. 183 yd²
C. 193 yd²
D. 171 yd²
The area of the plot is 193 sq.yd.
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, A developer buys an empty lot to build a small house.
To find the area, we need to be divided the figure into triangles and rectangles
Area of the first triangle = (1/2) * base * height
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5=85 sq. unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq. unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
Adding all the areas to get the area of the plot = 85+36+63+9
Hence, Area of the plot = 193 sq.yd.
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Write the expression as a power and evaluate it.
8•2^7
Answer:
1024
Step-by-step explanation:
8 times 2 to the 7th power
2 by the 7th power 128 times 8 1024
The equation
Ax+By=−18
A
x
+
B
y
=
−
18
goes through the coordinates (-3, 10) and (6, -2).
By solving a system of equations, we will see that the equation is:
-4*x - 3*y = -18
How to find the equation?We know that the linear equation:
A*x + B*y = -18
We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:
A*-3 + B*10 = -18
A*6 + B*-2 = -18
So we have a system of equations:
-3A + 10B = -18
6A - 2B = -18
if we add the two times the first equation and the second one we get:
2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18
18B = -3*18
B = -3
by replacing that value of B in one of the equations we will be able to solve it for A.
6*A - 2*(-3) = -18
6*A + 6 = -18
6*A = -18 - 6 = -24
A = -24/6 = -4
The equation is:
-4*x - 3*y = -18
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Thelma and Patrick went to a cafe
for lunch. One of them is a
vegetarian. Thelma ordered a
turkey sandwich with extra
mustard. Who is the vegetarian?
Patrick is vegetarian and Thelma is non vegetarian.
What are vegetarian?
The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.
Main Body:
As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.
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A relation is shown: {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)} Which set of information is true about the relation shown?
The set of information that is true about the relation is:
Domain: {3, 4, 5, 6}
Range: {-8, -1, 2, 7}
The relation is not a function.
How to Determine a Relation that is a Function?A relation that represents a function will have each of its domain elements related to exactly one range element.
All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,
Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.
Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:
The domain of the relation is: {3, 4, 5, 6}
The range of the relation is: {-8, -1, 2, 7}
The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.
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q(x) = -x-2
r(x) = x² + 2
Find the following.
(r∙q)(-5) =
(q∙r)(-5) =
Answer: 5q-5r -5q+5r
Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x
The exact solutions of the given equation in the interval are;
A: x = 0, π/2, π, ³/₂π
How to find the exact solutions of trigonometric equations?
We are given the equation as;
sin 4x = –2sin 2x
Writing the equation in standard form gives;
sin 4x + 2sin 2x = 0
Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;
2sin 2x cos 2x + 2sin 2x = 0
Factorize to get;
2sin 2x(cos 2x + 1) = 0
A. sin 2x = 0
The unit circle will give us 3 solutions for 2x as follows;
2x = 0
Thus; x = 0
2x = π
Thus; x = π/2
2x = 2π
Thus; x = π
B. cos 2x = - 1
The unit circle gives 2 solutions for 2x as;
2x = π
Thus; x = π/2
2x = 3π
Thus; x = ³/₂π
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Complete question is;
How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?
6.) One clothing Store has a dress for $6.20
and a belt for $3.50. Customers
buy 3 dresses for $15.20. How much
would be saved by buying 3 dresses
Than by buying per piece?
Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.
What are mathematical operations?The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.
Mathematical operations determine the results of mathematical expressions and problems.
Cost of a dress = $6.20
Cost of 3 dresses = $15.20
Cost per dress if 3 dresses were bought = $5.067
Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)
Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.
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round this number to the hundredth 3.6432
2. Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It
turns out Clare's work has three mistakes!
8(2 + 7x)
10+56x
10+56x
10
12
3
16
3x - (2+5x)
3x - 2 + 5х
8r-2
642-2
64x
The mistakes that Claire made in solving the equation are;
1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.
2) - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x
3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x
How to solve Linear Equations?
We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)
Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x
Step 2; Simplify the right hand side to get;
16 + 56x = -2x - 2
Step 3; Rearrange to get;
16 + 2 = -58x
Step 4; Add up the left hand side to get;
18 = -58x
Step 5; Divide both sides by -58 to get;
x = -9/29
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Complete question is;
Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It
turns out Clare's work has three mistakes!
find all three mistakes explain the below
8(2 + 7x) = 3x - (2+5x)
10 + 56x = 3x - 2 + 5х
10 + 56x = 8x - 2
10 = 64x - 2
12 = 64x
x = 3/16
hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Answer:
$420
Step-by-step explanation:
multiple 10.50 by 40 to get 420
-3x+16+5x+8 x=??????????
The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)
How to evaluate the equation?From the question, the equation is given as
-3x+16+5x+8
To start with, we need to rewrite the expression
So, we have the following representation
-3x + 16 + 5x + 8
The above expression is not an equation
Instead, it is an expression
This is so because there is no equality symbol i.e. = in the expression
So, we collect the like terms
-3x + 5x + 8 + 16
Solving further, we need to evaluate the like terms
So, we have the following equation
-3x + 5x + 24
Evaluate the like terms again
So, the equation becomes
2x + 24
The above expression cannot be further simplified, however, it can still be factored
Factor out 2 from the expression
This gives
2(x + 12)
Hence, the solution is 2(x + 12)
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Can an equation of a line in standard form be written in a way where A, B, or C are either negative or positive? It’s hard to explain… for example
-x+y=-2
Can that be a way to do it? Or would the correct way be like
x-y=2?
Or what about
2x-2y=4? Can I divide by 2 on both sides to rewrite it as
x-y=2? I’m just wondering….
Answer:
2x-2y=4 that is the best way u can write it
A special lottery is to be
held to select the student
風
who will live in the only
deluxe room in a
dormitory. There are 100 seniors, 150
juniors, and 200 sophomores who
applied. Each senior's name is placed in
the lottery 3 times; each junior's name, 2
times; and each sophomore's name, 1
time. What is the probability that a
senior's name will be chosen?
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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Solve the application problem.
Find the area of a rectangular garden that measures 4 feet by 6/7 feet.
A. 3 3/7 ft
B. 9 5/7 ft^2
C. 9 5/7 ft
D. 3 3/7ft^2
Answer:
D. 3 3/7 ft²
Step-by-step explanation:
A = LW
A = 4 ft × 6/7 ft²
A = 24/7 ft²
A = 3 3/7 ft²
Mia is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 15 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 18^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^{\circ}
∘
. If her eyes are 1.75 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters
How to find the distance between the pointsinformation given in the question
Mia stands at a horizontal distance of 15 meters from the building
The angle of elevation from her eyes to the roof ((point AA)) is 18
the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^
her eyes are 1.75 meters from the ground
The direction of movements describes a right angle triangle of
opposite = height of antenna + height of the building
adjacent = 15 meters
The distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The the height of the antenna is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only
tan 53 = opposite / 15
opposite = 15 * tan 53 = 19.906 meters
opposite = 15 * tan 18 = 14.266 meters
Height of the antenna
= 19.606 - 14.266
= 5.34 meters
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In a raffle, 100 tickets are sold. George buys 10 tickets Julia by 5 tickets. There is one winning ticket. Find a probability that
a. George will win
b. jullia will win
The probability that George will win is 1/10 and the probability that Julia will win is 1/20.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.The probability is calculated by dividing the total number of outcomes by the total number of potential events.So, calculate the probability as follows:
Probability formula: P(E) = Favourable events/Total eventsWe know,
The total number of tickets sold is 100.George has 10 tickets and Julia has 5.(A) George's probability of winning:
P(E) = Favourable events/Total eventsP(E) = 10/100P(E) = 1/10(B) Julia's probability of winning:
P(E) = Favourable events/Total eventsP(E) = 5/100P(E) = 1/20Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.
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A_______ is a function which involves only _______ integer powers or only positive integers exponents the __________of any polynomial is the highest power present in it in the ____________ polynomial function y=4+2x+x
A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the quadratic equation, cubic equation, polynomial function.
example :
y=4+2x+x
y = 3x + 4
y = 3x + 4 is a polynomial that has exponent equal to 1.
Therefore A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the quadratic equation, cubic equation, polynomial function.
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