12 and 3/8 simplified
Answer:
(99/8)
Step-by-step explanation:
3
12 -------
8
8 × 12 = 96
96 + 3 = 99
99
-------
8
I hope this helps!
Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay. One of their
customers, Mod World, purchased 24 cartons for $210. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F = Face masks.
Number of cartons of cloth face masks purchased will be 19 and number of cartons of hand-sanitizer purchased will be 5.
We had given that Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay.
Also given that Mod World, purchased 24 cartons.
Let number of cartons of cloth face masks be x and let number of cartons of hand-sanitizer be y.
As total carton purchased is 24.
∴ x + y = 24 --(1)
also Mod World, purchased 24 cartons for $210.
∴ Also price of cartons of cloth face masks is $10 and cartons of hand-sanitizer is $4 which is buyed at $210.
∴ 10x + 4y = 210 --(2)
Now multiplying equation (1) by 10
∴ 10x + 10y = 240 --(3)
Now subtracting (2) from (3) by simplification
∴ y = 5
∴ x = 19
Number of cartons of cloth face masks purchased will be 19 and number of cartons of hand-sanitizer purchased will be 5.
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If theta is in quadrant II and cos theta= -3/5, what is sin 2 theta + cos 2 theta?
ANSWER
sin(2θ) + cos(2θ) = -31/25 = -1.24
EXPLANATION
If we do the inverse of the cosine to -3/5 we would get the angle θ. Then we can know the value of the sine:
[tex]\sin \theta=\sin (\cos ^{-1}(-\frac{3}{5}))=\frac{4}{5}[/tex]So we have:
• sin(θ) = 4/5
,• cos(θ) = -3/5
To find sin(2θ) + cos(2θ) we'll have to use the trigonometric identities:
[tex]\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ \cos 2\theta=1-2\sin ^2\theta \end{gathered}[/tex]Since we have the sine and cosine of theta, we can solve this:
[tex]\sin 2\theta=2\cdot\frac{4}{5}\cdot(-\frac{3}{5})=-\frac{24}{25}[/tex][tex]\cos 2\theta=1-2(\frac{4}{5})^2=1-2\cdot\frac{16}{25}=1-\frac{32}{25}=-\frac{7}{25}[/tex]The sum is:
[tex]\sin 2\theta+\cos 2\theta=-\frac{24}{25}-\frac{7}{25}=-\frac{31}{25}=-1.24[/tex]a child is covering a square board with mosaic tiles the board is 40×40cn each tile is 2 cm ×2 cm how many mosaic tiles are needed for one complete now
Answer:
Step-by-step explanation:
The area of the floor is 4×3=12 sqare meters
=12×100×100= 120000 square centimetres.
Area of each tile is 20×20=400 square centimetres.
Therefore number of tiles required will be
120000÷400 =300.
300 tiles will be required to cover the floor.
find n(A) for the following set A:{x : x is a letter in the word "nonintervention"} n(A) = _________
Given,
{x : x is a letter in the word "nonintervention"}
A={x : x is a letter in the word "nonintervention"}
The roster form of the set is,
A={e, i, n, o, v, t, r}
The number of elements in the set A is,
n(A)=7
Hence, the number of elements in the set A is 7.
A map has a scale of 1:2500. On the map a reservoir has an area of 2cm2.
what is the area of the reservoir? give your answer in m2
The actual area of the reservoir in m² as required in the task content is; 0.5m².
Conversions using scale factors.It follows from the task content that the actual area of the reservoir is to be determined.
Hence, since it is given that the area of the reservoir on the map is 2cm² and the map has a scale of 1: 2500.
Hence, it follows from proportions that the area of the reservoir is; 2cm² × 2500 = 5000cm².
However, when expressed in m²; the actual area of the reservoir is; 5,000/10000 = 0.5m².
Ultimately, the area of the reservoir in m² is; 0.5m².
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1.Which expression is equivalent to (92)8?A. -81321B.9161C.9 10D.818
Given the standard form:
[tex]\begin{gathered} 5\times10^{-4} \\ \end{gathered}[/tex]This can be expressef as a decimal by shifting the decimal point to the back 4 times (since the power is a negative 4) as shown:
[tex]\begin{gathered} 0.0005 \\ \end{gathered}[/tex]Hence the equivalent value for the standard form is 0.0005. Option B is correct
Amy wants to save $500 to buy a TV. She saves $17 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function.
A (w) = 500 - 17w
(a). How much money does Amy still need after 7 weeks?
(b). If Amy still needs $211, how many weeks has she been saving?
After 7 weeks she would have the total of 119$
A. $381
B. 17 weeks
500-211=289/17=17
Growing linearly, the balance owed on your credit card doubles from $600 to $1200 in 6 months. If the balance were growing according to the exponential function f(x)=600(1+0.1220)^x where x represents the number of months, what would the balance be after 6 months? Round your answer to the nearest cent.
Evaluate the given expression at x=6. This is, replace every x in the equation for 6 and solve:
[tex]\begin{gathered} f(6)=600(1+0.1220)^6 \\ f(6)=600(1.1220)^6 \\ f(6)=600\cdot(1.99506) \\ f(6)=1197.04 \end{gathered}[/tex]The balance after 6 months is 1197.04.
Is (x+1) a factor of -2x^5-4x^4+x-10?
Notice that:
[tex]-2x^5-4x^4+x-10,[/tex]cannot be expressed as a product of factors, meaning that
[tex](x+1),[/tex]is not a factor of the given polynomial.
Answer: Not a factor.
Part A answer and explanation pls
Answer:
[tex]\frac{3}{13}[/tex]
Step-by-step explanation:
the fraction is formed by the number who prefer historical movies to the total preferring all movies.
total = 24 + 18 + 6 + 30 = 78
number preferring historical movies = 18
then fraction preferring historical movies is
[tex]\frac{18}{78}[/tex] ( divide numerator/ denominator by 6 )
= [tex]\frac{3}{13}[/tex] ← in simplest form
Answer:
From the Graph the total number of students who preferred historical movies = 18.
Similarly total number of students = 24+18+6+30
= 78
Fraction of student who prefer Historical movies = 18/78
= 3/13.
Where is the result of combining the terms represented by the titles below?A. x^2+x-5B. x^2+2x+1C. x+1D. x+5
if we take the black boxes as representation of negative numbers, and the white boxes as a representation of positive numbers, then we get:
[tex]-x^2+x-x-x+1+1+1+1-1+x^2-1-1+x+x[/tex]after combining the similar terms we get:
[tex](-x^2+x^2)+(x-x-x+x+x)+(1+1+1+1-1-1-1)=x+1[/tex]therefore, the final expression is x + 1
Is my answer correct?
Answer:
Of course it is
Step-by-step explanation:
In the expression: 9 + 3y + 6 + y
Combining like terms, the expression becomes: 3y + y + 9 + 6
Final answer: 4y + 15 which is option B
So you're correct
HELP ME!!!!!
One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
42.25°
47.75°
84.5°
90°
The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25° so option (A) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
Let's suppose the two congruent interior angles are x degrees.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠x+ m∠x + 95.5° = 180°
2m∠x = 180° - 95.5°
m∠x = 84.5/2 = 42.25°
Hence "The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25°".
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P (0.3 < Z < 1.4) =0.30130.14030.91921.4014
Answer
P (0.3 < Z < 1.4) = 0.3013
Explanation
P (0.3 < Z < 1.4) = P (0 < Z < 1.4) - P (0 < Z < 0.3)
P (0.3 < Z < 1.4) = 0.4192 - 0.1179
P (0.3 < Z < 1.4) = 0.3013
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is less than 5.
Event B: The number rolled is even.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event "A or B": {0}
(b) Event "A and B": {0}
(c) The complement of the event A
According to the solving the probability are as follows:
a) Event "A or B": {1, 2, 3, 4, 6}
(b) Event "A and B": {2, 4}
(c) The complement of the event A: {5, 6}
Define the experiment's sample space and event:The term "sample space" refers to a collection of probable results from a random experiment. The letter "S" indicates that this is the sample space. Events are a subset of what might happen in an experiment. Depending on the experiment, the outcomes in a sample area could change. In discrete or finite sample spaces, there are only a finite number of possible outcomes.
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
According to the given data:the sample space is, 1, 2, 3, 4, 5, 6 i.e., U = {1, 2, 3, 4, 5, 6}
Event A: The number rolled is less than 5
i.e., A = {1, 2, 3, 4}
Event B: The number rolled is even
i.e., B = {2, 4, 6}
Event A Or B A∪B = {1, 2, 3, 4} ∪ {2, 4, 6}
= {1, 2, 3, 4, 6}
Event "A and B"A∩B = {1, 2, 3, 4} ∩ {2, 4, 6}
= {2, 4}
Compliment of the event A
Comp(A) = U/ A = {1, 2, 3, 4, 5, 6} / {1, 2, 3, 4}
= {5, 6}
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Triangle ABC is dilated by a scale factor of 4 to form triangle A’B’C
The coordinates of Vertex A’ are
The Coordinates of Vertex B’ are
The coordinates of Vertex C’ are
PLS HELP!!
Solve the compound inequality -8≤x+4<5
Answer:
-12≤x<1
Step-by-step explanation:minus both side by 4
(05.05 MC)A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete thetable to analyze the data and answer the questions:Likes hamburgersboes not like hamburgers TotalLikes burritos41Does not like burritos54135Total110205Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)Part & What is the marginal relative frequency of all customers that like hamburgers? (3 points)Part C Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use completesentences to explain your answer. (5 points)
EXPLANATION:
Given;
We are given a frequency table which displays a survey of numbers of customers that like hamburgers and burritos and those that do not like hamburgers and burritos.
Required;
We are required to analyze the table and use the values to answer the questions that follow.
Solution;
We shall begin by completing the table as follows;
Part A:
What percentage of the survey respondents do not like both burritos and hamburgers?
The percentage that do not like hamburgers is
[tex]Does\text{ }not\text{ }like\text{ }hamburgers=\frac{95}{205}[/tex]The percentage that do not like burritos is
[tex]Does\text{ }not\text{ }like\text{ }burritos=\frac{135}{205}[/tex]The percentage that does not like both burritos and hamburgers is;
[tex]\frac{54}{205}=0.263414634146[/tex]Expressed as a percentage, this is
[tex]\begin{gathered} Percentage=0.263414634146\times100 \\ \\ Percentage=26.3414634146 \\ \\ Percentage=26.34\%\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }hundredth) \end{gathered}[/tex]The marginal relative frequency of all customers that like hamburgers is the total of all hamburger lovers divided by the total of all respondents.
[tex]\begin{gathered} Marginal\text{ }relative\text{ }frequency=\frac{hamburger\text{ }lovers}{total\text{ }respondents}=\frac{110}{205} \\ \\ Marginal\text{ }relative\text{ }frequency=0.536585365854 \\ \\ Marginal\text{ }relative\text{ }frequency=53.66\%\text{ }(rounded\text{ }to\text{ }2\text{ }decimal\text{ }places) \end{gathered}[/tex]ANSWER:
Part (a) 26.34%
Part (b) 53.66%
Algebra 14.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! GotWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanksThe administrative assistant at a software company often provides breakfast when there is amorning meeting. For last week's sales meeting, she purchased 6 dozen doughnuts and 2dozen croissants, spending a total of $42. In preparation for yesterday's safety meeting, shespent $40 on 2 dozen doughnuts and 5 dozen croissants. Assuming she purchased the itemsat the same bakery both times, how much does a dozen of each cost?A dozen doughnuts costs $and a dozen croissants costs $Submit
SOLUTION
Define a variable for the unkwons
[tex]\begin{gathered} \text{Let } \\ A\text{ dozen of doughnuts cost=\$x} \\ A\text{ dozen of Croissant cost=\$y} \end{gathered}[/tex]Then
6 dozen of doughnuts and 2 dozen of croissant cost $42, is written as
[tex]6x+2y=42\ldots\text{equation 1}[/tex]Similarly
$40 for 2 dozen of doughnuts and 5 dozen of croissant is witten as
[tex]2x+5y=40\ldots\text{equation 2}[/tex]Applying Elimination to solve the two system of equation, we have
[tex]\begin{gathered} 6x+2y=42\ldots\text{equation 1} \\ 2x+5y=40\ldots\text{equation 2} \\ To\text{ eliminate x multiply equation 2 by 3 and equation 1 by 1} \\ 1\times(6x+2y=42)\rightarrow6x+2y=42 \\ 3\times(2x+5y=40)\rightarrow6x+15y=120 \end{gathered}[/tex]Then, subtract the equation obtained above
[tex]\begin{gathered} 6x+2y=42 \\ 6x+15y=120 \\ -13y=-78 \\ \text{Divide both sides by -13} \\ -\frac{13y}{-13}=-\frac{78}{-13} \\ \\ y=6 \end{gathered}[/tex]Hence Y=6
Then you Eliminate Y from eqaution 1 an d 2 by
Multiplying equation 1 by 5 and equation 2 by 2
[tex]\begin{gathered} 5\times(6x+2y=42)\rightarrow30x+10y=210 \\ 2\times(2x+5y=40)\rightarrow4x+10y=80 \end{gathered}[/tex]The sunbtract the equation obtained
[tex]\begin{gathered} 30x+10y=210 \\ 4x+10y=80 \\ 26x=130 \\ \text{Divide both sides by 26} \\ \frac{26x}{26}=\frac{130}{26} \\ \\ x=5 \end{gathered}[/tex]Hence X=5
Therefore
A Dozen of doughnuts cost $5
A Dozen of Croisant cost $6
A family budget estimator shows that the Richardson family would need 990272a year to live within their budget in Athens, Texas. If Mrs. Richardson works a 22-hour week and Mr. Richardson works a 40-hour week, how much hourly incomecould they both eam to live within their budget in Athens?
Mrs. Richardson and Mr. Richardson have to make their hourly income 306.314 to live within their budget in Athens.
What is income?
Income is the amount of money that an individual or an organization gets in return for their services or goods offered. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
Given in the question,
The Richardson family needs 990272 per year to in their budget.
Mrs. Richardson works 22 hours a week.
Mr. Richardson works 40hours a week.
We need to calculate their hourly income.
Lets first calculate total weeks in a year.
We know that, a year has 365 days and a week has 7
So, total no. of weeks in a year = 365/7 = 52.143 weeks.
no. of weeks in a year = 52.143 weeks
Their weekly income = yearly income/no. of weeks in a year
So, weekly income = 990272/52.143
weekly income = 18991.466
Their hourly income = weekly income/working hours per week
Their weekly income is 18991.466 and,
working hours = 22 + 40 = 62 hours.
Their hourly income = 18991.466/62
Hourly income = 306.314
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Given the following table of values for f(x), find f(0).
x −3 −1 0 3 6 9
f(x) 1 8 1 0 13 −3
The value of the function at x = 0 will be 1.
What is a function?
A statement, principle, or rule that creates a relationship between two variables is known as a function. Functions are abundant in mathematics and are required for the creation of complex relationships.
When the required parameters and natural laws are given values, the expression yields the calculation result that the mathematical model represents.
The table represents a function.
x f(x)
-3 1
-1 8
0 1
3 0
6 13
9 -3
In the above table, we can see that at the value of x = 0 in the function the value of the whole function is 1.
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PLEASE HELP The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is $32.13 and the cost for using 35 HCF IS 61.83. . What is the cost for using 19 HCF of water?
Based on the system of equations, the cost of using 19 HCF of water is $35.43
What is an equation?An equation is a mathematical statement that two or more values are equivalent.
Equations are stated to show that two mathematical expressions are equal using the equation sign (=).
Cost of using 17 HCF of water = $32.13
Cost of using 35 HCF of water = $61.83
Total cost of 17 HCF water = 17x + a
17x + a = 32.13 ... equation 1
Total cost of 35 HCF water = 35x + a
35x + a = 61.83 ... equation 2
Subtract equation 1 from equation 2:35x + a = 61.83
-17x + a = 32.13
18x = 29.70
18x = 29.7
x = 29.7/18
x = 1.65
Find a:17x + a = 32.13 ... equation 1
17(1.65) + a = 32.13
28.05 + a = 32.13
a = 4.08 (32.13 - 28.05)
The cost of 19 HCF of water:= 19(1.65) + 4.08
= $35.43
Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.
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Type the correct answer in each box.If matrix C represents (A − B) + A, the value of the entry represented by c41 is and the corresponding entry in (A + B) − A is .
Given the matrices A and B:
[tex]\begin{gathered} A=\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix} \\ \\ B=\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \end{gathered}[/tex]We know that:
[tex]C=(A-B)+A=2A-B[/tex]Then, using the matrices A and B:
[tex]\begin{gathered} C=2\cdot\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \\ \\ C=\begin{bmatrix}{-10} & {6} & {16} & {} \\ 6 & {12} & {-10} & {} \\ 10 & {-18} & {0} & {} \\ 14 & 6 & 8 & {}\end{bmatrix}+\begin{bmatrix}{7} & {8} & {5} & {} \\ -{7} & -{9} & -{2} & {} \\ -{2} & {-5} & {7} & {} \\ {-2} & -{8} & {7} & {}\end{bmatrix} \\ \\ \therefore C=\begin{bmatrix}{-3} & 14 & 21 & {} \\ -1 & {3} & {-12} & {} \\ 8 & {-23} & 7 & {} \\ 12 & -2 & 15 & {}\end{bmatrix} \end{gathered}[/tex]And the element C₄₁ (fourth row and first column) is:
[tex]C_{41}=12[/tex]Now, for the matrix (A + B) - A = B:
[tex]B_{41}=2[/tex]Find the x - and y-intercepts of the graph of the linear equation 3x - y = 2. The x-intercept is The y-interceptis
• x-intercept can be found by letting y equal to 0.
,• y-intercept can be found by letting x equal to 0.
X intercept is the x-axis cutting point of the graph.
Y intercept is the y-axis cutting point of the graph.
The equation given is:
[tex]3x-y=2[/tex]First, finding x intercept (let y = 0):
[tex]\begin{gathered} 3x-y=2 \\ 3x-0=2 \\ 3x=2 \\ x=\frac{2}{3} \end{gathered}[/tex]Second, find y intercept (let x = 0):
[tex]\begin{gathered} 3x-y=2 \\ 3(0)-y=2 \\ 0-y=2 \\ y=-2 \end{gathered}[/tex]Hence,
x-intercept: x = 2/3y-intercept: y = -2H-4/j=k for help
Please
Given:
The expression is 2p +5r = q.
The objective is to solve for p.
Explanation:
For the value of p, the expression can be solved as,
[tex]\begin{gathered} 2p+5r=q \\ 2p=q-5r \\ p=\frac{q-5r}{2} \end{gathered}[/tex]Hence, the expression for p is, (q-5r)/2.
How do I simplify radicals in simplest radical form?
Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c
Examples of radicals are
[tex]\sqrt[]{4},\sqrt[2]{8},\sqrt[3]{16}[/tex]For exmaple,
Given the radical
[tex]\sqrt[]{12}[/tex]To simplify into the simplest radical,
Factorize the perfect square
[tex]\sqrt[]{12}=\sqrt[]{4\times3}[/tex]Then we take out the pairs
[tex]\begin{gathered} \sqrt[]{12}=\sqrt[]{4}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2\times2}\times\sqrt[]{3} \\ \sqrt[]{12}=\sqrt[]{2^2}\times\sqrt[]{3} \end{gathered}[/tex]Simplify the result
[tex]\begin{gathered} \text{Where} \\ \sqrt[]{2^2}=2 \\ \sqrt[]{12}=2\times\sqrt[]{3} \\ \sqrt[]{12}=2\sqrt[]{3} \end{gathered}[/tex]Hence, the simplified radical of the example used is
[tex]\sqrt[]{12}=2\sqrt[]{3}[/tex]Yea I do it all right I just got the one
Answer:
[tex]v_0=20.7\frac{m}{s}[/tex]
Explanation:
We are given the equation for the height:
[tex]h(t)=10+v_0t-4.9t^2[/tex]If we differentiate this equation, we get the equation of the velocity:
[tex]h^{\prime}(t)=v(t)=v_0-9.8t[/tex]The problem tells us that the object hits the ground at a velocity of -25m/s. We can write this:
[tex]-25=v_0-9.8t_0[/tex]Where t0 is the time when the object hits the ground, and the velocity is -25m/s
Now, we can solve for v0:
[tex]v_0=9.8t_0-25[/tex]And if we use this in the height h(t) equation, we can find the value of t0. At t0, the height is 0. Thus:
[tex]0=10+(9.8t_0-25)t_0-4.9t_0^2[/tex]And solve:
[tex]\begin{gathered} 0=10+9.8t_o^2-4.9t_0^2-25t_0 \\ 0=10-25t_0+4.9t_0^2 \end{gathered}[/tex]Next, we can use the quadratic formula to solve this:
[tex]\begin{gathered} t_{\pm}=\frac{-(-25)\pm\sqrt{(-25)^2-4\cdot4.9\cdot10}}{2\cdot4.9}=\frac{25\pm\sqrt{625-196}}{9.8}=\frac{25\pm\sqrt{429}}{9.8}=\frac{25\pm20.71231}{9.8} \\ . \\ t_+=\frac{25+20.71231}{9.8}=4.664521seconds \\ . \\ t_-=\frac{25-20.71231}{9.8}=0.43751seconds \end{gathered}[/tex]Let's see which of the two solutions is the time we are looking for.
Let's go back to our solution for v0:
[tex]v_0=9.8t_0-25[/tex]If we use t0 = 0.43751 s:
[tex]v_0=9.8\cdot0.46751-25=-20.7123m/s[/tex]This means that the initial velocity is negative, thus the object goes downwards. But, the problem tells us that initially the object is thrown upwards.
The correct value of t0 = 4.66 seconds
Now we can find v0:
[tex]v_0=9.8\cdot4.664521-25=20.712[/tex]Thus, v0 = 20.7 m/s
John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1
notebook and what is the cost of 1 pen?
Answer:
$ 0.75 for one pen
$1.05 per notebook
Step-by-step explanation:
John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1 notebook and what is the cost of 1 pen?
John: 5n + 7p = 10.5
let's solve for n:
5n + 7p = 10.5
subtract 7p from both sides:
5n + 7p -7p = 10.5 - 7p
5n = 10.5 - 7p
divide both sides by 5:
5n/5 = (10.5 - 7p)/5
n = 2.1 - 7/5 p
Ariana: 4n + 4p = 7.20
Let's substitute in: n = 2.1 - 7/5 p
4n + 4p = 7.20
4(2.1 - 7/5p) + 4p = 7.20
multiply left side:
8.4 - 5.6p + 4p = 7.2
subtract 8.4 from both sides:
8.4 - 5.6p + 4p - 8.4 = 7.2 - 8.4
- 5.6p + 4p = -1.2
combine p terms on left side:
-1.6p = -1.2
divide both sides by -1.6:
-1.6p/(-1.6) = -1.2/(-1.6)
p = 0.75 cents for one pen
Now solve to find the price of a notebook:
4n + 4p = 7.20 when p = 0.75
4n + 4(0.75) = 7.20
4n + 3 = 7.20
subtract 3 from both sides:
4n + 3 - 3 = 7.20 - 3
4n = 4.2
divide both sides by 4:
4n/4 = 4.2/4
n = 1.05 per notebook
CHECK: when n = 1,05 and p = 0.75
John: 5n + 7p = 10.5
5(1.05) + 7(0.75) = 10.5
10.5 = 10.5
Ariana: 4n + 4p = 7.20
4n + 4p = 7.20
4(1.05) + 4(0.75) = 7.20
7.2 = 7.2
Answer assumes no additional sales tax.
help me I'm practicing
we calculate the area of one trangle and multiply by 2
we apply formula of the triangle area
[tex]A=\frac{b\times h}{2}[/tex]where b is the base and h the height of the triangle
then replacing
[tex]\begin{gathered} A=\frac{6\times5.2}{2} \\ \\ A=15.6 \end{gathered}[/tex]area of one triangle is 15.6square centimeters
Area of both triangles
[tex]\begin{gathered} 15.6\times2 \\ =31.2 \end{gathered}[/tex]Area of the two triangle bases is 31.2 square centimeters