Explain how to estimate the product ofof 12 3/8 x 6 7/8Use complete sentences in your answer.
Given:
12 3/8 x 6 7/8
We can round 12 3/8 down to 12 because converting 12 3/8 to decimal will give 12.375.
We can round up 6 7/8 which is equivalent to 6.875 to 7
Hence, the estimate is 12 x 7 = 84
Match these equation balancing steps with the description of what was done in each step.Step 1:12x - 6 = 10 6x - 3 = 5 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 2: 6x - 3 = 5 6x = 8 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 36x = 8 x= 4/3 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2
Step 1:
6x - 3 = 5
[tex]\begin{gathered} \text{add 3 to both sides} \\ 6x-3+3=5+3 \\ 6x=8 \end{gathered}[/tex]step 2:
6x = 8
[tex]\begin{gathered} \text{Divide both sides by 6} \\ \frac{6x}{6}=\frac{8}{6} \\ x=\frac{4}{3} \end{gathered}[/tex]Step 3:
x = 4/3
[tex]\begin{gathered} \text{divide both sides by 2} \\ x=\frac{8}{6}=\frac{4}{3} \end{gathered}[/tex]
Students and adults purchased tickets for a recent school play. All tickets were sold atthe ticket booth (discounts of any type) were not allowed.Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 wascollected. 200 tickets were sold.a. Write a system of equations that can model the number of student and adulttickets sold at the ticket booth for the play.
Given:
Cost of students tickets is, c (s) = $8.
Cost of adult tickets is, c (a) = $10.
Total cost collected for by selling the tickets is, c (t) = $1,760.
Number of tickets sold is, n = 200.
The objective is to find the system of equations that can model the number of students and adults tickets sold at the booth.
Consider the number of students as x and number of adults as y.
Then, the equation of total numner of students will be,
[tex]\begin{gathered} \text{Number of students+Number of adults=n} \\ x+y=200\ldots\ldots\ldots..(1) \end{gathered}[/tex]Now, the cost equation can be calculated as,
[tex]\begin{gathered} c(s)\cdot x+c(a)\cdot y=c(t) \\ 8x+10y=1760\ldots\ldots..\ldots..(2) \end{gathered}[/tex]Hence, the system of equations that can model the number of students and adults tickets are x + y = 200 and 8x + 10y = 1760,
Which choice best represents the sum of (5 + 8x -3) and (9x -6)1: 17x + -42: 17x + 43: x + 144: x + - 14
We can solve the expression as:
[tex]\begin{gathered} (5+8x-3)+(9x-6) \\ 2+8x+9x-6 \\ 17x-4 \end{gathered}[/tex]The answer is 1. 17x-4.
Roselle has three cups of popcorn and 6 oz of soda for a total of $246 calories. Carmel has one cup of popcorn and 14 oz of soda for a total of $274 calories. determine the number of calories per cup of popcorn and per ounce of soda
Let 'x' be the number of calories per cup of popcorn, and 'y' be the number of calories per ounce of soda.
Given that 3 cups of popcorn and 6 oz of soda constitute 246 calories,
[tex]3x+6y=246[/tex]Also given that 1 cups of popcorn and 14 oz of soda constitute 274 calories,
[tex]x+14y=274[/tex]Solve the equations using Elimination Method.
Subtract 3 times equation 2 from equation 1,
[tex]\begin{gathered} (3x+6y)-3(x+14y)=246-3(274) \\ 3x+6y-3x-42y=246-822 \\ -36y=-576 \\ y=16 \end{gathered}[/tex]Substitute this value in equation 1, to obtain 'x' as,
[tex]\begin{gathered} 3x+6(16)=246 \\ 3x+96=246 \\ 3x=150 \\ x=50 \end{gathered}[/tex]Thus, the solution of the system of equations is x=50 and y=16.
Therefore, there are 50 calories per cup of popcorn, and 16 calorie per ounce of soda.
Consider the following function. Complete parts (a) through (e) below.f(x)=x²-2x-8The vertex is.(Type an ordered pair.)c. Find the x-intercepts. The x-intercept(s) is/are(Type an integer or a fraction. Use a comma to separate answers as needed.)d. Find the y-intercept. The y-intercept is(Type an integer or a fraction.)e. Use the results from parts (a)-(d) to araph the quadratic function.
Given the function:
[tex]f(x)=x^2-2x-8[/tex]It is a quadratic function where:
a=1
b= -2
c= -8
The x-coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Substituting in the original equation to obtain the y-coordinate, we obtain:
[tex]y=(1)^2-2(1)-8=1-2-8=-9[/tex]So, the vertex is (0, -9)
c. For the intercept at x we make y = 0:
[tex]0=x^2-2x-8[/tex]And solve for x by factorization:
[tex]\begin{gathered} (x-4)(x+2)=0 \\ Separate\text{ the solutions} \\ x-4=0 \\ x-4+4=0+4 \\ x=4 \\ and \\ x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]So, the x-intercepts are:
(-2, 0) and (4,0)
Answer: (-2,0), (4,0)
d. For the intercept at y we make x = 0:
[tex]y=(0)^2-2(0)-8=-8[/tex]So the y-intercept is (0, -8)
Answer: (0, -8)
e. Graphing the function:
A science fair poster is a rectangle 36 inches long and 24 inches wide what is the area of the poster in square feet with sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided information, we are going to calculate the area of the rectangle ins square inches and after we are going to convert it to square feet, so we obtain the following:
Area of the rectangle=36 inches * 24 inches = 864 square inches
Now, let's convert it to square feet, then we have:
[tex]\begin{gathered} 864in^2\cdot\frac{1ft^2}{144in^2} \\ =6ft^2 \end{gathered}[/tex]Finally we obtain that the area in square feet of the rectangle is 6 square feet.
7/5-6/5+3/2=17/10=1 7/10
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
[tex]\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{14+15}{10}-x=\frac{6}{5}[/tex]that is:
[tex]\frac{29}{10}-x=\frac{6}{5}[/tex]solving for x, we obtain:
[tex]\frac{29}{10}-\frac{6}{5}=x[/tex]that is:
[tex]x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}[/tex]so that, the blank space would be:
[tex]\frac{17}{10}[/tex]and the complete expression would be:
[tex]\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}[/tex]6. 6.5 ounces →g7.45 miles → km8.2.3 miles → cmCovert #6#7#8
Answer:
6. 184.275 gr
7. 72 km
8. 368000 cm
Explanation:
To make these conversions, we need to know the following relationships:
1 ounce = 28.35 gr
1 mile = 1.6 km
1 km = 100000 cm
Then, we can convert each expression as follows:
6.5 oz x 28.35gr / 1 oz = 184.275 gr
45 mi x 1.6 km / 1 mi = 72 km
2.3 mi x 1.6 km/ 1 mi = 3.68 km x 100000 cm/ 1km = 368000 cm
Therefore, the answers are:
6. 184.275 gr
7. 72 km
8. 368000 cm
Point O is the center of this circle. What is m
The value of the angle ∠CAB subtended at the circumference of the circle is 48° .
It is given that the center of the circle is at O.
∠AOB = 96° .
We know that the angle subtended by an arc at the center is twice that subtended at the circumference.
Therefore ∠CAB = 1/2 of ∠AOB
or, ∠CAB = 1/2 × 96°
or, ∠CAB = 48°
An arc is any segment of a circle's circumference. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
The circle in the following illustration features an arc that subtends an angle at both the center O and a point on the circumference AB is a chord.
The angle of an arc at the center of a circle is twice as large as its angle elsewhere on the circle's edge.
Therefore the value of ∠CAB is 48° .
To learn more about circle visit:
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in the function y=-2(x-1)+4 what effect does the number 4 have onthe graph, as compared to the graph of the function 7OA. t shifts the graph down 4 unitsO B. t shifts the graph 4 units to the leftOcHshifts the graph up 4 unitsOD.t shifts the graph 4 units to the right
Given:
y = -2(x - 1) + 4
The effect the number 4 has on the graph of the function is that there will be a vertical shift of 4 units up.
+4 here indicates a vertical shift of 4 upwards
ANSWER:
C) It shifts the graph up 4 units
The question is in the picture. Using the answer choice word bank, fill in the proportion to find the volume of the larger figure.
It is given that two similar solids have surface areas of 48 m² and 147 m², and the smaller solid has a volume of 34 m³.
It is required to find the volume of the larger solid.
Recall that the if the scale factor of similar solids is a/b, then the ratio of their areas is the square of the scale factor:
[tex]\frac{\text{ Area of smaller solid}}{\text{ Area of larger solid}}=\frac{a^2}{b^2}[/tex]Substitute the given areas into the equation:
[tex]\frac{48}{147}=\frac{a^2}{b^2}[/tex]Find the scale factor a/b:
[tex]\begin{gathered} \text{ Swap the sides of the equation:} \\ \Rightarrow\frac{a^2}{b^2}=\frac{48}{147} \\ \text{ Reduce the fraction on the right with }3: \\ \Rightarrow\frac{a^2}{b^2}=\frac{16}{49} \\ \text{ Take the square root of both sides:} \\ \Rightarrow\frac{a}{b}=\frac{4}{7} \end{gathered}[/tex]Recall that if the scale factor of two similar solids is a/b, then the ratio of their volumes is the cube of the scale factor:
[tex]\frac{\text{ Volume of smaller solid}}{\text{ Volume of larger solid}}=\left(\frac{a}{b}\right)^3[/tex]Let the volume of the larger solid be V and substitute the given value for the volume of the smaller solid:
[tex]\frac{34}{V}=\left(\frac{a}{b}\right)^3[/tex]Substitute a/b=4/7 into the proportion:
[tex]\begin{gathered} \frac{34}{V}=\left(\frac{4}{7}\right)^3 \\ \\ \Rightarrow\frac{34}{V}=\frac{4^3}{7^3} \\ \\ \Rightarrow\frac{34}{V}=\frac{64}{343} \end{gathered}[/tex]Find the value of V in the resulting proportion:
[tex]\begin{gathered} \text{ Cross multiply:} \\ 64V=343\cdot34 \\ \text{ Divide both sides by }64: \\ \Rightarrow\frac{64V}{64}=\frac{343\cdot34}{64} \\ \Rightarrow V\approx182.22\text{ m}^3 \end{gathered}[/tex]Answers:
The required proportion is 34/V =64/343.
The volume of the larger solid is about 182.22 m³.
Two number cubes are rolled what is the probability that the sum of the numbers rolled is either a 1 and a 4 in either order
The first thing we have to know is that a cube with numbers is a dice that has 6 faces and that its numbers go from 1 to 6, so the probability that the sum of both dice gives 1 is zero, since the minimum that we are going to give is 2
[tex]P(sum=1)=0[/tex]Now for the sum of both dice of 4 we have the following combinations
• 1 and 3
,• 3 and 1
,• 2 and 2
We have 3 combinatorics that we have to get the probability of each of the combinations in order to find our final probability
[tex]\begin{gathered} P(1|3)=P(1)P(3)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(3|1)=P(3)P(1)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(2|2)=P(2)P(2)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \end{gathered}[/tex]The probability that the sum of 4 would be the sum of the probabilities of the combinatorcs
[tex]\begin{gathered} P(sum=4)=P(1|3)+P(3|1)+P(2|2) \\ P(sum=4)=\frac{1}{36}+\frac{1}{36}+\frac{1}{36} \\ P(sum=4)=\frac{3}{36} \\ P(sum=4)=\frac{1}{12} \end{gathered}[/tex]What is the probability of getting a 1 and a 4 in either order?The probability of getting any number on a die will be 1/6 if we can get a 1 or a 4 then our population will be 2/6
[tex]\begin{gathered} P(1|4)=\frac{2}{6} \\ P(4|1)=\frac{2}{6} \\ P(1\&4)=\frac{2}{6}\cdot\frac{2}{6} \\ P(1\&4)=\frac{4}{36} \\ P(1\&4)=\frac{1}{9} \end{gathered}[/tex]Find the sum of the interior angles of the shape. Use the remaining angles to solve for x. Polygons Help91°120°899Sum of interior angles =degreesX =degrees
Solution
For this case we have 4 sides
Then the sum of the interior angles is givne by
[tex]180(n-2)=180(4-2)=180\cdot2=360\text{ }[/tex]Sum of interior angles is 360º
And if we solve for x we can do this:
360-91-120-89= 60
x= 60 º
The number of calories burnes by a 90-pound cyclist is proportional to the numer of hours the cyclist rides. the equation to represent this relationship is Y=225×. What is the constant of proportionality?
Answer
Constant of proportionality = 225
Explanation
If y varies directly as x, this can be written as
y ∝ x
Introducing the constant of variation, k, we have
y ∝ x
y = kx
So, for this question,
y = 225x
Constant of proportionality = 225
Hope this Helps!!!
6) What is the equation of the following graphed function?Is the vertex a maximum or minimum?What are the solutions to the function?What is the y-intercept?уmobruo uove56$ x
If we know the roots (solutions) we can find the equation of the second-degree function using the formula above:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]In this case, a = -1, x1 = 2 and x2 = 4. Therefore the equation will be:
[tex]f(x)=-1(x-2_{})(x-4_{})[/tex][tex]f(x)=-x^2+6x-8[/tex]The vertex is maximum (see that the function has a clear max value).
The solutions to the function are the roots (place in the x-axis where the function cross). They are 2 and 4.
The y-intercept is the point with the format (0,y). Thus to find this point we can substitute 0 into the function:
[tex]f(0)=-0^2+6\times0-8[/tex][tex]f(0)=-8[/tex]The y-intercept will be y = -8.
Julia has been measuring the length of her baby's hair. The first time it was 6 cm long and after one month it was 2 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.
Given that,
The length of baby's hair at first time = 6cm
After a month, the length was 2 cm longer = 6 + 2 = 8 cm
As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm
It results in a sequence with a common difference of 2,
6, 8, 10, 12, ............
If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:
an = a1 + (n-1)*d
Here,
a1 = first term = 6
d = common difference = 2. (8-6 or 10 - 8 = 2)
Now, put all the values in the equation,
an = a1 + (n-1)*d
an = 6 + (n-1)*2
an = 6 + 2n - 2
an = 2n + 4
an = 2(n+2)
Hence, the function that represents growth is an = 2(n+2).
By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:
n = 1
an = 2(n+2) = 2(1+2) = 2 (3) = 6
=> ordered pair (1, 6)
n = 2
an = 2(n+2) = 2(2+2) = 2 (4) = 8
=> ordered pair (2, 8)
n = 3
an = 2(n+2) = 2(3+2) = 2 (5) = 10
=> ordered pair (3, 10)
n = 4
an = 2(n+2) = 2(4+2) = 2 (6) = 12
=> ordered pair (4, 12)
With the ordered pairs, you can plot the graph.
A cylinder shaped above ground pool is 4.5 deep. If the diameter of the pool is 16 ft, determine the capacity of the swimming pool in cubic feet. Write your awnser in terms of pi
For this exercise you need to use the following formula for calculate the volume of a cylinder:
[tex]V=\pi r^2h[/tex]Where "r" is the radius and "h" is the height of the cylinder.
In this case you can identify that:
[tex]h=4.5ft[/tex]You know that the diameter of the pool is 16 feet. Since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{16ft}{2} \\ \\ r=8ft \end{gathered}[/tex]Knowing the radius and the height of the pool, you can substitute them into the formula and then you have to evaluate, in order to find the capacity of the swimming pool in cubic feet:
[tex]\begin{gathered} V=\pi(8ft)^2(4.5ft) \\ V=288\pi\text{ }ft^3 \end{gathered}[/tex]The answer is:
[tex]288\pi\text{ }ft^3[/tex]findvthe volume of the cylinder below to the nearest cubic foot.
Answer: The volume of the cylinder is 164.9 cubic foot
Given data
The diameter of the cylinder = 5ft
Height of the cylinder = 8.4 ft
Radius = diameter / 2
radius = 5/2
Radius = 2.5 ft
[tex]\begin{gathered} \text{Volume = }\pi\cdot r^2\cdot\text{ h} \\ \text{Volume = 3.14 }\cdot2.5^2\cdot\text{ 8.4} \\ \text{Volume = 3.14 x }6.25\text{ x 8.4 } \\ \text{Volume = }164.85ft^3 \\ Tothenearesttenth164.9ft^3 \end{gathered}[/tex]The answer is 164.9 cubic foot
can someone please help me with this please explain (and if you can please add an example)
Given: A square pyramid with a base length of 5 inches and a height of 9 inches.
Required: To find the volume of the given square pyramid.
Explanation: The volume of the square pyramid is given by the formula
[tex]V=\frac{a^2\times h}{3}[/tex]Where a is the base length, and h is the height of the square pyramid.
Hence,
[tex]\begin{gathered} V=\frac{5^2\times9}{3} \\ =75\text{ in}^3 \end{gathered}[/tex]Final Answer: The volume of the square pyramid is 75 cubic inches.
What is numeral value of 3/4 + 5/8
The given expression is
[tex]\frac{3}{4}+\frac{5}{8}[/tex]We have to sum these fractions with the cross-rule. The image below shows this method.
An animal shelter provides a bowl with 1.35 liters of water for 6 cats.About how much water will be left after the cats drink their average daily amount of water?Water ConsumptionAverage Amount(Liters per day)AnimalCanada Goose0.24Cat0.15Mink0.10Opossum0.30Bald Eagle0.16liter(s) of water will be left after the cats drink their average daily amount of water.
Data
1.35 litres of water
6 cats
0.15 litres per day
Procedure
Amount of water taken by the 6 cats
[tex]0.15\cdot6=0.9[/tex]Left
[tex]1.35-0.9[/tex]0.45 litres of water will be left
Two points A(0,-4), B(2,-1)determine line AB.What is the equation of the line AB? y= _1_x + _2_What is the equation of the line perpendicular to lineAB, passing through the point (2,-1)? y= _3_x + _4
1.
Let:
[tex]\begin{gathered} (x1,y1)=(0,-4) \\ (x2,y2)=(2,-1) \\ so\colon \\ m1=\frac{y2-y1}{x2-x1}=\frac{-1-(-4)}{2-0}=\frac{3}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m1(x-x1) \\ y-(-4)=\frac{3}{2}(x-0) \\ y+4=\frac{3}{2}x \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]2.
If two lines are perpendicular, then:
[tex]\begin{gathered} m1\times m2=-1 \\ \frac{3}{2}\times m2=-1 \\ m2=-\frac{2}{3} \end{gathered}[/tex]Let:
[tex](x1,y1)=(2,-1)[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-(-1)=-\frac{2}{3}(x-2) \\ y+1=-\frac{2}{3}x+\frac{4}{3} \\ y=-\frac{2}{3}x+\frac{1}{3} \end{gathered}[/tex]I need help finding the answer and to show work
6) 4r + 8 + 5 = -15 - 3r
4r + 3r = -15 -8 - 5
7r = -28
r = -28/7
r = -4
8) 3n - 15 = 7n + n
-15 = 7n + n - 3n
-15 = 5n
n = -15/5
n = -3
2. Yan also has three times as many apples as Xavier. Write a second expression for how many apples Yanhas.
For this case, let be "x" the number of apples Xavier has and "y" the number of apples Yan has.
According to the information given in the exercise, you know that Yan has three times as many apples as Xavier. In other words, to find the number of apples Yan has, you need to multiply the number of apples Xavier has by 3.
Then, knowing the above, you can write the following equation:
[tex]y=3x[/tex]Therefore, you can determine that an expression that represents how many apples Yan has, is the one shown below:
[tex]3x[/tex]How can I draw a histogram to illustrate the information? How do I calculate the median age of the population?
We can see from the question that we have 8 class intervals, and they are all of the same lengths. We have the frequency for age in each interval.
We need to remember that a histogram is similar to a bar plot. However, it does not have any description on the x-axis. Instead, it will have the given class intervals.
In this case, we have that the class intervals do not overlap, and it is easier to graph the histogram as follows:
1. We need to graph the class intervals on the x-axis, and then we have to draw the frequencies for each interval on the y-axis.
Find the real and imaginary solution of (w^3) - 1000=0
Explanation
Given
[tex]w^3-1000=0[/tex]We will have;
[tex]\begin{gathered} w^3=1000 \\ \mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2} \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}\frac{-1+\sqrt{3}i}{2},\:w=\sqrt[3]{1000}\frac{-1-\sqrt{3}i}{2} \\ hence;w=10,w=10\times\frac{-1+\sqrt{3}i}{2},\:w=10\times\frac{-1-\sqrt{3}i}{2} \\ w=10,\:w=-5+5\sqrt{3}i,\:w=-5-5\sqrt{3}i \end{gathered}[/tex]Answer: Option D
A principal of $600 earns 3.2% interest compounded monthly. What is the effective interest (growth) rate? (Hint: make the equation look like abt.) About how long does it take to reach $1000?
Answer:
Explanation:
The formula for calculating the effective interest rate is expressed as
R = (1 + i/n)^n - 1
where
R is the effective interest rate
i is the nominal rate
n is the number of compounding periods in a year
From the information given,
n = 12 because it was compounded monthly
i = 3.2% = 3.2/100 = 0.032
Thus,
R = (1 + 0.032/12)^12 - 1
R = 0.03247
Multiplying by 100, it becomes 0.03247 x 100
Effective interest rate = 3.25%
We would apply the formula for calculating compound interest which is expressed as
A = a(1 + r/n)^nt
where
a is the principal or initial amount
t is the number of years
A is the final amount after t years
From the information given,
A = 1000
a = 600
n = 12
We want to find t
By substituting these values into the formula, we have
1000 = 600(1 + 0.032/12)^12t
1000/600 = (1.00267)^12t
Taking natural log of both sides, we have
ln (1000/600) = ln (1.00267)^12t = 12tln(1.00267)
12t = [ln (1000/600)]/ln (1.00267) = 191.5758
t = 191.5758/12
t = 16
It takes 16 years for the amount to reach $1000
What is 73 divided by 6
Answer:
12,1666666667
Step-by-step explanation:
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Let
x -----> number of dimes coin
y -----> number of quarters coin
we have that
x=y ------> equation 1
and
0.10x+0.25y < 4 ------> inequality 1
substitute equation 1 in inequality 1
0.10x+0.25x < 4
solve for x
0.35x<4
x < 11.4
For 12 dimes
the value of x=12 not satisfy the inequality
that means
He couldn't have 12 dimes