At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway?
A. 9y = 12x + 5
B. 9x = 12y + 8
C. 12y = -9x + 2
D. 12x = -9y + 4
______________________________________________________
Parallel equations have the same slope
6y = 8x - 11
y= 8/6 x - 11/6
y= 4/3 x-11/6
y = m x +b (m is the slope )
_____________________________________________
You need to find the other equation with the same slope
____________________________
A. 9y = 12x + 5
y = 12/ 9 x + 5/9
y = 4/3 x + 5/9
_________________________
B. 9x = 12y + 8
12 y= 9x-8
y= 9/ 12 x- 8/12
y= 3/4 x - 4/6
discarded
________________________
C. 12y = -9x + 2
y = -9/12 x + 2/12
y = -3/4 x + 1/6
discarded
_________________________
D. 12x = -9y + 4
12x -4 = -9y
y = -12/9 x +4/9
y = -4/3 x+4/9
discarded
_______________
So then, A 9y = 12x + 5 is the equation that could represent the new runway because is parallel to the highway 6y = 8x - 11.
how much would EZ Excavation charge to haul 40 cubic yards of dirt
Given the line on the graph, we have that it passes through the points (1,25) and (2,50), then we can find the relation function with the slope-point equation of the line:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{50-25}{2-1}=\frac{25}{1}=25 \\ y-y_1=m(x-x_1) \\ \Rightarrow y-25=25(x-1) \\ \Rightarrow y=25x-25+25=25x \\ y=25x \end{gathered}[/tex]we have that the cost of the dirt is given by the equation y=25. To find how much would it be for 40 cubic yards of dirt, we make x=40 and we get the following:
[tex]\begin{gathered} x=40 \\ \Rightarrow y=25\cdot40=1000 \\ y=1000 \end{gathered}[/tex]therefore, the cost to haul 40 cubic yards of dirt is $1000
the answers to questions 4 & 5 please!!
The height of the cone is (c) 5 cm.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.So, the volume of a cone is: V = 1/3πr²h
V is 83.73 and r is 4.Now, calculate the height of the cone as follows:
V = 1/3πr²h83.73 = 1/3π4²h83.73 = 1/3π16h3(83.73) = 3.14(16)h251.19 = 50.24hh = 251.19/50.24h = 4.9999Rounding off: 5 cm
Therefore, the height of the cone is (c) 5 cm.
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For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose isA. 12B. 8C. 4D. 6
Okay, here we have this:
She can eat the following options:
Sandwich with ham with or without cheese. Two choices.
Sandwich with bologna with or without cheese. Other two choices
This mean that she can eat:
Sandwich with ham with cheese with water or juice. Two options.
Sandwich with ham without cheese with water or juice. Two options.
Sandwich with bologna with cheese with water or juice. Two options.
Sandwich with bologna without cheese with water or juice. Two options.
Finally we obtain a total of: 2+2+2+2=8 options of lunches.
Thw
what is P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors.
So we have to write the following polynomial expression as a product of two factors:
[tex]P(x)=2x^3+5x^2+5x+6[/tex]In order to do this we should find one of its roots first i.e. a x value that makes P(x)=0. If we use r to label this root we can write P like:
[tex]P(x)=(x-r)\cdot(ax^2+bx+c)[/tex]Where a, b and c are numbers that we can find using Ruffini's rule. So first of all let's find a root. We can use the rational root theorem. It states that if P(x) has rational roots then they are given by the quotient between a factor of the constant term (i.e. the number not multplied by powers of x) and a factor of the leading coefficient (i.e. the number multiplying the biggest power of x). In this case we have to look for the factors of 6 and 2 respectively. Their factors are:
[tex]\begin{gathered} 6\colon6,-6,3,-3,2,-2,1,-1 \\ 2\colon2,-2,1,-1 \end{gathered}[/tex]And the quotients and possible values for r are:
[tex]6,-6,3,-3,2,-2,\frac{3}{2},-\frac{3}{2},1,-1,\frac{1}{2},-\frac{1}{2}[/tex]So one of these numbers make P(x) equal to zero. For example if we take x=-2 we get:
[tex]\begin{gathered} P(-2)=2\cdot(-2)^3+5\cdot(-2)^2+5\cdot(-2)+6 \\ P(-2)=-16+20-10+6=0 \end{gathered}[/tex]So -2 is a root of P(x) which means that we can take r=-2.
Now we can use Ruffini's law. On the first row we write the coefficients of P(x). Then the first one is repeated in the third row:
Now we multiply 2 by -2 and we write the result under the second coefficient. Then we add them:
Now we do the same with the 1:
And then we multiply 3 and -2 and add the result ot the last coefficient:
The numbers 2, 1 and 3 are the values of a,b and c respectively. Then we can write P(x) as a product of two factors and the answer is:
[tex]P(x)=(x+2)(2x^2+x+3)[/tex]what is the slope of the line represented by y = -5 + 2?
Question:
Find the slope of
[tex]y=-5x+2[/tex]Answer:
Remember that when we have the equation of a line in the form
[tex]y=mx+b[/tex]The slope of the line is the number that accompanies x (A.K.A Coefficient)
Therefore, the slope of the line is -5
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is %180. Answer the questions below and show all work.1. What is the common difference for the deposits made each month?2. Write an explicit formula for this arithmetic sequence. 3. What is the amount of Ginny's deposit in the 12th month?4. At what month will Ginny first make a deposit that is at least $500?
SOLUTION
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $ 180.
Since it follows an arithmetic sequence, T n = a + ( n- 1 ) d
Month 3 , T 3 = a+ ( 3 - 1 ) d = 150
a + 2 d = 150 --------------------- equ 1
Month 5 , T 5 = a + ( 5 - 1 ) d = 180
a + 4 d = 180 ...........................equ 2
Solving the two equations, we have :
a - a + 4 d - 2 d = 180 - 150
2 d = 30
Divide both sides by 2 , we have:
d = 15
Let us put d = 15 in equ 1 , we have a + 2 d = 150
a + 2 ( 15 ) = 150
a + 30 = 150
a = 150 - 30
a = 120
From the solution,
Month 1 = 120
Month 2 = 120 + 15 = 135
Month 3 = 135 + 15 = 150
Month 4 = 150 + 15 = 165
Month 5 = 165 + 15 = 180
1. What is the common difference for the deposits made each month? d = 15
2. Write an explicit formula for this arithmetic sequence.
Recall that Tn = a + ( n - 1 ) d
Tn = 120 + ( n - 1 ) 15
Tn = 120 + 15 n - 15
Tn = 120 - 15 + 5n
Tn = 105 + 15n
3. What is the amount of Ginny's deposit in the 12th month?
Tn = 105 + 15n
T 12 = 105 + 15 ( 12 )
T 12 = 105 + 180 = 285
4. At what month will Ginny first make a deposit that is at least $500?
Using Tn = 105 + 15 n = 500
105 + 15 n = 500
15 n = 500 - 105
15 n = 395
Divide both sides by 15 , we have :
n = 26 . 33
n = 27
Una clase tiene 42 alumnos. Se puede determinar que 3/9 son niños y 4 6 son niñas, ¿Cuántos niños y cuantas niñas hay en la clase?
The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
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Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?
15. Given f (n)=3( 12), what is the value off (8) ?
We have some function f(x) and want to evaluate the function for some value of x, in this case for x=8.
Evaluate a function means replace the x for the value you want to evaluate, in this case for 8, so:
[tex]\begin{gathered} f(x)=3(1-x) \\ f(8)=f(x=8)=3(1-8) \\ f(8)=3\cdot(-7)=-21 \end{gathered}[/tex]used to name a point
Answer:
It is represented by a dot and named by a capital letter
Step-by-step explanation:
Nicole wants to use his 18% employee discount to buy a video game that is priced at $69.99. A 6.5% sales tax is applied to the discounted price. What will be the total cost of the video game, including the sales tax?
Given:
The discount rate, D=18%.
The mared price, M=$69.99.
The sales tax percentage on discounted price, s=6.5%.
The discounted price is,
[tex]\begin{gathered} C=\frac{(100-D)}{100}\times M \\ C=\frac{100-18}{100}\times69.99 \\ C=57.39 \end{gathered}[/tex]The sales tax on the discounted price is,
[tex]\begin{gathered} S=\frac{s}{100}\times C \\ S=\frac{6.5}{100}\times57.39 \\ S=3.73 \end{gathered}[/tex]The total cost of the video game including the sales tax is,
[tex]\begin{gathered} T=C+S \\ T=57.39+3.73 \\ T=61.12 \end{gathered}[/tex]Therefore, the total cost of the video game including the sales tax is $61.12.
a cyclist rides her bike at a speed of 30 kilometers per hour. what is the speed in miles per hour? how many miles will the cyclist travel in 5 hours?
Answer:
the answer is 9.321 miles
The entire graph of the function h is shown in the figure below.
Write the domain and range of h using interval notation.
(a) domain=
(b) range =
The Domain is [-2, 5] and Range is [3, -4]
What is Domain and range ?
The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.
a.) Here in graph, see the x-axis for to find Domain
You'll notice that -2 is point where the point is marked as lowest after that there is no line or point is there and the highest it goes up to the blue line is reached is 5 in x-axis.
so, the Domain is [-2, 5]
b.) For the range you to look at y-axis, just observe the highest and lowest point in graph you'll be able to find range.
hence, the Range is [3, -4]
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If 1000 pennies are put into rolls of 50 pennies, how many rolls will be made?
Answer:
12
Step-by-step explanation:
50x2=100
100x10=1000
2+10=12
what is the area of the Shaded region used 3.14
In this problem, the area of the shaded region is equal to the area of the complete square, minus the area of the four circles
so
REmember that
The length side of the complete square is equal to two times the diameter of one circle
A=(2*12)^2-4*pi*(12/2)^2
assume pi=3.14
A=576-4(3.14)(36)
the area of the Shaded region is A=123.84 ft^2Solve for basic equation x2x+3=-3x-12
Solution
We have the following equation:
2x +3 = -3x-12
We can solve for x on this way:
5x = -12-3
5x = -15
Dividing both sides by 5 we got:
x= -3
For the data values 69, 54, 27, 43, 69, 56, the mean is 53.
From the table given,
To find the x - mean,
By the summation of all the x - mean
The value of x - mean is
[tex]x-\operatorname{mean}=16+1-26-10+16=-3[/tex]Hence, the value of x - mean is -3
To find the (x - mean)²
By the summation of all the values of (x - mean)²
The value of (x - mean)² is
[tex](x-\operatorname{mean})^2=256+1+676+100+256=1289[/tex]Hence, the value of (x - mean)² is 1289
I know this is something super easy, but I always forget the steps on how to figure this out, I tried to put 30 and number one spot, I tried putting 82 and number two spot, and I tried putting 50 and number one spot but when you add that up that's a lot more than 360. I just need help please
Anlge directly opposite to 2= 180 - 82= 98
Sum of angles in the triangle (98, 50, x ) = 180
98+50+x = 180
x + 148 = 180
x = 180 - 148= 32
m<1 = x because they are alternate
so m<1 = 32
m<2 + 82 = 180 ( sum of angles in a straight line)
m<2 = 180 - 82 = 98
m< 3 = 50 because they are alternate
Or
m<3 + m<2 + m<1 = 180 ( sum of angles in a triangle)
m< 3 + 98+ 32 = 180
m<3 =180 - 130 =50
Summary
m< 1= 32 degrees
m<2= 98 degrees
m<3 = 50 degrees
Which vehicle has the smallest total volume?What is the volume?
The formula for the volume is,
[tex]V=\text{length}\cdot\text{ width}\cdot\text{ height}[/tex]Determine the volume of Van.
[tex]\begin{gathered} V=10\cdot6\frac{1}{2}\cdot6 \\ =60\cdot\frac{13}{2} \\ =390 \end{gathered}[/tex]Determine the volume of small truck.
[tex]\begin{gathered} V_1=11.3\cdot7.5\cdot6.75 \\ =572.0625 \end{gathered}[/tex]Determine the volume of 2-bedroom moving truck.
[tex]\begin{gathered} V=14\frac{1}{2}\cdot\frac{77}{12}\cdot7\frac{1}{6} \\ =\frac{29}{2}\cdot\frac{77}{12}\cdot\frac{43}{6} \\ =666.798 \end{gathered}[/tex]Determine the volume of 3 bedroom truck.
[tex]\begin{gathered} V=20.5\cdot7.7\cdot8.5 \\ =1341.725 \end{gathered}[/tex]Determine the mega moving truck.
[tex]\begin{gathered} V=22\frac{1}{4}\cdot7\cdot9\frac{1}{3} \\ =1453.666 \end{gathered}[/tex]The smallest volume is equal to
For each level of confidence o below, determine the corresponding normal confidence interval. Assume each confidence interval is constructed for the same sample statistics.Drag each normal confidence interval given above to the level of confidence
Note that the width of the confidence interval increases as the confidence level increases.
Since the confidence intervals constructed are for the same sample statistic, the higher confidence interval will have a higher width.
The confidence levels have the following widths:
Therefore, the confidence intervals are matched such that the lowest interval has the smallest confidence level and the highest has the largest confidence level. This is shown below:
Given the zeros of the following polynomial 2 +2i, 3, - 4 select the corresponding factors AND the polynomia O (x + 2i) (2 - 2i) (2 - 3)(x+4) o f(c) = 24 - 23 822 - 42 - 48 0 (2 – 2i) (x + 2i) (2+3)(– 4) 24 – 13 + 82 40 - 48 0 (0 - 2) (+2)(x - 3)(x +4) 24 - 23 - 822 + 4x + 48 1 3 N
a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]The nutrition label on Erin's box of animal crackers states that 16 crackers contain 24 grams of carbohydrates. Erin ate 12 animal crackers from the box. What is the number of grams of carbohydrates in 12 animal crackers? A.8 grams B. 12 grams C. 18 gramsD. 20 grams
16 crackers are proportional to 24 grams of carbohydrates. To find the number of grams of carbohydrates in 12 animal crackers, we can use the next proportion:
[tex]\frac{16\text{ crackers}}{12\text{ crackers}}=\frac{24\text{ grams}}{x\text{ grams}}[/tex]Solving for x,
[tex]\begin{gathered} 16\cdot x=24\cdot12 \\ x=\frac{288}{16} \\ x=18\text{ grams} \end{gathered}[/tex]Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount?
The formula for simple interest is where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied.
2
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To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of?
Type your response here: rate= interest/$1000
Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying.
Type your response here:
Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate?
Type your response here:
Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable.
Type your response here:
Solve for the value of the unknown variable.
Type your response here:
1. One cannot figure out how much the interest rate is based on the amount charged to the credit card unless other variables are supplied.
2. We know the values of the following variables now:
The interest amountThe principal amount.3. The interest rate is 2.2% per month.
4. The period that this interest rate applies is monthly, called the MPR.
5. The annual interest rate (APR) is 26.4%.
6. The known variables about this payday loan are the interest amount, the interest rate, and the period.
7. A formula to solve for the unknown variable, principal/credit amount, is P = I / (RT), where I = interest, R = rate, and T = time period.
8. The solution for the value of the unknown variable, Principal, is $3,900.
Minimum monthly payment = interest amount = $22
Credit card bill = $1,000
Rate = interest/$1,000
Rate = $22/$1,000 = 0.022
= 2.2%
MPR = 2.2%
APR = 26.4% (2.2% x 12)
Payday Loans:The service charge for a 2-week loan = $15
Interest rate = 10%
Principal/Payloan = $3,900 ($15 / (10% x 2/52)
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a scientist need to 6000 calories per day. Based on the percentage of total daily calories and the number of calories needed, how many biscuits, packages of pemmican, butter and coco does a person need each day?
EXPLANATION:
Given;
We are told that a scientist needs 6000 calories per day.
We are also given a table showing the percentage of daily calories he can get from three types of food.
These are;
[tex]\begin{gathered} Biscuits---40\% \\ pemmican---45\% \\ Butter\text{ }and\text{ }cocoa---15\% \end{gathered}[/tex]Required;
We are required to calculate how many of each type of food he would need to eat each day.
Step-by-step solution;
We shall solve this by first determining how many calories can be gotten from each type of food based on the percentage given. This is calculated below;
[tex]\begin{gathered} Biscuits: \\ 6000\times\frac{40}{100}=2400 \end{gathered}[/tex]This means if he gets 75 calories from one biscuit, then to get 2,400 calories he would have to eat;
[tex]\begin{gathered} 75cal=1b \\ 2400cal=\frac{2400}{75} \\ 2400cal=32 \end{gathered}[/tex]The scientist would have to eat 32 biscuits to get 2400 calories.
[tex]\begin{gathered} Pemmican: \\ 6000\times\frac{45}{100}=2700 \end{gathered}[/tex]This means if he gets 135 calories from one pack of dried meat, then to get 2700 calories he would have to consume;
[tex]\begin{gathered} 135cal=1pack \\ 2700cal=\frac{2700}{135} \\ 2700cal=20 \end{gathered}[/tex]Therefore, the scientist would have to eat 20 packs of pemmican to get 2700 calories
[tex]\begin{gathered} Butter\text{ }and\text{ }Cocoa: \\ 6000\times\frac{15}{100}=900 \end{gathered}[/tex]This means if he eats 1 package of Butter and cocoa he gets 225 calories. To get 900 calories he would have to eat;
[tex]\begin{gathered} 225cal=1pack \\ 900cal=\frac{900}{225} \\ 900cal=4 \end{gathered}[/tex]Therefore, the scientist would have to eat 4 packs of Butter and cocoa.
We now have the summary as follows;
ANSWER:
[tex]\begin{gathered} Biscuits=32 \\ Pemmican=20\text{ }packs \\ Butter\text{ }and\text{ }cocoa=4\text{ }packs \end{gathered}[/tex]A family of four went to an amusement park for their vacation. They started the vacation with $426.They spent a total of $198 the first three days.If they divided the remainder of the money evenly between the family members for souvenirs, how much did each person have to spend?
They started the vacation with $426
After spending $198 the first three days, the remainder is $426 - $198 = $228
Given that there are 4 family members, we have to divide this remainder by 4, that is, $228/4 = $57
Each person has $57 to spend
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Given 4 h + 6 = 30
4 h = 30 - 6
4 h = 24
Divide both sides by 4, we have:
h = 24 /4
h = 6
1. A coat at the Utopian Coat factory cost $99.99. The sales tax is 7%. Find the sales tax and the total cost of the jacket. (Round to the nearest cent).
The Solution:
Given that a coat costs $99.99 and the sales tax is $75.
We are required to find the actual sales tax and the total cost of the coat.
Step 1:
We shall find the sales tax.
[tex]\begin{gathered} \text{ Cost of the coat=\$99.99} \\ \\ \text{Sales tax of 7\% }=\frac{7}{100}\times99.99=0.07\times99.99 \\ \\ =6.999\approx\text{ \$7.00 (or 700 cent)} \end{gathered}[/tex]Thus, the sales tax is $7.00 or 700 cents.
Step 2:
We shall find the total cost of the coat.
The total cost of the coat is the sum of the coat's cost and the sales tax.
[tex]\text{ The total cost=99.99+6.999=106.989}\approx\text{ \$106.99}[/tex]Therefore, the correct answers are:
Sales tax =$7.00 or 700 cents.
Total cost = $106.99 or 10699 cents..99 or 10699 cents.
What’s the correct answer answer asap for brainlist
Answer:
Answer is B. Harding, Coolidge, and Hoover
:)
For each of the following scenarios state the domain (starting set) show and state the mapping, and decide if it is a function. Be sure to label your set and indicate the direction of the relation.
Domain: Number of pages
Range:Number of books
Mapping: Number of pages to the number of books.
Explaination: The number of pages is the independent variable and the number of books is the dependent variable.
The given mapping is a function as total number of pages can not have more than two output (number of books).
what are the equations of the asysyoptes of the rational function
To find the asymptotes, we have to solve the following.
[tex]x^2-4x+3=0[/tex]We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.
[tex](x-3)(x-1)=0[/tex]So, the solutions are x = 3 and x = 1.
Hence, the asymptotes x = 1 and y = 1/2.The graph below shows the function.
Which probem situation can be represented by the equation below?3x +3 <11F Joe and Hannah together got less than 11 questions correct on their quizzes. Joe got 3 more questions correct than Hannah. What is x, the number of quiz questions Hannah got 3 correct?G A coin collection of dimes and quarters has less than 11 coins. The collection has more than 3 times as many quarters as dimes. How many dimes, x, is in the collection?H Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?J The length of a rectangle is 3 inches more than the width, x. Three times the length is less than 11. What is the width of the rectangle?
Let x be correct questions of Joe and y be correct quiz question of Joe. The in equality for Joe and Hannah together questions is,
[tex]x+y<11[/tex]Joe got 3 more questions correct than Hannah, means equaltion is,
[tex]y=x+3[/tex]So inequality obtained is,
[tex]\begin{gathered} x+x+3<11 \\ 2x+3<11 \end{gathered}[/tex]Thus option F is incorrect.
Let x be number of dimes and y be number of quarters. So inequality for collection of coins is,
[tex]x+y<11[/tex]The number of quarters are,
[tex]y=3x[/tex]So resultant inequality is,
[tex]\begin{gathered} x+3x<11 \\ 4x<11 \end{gathered}[/tex]Thus option G is incorrect.
Let larger number be y. So sum of numbers is less than 11, means
[tex]x+y<11[/tex]The equation of larger number in terms of smaller number is,
[tex]y=2x+3[/tex]Substitute the value of y in the inequality to obtain the desired inequality.
[tex]\begin{gathered} x+2x+3<11 \\ 3x+3<11 \end{gathered}[/tex]Thus inequality obtained is 3x + 3 < 11.
Thus option H is correct.
Correct option : Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?