Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
Answers
24 ≤ y ≤ 33
x ≤ 10
y ≥ 3x
So, (0, 33) & (4.8, 30.5)
Therefore, (0, 33) & (4.8, 30.5) are the correct answers.
The given constraints are
(a) y ≥ 24 ft
(b ) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The acceptable region is shown shaded.
A (0, 33) satisfies all conditions
B (4, 36) fails condition (d)
C (4.8, 30.5) satisfies all conditions
D (9, 26) fails condition (c)
E (2, 22) fails condition (a)
Answer:
The acceptable points are A and C.
Related Questions
The length of a rectangle is twice the width. the perimeter is 32 cm more than the width. find the dimensions of the rectangle.
Answers
Length: 2x
Perimeter=2x+2x+x+x=6x
32 cm more than width means x+32
6x=x+32
5x=32
x=6.4
Dimension is 6.4×12.8 (width×length)
The dimensions of the rectangle are 6.4 and 12.8 respectively.
What is the perimeter of the rectangle?The formula for calculating the perimeter of a rectangle is given by :
P = 2 ( L + w )
The length of a rectangle is twice the width. And the perimeter is 32 cm more than the width.
L = 2w
Now substituting into the formula , we have
Width: x
Length: 2x
Perimeter P = 2 ( L + w ) = 2(3x) = 6x
Since 32 cm more than width means x+32
6x = x + 32
5x = 32
x = 6.4
Hence, Dimension is 6.4 × 12.8.
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Which linear inequality is represented by the graph?y ≤ x − 1y ≥ x − 1y < 3x − 1y > 3x − 1
Answers
Equation of a straight line graph is given in the form [tex]y = mx+c[/tex] where [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the y-intercept.
The graph given shows the line intercept y-axis at (0, -1)
To work out the slope, choose any two coordinates then find their vertical and horizontal distance. Say we choose (0, -1) and (3, 0)
The vertical distance is 1 and the horizontal distance is 3, so the slope is
[tex]m = \frac{-1-0}{0-3}= \frac{-1}{-3}= \frac{1}{3} [/tex]
Then form the equation for the line
[tex]y=mx+c[/tex]
[tex]y= \frac{1}{3}x-1 [/tex]→ Multiply each term by 3
[tex]3y = x - 3[/tex]
Now the inequality part, the shaded region is above the line, so the values intended are 'greater than' and the line is a bold line, so the inequality is 'greater than or equal to' and the symbol is ≥
The inequality is then
3y ≥ x - 3
Note: None of the options show this answer. Maybe check if the original options have been copied correctly.
Solution: As the line shown in the graph passes through (3,0) and (0,-1).
So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by
→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]
→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]
So ,the equation of line is ,→3 y = x-3
→ x- 3 y -3= 0 or y=x/3 -1
take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S
Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.
it means the above equation can be written as , y≥x/3 -1.
None of the option is correct.
the probability distribution table shows the proportion of people living in the five different regions of a city there are now 4200 residents in the city.
How many live in the south region?
Photo attached
Answers
4200 ×.16 = 672
672 residents
Answer: Number of residents live in south region= 672 residents.
Step-by-step explanation:
Given:- Total residents in the city =4200
let A be the event of residents live in south region the,
Probability of residents live in south region P(A) = 0.16
So, Number of residents live in south region=Product of probability of residents live in south region and total residents in the city =0.16×4200=672 residents.
You are playing a game. you lose 4.8 points,lose another 7.6 points, and then win 2.5 points. what is the overall change in your score
Answers
Finally, you lose 9.9 points.
The Overall Change in score is 9.9 points.
What is overall change?
Overall Change is the difference of initial average and final average.
Given that you are playing a game and lose 4.8 points and again loose 7.6 points and finally win 2.5 points.
According to question we have
4.8 + 7.6 = 12.4
Then 12.4 - 2.5 = 9.9 points
Hence, Overall Change in the score is 9.9 points.
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lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily. How much interest has Lloyd earned?
5,189.00
8,024.70
3,090.64
8,094.50
Answers
Answer:
Option C is the answer: $3,090.64
Step-by-step explanation:
Lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily.
Means p = 5003.86
r = 3.7% or 0.037
t = 13
n = 365 (assuming there are 365 days in a year)
[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=5003.86(1+\frac{0.037}{365} )^{4745}[/tex]
=> [tex]A=5003.86(1.00010136)^{4745}[/tex]
A = $8094.09
Interest earned = [tex]8094.09-5003.86=3090.26[/tex] dollars
This is closest to option C, hence, option C is the answer.
The length of a rectangle is 1 ft more than double the width, and the area of the rectangle is 45 ft2 . find the dimensions of the rectangle.
Answers
A = 45
L = 2W + 1
45 = W(2W + 1)
45 = 2W^2 + W
2W^2 + W - 45 = 0
(2W - 9)(W + 5) = 0
W + 5 = 0
W = -5...not this one because it is negative
2W - 9 = 0
2W = 9
W = 9/2
W = 4.5 <=== the width is 4.5 ft
L = 2W + 1
L = 2(4.5) + 1
L = 9 + 1
L = 10 <=== the length is 10 ft
The width of the rectangle is 4.269ft and the length is 8.538 ft.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, The length of a rectangle is 1 ft more than double the width.
Assuming the width to be x ft, therefore length would be (2x + 1) ft.
We know area of a rectangle(A) = length×width.
∴ x×(2x + 1) = 45.
2x² + 2x = 45.
2x² + 2x - 45 = 0.
[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:2\left(-45\right)}}{2\cdot \:2}[/tex].
[tex]x_1=\frac{-2+2\sqrt{91}}{2\cdot \:2},\:x_2=\frac{-2-2\sqrt{91}}{2\cdot \:2}[/tex].
[tex]x=\frac{-1+\sqrt{91}}{2},\:x=-\frac{1+\sqrt{91}}{2}[/tex].
[tex]\left(\m\quad x=4.26969\dots ,\:x=-5.26969\dots \right)[/tex].
∴ x = 4.269ft is the admissible value as length can not be negative.
∴ length is 8.538 ft.
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A science museum charges an admission fee of $10 per adult and $6 per child. If the museum had 2,000 visitors on a particular day and the total collection was $18,800, how many adults and children visited the museum?
Answers
c = child
10a + 6c = 18,800
a + c = 2,000
In the second equation, subtract c from both sides.
a = 2000 - c
Put this into the first equation.
10(2000 - c) + 6c = 18800
Multiply everything in the parenthesis by 10.
20,000 - 10c + 6c = 18,800
Combine like terms.
20,000 - 4c = 18,800
Subtract 20,000 from both sides.
-4c = -1,200
Divide -4 on both sides.
c = 300
Put this into the second equation.
a + 300 = 2,000
Subtract 300 from both sides.
a = 1,700
Hope this helps!
∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 . What is the value of x? Enter your answer in the box.
Answers
5x+10=7x-12
10=2x-12
22=2x
11=x
Find the quotient. y 9 ÷ y 3 y3 y6 y9 y27
Answers
answer
y^6
Answer:
The quotient is [tex]y^6[/tex]
Step-by-step explanation:
Given expression is,
[tex]y^9\div y^3[/tex]
[tex]=\frac{y^9}{y^3}[/tex]
By using quotient of powers property of exponent,
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]
[tex]=y^{9-3}[/tex]
[tex]=y^6[/tex]
Hence, the quotient is [tex]y^6[/tex]
Second option is correct.
Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bedroom that measures 12 feet by 14 feet. He multiplies 12 x 14 = 168 to get an exact answer of how much border he needs. He concludes that he does not have enough border for the whole job.
1. Tell how you can critique Jason’s reasoning.
2. Critique Jason’s reasoning
3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense
Answers
the tape is 75 feet long
the bedroom is 12 feet by 14 feet.
1. Tell how you can critique Jason’s reasoning.
If you want to Critique Jason's reasoning, you could a) ask yourself the same questions that Jason did and see if you would come with the same answers and used the same analysis or b) analyse Jason's answer to see if he did a mistake or missed an important detail and made a thought mistake
2. Critique Jason’s reasoning
I will use the option b from above:
?
Jason first multiplied 12 x 14 = 168. This multiplication is correct, but what did he get? He needed to get the perimeter of the bedroom because it was only the wallpaper border, not the wallpaper itself - so getting the perimeter was needed, but this we get by the formula ( 2* *(length+width), not length* width - as Jason did.
So Jason made a mistake here! his actual answer should be 2*(12+14)=2*26=52, so the tape of 75 feet would have been enough!
3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense
Using an overestimate is often a good idea- in case some of the tape gets damaged, he will have some left. However, since his calculations are wrong by a lot (he multiplies rather than adds and multiplies by 2), his overestimate will be a lot higher than would be practical - he would be left with a lot of leftovers and spend too much money. So his reasoning does not make sense
Keira created color panels for a wall using a mix of only red and blue paints. She plotted the quantities of red and blue paints used for each mix and connected them using a line segment, as shown in the graph below:
A line graph titled Color Mix, with Quantity of Blue Paint, in millimeters, on the X axis and Quantity of Red Paint, in millimeters, on the Y axis. The X axis has a scale from 0 to 9 with an increment of 1. The Y axis has a scale of 0 to 18 in increments of 2. A straight line connecting 3, 2 and 7, 12 is drawn. Which statement best describes the domain of the function represented in the graph? (1 point)
Answers
Answer:
3 ≤ x ≤ 7
Step-by-step explanation:
Why, because i said so, and also because i got it right in the quiz
Answer:
3 ≤ x ≤ 7
Step-by-step explanation:
Translate and solve: the quotient of a number x and -8 is 25
Please help,
Thank you :)
Answers
x/-8 = -25
Thus, to solve for x, multiply both sides by -8:
x/-8(-8) = -25(-8)
x = 200
What is a undo table in math
Answers
Final answer:
An undo table in mathematics refers to using inverse functions to reverse the effect of their counterpart operations, such as using the square root to undo a square, and logarithms to revert exponential calculations.
Explanation:
An undo table in math refers to a concept rather than a literal table. It encompasses mathematical operations that effectively reverse the effect of their counterparts. For example, to undo a squaring operation, we use a square root; similarly, to reverse an exponentiation, we utilize a logarithm. In essence, these operations are known as inverse functions.
Let's take the scenario of finding the side length of a right triangle. Given the triangle's side b and hypotenuse c, the Pythagorean Theorem states that a² + b² = c². To solve for side a, one would rearrange the equation to a² = c² - b². Then, to find a, we have to undo the square by taking the square root of both sides, resulting in a = √(c² - b²).
Mathematics is not about rote memorization of rules but understanding the logic and relationships between numbers. As such, when faced with the operation of squaring, we 'undo' it by understanding the core concept of square roots. Similarly, subtraction undoes addition, division undoes multiplication, and the inverse functions of trigonometric and exponential expressions undo their respective basic functions.
Therefore, the natural logarithm (ln) and the exponential function are inverses of each other and hence can undo each other as well.
The equation 4(2x + 3y) =4(3y +2x) is an example of which property? Question 4 options:
A. Distributive Property
B. Identity Property of Addition
C. Associative Property of Addition
D. Commutative Property of Addition
Answers
The equation 4(2x + 3y) = 4(3y + 2x) is representing the Commutative Property of Addition, which means the order in which you add numbers does not change the sum.
Explanation:The equation in your question, 4(2x + 3y) = 4(3y +2x), is an example of the Commutative Property of Addition. This property means that the order in which you add numbers does not change the sum. In this case, (2x + 3y) and (3y + 2x) are the same because of the Commutative Property of Addition, the order of 2x and 3y doesn't impact the result. The multiplication by 4 on both sides does not change this property being applied.
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20 points! Please help! a/b = c for b = ?
Answers
at least i think so
Given that AE is a tangent of the circle with the center at B, BC = 3.5, and AE = 24, which is the length of EC?
7
13
25
49
Answers
We are actually given here a right triangle where EC is the hypotenuse. The length of one side is AE = 24, and the other side AC is simply twice BC, so AC = 7:
EC^2 = AE^2 + AC^2
EC^2 = 24^2 + 7^2
EC = 25
the sum of three integers is 92. the second number is three times the first number. the third number is ten less than twice the first number. find the integers
Answers
1st number = x
2nd number = 3x
3rd number = 2x-10
x +3x + 2x-10 =92
6x - 10 = 92
6x =102
x = 102/6
x = 17
1st number = 17
2nd number = 17*3 = 51
3rd number = 17 *2 = 34-10 = 24
17 + 51 + 24 = 92
3 numbers are 17, 51 and 24
tom can wash 44 plates in 3 minutes. how many seconds will it take him to wash 12 wash? show your work.
Answers
I can’t seem to figure out how I would graph this? Someone help please
Answers
The coordinate of the midpoint of segment AB is (-3, 2). Find the coordinate of A if the coordinate of B is (0, 2).
A =
(-6,2)
(-3/2,2)
(3,2)
Answers
Write the ratios for sin a and cos
a. sin a = 14/50, cos a = 48/50
Answers
Answer:
The ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
Step-by-step explanation:
As given the expression in the question be as follow .
[tex]sin\ a = \frac{14}{50}[/tex]
[tex]cos\ a = \frac{48}{50}[/tex]
Thus the ratio of the sin a and cos a .
[tex]\frac{sin\ a}{cos\ a} = \frac{\frac{14}{50}}{\frac{48}{50}}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14\times 50}{48\times 50}[/tex]
[tex]\frac{sin\ a}{cos\ a} = \frac{14}{48}[/tex]
Simplify the above
[tex]\frac{sin\ a}{cos\ a} = \frac{7}{24}[/tex]
Therefore the ratios for sin a and cos a is [tex]\frac{7}{24}[/tex] .
divide three fourths ÷ two fifths
Answers
15/8
1.875
1 7/8
Hope this helps...
3/4 ÷ 2/5 =
3 x 5= 15 7
------- --- = 1 ----
4 x 2= 8 8
Hope this helps!
Dona found that she had 7 almonds left over after filling a number of bags with 25 almonds each. She let b represent the number of bags and wrote an expression to represent the total number of almonds. She found that mr022-1.jpg and then substituted to find the total number of almonds.
Answers
7 almonds are left
25 bags in each bag
25almonds x 20 bags= 500 almonds
500 almonds + 7 left = 507 total almonds
25b +7 would be the correct expression
The total number of almonds can be represented by the equation:
x = 25b + 7
How to solve Algebra Word problems?We can use the information given in the question to set up an equation to represent the total number of almonds.
Let b represent the number of bags, and
let x represent the total number of almonds.
According to the problem, each bag contains 25 almonds, and there are 7 almonds left over. Therefore, the total number of almonds can be represented by the equation:
x = 25b + 7
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An employee works 21 days per month if they worked an average of 7.5 hours per day how many hours do they work per month
Answers
You can verify that by dividing 157.5 by 21 to see how many hours she worked in a day.
157.5 divided by 21 is 7.1 hours
My answer is correct!
Wat is $60 for 8h unit rate
Answers
Which expression is equivalent to 3x(1.05)?
A: 3x + 3x + 3x
B: 1.05x + 1.05x + 1.05x
C: x + 3.15
D: 1.05x + 3
Answers
answer
B: 1.05x + 1.05x + 1.05x
The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?
Answers
Answer:
D
Step-by-step explanation:
"the male interquartile is not accurate because the first quartile is missing"
Find the hypotenuse of the right triangle if the perpendicular leg is 12 and base is 5
Answers
hypotenuse power two = 12 power 2 + 5 powered 2
= 144 + 25= 169
so hypotenus = radical 169 = 13
John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?
Answers
Final answer:
John received 10 nickels, 20 dimes, and 42 quarters.
Explanation:
Let's solve this problem step by step:
Let's assume the number of nickels = x
Number of dimes = x + 10 (10 more dimes than nickels)
Number of quarters = x + 10 + 22 (22 more quarters than dimes)
Given that the total value of change is $13, we can form the equation:
0.05x + 0.10(x + 10) + 0.25(x + 10 + 22) = 13
Simplifying the equation, we get:
0.05x + 0.10x + 1 + 0.25x + 7.75 = 13
Combining like terms, we get:
0.40x + 8.75 = 13
Subtracting 8.75 from both sides:
0.40x = 4.25
Dividing by 0.40:
x = 10.625
Since we can't have a fractional number of nickels, we round down to the nearest whole number.
Therefore, John received 10 nickels, 10 + 10 = 20 dimes, and 10 + 10 + 22 = 42 quarters.
The sum of two numbers is 44 . the larger number is 12 more than the smaller number. what are the numbers?
Answers
x+(12+x)=44
2x+12=44
2x=32
x=32/2
x=16
The two numbers are 16, 28
Hope I helped :)