Several hours after departure the two ships described to the right are 50 miles apart. If the ship traveling south traveled 10 miles farther that the other how many miles did they each travel.
Answers
Answer:
[tex]Ship\ A = 40\ miles[/tex]
[tex]Ship\ B = 30\ miles[/tex]
Step-by-step explanation:
Given
[tex]d = 50[/tex] --- distance apart
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
The question can be represented with the attached image.
Required
Solve for x
Using Pythagoras theorem, we have:
[tex]x^2 + (x + 10)^2 = 50^2[/tex]
Open bracket
[tex]x^2 + x^2 + 20x + 100 = 2500[/tex]
Collect like terms
[tex]x^2 + x^2 + 20x + 100 - 2500 = 0[/tex]
[tex]2x^2 + 20x -2400 = 0[/tex]
Divide through by 2
[tex]x^2 + 10x -1200 = 0[/tex]
Expand
[tex]x^2 + 40x - 30x -1200 = 0[/tex]
Factorize
[tex]x(x + 40) - 30(x +40) = 0[/tex]
Factor out x + 40
[tex](x - 30)(x +40) = 0[/tex]
Split and solve for x
[tex]x - 30 = 0\ or\ x + 40 = 0[/tex]
[tex]x = 30\ or\ x = -40[/tex]
Distance can not be negative
So:
[tex]x = 30[/tex]
Recall that:
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
This implies that:
[tex]Ship\ B = 30\ miles[/tex]
[tex]Ship\ A = 30 + 10\ miles[/tex]
[tex]Ship\ A = 40\ miles[/tex]
Related Questions
The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. (2 points)
a. −4(x − 3)2 − 29; The maximum height of the water is 3 feet.
Selected:b. −4(x − 3)2 − 29; The maximum height of the water is 29 feet.This answer is incorrect.
c. −4(x − 3)2 + 7; The maximum height of the water is 7 feet.
d. −4(x − 3)2 + 7; The maximum height of the water is 3 feet.
Answers
Answer:
d!
Step-by-step explanation:
Answer:
−4(x − 3)2 + 7
Step-by-step explanation:
I took the test
Question One
The length and width of a rectangle is 12 in. And 5 in. The width of a similar rectangle is 8 in. What is the length of the similar rectangle?
Answers
Answer:
Step-by-step explanation:
Set up proportions. Make sure length and widths line up!
[tex]\frac{12}{5} =\frac{x}{8}[/tex]
Then do butterfly method.
[tex]12(8) = 5x[/tex]
Solve for x.
[tex]96 = 5x\\\\x= 19.2 in[/tex]
Hope that helped!
Please help meeee! A new crosswalk is being built between the parallel sidewalks of Circle Avenue. The edges of the crosswalk are parallel. One angle that the crosswalk makes with the sidewalk measures 78 degrees, as shown. Determine the measures of the missing angles. The drawing is not drawn to scale.
Answers
Answer:
[tex]A = 78^\circ[/tex]
[tex]B = 102^\circ[/tex]
[tex]C = 102^\circ[/tex]
Step-by-step explanation:
Given
The attached image
Required
Find A, B and C
Because the sides of the crosswalk are parallel and the sidewalks are also parallel, then the following relationships exist
[tex]A = 78^\circ[/tex] ---- alternate interior angles
[tex]B = C[/tex] ---- alternate interior angles
To solve for B, we have:
[tex]B + 78 = 180[/tex] --- the sum of the base angles
[tex]B = 180 - 78[/tex]
[tex]B = 102^\circ[/tex]
Recall that:
[tex]B = C[/tex]
[tex]C = 102^\circ[/tex]
If g(x) = 1/4X-4 find
g(-4) = [g1]
g(12) = [g2]
Answers
Answer:
G1 = -5 G2 = -1
Step-by-step explanation:
plug in the values given into X and solve
g1= 1/4(-4) -4
g1 = -1 -4
g1 = -5
g2= 1/4(12) -4
g2= 3 -4
g2= -1
3. Gas is $2.09 per gallon at the gas station. If
Nate filled up his car and spent $33.44, how
many gallons did he put in his car?
X
many
t how
gallary
Equation
Solution
Work it out
Answers
The following frequency table shows the number of children that each member of Moms Club has. Find the median number of children.
Answers
The median number of children is 3.
The given frequency table shows the number of children that each member of the Moms Club has.The number of children as given in the table is 1, 2, 3, 4, and 5.The number of members as given in the table is 1, 1, 2, 0, and 1.The median is the number that divides a data sample distribution's upper half from its lower half in statistics and probability theory. It can be regarded as the "midway" value for a set of data.The middle value of the number of children from the above given data is 3.To learn more about median, visit :
https://brainly.com/question/28060453
#SPJ1
Answer:
2 child
Step-by-step explanation:
Find value a, b and c
Answers
Answer:
a= 30 degree
b= 120 degree
c= 150 degree
Please help. I’ll give brainlest!! No links
Answers
Answer:
352
Explanation
Answer:
352 square inches
Equation to find the surface area:
A=2(wl+hl+hw)
Steps:
2·(4·12+8·12+8·4)=352
If you have any questions revolving around this topic,feel free to ask me and i will be happy to help,Good luck!
CAN SOMEONE HELP ME PLEASE !!
Answers
Answer:
A
Step-by-step explanation:
(MATH) (6) ((PHOTO))
label is sq yd
Answers
Answer:
20 sq yd
Step-by-step explanation:
To find the total amount of sq yd's of paint needed, you have to find the area.
The area of a triangle is: A = 1/2 bh
We know:
b = base = 8
h = height = 5
Plug in and solve:
A = 1/2 (8) (5)
A = 1/2 (40)
A = 20
You wonder what is the average number of credits Le Moyne students take per semester. You speak with the Le Moyne registrar, and they tell you that Le Moyne students take an average of 17 credits per semester with a population standard deviation of 2.5 credits. We plan to take a sample of 49 students and ask each student how many credits they plan to take. Assume that the population mean is 17 credits and the populations standard deviation is 2.5 credits. What does the CLT say about the distribution of the sample mean of 49 students
Answers
Answer:
The CLT says that the distribution is approximately normal, with mean of 17 credits and standard deviation of 0.3571 credits.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that the population mean is 17 credits and the populations standard deviation is 2.5 credits.
This means that [tex]\mu = 17, \sigma = 2.5[/tex]
What does the CLT say about the distribution of the sample mean of 49 students?
It is approximately normal.
The mean is 17.
Due to the sample of 49, n = 49, and the standard deviation is [tex]s = \frac{2.5}{\sqrt{49}} = 0.3571[/tex]
The CLT says that the distribution is approximately normal, with mean of 17 credits and standard deviation of 0.3571 credits.
12.
The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers?
Answers
Answer:
70kilometers
Step-by-step explanation:
first we must find how much one half of a centimeter is
well, its easy, theres already a half for the distance, and the representation is an even number, so cut it in half.
20-10 is 10
and now the multiplication
20x3=60
60+10=70
70 kilometers
(MATH) (6) ((PHOTO))
label is m
Answers
Multiply the length by the height:
6.5 x 2 = 13
The width is the volume divided by 13
Width = 52/13 = 4 m
What percentage of values are between 25 and 45
Answers
Answer:
I'm not that good at this but I'll try.
The difference between 25 and 40 is 15
The difference between 80 and 5 is 75
So, 15/75 = 0.20 or 20%
Sorry, that all I can come up with
Step-by-step explanation:
Question: Edwin usually makes 20 cookies with this recipe, but only wants 5 cookies.
How much is 1/2 teaspoon of vanilla to make 5 cookies?
(PLEASE HELP!!)
the wrong answers that u guessed just to get points and links and other stuff that is not answering this will be reported
Answers
Answer:
1/2 teaspoons of vanilla would be too much, the correct amount to use would be 0.125 teaspoons.
Step-by-step explanation:
Since 1 stick butter, 1/2 cup sugar, 1/2 teaspoon vanilla, 3 tablespoons milk, 1 1/2 cup flour, 2 teaspoon baking powder, 1/4 teaspoon salt is the regular recipe for 20 cookies, we would first have to divide 20 by 5 which would equal 4. And just like we had to divide the number of cookies down we have to divide the amount of vanilla down. So now we could turn 1/2 into a decimal which is 0.5. And 0.5 divided by 4 is 0.125.
So Edwin would need 0.125 teaspoons of vanilla so 0.5 ( 1/2 ) teaspoons of vanilla would be too much.
What is the area of the figure on the coordinate plane below?
Answers
Answer:
70 square units
Step-by-step explanation:
1 box is 2 units
Width = 7 units
Length = 10 units
7 × 10 = 70 square units
GEOMETRY!! I will give brainliest
Answers
Answer
The triangle is scalene triangle
Answer:
Scalene triangle
Step-by-step explanation:
Use the ALEKS calculator to find 35% of 67. Do not round your answer.
Answers
Answer:
23.45
Step-by-step explanation:
35 percent of 67=23.45
35×67=2345
2345/100=23.45
An aquarium owns 5 identical tanks. All together, the tanks can hold 86 gallons of water. How much water can each tank hold?
Answers
Answer:
17.2
Step-by-step explanation:
86/5=17.2
4) This shape is made from rectangles.
6 cm
Not drawn
accurately
12 cm
8 cm
11 cm
Answers
what is the answer
Move the correct number to the first box to show the answer. Then, move numbers to the other boxes to explain the answer.
Answers
Answer:
[tex]\frac{1}{4} * 3 = \frac{3}{4}[/tex]
Because:
[tex]\frac{1}{4} * 3 = \frac{1}{4} +\frac{1}{4} + \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{4} * 3 = [\ ][/tex]
Because
[tex]\frac{1}{4} * 3 = [\ ] + [\ ] + [\ ][/tex]
Required
Fill in the box
[tex]\frac{1}{4} * 3 = [\ ][/tex]
This can be written as:
[tex]\frac{1}{4} * 3 = \frac{1* 3 }{4}[/tex]
Solve the numerator
[tex]\frac{1}{4} * 3 = \frac{3}{4}[/tex]
(b) Because
[tex]\frac{1}{4} * 3 = [\ ] + [\ ] + [\ ][/tex]
The above implies that
[tex]\frac{1}{4}[/tex] be added in 3 places
i.e.
[tex]\frac{1}{4} * 3 = \frac{1}{4} +\frac{1}{4} + \frac{1}{4}[/tex]
In order to add the fractions 2/5 + 3/4, first, we need to find the least common denominator. The LCD for 4 & 5 is 20. Now that we know the LCD is 20, what are the new equivalent fractions?
Answers
Answer:
8/20 and 15/20 and then you add to get 23/20 AKA 1 3/20
Step-by-step explanation:
Since you multiply 5 by 4 to get the LCD, apply the same method to the top: 2 times 4 is 8
Next do the same for the other fraction: 4 times 5 is 20 so apply that to get 3 times 5 is 15
Your final fractions will be 8/20 and 15/20
Then add and reduce to get 1 3/20
If the equation below represents the total cost of 3 boxes of cereal and 2 loaves of bread is $15," then x represents
3x + 2y = 15 t
A the number of boxes of cereal
B the number of loaves of bread
Cthe cost of a box of cereal
Dthe cost of a loaf of bread
Answers
Answer:
C. The cost of a box of cereal
Step-by-step explanation:
In the question, we are given the number of 3 boxes of cereal, 2 loaves of bread, and that the total cost is $15. We can see these numbers in the equation, and putting it into context, we see that the 15 is on the right side of the equation, which indicates cash. Therefore, the 3 and 2 are accounted for, but their prices are unknown. X is a placeholder for the unidentified cost of a box of cereal, and we know that it's the boxes of cereal and not the loaves of bread because there are 3 and not 2.
A pair of jeans is on sale for $30, 25% off the original price. What is the original price?
Answers
Step-by-step explanation:
Let $p be the original price.
[tex](1 - 25\%)p = 30 \\ \frac{75}{100}p = 30 \\ p = 40[/tex]
∴ The original price is $40.
1. You are rolling a pair of dice. What's the probability of getting different numbers on both dice?
Answers
Answer:
5/6Step-by-step explanation:
Total outcomes:
6*6 = 36Outcomes with same numbers on both dice:
6Outcomes with different numbers on both dice:
36 - 6 = 30Probability of different numbers on both dice:
30/36 = 5/6Plz help me I will give you 40 points and Brainly
Answers
Answer:
1) slope 3/2, y-intercept 7/2
2y-3x=7
2) slope 1/5, y-intercept 3
5y-x=15
3) slope 1/5, y-intercept 4/5
-x+5y=4
4) slope 5/2, y-intercept 7/2
2y=5x+7
Step by step explanation:
1) 2y-3x=7
2y=3x+7
y=3/2y+7/2
2)5y-x=15
5y=x+15
y=1/5x+3
3)-x+5y=4
5y=x+4
y=1/5x+4/5
4)2y=5x+7
y=5/2x+7/2
Help Please!! Struggling with this for a while
Answers
(PLEASE HELP) A teacher surveyed a sample of students from Lake Middle School. He asked the students where they'd like to go for a field trip. He recorded these results:
• 80 chose the aquarium.
• 60 chose the science center.
• 30 chose the planetarium.
• 40 chose the farm.
The teacher wants to figure out the relative frequency of a student choosing the aquarium. He'll then estimate how many students out of all 1000 at the school are likely to choose the aquarium.
(he surveyed 210 students and about 38% of them chose the aquarium)
Write and solve a proportion that the teacher can use to estimate how many students in the whole school would choose the aquarium.
Answers
Answer:
relative frequency of choosing aquarium is 80/210
about 400 students out of 2000 will choose aquarium
Step-by-step explanation:
relative frequency of choosing aquarium is 80/210
proportion:
a = students who choose aquarium
80/210 = a/1000
210a = 80000
a = 80000/210 which is close to 80000/200 which equals 800/2 or about 400 students
Help!! Me pls!! I don't understand this question
Answers
Answer:
B. 64
......there are nine nolumbers in every interval . ..
Answer:
64
Step-by-step explanation:
91-82=9
minus every number by 9
which of the following phrases describes the expression 12 - 2x
A. 2 decreased by 12 times a number
B. a number times the quantity 12 decreased by 2
C. 12 decreased by 2 times a number
D. 2 times a number decreased by 12
Answers
Answer:
C
Step-by-step explanation:
12 decreased by 2 times x