We want to find word problems that gives rise to the following systems of algebraic equations.
a)
x+y=13
x-y=1.
Answer: The sum of the ages of two students is 13. The difference between their ages is 1. Find the ages of the two students.
b)
3x-30y=15
2x+10y=40
Answer:
The difference between 3 times Dan's age and 30 times Mark's age is 15. If the sum of 2 times Dan's age and 10 times Mark's age is 40. Find the ages of Dan and Mark.
c)
8x+3y=37
8x-3y=50
Answer:
The sum of 8 times an eagle's distance above sea level in feet and a herring's distance below sea level is 37 feet. The difference between 8 times an eagle's distance in feet above sea level and 3 times the herring's distance below sea level is 50. Find the distance of the eagle and the herring relative to the surface of the sea.
d) x-5y=4
3x+5y=32
The difference between a pig's age and 5 times the age of a piglet is 4 years. If the sum of 3 times pigs and 5 times the piglet's age is 32 years, find the ages of the pig and its piglet.
What is the surface area of the triangular prism?
A triangular prism. The rectangular sides are 5 feet by 4 feet, 5 feet by 5 feet, and 5 feet by 3 feet. The triangular sides have a base of 4 feet and height of 3 feet.
What is the surface area of the triangular prism?
60 square feet
72 square feet
82 square feet
84 square feet
Answer:
My friends
Step-by-step explanation:
the surface area of the triangular prism is
60 square feet
This is hard hi and I'm guessing 60 also
Sammy and his family took a hiking trip to the mountains. They started out with 20 pounds of food. They plan on eating 4 pounds of food each day. Write a. Equation that relates the remaining food supply r to the number d
Answer:
The answer is r = 20 - 4d
Step-by-step explanation:
They started out with 20 pounds of food and consume 4 pounds each day which implies after d number of days, they would have consumed 4d pounds.
Hence, the remaining amount of food (r) = 20 - 4d
Find the midpoint of the line segment with end coordinates of:
(
−
2
,
−
2
)
and
(
2
,
−
8
)
Answer:
(0,-5)
Step-by-step explanation:
(−2,−2)
and
(2,−8)
Midpoint: (-2+2)/2, (-2-8)/2
0/2, -10/2
(0,-5)
(5 × 4) × (16 ÷ 8) × (24 − 22) =
Answer:
= 80
Step-by-step explanation:
(5 × 4) × (16 ÷ 8) × (24 − 22) =
20 * 2 * 2 =
80
The average rate of change of a function is less from = x equals 1 to = x equals 4 than from = x equals 5 to = x equals 8 . What type of function could it be? Explain
Answer:
Step-by-step explanation:
Given that,
Rate of change of a function
1. From x = 1 to x = 4
2. From x = 5 to x =8
Then,
Rate of change for first condition
∆x/∆t = (x2-x1) / (t2-t1)
∆x/∆t = (4-1) / (t2-t1)
∆x/∆t = 3 / (t2-t1)
Rate of change for second condition
∆x/∆t = (x2-x1) / (t2-t1)
∆x/∆t = (8-5) / (t2-t1)
∆x/∆t = 3 / (t2-t1)
The rate of change are equal, it shows that the slope are equal.
So, it is a straight line function.
Since it has equal rate of change..
What is 2 divided by 565
Answer:
.003539823 to be exact
Step-by-step explanation:
well 565 cant go into 2 one time so it be a decimal.
help with this pls is important
Answer:
#1: x=6, -1
#2: x=2, 3
#3: x = - 4/3, 2
#4: x = -5/2, -2
#5: x = 1/2, -7/2
#6: x= -1/2, 2/3
#7: x = 1/3, 1/4
Step-by-step explanation:
You’re gonna have to copy this down quickly because if they see that I don’t have an explanation, they are going to delete my comment. So hurry!!!
Answer:
Step-by-step explanation:
NEED HELP ASAP.....At the 2012 Summer Olympic Games in London, in the Men's Shot Put qualifying round, the distances ranged from 17.58 meters to 21.36 meters with a mean distance of 19.64 meters and a standard deviation equal to 0.92 meters. If the distribution were truly a normal distribution, what percent of the athletes would have had a distance greater than 20.56 meters, one standard deviation above the mean? There were 40 athletes in the competition. How many athletes does that represent?
OPTIONS:
-about 6 athletes
-about 14 athletes
-about 20 athletes
-about 26 athletes
-about 34 athletes
Answer:
About 6 athletes.
Step-by-step explanation:
We are concerned only with the percent of athletes that are above one standard deviation.
Between one standard deviation and two standard deviations, there is 13.6% of the athletes.
From 2 to 3, there is 2.1%. Above 3, there is 0.2%.
The sum of those percentages is 15.9% of 40 = 0.159 · 40 = 6.36 or about 6 athletes.
Hope this helps.
The solution is: About 6 athletes does that represent.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
We are concerned only with the percent of athletes that are above one standard deviation.
Between one standard deviation and two standard deviations, there is 13.6% of the athletes.
From 2 to 3, there is 2.1%. Above 3, there is 0.2%.
The sum of those percentages is 15.9% of 40
= 0.159 · 40
= 6.36 or about 6 athletes.
Hence, The solution is: About 6 athletes does that represent.
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Which statement about histograms is true?
A. Data is organized in categories.
B. Data appears as bars that are all about the same height.
C. Data is organized in equal intervals.
D. Data appears as bars that do not touch.
Answer:
C. Data is organized in equal intervals. i think
Step-by-step explanation:
The correct statement about histograms is that data is organized in equal intervals. A histogram represents data through bars of different heights, corresponding to their frequency, grouped into specified ranges.
Explanation:In regards to histograms in mathematics, the true statement is: C. Data is organized in equal intervals. A histogram is a type of graphical representation that organizes a group of data points into a specified range. The data is portrayed via bars of different heights, where each bar groups numbers into ranges. These bars touch each other where the height of each bar corresponds to its frequency of data points. Unlike bar charts, histograms do not display data in separate categories, but as continuous data grouped into ranges, hence they are arranged in equal intervals.
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Between which two ordered pairs does the graph of f(x) = one-halfx2 + x – 9 cross the negative x-axis?
Answer:
Step-by-step explanation:
we have that
[tex]f(x) = x^2 + x - 9[/tex]
Using a graph tool
see the attached figure
The function represent a vertical parabola that open up
the vertex is a minimum-------> is the point (-0.5, -9.3)
The x-intercepts are the points when the y coordinate is equal to zero
The x-intercepts are the points (-3.5, 0) and (2.5, 0)
so
the function cross the negative x-axis at point
therefore, the answer is
(-4, 0) and (-3, 0)
Answer:
(-6,0)(-5,0)
Step-by-step explanation:
Solve the equation for y. Then find the value of y for each value of x.
y + 4x = 11; x = -1, 0,3
Solve the equation for y.
y=1
What is it ?
Answer:
y+4(-1)=11
y=11+4
y=15.
ii)y+4(0)=11
y=11
ii)y+4(3)=11
y=11-12
y=-1
when y=1
1+4x=11
4x=11+1
4x=12
x=3
A bag has 2 blue marbles 3 red marbles and 5 white marbles. Which event has a probability greater than 1/5 select three options
Answer:
all
Step-by-step explanation:
all of them has the probability
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.
Which linear inequality is represented by the graph?
y > Two-thirdsx – 2
y < Two-thirdsx + 2
y > Two-thirdsx + 1
y < Two-thirdsx – 1
y < 2/3x - 1
Step-by-step explanation:Find the Equation of the line
P1(-3,-3) P2 (3,1)
1.) Find the Slope
Rise: 1-(-3) = 4
Run: 3-(-3) = 6
m = [tex]\frac{Rise(Changeiny)}{Run(Changeinx)}[/tex] = [tex]\frac{4}{6}[/tex]=[tex]\frac{2}{3}[/tex]
2.) Find y intercept (B)
y = 2/3x + b
-3 = 2/3(-3) + b <-Plug a point in
-3 = 2 + b
-2 -2
-1 = b
3.) Equation
y = 2/3x - 1
Write an inequality
Since y must be below the line, that means y is less than the equation used to find the line.
y < 2/3x - 1
Though I was not able to get the right answer I'll just answer what has the right equation.
Answer:
y < Two-thirdsx – 1
Step-by-step explanation:
Which are steps that could be used to solve 0 = 9(x2 + 6x) – 18 by completing the square? Check all that apply.
18 + 81 = 9(x2 + 6x + 9)
18 + 9 = 9(x2 + 6x + 9)
18 + 36 = 9(22 + 6x + 36)
11 = (x + 3)2
07342 = (x + 6)2
199 = (x + 3)2
Answer:
A) 18+81=9(x^2+6x+9)
D)11+(x+3)^2
Step-by-step explanation:
To solve this by completing the square, we want to get it to the form of: (x + 3)^2 = 9
There are multiple ways to get there.
First we could divide by 9 to get.
x^2 + 6x = 0
Then, add 9 to both sides to get:
x^2 + 6x + 9 = 9
Factor the left side:
(x + 3)^2 = 9
Now, you can solve this equation by completing the square.
(*I think you have a typo in your answer choices)
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Please help me with this question. Will mark brainliest!!
Answer:
77
Step-by-step explanation:
im rusty but u double 75 i think add the arc thing which is 133 and subtract that from 360 to get 77
20% of a is 11. What is a? *
20% of a = 11
[tex]\frac{20}{100}[/tex] a = 11
[tex]\frac{1}{5}[/tex] a = 11
a = 55
I hope this helps! If you have any questions, feel free to ask.
Answer.
2.2
Why:
in percents you always put the percent above 100% ( so it'll look like this---- 20/100) and your number that is left out would be 11 so you put it by your percent like this----20 a
100 11
so now you do divide and multiply: you divide 20 by 100 and multiply by 11 to get a which is 2.2
One letter weighs 12 ounces. The mail carrier is allowed to carry 30 pounds. How many letters is he able to carry? 16 letters 32 letters 40 letters 480 letters
Answer: He is able to carry 40 letters
Step-by-step explanation: The total weight the mail carrier is allowed is 30 pounds, whereas each letter weighs 12 ounces.
What we need to do is simply find the rate of conversion between an ounce and a pound.
By conversion, 1 ounce equals 0.0625 pounds, that is;
1 ounce = 0.0625 pounds
Therefore 12 ounces would be 0.0625 times 12 which equals, 0.75 pounds. This means one letter weighs an equivalent of 0.75 pounds. If the mail carrier is allowed to carry a total of 30 pounds, then he can carry;
No of letters = Total weight allowed/weight of one letter
No of letters - 30/0.75
No of letters = 40
Hence the mail carrier is able to carry 40 letters.
Your Answer is C. He can carry 40 letters.
Step-by-step explanation:
Hope it helps!
Good luck!
two angles in a triangle measure (2.3x+25)° and (5.8x+11)°. what is the value of x if the two angles are congruent to one another?
A. x= 34.2
B. x= 10.3
C. x= 6.6
D. x= 4
Answer:
The answer is D. x= 4
Step-by-step explanation:
The angles are congruent so
2.3x +25 = 5.8x + 11
2.3x - 5.8x = 11 - 25
-3.5x = -14
x = 14/3.5
x = 4.
Answer:
The answer to your question is the letter D.
Step-by-step explanation:
Data
First angle 2.3x + 25
Second angle 5.8x + 11
Process
1.- This angles are congruents, this menas that they measure the same so to find x, equal both values.
2.3x + 25 = 5.8x + 11
2.- Solve for x
2.3x - 5.8x = 11 - 25
3.- Simplification
-3.5x = -14
x = -14/-3.5
4.- Result
x = 4
27/45=_/5?
2/6=_/3?jjjjjj
Answer:
27/45=3/5
2/6=1/3
Step-by-step explanation:
In a survey of 250 students, 60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog
Answer:
Step-by-step explanation:
Given:
250 students And respective percentage of students who are having dogs and cats.
To Find:
60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog
Solution:
Taking each condition as follows:
60% of 250 have cats
i.e 0.6 *250= 150 students have cats
So 150 students of that 70% has dogs
i.e 0.7*150=15*7=105 students have dogs
Now 40 % of 250 dont have cats
i.e 0.4*250=100 students dont have cats
So Of which 75 % have dogs
i.e 0.75*100= 75 students will have dogs.
Now making tabular forms to understand properly,
(Refer the Attachment)
Ciro made a sign in the shape of a trapezoid. The parallel sides measured 18 inches and 35 inches. The distance between these sides was 19 inches. What was the area of Ciro's sign?
Final answer:
The area of Ciro's trapezoidal sign is calculated using the formula for the area of a trapezoid, which is 503.5 square inches.
Explanation:
The student's question involves calculating the area of a trapezoid. The formula for the area of a trapezoid is ½(√ + ∛)×h, where √ and ∛ are the lengths of the parallel sides and h is the distance between these sides. Given that √ = 18 inches, ∛ = 35 inches, and h = 19 inches, plug these values into the formula to get:
Area = ½(18 inches + 35 inches) × 19 inches
Area = ½(53 inches) × 19 inches
Area = 26.5 inches × 19 inches
Area = 503.5 square inches
So, the area of Ciro's sign, which is trapezoidal is 503.5 square inches.
What is the measure of AngleDEF?
Triangle D E F. Angle D is 28 degrees. Angle F is 47 degrees.
25 degrees
75 degrees
90 degrees
105 degrees
Answer:
Angle E should be 105 degrees.
Step-by-step explanation:
Since a triangle equals 180, you subtract 47° and 28° from that and come up with 105°.
The angle E is 105 degrees when Angle D is 28 degrees. Angle F is 47 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Let the triangle be DEF.
Angle D is 28 degrees. Angle F is 47 degrees.
We need to find the angle E
By angle sum property we know the sum of three angles of a triangle is 180 degrees.
28+47+x=180
75+x=180
Subtract 75 from both sides
x=180-75
x=105 degrees.
Hence, the angle E is 105 degrees when Angle D is 28 degrees. Angle F is 47 degrees.
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Select the correct answer.
An elevator at a department store must carry fewer than 17 people at a time. An elevator operator is present in the elevator at all times. If
x customers can travel in the elevator with the elevator operator, which inequality represents this situation?
A X+1 <17
B. x>18
C. x+1<16
D. X<17
E. x+1 >18
Answer:
a
Step-by-step explanation:
In 56 years, Kevin will be 9 times as old as he is right now.
How old is he right now?
Answer:
he's 7 years old
Answer:
Step-by-step explanation: Kevin will actually be 6 years and 2 months old
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are queens.
To find the probability of getting all 4 cards that are queens, we calculate the number of favorable outcomes and the total number of possible outcomes. The probability is the number of favorable outcomes divided by the total number of possible outcomes.
Explanation:To find the probability of getting all 4 cards that are queens, we need to calculate the number of favorable outcomes (4 queens) and the total number of possible outcomes when 4 cards are dealt from a shuffled deck of 52 cards.
The total number of possible outcomes can be calculated using combinations. We can use the formula C(n, r) = n! / (r!(n-r)!), where n is the total number of items (52 cards) and r is the number of items to be selected (4 cards). So, C(52,4) = 52! / (4!(52-4)!) = 270,725.
The number of favorable outcomes is 4 since we want all 4 cards to be queens.
Therefore, the probability is the number of favorable outcomes divided by the total number of possible outcomes: P(all 4 cards are queens) = 4/270,725 = 0.00001475 (rounded to 5 decimal places) or approximately 0.0015%.
Hey I am needing help
Which fraction would be between 5/8 and 13/16
Answer:
11/16 and 12/16=3/4
Step-by-step explanation:
First we need to get a common denominator
5/8*2/2 = 10/16
The fractions between 10/16 and 13/16
are 11/16 and 12/16
We can simplify 12/16 =6/8=3/4
There are many others if we go with a higher common denominator. These are just two examples
If you place a 29-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bottom of the building?
Answer:
Step-by-step explanation:
20
Estimate the number of cell phone subscribers in 2008. Round to the nearest tenth.
Answer:
For this case we have an exponential function of the form:
Where,
A: initial number of subscribers
b: rate of change
x: number of years
Part A:
The equation modeling the problem is given by:
For the year 2008 we have x = 2.
Substituting values:
Part B:
For the year in which the company reaches 278 million we have
Thus, the company reaches 278 million in the year 2009.
Step-by-step explanation:
Identify the axis of symmetry for the following equation:
y = x^2 + 10x + 26
A) x = -5
B) x = 2
Answer:
The answer to your question is the letter A.
Step-by-step explanation:
Data
y = x² + 10x + 26
Factor the right side of the equation
y - 26 = x² + 10x
-Complete the perfect trinomial square
y - 26 + (5)² = x² + 10x + (5)²
-Simplify
y - 26 + 25 = x² + 10x + 25
y - 1 = (x + 5)²
Vertex = (-5 , 1)
The function given is a vertical parabola whose axis of symmetry goes through x = -5
Which formula should be used to find the circumference of a circle?
A C = pi d
B C = 2 pi d
C C = pi r
D C = StartFraction pi over d EndFraction
Answer:
A
Step-by-step explanation:
[tex]C=\pi d\\[/tex]
or
C=pi times 2r
Answer:
A
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