Using a system of equations, it is found that:
b) The domain of the solution is that Steve ran 11 miles.
c) Variable S gives the distance ran by Steve.
d) The algebraic expressions are: K = 4 + S, K + S = 26.
e) The equation is: 4 + S + S = 26.
What is a system of equations?
A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this situation, the variables are given as follows:
Variable K: Distance ran by Kevin.
Variable S: Distance ran by Steve.
Kevin ran 4 miles more than Steve ran, hence:
K = 4 + S.
The sum of their distances is 26 miles, hence:
K + S = 26.
Replacing the first equation K = 4 + S on the second, we have that:
4 + S + S = 26
2S = 22
S = 11 miles.
how many solutions are in 7x-4=-3x+5+10x
find the equation of the line
Answer:
1 is 2 and 2 is 2
Step-by-step explanation:
sound travels at a rate of about 1.1*10^3 feet per second. Suppose a mining company detonates a bundle of dynamite at a distance of 625 feet from a canyon wall. At the time of a detonation the miners sit safely at a distance of 2,600 feet from the dynamite. How long after detonation will the miners hear the echo of the blast off the canyon wall? Round to the nearest tenth if necessary.
what in your opinion is the moral in the story ?
Toolkit Function: f\left( x \right) = \sqrt x Transformation Description: Left 1What is the equation for the transformed function?f(x) = ‾‾√+1f(x) = +1‾‾‾‾‾√f(x) = 1‾‾‾‾‾√f(x) = −1‾‾‾‾‾√
we know that
The parent function is
[tex]f(x)=\sqrt{x}[/tex]The transformation is to shift 1 unit to the left
so
The rule of this translation is given by
(x,y) -----> (x-1,y)
so
the equation for the transformed function is
[tex]f(x)=\sqrt{x+1}[/tex]some students decide to take a bike ride. for the first two hours they travel at a speed of 15 mi/hr, they then stop for lunch for an hour. the students then ride for another hour at 10 mi/hr. what was their average speed for the trip?
10 miles per hour is the average journey speed.
Given that,
Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.
Average speed is ( total distance ) / ( total time )
During the 1st 2 hrs:
distance = speed * time
distance = 15 *2 = 30 miles
During the last hour:
distance = speed * time
distance = 10 *1 = 10 miles
Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr
Therefore, their average speed for the trip is 10 mil/hr
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Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = ____
Amount of water in the second pool (in liters) = ____
(b)
Write an equation to show when the two pools would have the same amount of water.
______________
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.
Let x be the number of minutes water has been added.
(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = 23x + 728
Amount of water in the second pool (in liters) = 37x
(b)
Write an equation to show when the two pools would have the same amount of water.
this is when:
23x + 728 = 37x
subtract 23x from both sides:
23x + 728 - 23x = 37x - 23x
728 = 14x
divide both sides by 14:
728/14 = 14x/14
x = 52
So, pools are equal after 52 minutes.
What is the equation of the line?
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
It would take [tex]2.7[/tex] seconds, correct to 1 decimal place/nearest tenth.
Step-by-step explanation:
Step 1: Understanding the formula
The formula is given as [tex]h=16t^{2}[/tex], where [tex]h[/tex] represents the height, and [tex]t[/tex] represents the time.
Step 2: Substituting and solving
The question asks for the time that would take when the height is [tex]117~\text{feet}[/tex].
So, substitute [tex]117[/tex] for [tex]h[/tex] in the formula, since [tex]h[/tex] denotes the height:
[tex]h=16t^{2}\\117=16t^{2}[/tex]
Now, let's solve the equation to find the time, [tex]t[/tex]:
[tex]117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7[/tex]
So, it takes about [tex]2.7[/tex] seconds to travel [tex]117[/tex] feet, according to the formula.
The volume of this cube is 729 cubic yards. What is the value of y?
()) y =
yards
multiple choice in a single football game, a team scored 14 points from touchdowns and made x field goals, which are worth three points each. the team scored 23 points. how many field goals did the team make? a. 2 b. 3 c. 4 d. 5
The number of field goals the team made in the game is equal to b. 3
The number of field goals the team made can be determined using an algebraic expression. An algebraic expression can be defined as an expression or equation that consists of both letters and numbers in it.
If the team scored 14 points from touchdowns and made x goals which are worth three points each, then an algebraic expression can be given as;
3(x) + 14 = 23
Solving for x;
3x = 23 - 14
3x = 9
x = 9 ÷ 3
x = 3
Hence, the team made a total of 3 field goals that are worth three points each.
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The difference between the total surface area and curved
surface area of a hemisphere is 154 cm2, find its volume.
If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³
What is hemisphere?In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.
In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.
The difference between the total surface area and curved surface area of a hemisphere is 154cm.
Total Surface Area of Hemisphere = 3πr²
And Curved Surface Area of Hemisphere = 2πr²
It is Given that
Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.
Substituting the values, we get,
⇒ 3πr² - 2πr² = 154
⇒ πr² = 154
⇒ r² = 154/π
⇒ r² = 154 × (7/22)
⇒ r² = 7 × 7
⇒ r = 7.
Now, lets find the volume which is
Volume of Hemisphere = 2/3πr³
V = 2/3π(7)³
V = 2/3(22)(7)²
V = 2156/3
V = 718.66 cm³
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Can you please help me out with a question
The probability of the outermost ring is 55.6%
does the data give evidence of an association between scoring at least 21 points and the football team winning the game? there is a strong, negative association. there is a strong, positive association. there is a weak, negative association. there is a weak, positive association.
Considering the relative frequencies in this problem, the association between scoring 21 points and winning the game is as follows:
There is a strong, positive association.
What is a relative frequency?The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
From the table given at the end of the answer, we have that when the team scored at least 21 points, an interval composed of 28 games, the team won 25 games and lost only 3, hence the relative frequency of wins when the team scores at least 21 points is of:
25/28 = 0.8929 = 89.29%.
Due to this high frequency of wins, there is a strong and positive association between scoring 21 points and winning the game
What is the missing information?The table with the team's results is given by the image at the end of the answer.
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Describe how to solve the following:
a. 2√25
b. √150
Answer:
10 and 5[tex]\sqrt{6}[/tex]
Step-by-step explanation:
these cannot be solved as they are not equations, but can be simplified
using the rule of radicals
[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
then
2[tex]\sqrt{25}[/tex] = 2 × 5 = 10
[tex]\sqrt{150}[/tex]
= [tex]\sqrt{25(6)}[/tex]
= [tex]\sqrt{25}[/tex] × [tex]\sqrt{6}[/tex]
= 5[tex]\sqrt{6}[/tex]
3(x+1) +4 = 2x -2 + x
Answer:
No solution.
Step-by-step explanation:
3(x+1)+4=2x-2+x
-> distribute
3x+3+4=2x-2+x
-> simplify (add constants & x terms)
3x+7=3x-2
-> variable cancels out
7=-2
-> this is not true
Untrue statement; no solution.
Put empty parenthesis/brackets: [,] / (,) or simply put "no solution."
Find the value of x
A. x = 20
b. x = 32
c. x = 24
d. x = 28
Using proportions, it is found that the value of x would be 28.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We have been given two triangle, we need to find the value of x.
Then using proportions;
12/(x-7) = 8 / 14
Cross multiplication;
12 (14/8) = x - 7
3 (14/2) = x - 7
21 = x - 7
x = 21 + 7
x = 28
Therefore, the value of x is 28.
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PLEASE HELP I NEED THIS VERY VERY SOON!!!!
Tim and Jim leave Chicago traveling in opposite
directions. Jim travels 65 mph and Tim travels
63 mph. In how many hours will they be 1056
miles apart?
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
The times taken to travel 441 miles apart exists 8.25 hours
What is the time formula?Time can be defined as the dimension based on which the evolution of any system takes place. It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.
The formula for time, t = d/s which means time exists equivalent to distance divided by speed.
Given: Train running in the opposite direction
Speed of one train (S1) = 65 mph
Speed of one train (S2)= 63 mph
Distance to be covered = 1056 miles
Train exists running in the opposite direction, so their relative speed = (S1 + S2)
Relative speed = (65 + 63) = 128 mph
Now, time is taken to travel 1056 miles apart
Time = Distance / relative speed
Time = 1056/128 = 8.25 hours
Therefore, the times taken to travel 441 miles apart exists 8.25 hours
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What is the answer to # 11?
Answer:
40
Step-by-step explanation:
Go through PEMDAS
Exponents: 4∧0 = 1 and 1³ = 1
Multiply: 4 × 5 = 20 × 2 = 40
Add: 1 + 40 = 41
Subtract: 41 - 1 = 40
Six more than the quotient of a number and 9 equals 4
Answer: x= -18
Step-by-step explanation:
Your equation would be (x/9)+6=4
Subtract 6 by both sides.
Multiply 9 by both sides.
Then you should get -18.
Which number is closest to √30 ?
5.4
6.2
6.1
5.8
Answer: 5.4
Step-by-step explanation:
[tex]29.16 < 30 < 30.25 \implies 5.4 < \sqrt{30} < 5.5[/tex]
An apartment building has 32 one-bedroom
apartments, 24 two-bedroom apartments,
and 16 three-bedroom
apartments.
How many bedrooms are in the building?
Answer:
128
Step-by-step explanation:
You want the total number of bedrooms in a mix of 1-, 2-, and 3-bedroom apartments.
BedroomsThe total number will be the sum of the products ...
1 × number of 1-bedroom apartments = 1 × 32 = 32
2 × number of 2-bedroom apartments = 2 × 24 = 48
3 × number of 3-bedroom apartments = 3 × 16 = 48
That total is ...
32 +48 +48 = 128
There are 128 bedrooms in the apartment building.
what is the perimeter for a rectangle with a length of 12x - 7 and a width of 5
The perimeter of the rectangle given its dimensions is 24x - 4.
What is the perimeter?A rectangle is a two-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals of equal length that bisect each other at right angles.
The perimeter of rectangle is the sum of the lengths of the four sides of the rectangle.
Perimeter of a rectangle = 2 x (length + width)
2 x [(12x - 7) + 5)
2 x (12x - 2)
24x - 4
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The diagram shows a driveway to be paved. The Lincoln family needs to determine the amount of Hot Asphalt Mix to purchase in order to pave their new driveway, which will have a 6-inch base (thickness). The density of Hot Asphalt Mix depends on mix proportions and types of material used. Assuming a density of 145 pounds per cubic foot, how many tons of asphalt will the Lincoln family need to purchase?
Answer:
bbbbbbbbbbbbbbbb
kjajs
Write the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5)
The equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .
In the question ,
it is given that the required line is perpendicular to y=5/6x+7/6 .
on comparing it with the slope intercept form of the line , we get
slope(m₁)= 5/6
So, the slope of the perpendicular(m₂) line will be
m₂= -1/m₁
m₂= -6/5
hence, slope(m₂) of the perpendicular line = -6/5
Given that the perpendicular line is passing through (-7,5)
substituting the values in slope intercept form (y=mx+c) of the line , we get
5 = (-6/5)(-7) + c
5 = 42/5 + c
c = 5-42/5
= (25-42)/5
= -17/5
y intercept = -17/5
so , the equation of the perpendicular line is y = (-6/5)x -17/5 .
Therefore , the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-7,5) is y = (-6/5)x -17/5 .
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HELP ME PLEASE! My exams tmrw can someone explain one of these
A trail mix recipe calls for 3 cups of pecans for 15 packets. At this rate how many cups of pecans will he need for 90 packets?
Answer:
Step-by-step explanation:
3 cups for 15 packets would be 5 packets for each cup. So 1 cup is 5 packets of trail mix. Which means 5×90= 45
The answer is 45.
A manufacturer determines the cost of making a computer component is $3.232323 write the repeating decimal cost as a fraction and as a mixed number
Answer:
$320/99$3 23/99Step-by-step explanation:
You want the repeating decimal cost ...
[tex]\$3.\overline{23}[/tex]
written as a fraction and as a mixed number.
FractionOne can convert the repeating decimal to a fraction by multiplying it by a power of 10 equal to the number of repeating digits.
This cost number (C) has 2 repeating digits (23), so we want to multiply it by 10^2:
[tex]100C=10^2\times3.23\overline{23}=323.\overline{23}[/tex]
Now, we can subtract the original cost to cancel the repeating decimal fraction:
[tex]100C -C = 323.\overline{23}-3.\overline{23}=320[/tex]
Dividing by the coefficient of C, we have the fraction we want:
[tex]C=\boxed{\dfrac{320}{99}}[/tex]
Mixed numberThis is expressed as a mixed number by figuring the quotient and remainder.
[tex]\dfrac{320}{99}=\boxed{3\dfrac{23}{99}}[/tex]
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In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘
In △ D E F , D E = 7 , E F = 12 , and m ∠ D E F = ( 2 x − 6 ) ∘
A C > D F.
What is the range of possible values for x?
(a) 44 < x < 180
(b) 3 < x < 44
(c) 0 < x < 44
d) none of these
(e) x > 44
(f) 44 < x < 93
(g) x < 44
3 < x < 44
=============================================================
Explanation:
For triangles ABC and DEF we have these two pairs of congruent sides
AB = DE = 7BC = EF = 12In between sides AB and BC is angle ABC = 82
In between sides DE and EF is angle DEF = 2x-6
Since AC > DF, this must mean angle ABC is larger than angle DEF. This is because the longer a side is, the larger the opposite angle will be.
Therefore, this leads to angle ABC > angle DEF
--------------------------------------------------
This is what the steps will look like
angle ABC > angle DEF
angle DEF < ABC
0 < angle DEF < angle ABC
0 < 2x-6 < 82
0+6 < 2x-6+6 < 82+6
6 < 2x < 88
6/2 < 2x/2 < 88/2
3 < x < 44
x is between 3 and 44, excluding both endpoints.
Not sure how to solve this? Any tips are helpful!
likert scales are designed to be in measurement question options: nominal ratio internal ordinal it varies; they can be designed to be any level of measurement.
Likert scales are designed to be ordinal in measurement.
What is Likert scale and why is it used ?
The Likert scale is a psychometric scale that is used in survey questions that are based on it. It is one of the most popular sorts of survey questions. Respondents in a Likert scale survey are given precise options based on whether they "agree" or "disagree" with a particular survey question rather than just selecting "yes" or "no."
Likert scale survey questions are crucial for gauging a respondent's attitude or view toward a certain topic and are therefore a vital component of market research. Likert scales are commonly used to gauge respondents' levels of agreement with diverse claims using a five-, seven-, or nine-point scale. The Likert Scale was created by organizational psychologist Rensis Likert to evaluate the degree of agreement or disagreement on a symmetric agree-disagree scale. In general, a series of statements is used, each intended to look at a construct from a little different angle. The effectiveness of this method lies in the fact that it can be applied to both social science and marketing constructs.
Therefore, likert scales are designed to be ordinal in measurement.
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