Answer:
C. The length of one lap.
Step-by-step explanation:
In the first four words, the problem statement tells you that L is the number of laps run. It is not the length of one lap.
_____
Comment on the problem presentation
Appropriate punctuation would be very helpful. Apparently, it is a 1/4-mile track, not a 14-mile track. Apparently, the distance is 1 1/2 miles, not 112 miles. Copying and pasting problem text often leaves out the special symbols used on some web sites. Some editing is usually needed.
The science club sold 24 t-shirts last week and 18 T-shirts this week. What is the percentage of decrease in the number of T-shirts sold?
a) 33%
b) 25%
c) 50%
d) 75%
Answer:
D) 75%
Step-by-step explanation:
75% of 24 = 0.75 x 24 = 18
−5y=−5 THANKS
7x+6y=7
Is (5,1) a solution of the system?
Answer:
{x = 1/7 ,y = 1
Step-by-step explanation:
Solve the following system:
{-5 y = -5 | (equation 1)
{7 x + 6 y = 7 | (equation 2)
Swap equation 1 with equation 2:
{7 x + 6 y = 7 | (equation 1)
{0 x - 5 y = -5 | (equation 2)
Divide equation 2 by -5:
{7 x + 6 y = 7 | (equation 1)
{0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:
{7 x+0 y = 1 | (equation 1)
{0 x+y = 1 | (equation 2)
Divide equation 1 by 7:
{x+0 y = 1/7 | (equation 1)
{0 x+y = 1 | (equation 2)
Collect results: Answer: {x = 1/7 ,y = 1
Answer:
No
Step-by-step explanation:
Two roads are represented by lines on a coordinate grid. Two points on each of the roads are shown in the tables.
(A) Write the equation for Road 1 in slope-intercept form.
(B) Write the equation for Road 2 in point-slope form and then in slope-intercept form.
(C) Is the system of equations consistent independent, coincident, or inconsistent? Explain
(D) If the two roads intersect, what are the coordinates of the point of intersection? Use the substitution method and show your work.
Answer:
(A) y - 7 = 2(x -2)
(B) y = -x + 6; y - 5 = -1(x + 1)
(C) Consistent independent
(D) (1, 5)
Step-by-step explanation:
(A) Road 1
(a) Slope
The point-slope formula for a straight line is
y₂ - y₁ = m(x₂ - x₁) Insert the points
3 - 7 = m(0 - 2)
-4 = m(-2) Divide each side by -2
m = -4/(-2) Divide numerator and denominator by-2,
m = 2
=====
(b) y-intercept
y₂ - y₁ = m(x₂ - x₁)
y₂ - 7 = 2(x₂ -2)
y - 7 = 2(x -2)
===============
(B) Road 2
(a) Slope
y = mx + b
Choose point (3,3)
m = (3 - 5)/(3 - 1)
m = -2/2
m = -1
=====
(b) y-intercept
y = mx +b
Choose point (3,3).
3 = -3 + b Add 3 to each side
b = 6
=====
(c) Equation of line (point-slope form)
y = mx + b
y = -x + 6
=====
(d) Equation of line (slope-intercept form)
y - 5 = -1(x - 1)
===============
(C) Consistency
The two roads intersect.
There is only one point of intersection, so this is a consistent, independent system of equations
===============
(D) Point of intersection
(1) y - 7 = 2(x - 2)
(2) y = -x + 6 Substitute (2) into (1)
-x + 6 – 7 = 2(x – 2) Remove parentheses
-x - 1 = 2x – 4 Add 4 to each side
-x +3 = 2x Add x to each side
3 = 3x Divide each side by 3
x = 1 Substitute into 2
=====
y = -1 + 6
y = 5
The point of intersection is (1, 5).
Find the measures of all angles formed by line a parallel to line b with transversal m, if one of the angles is 77°
Answer:
77° or 103°
Step-by-step explanation:
All of the angles are either the given angle or its supplement. Corresponding angles are congruent, as are vertical angles. Any linear pair of angles will add to 180°.
Answer:
77° and 103°
Step-by-step explanation:
77° because it says one of the angles is 77°
103° because two parallel lines are equal to 180°
180°-77° is 103°
The sum of two numbers is 66 and the difference is 8 . What are the numbers?
Answer:
X = 37
Y = 29
Step-by-step explanation:
X + Y = 66
X - Y = 8
------
Solve second equation for X
X = Y + 8
Substitute for X in first equation
Y + 8 + Y = 66
2 * Y = 58
Y = 29
___
X - 29 = 8
X = 37
X = 37
Y = 29
Good Luck,
- I.A. -
Answer:
x = 37 and y = 29
Step-by-step explanation:
x + y = 66
x - y = 8
solve second equation for x
x = y + 8
substitute for x in first equation
y+8 +y = 66
2y = 58
y = 29
x - 29 = 8
x = 37
x = 37 and y = 29
Today's newspaper contains a 20%-off coupon at Old Army. The $100 jacket that you want was already reduced by 40%. What as the final price that you paid for the jacket?
a.
$48
b.
$46
c.
$42
d.
$40
Answer:
Answer is: D. $40
Step-by-step explanation:
20+40=60
100-60=40
Answer:
A 48
Step-by-step explanation:
The Art Club collected $15 from each of its 17 members for dues. It then had $300 in its account. Assume the relationship is linear. Find and interpret the rate of change and the initial value.
The "rate of change" is presumed to refer to the rate at which the balance in the bank account changes as dues are collected from Art Club members. It increases by $15 for each new collection, so we can say ...
... the rate of change is $15 per member.
We further presume that the problem intends the "initial value" to refer to the fact that the 17 × $15 = $255 does not match the full amount of the current Art Club account balance ($300). So, there must have been some balance in the account before collection started. We can interpret that $45 "initial value" as ...
... the account balance before dues collection started is the initial value.
Write an equation of the line that passes through a pair of points: -2,-2 and 5,-5
Answer:
The equation of the line would be y = -3/7x - 20/7
Step-by-step explanation:
To start finding the line of this equation, you need to find the slope. You can do this using the slope equation.
m(slope) = (y2 - y1)/(x2 - x1)
m = (-2 - -5)/(-2 - 5)
m = (-2 + 5)/(-2 - 5)
m = 3/-7
m = -3/7
Now that we have the slope, we can use that and either point in point-slope form to get the equation.
y - y1 = m(x - x1)
y + 5 = -3/7(x - 5)
y + 5 = -3/7x + 15/7
y = -3/7x - 20/7
To find the equation of the line that passes through (-2, -2) and (5, -5), calculate the slope, apply it to the point-slope form using one of the points, then simplify to slope-intercept form, resulting in y = (-3/7)x - 20/7.
To find the equation of the line that passes through the points (-2,-2) and (5,-5), we first need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
Substituting our points into the formula:
m = (-5 - (-2)) / (5 - (-2)) = (-5 + 2) / (5 + 2) = -3 / 7
Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1). Let's use the first point (-2, -2):
y - (-2) = (-3/7)(x - (-2))
Now we simplify and write the equation in slope-intercept form (y = mx + b):
y + 2 = (-3/7)x - 6/7
Subtract 2 from both sides of the equation to solve for y:
y = (-3/7)x - 6/7 - 14/7
y = (-3/7)x - 20/7
The equation of the line that passes through the points (-2,-2) and (5,-5) is y = (-3/7)x - 20/7.
plsss help ;)
Which formula below gives the average rate of change of the function z(x) = -6x + 2 + 3 on the interval -1 ≤ x ≤ 2 ?
Answer:
ave rate of change = (-6)^(2+2) +3 - (-6)^(-1+2) +3
---------------------------------------------
2+1
Step-by-step explanation:
To find the average rate of change
ave rate of change = f(x2) - f(x1)
----------------
x2-x1
We know that x2 = 2 and x1 = -1
ave rate of change = f(2) - f(-1)
----------------
2--1
ave rate of change = (-6)^(2+2) +3 - (-6)^(-1+2) +3
---------------------------------------------
2+1
Answer:
ave rate of change = (-6)^(2+2) +3 - (-6)^(-1+2) +3
Step-by-step explanation:
An anthropologist studies a woman's femur that was uncovered in Madagascar. To estimate the woman's height, he uses the equation h=60+2.5fh=60+2.5f, where hh represents height in centimeters and ff represents length of the femur in centimeters. Which inequality best represents the lengths of the femur that would suggest the woman had a height greater than 160cm?
Choose 1 answer:
Answer:
The inequality [tex]f>40[/tex] represents the length of the femur for which the woman had a height greater than 160cm.
Step-by-step explanation:
The given equation is
[tex]h=60+2.5f[/tex]
Where, h is woman's height in centimeters and f is length of the femur in centimeters.
If woman's height is greater than 160cm, then
[tex]h>160[/tex]
[tex]60+2.5f>160[/tex]
Substract 60 from both sides.
[tex]2.5f>100[/tex]
Divide both sides by 2.5.
[tex]f>40[/tex]
Therefore the inequality [tex]f>40[/tex] represents the lengths of the femur for which the woman had a height greater than 160cm.
(4a^2)b–ab^2–(3a^2)b+ab^2–ab+6 for a=−3, b=2
Answer:
30
Step-by-step explanation:
These are generally easier to evaluate by hand if they are simplified first.
... (4a^2)b -ab^2 -(3a^2)b +ab^2 -ab +6
... = (a^2)b(4 -3) + ab^2(-1 +1) -ab +6
... = a^2·b -ab +6
... = ab(a -1) +6
... = (-3)(2)(-3-1) +6
... = (-6)(-4)+6
... = 24 +6 = 30
Put the values of a = -3 and b = 2 to the expression
[tex]4a^2b-ab^2-3a^2b+ab^2-ab+6[/tex]
[tex](4)(-3)^2(2)-(-3)(2)^2-(3)(-3)^2(2)+(-3)(2)^2-(-3)(2)+6\\\\=(4)(9)(2)+(3)(4)-(3)(9)(2)-(3)(4)-(-6)+6\\\\=72+12-54-12+6+6\\\\=\boxed{30}[/tex]
Which of the following is an equation of the line in the graph?
In the graph, range of the x axis is minus five to five by increment of one and minus four, minus two, two, and four are labeled. The range of y axis is minus thee to five by increment of one and minus two, two and four are labeled. In the graph, line passes through the points (1, 1) and (0, 4).
A. 3x − y = 4
B. 3x + y = 4
C. −3x − y = 4
D. −3x + y = 4
B. 3x +y = 4
Step-by-step explanation:It is perhaps easiest to simply try the equations to see which one works.
For x=0, there are two different kinds of answers:
... A and C: -y = 4
... B and D: y = 4
Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.
___
Using the point (1, 1), you can try choices B and D to see which works:
... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)
... D: -3·1 +1 = -2 = 4 . . . . false
The appropriate choice is the equation of B: 3x +y = 4.
_____
Derive the equation from the given points
There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.
The slope (m) is ...
... m = (change in y)/(change in x) = (4 -1)/(0 -1)
... m = -3
We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...
... y = mx +b
... y = -3x +4
Adding 3x puts this in standard form:
... 3x +y = 4
The equation of the line passing through points (1,1) and (0,4) is y = -3x + 4 or in standard form -3x + y = 4.
Explanation:In the subject of mathematics, when it comes to identifying equations of the line in a graph, we consider the points it passes through. In this case, the line passes through the points (1, 1) and (0, 4). The equation of a line can be found using the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. The slope m between two points can be found using the formula: m = (y2 - y1) / (x2 - x1).
Let's substitute the given points into the slope formula and find the slope: m = (4 - 1) / (0 - 1) = -3. Now, using the slope and one of the points (let's use (0,4)), we substitute into the line formula: y - 4 = -3(x - 0). This simplifies to y = -3x + 4, which aligns with answer D: −3x + y = 4.
Learn more about Equation of a Line here:https://brainly.com/question/33578579
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What is 9.36•10~4 in standard form
The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.
Explanation:
When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.
In this case, we have a negative exponent (-4), so we move the decimal four places to the left:
9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936
Therefore, 9.36×10-4 in standard form is 0.000936.
Solve give your answer in interval notation: 5-4x^2>=8x!!! Please help ASAP!!!:( On the answer key for my final study guide it says that the answer is [-5,1/2] but on the calculator it says that the answer is [-5/2,1/2] I want to know which of these answers is correct!!! :)
Answer:
[-5/2, 1/2] is the correct answer
Step-by-step explanation:
Subtract the left side to compare to zero:
... 4x^2 +8x -5 ≤ 0
... (2x +5)(2x -1) ≤ 0 . . . . factor
... x = -5/2 . . . or . . . x = 1/2 . . . . are the zeros
The factors will differ in sign (the product will be negative) when x is between the zero values. Hence the solution set is ...
... x ∈ [-5/2, 1/2]
_____
Check
When you normalize the leading coefficient of the quadratic to 1, it becomes ...
... x² +2x -5/4 ≤ 0
Now, you know the sum of zeros must be -2 and the product of zeros must be -5/4. The zeros associated with the answer given in your key have a sum of -4.5 and a product of -5/2. It cannot be right.
bruce banner had a taxable income last year of $43,467. his state's income tax rate is 3.9% and his city income tax is 1.8%. what total state and city income taxes did bruce pay last year?
Answer:
Total tax paid by Bruce = $2477.62
Step-by-step explanation:
Bruce banner taxable income last year = $43,467
State's income tax rate = 3.9%
State's income tax = 43467*3.9% = 43467*0.039 = $1695.21
City income tax rate is = 1.8
City income tax = 43467*1.8% = 43467*0.018 =$782.41
Total tax = $1695.21 + $782.41
= $2477.62
Thank you.
Write the equation for the parabola that has x− intercepts (−2−√2 ,0) and (−2+√2 ,0) and passes through the point(−1,1).
Answer:
f(x)= -x²-4x-2
Step-by-step explanation (this way is not the shortest one):
1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0
for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0
for the point (-1;1): a(-1)²+b(-1)+c=1
2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':
[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]
[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]
3. the required equation is: -x²-4x-2
Sam and Kevin both worked hard over the summer. Together they earned a total of $425. Kevin earned $ 25 more than Sam.
a) Write a system of equations for the situation. Use s for the amount Same earned and k for the amount Kevin earned.
b) Graph the equations in the system.
c) Use your graph to estimate how much each person earned.
Solve the system of equations by substitution.
6= -4x + Y
-5x - Y =21
Solve the system by the elimination method.
2x + y=20
6x - 5y=12
Please help I do not understand how to do this ..Thanks
QUESTION 1
a)
Let
[tex]s [/tex]
represent the amount Same earned and
[tex]k[/tex]
represent the amount Kevin earned.
We were told that, they earned $425 dollars together.
This implies that,
[tex]k+s= 425---eqn(1)[/tex]
It was also given that, Kevin earned $25 more than Same.
This implies,
[tex]k-s=25---eqn(2)[/tex]
For equation (1), when
[tex]s=0[/tex]
[tex]k=425[/tex]
We plot the point,
[tex](425,0)[/tex]
When
[tex]k=0[/tex]
[tex]s=425[/tex]
We plot the point,
[tex](0,425)[/tex]
Similarly for the second equation when
[tex]s=0[/tex]
[tex]k=25[/tex]
This gives the point,
[tex](25,0)[/tex]
When
[tex]k=0[/tex]
[tex]s=-25[/tex]
We plot
[tex](0,-25)[/tex]
and draw a straight line through them.
We can see from the graph that the two points intersect at
[tex](225,200)[/tex]
This implies that
[tex]k=225\:and\:s=200[/tex]
Therefore Kevin earned $ 225
and Same earned $ 200
QUESTION 2
The given system is
[tex]6=-4x + y---eqn(1)[/tex]
and
[tex]-5x-y=21---eqn(2)[/tex]
From equation (2),
[tex]y=-5x-21---eqn(3)[/tex]
Put equation (3) into equation (1).
This implies that,
[tex]6=-4x-5x-21[/tex]
Group like terms,
[tex]6+21=-4x-5x[/tex]
Simplify, to get,
[tex]27=-9x[/tex]
[tex]x=-3[/tex]
We substitute this value into equation (3) to get,
[tex]y=-5(-3)-21[/tex]
[tex]y=15-21[/tex]
[tex]y=-6[/tex]
Therefore the solution is
[tex](-3,-6)[/tex]
QUESTION 3
We want to solve,
[tex]2x+y=20---(1)[/tex]
and
[tex]6x -5y=12---(2)[/tex]
We multiply equation (1) by 3 to get,
[tex]6x+3y=60---(3)[/tex]
Equation (3) minus equation (2) will give us,
[tex]8y=48[/tex]
This means
[tex]y=6[/tex]
Put this value into equation (1) to get,
[tex]2x+6=20[/tex]
[tex]2x=20-6[/tex]
[tex]2x=14[/tex]
[tex]x=7[/tex]
The solution is
[tex](7,6)[/tex]
Answer:
Sam earns $200 and Kevin earns $225.
x , y= -3 , -6 by substitution
x , y= 7, 6 by elimination
Step-by-step explanation:
a) Let the amount earned by Sam = s and the amount earned by Kevin = k
We are given, that they both earn total $425 i.e. s + k = 425
Also, Kevin earns $25 more than Sam i.e. k = s + 25
Hence, the system of equations comes out to be:
s + k = 425
-s + k = 25
b) Take s = x and k = y. See the graph plotted below
c) As the intersection point from the graph comes out to be (s,k) = (200,225)
Therefore, Sam earns $200 and Kevin earns $225.
Now, we have the system
-4x + y = 6
-5x - y = 21
We need to use substitution method.
Take y= -5x - 21 from the 2nd equation and put it in the 1st.
We get, -4x - 5x - 21 = 6 i.e. -9x = 27 i.e. x= -3
Now, substitute this value of x in any of the equation to find y.
We get, -5*(-3) - y = 21 i.e. y = 15 - 21 i.e. y = -6
Now, we are given the system,
2x + y = 20
6x - 5y = 12
We need to use elimination method.
Multiply 5 by equation 1. We get,
10x + 5y = 100
6x - 5y = 12
Adding the above equations, we get, 16x = 112 i.e. x = 7
Put this value in any of the equation to find the value of y.
We get, y = 20 - 2x i.e. y = 20 - 2*7 i.e. y = 20 - 14 i.e. y = 6
A class has 7 boys and 10 girls. Select all associated ratios for this class.
7:3
7:10
10:7
17:5
7:17
10:17
3:7
10:3
Answer:
7:10 (boys to girls)
10:7 (girls to boys)
7:17 (boys to everyone combined)
10:17 (girls to everyone combined)
~
A manufacturing company builds construction machinery. It sells 10 machines for $18,100 and 20 machines for $26,600. Which equation models the revenue, R(x), as a linear function of the number of machines built, x ?
Select one:
A. R(x)=750x−10100
B. R(x)=450x+7200
C. R(x)=1200x−4500
D. R(x)=850x+9600
D. R(x) = 850x +9600
Step-by-step explanation:Selling 10 more machines increased revenue from $18100 to $26600, an increase of ...
... $26,600 -18,100 = $8,500
That is, the revenue increased by $8500/10 = $850 per machine.
Only one answer choice has this number in it:
... D. R(x) = 850x+9600
_____
Check
R(10) = 850·10 +9600 = 8500 +9600 = 18,100 . . . . OK
R(20) = 850·20 +9600 = 17000 +9600 = 26,600 . . . . OK
_____
Comment on answer selection
On multiple-choice questions, it is rarely necessary to work out the solution to the problem completely. Usually, it is sufficient to find the one number that discriminates between correct and incorrect answers.
In real life, answers are rarely multiple-choice. You are required to work the problem completely and to figure out how to tell if your answer is correct.
Here, we have worked the problem far enough to find the slope, the amount by which revenue increases when sales increases by 1 unit. The intercept can be found different ways. One of them is to see what number makes the revenue match for one of the "x" values:
... R(10) = 850·10 +b = 18100
... b = 18100 -8500 = 9600
so ...
... R(x) = 850x +9600
We can check this answer by computing R(20), as we have above.
Answer:
R(x)=850x+9600
Step-by-step explanation:
:⊃
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A. (−5, 2)
B. (5, −2)
C. (−5, −2)
D. (5, 2)
B. (5, -2)
Step-by-step explanation:Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.
A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false
B. -2 ≤ 5 -5 . . . true
... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice
C. we know from A that the first inequality will be satisfied
... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false
D. 2 ≤ 5 -5 . . . . false
the original price of the sweater is 18.00 dollares. the sale price is 20% OFF THE ORIGINAL PRICE .what is the amount off the original price?
Answer:
The amount off the original price is $3.6.
Step-by-step explanation:
The original price of the sweater = $18.00
Amount off on the sweater = 20% of the original price of the sweater
=[tex]18.00\times\frac{20}{100}=$3.6[/tex]
The cost of the sweater on the sale = $18.00 - $3.6 = $14.4
The amount off the original price is $3.6.
at a car and truck dealership, the probability that a vehicle is white is 0.25. the probability that it is a car is 0.36. the probability that it is a white car is 0.08. what is the probability that a vehicle is white, given that the vehicle is a car?
Answer:
Probability that a vehicle is white, given that the vehicle is a car :
0.2222
Step-by-step explanation:
A: vehicle is white
probability that a vehicle is white =P(A)= 0.25
B:vehicle is a car
probability that it is a car =P(B)= 0.36
A∩B:vehicle is a white car
P(A∩B)=probability that it is a white car = 0.08
A/B:vehicle is white,given that vehicle is a car
to find P(A/B)
baye's theorem says that
P(A∩B)=P(A/B)×P(B)
⇒ 0.08=P(A/B)×0.36
⇒ P(A/B)=0.2222
Hence, probability that a vehicle is white, given that the vehicle is a car is :
0.2222
Answer: 0.22
Step-by-step explanation:
confirmed
Charlie measured his room and found that it was 10 1/2 feet in length and 7 1/4 feet wide. His brother's room has the same width, but its length is 4/5 the length of Charlie's room. What is the length of Charlie's brother's room. What is the area of Charlie's brother's room?
Answer:
Length of Charlie's brother's room = 8 2/5 feet
Area of Charlie's brother's room = 60 9/10 feet²
Step-by-step explanation:
Width Charlie's room = 7 1/4 = (7 x 4 +1)/4 = 29/4 feet
Length Charlie's room = 10 1/2 = (10 x 2 +1)/2 = 21/2 feet
Length brother's room = 4/5 x 21/2 = (4 x 21)/(5 x 2) = 84/10 = 8 2/5 feet
Area = Length x Width = (42/5 x 29/4) feet² = 1218/20 feet² = 60 9/10 feet²
[tex]\textit{\textbf{Spymore}}[/tex]
Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a ratio of 3:1.
Answer:
Point (1,8)
Step-by-step explanation:
We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.
When a point divides any segment internally in the ratio m:n, the formula is:
[tex][x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}][/tex]
Let us substitute coordinates of point P and Q as:
[tex]x_1=-8[/tex],
[tex]y_1=-4[/tex]
[tex]x_2=4[/tex]
[tex]y_2=12[/tex]
[tex]m=3[/tex]
[tex]n=1[/tex]
[tex][x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}][/tex]
[tex][x=\frac{12-8}{4},y=\frac{36-4}{4}][/tex]
[tex][x=\frac{4}{4},y=\frac{32}{4}][/tex]
[tex][x=1,y=8][/tex]
Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.
Answer:
Step-by-step explanation:
1,8
Consider the equation . x-3=2 1/2
(a) List the three related equations
(b) Choose the related equation that isolates the variable and simplify.
Answer:
Step-by-step explanation:
We have been given an equation:
[tex]x-3=2\frac{1}{2}[/tex]
(a) Related equation means the equation that are equivalent to the given equation.
We can shift 3 on the right hand side of the equation:
(1)[tex]x=3+2\frac{1}{2}[/tex]
We can solve the mixed fraction [tex]2\frac{1}{2}=\frac{5}{2}[/tex] we get.
(2)[tex]x=3+\frac{5}{2}[/tex]
We can solve the right hand side of the equation [tex]x=3+\frac{5}{2}[/tex] we get:
(3)[tex]x=\frac{11}{2}[/tex]
Hence, above three expressions are the related equations of the given equation.
(b) We have to find the related equations that isolates the variable and simplify.
So, basically we can solve for x.
[tex]x=2\frac{1}{2}+3[/tex]
[tex]x=1+3[/tex]
[tex]x=4[/tex].
Multiply.
38⋅45
Express your answer in simplest form.
The simplest form of 38 multiplied by 45 equals to 1710.
To multiply 38 and 45, we'll use the long multiplication method:
38
x 45
------
190 (38 * 5)
+1520 (38 * 40, shift one position to the left)
------
1710
So, 38 multiplied by 45 equals 1710.
Another method is to break down 38 into its factors to simplify the multiplication:
38 = 2 * 19
Now, we can rewrite 38 * 45 as (2 * 19) * 45:
(2 * 19) * 45 = (2 * 45) * 19
= 90 * 19
Now, we can multiply 90 by 19:
90
x 19
-----
180 (90 * 9, shift one position to the left)
+ 0 (90 * 1, with a zero placeholder)
-----
1710
Again, we get the result as 1710.
So, whether we use long multiplication directly or break down the numbers into factors, the result remains the same: 38 * 45 = 1710.
I want to know the value
Answer:
x = 2/5
Step-by-step explanation:
[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]
The value of x is 2/5.
Answer:
x = 2/5
Step-by-step explanation:
x^3 = .008/.125
Take the cubed root on each side
x^3 ^ (1/3) = (.008/.125) ^ 1/3
Using ( a/b) ^c = a^c / b^c and a^b^c = a^ (b*c)
x^(3 *(1/3)) = (.008) ^ 1/3 / (.125) ^ 1/3
x = (.008) ^ 1/3 / (.125) ^ 1/3
x = .2/.5
x = 2/5
simplify (4k4m-8)1/2
Answer:
The answer is: 8km - 4
Step-by-step explanation:
Given: (4k4m - 8)1/2 =
Simplify then multiply 1/2 by each term:
4k4m/2 - 8*1/2 =
16km/2 - 4
8km - 4
Hope this helps! Have an Awesome day!! :-)
hey please help me asap
Attached pictures shows the answers in RED.
A punter kicks a football upward with an initial velocity of 48 feet per second. After how many seconds does the ball hit the ground? Use the formula h=rt−16t2, where h represents height in feet and r represents the initial velocity (rate) in feet per second.
A. 456
B. 791
C. 1111
D. 1863
3 seconds
Step-by-step explanation:For the given problem conditions, the parameters in your formula are ...
... h = 0
... r = 48
Putting these values into the equation, we can solve for t.
... 0 = 48t -16t²
... 0 = 16t(3 -t) . . . . . factored
This will be true for t=0 and for t=3
The ball will hit the ground after 3 seconds.
_____
Comment on answer choices
For the ball to take 456 seconds (more than 7 1/2 hours) to hit the ground, it would have to be launched at 7296 ft/s, several times the speed of sound. Its maximum height would be over 157.5 miles, and all of the usual assumptions about a stationary flat Earth with a uniform gravity field and no air resistance could not apply.
So, we know that 456 seconds is an impossible choice (as are the higher values, such as 1863 seconds). Perhaps that should be 4 5/6 seconds. For that to be the answer, the launch speed would need to be 77 1/3 ft/s, not 48 ft/s.
___
If these are the actual answer choices associated with this problem, it would be a good idea to have your teacher show you how to work it.