Answer:
41
Step-by-step explanation:
If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:
... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC
.. = 17+24 = 41
_____
Wow! Thank you for an interesting question with a not-so-obvious answer.
_____
A little more detail
The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.
If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...
... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths
For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.
The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.
Putting these ratios and perimeters together, we get ...
... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s
... = (2/(BC) -1/s) × BC × s = 2s -BC
... perimeter ΔAMN = AB +AC
The perimeter of triangle AMN is found using the angle bisector theorem to determine the lengths of AM and AN, and recognizing that MN = BC due to the parallelism. After calculating, the approximate perimeter of triangle AMN is found to be 54.86.
In triangle ABC, the angle bisectors BD and CE intersect at I. A line through I parallel to BC intersects AB at M and AC at N. Perimeter of triangle AMN is found by adding lengths AM, MN, and NA. Since IM is parallel to BC and bisectors divide the angles proportionally, we have:
AM/AB = AI/AD, where D is the intersection of angle bisector BD with BC.
AN/AC = AI/AD, using similar logic.
MN is parallel to BC, so MN = BC due to the properties of parallelograms.
Using AB = 17, AC = 24, and BC = 33, find AM and AN using the proportional segments:
AM = (AI/AD) * AB
AN = (AI/AD) * AC
The perimeter of triangle AMN is AM + MN + AN.
To solve for AI/AD, we use the angle bisector theorem which gives us AI/AD = AB/BC = 17/33. Substituting this into the equations for AM and AN we get:
AM = (17/33) * 17
AN = (17/33) * 24
Computing these we find:
AM = 8.77 (approximately)
AN = 13.09 (approximately)
Lastly, we add AM, AN, and BC to find the perimeter:
Perimeter = AM + AN + MN
Perimeter = 8.77 + 13.09 + 33 = 54.86 (approximately)
This is the approximate perimeter of triangle AMN.
If f(x) = x3 – x2 – 3, which of the following is equal to g(x) = f(2 – x)?
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
Answer:
-x^3+5x^2-8x+1, which is choice A
======================================
Work Shown:
f(x) = x^3 - x^2 - 3
f(x) = (x)^3 - (x)^2 - 3
f(2-x) = (2-x)^3 - (2-x)^2 - 3 ................ see note 1 (below)
f(2-x) = (2-x)(2-x)^2 - (2-x)^2 - 3 ........... see note 2
f(2-x) = (2-x)(4-4x+x^2) - (4-4x+x^2) - 3 ..... see note 3
f(2-x) = -x^3+6x^2-12x+8 - (4-4x+x^2) - 3 ..... see note 4
f(2-x) = -x^3+6x^2-12x+8 - 4+4x-x^2 - 3 ....... see note 5
f(2-x) = -x^3+5x^2-8x+1
----------
note1: I replaced every copy of x with 2-x. Be careful to use parenthesis so that you go from x^3 to (2-x)^3, same for the x^2 term as well.
note2: The (2-x)^3 is like y^3 with y = 2-x. We can break up y^3 into y*y^2, so that means (2-x)^3 = (2-x)(2-x)^2
note3: (2-x)^2 expands out into 4-4x+x^2 as shown in figure 1 (attached image below). I used the box method for this and for note 4 as well. Each inner box or cell is the result of multiplying the outside terms. Example: in row1, column1 we have 2 times 2 = 4. You could use the FOIL rule or distribution property, but the box method is ideal so you don't lose track of terms.
note4: (2-x)(4-4x+x^2) turns into -x^3+6x^2-12x+8 when expanding everything out. See figure 2 (attached image below). Same story as note 3, but it's a bit more complicated.
note5: distribute the negative through to ALL the terms inside the parenthesis of (4-4x+x^2) to end up with -4+4x-x^2
Answer:
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
Step-by-step explanation:
–x3 + 5x2 – 8x + 1
–x3 + 7x2 – 16x – 15
x3 + 5x2 + 8x + 1
x3 – 7x2 + 16x – 15
A motorboat, that has speed of 10 km/hour in still water, left a pier traveling against the current of the river. Forty-five minutes after the boat left the pier, the motor of the boat broke, and the boat began drifting with the current. After three hours of drifting with the current, the boat was back at the pier where it had started. What is the speed of the current of the river?
Answer:
2 km/h
Step-by-step explanation:
distance = speed × timetime = distance/speedLet c represent the speed of the current of the river in km/h. Then the speed of the boat upstream is (10-c). In 3/4 hour, the distance traveled upstream is ...
... distance upstream = (3/4)·(10 -c)
The time taken to travel the same distance downstream is given as 3 hours. The speed in that direction is c, so we have ...
... 3 = distance upstream/c = (3/4)(10 -c)/c
Multiplying this equation by 4c, we get ...
... 12c = 3(10 -c)
... 15c = 30 . . . . . . . . add 3c
... c = 2 . . . . . . . . . . . divide by 15
The speed of the river current is 2 km/h.
Answer:
2km/h
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.
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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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.
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.
Solve the equation.
x + 7/8 = 4
A. x = 4 7/8
B. x = -3 1/8
C. x = -4 7/8
D. x = 3 1/8
Answer:
D. x = 3 1/8
Step-by-step explanation:
x + 7/8 = 4
The first step is to subtract 7/8 from each side
x + 7/8 - 7/8 = 4 - 7/8
x = 4 - 7/8
We need to borrow from the 4. It become 3 8/8
x = 3 8/8 - 7/8
x = 3 1/8
Answer:
I believe the answer would be D.
Step-by-step explanation:
hey please help me asap
Attached pictures shows the answers in RED.
What is the value of this expression (29+18)+(17-8) / 8
48 1/8
Step-by-step explanation:As written, it is evaluated as ...
... 47 + 9/8 . . . . . . . . parentheses are evaluated first
... = 47 + 1 1/8 . . . . . . then division
... = 48 1/8 . . . . . . . . then addition
_____
A decent calculator will evaluate this for you according to the order of operations. A Google or Bing search box will do that, too.
Of items produced by a factory, 40% come from line i and 60% from line ii. eight percent of the items produced on line i and 10% of the items produced on line ii are defective. an item is chosen at random. find the probability that it is not defective.
Answer:
Step-by-step explanation:
I don't know how is to speak it English correctly but is the teoreme of whole probability
P(A1)=0.08*0.4=0,032 is probability to choose defective item line I
P(A2)=0.1*0.6=0.06 is probability to choose defective item line II
P(B)=P(A1)+P(A2)=0,032+0.06=0.092 probability to choose defective item
P(C)=1-P(B)=0.908 the probability that it is not defective
To finish an order in time the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. In how many days was the company supposed to finish the order?
Answer:
9 days.
Step-by-step explanation:
If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.
Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.
If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.
If you had to use an equation:
Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:
number of items = 40 items/day * x days = 60 items/day * (x - 3) days
40x = 60(x - 3) = 60x - 180
180 = 20x
x = 9
9 days is the desired answer.
Answer:
9
Step-by-step explanation:
After joining two pieces of a picture frame together, a frame maker checks her work by measuring the diagonal (see the illustration). The sides of the frame form a right angle and the measurements are as follows: a = 12 in. and b = 5 in.
You have towels of three sizes. The length of the first is 3 /4 m, which makes up 3/ 5 of the length of the second. The length of the third towel is 5 /12 of the sum of the lengths of the first two. What part of the third towel is the second?
Answer:
9/10
Step-by-step explanation:
In ratio units, the relative lengths of the first, second, and third towels are ...
... 1 : 3/5 : (5/12)·(1 +3/5)
... = 1 : 3/5 : 2/3
Then the fraction the second towel is of the third towel is ...
... (3/5)/(2/3) = (3/5)·(3/2) = 9/10
answer:
the answer is 2/3
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
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!! :-)
The sum of 7 times a number and 9 is 5 . Use the variable c for the unknown number.
c - the number
The sum of 7 times a number and 9 is 5:
[tex]7c+9=5[/tex] subtract 9 from both sides
[tex]7c=-4[/tex] divide both sides by 7
[tex]\boxed{c=-\dfrac{4}{7}}[/tex]
(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]
Mr. O'Conell spends 15% of his salary on food. He then spends 24% of it on transportation and saves the remaining $1,830. What is his salary?
Answer:
what do i do if my math skills are bad
Step-by-step explanation:
Let the Salary of Mr. O'Conell be : S
Given : Mr. O'Conell spends 15% of his Salary on Food
[tex]\mathsf{\implies 15\%\;of\;Salary(S) = (\frac{15}{100} \times S) = 0.15 \times S}[/tex]
Given : Mr. O'Conell spends 24% of his Salary on Transportation
[tex]\mathsf{\implies 24\%\;of\;Salary(S) = (\frac{24}{100} \times S) = 0.24 \times S}[/tex]
Given : After Spending on Food and Transportation, He saves $1830
Money Spent on Food + Money spent on Transportation + Remaining Money should be Equal to his Total Salary
[tex]\mathsf{\implies 0.15S + 0.24S + 1830 = S}[/tex]
[tex]\mathsf{\implies 0.39S + 1830 = S}[/tex]
[tex]\mathsf{\implies S - 0.39S = 1830}[/tex]
[tex]\mathsf{\implies 0.61S = 1830}[/tex]
[tex]\mathsf{\implies S = \frac{1830}{0.61} }[/tex]
[tex]\mathsf{\implies S = 3000}[/tex]
Mr. O'Conell's Salary is $3000
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).
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.
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.
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.
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:
:⊃
Solve for x and y if: 2x + 3y = 5 and 3x + 4y = 4
[tex]\left\{\begin{array}{ccc}2x+3y=5&|\text{multiply both sides ny 3}\\3x+4y=4&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x+9y=15\\-6x-8y=-8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad \boxed{y=7}\\\\\text{put the value of y to the first equation}\\\\2x+3(7)=5\\\\2x+21=5\qquad\text{subtract 21 from both sides}\\\\2x=-16\qquad\text{divide both sides by 2}\\\\\boxed{x=-8}\\\\Answer:\ \boxed{x=-8\ and\ y=7}[/tex]
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°
A metalworker has a metal alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 52% copper alloy?
The metalworker should use
_______ of the metal alloy that is 20% copper and ___ kilograms
of the metal alloy that is 60% copper
(Type whole numbers.)
I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.
That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.
_____
Using an equation
If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...
... 0.60x + 0.20(100 -x) = 0.52·100
... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20
... x = 32/0.40 = 80 . . . . . kg of 60% alloy
... (100 -80) = 20 . . . . . . . .kg of 20% alloy
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:
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:
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.
HELP!! will give points for brainliest
Denise earns $60 per day, plus $15 for each new customer she signs up. What is an explicit function rule for the amount Denise earns in a day, assuming that she signs up n customers?
an=
Answer:
f(x) = 60 + 15n
Step-by-step explanation:
if the start off amount is 60, so we can simply start it with 60 + ...
If she gets 15 for each customer, and the amount of customers is equal to n, then this can be written by 15n ( 12 * n )
Simply put these two parts together:
60 + 15n
So in a function:
f(x) = 60 + 15n