Answer:
Andrew failed to change the direction of the inequality
Step-by-step explanation:
You want to know the mistake in Anderw's work solving the inequality ...
−4(x + 8) + 25 ≤ −2 + 1(x − 50)
Solution−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≥ 9
Andrew's mistake was failing to reverse the inequality symbol when dividing by a negative number (-5) at the last step.
__
Additional comment
The last steps of the solution could be written ...
-5x ≤ -45
45 ≤ 5x . . . . . . . add 5x+45 to both sides
9 ≤ x . . . . . . . . . divide by 5 (no reversal of ≤ is needed)
A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?
The dimensions of the rectangular window that gives a maximum area are as follows;
Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet
What is the maximum value of a function?The maximum value of a function is given by the point at which the graph of the function has the highest value.
The parameters of the window are;
Length of the framing material available = 12 ft.
The shape of the window = A semicircle on top of a regular rectangular window
Required; The dimension of the rectangular part of the Norman window that allows the most light
Solution;
Diameter of the semicircular part of the window = The width of the rectangular part
Let x represent the width of the window, we have;
Perimeter of the semicircle = π·x/2
Side length of the rectangular window = (12 - π·x/2 - x)/2
Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2
Area of the semicircle = π·x²÷4
Area of the window, is therefore;
[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]
At the maximum area, of the rectangular part, we have;
[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]
x·π + 2·x - 12 = 0
The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet
The length of the rectangle is therefore;
[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]
The length of the rectangular window = 3 feet
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1. The cost of bell peppers varies directly with the weight of bell peppers, as shown in the table. Write a direct variation equation to represent this relationship. Then identify the constant of variation and interpret its meaning.
The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The difference between two consecutive entries is constant, as we can see = 1.75
⇒ 7 - 5.25 = 1.75
⇒ 8.75-7 = 1.75
⇒ Slope(m) = 1.75
The slope represents the variable's rate of change.
y - 3 = m(x - 5.25)
y - 5.25 = 1.75(x-3)
y = 1.76x
Thus, the constant of variation is 1.75
This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.
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The question seems to be incomplete the correct question has been attached
Which linear function is graphed on the grid?
90
80
70
60
8
50
30
20
10
-9-8-7-6-5- -3 -2 -1
-10
20
у
-30
-40
-50
-60
-70
-80
88
-90
1234
56789
X
The linear function that is graphed on the grid is g(x) = (15/2)x + 45 , the correct option is (d) .
In the question ,
a linear function graph is shown ,
we have to find that linear function .
So , From the given graph we can see that
the graph passes from the points (2 , 60) and (6 , 90)
in order to find the equation , we first need to find the slope .
slope = (90 - 60)/(6 - 2)
= 30/4
= 15/2
So , the equation of the line passing through the points (2 , 60) and slope 15/2 is
(y - 60) = 15/2(x - 2)
y - 60 = (15/2)x - 15
Adding 60 to both the sides ,
we get
y - 60 + 60 = (15/2)x - 15 + 60
y = (15/2)x - 15 + 60
y = (15/2)x + 45
function is (15/2)x + 45
Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45 .
The given question is incomplete , the complete question is
Which linear function is graphed on the grid shown below ?
(a) g(x) = (2/15)x - 6
(b) g(x) = (2/15)x + 45
(c) g(x) = (15/2)x - 6
(d) g(x) = (15/2)x + 45
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If a circle has an Area of 84.9056, find the radius and the circumference of the circle.
(Use π=3.14 and do not round.)
Radius =
Circumference =
Answer: Radius is estimated to = 5.2
Circumference is estimated to = 32.66
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 3 kg, the acceleration of the object is 25 m/s^2. If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.
How can the acceleration be calculated?We were told that the constant force acts upon an object, and the acceleration of the object varies inversely with its mass, which can be interpreted as :
A = k/M
where M is the mass of the object.
A = acceleration
the k= proportionality constant
then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2
then substitute into the equation as:
25 =k*3
k= 25/3
then we were told that when mass is 5 kg, then acceleration will be ?
A= (25/3 )/5 = 1.667m/s^2.
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factorise fully 15x³ + 3x²y
Answer: 3x²(5x+y)
Step-by-step explanation:
15x³ + 3x²y
Apply exponent rule: 15x²x+3x²y
Rewrite 15 as 5*3: 5*3x²x+3x²y
Factor out common terms 3x²: 3x²(5x+y)
Hope this helps!!! :)
Select the equation of the graph line above. (A) y = x + 5 (B) y = 3x + 5 (C) y = x - 5 (D) y = 3x - 5
Answer: (D) [tex]y=3x-5[/tex]
Step-by-step explanation:
Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].
Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].
I need help asap thank you..
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
How many solutions does the equation have?
12x + 6 = 14(2x – 24) because when simplified we get?
a) 6=-6
a) infinitely many solutions
b) x=-6
b) one solution
c) 6=6
c) no solution
Answer:
One solution: x =21.6
Step-by-step explanation:
Equation
12x + 6 = 14(2x – 24) Remove the brackets
Solution
12x + 6 = 28x - 336 Add 336 to both sides.
12x + 6+336 = 28x - 336 Combine
12x + 342 = 28x -336+336
12x + 342 = 28x Subtract 12x from both sides.
12x-12x + 342 = 28x - 12x Combine
342 = 16x Divide by 16
342/16 = 16x/16
21.6=x
A hotel has a budget of $63,750 to repaint the lobby and some hotel rooms. The hotel spent $26,700 on painting the lobby. Each room costs $4,250 to paint. The inequality 26,700 + 4,250n ≤ $63,750 can be used to determine the number of rooms (n) the hotel can repaint.
Which statement about the number of rooms that can be painted is true?
A.
The hotel can repaint 9 rooms.
B.
The minimum number of rooms that can be repainted is 2.
C.
The maximum number of rooms that can be repainted is 2.
D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
The statement that is true about the number of rooms that can be painted using inequality is; D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
How to solve Inequality Word problems?We are given;
Budget of hotel to repaint the lobby and some hotel rooms; $63750
Amount spent on painting the lobby = $26700
Cost to paint each room = $4250
Thus, the inequality to represent the given situation is;
26,700 + 4,250n ≤ $63,750
where;
n is number of rooms the hotel can repaint
Subtract 26700 from both sides of the inequality to get;
4250n ≤ 37050
n ≤ 37050/4250
n ≤ 8.717
Since we can't paint only a portion, we leave it as a maximum of 8 rooms
Looking at the given options, the only correct one is option D.
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A trail mix is made by adding cashews that sell for $2.75 per pound to chocolate candies that sell for $1 per pound. How many of each should be used to get 50 pounds of trail mix that sells for $2 per pound?
Complete the statements.
The 50 pounds of trail mix includes [DROP DOWN 1] pounds of cashews and [DROP DOWN 2] pounds of chocolate candies.
The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.
What pounds of cashew and chocolate candies should be mixed to make the trail mix?let
x = pounds of cashewy = pounds of chocolate candiesx + y = 50
2.75x + y = 50 × 2
Solve the equation simultaneously
x + y = 50
2.75x + y = 100
Substract the equations2.75x - x = 100 - 50
1.75x = 50
x = 50/1.75
x = 28.57 pounds
Substitute into
x + y = 50
28.57 + y = 50
y = 50 + 28.57
y = 21.43 pounds
So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.
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Bimpe rues 5km per hour faster thean she walk- If she runs for 45 minute and walks for 3 hour.
! BE A GOOD NAJM/ NAJMAH, AL
Answer:
See below
Step-by-step explanation:
I think you may have left some info out of your question post, but here is something that may help you:
x = walk speed km/hr
x + 5 = run speed km/hr
45 min = 3/4 hr = .75 hr
(.75)(x+5) + 3 * x = total distance in km
3.75x + 3.75 = total distance
Consider the two points F(-9,0) and G(9,0) as the foci of an ellipse. The length of the major axis is 36. Give the equation of the ellipse.
well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]
[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]
Check the picture below.
The lengths of the three sides of a triangle (in feet) are consecutive even integers. If the perimeter is 60 feet, find the value of the shortest of the three side lengths.
Step-by-step explanation:
3 consecutive even integer numbers :
x
x + 2
x + 4
their sum is the perimeter : 60 ft.
x + x + 2 + x + 4 = 60
3x + 6 = 60
3x = 54
x = 18
the shortest of the 3 sides is 18 ft.
and then we have the other 2 sides with 20 and 22 ft.
Evaluate this expression. (6x103) ÷ (3x102) express your answer in scientific notation.
9514 1404 393
Answer:
2×10¹
Step-by-step explanation:
For division, mantissas divide, and exponents subtract.
Answer:
2*10^1
Step-by-step explanation:
Process
When you divide powers, they can be subtracted -- numerator - denominator in powers
The numbers divide the way you normally would if the question is 6/3 = 2
Numerator power = 3
denominator power = 2
Solution
6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20
20 = 2 * 10^1
2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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Hector also kept track of the remaining gasoline. The equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d)
The missing values for gallons of gasoline remaining is 11,6,1.
Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).
We want to find the missing values for gallons of gasoline remaining.
The given equation is g=16-(1/20)d
When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get
g=16-(1/20)100
g=16-5
g=11
When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get
g=16-(1/20)200
g=16-10
g=6
When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get
g=16-(1/20)300
g=16-15
g=1
Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.
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What is the solution to the equation 3m-4-3/2m+8=0?
Om = -24
Om = -12
Om = -6
O m = -4
Answer:
[tex]m=-8/3[/tex], the options are wrong
Step-by-step explanation:
[tex]3m-4-\frac{3}{2}m+8=0 \\ \\ 6m-8-3m+16=0 \\ \\ 3m+8=0 \\ \\ m=-\frac{8}{3}[/tex]
The question is incorrect.
pls help ill give brainliest
Answer:
b= -2
Step-by-step explanation:
This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2
-Hope this helped
Answer: x=6.
Step-by-step explanation: First go to the Algebra Calculator.
what is 100÷200 need help
on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.
What is division?
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.
To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.
We need to find 100/200,
on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).
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Carlos goes out to lunch. The bill, before tax and tip, was $13.80. A sales tax of 3% was added on. Carlos tipped 23% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:i think its 13.70 or 14.00
Step-by-step explanation:
Answer:
$3.27
Step-by-step explanation:
$13.80 x 1.03 (which will add the 3% to the total, skipping a step) = $14.21
Then take $14.21 x .0.23 which will give you just the tip amount of $3.2683 or rounded to the nearest cent, $3.27
WILL MARK BRAINLIEST
Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x-6
Answer:
y = (-1/4)x + 9/4
Step-by-step explanation:
i got u
30 points for this one man like that is a lot of points
Answer:
it is a subset where you are going to make sets from that one set
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin now has: 6 + m
Please help me w this hehehehehh
Answer:
-25x-45y, because if we have got + and -, so we will write minus.
Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
Answer: 35
Step-by-step explanation:
If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.
Using the quadratic formula to solve 11x2-4x=1, what’s re the values of x
Do I need to apply the chain rule when I derive [ln(g(x))]^2?
To solve the given derivative we need to apply the chain rule.
Given that, [ln(g(x))]².
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].
Find the derivative using the chain and power rules.
ln(g²x²)/x
Therefore, to solve the given derivative we need to apply the chain rule.
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Please help ASAP
See Attached!!
When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.
When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.
The answers:
a) False, degrees not added,b) False, degrees added but not multiplied.Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
The equation of the line in the graph is y = 4x - 9..
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
The line forms a linear equation.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, -9)(3, 3) let's find the slope
m = 3 + 9 / 3 - 0
m = 12 / 3
m = 4
Therefore, let's find the y-intercept using (0, -9).
-9 = 4(0) + b
b = -9
Therefore, the equation is y = 4x - 9.
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