The critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
The critical point is a single value at which the function is not differentiable
The inequality is given as:
(x² - 9 x) / (x - 5) < 0.
Factorize the numerator
x (x - 9) / (x - 5) < 0.
Equate it to 0, we get that:
x (x - 9) = 0 or x - 5 = 0
x = 0 or x - 9 = 0 or x - 5 = 0
So, the critical points will be:
x = 0 or x = 9 or x = 5.
Therefore, the critical points are 0, 5 and 9 for the inequality (x² - 9 x) / (x - 5) < 0.
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The length of a race is 9/10 mile. Andrew wants to place a flag every 1/3 mile. He has
3 flags. Does he have enough flags?
Answer:
Yes, he will have more than enough flags, 1/3*3 flags is 1 mile, the race is only 9/10 miles.
Step-by-step explanation:
Carlos read 150 words in one minute. He
read 5 times as many words as his younger
brother. How many words did his younger brother
read in one minute?
Answer:
30
Step-by-step explanation:
150/5 = 30
Answer: 30
Step-by-step explanation:
I’m confused! About this whole thing can someone help me
Answer:
Step-by-step explanation:try using quizlet
10. A chemist needs to mix an 18% acid solution with a 45% acid solution to obtain 12 liters of
36% solution. How many liters of each of the acid solutions must be used?
Answers:
4 liters of the 18% acid
8 liters of the 45% acid
========================================================
Explanation:
Let's call the bottles A and B
Bottle A has 18% acidBottle B has 45% acidx = amount, in liters, of bottle A used
12-x = amount, in liters, of bottle B used
Bottle A has 0.18x liters of pure acid
Bottle B has 0.45(12-x) liters of pure acid
These amounts must add to 0.36*12 = 4.32 liters of pure acid since we want 12 liters of a 36% solution.
So,
0.18x + 0.45(12-x) = 4.32
0.18x + 0.45(12)+0.45(-x) = 4.32
0.18x + 5.4-0.45x = 4.32
-0.27x + 5.4 = 4.32
-0.27x = 4.32 - 5.4
-0.27x = -1.08
x = (-1.08)/(-0.27)
x = 4 liters which is the amount of bottle A needed
12-x = 12-4 = 8 liters is the amount of bottle B needed
--------------------
Check:
Using 4 liters of bottle A means we contribute 4*0.18 = 0.72 liters of pure acid from this bottle alone.
Using 8 liters from bottle B adds another 8*0.45 = 3.6 liters of pure acid
Then, 0.72+3.6 = 4.32 which matches with the 4.32 mentioned earlier. Therefore, the answer is fully confirmed.
The cost of 4 boxes of pens and 3 boxes of pencils is $22.55. The cost of 3 boxes of pens and 2 boxes of pencils is $16.45. Find the cost of each.
Answer:
One pen is $4.25 and one pencil is $1.85.
Step-by-step explanation:
Let cost of pens be x and cost of pencils be y.
1. 4x+3y=22.55
2. 3x+2y=16.45
Sub. 1.-2.,
x+y=22.55-16.45
x=6.1-y
Sub. x=6.1-y into 1.,
y=1.85
x=4.25
Answer:
Cost of a box of pens = $4.25
Cost of a box of pencils = $1.85
Step-by-step explanation:
Given information:
Cost of 4 boxes of pens and 3 boxes of pencils = $22.55Cost of 3 boxes of pens and 2 boxes of pencils = $16.45Define the variables:
Let x = the cost of a box of pens.Let y = the cost of a box of pencils.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]
[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]
Multiply Equation 1 by 3:
[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]
[tex]\implies 12x + 9y = 67.65[/tex]
Multiply Equation 2 by 4:
[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]
[tex]\implies 12x + 8y = 65.80[/tex]
Subtract the equations to eliminate the term in x:
[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 3x + 2y = 16.45[/tex]
[tex]\implies 3x + 2(1.85) = 16.45[/tex]
[tex]\implies 3x + 3.7 = 16.45[/tex]
[tex]\implies 3x =12.75[/tex]
[tex]\implies x=4.25[/tex]
Solution
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how do you get the 40-4=36units, can you explain
oml i need help with this
Answer:
[tex]2x^{4} - 3x^{2} + 7x[/tex]
Step-by-step explanation:
Define overlapping.
Answer:
to extend over or past and cover a part of The roof shingles overlap each other. 2 : to have something in common with Baseball season overlaps the football season in September. 1 : to occupy the same area in part The two towns overlap.
Step-by-step explanation:
What’s the y and c intercept
Answer:
x - intercept; (80, 0)
y - intercept; (0, ∞)
Step-by-step explanation:
Let Week be w and Amount be A;
We see an inverse proportionality;
[tex]{ \rm{w \: \alpha \: \frac{1}{A } }} \\ \\ { \rm{w = \frac{m}{A} }}[/tex]
m is a constant of proportionality;
When w is 1, A = 68
[tex]{ \rm{ 1 = \frac{m}{68} }} \\ \\ { \rm{m = 68}}[/tex]
Therefore;
[tex]{ \tt{w = \frac{68}{A} + c }} \\ [/tex]
c is a constant;
When w is 0, A is 80
[tex]{ \rm{0 = \frac{68}{80} + c}} \\ \\ { \rm{c = - \frac{17}{20} }}[/tex]
Overall equation:
[tex]{ \rm{y = \frac{68}{x} + \frac{17}{20} }} \\ [/tex]
For x-intercept, y = 0
[tex]{ \rm{ \frac{17}{20} = \frac{68}{x} }} \\ \\ { \rm{x = 80}}[/tex]
For y-intercept, x = 0
y = ∞
.......................
Answer:
Step-by-step explanation:
6.92
Please show work, and brainliest will be yours.
the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cm (false)Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cm (false)Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm" (true)How to get the converse, inverse, and contrapositive statements?
For a conditional statement of the form:
If P, then Q
The other statements are:
Converse: if Q then PInverse: not P, then not Q.Contrapositive: not Q, then not P.Here the conditional is:
"if a figure is a rectangle with sides 2 cm and 3cm, then it has a perimeter of 10cm"
We can identify:
P = a figure is a rectangle with sides 2 cm and 3cm
Q = it has a perimeter of 10cm
Then the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cmThis clearly is false, as we can have a circle with a perimeter of 10 cm.
Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cmThis is also false, the figure can be a rectangle with sides of 1cm and 4 cm for example.
Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm"This is true. if the figure does not have a perimeter of 10cm, then it can't be a rectangle with sides of 2cm and 3cm
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PLEASE HELP URGENT
If m<4=37°, find m<1,m<2,m<3
i would need a photo of the lines to find the values of other angles
Antonio is making bread. He has 9/2 cups of flour. Each loaf uses 2/3 cup of flour
How many whole loaves of bread can Antonio make? Will he have flour left over
?
Antonio can make 6 whole loaves of bread, and he will be left with 1/2 cup of flour, which is used to make 3/4th of a loaf.
In the question, we are given that Antonio is making bread. He has 9/2 cups of flour. We are also informed that each loaf uses 2/3 cup of flour.
We are asked for the number of whole loaves of bread that Antonio can make, and also, we are asked whether he will be left with some flour or not. If yes, then how much?
To find the number of loaves Antonio will make, we will divide the quantity he has by the quantity required for one loaf.
Thus, the number of loaves = (9/2) ÷ (2/3) = 9/2 × 3/2 = 27/4 = 6 3/4.
We will ignore the fractional part as we are asked for whole loaves. Thus, we can say that Antonio will make 6 whole loaves.
Also, he will be left with 3/4th of a loaf, that is, 3/4 of 2/3 cup of flour = 1/2 cup of four.
Thus, Antonio can make 6 whole loaves, and he will be left with 1/2 cup of flour, which is used to make 3/4th of a loaf.
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An open rectangular box (no top) with volume 9 cubic meters has a square base. Express the surface area S of the box as a function of the length x of one of the sides.
In linear equation, S = x2 + 36/x the surface area S of the box as a function of the length x of one of the sides.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let x = length of the sides of the base, and h = the height. The volume is given as 9 m3
Volume = area of base * height
9 = x2*h
So 9/x2 = h
The surface area, S, of the box is:
S = (Area of Base) + 4*(Area of a Vertical Side)
S = x2 + 4 * (xh)
Substitute 5/x2 in place of h:
S = x2 + 4 * x * (9/x2)
S = x2 + 36/x
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Can you help solve this problem?
Answer:
22 and 23
Step-by-step explanation:
The first step is to make an equation that models this problem. Since the two numbers are consecutive, make them [tex]x[/tex] and [tex]x+1[/tex].
Since it says three times the larger number is 47 more than the smaller number, that means
[tex]3 (x+1) = x+47[/tex]
[tex]3x+3 = x+47[/tex]
[tex]2x+3=47[/tex]
[tex]2x=44[/tex]
[tex]x=22[/tex]
The smaller number is 22, and the larger number is 23.
Simplify the polynomial expression. (1/2x +2)(1/2-2x)+(1/4x+7/2)
Simplifying the given polynomial expression is; -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)
How to Simplify Polynomial Expressions?We want to simplify the polynomial expression;
((1/2)x + 2)((1/2) - 2x) + ((1/4)x + (7/2))
Let us expand the first bracket to get;
((1/2)x * (1/2) + (2 * (1/2)) - ((1/2)x * 2x) - (2 * 2x))
⇒ (1/4)x + 1 - x² - 4x
⇒ 1 + (15/4)x - x²
Thus, our expression is now;
(1 + (15/4)x - x²)((1/4)x + (7/2))
This can be multiplied out to give;
(1/4)x + (15/16)x - (1/4)x³ + (7/2) + (105/8)x - (7/2)x²
= -(1/4)x³ - (7/2)x² + (107/8)x + (15/16)x + (7/2)
= -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)
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A change in temperature of 6°C is equivalent to a change in temperature of
°F.
When Arjun makes strawberry milk, he adds 90\,\text{mL}90mL90, start text, m, L, end text of milk for every 20\text{ mL}20 mL20, start text, space, m, L, end text of strawberry syrup. Arjun's brother, Eli, adds 180\,\text{mL}180mL180, start text, m, L, end text of milk for every 45\text{ mL}45 mL45, start text, space, m, L, end text of strawberry syrup.
Which strawberry milk has a stronger strawberry taste?
Eli's strawberry milk has a stronger strawberry taste than Arjun.
According to the question we have been given that
Arjun , adds milk = 90ml
in strawberry syrup = 20ml
Eli, adds milk = 180ml
in strawberry syrup = 45ml
We need to find whose strawberry milk has stronger strawberry taste that is we have to find the concentration of the solution.
The formula for the concentration is given as :
Concentration of the solution = [tex]\frac{volume of solute}{volume of solution}[/tex] * 100%
For Arjun,
Volume of solvent = 90ml
Volume of solute = 20ml
Volume of solution = 20+90 ml = 110 ml
Concentration = (20/110)*100%
= 18.18%
For Eli,
Volume of solvent = 180ml
Volume of solute = 45ml
Volume of solution = 180+45 ml = 225 ml
Concentration = (45/225)*100%
= 20%
As we can see that the Eli's concentration of the solution is greater than Arjun's. Hence Eli's strawberry milk has a stronger strawberry taste.
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Jim and Henry have played 41 tennis matches.
Jim has won 23 times.
Henry won the rest.
a) Estimate the probability that Jim wins.
b) Estimate the probability that Henry wins.
Answer:
a) The probability that Jim wins is 0.56.
b) The probability that Henry wins is 0.44.
Step-by-step explanation:
Hope this helps!
ASAP
the actual distance on a map is 50km and on the map it corresponds to 4cm on map
Answer:
1 cm : 12.5 m
Step-by-step explanation:
Answer: 1250000:1
Step-by-step explanation:
Scale factor: 50 km/4 cm=25 km/2 cm
25 km/2 cm=
(25 * 1000 m)/(2 * 1/100 m)= ==> convert to common measurement which is meters.
(25000 m)/(2/100 m)=
(25000*100 m)/(2*100/100 m)=
2500000 m/2 m=1250000/1
Calculate the coordinates of the points where the line y = 1 - 2x cuts the curve x^2+ y^2 = 2
Answer:
[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]
In decimal form this would be (1, -1) and (-0.2, 1.4)
Step-by-step explanation:
Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets
The equations are
Line Equation [tex]y = 1 - 2x[/tex] (1) and
Circle Equation [tex]x^2+ y^2 = 2[/tex] (2)
[tex]y=1-2x[/tex]
Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]
Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]
So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]
Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a is the coefficient of x ², b is the coefficient of x and c is the constant
So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]
Now,
[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]
= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]
Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]
[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex] [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]
[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]
To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation
[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]
So the two points of intersection are
[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].
In decimal form this would be (1, -1) and (-0.2, 1.4)
See attached graph
PLEASE HELP !! 51 POINTS !!
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given.
Student A
Step 1: cosecant theta over cosecant theta minus sine theta over cosecant theta
Step 2: 1 minus sine theta over the quantity 1 over sine theta end quantity
Step 3: 1 − sin2 θ
Step 4: cos2 θ
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answer:
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Step-by-step explanation:
Brianna practices the piano for 30 minutes per day. Write an expression for the number of hours she practices after n days.
Find the number of hours Brianna practices in 2, 4, and 10 days.
(Thank you in advance for helping me)
Answer: 1/2 * n
1 hour of practice in 2 days
2 hours of practice in 4 days
5 hours of practice in 10 days
Step-by-step explanation:
60 minutes=1 hour
30 minutes * 1 hour/60 minutes=
30*1/60=
30/60=1/2 hour.
1/2 * n
1/2 * 2 = 1 hour of practice in 2 days
1/2 * 4 =
4/2 = 2 hours of practice in 4 days
1/2 * 10=
10/2 = 5 hours of practice in 10 days
Find an expression which represents the sum of (3x+9y) and (5x+7y) in simplest forms
The sum of the expression in simplest form is 8( x + 2y)
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expressions;
(3x+9y) and (5x+7y)
Let's find the sum
3x + 9y + 5x + 7y
collect like terms
3x + 5x + 9y + 7y
8x + 16y
Find common factor
8( x + 2y)
Thus, the sum of the expression in simplest form is 8( x + 2y)
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here are the points on the graph that im finding slope to 3 , 135 and 5 ,225 and 7, 315
EDIT I FOUND THE ANSWER
The slope of the line having points (3,135), (5,225), and (7,315) is 45
Slope:
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
The formula of slope for a line(m)=[tex]\frac{y2-y1}{x2-x1}[/tex]
Given the points (3,135) , (5,225) and (7,315)
Consider any two points, Let's say (3,135) and (5,225).
Slope=[tex]\frac{225-135}{5-3}[/tex]
Slope=45
Therefore, The slope of the line having points (3,135), (5,225), and (7,315) is 45
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The volume of a rectangular pyramid is 1020 units. If the length of the rectangular
base measures 10 units and the width of the rectangular base measures 18 units, find
the height of the pyramid.
The volume of a rectangular pyramid is 1020 units is 5.67 units
The volume of a rectangular pyramid is 1020 units.
volume of rectangular pyramid = LBH
L= length of the rectangular base
B= width of the rectangular base
H= height of the pyramid
here L= 10units B= 18 units
V= LBH
H=V/(LB)
= 1020/(10)(18)
= 5.67 units
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units. The definition of length is interrelated with volume
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Carol Heinrich has lateral filing cabinets that need to be placed along the wall of a storage closet. The filing are each 1 1/2 feet wide and the wall is. 6 feet long. Decide how many cabinets can be placed along the wall
The number of cabinets that can be placed along the wall is 15.
How to calculate the value?It should be noted that in this scenario, we simply have to calculate the perimeter.
This will be:
= 2(length + width)
= 2(1 1/2 + 6)
= 2(7 1/2)
= 15
Therefore, the number of cabinets that can be placed along the wall is 15.
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51 is a multiple of 2,3,5,6,9,10 or none
Based on the numbers given, we can say that 51 is a multiple of 3.
What is 51 a multiple of?51 is not a prime number which means that it has factors and it is a multiple of several numbers.
The factors of 51 include:
1, 3, 17, and 51
Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.
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How is the sentence "10 more than p is -3" written as an equation
p-3 = 10
p+10=-3
p+10=3
p 10-3
The equation for the sentence 10 more than p is -3" will be B. p + 10 = -3.
How to calculate the value?It should be noted that an equation illustrates the relationship between the variables that are given.
In this case, the equation for the sentence 10 more than p is -3" will be:
p + 10 = -3
p = - 3 - 10
p = -13
The value of P is -13.
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I need help with this question
The direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
A mouse is trapped in a maze.
He walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
Based on the data given:
tanA = 8/(-10+15) = 8/5
A = tan⁻(8/5)
A = 58 degrees
The direction will be 58 degrees east-north
Thus, the direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
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