Answer:
y = 6l + 43
Step-by-step explanation:
y=mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y intercept is when x = 0, so the initial cost before buying the laces, which was the cost of the sneakers
b = 43
The slope is you purchase one pair of laces, it increases by 6 each time
m = 6
The y coordinate will represent the total cost spent
y
The x coordinate will represent the total number of laces purchase and we are told that the variable is l
x = l
combine:
y = 6l + 43
A spinner has 4 equal-sized sectors. They are green, yellow, orange, and purple. If you spin the spinner 52 times, how many times do you expect it to land on purple?
If you spin the spinner 52 times, we expect the spinner to land on purple approximately 13 times in 52 spins.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
Since there are 4 equal-sized sectors on the spinner, the probability of landing on purple on any given spin is 1/4.
To find the expected number of times the spinner will land on purple in 52 spins, we can multiply the probability of landing on purple by the total number of spins:
Expected number of times landing on purple = (Probability of landing on purple) x (Total number of spins)
Expected number of times landing on purple = (1/4) x (52)
Expected number of times landing on purple = 13
Therefore, we expect the spinner to land on purple approximately 13 times in 52 spins.
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I honestly am confused on this one
Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.
Region II only please
If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set
[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]
and as a type II region,
[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]
where we solve y = √(x + 1) for x to get x as a function of y.
A. The area of the type I region is
[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]
B. The area of the type II region is of course also
[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]
I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).
Owen’s rectangular garden has a length of (x+3) feet and a width of (x−4) feet. If the area of the garden is 18 square feet, what are the dimensions of the garden?
Answer:
length: 9 units width: 2 units
Step-by-step explanation:
The formula to find the area of a rectangle is length*width (LW)
x+3 is the length and x-4 is the width; together they multiply up to 18
(x+3)(x-4) = 18
x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)
x^2 - x - 12 = 18 (combine like terms on the left side)
x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)
Think what two numbers multiply up -30 and add up to -1 (5 and -6)
(x+5)(x-6) = 0 (factor it)
x+5 = 0 and x-6 = 0 (solve using zero-product property)
x = -5 and x = 6 (solve)
x = 6 (only this one works since you cannot have a negative side length)
(6+3)(6-4) = 18 ? (plug in to find side lengths and check)
9 * 2 = 18 (Correct!)
Answer:
length: 9 ft
width: 2 ft
Step-by-step explanation:
This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.
__
difference in dimensionsThe difference in length between the long side (x+3) and the short side (x-4) is ...
(x +3) -(x -4) = 3+4 = 7 . . . . feet
area factorsThe area formula is ...
A = LW
The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:
18 = 1×18 = 2×9 = 3×6
Of these factor pairs, the values 2 and 9 differ by 7.
The garden is 9 feet long and 2 feet wide.
_____
Additional comment
We can check to see if these numbers are consistent with the given expressions:
x+3 = 9 ⇒ x = 6
x -4 = 6 -4 = 2 . . . . the other dimension we found
__
If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.
The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.
Write each expression in exponential form
[tex]\sqrt[4]{6^5}[/tex]
Answer:
[tex]4*6^\frac{5}{2}[/tex]
Step-by-step explanation:
Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].
[tex]4*6^\frac{5}{2}[/tex]
A minivan with a gross weight of 5700 pounds is parked on a street with a slope of 5°. Find the magnitude of the force required to keep the vehicle from rolling
down the hill. What is the magnitude of the force perpendicular to the hill?
Answer:
The minivan must keep a thrust of 496.79 pounds from rolling down the hill while the perpendicular force to the hill would be 5678.31 pounds. The picture illustrates the solutions to the problem.
The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.
What is a vector?The quantity which has magnitude, direction, and follows the law of vector addition is called a vector.
A minivan with a gross load of 5700 pounds is stopped on a road with a slant of 5°.
Balance the force along the hill. Then the value of the force is given as,
F = W sin θ
F = 5700 x sin 5°
F = 5700 x 0.087
F = 496.79 pounds
The magnitude of the force perpendicular to the hill will be given as,
N = W cos θ
N = 5700 x cos 5°
N = 5700 x 0.9962
N = 5678.31 pounds
The magnitude of the force parallel and perpendicular to the hill will be 496.79 pounds and 5678.31 pounds, respectively.
The diagram is given below.
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Common Core Performance Assessment.
The Name Game
Pairs of students in Mr. Kuan's class are playing the
Name Game. One team member is given a list of attributes
and has to draw a shape to match the description. The other
team member must then name the shape. The first pair to
complete the task wins.
Wilfredo was given a list with the information at the right.
He drew a shape and his partner, Olivia, named it. What shape
did Wilfredo draw? Answer Exercises 4-7 to solve the problem.
.
•
4. MP.1 Make Sense and Persevere What are you asked to do?
What can you do to persevere when solving the problem?
5. MP.6 Be Precise What math terms and numbers can help you
solve the problem?
6. MP.7 Use Structure What do you know about a quadrilateral?
Use what you know to draw and name a shape that matches
the information in the list.
. MP.3 Construct Arguments Is there more than one possible
way for Wilfredo to draw the shape? Explain.
A quadrilateral
2 sides are parallel
2 sides are equal
2 right angles
Attend to precision by
identifying words and
numbers that can help you
solve the problem.
.
.
Answer: Common Core Performance Assessment.
The Name Game
Pairs of students in Mr. Kuan's class are playing the
Name Game. One team member is given a list of attributes
and has to draw a shape to match the description. The other
team member must then name the shape. The first pair to
complete the task wins.
Wilfredo was given a list with the information at the right.
He drew a shape and his partner, Olivia, named it. What shape
did Wilfredo draw? Answer Exercises 4-7 to solve the problem.
.
•
4. MP.1 Make Sense and Persevere What are you asked to do?
What can you do to persevere when solving the problem?
5. MP.6 Be Precise What math terms and numbers can help you
solve the problem?
6. MP.7 Use Structure What do you know about a quadrilateral?
Use what you know to draw and name a shape that matches
the information in the list.
. MP.3 Construct Arguments Is there more than one possible
way for Wilfredo to draw the shape? Explain.
A quadrilateral
2 sides are parallel
2 sides are equal
2 right angles
Attend to precision by
identifying words and
numbers that can help you
solve the problem.
Step-by-step explanation:
» Solve the equation 9(k − 2) = −6.
-
k = 1
Answer:
False
Step-by-step explanation:
9(k-2)=-6 and k=1
9(1-2)=-6
9(-1)=-6
-9=-6
No, -9 doesn't equal -6.
So this system of equations is false.
Hope this helped! :)
If a dress costs $27.00 when it’s on sale for 10% off, what is its original cost?
Answer:
the answer is $24.3
Step-by-step explanation:
Give the degree measure of the arc intercepted by the chord described. Round to the nearest tenth if necessary:
A chord congruent to the radius.
Answer: 60 degrees
Step-by-step explanation:
1. Make a right triangle where the right angle is and label the hypotenuse r.
2. Since the chord is equal to r and a 90-degree angle is formed at the intersection, the chord is bisected. Therefore, the chord segment is 1/2 r.
3. Since we have to solve for the intercepted arc, we must find the central angle ( the angle of the right triangle closest to the dot/center) of the arc, which in this case is the sin, or 0.5r/r.
4. We must get rid of the fraction in the numerator, so multiply both the numerator and denominator by 2 which gets you 1r/2r.
5. The r's cancel out, leaving you with 1/2.
6. Since we have to find the angle measure, you must take the negative sin of 1/2 which is 30 degrees.
7. Finally multiply by 2 since you only solved one bisected portion to get 60 degrees.
Answer:
Step-by-step explanation:
60
The volume of a water tank is 396 m^3. If it is 7.2 m long and 5.5 m wide. what is the depth of the tank ?
Answer :
Depth of the tank is of 10mStep-by-step explanation :
We have been provided with the volume of water tank , it's length and breadth. We are asked to calculate the depth of tank (height), so we all know that water tank is always is in the shape of cuboid.
We would be using the formula of calculating the volume of cuboid and substitute the values in it.
V = l × b × hHere,
l is length b is breadth h is heightWe have :
Volume (V) = 396m³length (l) = 7.2mbreadth (b) = 5.5m height (h) = ?Substituting the values :
>> 396 = 7.2 × 5.5 × h
>> 396 = (72 / 10) × (55 / 10) × h
>> 396 = 72 × 55 × h / 100
>> 396 = 3960 × h / 100
>> 396 × 100 = 3960 × h
>> 39600 = 3960h
>> h = 39600 / 3960
>> h = 3960 / 396
>> h = 10
__________________________
Workers need to know the area of a park to determine how much grass seed to order. A worker drew a sketch of the park to find its area. Which is the area of the park?
The area of the park is 1640 square meters.
What is a quadrilateral?A quadrilateral is a plane shape with four sides and four angles.
The above figure is made up of two quadrilateral; a square and a trapezium.
Analysis:
Area of park = area of square + area of trapezium
Area of park = 1/2(a + b)h + s x s
where a = length of smaller parallel side of the trapezium = 40m
b = length of the larger parallel side = 48m
h = height of trapezium = 35m
s = length of side of square = 10m
Area of park = 1/2(40 + 48)x35 + 10 x 10 = 1640 square meters
In conclusion, the area of the park is 1640 square meters
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The table below shows the ages of 24 students.
Age (years)
16
17
18
19
Number of Students
4
9
8
3
What is the median of these ages?
Answer:
17
Step-by-step explanation:
The median of a data set can simply be thought of as the middle value/number.
You could list all values out:
16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19
and then find what the middle of 24 would be (There are an even number of values, so both numbers in places 12 and 13 are considered the median, meaning that we find the average of these two values to be our median)
the 12th value is 17, and the 13th value is 17, meaning that the median is 17.
-----------------------
You could also calculate what would be 12 "in" from the data set. The first 4 values are 16 (12 - 4 = 8 ; 8 values left to go until middle) And then take the remaining 8 places to find the 12th value (9 - 8 = 1), so you know that the 12th value is the 8th repetition of 17.
There is still one more value of 17, so that is also the 13th placed value.
In this method of finding the middle number, the median is still 17.
The median of these ages is 17.
What is the median?The median exists as the middle number in a sorted checklist of numbers and can be better descriptive of that data set than the average. The median exists sometimes utilized as objected to the mean when there exist outliers in the sequence that might skew the average of the values.
The median of a data set can only be considered as the middle value.
Let the values be 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19
To find the middle of 24 would be (There exist an even number of values, so both numbers in places 12 and 13 exist considered the median) the 12th value stands at 17, and the 13th value stands at 17, indicating that the median exists at 17.
You have to calculate an estimate of 12 "in" from the data set. The first 4 values exist 16 (12 - 4 = 8; 8 values left to go until middle)
Consider the remaining 8 places to estimate the 12th value (9 - 8 = 1)
The 12th value exists in the 8th repetition of 17.
Therefore, the median of these ages is 17.
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Which is a solution for the equation 2x - 4y = 12?
Answer:
So basically you solve for y
so its gonna be -4y = 12-2x, then divide everything by -4 to solve for y which will be equal to -3 + 1/2x
just write it as 1/2x -3 cause its better
Hope that answers your question
Step-by-step explanation:
Answer:
y = -3 +1x/2
Step-by-step explanation:
2x - 4y = 12
-4y = 12 -2x
y = 12/-4 - 2x/-4
y = -3 +x/2
evaluate 20÷(5 X 2/5 )+ 3 pls help
what is 6 divided by a number that will give you 12
▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◀︎
[tex]Hello[/tex] [tex]There![/tex]
We need to find what number, if 6 is divided by it, gives us 12.
This isn't hard, I promise! I am going to take you through a few steps, and we'll find the answer.
Are you ready? Then let's begin...:)
[tex]Procedure:[/tex]
✦ We can think about it as: 6 divided by what number gives us 12?
(let the number be z)
[tex]^6/_z=12[/tex]
Multiply both sides by z
[tex]6=12z[/tex]
Divide both sides by z
[tex]z=^6/_{12}[/tex]
Which is the same as
[tex]z=^1/_2[/tex]
hope it's helpful!wishing you a great day![tex]Greetings![/tex]
--
KAJE PIERS' basketball court is rectangular with a length of 8x feet and a width of (x + 3) feet.
• Determine the perimeter of the basketball court.
• Determine the area of the basketball court.
The perimeter and area of the basketball court is 18x + 6 and 8x² + 24x respectively.
perimeter of a rectangleLength = 8xWidth = (x + 3)Perimeter of basketball court = 2(length + width)
= 2(8x + x + 3)
= 2(9x + 3)
= 18x + 6
Perimeter of basketball court = 18x + 6
Area of basketball court = length × width
= 8x × (x + 3)
= 8x² + 24x
Area of basketball court = 8x² + 24x
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Example
In rectangle PRST, ST and RT are extended as shown.
What is mLUTV?
Since LPTS is a right angle, LPTR and
LRTS are complementary angles.
x + (2x-57) = 90
3x - 57 = 90
3x = 147
X = 49
So, m/UTV = 41°.
(2x-57)
T
LRTS and LUTV are vertical angles,
so m/UTV = m/RTS.
m/UTV = (2x - 57)°
= [2(49) - 57]⁰°
= 41°
S
Name another pair of complementary angles and another pair of vertical angles
Find m
Nani wait what I don't know
At a swimming pool the ratio of children to adults was 3 : 2
Out of 930 people, how many were adults?
Answer:
372
Step-by-step explanation:
We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.
930 / 5 = 186
This means that there are 186 groups of 3 children to 2 adults
So, in each of the 186 groups, there are 2 adults.
Therefore, we can multiply (186)(2)
to find the total number of adults: 372
The number of the children and adult will be 558 and 372.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
At a swimming pool, the ratio of children to adults was 3 : 2.
C / A = 3 / 2
Then solve the equation for C, then the equation will be
C = (3/2)A
The total number of the people is 930. Then the equation will be
C + A = 930
Substitute the value of C in the above equation. Then the equation will be
(3/2)A + A = 930
(5/2)A = 930
A = 930 x (2/5)
A = 372
The number of the adult will be 372.
Then the number of the children will be
C + 372 = 930
C = 930 – 372
C = 558
The number of the children will be 558.
Thus, the number of the children and adult will be 558 and 372.
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Which equation is represented by the graph below?
On a coordinate plane, a curve starts at (0, negative 3) in quadrant 4 and then increases into quadrant 1 and approaches y = 3.
y = e Superscript x
y = e Superscript x Baseline minus 1
y = l n x
y = l n x minus 1
The equation represented by the graph will be y = eˣ. Then the correct option is A.
The missing graph is given below.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The exponential graph is always positive and the graph is also positive of the Real value of x.
The equation represented by the graph will be y = eˣ.
Then the correct option is A.
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Help please
What is the answer???
Which of the following is the most appropriate unit to describe the rate at which a person reads? (2 points) Group of answer choices Minutes per word, because the independent quantity is the minutes Minutes per word, because the independent quantity is the words Words per minute, because the independent quantity is the minutes Words per minute, because the independent quantity is the words
Option third "words per minute, because the independent quantity is the minutes" is the correct choice.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
We have a statement:
Which of the following is the most appropriate unit to describe the rate at which a person reads?
As we know the rate of change is the ratio of change in y to change in x.
y is the dependent quantity and x is the independent quantity.
Rate of change = change in y/change in x
Rate at which a person reads = words/minute
Word is the dependent quantity and minute is the independent quantity.
Thus, option third "words per minute, because the independent quantity is the minutes" is the correct choice.
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Which is a zero of the function f(x)=3x−12?
==================================================
Explanation:
Replace f(x) with 0 and solve for x.
f(x) = 3x-12
0 = 3x-12
3x-12 = 0
3x = 12
x = 12/3
x = 4 is a zero, aka root, of the function
---------------
Check:
f(x) = 3x-12
f(4) = 3(4)-12
f(4) = 12-12
f(4) = 0
The answer is confirmed.
can you figure thus out?
A number is between 300 and 400. If it is divided by 2, the remainder is 1. If it is divided by 4, 6, or 8, the remainder is 3. If it is divided by 10, the remainder is 5. If it is divided by 3, 5, 7, or 9, the remainder is zero. What is the number?
Answer:
315
Step-by-step explanation:
The number is divisible by 3,5,7 and 9. Since 3 is a factor of 9, this number is divisible by 5,7, and 9.
5x7x9= 315.
If f is a fiction defined by the equation y=f (x), then x is called the ___ variable and y is the ___ variable.
E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS
The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
The given function is f(z)=3z-8.
We need to find the value of f(-4), f(2), f(z-7).
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now to find f(-4), replace z from -4.
f(-4)=3(-4)-8=-12-8=-20
Now to find f(2), replace z from 2.
f(2)=3(2)-8=6-8=-2
Now to find f(z-7), replace z from z-7.
f(z-7)=3(z-7)-8=3z-21-8=3z-29.
Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
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Find the measure of the remote exterior angle. m/x (198-5n)
m2y = (5n+37)
m²z = (n+7)
The measure of the remote exterior angle is 128°.
How to calculate the angle?From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)
198 - 5n = 6n + 44
Collect like terms
154 = 6n + 5n
154 = 11n
n = 154/11
n = 14
The value of angle x will be:
= 198 - 5n
= 198 - 5(14)
= 198 - 70
= 128
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Question 16 (5 points)
Find the domain of the function y = 5/3 tan(³/4^x).
A) All real numbers except 0 and odd integer multiples of 4
/3
B) All real numbers except odd integer multiples of 2/3
C) All real numbers except 0 and odd integer multiples of 2/3
OD) All real numbers except odd integer multiples of 4¹
/3
The domain is All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.
What is a function ?A function is defined as a mathematical statement that identifies the relation between a dependent and an independent variable.
A function has a defined range and domain.
In the given function
y = (5/3)tan(3x/4)
Domain is the all the value at which the function is defined .
Tan x is defined for every value except at
x = (2n+1)π/2
The domain of the function y = (5/3)tan(3x/4) is
3x/4 = (2n+1)π/2
x = (2n+1)2π/3
Therefore the domain is All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.
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What is the solution for x in the equation?
-3x+7x-8 = 34+9x-2
OA =
8
OB.
OC. * = -8
OD. = 8
*
118
Answer:
10
Step-by-step explanation:
-3x+7x-8=34+9x-2
(Combine like terms)
4x-8=32
(Add 8 to each side)
4x=40
(Divide by 4)
X=10
A student is reading a newspaper article about a new playground being built in the community. The article says that the playground will benefit the community for a number of reasons. The student wants to figure out whether the author’s claims are strong. In 1–2 sentences, explain how the student could analyze and evaluate the author’s claims.
The student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
How to verify a claim?
We are told that the author of the article is making a claim that a playground will benefit a particular community.
Now, when trying to verify a claim by someone it is very important to try to get facts and figures about that fact to start with before asking for opinions.
Thus, what the student do is that he should look for opinions, the student should check if the author's claims are more opinions or facts. The student should see how the author's claims are helpful.
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Try: Re-reading the question.
Answer: The student should check if the author's article provides more facts or evidence than opinions.
What is the difference between facts and opinions? Facts provide real statements that have been proved with solid evidence by experts. Meanwhile, on the other hand, opinions are what people think. It is more like thinking than something with evidence. It hasn't or can't be proved. If it includes more facts then the author's claims are strong with solid evidence. If it includes more opinions then the author's claims are not strong, they are weak. Since it's only the author's point of view.