Divide the total amount of fabric by the amount needed to create a purse to find how many purses will she be able to make.
Since she has 10 yards of fabric and each purse requires 1/3 of a yard, then, divide 10 over 1/3:
[tex]10\div\frac{1}{3}=\frac{10}{1}\div\frac{1}{3}=\frac{10\times3}{1\times1}=\frac{30}{1}=30[/tex]Therefore, Angelina will be able to make 30 purses using 10 yards of fabric.
the line AB is drawn on the grid.(i) Write down the coordinates of A
The coordinate of point A = (0, 1)
Explanation:Given:
the line AB is drawn on the grid
To find:
the coordinates of A
The coordinates of a point is in the form: (x, y)
To determine the coordinates of A, we will trace the y axis and x-axis.
At point A, x = 0, y = 1
The coordinate of point A = (0, 1)
Find the midpoint of the line segment IJ where I (3,-9) and J (-10,-5)
Answer:
M (-7/2, -7)
Explanation:
Given the coordinates as I(3, - 9) and J(-10, -5), we can go ahead and determine the midpoint of the line segment IJ using the midpoint formula stated below;
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So we have that x1 = 3, x2 = -10, y1 = -9, and y2 = -5.
Let's go ahead and substitute the above values into our formula and simplify;
[tex]\begin{gathered} M\lbrack\frac{3+(-10)}{2},\frac{-9+(-5)}{2}\rbrack \\ =M(\frac{3-10}{2},\frac{-9-5}{2}) \\ =M(-\frac{7}{2},\frac{-14}{2}) \\ =M(-\frac{7}{2},-7) \end{gathered}[/tex]x³=yis this a linear or nonlinear equation
ANSWER:
No, it is not a linear equation
Explanation:
Given:
x³=y
Equations are categorized base on the highest exponent of their variables.
An equation with an exponent less rthan equal to 1 is a linear equation, am equation with an exponent of 3 is a cubic equation
This equation x³=y is a non linear equation. It can also be called a cubic equation because x has an exponent of 3.
Also the satndard form of a linear equation is:
y = mx + b
In this case, x³=y is not in that form, so it is not a linear equatio.
y = x³
I need help on this
To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]What is the answer to this question?
The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.
What is termed as the reflection of the point?A reflection point represents when a figure is built around a single point recognized as point of reflection or the figure's center. On the other side, per each point in the graph, some other point is observed directly opposite it.For the given question.
Line m is the line along which reflection of point P is taken.
Then, line m is called the "perpendicular bisector" of line PP'.
P is the object and P' will be the image of the point P.
Thus, the complete definition of the reflection is given as-
The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.
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hi! im mia, and i need help with math!question: Write a statement that correctly describes the relationship between these two sequences: 6, 7, 8, 9, 10, and 18, 21, 24, 27, 30.
The Solution:
Given the pair of sequences below:
[tex]\begin{gathered} \text{ First sequence: 6,7,8,9,10} \\ \\ \text{ Second sequence: 18,21,24,27,30} \end{gathered}[/tex]We are asked to write a statement that correctly describes the relationship between the two sequences.
The two sequences are both linear sequences. Their common differences are:
[tex]\begin{gathered} \text{ First sequence: d=T}_3-T_2=\text{T}_2-T_1 \\ =8-7=7-6=1 \\ \text{ So, the co}mmon\text{ difference is 1} \end{gathered}[/tex]The general formula for the first sequence is
[tex]T_n=a+(n-1_{})d=6+(n_{}-1)1=6+n-1=5+n[/tex]Similarly,
[tex]\begin{gathered} \text{ Second sequence}\colon\text{ } \\ d=\text{T}_3-T_2=\text{T}_2-T_1 \\ d=24-21=21-18=3 \\ \text{ So, the co}mmon\text{ difference is 3} \end{gathered}[/tex]The general formula for the second sequence is
[tex]S_n=18+(n-1_{})3=18+3n_{}-3=15+3n=3(5+n)[/tex]Thus, the relationship between the two sequences is:
[tex]S_n=3T_n[/tex]Where
[tex]\begin{gathered} S_n=\text{ the second sequence} \\ T_n=\text{ the first sequence} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]S_n=3T_n[/tex]4x- 1/2+ 2/3x combine like terms
Okay, here we heve this:
We need to combine like terms in the following equation:
[tex]\begin{gathered} 4x-\frac{1}{2}+\frac{2}{3}x \\ =(4x+\frac{2}{3}x)-\frac{1}{2} \\ =\frac{14}{3}x-\frac{1}{2} \end{gathered}[/tex]Consider the equation below. 4(x - 4) + 6x = 14 Part A: Enter the value for x that makes the equation true. X = Part B: Explain the algebraic steps you took to get the solution. thea Part C: Explain how you know your solution in Part A is correct.
Part A) To find out the value for x that makes it an identity, (true), we need to solve it.
4(x-4) +6x=14 Distiribute
4x -16 +6x = 14 Combine like terms
2x -16 = 14 Add 16 to both sides
2x = 30 Divide both sides by 2
x =15
Part B) Above explained.
Part C) We can know it by plugging it into the original equation:
4(15 -4) +6(15) = 14
4(11) +90 = 14
44
How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
Four times a number decreased by three is between -15 and 41?
Answer:
The number will lie between -3 and 11
Step-by-step explanation:
Let the number be 'x'
According to the question,
-15 < 4x - 3 < 41
-12 < 4x < 44 (Adding 3)
-3 < x < 11 (Dividing by 4)
Please give me the answers asap the time is running down
Explanation
Given the question
[tex]|x|<13[/tex]To get the values of x, we will consider two possibilities which are:
[tex]\begin{gathered} x\text{ being positive},\text{ so that} \\ x<13 \end{gathered}[/tex]And
[tex]\begin{gathered} x\text{ being negative} \\ -x<13 \\ x>-13 \end{gathered}[/tex]Therefore, the value of x is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: -13So the correct option is
[tex]\begin{bmatrix}\mathrm{Solution\colon}\mleft\lbrace x|\: \mright? & \: -13Option A is correctThe first option is correct
what is the area of a circle with the radius of 10, then rounding the answer to the nearest tenth?
Given a circle with a radius = r = 10 in
The area of the circle is given by the following formula:
[tex]A=\pi\cdot r^2[/tex]Substitute with r= 10
so, the area will be:
[tex]A=\pi\cdot10^2=\frac{22}{7}\cdot10^2=\frac{22}{7}\cdot100=314.2857[/tex]Rounding the answer to the nearest tenth:
So, the answer will be area = 314.3 square inches
Can someone please help me with this problem? I’ve been struggling with it
Consider the following table for interval notation:
First row:
x<0 is the same as:
[tex]-\inftyThen, the graph of that interval looks like:And the interval notation for that inequality is:
[tex](-\infty,0)[/tex]Second row:
-2
The graph of this inequality is:
The interval notation is:
[tex](-2,1\rbrack[/tex]Third row
The inequality that is represented by that interval is:
[tex]-3\le x[/tex]Its graph is:
Fourth row
The interval represented in that graph is:
[tex]\lbrack0,6)[/tex]The inequality represented by that interval is:
[tex]0\le x<6[/tex]A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents.
Let:
C(n,m) = Total cost
n = number of t- shirts ordered
m = fee for each color to be printed on the shirts
Therefore, the total cost of the order would be given by the following equation:
C(n,m) = $2n + $50m
Where:
n = 75
C(n,m) = $2(75) + $50m
C(n,m) = $150 + $50m
the variable y is directly proportional to x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.
Due to y is proportional to x, you have the following equation:
[tex]y=kx[/tex]where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.
k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:
y = kx solve for k
k = y/x replace by known x and y values
k = -0.6/0.24
k = -2.5
Hence, the constant of proportionality is -2.5.
Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:
y = kx solve for x
x = y/
Sofia got a raise from her annual salary of $43,000 to $44,505. whay percent was her raise?
is it a function? X (-2, -1, 0, 1, 2 ) Y (-7, -2, 1, -2, -7 )
To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x
As in the given data each value of x has just one value of y. Then, it is a function.
Dan's dog walking job pays $15 per hour his job as a car wash attendant pays $400 each week Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. Which three equalities can model this situation? select all the correct answers.
Answer:
520<400+15x
15x>120
15x+400>520
Explanation:
Pay of Dan's car wash attendant job =$400 per week
The amount he earns per hour walking dogs = $15
Let the number of hours spent walking dogs in a week = x
Therefore, total earning for walking dogs =$15x
Since he wants to earn more than $520, we have that:
[tex]15x+400>520\text{ (Option F)}[/tex]We can rewrite this as:
[tex]520<400+15x\text{ (Option B)}[/tex]If we collect like terms, we have:
[tex]\begin{gathered} 520-400<15x \\ 120<15x \\ \implies15x>120\text{ (Option C)} \end{gathered}[/tex]So the inequalities are:
0. 520<400+15x
,1. 15x>120
,2. 15x+400>520
? Question
Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest,
compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded
continuously.
If y represents the account balance after t years, which two equations form the system that best models this situation?
For the conditions stated, y=1500+2250t and y=1200+1200t, respectively, will be necessary equations because both Rachel and Jeffery are opening savings accounts. Rachel places $1,500 in a savings account that accrues annual compound interest of 1.5%. Jeffery places $1,200 in a savings account that accrues continuously compounded interest of 1% per year.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
according to given condition,
y=1500+1500*1.5t
y=1500+2250t
y=1200+1200*1t
y=1200+1200t
So the required equation will be y=1500+2250t and y=1200+1200t for the conditions given as Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest, compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded continuously.
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During a heavy rainstorm a city in Florida received 12 1/4 inches of rain in 25 1/2 hours.What is the approximate rainfall rate in inches per hour?
Data:
The city received 12 (1/4) inches of rain in 25 (1/2) hours.
Procedure:
Rewriting the numbers as decimals.
[tex]12\cdot\frac{1}{4}=12.25[/tex][tex]25\cdot\frac{1}{2}=25.5[/tex]To find the approximate rainfall rate in inches per hour, we have to do as follows:
[tex]\frac{12.25}{25.5}\approx0.48\frac{in}{h}[/tex]Rounding the result, we get...
[tex]0.48\approx0.5\approx\frac{1}{2}[/tex]Answer: D. about 1/2 inch per hour
The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28
Here, we want to get the probability that a selected outcome is divisible by 3
What we have to do here is ti select numbers that are multiples of 3 and add their probabilities
From the given table, the outcomes that are multiples of 3 are;
3 and 6 only
So, we proceed to add the probabilities of these outcomes
Mathematically, we have this as;
[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]INT. ALGEBRA: Write an equation that passes through (-10,-30) and is perpendicular to 12y-4x=8
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
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a mother duck lines her 8 ducklings up behind her. in how many ways can the ducklings line up?
In position one, we can have any of the 8 ducks
In position two, we can have 7 ducks, since one has to occupy position one
and so on
then, we have:
[tex]8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=8![/tex]the factorial of 8 is 40320
Find the formula for an exponential function that passes through the 2 points given
The form of the exponential function is
[tex]f(x)=a(b)^x[/tex]a is the initial value (value f(x) at x = 0)
b is the growth/decay factor
Since the function has points (0, 6) and (3, 48), then
Substitute x by 0 and f(x) by 6 to find the value of a
[tex]\begin{gathered} x=0,f(x)=6 \\ 6=a(b)^0 \\ (b)^0=1 \\ 6=a(1) \\ 6=a \end{gathered}[/tex]Substitute the value of a in the equation above
[tex]f(x)=6(b)^x[/tex]Now, we will use the 2nd point
Substitute x by 3 and f(x) by 48
[tex]\begin{gathered} x=3,f(x)=48 \\ 48=6(b)^3 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{48}{6}=\frac{6(b)^3}{6} \\ 8=b^3 \end{gathered}[/tex]Since 8 = 2 x 2 x 2, then
[tex]8=2^3[/tex]Change 8 to 2^3
[tex]2^3=b^3[/tex]Since the powers are equal then the bases must be equal
[tex]2=b[/tex]Substitute the value of b in the function
[tex]f(x)=6(2)^x[/tex]The answer is:
The formula of the exponential function is
[tex]f(x)=6(2)^x[/tex]In the figure, m < 1= (x-6)º and m2 2= (5x).
We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.
Thus, the sum of x-6 and 5x, must be equal to 90°.
(a) Write an equation:
[tex]x-6+5x=90[/tex](b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.
Combining like terms:
[tex]6x-6=90[/tex]Adding 6 from both sides:
[tex]\begin{gathered} 6x-6+6=90+6 \\ 6x=96 \\ \end{gathered}[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{96}{6} \\ x=16 \end{gathered}[/tex]Now that we have x, we find angle 1:
[tex]m\angle1=x-6=16-6=10[/tex]And the measure of angle 2:
[tex]m\angle2=5x=5(16)=80[/tex]How do I solve for x? Would my answer be 27?
SOLUTION
Exterior property of a triangle
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Hence,
[tex](5x+13)^0=(4x+2)^0+(2x-9)^0[/tex]Simplify and evaluate for x
[tex]\begin{gathered} 5x+13^0=4x+2^0+2x-9^0 \\ 5x+13^0=4x+2x+2^0-9^0 \\ 5x+13^0=6x-7^0 \\ \text{Collect like terms} \\ 13^0+7^0=6x-5x \\ 20^0=x \\ \therefore x=20^0 \end{gathered}[/tex]Therefore,
[tex]x=20^0[/tex]A birthday cake has a diameter of 9 inches. A wedding cake has a diameter of 14 inches. What is thedifference in area between the top surfaces of the two cakes?
90.32 square inches
Explanation
Step 1
the area of the circle is given by:
[tex]\text{Area}=\frac{\pi}{4}\cdot diameter^2[/tex]Step 2
find the areas
birthday cake
[tex]\begin{gathered} \text{Area}_b=\frac{\pi}{4}\cdot9^2 \\ \text{Area}_b=\frac{81\pi}{4} \\ \text{Area}_b=\frac{254.46}{4} \\ \text{Area}_b=63.61\text{ square inches} \end{gathered}[/tex]Now, the wedding cake
[tex]\begin{gathered} \text{Area}_w=\frac{\pi}{4}\cdot14^2 \\ \text{Area}_w=\frac{\pi}{4}\cdot196\text{ square inches} \\ \text{Area}_w=49\cdot\pi\text{ square inches} \\ \text{Area}_w=153.93\text{ square inches} \end{gathered}[/tex]Step 3
finally, find the difference
[tex]\begin{gathered} \text{difference}=153.93\text{ square inches-63.61 inches} \\ \text{difference}=90.32 \end{gathered}[/tex]so, the answer is 90.32 square inches
Help please.
We have the equation negative 9 minus this whole expression, 9x minus 6—this whole thing is being subtracted from negative 9—is equal to 3 times this whole expression, 4x plus 6.
Solve the Equation
The value of x in the equation given is x = -4/7.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The information given will be illustrated as:
9 - (9x - 6) - 9 = 3(4x + 6)
9 - 9x + 6 - 9 = 12x + 18
Collect like terms
-9x + 6 = 12x + 18
-9x - 12x = 18 - 6
-21x = 12
Divide
x = 12/-21
x = -4/7
This illustrates the concept of equations.
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The formula for the perimeter of a
rectangle is P = 2l + 2w. Solve the formula for
w.
I need help on a problem
Those are similar triangles, which means, they are related by a ratio
For example in this case,
7: 10
to find x
10 / 7 = x/3
x= 10*3 /7
x= 30/ 7
x= 4.29
____________
