She has a budget of $165, so the total cost of the yoga mat and the classes has to be equal or less than $165.
[tex]C\le165[/tex]The cost is equal to the cost of the yoga mat ($13.25) and the cost of the classes ($12*c, being c the number of classes).
We can write this as:
[tex]C=13.25+12c[/tex]We then can combine both equations and get:
[tex]13.25+12c\le165[/tex]That inequality represents that the total expenses of Natalie have to be equal or less than $165.
Answer: 13.25 + 12c <= 165
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2+6x+19=4x
The intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method is (x + (√3 - 2)/2)² = 77/4.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by:
ax² + bx + c = 0.
In this exercise, you're required to determine the intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method. Therefore, we would re-write the quadratic equation by subtracting 19 from both sides as follows:
x² + 6x + 19 = 4x
x² + 6x + 19 - 19 = 4x - 19
x² + 6x = 4x - 19
x² + 6x - 4x = 19
x² + 2x = 19
In order to complete the square, we would have to add (half the coefficient of the x- term)² to both sides of the quadratic equation as follows:
x² + 2x + (1/2)² = 19 + (1/2)²
x² + 2x + 1/4 = 19 + 1/4
(x + (√3 - 2)/2)² = 77/4
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Complete Question:
What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?
x² + 6x + 19 = 4x
you are running a fuel economy study. one of the cars you find where blue
Answer:
Explanation:
For Blue Car:
Distance = 33 & 1/2 miles
Gasoline = 1 & 1/4 gallons
For Red Car:
Distance = 22 & 2/5 miles
Gasoline = 4/5 gallon
To determine the rate unit rate for miles per gallon for each car, we use the following formula:
[tex]Unit\text{ Rate = }\frac{\text{Distance}}{\text{Gasoline consumption}}[/tex]First, we find the unit rate for blue car:
[tex]\begin{gathered} \text{Unit Rate=}\frac{33\text{ }\frac{1}{2}\text{ miles}}{1\text{ }\frac{1}{4}\text{ gallons}} \\ \end{gathered}[/tex]Convert mixed numbers to improper fractions: 33 & 1/2 = 67/2 and 1 & 1/4 = 5/4
[tex]\begin{gathered} \text{Unit Rate = }\frac{\frac{67}{2}}{\frac{5}{4}} \\ \text{Simplify and rearrange:} \\ =\frac{67(4)}{2(5)} \\ \text{Calculate} \\ =\frac{134\text{ miles}}{5\text{ gallon}}\text{ } \\ or\text{ }26.8\text{ miles/gallon} \end{gathered}[/tex]Next, we find the unit rate for red car:
[tex]\begin{gathered} \text{Unit Rate = }\frac{22\frac{2}{5}}{\frac{4}{5}} \\ \text{Simplify and rearrange} \\ =\frac{\frac{112}{5}}{\frac{4}{5}} \\ =\frac{112(5)}{5(4)} \\ \text{Calculate} \\ =28\text{ miles/gallon} \end{gathered}[/tex]Therefore, the car that could travel the greater distance on 1 gallon of gasoline is the red car.
Growing up, Mrs. Reeder's favorite book was THE ADVENTURES of TOM SAWYER.Now that she is a teacher, she buys 25 copies to read with her class. If each book coast $7.19, how much does Mrs. Reeder spend?
According to the given data we have the following:
Total copies she buys= 25 copies
book cost=$7.19
Therefore, in order to calculate the amount of money that Mrs. Reeder spend we would have to make the following calculation:
Amount of money that Mrs. Reeder spend= quantity of copies * book cost
Amount of money that Mrs. Reeder spend=25 copies*$7.19
Amount of money that Mrs. Reeder spend=$180
The amount of money that Mrs. Reeder spend was $180
Find the midpoint for the line segment whose endpoints are (-10,11) and (-1,-15).
Answer:
( -11/2, -2)
Step-by-step explanation:
Finding the midpoint
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and then divide by 2
(-10+-1)/2 = -11/2
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and then divide by 2
(11+-15)/2 = -4/2 = -2
The mid point is ( -11/2, -2)
Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round youranswer to the nearest tenth if necessary.
Let x be the measure of JK so we get that
[tex]\frac{23}{5}=\frac{x}{3.5}\rightarrow x=3.5\cdot\frac{23}{5}=16.1[/tex]Convert degrees to radians:288° = __ πEnter your answer to the tenths place
Given:
[tex]288^{\circ}[/tex]To convert degrees into radians:
We know that,
[tex]\text{Radian}=\theta\times\frac{\pi}{180}[/tex]So, we get
[tex]\begin{gathered} \text{Radian}=288\times\frac{\pi}{180} \\ =\frac{144\pi}{90} \\ =\frac{16\pi}{10} \\ =\frac{8\pi}{5} \end{gathered}[/tex]Thus, the answer is,
[tex]\frac{8\pi}{5}[/tex]Find the percent change to the nearest percent for the function following
f(x) = 3(1 -.2)^-x
The percentage change of the function given in the task content as required is; 20%.
Percent change in exponential functions.It follows from the task content that the percentage change of the function is to be determined.
The percentage change in exponential functions is represented by the change factor, an expression on which the exponent is applied.
On this note, since the function given is an exponential function in which case, the change factor is; (1 - .2).
It consequently follows that the change implies a 20% decrease. This follows from the fact that 20% is equivalent to; 0.2.
Ultimately, the percentage change of the function is; 20%.
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Write a word problem to fit the following rates: 72 tokens/12 games, ◾️ tokens/10 games
We have to write a word problem using,
• 72 tokens/12 games
,• tokens/10 games
We can first give an information related to 72 tokens PER 12 games.
Then we can ask "how many tokens" per 10 games.
Let us devise a word problem.
The local game center sells tokens to play online games. Jeremy used 72 token to play 12 online games. At this rate, how many token would Jeremy use to play 10 online games?
The above problem uses both the information provided.
Fill in each blanks so that the resulting statement is true
The next step is to subtract -21x from 9x, which obtains 30x.
Then bring down -2 and form the new dividend 30x - 2
Explanation:Given:
[tex]\frac{9x^2+9x\text{ - 2}}{3x\text{ - 7}}[/tex]To determine the next step in the division, we need to solve the long division:
From our calculation, we subtract -21x from +9x and this gives 30x. We bring down -2 to combine with 30x. The result is 30x - 2
The next step is to subtract -21x from 9x, which obtains 30x.
Then bring down -2 and form the new dividend 30x - 2
Using the origin as the center of dilation and a scale factor of k=1/2 find the coordinates of the vertices of the image of the polygon below
Given
Using the scale of 1/2
This means we divide each coordinate by 2
[tex]\begin{gathered} (0,3)=(0,1.5) \\ (-4,0)=(-2,0) \\ (2,0)=(1,0) \\ (0,-3)=(0,-1.5)_{} \end{gathered}[/tex]Which statement describes how the reasonable domain
compares to the mathematical domain?
A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.
Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:
f(w) = 6w – 8
f(2) = 6(2) – 8
f(2) = 12 – 8
f(2) = 4.
For the length of this rectangle, we have:
Length = 2w - 4
Length = 2(2) - 4
Length = 4 - 4
Length = 0
Therefore, the width of this rectangle must be real numbers that are greater than 2.
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Complete Question:
A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.
Which statement describes how the reasonable domain compares to the mathematical domain?
Both the mathematical and reasonable domains include only positive real numbers.
Both the mathematical and reasonable domains include only positive whole numbers.
The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.
Please answer part a and b questions are in the picture
Part A
we have that
A(4) ----> looking at the graph
A(4) means----> population in the year 1994
so
A(4)----> less than 2 million
and
B(4) -----> greater than 2 million
therefore
the answer Part a is option B
Part B
there is only one value of t where A(t)=B(t)
the value of t is 6 (the year 1996)
How do you solve letter b using a subtraction equation with one variable that has a solution of 2/3. A step by step guide would be helpful.
Let's set x as the variable that has a solution of 2/3.
A possible equation is:
[tex]1-x=y[/tex]Now, in order to know the y-value, replace the x-value=2/3 and solve for y:
[tex]\begin{gathered} 1-\frac{2}{3}=y \\ we\text{ can replace 1 by 1/1} \\ \frac{1}{1}-\frac{2}{3}=y \\ \text{The subtraction of fractions can be solved as} \\ \frac{1\times3-1\times2}{1\times3}=y \\ \frac{3-2}{3}=y \\ \frac{1}{3}=y \end{gathered}[/tex]Now, replace the y-value in the initial equation, and we obtain:
[tex]1-x=\frac{1}{3}[/tex]If you solve this equation, you will get x=2/3.
(h) through (5,0), y-intercepto 0
We first need to calculate the slope of the line.
m=(0-0)/(5-0)=0 since the slope is equal to zero we have that the line is horizontal.Then the equation is
[tex](y-0)=0(x-0)\Rightarrow y=0[/tex]the equation is y=0
es26. Name the relationship between the anglesand solve for x.12x + 417x + 2
From the given figure, we can see that the angle (12x+4) and the angle (17x+2) lie on the same straight line.
Theerfore, they are supplimentary to each other.
Which expression is equivalent to cot2B(1 – cos-B) for all values of ß for which cot2B(1 - cos2B) is defined?
From the Pythagorean identity,
[tex]\sin ^2\beta+\cos ^2\beta=1[/tex]we have
[tex]\sin ^2\beta=1-\cos ^2\beta[/tex]Then, the given expression can be rewritten as
[tex]\cot ^2\beta\sin ^2\beta\ldots(a)[/tex]On the other hand, we know that
[tex]\begin{gathered} \cot \beta=\frac{\cos\beta}{\sin\beta} \\ \text{then} \\ \cot ^2\beta=\frac{\cos^2\beta}{\sin^2\beta} \end{gathered}[/tex]Then, by substituting this result into equation (a), we get
[tex]\begin{gathered} \frac{\cos^2\beta}{\sin^2\beta}\sin ^2\beta \\ \frac{\cos ^2\beta\times\sin ^2\beta}{\sin ^2\beta} \end{gathered}[/tex]so by canceling out the squared sine, we get
[tex]\cos ^2\beta[/tex]Therefore, the answer is the last option
during happy hour appetizers are at 30% off how much would each appetize your cost show the original price your math and discounted price
EXPLANATION
Let's see the facts:
Appetizers = 30%
The discount price is given by the following equation:
Discount percentage=
Could you send me a screenshot of the question for better understanding, please?
I'm graphing and I need to find out how mutch it costs for 4.5 inches of the construction. and the construction is $25.50 per inch
You have to determine the cost for 4.5 inches of the construction using the graph.
The height is on the y-axis, and the cost is on the x-axis.
First, locate 4.5 in the y-axis, which is the value in the midpoint between 4 and 5.
Draw a horizontal line until you intersect with the line, then draw a vertical line from the function until the x-axis:
The line crosses the x-axis at the midpoint between values 102 and 127.5 to determine the value at this point you have to average both costs:
[tex]\frac{127.5+102}{2}=\frac{229.5}{2}=114.75[/tex]The cost of 4.5 inches of construction is $114.5
which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices
Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
A committee of six people is chosen from five senators and eleven representatives. How many committees are possiblethere are to be three senators and three representatives on the Committee
SOLUTION
This means we are to select 3 persons from 5 senators and 3 persons from 11 representatives. This can be done by
[tex]^5C_3\times^{11}C_3\text{ ways }[/tex]So we have
[tex]\begin{gathered} ^5C_3\times^{11}C_3\text{ ways } \\ 10\times165 \\ =1650\text{ ways } \end{gathered}[/tex]Hence the answer is 1650 ways
The price of Stock A at 9 A.M. was $15.21. Since then, the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B was $15.96. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The price of the two stocks will be same in 1 hours .
in the question ,
it is given that
the price of the stock A at 9 A.M is $15.21
price increases at the rate of 0.07 each hour .
so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42
and the price of the stock A after x hours from 12 P.M. is given by the equation
stock A = 15.42 + 0.07(x)
the price of stock B at 12 P.M. is $15.96
price decreases at the rate of 0.15 each hour .
the price of the stock B after x hours from 12 P.M. is given by the equation
stock B = 15.96 - 0.15(x)
since the price of the two stocks is same , we equate both the equations .
15.42 + 0.07(x) = 15.96 - 0.15(x)
15.42 + 0.07x = 15.96 - 0.15x
0.15x + 0.07x = 15.42 - 15.21
0.22x = 0.21
x = 0.9545
x ≈ 1
Therefore , The price of the two stocks will be same in 1 hours .
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From the diagram below, if side AB is 36 cm., side DE would be ______.
Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
name the sets of numbers to which the number 62 belongs
62
real numbers (not imaginary or infinity)
rational numbers
Integers ( no fraction, included negative numbers)
Whole numbers (no fraction)
Natural numbers (counting and whole numbers)
For each set of three side lengths in the table, determine how many unique triangles can be formed. Select the appropriate circle in each row.
The first one the 3 sides are equal to 1, this mean that it is a equilater triangle, so it is possible to made exactly one unique triangle.
now for the other triangles we will add the two shortest sides of the triangle, and if they are more than the greater side of the triangle, then it will be a unique triangle, if not there will be more than one triangle
for the second one:
[tex]3+4=7>5[/tex]so the second one have exactly one unique triangle.
for the number 3:
[tex]5+10=15=15[/tex]So in this case there is none unique triangles.
for the number 4:
[tex]6+16=22<26[/tex]So in this case there is none unique triangles.
and for the number 5:
[tex]10+50=60>55[/tex]So we hace exactly one unique triangle.
Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
B
12 + 24R ≤ 100
12+24R 100
24+12R 100
24+12R 100
Answer:
24 + 12R ≥ 100Step-by-step explanation:
List the conditions as per question:
Number of pieces of sushi ordered = 24,Number of pieces required in total at least 100,Number of rolls to be ordered = R,Each roll contains = 12 pieces.Inequality to represent the total number of pieces of sushi is:
24 pieces and R rolls of 12 pieces to get at least 100 pieces, or 24 + 12R ≥ 100Hi, I always have a hard time with these, the whole question is in the picture.
we have that
x1 ----> number of cars with a 7,000 gal capacity
x2 ---> number of cats with a 14,000 gal capacity
x3 ---> number of cars with a 28,000 gal capacity
so
7000x1+14000x2+28000x3=462000
using a 3x3 system of equations solver
the solution is
x1=-2s-4t+66
x2=s
x3=t
The answer is option B
Here is a list of questions about the students and teachers at a school. Select the questions that are statistical questions.
As observed, all the questions in the list can be answered on the basis of some data collection and analysis.
So they all can be considered as statistical questions.
Thus, all the questions in the given list are statistical questions.
1.
If you have to answer the question for most popular lunch choice, you have to collect data of the lunch choices by a large portion of the called population. Then the lunch choice corresponding to highest frequency will be considered as the most popular lunch choice. Since the conclusion is data driven, this is a statistical question.
2.
In order to answer the question, you need to collect the information about the name of school each of the called population is admitted to. If all the students are found to be admitted to the same school, then the name of that school would be the answer.
Here also, the conclusion is data driven, so this is also a statistical question.
3.
To answer this question, you have to gather all the teaching staff of the school, and take individual answers to which subject they teach. The number of teachers who answered math will be the answer for this question.
Here also, the conclusion is data driven, so this is also a statistical question.
4.
To answer this question, you have to gather the individual age of each teacher in the school. The age corresponding to the maximum frequency would be the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
5.
To answer this question, you have to collect data about how much sleep each student gets in the school. Then only you can answer this question.
Since the conclusion is data driven, this is a statistical question.
6.
To answer this question, you have to collect data that how many students travel by which mode of transport to travel from home to school. The mode corresponding to highest frequency is the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
Thus, it is seen that all the six questions are statistical questions.
you decide to work part time at a local supermarket. The job pays $14.50 per hour and you work 24 hours per week. Your employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Complete parts a through F
The gross pay that the employee will get is $276.14.
How to calculate the amount?The job regarding the question pays $14.50 and the person works 24 hours per week. The weekly pay will be:
= 24 × $14.50
= $348
Also, the employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Therefore, the gross pay will be:
= Weekly pay - Federal tax - Fica tax - state tax
= $348 - (10% × $348) - (7.65% × $348) - (3% × $348)
= $348 - $34.80 - $26.62 - $10.44
= $276.14
The pay is $276.14.
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am I correct? Somone please help
Answer:
≠Step-by-step explanation:
7/5 = 1.4
15/10 = 1.5
so 7/5 is not equal to 15/10
the good answer is ≠What is the area of this rectangle?
3
7b ft
7
3
b+21 ft
Step-by-step explanation:
the area of a rectangle is
length × width.
in our case that is
(7/3 × b + 21) × (3/7 × b) =
= 7/3 × 3/7 × b × b + 21 × 3/7 × b =
= 1 × b² + 3×3 × b = b² + 9b = b(b + 9) ft²
so, the area is
b² + 9b = b(b + 9) ft²
remember, an area is always a square "something".
a volume a cubic "something".
so, when the lengths are given in feet, the areas are square feet or ft².