1) Writing that statement as an inequality we have:
[tex]\begin{gathered} \frac{y}{2}>22\text{ } \\ Multiplied\text{ by 2 on both sides} \\ y>44 \end{gathered}[/tex]2) Hence, we can say that if one-half of a number y is more than 22
then y > 44
E Which point is located at (4, -2)? 3 G 다
The given coordinate tells us that when x = 4, y = - 2
Looking at the graph, the point where x = 4 and y = - 2 is point D
What is the effect on the graph of f(x) = 1 when it is transformed to g(x) = 1 + 17? O A. The graph of f(x) is shifted 17 units up. O B. The graph of f(x) is shifted 17 units to the left. O C. The graph of f(x) is shifted 17 units to the right O D. The graph of f(x) is shifted 17 units down.
What is the effect on the graph of f(x) = 1 when it is transformed to g(x) = 1 + 17? O A. The graph of f(x) is shifted 17 units up. O B. The graph of f(x) is shifted 17 units to the left. O C. The graph of f(x) is shifted 17 units to the right O D. The graph of f(x) is shifted 17 units down.
we have that
f(x)=1 ----> is a horizontal line (y intercept is (0,1)
f(x)=1+17=18 -----> is a horizontal line (y -intercept is (0,18)
therefore
there are a translation 17 units up
the answer is the option ADetermine whether the event below is mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary. Rolling a pair of dice and doubles or a sum of 6 is rolled.Not mutually exclusive.
The given event is not mutually exclusive.
Remember that mutually exclusive events are those events that can't be both true, that is, if one event is true, then the other is false.
The probability of this event would be
[tex]P=\frac{6+5-1}{36}=\frac{10}{36}=\frac{5}{18}\approx0.28[/tex]Therefore, the probability is 0.28, or 28%, approximately.The main printer in the Ivy Tech library can produce an average of 639copies every hour. For every 36 pages, it costs the college $0.06 forelectricity and supplies. If the library is open from 9AM to 9PM, howmuch money does the college use on printing each day?
You know that:
- An average of 639 copies per hour can be produced by the main printer.
- The cost for electricity and supplies is $0.06 for every 36 pages produced.
- The library is opened for 12 hours.
Let be "x"the cost (in dollars) for electricity and supplies for 639 copies produced in 1 hour.
You can set up the following proportion:
[tex]\frac{0.06}{36}=\frac{x}{639}[/tex]Solve for "x":
[tex]\begin{gathered} (\frac{0.06}{36})(639)=x \\ \\ x=1.065 \end{gathered}[/tex]Knowing that the cost for electricity and supplies for 639 copies produced in 1 hour is $1.065, youo can multiply it by 12, in order to calculate how much money the college uses on printing each day:
[tex](1.065dollars\text{)}(12)=12.78dollars[/tex]The answer is: The college uses $12.78 on printing each day.
the function g(x) was obtained by transforming f(x)=1/x Use the description of the transformation to write the equation representing g(x).f(x) Is vertically stretched by a factor of 2, reflected about the X axis, then shifted 5 units.
Since f(x) is vertically strectched by a factor 2, we get
[tex]f(x)\longrightarrow\frac{2}{x}[/tex]next, it is reflectec about the x-axis, then we have
[tex]\frac{2}{x}\longrightarrow-\frac{2}{x}[/tex]Finally, its shifted 5 units on x axis, then we have
[tex]-\frac{2}{x}\text{ --> }-\frac{2}{x+5}[/tex]which corresponds to option 2
The vertices of ACDE are C(-1, 1), D(3,5), and E(5. - 4). Translate ACDE using vectorr(3. – 1).Enter the correct ordered pair for C', D', and E'. Do NOT use any spaces in your answer.C'D'E
C (-1,1)
D (3,5)
E (5,-4)
now we are going to translate ACDE using vector r(3,-1)
C'(2,0)
D'(6,4)
E'(8,-5)
use distributive property to fill in the blanks (4×7) - (4×3) = ___ × (7-3)
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.2% a.) how much will the interest amount to ?b.) what amount must Miguel pay Julio at the end of 6 months ?
Given:
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition.
He agreed to pay Julio in 6 months with simple annual interest at 6.2%
So, the interest = r = 6.2% = 0.062
the time = t = 6 months = 6/12 years = 1/2 year
a.) how much will the interest amount to?
The interest is given by the formula:
[tex]I=P\cdot r\cdot t[/tex]Substitute with the given values:
[tex]I=500\cdot0.062\cdot\frac{1}{2}=15.5[/tex]So, the interest = I = $15.5
b.) what amount must Miguel pay Julio at the end of 6 months?
So, Miguel will pay the amount that he borrowed and the interest
so, he will pay:
[tex]P+I=500+15.5=515.5[/tex]So, the answer will be: $515.5
make your own quadratic function in standard form then determine the vertex of your propolis the axis of symmetry the y-intercept then graph using Circle curve line tools
The general form of a quadratic equation is expressed as
ax^2 + bx + c
An example of a quadratic equation is
2x^2 - 4x - 2
The graph of this equation is shown below
The vertex of the graph is value of x and y at the bottom of the curve. Looking at the curve, the vertex is (1, - 4)
The axis of symmetry is the vertical line that divides the curve into two equal halves. The axis of symmetry of this curve is the line, x = 1
The y intercept is the point where the curve cuts through the y axis. From the graph, y intercept = - 2
A teenager in a highrise building looks out his window at another building across the street and realizes a crime is being committed. If the buildings are 60 feet apart, and the teenager is looking down into the other building with an angle of depression of 20°, how many feet lower is the floor where the crime is being committed? If each floor is 10 feet, about how many floors down is it?
Hello!
The first step to solving this exercise is to draw the situation, look:
Now we can solve this exercise. Notice that we want to know the height that I called "X".
To find it, we must use the tangent of 20º, look:
[tex]\tan (20\degree)=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} \frac{0.364}{1}=\frac{60}{x} \\ \\ 0.364x=60 \\ x=\frac{60}{0.364} \\ \\ x\cong164.83 \end{gathered}[/tex]If each floor is 10 feet:
[tex]\frac{164.83}{10}=16.483\text{ floors}[/tex]If you have to approximate, you can say that it is 16.5 floors down.
Mira was solving for y in the following problem l. However, she did something wrong. Describe and correct the error in the work shown.2x-y=5y=-2x+5
The initial equation is:
[tex]2x-y=5[/tex]Then, in order to isolate y, we need to subtract 2x from each side of the equation:
[tex]\begin{gathered} 2x-y-2x=5-2x \\ -y=-2x+5 \end{gathered}[/tex]Then, we multiply both sides by -1:
[tex]y=2x-5[/tex]The equation Mira wrote is y=-2x+5. So we can see that her error was not changing the signs of the terms in the right side of the equation.
In order to correct her error, we just need to change the signs in the right side of the equation:
[tex]\begin{gathered} y=-(-2x+5) \\ y=2x-5 \end{gathered}[/tex]The segments shown below could form a triangle.
9
A
C
C
B
4
B
A
15
True or false
No/False - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
In light of the question -In geometry, a triangle is a closed two-dimensional figure with three sides, three corners, and three vertices.Triangles are considered polygons with the fewest sides. In this article, we will discuss in detail what a triangle is, its types, properties and formulas.Learn more about triangles here. In geometry, a triangle is a type of polygon with three sides and three vertices. A triangle is considered a three-sided polygon.The sum of the three angles of a triangle is 180°. A triangle is contained in a single plane. There are six types of triangles based on their side and angle measurements.A triangle has only three sides joined by corners. Therefore, no matter what kind of triangle it is, it always has three sides.CalculationNo - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
While 9+15 >4
and 4+15 >9
9+4 is not greater than 15 - so this triangle cannot be made.
learn more about triangles here :
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Tom's Bakery recently spent a total of $800 on new equipment, and their average hourlyoperating costs are $10. Their average hourly receipts are $90. The bakery will soon makeback the amount it invested in equipment. What would the total expenses and receipts bothequal?TimeelapsedWrite a system of equations, graph them, and type the solution1.000SmartScore
Hello there. To solve this question, let's call the average hourly operating costs as C and the average hourly receipts as R.
We get that 90R - 10C = 800, since this is the amount the bakery has spent on equipments and it is said he will soon get back this invested money.
Dividing both sides by 10, we get 9R-C = 80
The graph will be a line. We want to find then C = R, so we can get:
-R + 9R = 80
8R = 80
R = 10
So, we have a cost of $100 and receipt of $900 in order to get back that money.
supposed your friend was born, your friends parents deposited $2000 in an account paying 3.5% interest compound monthly. what will the account balance be after 15 years?
If we have a deposit of $2000, invested at an an annual interest rate of 3.5% compounded monthly, we can calculate the final value of that deposit in 15 years as:
[tex]FV=PV(1+\frac{r}{m})^{m\cdot n}[/tex]where:
FV: final value of the deposit.
PV: initial deposit (PV = 2000)
r: annual interest rate (r = 0.035)
m: subperiod (as the compound is monthly, and there are 12 months in a year, we have m = 12).
n: period (n=15)
Then, the expression gives us a value of:
[tex]\begin{gathered} FV=PV(1+\frac{r}{m})^{m\cdot n} \\ FV=2000(1+\frac{0.035}{12})^{12\cdot15} \\ FV\approx2000(1.002917)^{180} \\ FV\approx2000\cdot1.689 \\ FV\approx3378 \end{gathered}[/tex]Answer: the account balance after 15 years will be $3378.
a. If Links printing store will make a 150 copies for the cost of $15.00, then what is theunit rate of price per copy?
ANSWER
$0.10
EXPLANATION
We have that 150 copies are made for a total cost of $15.00
The unit rate of price per copy is the price of each copy of the printing.
To find the unit rate of price per copy, we have to divide the total price by the total number of copies.
So, we have:
[tex]\frac{15}{150}\text{ = \$0.10}[/tex]This means that the unit rate of price per copy is $0.10
A changes and8. The graph of y = cos z is transformed to y = a cos (2-c) + d by a vertical expansion by a factor of 2, then translated units right and 2 units up.The new equation is:y=2 cos (x + 5) - 2y= 2 cos (x - 1) +2y= {cos (x - 1) + 2y=2 cos ( - ) - 2
Option 2 is correct.
For this assignment, leave all answers as simplified fractions.A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the theoretical probabilityof drawing one tile at random for each of the following.1. P(M)2. P(S)3. P)4. P(not M)5. P(not S)6. P(not 1)
ANSWER
[tex]\begin{gathered} 1)\frac{1}{11} \\ 2)\frac{4}{11} \\ 4)\frac{10}{11} \\ 5)\frac{7}{11} \end{gathered}[/tex]EXPLANATION
From the given question;
MISSISSIPPI has 11 words
The number of M is 1
The number of S is 4
Hence;
1.
[tex]P(M)=\frac{1}{11}[/tex]2. P(S);
[tex]P(S)=\frac{4}{11}[/tex]4. P(not M) ;
[tex]\begin{gathered} 1-P(M) \\ =1-\frac{1}{11} \\ =\frac{10}{11} \end{gathered}[/tex]5. P(not S);
[tex]\begin{gathered} P(not\text{ S})=1-P(S) \\ =1-\frac{4}{11} \\ =\frac{7}{11} \end{gathered}[/tex]4. Describe the pattern. Choose the correct answer below. O A. The difference in the powers is equal to the sum of the bases. OB. The difference in the powers is equal to the difference in the bases. O C. The sum of the powers is equal to the sum of the bases. OD. There is no pattern.
Problem
Solution
Lets analyze one by one the possible options and we have:
O A. The difference in the powers is equal to the sum of the bases.
FALSE 2^2 and 1^2, we have 2-2=0 is different from 2+1=3
OB. The difference in the powers is equal to the difference in the bases.
FALSE , again if if we check 2^2 and 1^2 we have 2-1=1 and 2-2=0 and are not equal
O C. The sum of the powers is equal to the sum of the bases.
FALSE if we check 2^2 and 1^2 we have 2+1=3 and 2+2=4 and are not equal
OD. There is no pattern.
The best choice would be this one
Jeff's restaurant sells hamburgers. The amount
charged for a hamburger (h) is based on the cost for a plain hamburger plus an additional charge for each topping (t) as shown in the equation below.
h = 0.60t+5
What does the number 0.60 represent in the equation?
A. the number of toppings
B. the cost of a plain hamburger
C. the additional cost for each topping
D. the cost of a hamburger with 1 topping
Answer:
Step-by-step explanation:
b the cost of the plain burger
What criteria can you use to show these two triangles are congruent?choice:SSAAASHLSAS
ANSWER
SAS
EXPLANATION
SAS criterion is an acronym for Side-Angle-Side criterion. Two triangles are congruent if the two sides and included angle of one triangle are equal to the corresponding sides and included angle of the second triangle, according to this criterion.
Please help!
1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to
determine fuel consumption of both cars. Car A travel x² + 3x miles and Car B travels 2x + 8 miles. Based upon tire wear (x), the cars will use x² + 4x gallons of fuel.
a.) What is the mileage
(miles/gallons) for each car?
Car A:
Car B:
b.) What is the total mileage for both cars in simplified form? (3 points)
Total:
2.)Solve for x: (5 points)
3r+3=−x+6
The mileage of Car A, Car B, and the average of is (x+3)/(x+4), 2/x and [tex]\frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
It is given that the distance traveled by the car A = x² + 3x
And the distance traveled by car B = 2x + 8
The mileage is given by mile/gallon.
So, the mileage of Car A = distance traveled by car A/gallons of fuel used.
Then,
Mileage of Car A = [tex]\frac{x^{2} +3x }{x^{2} +4x} =\frac{x(x +3)}{x(x+4)} = \frac{x+3}{x+4}[/tex] miles /gallons
Similarly, the mileage of Car B = distance traveled by car B/gallons of fuel used.
Then,
Mileage of Car B = [tex]\frac{2x+8}{x^{2} +4x} = \frac{2(x+4)}{x(x+4)} =\frac{2}{x}[/tex] miles/gallons
Now, the total mileage of A and B is the average of car A and car B,
Mileage of Car A + Mileage of Car B = [tex]\frac{x^{2} +3x }{x^{2} +4x} + \frac{2x+8}{x^{2} +4x} = \frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
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How many general tickets should the college sell to maximize revenue
Notice that, since 5000 tickets are reserved for students, there are 13000 available tickets that can be acquired by students or the general public.
Since the cost of a general public ticket is greater than that of a student ticket, we can increase the revenue to its maximum by selling the remaining 13000 tickets to the general public only.
Therefore, the answer is 13,000
Two farmers John and Harry cultivates twovarieties of rice namely Basmati and Naura.The sale price of these varieties of rice by boththe farmers are as follows:John sells Basmati at $5.00/kg and Naura at$3.50/kg. While Harry sells Basmati at$6.50/kg and Naura at $2.60/kg.Use the matrix to present the prices of rice bytwo farmers.
Sales price for the rice varieties:
John:
Basmati cost = $5 per kg
Naura cost = $3.5 per kg
Harry:
Basmati cost = $6.5 per kg
Naura cost = $2.6 per kg
Writing in the form matrix:
[tex]\begin{gathered} let\text{ first column represent basmati rice} \\ let\text{ the 2nd column represent Naura rice} \\ In\text{ matrix, x and y can be represented as:} \\ \begin{bmatrix}{x\text{ column}} & {y\text{ column}} \\ {}{{x\text{ column}}} & {{y\text{ column}}}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = Basmati, y = Naura} \\ \\ \begin{bmatrix}{5.00} & {3.50} \\ {6.50} & {2.60}\end{bmatrix}\text{ \lparen option B\rparen} \end{gathered}[/tex]Hello! I need help with this questionTriangle DOG was rotated to create triangle D'O'G''. Describe the transformation using details and degrees.
Answer:
180 degrees rotation about the origin
Explanation:
First, we need to identify the coordinates of DOG and D'O'G' as follows
D(-2, 1) ---> D'(2, -1)
O(-3, 3) ---> O'(3, -3)
G(1, 1) ---> G'(-1, -1)
Therefore, the rule for the transformation is
(x, y) ---> (-x, -y)
This rule is the rule for a 180 degrees rotation about the origin. So, the transformation is a 180 degrees rotation about the origin.
FACTS:In 2010, the glacier was 1000 meters in length; it had retreated 255 meters in 15 years.Questions:1. Calculate the average annual rate of retreat of the glacier
Let's represent the given (length, years) as (x, y)
at time 0 year, the glacier is 1000 meters
at time 15 years, the glacier retreated 255 meters and that's 1000 - 255 = 745
so we have the points (0, 1000) and (15, 745)
Using the slope formula :
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where m represents the average annual rate of retreat.
[tex]m=\frac{745-1000}{15-0}=\frac{-255}{15}=-17[/tex]The average annual rate of retreat of the glacier is 17 meters per year
A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle melted to 1.5 inches.I think the way to start this is x = 1.5 inches but I'm stuck.
Given the following question:
Candle = 4 inches tall
Burns at a rate of 0.6 inches per hour
x = hours
[tex]4-0.6x=1.5[/tex]4 representing the height of the candle
0.6 representing the rate the candle burns
x = the amount of time in hours the candle burns
1.5 = the height of the candle after it burned for x hours
[tex]\begin{gathered} 4-0.6x=1.5 \\ 0.6x=4-1.5 \\ 0.6x=2.5 \\ x=2.5\div0.6 \\ x=4.166 \\ =4.166\text{ hours} \end{gathered}[/tex]&Maps CClever | Portal e Learner Home e Learning Path - Eng... Mail- Makayla D. Submit Test R Pretest: The Real Number System rag the tiles to the boxes to form correct pairS. atch the pairs of equivalent expressions. (-1440)-1+ 46+ (54-26)+(28+) 8-15 -3-(8+6) -11 -10+8)+(76-5) -15 Dor Moxt
hello
to solve this question, we need to write out the expressio
okay I think your name was Mrs Huggins can you please help me with the rest of this fraction I'm really struggling and I accidentally signed off because of a network error I'm really sad please
In a previous session we worked on the subtraction of the mixed numbers 2 1/8 and 1 7/8 and reached the following result:
[tex]2\frac{1}{8}-1\frac{7}{8}=\frac{17}{8}-\frac{15}{8}=\frac{2}{8}[/tex]This fraction 2/8 can be simplified. Both values 2 and 8 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator of the fraction by 2:
[tex]\frac{2\div2}{8\div2}=\frac{1}{4}[/tex]what happens to F(x) when x is negative but approaches zero for the function F(x)=1/x whose graph is show below?*PHOTO*
We have the following function:
[tex]F(x)=\frac{1}{x}[/tex]According to the graph, the function tends to minus infinity when x takes negative values close to zero.
Answer: B. F(x) is a negative number
The functions f and g are defined as follows:f(x)=2x^2-3xg(x)=-5x-1Find f(-3) and g(7)Simplify your answers as much as possible
f(x) = 2x^2 - 3x
f(-3) = 2(-3)^2 - 3(-3)
f(-3) = 2(9) + 9
f(-3) = 18 + 9
f(-3) = 27 This is the first solution
g(x) = -5x - 1
g(7) = -5(7) - 1
g(7) = -35 - 1
g(7) = -36 This is the second solution