A bakery made 10 birthday cakes and 3 wedding cakes in one week. Enter the values that form the ratio of the number of birthday cakes the bakery made to the number of wedding cakes the bakery made.
Find the value of x. Then find the measures of B and C
5 -2 (4a + 1) + 3a = 13 what is (a) equal to a) - 6/5 b) - 2 c) 2 d) 6/5
The solution of the equation 5 -2 (4a + 1) + 3a = 13 is 2/3.
What is an equation?An equation is an expression that indicates the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the equation as follows;
5 -2 (4a + 1) + 3a = 13
Therefore, solving the equation
3(4a+1)+3a=13
12a+3+3a=13
15a+3=13
15a=10
a=2/3
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A book is opened, and the PRODUCT of the two visible page numbers is found to be 306. The equation which correctly represents this situation is A) x2 = 306 B) 2x2 = 306 C) x2 + x = 306 D) 2x2 + x = 306
Answer:
Option C is correct
[tex]x^2+x = 306[/tex]
Step-by-step explanation:
Let the consecutive page number be x and x+1
As per the statement:
A book is opened, and the PRODUCT of the two visible page numbers is found to be 306.
" PRODUCT of the two visible page numbers" translated to x(x+1)
then;
[tex]x(x+1) = 306[/tex]
Using distributive property, [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]x^2+x = 306[/tex]
Therefore, the equation which correctly represents this situation is [tex]x^2+x = 306[/tex]
Last week, maria drove 231 miles. This week, she drove k miles. Using k, write an expression for the total mumber of miles she drove in two weeks?
The expression for the total number of miles Maria drove in two weeks is 231 + k miles.
Explanation:In order to find the total number of miles Maria drove in two weeks, we first need to find the sum of the miles she drove last week and the miles she drove this week.
Last week, Maria drove 231 miles.
This week, she drove k miles.
Therefore, the expression for the total number of miles she drove in two weeks is 231 + k miles.
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70 POINTS!
{Questions 54 & 58}
The function f is one to one. Find to inverse. State the domain & the range of f & f^-1. Graph f & f^-1, & y=x on the same coordinate axes.
Show work please.
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
InversesA function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
for every x in the domain of f, f -1[f(x)] = x, andfor every x in the domain of f -1, f[f -1(x)] = xThe domain of f is the range of f -1 and the range of f is the domain of f -1.
Graph of the Inverse FunctionThe inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
Item 9 A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use xx to represent the number of one-person tubes rented and yy to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
The group rents 11 one-person tubes and 4 cooler tubes and the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Define Variables:
x = number of one-person tubes rented
y = number of cooler tubes rented
Translate information into equations:
Total tubes: The group rents a total of 15 tubes. Translate this into an equation:
x + y = 15
Cost: Each one-person tube costs $20 and each cooler tube costs $12.50. Use these known costs to represent the total cost:
20x + 12.5y = 270
System of Equations:
x + y = 15
20x + 12.5y = 270
Solving for x and y:
Elimination
Multiply the first equation by -12.5:
-12.5x - 12.5y = -187.5
Add the top and bottom equations:
7.5x = 82.5
Divide both sides by 7.5:
x = 11
Substitute the value of x back into the first equation to solve for y:
11 + y = 15
y = 4
The group rents 11 one-person tubes and 4 cooler tubes.
Therefore, the two system of equations are:
x + y = 15
20x + 12.5y = 270
And the solution: x = 11, y = 4.
Complete question:
A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. a one person tube costs $20 and a cooler tube costs $12.50 How many of each type of tube does the group rent? what are the two system of equations?
The system of equations representing the situation is x + y = 15 and 20x + 12.50y = 270. The group rents 11 one-person tubes and 4 cooler tubes.
Let's denote:
x as the number of one-person tubes rented
y as the number of cooler tubes rented
Given:
The cost of renting one-person tube is $20
The cost of renting a cooler tube is $12.50
The total amount spent by the group is $270
We can set up the following system of linear equations to represent the situation:
The total number of tubes rented:
x (number of one-person tubes) + y (number of cooler tubes) = 15 (total tubes)
The total cost spent:
20x (cost of one-person tube) + 12.50y (cost of cooler tube) = 270
So, the system of equations is:
x + y = 15
20x + 12.50y = 270
To find the number of each type of tube rented, we can solve this system of equations.
Now, let's solve this system of equations:
From equation 1, we can express x in terms of y:
x = 15 - y
Substitute this expression for x into equation 2:
20(15 - y) + 12.50y = 270
Now, solve for y:
300 - 20y + 12.50y = 270
-7.50y = -30
y = 4
Now that we have found y, let's substitute it back into equation 1 to find x:
x = 15 - 4
x = 11
So, the group rents 11 one-person tubes and 4 cooler tubes.
Complete Question:
A company that offers tubing trips down a river rents tubes for a person to use and "cooler' tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Usex to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. How many of each type of tube does the group rent?
1 Person Tube = $20, Cooler Tube = $12.50.
The system of equations is ___ and ___.
The group rents ___ one-person tubes and _____ cooler tubes.
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed,32 plant to buy a school newspaper. If 360 students bought papers,predict the number of students enrolled at the school.
The number of students enrolled at the school is 540.
A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed, 32 plan to buy a school newspaper. If 360 students bought papers, predict the number of students enrolled at the school. To solve this, we use a proportion based on the survey results to predict the total enrollment. The proportion of students who plan to buy the newspaper based on the survey is 32 out of 48, which simplifies to 2 out of 3 when reduced. If 360 students actually bought the paper, and assuming the proportion holds for the entire school, we can set up the equation:
2/3 = 360 / total students
To find the total number of students, solve for 'total students':
total students = 360 × 3 / 2
total students = 540
Therefore, based on the survey results and the actual number of newspapers bought, we can predict there are 540 students enrolled at the school.
∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.
Answer:
1= 45
2= 135
Step-by-step explanation:
(did it on usatp)
solve and express the solution set in simplest form. 8x-2/9 = 2/1
Final answer:
The solution to the equation 8x-2/9 = 2/1 is obtained by multiplying both sides by 9, adding 2 to both sides, dividing by 72, and simplifying the fraction to get x = 5/18.
Explanation:
To solve the equation 8x-2/9 = 2/1, we first want to isolate the variable x. Here are the steps to do this:
Multiply both sides of the equation by 9 to eliminate the denominator on the left side, which gives us 72x - 2 = 18.
Add 2 to both sides to get 72x = 20.
Divide both sides by 72 to solve for x, resulting in x = 20/72.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. The solution in simplest form is x = 5/18.
13/40 as a decimal and percent
Answer:
Step-by-step explanation:
13/40 as a decimal = 0.325
0.325
40√ _ 130
120
_100
80
_200
200
13/40 as percent
13/40 x 100% = 0.325 x 100% = 32.5%
what is the ratio of 12 percent
state the degree of the polynomial xy+3x2-7+x
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answer:
The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Another term for dual enrollment is:
Answer:
Another term for dual enrollment is: Concurrent enrollment.
Step-by-step explanation:
Concurrent enrollment or dual enrollment are those programs where students gets enrolled in two schools simultaneously.
There are many types of dual enrollment programs available for students like studying in high school students along with taking college classes etc.
A trail is 7/12 mile long, which trail is shorter, than 7/12
3/8,5/6,3/4,2/3
Among the given options, the trail which is shorter than 7/12 is 3/8
Determining the magnitude of a fractionFrom the question, we are to determine which trail is shorter than 7/12
To determine which of the given fractions is shorter than 7/12, we will express all the fractions in a common denominator
The given fraction are
3/8, 5/6, 3/4, 2/3
Using a common denominator of 48,
7/12 = 28/48
For the given options,
3/8 = 18/48
5/6 = 40/48
3/4 = 36/48
2/3 = 32/ 48
Now, we will compare their numerators. The fraction which has a numerator that is smaller than the numerator in 28/48 is the fraction smaller than 7/12.
Among the fraction, 18 is the smallest of the numerators and it is lesser than 28.
18/48 corresponds to 3/8
Hence, the trail which is shorter than 7/12 is 3/8
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Calculate the average rate of change of the function f(x) over the interval -[4,-1] using the formula. A_____ The value of f(-1) is.B._____The value of f(-4) is. C.________ the average rate of change of f(x) over the interval [-4,-1] is D.________
GRAPH WITH QUESTION: Y intercept:5 X intercept: -2.5 slope: 2
A: [f(-4)-f(-1)]/[-5]
[f(-1)-f(-4)]/[-5]
[f(-1)-f(-4)]/[3]
[f(-4)-f(-1)]/[3]
B. 3
2
-1
C. -4
-3
4
D. -2
-1.5
2
4
The general form of the equation of a circle is x2+y2−4x−8y−5=0.
What are the coordinates of the center of the circle?
Enter your answer in the boxes.
( , )
Answer:
(2,4)
Step-by-step explanation:
If h(x) = 3 + 2f(x) , where f(1) = 3 and f '(1) = 4, find h'(1).
what is the cosine ratio for ∠F? p.s. show how you got your answer!
Answer:
cosF = [tex]\frac{3}{5}[/tex] is the answer.
Step-by-step explanation:
In a right angle triangle cosine of any angle = [tex]\frac{Base}{Hypotenuse}[/tex]
In the given triangle base or adjacent side of the angle is = 6
Hypotenuse given as 10
So by putting the values of hypotenuse and base in the formula
∠F = [tex]\frac{6}{10}=\frac{3}{5}[/tex]
Therefore cosine of angle [tex]cosF=\frac{3}{5}[/tex] is the answer.
roberto has 12 tiles. each tile is 1 square inch. he will arrange them into a rectangle and glue 1-inch stones around the edge. how can roberto arrange the tiles so that he uses the least number of stones?
Answer:
the answer is 4 and 2
Step-by-step explanation:
HELP HELP HELP !!!!!!!!
A jar contained 6 red marbles, 10 green marbles, and 8 blue marbles. A marble was selected at random, the color was recorded, and the marble was placed back in the jar. The table shows the results after 60 trials.
What was the relative frequency of selecting a red marble?
Enter your answer in the box to the nearest percent.
%
Outcome Number of times outcome occurred
Red : 13
Green: 30
Blue: 17
Describe the image of D first reflected across line l, then across line m.
Answer:
Let's approach this step by step.
First, reflect D across line l.
From there, reflect that image across line m.
Your final image should be the letter D.
Check out the image provided.
Hope this helped someone!
Step-by-step explanation:
................
2/5 of house household own pets . Of the household pets 1/3 have cats. What is the fraction of the household own cats
Fraction of household owning pets = [tex] \frac{2}{5} [/tex]
[tex] Fraction \; of \; household \; owning \; cats \; \\\\=\; \frac{1}{3} \; of\; Fraction \; of\; household\; owning \; pets \\\\=\frac{1}{3} \times\frac{2}{5} \\ \\Multiply \; numerator\; with\; numerator\; and\; denominator\; with\; denominator\\\\= \frac{1 \times 2}{3 \times 5}= \frac{2}{15} [/tex]
Conclusion:
The fraction of the household own cats is two-fifteenth
your banking cupcakes for the school dance and your recipe makes 24 cupcakes and needs 2 cups of milk . you need to make 288 cupcakes how many quarts of milk will you need
A rabbit weighed 4,305.6 grams. What is this weight in kilograms?
Final answer:
To convert 4,305.6 grams to kilograms, divide the gram value by 1000, resulting in 4.3056 kilograms, since there are 1000 grams in a kilogram.
Explanation:
The question asks to convert the weight of a rabbit from grams to kilograms. To perform this conversion, we need to know that 1 kilogram is equal to 1000 grams. Thus, we can convert the rabbit's weight by dividing the total grams by 1000 to get the weight in kilograms.
The rabbit weighed 4,305.6 grams. To convert this to kilograms, we divide by 1000:
Divide 4,305.6 by 1000.The result is 4.3056 kilograms.Thus, the weight of the rabbit is 4.3056 kilograms.
Trig question -- please help if you can!
I have to write y = r cos(θ + R) and z = r sin(θ + R) in terms of y, z, and R. I'm not really sure how to do this, so would you mind showing work so I can learn the steps properly? (teacher hasn't taught this super well, haha) Thank you!!
Trigonometric Identities Help!?
simplify 28-(8+4). (4-2).
The value of 28-(8+4). (4-2) is 4
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
28-(8+4). (4-2)
=28-(32-16+16-8)
=28-24
=4
Therefore, the value of the algebra will be 4
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To simplify 28-(8+4)·(4-2), calculate the operations within the parentheses first, resulting in 28-12·2. Multiplying 12 by 2 gives 24, and subtracting this from 28 yields the simplified answer, which is 4.
Explanation:The question requires us to simplify the expression 28-(8+4)·(4-2). We start by simplifying the operations inside the parentheses:
Next, we multiply the results from the parentheses:
Lastly, we subtract this value from 28:
Therefore, the simplified expression is 4.
3(10+2j) please help me