Answer:
[tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]
Step-by-step explanation:
Two functions are inverse where their composition results in a variable only:
[tex]f(g(x))=x[/tex]
So, we have to insert the right numbers in place of letters a, b, c and d, to fulfil this definition. Those value would be: [tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]
Replacing these values, we have:
[tex]f(x)=x+2[/tex]
[tex]g(x)=1x-2=x-2[/tex]
Applying the composition [tex]f(g(x))[/tex]:
[tex]f(g(x))=\frac{cx-d+a}{b}[/tex]
We observe that with this values, these functions are inverse, because it composition results x.
[tex]f(g(x))=\frac{1x-2+2}{1}=x[/tex]
Therefore, the values are [tex]a = 2; \ d = 2; \ c=1; \ b=1[/tex]
****UGRENT****A popular board game company hired a group of students to build a gigantic float for an upcoming parade. The main attraction of the float will be two large number cubes. The side length of each number cube must be 18 ft.
How much material is need to cover all sides of both number cubes?
Answer:3,888
Step-by-step explanation: hope I helped
A recent survey of 2500 seventh graders from across the state shows 2 out of 5 of them do not eat breakfast. How many of the students surveyed do not eat breakfast?
Out of the 2500 seventh graders surveyed, 1000 of them do not eat breakfast, based on the proportion of 2 out of 5.
To find out how many seventh graders surveyed do not eat breakfast, we can use the proportion of students who do not eat breakfast from the survey results.
Given:
- Total number of seventh graders surveyed: 2500
- Proportion of seventh graders who do not eat breakfast: [tex]\( \frac{2}{5} \)[/tex]
To find the number of seventh graders who do not eat breakfast, we multiply the total number of seventh graders surveyed by the proportion who do not eat breakfast:
[tex]\[ \text{Number of students not eating breakfast} = \frac{2}{5} \times 2500 \]\[ \text{Number of students not eating breakfast} = \frac{2 \times 2500}{5} \]\[ \text{Number of students not eating breakfast} = \frac{5000}{5} \]\[ \text{Number of students not eating breakfast} = 1000 \][/tex]
Therefore, out of the 2500 seventh graders surveyed, 1000 of them do not eat breakfast.
when 6 less than 3 lots of a number is doubled the result is 18
The unknown number is 5.
Let's represent the unknown number as "x."
The statement "6 less than 3 lots of a number" can be written as 3x - 6.
The next part of the statement is "doubled the result is 18," which translates to 2 * (3x - 6) = 18.
Now, we can solve for "x" using the equation:
2 * (3x - 6) = 18
Expand the expression on the left side:
6x - 12 = 18
Next, isolate "6x" by adding 12 to both sides:
6x = 18 + 12
6x = 30
Now, solve for "x" by dividing both sides by 6:
x = 30 / 6
x = 5
Therefore, the unknown number is 5.
To verify:
"6 less than 3 lots of 5" is (3 * 5) - 6 = 15 - 6 = 9.
"Double the result" of 9 is 2 * 9 = 18, which matches the given result. Hence, the solution is correct.
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anyone can help make sure my answers is right. Thanks
Which shows the decimal 0.14 repeated expressed as a fraction in simplest form?
Select three equations that have no solution.
A.19 + b + 12b – 8 – 5b = 2b – 7 + 3b + 3b – 4
B.4b – 9b – 13 – 6 + 16b = 1 – 8 + 6b + 5b – 12
C.7 + 7b – 2 – 15b + b = 4b – 5 – 11b + 2 + 10
D.10b + 8b + 9 – 18b + 3 = 5 + 6b – 2b – 12 + 7
E.9 – 19b – 9 – 2b + 7b = 4b + 3 + 14 – 4b – 17
F.8b – 10 + b + 3b + 2 = 7 + 2b + 10b – 18 – 3
The three equations that have no solutions are A ,C and F
What is Linear Equation in 1 variable?
The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution
Given data ,
A )
19 + b + 12b – 8 – 5b = 2b – 7 + 3b + 3b – 4
On Simplifying , we get
8b + 11 = 8b - 11
Hence , the option has no solution
B )
4b – 9b – 13 – 6 + 16b = 1 – 8 + 6b + 5b – 12
On Simplifying , we get
11b - 19 = 11b - 19
Adding 19 on both sides , we get
11b = 11b
Divide by 11 on both sides , we get
b = b
Hence , the option has a solution
C )
7 + 7b – 2 – 15b + b = 4b – 5 – 11b + 2 + 10
On Simplifying , we get
- 7b + 5 = - 7b + 7
Hence , the option has no solution
D )
10b + 8b + 9 – 18b + 3 = 5 + 6b – 2b – 12 + 7
On Simplifying , we get
0 + 12 = 4b + 0
4b = 12
Divide by 4 on both sides , we get
b = 3
Hence , the option has a solution
E )
9 – 19b – 9 – 2b + 7b = 4b + 3 + 14 – 4b – 17
On Simplifying , we get
0 - 14b = 0
b = 0
Hence , the option has a solution
F )
8b – 10 + b + 3b + 2 = 7 + 2b + 10b – 18 – 3
On Simplifying , we get
12b - 8 = 12b - 12
Hence , the option has no solution
Therefore , the three equations that have no solutions are A ,C and F
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If the height is 4.41 inches and the volume is 0.734, what will the side length of the pyramid’s base be? Is the number rational or irrational? Why?
The side length of the pyramid's base is approximately 0.7071 inches, and it is an irrational number.
To find the side length of the pyramid's base, we need to use the formula for the volume of a pyramid, which is given by:
[tex]\[ V = \frac{1}{3}Bh \][/tex]
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Given that the volume V is 0.734 cubic inches and the height h is 4.41 inches, we can rearrange the formula to solve for the area of the base B :
[tex]\[ B = \frac{3V}{h} \][/tex]
Substituting the given values:
[tex]\[ B = \frac{3 \times 0.734}{4.41} \] \[ B = \frac{2.202}{4.41} \] \[ B \approx 0.5 \text{ square inches} \][/tex]
Now, assuming the base is a square (since we are looking for the side length), the area of the base B is also equal to the side length squared:
[tex]\[ B = s^2 \][/tex]
where \( s \) is the side length of the base. Therefore:
[tex]\[ s^2 = 0.5 \][/tex]
Taking the square root of both sides:
[tex]\[ s = \sqrt{0.5} \] \[ s \approx 0.7071 \text{ inches} \][/tex]
The side length of the pyramid's base is approximately 0.7071 inches.
To determine if this number is rational or irrational, we consider the definition of rational numbers. A rational number is one that can be expressed as the quotient of two integers. The square root of 0.5 can be rewritten as:
[tex]\[ s = \sqrt{0.5} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}} \][/tex]
To rationalize the denominator, we multiply the numerator and the denominator by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ s = \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} \][/tex]
Since [tex]\( \sqrt{2} \)[/tex] is an irrational number, the side length s is also irrational because it cannot be expressed as the quotient of two integers.
please help i will mark brailiest
Answer:
its 49
Step-by-step explanation:
Use ratio box to solve problem
Five hundred fifty students attended the assembly. If the ratio of boys to girls in the assembly was 5 to 6, how many girls attended the assembly
Final answer:
To find the number of girls attending an assembly given a boys-to-girls ratio, divide the total students by the total parts of the ratio and then multiply by the girls' part of the ratio. 300 girls attended the assembly.
Explanation:
Ratios provide us with comparative information. In this case, the ratio of boys to girls is 5 to 6. To find the number of girls, we need to divide the total students by the total parts of the ratio (5 + 6) and then multiply by the girls' part of the ratio:
Calculate total parts of the ratio: 5 (boys) + 6 (girls) = 11.
Divide total students by total parts of the ratio: 550 / 11 = 50.
Multiply by the girls' part of the ratio: 50 (students per part) * 6 (girls) = 300 girls attended the assembly.
if a 42.9ft tall flagpole casts a 253.1ft long shadow then how long is the shadow that a 6.2ft tall woman casts?
What is the solution to this equation
Answer with explanation:
⇒The given equation of line in two variable is :
y = 10 x + 15
If we have to find the solution of the equation of a unique line,as on a line there are infinite number of points lying on it.
So, Line, y=10 x + 15, has infinite number of solution.
Substituting different value of , x we will get different value of y,and by Substituting Different values of y, we will get different values of x.
→→If, x=k, then solution set of line, y=10 x + 15 ,will be,
(x,y)=All the points lying on the line, that is of the form,(k, 10 k +15).
If the profits in your consulting business increase by 5% one year and decrease by 3% the following year, your profits are up by ____% over two years. How do I solve this question?
Final answer:
To calculate the change in profits over two years with a 5% increase followed by a 3% decrease, the successive percentage change formula was used which resulted in a value 1.85% (approximately).
Explanation:
To solve the question, we need to consider the successive percentage changes in profits over two years. If profits increase by 5% one year and decrease by 3% the following year, we can calculate the overall percentage change using the formula for successive percentage changes.
Let's assume the initial profit is $100. After increasing by 5%, the profit becomes $105. Then, after decreasing by 3%, the profit becomes $105 * (1 - 0.03) = $105 - $3.15 = $101.85. Therefore, over two years, profits are up by 1.85% (approximately).
I am a number less than 3000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder is 44. What number am I?
Help me asap please!!
Rewrite the following equation in slope-intercept form. 3x − 18y = 20 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin.
What is the scale factor of the dilation?
A.) 0.25
B.) 0.5
C.) 2
D.) 4
By what percent will a fraction increase if its numerator is increased by 60% and its denominator is decreased by 20%?
What is the surface area of the figure shown? (Use 3.14 for π.)
A. 178.98 in.2
B. 178.98 in.3
C. 235.5 in.2
D. 235.5 in.3
You buy a watch for $60. There is a 6% sales tax. What is your total cost for the watch?
PLEASE HELP ASAP!!!
A circular sinkhole has a circumference of 75.35 meter. A week later, it has a circumference of 150.42 meters.
a.) Estimate the diameter of the sinkhole each week
b,) How many times greater is the diameter of sinkhole now compared to the previous week?
Please explain your anwser ( i didn't understand the part about EACH WEEK)
Thanks in advance!
Final answer:
Using the circumference formula, the estimated diameters of the sinkhole are approximately 24 meters for the first week and 48 meters for the second week. The diameter in the second week is 2 times greater than in the first week.
Explanation:
The question asks for the estimation of diameters of a circular sinkhole at two different times based on their circumferences and how much greater the diameter is in the second week as compared to the first week.
To estimate the diameter of the sinkhole, we use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter. We rearrange the formula to solve for the diameter, giving us d = C/π. Using π ≈ 3.14, we calculate the diameter for each week. In the first week, the diameter is approximately 75.35 meters/3.14 = 24 meters, and in the second week, it's approximately 150.42 meters/3.14 = 48 meters.
To find how many times greater the second diameter is compared to the first, we divide the second diameter by the first diameter: 48 meters/24 meters = 2. This means the diameter of the sinkhole in the second week is 2 times greater than the first week.
5 years = ______ months
Which expression represents the calculation “subtract 30 from 40, then multiply by 4"? A) (30 − 40) × 4 B) 40 − (30 × 4) C) 4 − (40 × 30) D) 4 x (40 − 30)
I WILL GIVE BRAINLIEST!!!!
A line is shown on the coordinate grid.
Which is the equation of this line?
Question 5 options:
y = -1/3 X + 3
y = -3x - 1
y = 1/3 X - 1
y = 3x + 3
Zachary is solving the following equation
3/4(x - 8)= 12
Which is the best first step to begin to simplify the equation?
A.Multiply both sides of the equation by 3/4
B.Divide both sides of the equation by 4/3
C.Distribute 3/4 over (x - 8)
D.Distribute 4/3 over (x - 8)
Answer:
C. Distribute 3/4 over (x - 8)
Step-by-step explanation:
There are multiple ways to begin solving this problem.
If we want to cancel the 3/4 without using the distributive property, we would divide both sides by 3/4. Dividing by 4/3 will not cancel it.
When dividing by fractions, we multiply by the reciprocal; this would be multiplying both sides by 4/3. Multiplying by 3/4 will not cancel it.
Using the distributive property, we multiply (x-8) by the number in front of parentheses, 3/4. We cannot distribute 4/3, since it is not part of the equation.
Josh book has 64 pages. Josh read 27 pages in the morning He reads 18 more pages that night How many pages does josh need to read to finish the book
Final answer:
Josh has read a total of 45 pages after reading 27 pages in the morning and 18 at night. With 64 pages in the book, he needs to read 19 more pages to finish it.
Explanation:
Josh's book has 64 pages in total. He read 27 pages in the morning and 18 more pages at night. To calculate the number of pages Josh still needs to read to finish the book, we do some quick math:
Add the number of pages read in the morning to the number read at night: 27 pages + 18 pages = 45 pages.Subtract the total number of pages read from the total number of pages in the book: 64 pages - 45 pages = 19 pages.Therefore, Josh needs to read 19 more pages to finish his book.
The sketch shows two parallel lines cut by a transversal. Angle 1 is 58°. What is the measure of angle 7?
The measure of angle 7 for the given set of parallel lines with given measure of angle 1 as 58 degrees is equal to 122°.
Here line m is parallel to line n and 'q' is the transversal.
In general, when two parallel lines are cut by a transversal, any pair of corresponding exterior angles are congruent.
Angles 1 and 5 are corresponding pair of exterior angles, which are always congruent.
So, the measure of angle 5 is the same as the measure of angle 1, which is 58°.
And measure of angle 5 and angle 7 are linear pair .
This implies,
Measure of ( angle 5 + angle 7 ) = 180°
⇒Measure of angle 7 = 180° - 58°
⇒Measure of angle 7 = 122°
Therefore, the measure of the angle 7 is equal to 122 degrees.
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The above question is incomplete, the complete question is:
The sketch shows two parallel lines cut by a transversal. Angle 1 is 58°. What is the measure of angle 7?
Attached figure.
If a large Rubik's cube has a volume of 1331 cubic inches what is its surface area ?
PLEASE HELP ME!!! Will mark brainliest
a) A two-digit number is 18 more than that number reversed. What could that number be? List all possibilities.
b) The sum of digits in a two-digit number is 14. If you double the reversed number and add the result to the original number, the sum would be 222. Find the original number.
c) The sum of the digits of an odd 2-digit number is 17. What is the number?
A recipe calls for 2 cup so of flour, 1/4 cup sugar, 1/3 cup milk. What Ismaili the total volume of the three ingredients?
Categorize these samples as representative or not representative of the given populations.
Answer:
1) Tina interviews the school's soccer team about the exercise habits of the students at her school. (implying all the students). This means that Tina only goes to the soccer team instead of the whole school to find out the whole school's exercise habit.
2) Alana also counts as representatives, because she did not interview ALL of the teachers, rather just a selected majority (in this case)
5) For Jeremy, he only interviews 5 students from each class rather than all students
Not Representatives: Each person is given a choice of opinion and does not affect other people.
3) Joe talks to fathers of high school students, which could be larger than just 'representatives', and implies a larger group of people, and is not as selective as having representatives
4) Social Media constitutes of a large group of people, generally larger than a school, and if people take time to take the survey, it will generate a larger test-group. Also, everybody answering the survey would take time to think about themselves, and only represent themselves, and not others.
Step-by-step explanation:
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