The student's question is a math problem involving consecutive numbers and a basic linear equation. The page numbers of an open book are consecutive, implying the left page is x and the right is x+1. Solving the equation x+(x+1)=333 results in the left page being 166 and the right page 167.
Explanation:The problem can be approached using the basic concept of consecutive integers in Mathematics. If the total sum of the two page numbers is 333, this means we are dealing with two consecutive numbers (since the left and right page numbers of an open book are always consecutive). Let's represent the left page number as x (unknown at this point). So, the right page number would be x+1 setting up our equation as x+(x+1)=333. Solving this equation will help us find the actual page numbers.
First combine like terms in your equation: 2x+1=333. Subtract 1 from both sides to isolate the term with x: 2x = 332 Divide both sides by 2 to solve for x: x = 166. This is our left page number. Substitute x in to x+1 to find the right page number: x+1 = 167. This is our right page number.
So, the left and right page numbers are 166 and 167 respectively.
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Please answer as soon as possible.
Answer:
9(4 +3)5(9 +5)8(2+9)Step-by-step explanation:
Problems like these are aided immensely by your knowledge of multiplication tables.
1) 36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6
27 = 1·27 = 3·9
The greatest common factor is 9, so the sum can be written as 9(4+3).
__
2) 45 = 1·45 = 3·15 = 5·9
25 = 1·25 = 5·5
The greatest common factor is 5, so the sum can be written as 5(9+5).
__
3) 16 = 1·16 = 2·8 = 4·4
72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9
The greatest common factor is 8, so the sum can be written as 8(2+9).
Recipe for cookies calls for 3 1/4 cups of sugar Amy has already put three and one nights cup how many more cups so she need to put in
Answer:
So she need [tex]\frac{5}{36}\ cups[/tex] more to put in.
Step-by-step explanation:
Given:
Recipe for cookies calls for 3 1/4 cups of sugar.
Amy has already put three and one nine cups.
Now, to find the number of cups she need to put in.
Number of cups of sugar for recipe calls = [tex]3\frac{1}{4} =\frac{13}{4}\ cups.[/tex]
Amy has already put = [tex]3\frac{1}{9} =\frac{28}{9}\ cups.[/tex]
So, to get the number of cups she need to put in we subtract number of cups of sugar for recipe calls from number of cups of sugar for recipe calls:
[tex]\frac{13}{4} -\frac{28}{9}[/tex]
Subtracting by taking the same denominator:
[tex]=\frac{117-112}{36}[/tex]
[tex]=\frac{5}{36}[/tex]
Therefore, so she need [tex]\frac{5}{36}\ cups[/tex] more to put in.
8. A farmer owns a total of 10 acres of land. The land is separated into 6
equally sized sections. How many
acres are in each section?
Write your answer as a mixed number in simplest form.
Answer: 8/5 or 1 ⅗ acres
Step-by-step explanation:
Ikyjah’s cat is stuck up a tree. To rescue it, he places the base of a 10 ft ladder 3 ft away from the base of the tree. What is the height of the branch which the cat is stuck on?
The height of the branch is 9.54 ft
Step-by-step explanation:
Apply Pythagorean relationship in this question where the length of the ladder is the hypotenuse, and the distance from the tree base is the shortest side.Finding the height will be;
a²+b²=c²
a²+3²=10²
a²=10²-3²
a²=100-9
a²=91
a=√91=9.54 ft
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Keywords: cat, stuck, tree. rescue,base, ladder, height , branch
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A Web music store offers two versions of a popular song the size of the standard version is 2.7 MB the size of a high-quality version is 4.1 MB yesterday there were 1130 downloads of the song for a total download size of 3723 MB. How many downloads of the high-quality version where there
Answer:
480
Step-by-step explanation:
Let h represent the number of high-quality downloads. Then the total download size is ...
4.1h +2.7(1130-h) = 3723
1.4h = 672 . . . . . . . . . . . . . . subtract 2.7·1130 = 3051
h = 480 . . . . . . . divide by 1.4
There were 480 downloads of the high-quality version.
The number of cars Gary sold each month was 12, 5, 9, 11, 14, and 10.
What was Gary's median number of sales per month?
o
10.2
0
0 0
Answer:
11.5
Step-by-step explanation:
(11+12)/2=11.5
A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars
A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?
Answer:
There were 69 adults and 284 seniors
Solution:
Let "a" be the number of adults
Let "s" be the number of seniors
Cost of 1 adult = $ 8
Cost of 1 senior = $ 4
On a particular day when 353 people paid an admission
Therefore,
number of adults + number of seniors = 353
a + s = 353
a = 353 - s ---------- eqn 1
The total receipts were 1688 dollars
Therefore, we frame a equation as:
number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688
[tex]a \times 8 + s \times 4 = 1688[/tex]
8a + 4s = 1688 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
8(353 - s) + 4s = 1688
2824 -8s + 4s = 1688
4s = 2824 - 1688
4s = 1136
s = 284Substitute s = 284 in eqn 1
a = 353 - 284
a = 69Thus there were 69 adults and 284 seniors in movie theater
there were 55 adults and 284 seniors who paid admission.
Let's denote:
- ( A ) as the number of adults.
- ( S ) as the number of seniors.
Given:
- The price for adults is $9.
- The price for seniors is $5.
- The total number of people who paid admission is 339.
- The total receipts were $1915.
We can set up a system of equations based on the given information:
1. The total number of people who paid admission:
[tex]\[ A + S = 339 \][/tex]
2. The total receipts:
[tex]\[ 9A + 5S = 1915 \][/tex]
Now, we can solve this system of equations.
Let's solve equation 1 for one of the variables (let's solve for ( A )):
[tex]\[ A = 339 - S \][/tex]
Now, substitute this expression for( A ) into equation 2:
[tex]\[ 9(339 - S) + 5S = 1915 \][/tex]
Now, solve for \( S \):
[tex]\[ 3051 - 9S + 5S = 1915 \][/tex]
[tex]\[ -4S = 1915 - 3051 \][/tex]
[tex]\[ -4S = -1136 \][/tex]
[tex]\[ S = \frac{-1136}{-4} \][/tex]
[tex]\[ S = 284 \][/tex]
Now, we can find ( A ) using the value of ( S ) we found:
[tex]\[ A = 339 - 284 \][/tex]
[tex]\[ A = 55 \][/tex]
So, there were 55 adults and 284 seniors who paid admission.
complete question given below:
A movie theater charges 9$ for adults and 5 for seniors.on a particular day when 339 people paid an admission,the total receipts were 1915$ how many who paid were adults and how many who paid were seniors
Solve:
The total cost (C) in dollars for building an office of x square feet is given
by the function C(x) = 107,500 + 150x.
If the total cost was $385,000.00, how many square feet was the office?
Answer:
x=1850
Step-by-step explanation:
C(x) is a stand-in for total cost
since we are given the total cost we can replace the variable with its value
385000=107500+150x
now all we have to do is solve
start by subtracting 107500 from both sides
385000=107500+150x
277500=150x
now we finish solving by dividing both sides by 150
277500=150x
x=1850
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a=πr^2 solve for π please help
Answer:
π = a/(r²) = a÷(r²)
Answer:
pie is equal to the square root of A divided by r
Step-by-step explanation:
Set the equation first...a=pie times r squared. Then u need to get rid of everything to make pie by itself. U square both sides or all the equation. the square cancels out and on the other side, it will be the square root of a. Next, divide by r on each sides. The r cancels out. Then it's gonna be pie =the square root of a all over r. It can't be a/r square because in the original...pie is being multiplied by r which is squared so that means both variables are squared. U cant find pie if the square is stopping it so u square for the very first step
yea i’m confused so like help?
Answer:
0,1 is greater because...
Answer:0,1
Step-by-step explanation:
Given: f(x) = +5 and g(x) = x - 2.
What are the restrictions of the domain of f(g(x))?
O X=-5
O X=-3
o * 2
o There are no restrictions.
Answer:
14838388÷+113
Step-by-step explanation:
because it has two zeros
Answer:
its b
Step-by-step explanation:trust
Which values of x is the solution set of the inequality 7 (x+1) > -14?
The solution of given inequality is: [tex]x>-3[/tex]
Solution:
Given inequality is:
[tex]7(x+1)>-14[/tex]
We have to find the value of "x"
Let us solve the given inequality
Divide both sides of inequality by 7
[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]
Simplify the above expression
[tex](x+1)>-2[/tex]
[tex]x+1>-2[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]
[tex]x+1-1>-2-1\\\\x>-3[/tex]
Thus the value of x is [tex]x>-3[/tex]
find a bank account balance if the account starts with $100 has an annual rate of 4% and the money left in the account for 12 years
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There are 100 students at a swim meet. Every 3rd finisher in the race receives a medal. Every 5th finisher gets a ribbon. How many people will receive a medal AND ribbon.
Final answer:
Calculating the least common multiple (LCM) of 3 and 5 to determine that 6 students will receive both a medal and a ribbon at a swim meet of 100 students.
Explanation:
To find the number of students at the swim meet who will receive both a medal and a ribbon, we need to look for the common multiples of 3 and 5, as medals are given to every 3rd finisher and ribbons to every 5th finisher. The least common multiple (LCM) of 3 and 5 is 15, which means every 15th student will receive both a medal and a ribbon. Since there are 100 students, we simply divide 100 by 15 and then take the integer part of the result, because we can't have a fraction of a person.
100 ÷ 15 equals approximately 6.66. The integer part is 6, which means 6 students will receive both a medal and a ribbon.
4. A geometric sequence is defined recursively by a(1) = 40 and a(n)= a(n-1)
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
The complete question is:
A geometric sequence is defined recursively by
[tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
Answer:
The 9th term is larger than 1/10.Explanation:
You are given the first term, [tex]a_(1)=40[/tex] , and the recursive formula
[tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]
Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).
(a) First four terms of the sequence
[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]
Those are the first four terms.
(b) 9th term
You can write the explicit formula of the sequence as:
[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]
Thus, for the 9th term, n = 9, and the term is:
[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]
Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.
The function y = log (x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
On a coordinate plane, a curve starts at (negative 1, negative 5) and curves up into quadrant 1. It approaches y = 1.
On a coordinate plane, a curve starts at (1, negative 4) and curves upwards. It approaches y = negative 1.
On a coordinate plane, a curve starts at (negative 1, negative 1) and curves up into quadrant 1. It approaches y = 5.
On a coordinate plane, a curve starts at (1, negative 3) and curves up into quadrant 1. It approaches y = 5.
See the graph below
Explanation:
We need to remember the following rules:
[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]
Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:
[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]
Below you can see the graph. The red one is the original function while the blue one is the translated one.
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Answer:
B
Step-by-step explanation:
Took test on edge
Which postulate proves that the two triangles are congruent?
A. SAS
B. SSS
C.AA
D.ASA
Answer:
B. SSS
Step-by-step explanation:
All of the sides are the same
SSS postulate proves that the two triangles are congruent.
What is Congruency of Triangle?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) ASA (angle-side-angle)Given:
From the figure we have two triangles named as FED and CBA
Now, In triangles FED and CBA
FE = AC
ED = BA
FD = BC
So, by SSS Congruency Criteria triangles FED and CBA are Congruent.
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If f(x) = 4x - 2, what is the y-intercept of f^-1 (x)?
1/4, 1/2, -1/2, -2
Answer:
1/2
Step-by-step explanation:
The y-intercept is [tex]\frac{1}{2}[/tex].
Given that f(x) = 4x-2.
To find the inverse function:
1) Write f(x) = y
2) Switch x and y.
3) Solve for y.
4) Write [tex]y=f^{-1}\left(x\right)[/tex].
So,
[tex]f(x) = 4x - 2\\y=4x-2\\x=4y-2\\4y=x+2\\y=\frac{\left(x+2\right)}{4}\\y=\frac{1}{4}x+\frac{2}{4}\\y=\frac{1}{4}x+\frac{1}{2}\\f^{-1}\left(x\right)=\frac{1}{4}x+\frac{1}{2}[/tex]
Comparing this with y=mx+b,
b = y-intercept = [tex]\frac{1}{2}[/tex]
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6 times 4 - 12 divided by 3 - 8
Answer:
-4
Step-by-step explanation:
6 times 4 equals 24
24 minus 12 equals 12
12 divided by 3 equals 4
4 minus 8 equals -4
(btw i did this in the order from the question and not BIDMAS )
I’m so condfused! Can someone please get the answer for me?
Answer:
36
Step-by-step explanation:
If you see this kind of problem do this two steps:
1. Multiply the numerator and the multiplier.
2. Divide the result with the denominator.
[tex]\frac{3}{10}[/tex] × 120
3 × 120 = 360 (STEP 1)
360 ÷ 10 = 36 (STEP 2)
Answer:
36
Step-by-step explanation:
Write the mixed number -7 1/7 as an improper fraction.
Answer:
-50/7
Step-by-step explanation:
-7 1/7=-50/7
Because 7*7+1=49+1=50, and don't forget the negative sign.
PLEASE HELP 15 POINTS.
the lines a and b intersect at point D. What is the value of z? Enter your answer in the box. z = Lines a and b intersect at point D. Acute vertical angles measure five z plus eight degrees and four z plus twenty degrees.
Answer:
[tex]z=12[/tex]
Step-by-step explanation:
The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.
Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Congruent angles have equal measures.
Hence,
[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]
Answer:
12
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities? y < 2x – 5 y > –3x + 1 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
The graph representing the solution to the system of inequalities y < 2x - 5 and y > -3x + 1 would have a dashed line for the first inequality and a solid line for the second one, with the intersected shading to the left of the lines.
Explanation:The student's question centers around identifying which graph depicts the solution to the given system of linear inequalities: y < 2x - 5 and y > -3x + 1. The solution to a system of inequalities is represented by the area of intersection between the two shaded regions of the graphs. The first inequality, y < 2x - 5, is a line with a positive slope that passes through (0, -5) and the shading is below the line because 'y' is less than the expression on the right. The second inequality, y > -3x + 1, is a line with a negative slope that passes through (0, 1), and the shading is above the line because 'y' is greater than the expression on the right. Based on these conditions, the correct graph would be the one with a dashed line (indicating 'less than' or 'greater than' but not 'equal to') for the first equation and a solid line (indicating 'less than or equal to' or 'greater than or equal to') for the second equation where the shading on the left side of the lines intersect.
Remember, the slope of a line indicates how steep the line is and is calculated by rise over run. The y-intercept of a line is where the line crosses the y-axis. These key features, along with the type of inequality symbol, determine where and how to shade the graph for a system of linear inequalities.
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Data is often displayed using numbers and categories.
Which types of graphs are most appropriate for displaying categorical data? Check all of the boxes that apply.
the graphs picture is not provided (incomplete question. explanation:
Answer:bar graphs and pie charts
Step-by-step explanation:
edge 2021
Which statement could be used to explain why the function h(x) = x has an inverse relation that is also a function?
Answer:
Since h(x) is a one-to-one function, this means its inverse is also a function
Step-by-step explanation:
The key idea here is knowing that a function needs to be a 'many - to -one' operation (Many could also include one-to-one functions. The key if that for any x, there is only one f(x) value).
This means that for a function to have an inverse, it needs to be one-to-one. Since the domain and range switch when we look at inverse relations, and so if we have a many-to-one function, then it's inverse would be one-to-many. But we need it to be one-to-one. So the original function would need to be one-to-one.
However the short answer is to just know the 'theorem' which says that a function has an inverse function if and only if it is a one-to-one function.
Answer: c, the graph of the inverse of h(x) passes through the horizontal line test.
Step-by-step explanation:
Edge 2020
classify the triangle by its angels :
A. acute
B. right
C. obtuse
D. scalene
Answer:
B. right
Step-by-step explanation:
In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.
16-(-12)=
As soon as possible please
Identify all factors of the expression 〖4x〗^2+17x-15.
The factors of given expression are: -5 and 3/4
Step-by-step explanation:
Given equation is:
[tex]4x^2+17x-15[/tex]
Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15
[tex]4x^2+20x-3x-15[/tex]
[tex]= 4x(x+5) - 3(x+5)[/tex]
[tex]=(4x-3)(x+5)[/tex]
Now
[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]
[tex]x+5 = 0\\x = -5[/tex]
Hence,
The factors of given expression are: -5 and 3/4
Keywords: Quadratic equation, factors
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A politician’s support grew from 42% by 3 percentage points to 45%. What percent (relative) change is this?
Answer:
The percent (relative) change is 7.14 percent (%).
Step-by-step explanation:
We are given that the original support value is at 42%.
Then the support increased by 3%, to reach 45%.
We want the Percentage Change (i.e. relative) change of this increase, which can be computed as:
[tex]\frac{X_{F}-X_{O}}{X_{O}}*100[/tex]
where [tex]X_{F}[/tex] is the final value reached
[tex]X_{O}[/tex] is the original value
So plugging in our known values and computing we have:
[tex]\frac{45-42}{42}*100= \frac{3}{42}*100 = 0.071428*100=7.14[/tex] percent increase.
Now lets go back and check if we are correct.
[tex]42+42\frac{7.14}{100}=42+2.9988=42+3=45[/tex]
So it works!
A regular polygon has an interior angle of 165 degrees. How many sides does it have?
Answer:
24
Step-by-step explanation:
First find the exterior angle: 180 - 165 = 15
Then 360 ÷ 15 because 360 divided by he exterior angle of a regular polygon is equal to the number of sides.
Answer:
Hello, 24
Step-by-step explanation:
Ingerior angle = 165
Exterior angle = 180 - 165 = 15
The sum of exterior angles of any polygon is 360
Number of sides = 360/15 = 24 A polygon is any two dimensional shape formed with the straight lines. Triangles, pentagons, quadrilaterals, and hexagons are all examples of the polygons. The name itself tells as to how many sides the shape has. For example, a triangle has three sides, whereas a quadrilateral has four sides.
Thus, when the regular polygon have if each of its interior angle is 165° then,
The corresponding exterior angle must be 180-165 = 15°
The sum of ALL the exterior angles is 360°
Sides of exterior angles is 360/15 = 24
Therefore the number of sides a regular polygon will have is 24 Have a Awesome Day!