Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.
To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:
46 - 7 = 39
39 - 7 = 32
32 - 7 = 25
25 - 7 = 18
18 - 7 = 11
11 - 7 = 4
As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.
So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.
Step-by-step explanation:
Find the measure of ∠ 1
The measure of ∠ 1 is 68.7°
What is linear pair angles?Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given is a figure of angles showing the pair of linear angles.
Therefore, by the definition of linear pair angles,
∠ 1 + 111.3° = 180°
∠ 1 = 180° - 111.3°
∠ 1 = 68.7°
Hence, the measure of ∠ 1 is 68.7°
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if 11 is to 22, and 22 to 242, then from 242 to what
Answer:
it's equal to = 242 =484. I think so that's the right answer please
1) A publisher wants to determine the thickness of a book they will print soon. The book has a front cover and a back cover, each of which have a thickness of
1/4 in. The publisher can choose on what type of paper to print the book.
Bond paper has a thickness of 1/4 in. per 100 pages.
Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper.
Ledger paper has a thickness of 2/5 in. per `100` pages. Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on ledger paper.
2) If the publisher selects front and back covers with a thickness of 1/3 in. each, how would this change the equations you wrote on the previous slides?
1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x
1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x
2) The equation will be; y = ²/₃ +¹/₄x
How to solve Algebraic Word Problems?1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;
The addition of both gives to the book thickness of;
1/4 + 1/4 = 1/2 inch, despite how many pages the book has.
We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:
y = ¹/₂ + ¹/₄x
where;
y is the width of the book in inches.
x is every hundred pages printed on bond paper.
1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;
y = ¹/₂ + ²/₅x
2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;
y = 2(1/3) +¹/₄x
y = ²/₃ +¹/₄x
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PLEASE HELP ME DUE TODAY NOW ASAP THANKS
The rate of change of the end points of the line is 32/10
What is slope?
Slope is defined as the rate of change of y with respect to x. Also it is defined as increase in y over increase in x or decrease in y over decrease in x
slope is denoted by the formula = Δy/Δx
Where Δy = change in y
Δx= change in x
The given points are (-9, -2) and (5, 119/5)
The slope of the end points (119/5 + 21)/(5+9)
The slope is (119+105)/5
M= 44.8/14
The slope is 3.2 = 32/10
Therefore the rate of change is given as 32/10
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a particular dress requires 3 1/4 yards of fabric for manufacturing. if the matching jacket requires 1/6 yards less fabric, how much fabric is needed for both pieces?
Answer: The matching jacket requires 1/6 yards less fabric than the dress, which is 3 1/4 - 1/6 = 3 1/4 - 2/12 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 3/12 yards of fabric.
To add these two amounts of fabric together, you need to add the yards and the inches separately.
For the dress: 3 1/4 yards = 3 + 1/4 = 3 + 0.25 = 3.25
For the jacket: 3 3/12 yards = 3 + 3/12 = 3 + 0.25 = 3.25
So, for both pieces, the required fabric is 3.25 + 3.25 = 6.5 yards
Step-by-step explanation:
A bus rental company charges $60 for booking a bus and $120 for each hour the bus is rented. A tour group pays $780 to rent a bus. HELP WANTED TY!!
Select the equation that represents the given situation and find the number of hours the tour group rented the bus.
A. 60x + 120 = 780 ; 11 hours
B. 60x + 120 = 780 ; 6 hours
C. 120x + 60 = 780 ; 11 hours
D. 120x + 60 = 780 ; 6 hours
Answer:d. 120x+60=780
Step-by-step explanation:
120 cost per x hours
Flat Rental cost 60
120x+60=780
-60 as the flat rate which won’t change based on time.
120x=720
Divided by a rate of 120 per hour
x=6 hours
‐3 + 4(a – 3b + 2) – 5(2 – a + 3b)
Answer: 15a – 12b – 5.
Step-by-step explanation: To solve this equation, we need to distribute the constants in front of the parentheses. Doing so, we get:
-3 + 4(a – 3b + 2) – 5(2 – a + 3b)
= -3 + 4a – 12b + 8 – 10 + 15a – 15b
= (15a – 12b) + (-10 + 8) – 3
= 15a – 12b + -2 – 3
= 15a – 12b – 5
Thus, the solution to the equation is 15a – 12b – 5.
Which graph is defined by the function given below?
y=(x + 2)(x+7)
10-
A.
-10
OA. Graph A
OB. Graph B
C. Graph C
OD. Graph D
10+
B.
10-
10
10-
D.
Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The function's zeros are
0=x+2 x=-2
and
0=x+7 x=-7
Consequently, the graph at y=0 where the function crosses those two points .
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sasha needs 3/4 cup of flour to make a batch of muffins and 1 2/3 cups of flour to make loaf of bread. How many cups of flour does sasha need to make both a batch of muffins and a loaf of bread
Using the addition operation, the number of cups of flour Sasha needs to make both a batch of muffins and a loaf of bread is 2⁵/₁₂ cups.
How is the number or quantity determined?We can use the addition operation to determine the quantity of flour that Sasha needs.
We add the cups of flour needed for both items to determine the total quantity.
The quantity of flour for making a batch of muffins = 3/4 cups
The quantity of flour for making a loaf of bread = 1²/₃ cups
The total quantity of flour needed for making a batch of muffins and a loaf of bread = 2⁵/₁₂ cups (³/₄ + 1²/₃)
(³/₄ + 1²/₃)
= ³/₄ + ⁵/₃
= (9 + 20)/12
= 29/12
= 2⁵/₁₂
Thus, to make a batch of muffins and a loaf of bread, Sasha needs 2⁵/₁₂ cups of flour.
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Solve the equation 5(4x-1.5x) + 12 = 4x- 124 for X
[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]
Draw a number line to show 2/8 and 4/16 are equivalent.
Step-by-step explanation:
think of it as a ruler the small dashes represents the 16ths and the big dashes represents the 4ths. They are on the same line therefore they are equal.
Ashanti cashed her paycheck at Cash-n-Go. The fee at Cash-n-Go is 7.5% of the amount of the check. Her paycheck was $670. How much was the fee for Ashanti to cash her paycheck?
Answer:
$50.25
Step-by-step explanation:
7.5% as a decimal is 0.075.
So, the fee is [tex](0.075)(670)=\$50.25[/tex].
WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
Answer: 2.403 × 10^3 atoms
Step-by-step explanation:
10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.
PLIS HELP
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation y = 5x + 62, where x represents the number of t-shirts sold. If they sell 74 shirts, what will the total cost be?
The total cost of the 74 shirts will be;
⇒ $432
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Now,
Since, The equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Hence, For 74 shirts, the cost is fund by substitute x = 74 in above equation,
⇒ y = 5x + 62
⇒ y = 5 × 74 + 62
⇒ y = $432
Thus, The total cost of the 74 shirts = $432
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A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked.
Suppose that x and y are related by the equation y = 53+2x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per day in the road's length?
miles
What was the road's length when the crew started working?
Answer: The equation y = 53+2x relates the variables x and y, where x represents the number of days the crew has worked and y represents the total length of the road.
The change per day in the road's length is given by the coefficient of x in the equation, which is 2. Thus, the change per day in the road's length is 2 miles.
The road's length when the crew started working is given by the constant term in the equation, which is 53. Thus, the road's length when the crew started working was 53 miles.
Step-by-step explanation:
altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two
equal
segments. The length of the altitude is 36 inches, and the length of the base is 12
inches. Find the triangle's perimeter. Round to the nearest tenth of an
Answer:18
Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18
Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
UV is a segment Bisector.
What is a segment Bisector?A segment bisector is a line, ray, or segment that splits another line segment in half evenly at its center. The midpoint of the line segment is always bisected by the line, which divides it into two equally sized parts.
What is the bisector rule?The angle bisector theorem states that a triangle's opposite side is divided into two parts by an angle bisector that is proportional to the triangle's other two sides.
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A rectangle has a length of
2,000 cm and a width of 23 cm.
What is the area?
What is the perimeter?
Answer:
Area= 46,000
Permiter= 4,600
Step-by-step explanation:
The formula to find the area of a rectangle is Length(L) times Width(W).
So 2,000(L) times 23 (W)= 46,000.
The formula for perimeter is 2(l+w).
So you're going to go 2,000 + 23 = 2,300 times 2 which equals 4,600.
Hope that helped, have a great day!!
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Both of you are correct because using either way can solve the equation for the value of x.
How to solve for x ?In the case of solving for x in 2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.
Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :
Multiplying :
2/5 x = 14
5 / 2 x 2 / 5 x = 14 x 5 / 2
x = 35
Dividing :
2/5 x = 14
2 / 5 x / 2 / 5 = 14 / 2 / 5
x = 35
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Help if you know how to do this! I’d really appreciate it!
The value of x is 20 and the value of y is 8 from the given quadrilaterals.
What is a Congruent Polygon?The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.
Given that, ABCD≅EFGH
We know that, corresponding parts of congruent polygon are equal.
Now, (4y-4)°=28°
4y=32
y=8
(10x-65)°=135°
10x=200
x=20
Therefore, the value of x is 20 and the value of y is 8 from the given quadrilaterals.
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WILL MARK BRAINLIEST given angles A and B in quadrant I with tan = 7/24 and tan B = 15/8, find tan (A + B), find the exact value of each expression by applying the identity.
Using PEMDAS to resolve the trigonometric identity which involves trigonometric function, the value of tan A + tan B is 416 / 87
What is Trigonometric IdentityA trigonometric identity is an equation that is true for any value of the variables involved. These identities are useful in solving problems involving trigonometric functions. Examples include the Pythagorean identity, the sine and cosine addition formulas, and the double angle formulas.
In the given problem, we have a compound angle problem and we can solve it as;
tan A + tan B = [(tan A + tan B)] / [1 - tan A * tan B]
tan A = 7/24tan B = 15 / 8Substituting the values into the expression and solve;
tan A + tan B = [(7/24 + 15/8)] /[1 - (7/24)(15/8)]
Applying the rules of PEMDAS;
tan A + tan B = (13 / 6) / (29 / 64)
tan A + tan B = 416/87
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If a copy machine can copy 34 sheets of paper in one minute. How many sheets can it copy in 2 hours?
Answer:
Step-by-step explanation:
34x60
60 minutes in a hour
34x60=204
204+204= 408
408 copies in 2 hours
Answer:
4080
Step-by-step explanation:
First you would multiply 34 by 120. After you multiply those numbers you should get 4080 as your answer.
what is the quotient of g and 25
Answer:
the quotient of g and 25 is g/15.
Sean bakes 18 dozen chocolate cupcakes and 13 dozen vanilla cupcakes. About how many cupcakes did Sean bake? EXPLAIN now!!!
Sean baked 372 cupcakes in total.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Sean bakes 18 dozen chocolate cupcakes,
and 13 dozen vanilla cupcakes.
There are 12 cupcakes in one dozen.
To find the number of cupcakes:
Using multiplication operation,
18 x 12 = 216.
13 x 12 = 156.
The number of cupcakes = number of chocolate cupcakes + number of vanilla cupcakes.
The number of cupcakes = 216 + 156
The number of cupcakes = 372
Therefore, the number of cupcakes are 372.
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Shaikha types at a rate of 34 words per minute. How many words does she type in 2 minutes?
Answer:
68 words
Step-by-step explanation:
If 34 words are typed in a minute what about two minutes hence take 34×2
Answer:
68
Step-by-step explanation:
What is a rate?A rate can be a quantity, or frequency, measured against a different quantity or amount.
If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:
Let m = minutes, w = words per minute and t = total words
m × w = t
Simply just insert your numbers into the equation.
2 × 34 = 68
Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.
Two numbers are such that twice the greater number exceeds thrice the smaller one by 15 and 1/5 of the smaller and 1/9 of the greater number are together 10. Find the numbers.
Answer: The two numbers are $x = 5$ and $y = 7.5$.
Step-by-step explanation:
Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:
$$2y = 3x + 15$$
$$\frac{1}{5}x + \frac{1}{9}y = 10$$
We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get
$$10y = 15x + 75$$
$$9x + y = 90$$
Subtracting these equations, we get
$$8y - 9x = 15$$
Multiplying this equation by 8, we get
$$64y - 72x = 120$$
Adding this equation to 5 times the first equation, we get
$$69y - 72x = 120 + 75$$
$$69y - 72x = 195$$
Dividing both sides by 3, we get
$$23y - 24x = 65$$
Subtracting this equation from 4 times the second equation, we get
$$96y - 36x = 360 - 260$$
$$96y - 36x = 100$$
Dividing both sides by 60, we get
$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$
Substituting the expression for $y$ from the first equation, we get
$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$
This simplifies to
$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$
Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.
A(n)___ is a convex in which both pairs of opposite side are parallel
4th option: parallelogram
Lesson 17
Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?
The measure for θ is 25.747121°.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
Now, using Trigonometry
sin θ = Opposite side / Hypotenuse
by putting the given values we get
sin θ = 6.3 / 14.5
sin θ = 63/145
sin θ = 0.4344
θ =25.747121°
Hence, the angle is 25.747121°.
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HELP PLEASE show work if possible I WILL MARK BRAINLIEST TO BEST ANSWER
The Value for x and y as follow:
A) x=2 and y=-8
B) x = -2 and y = 5
C) x = -9/4 and y= -5/2
What is Elimination Method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Given:
A) 9x- 2y = 34...............(1)
5x+ 2y = -6..............(2)
Adding equation (1) and (2) we get
9x -2y = 34
5x + 2y = -6
_____________
14x = 28
x= 28/14
x= 2
and, 5x +2y= -6
5(2) + 2y= -6
2y = -6 -10
y = -8
B) x+ 6y = 28.....................(3)
2x -3y = -19................(4)
Multiply equation (2) by 2 we get
4x - 6y = -38.......................(5)
Adding equation (3) and (5), we get
x + 6y = 28
4x- 6y = -38
___________
5x = -10
x= -2
and, x+ 6y= 28
-2 +6y= 28
6y= 30
y=5
C) 8x -6y = -3................(6)
6x -5y = -1......................(7)
Multiply equation (6) by 5 and equation by (6), we get
40x - 30 y = -15
36 x - 30y = -6
- + +
____________
4x = -9
x= -9/4
and, 8x - 6y = -3
8(-9/4) - 6y = -3
-18 - 6y= -3
-6y = 15
y = -5/2
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If a house has decreased 35% since it was purchased and it currently values 117,000 what was purchase value
Step-by-step explanation:
that means the current value of $117,000 is 100 - 35 = 65% of the original price.
65% = $117,000
1% = 65%/65 = 117000/65 = $1,800
100% = 1%×100 = 1800×100 = $180,000
the original (100%) purchase value was $180,000.