The fraction is given as follows:
8.3/10.3.
How to obtain the fraction?The fraction is modeled as follows:
x/y.
In which:
x is the numerator.y is the denominator.From the features of the problem, a system of equations is built to identify the variables.
If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4, hence the first equation is of:
4x/(y - 2) = 4.
Hence:
4x = 4(y - 2)
4x = 4y - 8
x = y - 2.
If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4, hence the second equation is of:
(x + 15)/(2y - 2) = 5/4.
We know that x = y - 2, hence the value of y is obtained as follows:
(y + 13)/(2y - 2) = 5/4.
5(2y - 2) = 4(y + 13)
10y - 10 = 4y + 52
6y = 62
y = 62/6
y = 10.3.
Then the value of x is of:
x = y - 2
x = 10.3 - 2
x = 8.3.
Hence the fraction is:
8.3/10.3.
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Find area of figure with radius 20.8 ft, both terms of r and to the nearest tenth. Use 3.14 for r.
The area of this figure with radius 20.8 ft include the following: D. 432.64π ft² ≈ 1358.5 ft².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this mathematical expression:
Area = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of circle = π × 20.8²
Area of circle = 432.64π square feet.
Area of circle = 1358.5 square feet.
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Given
ℎ
(
�
)
=
4
�
+
4
h(x)=4x+4, find
ℎ
(
2
)
h(2)
Answer:
h(2)=12
Step-by-step explanation:
Given:
h(x)=4x+4
Find:
h(2)
Substitute 2 into x.
[tex]h(2)=4(2)+4[/tex]
Solve:
[tex]h(2)=12[/tex]
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance of (x) between the flagpole is 12 m.
The distance (y) from flagpole c to point s is 10 m.
The height of flagpole a is 4.4 m.
What is the height of flagpole c?
In linear equation, 60m is the height of flagpole c .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Height/ Shadow
Shadow of the pole = 12 m
Height of the pole = x m
Tim's shadow = Height of the pole - Tim's distance
12 m - 10 m = 2 m
Tim's height = 2 m
Hence:
x/12 = 2/10
Cross Multiply
2x = 12 × 10
x = 120/2
x = 60 m
Approximately = 60m
Hence, the height of the flagpole = 60m
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The point (10, 10) is the midpoint of C and D. Given that the coordinates of C are (15, s) and the coordinates of D are (t, 3), solve for the values of the variables s and t. Show your work (HELP ME PLEASE)
Answer: T= 5 and s =17
Step-by-step explanation: Use the midpoint formula
Solve for T
^xm=^xC+^xD/2
15+t/2=10
15+t=20
Solve for S
^ym=^yC+^yD/2
s+3/2=10
s+3=20
A blueprint of a concrete patio has a scale of 2 inches=5 feet. Use this to answer parts a, b, and c.
Expression for actual length and actual width of the concrete patio are
30x inches and 30y inches respectively.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Given,
A blueprint of a concrete patio has a scale of 2 inches=5 feet.
2 inches = 60 inches
scale factor = 60/2 = 30
Let length of the patio on the blue print is x inches
width of the patio on the blue print is y inches
then actual length of the 30x inches
actual width of the patio = 30y inches
Hence, 30x inches is actual length and 30y inches is actual width of the concrete patio.
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Find the value of z
6cm 15cm and right angle in triangle
For the given right triangle, the value of z is approximately 16.155 cm.
To find the value of z in a right triangle with sides 6 cm and 15 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (z) is equal to the sum of the squares of the lengths of the other two sides (6 cm and 15 cm).
So we can write the equation:
z^2 = 6^2 + 15^2
Simplifying the equation:
z^2 = 36 + 225
Adding the numbers on the right side of the equation:
z^2 = 261
Taking the square root of both sides of the equation:
z = √261
Approximating the square root:
z ≈ 16.155
Therefore, the value of z is approximately 16.155 cm.
Note: The question is incomplete. The complete question probably is: Find the value of z (hypotenuse) if the other dimensions are 6cm, 15cm and right angle in triangle.
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a process in which a number is changed, such as by adding, subtracting, dividing or multiplying is definition of _____
Answer:operation
Step-by-step explanation:
What type of figure is shown above?
Answer:
See below
Step-by-step explanation:
This is a triangular prism:
h = Perpendicular height of prism
Base shape = Triangle
t = Perpendicular height of triangle
Volume of triangular prism = Base Area × h
= Area of triangle × h
= [[tex]\frac{1}{2}[/tex] × Base of triangle × t] × h
= [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in] × 10 in
= 42.5 cubic inches
Total Surface Area = [2 × Base Area] + Lateral Surface Area
= [2 × Area of triangle] + [(Perimeter of triangle) × h]
= {2× [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in]} + [(5 in + 3 in + 3 in) × 10 in]
= 8.5 [tex]in^{2}[/tex] + 110 [tex]in^{2}[/tex]
= 118.5 square inches
A carnival charges $6 to enter and $.75 per ticket. Write a function rule that models this situation.
Rule:
The function rule that models this situation is that increase in the number of tickets would lead to an increase in the total cost charged for each individual.
What is a direct relationship between two values?A direct relationship between two values is said to exist when the increase in one value leads to the increase of the other.
The cost of 1 ticket = $.75
The cost to enter the carnival = $ 6
Therefore the total cost for each individual = 6+0.75 = $6.75
The cost for two tickets for two individuals = 2× 6.75 = $13.5.
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I thought of a number, this number doubled is 9 more than the number itself. what is my number?
Possible answer: 9
Step-by-step explanation:
9 doubled is 18, and that is 9 more than the original number itself.
Unless I'm wrong.
PLEASE HELP THIS IS S MATH TEST I NEED 4 QUESTIONS I'LL GIVE EXTRA POINTS
1 ).
Question
Select the values that are solutions of the inequality x/5≥3
2) Graph x<8
3)
Solve x−5≥1 and graph the situation
Question 4
Which graph represents the solution of 8≥x+6
Question 6
Solve 6m>24 then graph
1) values are 15, 16 and 17
2) Drawn in the graph (2)
3) [tex]x \geq 6[/tex] and graph (3)
Question 6) [tex]m > 4[/tex] and graph (6)
What is Inequality?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
1)
As per the given data:
Values are: 12, 13, 14, 15, 16, 17
Given inequality:
[tex]\frac{x}{5} \geq 3\\= x \geq 5\times3\\= x \geq 15[/tex]
The values of [tex]x[/tex] greater than or equal to 15 out of the given values are:
15, 16 and 17
15, 16, 17 are the solutions of the given equality.
2)
Given inequality:
[tex]x < 8[/tex]
For making the graph, first draw the point [tex]x=8[/tex]
The region to the left of the point [tex]x=8[/tex] will represent the graph as shown in the diagram.
3)
Given inequality:
[tex]x-5\geq 1[/tex]
= [tex]x \geq 1 + 5[/tex]
= [tex]x \geq 6[/tex]
For making the graph, first draw the point [tex]x=6[/tex]
The region to the right and including the point [tex]x=6[/tex] will represent the graph as shown in the diagram.
6)
Given inequality:
[tex]6m > 24[/tex]
= [tex]m > \frac{24}{6}[/tex]
= [tex]m > 4[/tex]
For making the graph, first the plot the point m = 4.
The region to the right of the point m = 4 will represent the graph as shown in the diagram.
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The elimination method was used to solve the following system of equations:
x2 – y = –3
x2 + y2 = 9
Which of the following is the correct y-coordinate of the solution? (5 points)
0
1
3
-4
Answer:
(c) 3
Step-by-step explanation:
You want the y-value of the solution to the equations ...
x² -y = -3x² +y² = 9EliminationWe are interested in the value of y, so it can be useful to eliminate x from the equation(s). The x² term appears in both, so it is convenient to subtract the first equation from the second.
(x² +y²) -(x² -y) = (9) -(-3)
y² +y = 12
y² +y -12 = 0 . . . . . . subtract 12
(y +4)(y -3) = 0 . . . . . factor
y = -4 or +3 . . . . . . . . values that make the factors zero
DomainSolving the first equation for y, we find ...
x² +3 = y . . . . . . . add y+3
We know that x² cannot be negative, so this tells us the values of y will be ...
y ≥ 3
Of the two solutions we found above, the value -4 is extraneous (not in the domain of y).
The y-coordinate of the solution is 3, choice C.
__
Additional comment
The solution is the point of intersection of the two curves shown in the attachment. The y-coordinate of that point is 3.
<95141404393>
David drove 603 miles in 9 hours.
At the same rate, how many miles would he drive in 13 hours?
Answer:871
Step-by-step explanation:If he drove 603 miles in 9 hours, he drove 67 miles per hour. So in 13 hours he will drive 67x13, which is 871.
Answer:
Step-by-step explanation:
David would drive 871 miles. This is because 603 ÷ 9 = 67.
So, you'd have to multiply 67 times 13. Because 67 is the average mph.
Rickquan, wants a balance of $565 in his account. He deposited $65 in
his account and will save $25 per week. How many weeks will it take
Rickquan to reach his goal?
20
Step-by-step explanation:
cause 565-65 is 500 and divide that by 25 is 20.
Answer:
20 weeks
Step-by-step explanation:
starting with an initial 65 adding money each week after 20 weeks he would've added 500
Which statements are always true about a system of linear equations?
(more than one answer)
(1) the solution of a system of linear equations is any values of the variables that satisfy any of the equations.
(2) a system of linear equations has only two equations.
(3) on a graph, the solution of a system of equations is any point on one of the lines.
(4) on a graph, the solution of a system of equations is the point where the lines intersect.
(5) a system of linear equations includes at least two linear equations.
6) the solution of a system of linear equations is any values of the variables that satisfy both equations at the same time.
Answer:
(4) on a graph, the solution of a system of equations is the point where the lines intersect.
(5) a system of linear equations includes at least two linear equations.
(6) the solution of a system of linear equations is any values of the variables that satisfy both equations at the same time.
I NEED HELP ON THIS ASAP!!!
The system of linear inequalities (x, y) has a solution that is (-1, 2)
What is the system of linear inequalityA system of linear inequalities is identical to a system of linear equations, but instead of equations, it is made up of inequalities. Many constraint scenarios are modeled using sets of linear inequalities.
We may determine the values of x and y in the above problem as;
x + y > 1 ...eq(i)
-x + y <= 3 ...eq(ii)
Solving both inequalities;
The solution is;
1 - x < y ≤ 3 + x
This is simple to plot on a graph, and the intersection will provide the answer;
The graph below shows the inequality's (x, y) solution, which is (-1, 2)
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A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4 6 5 7 3 5 What is the best explanation of how to find the experimental probability of rolling a 3? To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the number three. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials. Simplify if necessary. To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three. Simplify if necessary
The best explanation of how to find the experimental probability of rolling a 3:
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have the Data as:
Number Frequency Probability
1 4 0.13
2 6 0.20
3 5 0.17
4 7 0.23
5 3 0.10
6 5 0.17
total 30 1.00
To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.
= 5/30
= 1/6
= 0.166
= 16.6% or 17%.
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Suppose a car moving in straight line steadly increases it's speed each seconds first from 35 to 45km/h then 40 to 45 km/h then from 45 to 50km/h, What is the acceleration?
The acceleration of the car is not constant but is increasing steadily, starting at 10 km/h, decreasing to 5 km/h, and then remaining constant at 5 km/h.
To find the acceleration of the car, we need to use the formula:
acceleration = (final velocity - initial velocity) / time
Let's calculate the acceleration for each interval of time:
For the first interval, the initial velocity is 35 km/h and the final velocity is 45 km/h. The question says the speed increases each second.
Therefore, the acceleration is:
acceleration = (45 - 35) / 1 = 10 km/h
For the second interval, the initial velocity is 40 km/h and the final velocity is 45 km/h. Again, the acceleration is:
acceleration = (45 - 40) / 1 = 5 km/h
For the third interval, the initial velocity is 45 km/h and the final velocity is 50 km/h. The acceleration is:
acceleration = (50 - 45) / 1 = 5 km/h
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what is the measure of angle L?
what is x?
what is the measure of angle M?
SHOW YOUR WORK
The value of angle L, x and angle M is 55°, 35 and 60° respectively
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
From the triangle:
∠OLM + ∠MLN = 180° (sum of angles in a straight line)
125 + ∠MLN = 180°
∠MLN = 55°
Also:
∠MLN + ∠MNL + ∠LMN = 180 (sum of angle in a triangle)
substituting:
55 + (2x - 10) + 65 = 180
2x + 110 = 180
2x = 70
x = 35°
∠LMN = 2x - 10 = 2(35) - 10 = 60°
The value of angle M is 60°
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If the force of two forces is 12 N acting at an angle of 90° to one forces and their greatest force is 18 N, determine the two forces.
Answer:Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.
As the resultant force makes 90
∘
with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q
2
−P
2
=R
2
Q
2
−P
2
=(12)
2
Q
2
−P
2
=144 (1)
The sum of magnitudes of two forces is given as,
P+Q=18
Q=18−P (2)
Substituting the value from equation (2) in equation (1), we get
(18−P)
2
−P
2
=144
P=5N
Substituting the value of P in equation (1), we get
Q=18−5
=13N
Thus, the magnitude of the forces are 5N and 13N.
Step-by-step explanation:
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
The correct option is C. The IQR is the best measure of variability, and it equals 4.
What is IQR (interquartile range)?The IQR (interquartile range), a measure of variability that depicts the range of the middle 50% of the data, is used in box plots. It is determined as the gap between the first and third quartiles (Q1 and Q3) (Q1). Since the box in this instance spans the numbers 17 to 21 on the number line, Q1 equals 17 and Q3 equals 21. IQR = Q3 - Q1 = 21 - 17 = 4 as a result.
The difference between the dataset's maximum and minimum values is represented by the range, another measure of variability. As a result of its sensitivity to extreme values, it is less reliable than the IQR. Although the range in this instance is equal to 27 - 10 = 17, it could not correctly reflect the variety of the data.
Therefore, the IQR is the most appropriate measure of variability for this data, and its value is 4.
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PLEASE HELP!! im desperate A chef uses a bowl shaped like the one below to prepare her avocado lime sauce. Due to the amount of mixing involved in this recipe she does not want to fill the bowl up entirely to the top. She estimates she can only fill the bowl up to about 2/3 its capacity. What is the volume of contents the chef will be able to fill the bowl with using her estimation?
1429 cubic centimeters is the volume of contents the chef will be able to fill the bowl.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that Chef uses a bowl shape which has radius of 8cm to prepare her avocado lime sauce.
We have to find the volume of contents the chef will be able to fill the bowl with using her estimation upto 2/3.
Firstly let us find volume of bowl.
Volume=4/3πr³
=4/3×3.14×(8)³
=2143.5
To find the amount of contents the chef can fill the bowl with, we need to multiply this volume by 2/3,
So 2143.5×2/3
1429.04 cubic centimeters.
Hence, the chef will be able to fill the bowl with about 1429 cubic centimeters of avocado lime sauce.
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how do i solve this -> y=x+46, y=7x+16
Answer:
x=5, y=51
Step-by-step explanation:
y = x + 46
y = 7x + 16 substitute equation 1 into equation 2 to get an expression all in terms of x, then solve for x
7x + 16 = x + 46
6x = 30
x = 30/6 = 5 substitute this into either equation and solve for y
y = 5 + 46 = 51
what is 62 kilos in pounds
62 kilograms was found to be equal to approximately 136.7 pounds using conversion formula.
To convert kilograms to pounds, the following formula is used:
Pounds = Kilograms x 2.20462
Plugging in 62 kilograms, we get:
Pounds = 62 x 2.20462
Pounds ≈ 136.7
Therefore, 62 kilograms is approximately equal to 136.7 pounds.
The pound (symbol: lb) is defined as exactly 0.45359237 kilograms, or approximately 16 ounces. There are also different types of pounds, such as the avoirdupois pound (used for general purposes) and the troy pound (used for precious metals).
The kilogram (symbol: kg) is used to measure the mass of an object or substance. For example, it can be used to measure your own body weight, the weight of a bag of groceries, or the mass of a planet. The prefix "kilo-" means "one thousand", so a kilogram is equal to 1,000 grams.
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A human body that is performing light work generates about 700.0 BTUs of body heat per hour. If a room that is 12.0 x 13.0 x 11.0 is being painted by 3 people, how many BTUs per cubic foot do they produce in 2 hours
2.45 BTUs/ft³ is produced in 2 hours.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.It is given that a human body that is performing light work generates about 700 BTUs.
Total heat generated by 3 peoples in 1 hour -
Q{heat} = 3 x 700
Q{heat} = 2100 BTUs/hr
For the two hours -
Q{T} = 2100 x 2
Q{T} = 4200 BTUs ... { 1 }
Volume of the room -
V{R} = 12 x 13 x 11
V{R} = 1716 ft³ ... { 2 }
So, we can write as -
BTUs per cubic foot produced in 2 hours is -
{r} = Q{T}/V{R}
{r} = 4200/1716
{r} = 2.45 ft³
Therefore, 2.45 BTUs/ft³ is produced in 2 hours.
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HELPPPP PLEASEEEEEEEE
Answer:
Step-by-step explanation:
square root of 100 is 10 and the only point that is on 10 is f so f = 10 or square root of 100
square root of 80 equals about 8.9 and the only point on 8.9 d so d is equal to square root of 80
3 * pi is about 9.4 and the only option left is e so e = 3 * pi
47% is it growth or decay
7 x 5 im 8 in 4th grade
Answer:
35 :)
Step-by-step explanation:
Answer:
35
Step-by-step explanation:7x5=35
You need to know your multiples.
7, 14, 21, 28, 35, 42, 49, 56, and so on.......
2x+3y=11
x-3y = 1
What is the solution (x, y) to the given system of
equations?
Answer:
(x, y) = (4, 1)
i don't have an explanation lol
The amount of corn exported by a country
increased exponentially each year between
2007 and 2016.
In 2012, the country exported 210,000 tonnes
of corn.
In 2016, the country exported 806,736 tonnes
of corn.
Work out how much corn the country exported
in 2007.
Give your answer to the nearest tonne.
PLEASE HELP ME THIS IS DUE TOMORROW AND I DONT WANT A DETENTION
Answer: corn 806,736
Step-by-step explanation: