The ordering of the rational and irrational numbers from greatest to least is given by:
4 and 2/3, cube root of 51, -π, -17/5.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.To order numbers on the number line, we have that:
For negative numbers, the smaller the integer part is, the greater is the number, for example -2 > -3.For positive numbers, the greater the integer part is, the greater is the number, for example 3 > 2.If the integer parts are equal, we look at the decimal part, following the same logic as above.
For this problem, the numbers are given as follows:
Cube root of 51 = 3.71.4 and 2/3 = 4.67.-π = -3.11415...-17/5 = -3.4.Hence the ordering of the rational and irrational numbers from greatest to least is given by:
4 and 2/3, cube root of 51, -π, -17/5.
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The midpoint of AB is M(-3,0). If the coordinates of A are (1,-4), what are the coordinates of B?
Applying the midpoint formula, the coordinates of B are: (-7, 4).
How to Apply the Midpoint Formula?The midpoint formula is:
M(x, y) = [(x2 + x1)/2, (y2 + y1)/2]
Given:
M(x, y) = (-3, 0)
A(x1, y1) = (1, -4)
B(x2, y2) = (?, ?)
Plug in the values into the midpoint formula:
M(-3, 0) = [(x2 + 1)/2, (y2 + (-4))/2]
Isolate each coordinate
-3 = (x2 + 1)/2
-6 = x2 + 1
-6 - 1 = x2
x2 = -7
0 = (y2 - 4)/2
0 = y2 - 4
y2 = 4
Therefore, applying the midpoint formula, the coordinates of B are: (-7, 4).
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Period
- Date
4. Open Response The ratio of Braydon's
number of laps he ran to the time he ran is
6:2. The ratio of Monique's number of laps
she ran to the time she ran is 10: 4. Explain
why these ratios are not in a proportional
relationship. (Lesson 2)
Answer:
(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
10:4 = 5:2
6:2 = 3:1
Not equal.
Rewrite the expression with a rational exponent as a radical expression.
The equivalent expression of (5 ^3/4)^2/3 is √5
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the equivalent expression?The expression is given as
(5 ^3/4)^2/3
Evaluate the product of the exponents
So, we have
(5 ^3/4)^2/3 = 5^(3/4 x 2/3)
Evaluate the product of the exponents
So, we have
(5 ^3/4)^2/3 = 5^(2/4)
Evaluate the quotient
So, we have
(5 ^3/4)^2/3 = 5^(1/2)
Express as square roots
So, we have
(5 ^3/4)^2/3 = √5
Hence, the equivalent expression of (5 ^3/4)^2/3 is √5
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Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days, she had nine more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days. Write an expression for the population of fruit flies Lavania observed after 6 days.
The expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109
How to write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days?The given parameters are
Day 1 = 20 fruit flies
Day 6 = 9 more than 5 times as many fruit flies on day 1
The above expression can be rewritten as
Day 6 = 9 + 5 * Day 1
This gives
Day 6 = 9 + 5 * 20
Evaluate the product
Day 6 = 9 + 100
Evaluate the sum
Day 6 = 109
Hence, the expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109
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Evaluate the expression for s = 5 and
t = 2. Simplify your answer.
10/st
Answer: 1
Step-by-step explanation:
s = 5, t = 2
10/5*2
= 10/10
=1
i dont get this need help asap THANK YOUU
Answer:
95
Step-by-step explanation:
Because they are opposite angle. Since TRV and SRV is opposite that means they are equal each other
For a fundraiser, a school club is selling raffle tickets for $2 each and healthy snacks for $1.50 each. What is the cost of 10 tickets and 8 snacks?
Marcel Park is weeding the rectangular vegetable garden. The garden has an area of 599.5 square feet. If the garden is 22 feet wide,how long is the garden? Justify your procedure!
Answer:
27.25 feet long
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
The area is 599.5 square feet and it is 22 feet wide. So in order to find the area we have to multiply the width (22 feet wide) and the legth (unknow number which will stand for "x"). Since we area multiplying the width and legth we need to do the inverse operation which is dividing. We didvide the area 599.5 by the width 22 to get 27.25 feet long.
22x = 599.5
----- -------- <------ Fraction bar/divide
22 22
x = 27.25
Check:
When a number is next to parenthesis it means to multiply the 2 numbers.
22 (27.25) = 599.5
599.5 = 599.5
True statement.
please help me this is so confusing. I need help.
Answer:
Step-by-step explanation:
OK, so you see how its like 4/10 right? (not four tenths but ya know four on top and ten underneath)
Look how for your Y axis it goes: 2, 4. 6, 8, 10
what comes after ten by counting by twos? 12!
Also the correct equation is; Y = K X ( Y =_ x) ( blank is whatever your constant of proportionality is.
Thank you Pre-Algebra\
Signed~ Earl
Spaghettios wraps all their cans in a paper label. One Spaghettios can is 8 inches tall with a diameter of 4 inches. How many square centimeters of paper would Spaghettios need to wrap 12 of their cans.
Answer:
384
Step-by-step explanation:
8x4=32 32x 12 cans=384 sq centimeters
y=2x-3
x+y=18
solve for x
solve for y
X= ?
Y=?
Answer:
x=7, y=11
Step-by-step explanation:
Using simultaneous equations we can sub y in equation 1 into equation 2.
Equation 1. y=2x-3
Equation 2. x+y=18
Since y=2x-3 we can replace it so that
2'. x+2x-3=18
Now simplify
= 3x-3=18
Add 3 onto both sides to undo the subtraction of 3 so that,
3x=21
Now divide both sides by three to undo the multiplication of 3 so that,
x=7
Now sub in x (which is 7) into one of the equations to find y
7+y=18
To undo the five, subtract 7 from both sides so that
y=11
2 of out 3 people enjoyed the dance . if there are 171 students at the school dance how many people didn’t enjoy
Answer:
57
Step-by-step explanation:
2 out of 3 can be expressed as 2/3. Since we are looking at the 1 out of 3 people, we can use the expression 1/3 x 171 or 171/3, which equals 57
Name:
Date:
3. 7-14m = 2m-5
x-8 = Unit 2: Equations & Inequalities
Homework 2: Variables on Both Sides
Directions: Solve each equation. SHOW ALL STEPS!
1. 4x + 1 = 2x-5
r+15=4r-6
Bell:
** This is a 2-page document! **
MPOR
2. y-3 = -3y - 43
4. -106 + 5 = 7b+ 5
6. 10-2v = -5v-50
481 = (
The solutions for each of the equations provided in the reference picture is as follows:
(1) [x = (-3)]
(2) [y = (-10)]
(3) (m=3/4)
(4) (b = 0)
(5) (r = 7)
(6) (v = -60)
As per question statement and reference picture, we are provided with 6 different equations which are
(1) [(4 x+1)=(2 x-5)]
(2)[(y-3)=(-3 y-43)]
(3) [(7-14 m)=(2 m-5)]
(4)[(-10 b+5)=(7 b+5)]
(5)[(r+15)=(4 r-6)]
(6)[(10-2 v)=(-5 v-50)]
We are required to find the solution of all the equations mentioned above.
Considering equation (1), we get,
{[(4 x+1)=(2 x-5)] }
or,(4 x-2 x)=[(-1)-5]
or, 2 x=-(1+5)
or, 2 x=-6
or, x={-6}/{2}=(-3)
Considering equation (2), we get,
{[(y-3)=(-3 y-43)] }
or, (y+3 y)=(3-43)
or, 4 y=(-40)
or, y=(-10)
Simplifying equation (3), we get,
{[(7-14 m)=(2 m-5)] }
or, (7+5)=(2 m+14 m)
or, 12=16 m
or, m={12}/{16}={3}/{4}
Simplifying equation (4), we get,
{[(-10 b+5)=(7 b+5)] }
or, (5-5)=(7 b+10 b)
or, 17 b=0
or, b=0
Simplifying equation (5), we get,
{[(r+15)=(4 r-6)] }
or, (15+6)=(4 r-r)
or, 3 r=21
or, r=7
Finally, Simplifying equation (6), we get,
{[(10-2 v)=(-5 v-50)] }
or, (5 v-2 v)=[(-10)-50]
or, 3 v=-(10+50)
or, 3 v=-60
or, v=(-20)
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PLEEEEAAASEEE HELPPPP.
F: a₁ = 15 and ag = -15
Find a30
yellow
Answer:
a30= -15
Step-by-step explanation:
Anna works at an electronics store as a
salesperson. Anna earns a 5% commission
on the total dollar amount of all phone
sales she makes, and earns a 7%
commission on all computer sales. Anna
made a total of $2100 in sales and earned
$119 in commission. Write a system of
equations that could be used to determine
the dollar amount of phone sales Anna
made and the dollar amount of computer
sales she made. Define the variables that
you use to write the system.
The variables that
x + y = 2100
5 x + 7 y = 11700
Let x = total dollar amount of sales of phone;
y = total dollar amount of sales of computer
for total sales of phones anna earns 5% commission
So anna 's commission = 5% of x
= 0.05x
for total sales of computer anna earns 7% commission
So anna 's commission = 7% of y
= 0.07y
Given the total sales; x + y = 2100
And commission; 0.05x + 0.07y = 117; or 5x + 7y = 11700
Therefore the system of equations are
x + y = 2100 …….equation (1)
5 x + 7 y = 11700 ……equation (2)
In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
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Find the next term in each sequence. 1,5,25,125, . . . . . .
Answer:
Just multiply each by 5
Step-by-step explanation:
5x125= 625
explanation:
multiply the previous term by 5
The base of a right pyramid is a regular hexagon with sides of length m. the altitude is m. find the total surface area of the pyramid.
The total surface area of the pyramid 806.12 [tex]m^{2}[/tex].
What is surface area?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
Side (s) = 12
Altitude (h) = 6
Area = 3√3/2*s² + 3*s*√(h²+3s²/4)
Area = 3√3/2*(12)² + 3*(12)*√[6²+3(12)²/4]
Area = 806.12 [tex]m^{2}[/tex]
A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it.
Area of a square is equal to the sum of the lengths of its sides, where an is a square side.
The surface area of a three-dimensional shape refers to the amount of open space that it occupies. A solid shape's volume is the amount of space it takes up.
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What is the area and perimeter of a circle (-4,2) (-3,4)
Step-by-step explanation:
Let radius of circle is r=18 units
Perimeter of full circle is given by 2πr
Thus, perimeter of three quarters circle is given by,
( ¾ × 2πr) + (2 × r)
The perimeter of this "circle" would be:
( ¾ × 2 × π × 18) + (2 × 18) = 27π + 36 ≈ 120.78 m
Simplify each complex fraction.
3 /x-4 / 1 - 2/x - 4
Simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex] is equal to 3/(x-6).
As given in the question,
Given complex fraction is [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]
Simplify the denominator by taking least common multiple,
[tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }\\\\\\= \frac{3}{\frac{x-4}{\frac{x-4-2}{x-4} } }\\\\\\= \frac{3(x-4)}{(x-6)(x-4)} \\\\\\=\frac{3}{x-6}[/tex]
Therefore, simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex] is equal to 3/(x-6).
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You are organizing your high school’s sports banquet. The banquet hall rental is $250. In addition to this one-time charge, the meal will cost $7 per plate. Let x = the number of people who attend.
Part a: Write an equation that represents the total cost C.
Part b: Write an equation that represents the average cost A per person.
Part c: Use the graph of the model shown below to estimate the number of people who must attend before the average cost drops to $15 per meal.
Part d: Describe what happens to the average cost as the number of people who attend increases.
The required answers are-
Part a: The equation that represents the total cost C is C = 250 + 7x.
Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.
Part d: The average cost keeps on decreasing exponentially and then becomes straight.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Rental of banquet hall = $250
One time charge for meal = $7 per plate
x = the number of people who attend.
Part a: The equation that represents the total cost C
Since there are x people in the banquet
So, number of plates = x
Thus, Total One time charge for meal = 7x
So Total Cost = Rental of banquet hall + Total One time charge for meal
⇒ C = 250 + 7x
this is the equation that represents the total cost C
Part b: The equation that represents the average cost A per person
Putting x = 1 in the above equation of total cost we get,
A = 250 + 7 = 257
this is the equation that represents the average cost A per person
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal
From the graph it is seen that there are 25 people who must attend before the average cost drops to $15 per meal.
Part d: what happens to the average cost as the number of people who attend increases.
The average cost keeps on decreasing exponentially and then becomes straight.
The required answers are-
Part a: The equation that represents the total cost C is C = 250 + 7x.
Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.
Part d: The average cost keeps on decreasing exponentially and then becomes straight.
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Which store has the best deal on t-shirts?
T-shirt Land: 6 pack of t-shirts for $15
Discount Tees: 10 pack of t-shirts for $27
The Shirt Shop: 4 pack of t-shirts for $12
Answer:
6 pack of t shirts for 15 :3
Step-by-step explanation:
POOL Eight-ball pool is a popular game played on a pool table that has six pockets. In eight-ball pool, there are 7 striped balls, 7 solid-colored balls, and a black eight ball. At the beginning of each game, players position the 15 balls in a rack in preparation for the first shot
Answer:
a: 57.3
b: 3.8
Step-by-step explanation:
a: The formula to solve a triangle is a=height*base/2
that makes a= 9.96*11.5/2
a=57.27~=57.3
b: because there is 15 balls take 57.27 and divide it by 15
57.27/15=3.8
Find the first five terms of each sequence. aₙ =n² + 2n
Answer:yes b
Step-by-step explanation:
because you subtract it
Find the indicated term of each arithmetic sequence. a₁ =k, d=k+4 ; a₉
The value of term a9 is 9k+32.
How to find the value of term a9?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the term of arithmetic sequence and common difference,
a1 = 4 and d = K+4.
now find the value of term a9.
a(n) = a1 + (n - 1)d
now, substitute a(n) = a9, a1 = k, d = k+4.
a9 = k + (9 - 1)(k+4)
a9 = k + 8(k+4)
a9 = k + 8k + 32
a9 = 9k +32
Hence,The value of term a9 is 9k+32.
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What is an equation of the circle with center (5,-2) and radius 8 ? Check your answer.
The equation of the circle with radius 8 and center at (5 , -2) is (x - 5)^2 + (y + 2)^2 = 64.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius 8 and center at (5 , -2), substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (5 , -2)
r = 8
(x - 5)^2 + (y - -2)^2 = 8^2
(x - 5)^2 + (y + 2)^2 = 64
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If z varies directly with the product of x and y(z=k x y) , then z is said to vary jointly with x and y .
a. The area of a triangle varies jointly with its base and height. What is the constant of variation?
For the area of triangle, the constant of variation is 1/2.
What is variational constant?
The link between the independent (x) and dependent (y) variables is shown by a constant of variation. A continuous relationship between the variables indicates to the user that there is one; it does not alter regardless of how the scenario changes.
It can be employed to ascertain how the dependent variable will alter in response to changes in the independent variable. For instance, if a person drives continuously at the same pace, they may calculate their distance by multiplying the number of hours they spent driving by the speed they were moving at. In this instance, the speed is the constant since it remained constant regardless of how long or how far they travelled during the journey.
A triangle's area is equal to (1/2) * (base) * (height).
It fluctuates in tandem with both the base length and the height.
The (1/2) represents the variational constant.
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An electric toothbrush costs $72, including a 20% price markup. What was the cost for the store to purchase the electric toothbrush? $14.40 $52.00 $60.00 $64.80
The cost of the toothbrush will be equal to $14.40. The correct option is A.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that an electric toothbrush costs $72, including a 20% price markup.
The price of the toothbrush will be calculated as,
P = ( 72 x 20 ) / 100
P = 1440 / 100
P = $14.40
Therefore, the cost of the toothbrush will be equal to $14.40. The correct option is A.
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Answer: 60.00
i did the test.
What is an equation of the parabola with vertex (1,4) and focus (1,6) ?
The equation of the parabola that has vertex at (1,4) and focus (1,6) is
(y - 4)² = 8(x - 1)y² - 8y + 16 - 8x + 8 = 0What is known as a parabola?A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
This will depend on its aperture
Since the vertex and the focal axis are on the same axis, we analyze that:
v (1, 4)f (1, 6) the focus is on the right so the parabola is of the form y = x².(x - 1)² = 4p(y - 4)
f = (1, 4 + p)
4 + p = 6
p = 6 - 4
p= 2
(x - 1)² = 4*2(y - 4)
(x - 1)² = 8(y - 4)
x² - 2x + 1 - 8y + 32 = 0
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b. Reasoning Could you have used elimination in another way? Explain.
x-2y+3z = 12
2x-y-2z = 5
2x+2y-z = 4
So we are given with three different equations,
[tex]$$\begin{aligned}&x-2 y+3 z=12 \rightarrow(1) \\&2 x-y-2 z=5 \rightarrow(2) \\&2 x+2 y-z=4 \rightarrow(3)\end{aligned}$$[/tex]
We will convert the individual equations into matrices,
[tex]$$\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\2 & -1 & -2 & 5 \\2 & 2 & -1 & 4\end{array}\right]$$[/tex]
[tex]\begin{aligned}&R_2 \leftarrow R_2-2 \times R_1 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\2 & 2 & -1 & 4\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_3 \leftarrow R_3-2 \times R_1 \\&=\left[\begin{array}{rrr|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\0 & 6 & -7 & -20\end{array}\right] \\&R_2 \leftarrow R_2 \div 3 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_1 \leftarrow R_1+2 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right] \\&R_3 \leftarrow R_3-6 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 9 & 18\end{array}\right]\end{aligned}[/tex][tex]\begin{aligned}&R_3 \leftarrow R_3 \div 9 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right] \\&R_1 \leftarrow R_1+2.3333 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_2 \leftarrow R_2+2.6667 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & 0 & -1 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]
[tex]i. e.$$\begin{aligned}&x=4 \\&y=-1 \\&z=2\end{aligned}$$[/tex]
Solution By Gauss elimination method is,
[tex]$x=4, y=-1$ and $z=2$[/tex]
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What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?
The expected value of chi-square statistics is not significantly different from the observed value.
What is chi-square statistics?
Chi-square statistics is defined as a measure that is used to denote the difference between the expected frequencies and the observed frequencies of an event. It is illustrated using the symbol, 'χ2'.
Deciding for the goodness of a fit
The assigned value of chi-square is 1.273 while the critical value is 13.388
The hypotheses for the goodness of fit test are given below:
Null Hypothesis: the expected value is not significantly different from the observed values
Alternate Hypothesis: the expected value is significantly different from the observed values
We know that the chi-square test is right-tailed.
Further, the value of test statistics is 1.273, which is less than the critical value, 13.388
Thus we fail to reject the null hypothesis and we accept it.
Hence, we can conclude that the expected value is not significantly different from the observed value.
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