bring the variable to the left side and bring all the remaining values to the right side.
How do you write a step-by-step inequality?Image search results for Write the inequality and solve it. -17 -14 ■ -21 -2 -9 -15
To fix an inequality, use these steps:
Step 1: Remove fractions by multiplying all terms by the fractions’ least common denominator.
Step 2 Simplify the inequality by merging like words on either side.
Step 3 Subtract or add amounts to get the unknown on one side and the digits on the other.
In algebra, the letter “x” is frequently used to represent an unknown value. It is referred to as a “variable” or “unknown” at times. X is a variable in x + 2 = 7, but we can deal with it.
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A travel guide has dimensions 8 in. by 10 in. What scale factor should be used to make an enlarged version that has dimensions 12 in. by 15 in.
The scale factor for the length is 12/8 = 1.5 and the scale factor for the width is 15/10 = 1.5
So the scale factor used to make an enlarged version is 1.5.
What is the scale factor?A scale factor is a value used to multiply the dimensions of an object in order to increase or decrease its size. It is often represented as a ratio, such as 1:2 or 1/2, which indicates that the new object is half the size of the original object. Scale factors can also be expressed as a decimal or a percentage, such as 0.5 or 50%. Scale factors can be used in various fields such as architecture, cartography, and graphic design.
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Four siblings have a total of 3/4 pound of candy leftover from Halloween. If they split
it equally, how much will each child have?
Answer:
Each child will have 3/16 pound of Halloween candy.
Step-by-step explanation:
To find out how much candy each sibling gets, we need to divide 3/4 by 4
3/4 divided by 1/4 = 3/16
Therefore, our answer is 3/16.
7.) On Monday the rate for a hotel suite is $299.00 a night plus 6% tax. That same room rents for $349.00 plus 6% tax on a Friday. What is the difference in costs including tax between the two nights?
Answer:
The difference in costs including tax between the two nights is $53
Step-by-step explanation:
To find the cost of the hotel suite on Monday including tax, we first calculate the amount of tax by multiplying the room rate by 6% (0.06):
$299.00 * 0.06 = $17.94
So the total cost of the room on Monday including tax is:
$299.00 + $17.94 = $316.94
Next we find the cost of the hotel suite on Friday including tax:
$349.00 * 0.06 = $20.94
So the total cost of the room on Friday including tax is:
$349.00 + $20.94 = $369.94
Finally, to find the difference in costs between the two nights, we subtract the cost of the room on Monday including tax from the cost of the room on Friday including tax:
$369.94 - $316.94 = $53
The difference in costs including tax between the two nights is $53.
Answer:
The difference in costs including tax between the two nights is $53--------------------------------
The cost x including a 6% tax is:
x + 6% =x + 0.06x = 1.06xThe difference in costs including tax is:
349*1.06 - 299*1.06 = (349 - 299)*1.06 = 50*1.06 = 53Eric went for a drive in his new car. He drove for 182.4 miles at a speed for 57 miles per hour. For how many hours did he drive?
Answer:
3.2 hours
Step-by-step explanation:
182.4÷57=3.2
time divided by speed equals time
22. What is the value of k such that x - 6 is a factor of
f(x) = 3x³ - 17x² - kx + 18? Justify your answer.
Answer:
k = 9
Step-by-step explanation:
According to the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0
given (x - 6) is a factor of f(x) then f(6) = 0 , that is
3(6)³ - 17(6)² - 6k + 18 = 0
3(216) - 17(36) - 6k + 18 = 0
648 - 612 - 6k + 18 = 0
36 - 6k + 18 = 0
54 - 6k = 0 ( subtract 54 from both sides )
- 6k = - 54 ( divide both sides by - 6 )
k = 9
(PLS HELP QUICKLY!) (ONLY HAVE 10 MINUTES!!! PLS HELP)
A fundraiser is being held to raise money for a new school playground. Of every $20 raised, $16 will be spent on playground equipment. If the goal of the fundraiser is $320.00 for playground equipment, how much money will it need to raise?
Answer:
$400
Step-by-step explanation:
If $16 will be spent, then you should do 320/16=20 to find out how many times people are donating. Since that answer what 20, they need people to give 20*20=400 oo be able to raise enough money fOr playground equipment
How do you know how many real solutions?
The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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Manish and Ravi are reading the same series of books. As of today, Manish has read a total of 544 pages. If he reads at the same pace, after 8 days he will read a total of 928 pages.
The total number of pages that Ravi has read is modeled by the equation y=51x+594, where x is the number of days after today, and y is the total number of pages read.
Who will finish the series first? Why?
Select the response that correctly answers both questions.
Responses
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish will finish first because he has already read more than Ravi as of today, and he reads more than Ravi each day.
The person that will finish the series first is;
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
How to interpret Linear Equation Problems?The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Total pages manish has read as at today = 544 pages
He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544
922 - 544 = 8m
m = 378/8
m = 47.25
Thus, his rate is 47.25 pages per day
The equation for Ravi is y = 51x + 594
This shows a rate of 51 pages per day
Thus, Ravi will finish first
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There are 20 gloves in a drawer: 5 pairs of black gloves, 3 pairs of brown,
and 2 pairs of gray. You select the gloves in the dark and can check them
only after a selection has been made. What is the smallest number of gloves
you need to select to guarantee getting the following?
(a) At least one matching pair
(b) At least one matching pair of each color
The number of gloves selected for each cases is 11 and 19 gloves respectively.
How is selection done?
In mathematics, most of the times selection is done using permutation and combination.
Putting things or numbers in order is known as a permutation.
Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
Given,
Total black gloves = 5 left hand+ 5 right hand
Total brown gloves = 3 left hand + 3 right hand
Total gray gloves = 2 left hand + 2 right hand
Now to find the least number of gloves for the given conditions, we start with the worst condition.
a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.
Now to make one pair, we need to select only one glove of the opposite hand of any colour.
Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves
b) In this case also we start with worst case.
For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and 2 gray gloves of any one hand.
Therefore to get matching pair of each colour, we have to take one more gray glove.
Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.
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An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 5 black squares, can be drawn on the checkerboard
The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
A square is a particular type of closed figure that has four straight sides, four right angles, and sides that are all the same length. As a result, we can say that: A square is a particular variety of rectangle. Rectangles are not always squares, but squares are always rectangles.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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The total number of rectangles you can draw using the grid lines exists 1296.
What are the peculiarities of rectangle?A shape with two opposing sides that are equal and parallel is called a quadrilateral. It has four sides, four 90-degree angles, and is a polygon. A rectangle is a two-dimensional form.
An example of a closed form with four straight sides, four right angles, and all sides being the same length is a square. Therefore, we can state that a square is a certain type of rectangle. Squares are not always rectangles, but rectangles are always squares.
Number 2 × 2 squares have 4 black squares
all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.
there are 6 × 6 = 36 3 × 3 squares
there are 5 × 5 = 25 4 × 4 squares
there are 4 × 4 = 16 5 × 5 squares
there are 3 × 3 = 9 6 × 6 squares
there are 2 × 2 = 4 7 × 7 squares
there is 1 8 × 8 square
Summing we get 91 squares
The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.
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y^2=1/5(x-4), (24,2)
D t
-60 0
-56 10
-24 90
-20 100
-8 130
0 150
Choose the correct statement.
Select one:
a.
The function is
D(t)=52t−150
b.
The function is
D(t)=25t−150
c.
The function is
D(t)=52t−60
d.
The function is
D(t)=25t−60
Answer: To determine the correct statement, you need to find a pattern in the values of D(t). You can do this by finding the difference between consecutive values of D(t).
The difference between -60 and 0 is 60.
The difference between 0 and 10 is 10.
The difference between 10 and 90 is 80.
The difference between 90 and 100 is 10.
The difference between 100 and 130 is 30.
The difference between 130 and 150 is 20.
The pattern that emerges is that the difference between consecutive values of D(t) is always 25. This means that the correct statement is "The function is D(t)=25t−60". The correct answer is therefore d.
Step-by-step explanation:
A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have
A pentagonal prism have 35 diagonals.
We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,
where n= the number of sides
We find the number of diagonals of a pentagonal prism.
As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.
For a pentagonal prism n = 10
So, using above formula the total number of diagonals would be,
d = [10 × (10 - 3)] / 2
d = (10 × 7) / 2
d = 70/2
d = 35
Therefore, the total number of diagonals would be = 35
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A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time
(i) the length of the hadow cat by another pole 10 m 50 cm high,
On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x/y = k, x = ky
where k is a constant.
Thus, x₁ / y₁ = x₂ / y₂
5.6 / 3.2 = 10.5 / y₂
5.6 × y₂ = 10.5 × 3.2
y₂ = (10.5 × 3.2) / 5.6
y₂ = 6
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What is g(4) when given the function g(x) = 6x + 32?
Answer:
The value of g(4) of the given function is 56.
the scale on a map is 1:5000000
two towns are 7cm apart on the map
work out the actual distance between the towns
Answer:
Step-by-step explanation:
scale,= 1 : 5000000
it means 1 cm depicts 5000000cm
or 50000m else 50km
the distance between two towns in map = 7cm
so the distance between two towns = 7 *50
= 350km
You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work
There are 8 half dollars and 9 quarters inside the cup.
We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.
Let h be the number of half dollars and q be the number of quarters.
The first equation represents the total number of coins in the cup:
h + q = 17The second equation represents the total value of the coins:
0.5h + 0.25q = 5.50To solve for h and q, we can use either the substitution or elimination method.
By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.
So, q = 17 - h
then substitute it into the second equation:
0.5h + 0.25(17 - h) = 5.50
By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9
So, there are 8 half dollars and 9 quarters inside the cup.
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P is the centroid of ΔXYZ. If XU = 48, what is PU?
The value of the PU in the given triangle is 19.
What is centroid?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
Given,
'p' is the centroid of triangle XYZ and XU is 57.
Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'
from the centroid Theorem, we can write;
XP = 2/3 * XU
plug the values 'XU' in the above equation:
XP = 2/3 *57
XP = 2*19
XP = 38
from figure:
XP + PU = XU
PU = XU - XP
Plug 'XU' and 'XP'
PU = 57 -38
PU = 19
therefore, the PU of the given triangle is 19 units.
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Complete question:
Adella wants to have $10,000. 00 saved in 5 years. Her local bank offers an account at 4% APR
compounding monthly. How much would she need to deposit to reach her goal?
$8000. 33
$8191. 67
$8189. 67
$8219. 29
The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.
What is compound interest?Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.
Given that:
A = $10,000
r = 4% = 0.04
t = 5 years
n = 12 (since the compounding is monthly)
P = ?
The compound interest is given as follows:
[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
Substituting the values in the formula we have:
[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]
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HELP ME PLEASE AND THANK YOUUU
Answer:
x=3 y=1
Step-by-step explanation:
-2/3x+3=2x-5
x=3
y=-2/3(3)+3
y=1
y=2(3)-5
y=1
A fifth grader takes a standardized achievement test (mean = 125, standard deviation = 15) and
scores a 148. What percent of children made higher than a 148?
the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
What is Percentile rank?When compared to other students in the same grade and topic, for instance, a student's percentile rank shows how well they performed. The percentile rank of a student indicates whether their score was on par with or higher than that of the norm group's percentage of pupils. In statistics, the percent of scores in a frequency distribution that are lower than a specific score is known as the percentile rank of that score. A percentile rank returns a numerical value, which really indicates the proportion of people who fall inside that range. Since it is a percentile, its range is always between 1 and 99, with 50 serving as its mean or average rank. Only normalized values or data are ever usable in this fashion.- Mean, $\boldsymbol{\mu}=125$.- Population standard deviation, $\sigma=15$.- Marks obtained by child $(X)=148$Need to find the percentile rank for child's score.
Let[tex]$\mathrm{X}$[/tex]denote marks obtained by the child in the achievement test.
The [tex]$\mathrm{Z}$[/tex]value is given as,
[tex]$$Z=\frac{X-\mu}{\sigma}$$[/tex]
Using equation (1), the required percentile rank for child's score is expressed as,
[tex]& Z=\frac{148-125}{15} \\[/tex]
[tex]& Z=1.533[/tex]
The probability value corresponding to the Z=1.533, obtained from the Z table is 0.93736.
Thus, the percentile is 0.93736.
Therefore, the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
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It costs $3 to bowl a game and $2 for shoe rental Write an expression for the total cost (in dollars) of g games.
Answer: , P = 2 +3g
Step-by-step explanation:
Question
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.
How to calculate the mean?From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
The maximum time (in seconds) that she can take on her last lap and still make the team will be:
= (60 × 5) - (63 + 62 + 65 + 58)
= 300 - 248
= 52
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the cube root parent function is reflected and stretched by four. it is translated six to the right and five down. write an equation that represents this new function
The equation for new function is,
⇒ f (x) = ∛( 1/4x - 6) - 5
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The parent function is,
⇒ g (x) = ∛x
Now, After reflected and stretched by 4, we get;
⇒ g (x) = f (1/4x) = ∛ 1/4x
And, After translated 6 units to the right, we get;
⇒ g (x) = f (x - 6) = ∛ 1/4x - 6
And, After 5 unit down, we get;
⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5
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A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest
having an altitude of 8849m. Calculate the value of ‘g’ at that point.
Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.
The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.
T = 2 × π × (square root of 1.00 m / 9.81 m/s²)
T = 2 * 3.1416 * (square root of 0.101936799)
T = 6.2832 * 0.319275428
T = 2.00 seconds
The period of this pendulum correct to 3 significant figures is 2.00 seconds.
The frequency of this pendulum is solved by the formula f = 1/T
f = 1/2.00 seconds
f = 0.500 hertz
Answer: 9.76 m/s^2
Step-by-step explanation:
........... I donr know what I'm doing-
Intercept = 1
Equation - y = -(2/5)x + 1
i don’t know this pls help
The perimeter of the right triangle is 228 inches
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.
Since it is a right triangle,
c² = 57² +76²
c² = 3249 + 5776
c² = 9025
c= √ 9025 = 95
Perimeter is the sum of all sides
Perimeter = 57+76+95 = 228 inches
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What grade is 2 step equations?
Teaching two step equations is a standard that needs to be taught in both 7th and 8th grade middle school PreAlgebra Math.
What is a 2 step equation?Two step equations are algebraic equations that can be solved in exactly two steps and gives the final answer of the variable in two steps. Generally two step equations are of the form ax + b = 0 where a and b are real numbers.
How do we solve 2-steps equation?A two-step equation is an equation that requires two steps to solve. We must eliminate any constant that is on the same side as the variable first. To solve first use the inverse operations to isolate the variable by itself. We can do only one operation in single step.
Now
we solve two steps equation in grade 7th and 8th.It is very easy to understand.
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How do you find the third side of a right triangle with two sides?
The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.
The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because , it is opposite to the angle 90°.
Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .
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In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
Answer: 15
Step-by-step explanation: In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N