Answer:
[tex]y=(x+2)^2-16[/tex]
Step-by-step explanation:
Dash Canada offers two long-distance telephone plans. Plan X costs 6.5 cents per minute for calls between 8 A.M. and 6 P.M. weekdays (business hours) and 4.5 cents per minute at other times. Plan Y costs 5.3 cents per minute any time.
Above what percentage of business-hour usage will Plan Y be cheaper?
The percentage of business-hour usage that the Plan will be cheaper will be 22.6%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, Plan X costs 6.5 cents per minute for calls between 8 A.M. and 6 P.M. weekdays and 4.5 cents per minute at other times. Plan Y costs 5.3 cents per minute any time.
The percentage of business-hour usage that the Plan will be cheaper will be:
= (6.5 - 5.3) / 5.3 × 100
= 1.2 / 5.3 × 100
= 22.6%
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simplify -
(sin^2 (half infinity symbol))/
(1-cos(half infinity))
- 1
The simplified form of the given expression is cos(∞/2)
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
(sin²(∞/2))/(1-cos(∞/2)) - 1
Use the formula: sin²(x) = 1- cos²(x)
=> (1-cos²(∞/2))/ (1-cos(∞/2)) - 1
Use the identity a²-b² =(a-b) (a+b)
[(1-cos(∞/2)*(1+cos(∞/2)]/ (1-cos(∞/2)) - 1
common terms cancel out
(1+cos(∞/2) - 1
= cos(∞/2)
Thus, the simplified form of the given expression is cos(∞/2)
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Solve for x.
2+√5x = 7
answer
x = 5
2+√5x = 7
√5x = 7-2
√5x = 5
squaring on both sides
(√5x)²=(5)²
5x=25
x=25/5
x=5
What is the solution to the equation below?
√√5x-2-1-3
Answer:
C. x = 18/5
Step-by-step explanation:
You want the solution to √(5x -2) -1 = 3.
Solution
Add 1 to isolate the radical.
√(5x -2) = 4
Square both sides.
5x -2 = 16
Add 2, then divide by 5.
5x = 18
x = 18/5
Last season the St. Paul High School basketball team won 15 games and lost 25 games. What percent of the games were won by the school?
Answer:
To find the percentage of games won by the school, you can divide the number of games won by the total number of games played, and then multiply by 100.
In this case, the school won 15 games and lost 25 games, for a total of 15 + 25 = 40 games played.
So, to find the percentage of games won, you would do:
(15 / 40) x 100 = 37.5%
So, the St. Paul High School basketball team won 37.5% of their games last season.
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A teenager charges $112 to babysit for 8 hours at this rate how much dose the teenager charge to babysit for 5 hours In dollars
The teenager charge $70 to babysit for 5 hours.
What is Unit rate?The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.
For instance, the unit rate will be 50km/5.5 hours = 9.09 km/hour if 50km is travelled in 5.5 hours.
Given:
A teenager charges $112 to babysit for 8 hours.
So, in one hour the charges would be
= 112/8
= $14
Now, the charges for 5 hours
= 14 x 5
= $70
Hence, the charges for 5 hour is $70.
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PLEASE HELP ASAP WHAT IS THIS:
75/7^3
A. 7^2
B. 7^8
C. 7
D. 1
The simplified form of the given mathematical expression (7⁵/7³) include the following: A. 7^2.
What is an exponent?In Mathematics, an exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
Based on the law of indices for division, we have the following:
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
By applying the law of indices for division, we have the following mathematical expression:
Mathematical expression = 7⁵/7³
Mathematical expression = 7⁽⁵ ⁻ ³⁾
Mathematical expression = 7²
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Complete Question:
Simplify the following expression:
7^5/7^3
A. 7^2
B. 7^8
C. 7
D. 1
Consider the equation. What is a constant term or variable term that makes the equation have infinite solutions?
5x + 20 = 5x +_____
A. 5x
B. 15
C. 20
D. -20
A constant term that makes the equation have infinite solutions include the following: C. 20
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.
This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.
By applying the rule for an infinitely many solutions, we have:
5x + 20 = 5x + 20
5x - 5x = 20 - 20
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claudi invest £25 000 at a rate of 2% per year calcualte the of intrest she will have earned in 5 years
Answer:
2602,02008
Step-by-step explanation:
25000*(1+0,02)^5 - 25000 = 2602,02008
Please help me solve this problem
Answer: 20 people
Step-by-step explanation:
If each car has 2 benches and 2 people fit on each bench, you have to multiply 2 x 2 which equals 4. Then you have to multiply the number of how many people fit on each car by the number of cars. ( 4 x 5 = 20 ) Hence the answer is 20 people.
Answer:
20 people
Step-by-step explanation:
2 benches × 5 cars = 10 benches
10 benches with 2 people on each of them (10×2)
=20
Write the word sentence as an inequality
The product of -2 and a number c is greater than 30
I started to learn English recently and I’m struggling doing this homework. Can someone give me a hand?
The area of a rectangle is 17 1/2 inches squared and it's shorter side is 3 1/2 inches squared. Draw a diagram that shows this information. What is the length of the longer side?
The length of the longer side of the rectangle is, 5 inch.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The area of a rectangle is 17 1/2 inches squared.
And, it's shorter side is 3 1/2 inches squared.
Now, We know that;
Area of rectangle = Length × width
Here, it's shorter side is 3 1/2 inches squared.
Hence, We get;
⇒ Area of rectangle = Length × width
⇒ 17 1/2 = Length × 3 1/2
⇒ 35/2 = Length × 7/2
⇒ Length = 35/2 × 2/7
⇒ Length = 5 inch
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True or False:
Land bridges across oceans used to connect all continents on Earth.
Answer:
True
Step-by-step explanation:
WhaRyle can make 35 shoes in 3 days, while Andrei can make 65 shoes in 5 days. How many shoes did they make in all? If they donated 150 shoes to the less fortunate ones, how many shoes were left? t is the message that the work wants to convey to us?
They can create 100 shoes in a day if they work together. They will have 150 shoes left if they donate 150 shoes to the less fortunate.
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
Ryle can make 35 shoes in 3 days and Andrei can make 65 shoes in 5 days.
⇒ 35 + 65
Apply the addition operation,
⇒ 100
Together, they can make 100 shoes in a day.
If they work for 3 days, they will make 300 pairs of shoes.
⇒ 300 - 150
Apply the subtraction operation,
⇒ 150
If they donate 150 shoes to the less fortunate, they will have 150 shoes left.
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7.2Practice B
find the value of each variable in the parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides.
How do you explain parallelogram?A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposed sides and opposite angles because both conditions are a direct result of this postulate.Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.The sides of a parallelogram are not all equal. In a parallelogram, only the opposing sides are equal.Given data :
5 a - 9 ( b + 84 )° = 3a + 5 ( 3b )°
5 a - 3a = (3b - b + 84)°
2a = 2b + 84
a = 2b + 84 / 2
a = 2b + 42
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When simplified, -x − x is: 2x. -2x. x. None of these choices are correct.
Answer: When simplified, -x − x is:
-2x
When you subtract x from -x, you are essentially adding the opposite of x to -x, which is -x.
-x + (-x) = -x + -x = -2x
-x and x have opposite signs so when you add them up, the signs cancel out and you are left with the coefficient -2 in front of the x.
Step-by-step explanation:
Three large cones hang from the ceiling in an office building in front of a bank of windows. The height of each cone is 12 feet and the circumference of the base of each cone is 8π feet. The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
What is the total surface area painted black? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
ft²
The total surface area painted black = 90.5 square feet to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Given:
Three large cones hang from the ceiling in an office building in front of a bank of windows.
The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.
The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
Circumference of the base of the cone = 8π feet.
2πr = 8π
πr = 4π
The surface area of the cone = πr x height
The surface area of the cone = 12 x 4π
The surface area of the cone = 48π.
The total surface area painted black = 60% of 48π.
The total surface area painted black = 90.5 square feet to the nearest tenth.
Therefore, the result is 90.5 square feet to the nearest tenth.
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Answer: 90.5 square feet is the correct answer
Step-by-step explanation:
Mai says that the equation 2x+2=X+1 has no solution because the left hand side is double the right hand side. Do you agree with Mai? Explain your reasoning
The requried solution of the given equation is x = -1. Mai's statement is incorrect.
What is the reasoning?Reasoning is defined as math in the form of a puzzle for the living world such as codded sequences, relations, correlation, etc. is called reasoning.
here,
Mai says that the equation 2x+2=X+1 has no solution because the left-hand side is double the right-hand side.
So,
2x + 2 = x + 1
2x - x = 1 - 2
x = -1, Mai's statement is incorrect because the equation has a solution.
Thus, the requried solution of the given equation is x = -1. Mai's statement is incorrect.
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g:x->1/x-3 range of the function
The range of the function g:x->1/x-3 is (−∞,0)∪(0,∞),{y|y≠0}
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
Set the denominator in
1x−3equal to 0
to find where the expression is undefined.
x−3=0
Add 3 to both sides of the equation.
x=3
The domain is all values of x
that make the expression defined.
Interval Notation:(−∞,3)∪(3,∞)
Set-Builder Notation:
{x|x≠3}
The range is the set of all valid y values.
Interval Notation:(−∞,0)∪(0,∞)
Set-Builder Notation:
{y|y≠0}
Domain: (−∞,3)∪(3,∞),{x|x≠3}
Range: (−∞,0)∪(0,∞),{y|y≠0}
Therefore, the range will be(−∞,0)∪(0,∞),{y|y≠0}
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Write the equation of the line, in slope-intercept form, with the
following information:
Slope: -1/5
Point (10,2)
The linear equation of the line is slope =-1/5 and point is 10,2
How to determine the line equation?The slope is given as:
m = -1/5
The point is given as:
10,2
A linear equation in slope intercept form is represented as:
y = m + p
So, we have:
y is intercept
mx is slope
p is point
y = -1/5x - 10
Add 10 to both sides
y + 10 = -1/5x
Express -1/5x as -1/5(x)
y + 10 = -1/5(x)
Subtract 0 from x
y + 10 = -1/5(x - 0)
Hence, the linear equation of the line is y = -1/5x - 10 and y + 10 = -1/5(x - 0)
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Last week, Layla paid herself $1439. If Steph worked 15 hours and Destiny worked 20 hours how many hours did Marco work
The number of hours Marco worked obtained from the equation formed using the information on the $1439 Layla worked, and the 15 and 20 hours Steph and Destiny worked is 36 hours
What is an equation?An equation is a mathematical or science statement expressing the equivalence of two expressions, located on either side of an '=' sign.
Part of the question obtained from the table, graph and equation in a similar question posted online are;
The details of the payment of the employees of the print shop, Stephine, Marco, and Destiny, and the owner of the print shop Layla are as follows;
The amount, Layla, the owner of the business earns = 2 × The amount the employees earn
Amount Stephine earns, working 15 hours = $157.50
Amount Destiny earns working 20 hours = $400
Marco's wage = 9·h = $9 per hour
When Layla earns $1439, Steph works for 15 hours, Destiny works for 20 hours, the number of hours Marco works can be found by expressing the information as an equation as follows;
1439 = 2 × 157.50 + 2 × 400 + 9 × h
h = (1439 - (2 × 157.50 + 2 × 400))/9 = 36
The number of hours Marco worked, h = 36
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Please help ASAP!!!
Write the equation of the line that is perpendicular to y=−13x+2 and passes through ( 2 , 8)
Considering the definition of perpendicular line, the equation of the line that is perpendicular to y=−13x+2 and passes through (2, 8) is y= 1/13x + 102/13.
What is a linear equationA linear equation o line can be expressed in the form y= mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Perpendicular linePerpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= -13x +2
where:
the slope m is -13.the ordinate to the origin b is 2.Since you multiply the slopes of two perpendicular lines, you get –1. So:
-13 × slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-13)
slope perpendicular line= 1/13
The line passes through the point (2, 8). Replacing the slope and the coordinates of the point in the expression of a line:
8= 1/13× (2) + b
8= 2/13 + b
8 - 2/13= b
102/13= b
Finally, the equation of the perpendicular line is y= 1/13x + 102/13.
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Help me out folks…..
Answer: C
Step-by-step explanation:
The problem says that one side of a right triangle has a length of 12 feet.
This means that when you use the Pythagorean theorem on the triangle, it should work.
The lengths that the Pythagorean theorem doesn't work are the ones that don't work.
I is true.
5^2+12^2=13^2
II is also true.
63+9^2=12^2
III is false, however. The Pythagorean theorem doesn't work.
Therefore, the answer is C. I and II only.
Answer: id say it would be C
Step-by-step explanation:
Can someone please help me? I really need this
Answer:
Step-by-step explanation:
D
Answer:
no they dont
Step-by-step explanation:
If x represents the hypotenuse of this right triangle, which equation can be used to find the value of x?
A.
B.
C.
D.
The equation that can be used to find the value of 'x' will be x² = (10)² + (8)². Then the correct option is C.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
If x represents the hypotenuse of this right triangle. then the value of the variable 'x' is calculated as,
x² = (10)² + (8)²
The equation that can be used to find the value of 'x' will be x² = (10)² + (8)². Then the correct option is C.
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Answer:
ccccccccccc
Step-by-step explanation:
took test
One-half the square of a number is equal
to 16 more than twice the number. What
is the number?
The number is x = 0 or 18.The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
What is algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z. Algebraic sign language. Many students find algebra intimidating since it's the first math course they take where they have to deal with variables, abstract ideas, and problem-solving skills. Additionally, there is sometimes insufficient effort made in the classroom to relate algebra to students' daily lives and explain why learning it is important.
Let x be the number. Translation of the given information into algebra gives
√(2x) = x/3
Solve for x. Note x ≥ 0.
2x = x2/9
If x ≠ 0,
2 = x/9 ⇒ x = 18
Solutions are x = 0 or 18.
The complete question is,
The square root of twice a number is equal to one-third of that number. Find the number.
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Please check image for questions!
2)Slope intercept form: y = -2x + 5
Point slope form: y - 5 = -2(x - 4)
Standard form: 2x + y = 13
3)Slope-Intercept Form: y = -2x + 10
Point-Slope Form: y - 6 = -2(x - 4)
Standard Form: -2x + y - 10 = 0
Define Slope interceptThe Slope-Intercept Form is a linear equation written in the form:
y = mx + b
where m is the slope and b is the y-intercept.
Define Point-Slope FormPoint-Slope Form is a linear equation written in the form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Define Standard FormStandard Form is a linear equation written in the form:
Ax + By = C
where A, B and C are constants.
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Find the value of x
Please help this is due today
Answer: X= 72°
Here if we see the figure is not labelled so I am assuming it to A,B,C AS MAIN TRIANGLE and BD bisector of angle ABC.
We have to find out that angle DBC.
ANGLE CAB = ANGLE DBA
Hence Angle CDB = ANGLE CAB + ANGLE DBA
27° + 27° = CDB = 54° = ACB ( if sides are equal then opposite angles are also equal.)
so required angle x = 180° - 54° - 54° ( sum of angle of triangle equals 180)
so x= 72°
District size in 1790
The U.S. population in 1790 was 3,615,920, and the House size was set at 105.
The ideal congressional district size (Standard Divisor) in 1790 was [answer].
(Give your answer rounded to one decimal place.)
The ideal congressional district size (Standard Divisor) in 1790 was 34437.33.
What is Standard divisor?The number of persons each House of Representatives seat represents is known as the "Standard Divisor" (SD). By dividing the total population of all the states by the total number of seats available for voting, the SD is determined. SD is calculated as Total U.S. Population / Total Number of Voting Seats.
The ratio of the entire population to the available seats (or other allocations) is known as the standard divisor. • The Hamilton system divides up any extra seats among the states with the largest fractional parts after allocating each state its lower quota initially.
Given,
population in 1790 was 3,615,920,
number of objects = 105
⇒ Standard divisor = total population / number of objects
⇒ Standard divisor = 3,615,920 / 105
⇒ Standard Divisor = 34437.33
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What is the volume of this object?
cubic units
Submit
www
The volume of a cube is a*a*a where a is length of the side,
What is Surface area of cube?
Surface area of cube can be defined as the product of six and square of a .
Given ,
to find the volume of cube.
Volume of a cube is the overall cubic gadgets occupied via it, in a 3-dimensional area. A cube is a 3D-shape, that has six faces, twelve edges and 8 vertices. hence, the extent of a cube is the space enclosed via its six faces. not like, 2nd shapes, it has additional dimensions aside from period and width, that is known as height or thickness. therefore, the quantity of dice is equal to fabricated from its duration, width and height. it's far measured in cubic gadgets. The extra the value of its dimensions the more is the quantity of dice.
Volume of cube is = a*a*a
where a is length of side of cube or edges.
or it can be also called
volume of cube = length*width*height
Hence, The volume of a cube is a*a*a .
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