The length of the side of the equilateral triangle is 20.76 inches.
Here it is given that the length of the altitude of the equilateral triangle is 18 inches.
The formula of the altitude(h) of the equilateral triangle is
h = [tex]\frac{\sqrt{3} }{2}[/tex]a
Here a is the side of an equilateral triangle.
So we have
18 = [tex]\frac{\sqrt{3} }{2}[/tex]a
a = 18 × 2/[tex]\sqrt{3}[/tex]
For the rationalization of the fraction multiply numerator and denominator by [tex]\sqrt{3}[/tex].
a = [tex]\frac{18 * 2 * \sqrt{3} }{\sqrt{3}\sqrt{3} }[/tex]
= [tex]\frac{18 * 2 * \sqrt{3} }{3}[/tex]
= 6 × 2 × √3
= 12×√3
= 12 × 1.73
= 20.76 inches
Therefore the length of the side of the triangle is 20.76 inches.
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Study island/////////////////////\
√2 is 1 approximately less than √6. (option A).
What is the relationship between √2 and √6?The square root of a number can be described as the factor of a number that when multiplied by itself would yield the number. For example, the square root of 16 is 4. This is because 4 multiplied by 4 is equal to 16. The sign used to represent square root is √.
The square root of 2 is 1.414
Th square root of 6 is 2.449
The difference in the square roots of 6 and 2 is : 2.449 - 1.414 = 1.04
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Use a double-angle identity to find the exact value of sin 120° .
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
[tex]\sin 2x=2\sin x \cos x \\ \\ \sin 120^{\circ}=2\sin 60^{\circ} \cos 60^{\circ} \\ \\ =2(\sqrt{3}/2)(1/2) \\ \\ =\frac{\sqrt{3}}{2}[/tex]
Tulip bulbs are on sale at two different stores. Which store offers a lower price per tulip bulb? Explain your reasoning or use a diagram to show your thinking.
● Store A: 4 tulip bulbs for
$9 ● Store B: 5 tulip bulbs for $11
Finn and Gabby are selling raffle tickets for a school fundraiser. If Gabby sold 17 fewer raffle tickets than Finn did, which of the following represents the relationship between f, the number of tickets Finn sold and g, the number of tickets Gabby sold?
A. f + g = 17
B. f - g = 17
C. fg = 17
D. f/g = 17
Answer:
B. f - g = 17
PLEASE ANSWER PLEASEEEEEEEEEEEEEEEEEEEEE
32 meters
18 meters
8 meters
6 meters
Answer:
18 meters
Step-by-step explanation:
24 is dilated by 3/4
Which means 24 * 3/4 or 24 * .75
i t h i n k
Find a value of 3x-2 when x =4
If x=4, then substitute x for 4, multiply by 3 since 3 was being multiplied by x, then subtract 2, which gets you 10
Amy gave the cashier $60 to pay for 3 giant dog pillows. The cashier gave her $6.15 in change. Each dog pillow cost the same amount.
What is the cost in dollars and cents for each dog pillow?
The cost in dollars and cents for each dog pillow is $17.95
What is the total cost of 3 giant dog pillows?
The total cost of the 3 giant dog pillows is determined as the amount Amy gave the cashier minus the change the cashier handed to Amy, in essence, the cost in dollars and cents for each dog pillow can now be computed the total cost of the 3 giant dog pillows divided by the number of dog pillows purchased
total cost for 3 giant dog pillows=total cost of amount given to cashier change received
total cost of amount given to cashier=$60
change received=$6.15
total cost for 3 giant dog pillows=$60-$6.15
total cost for 3 giant dog pillows=$53.85
cost per dog pillow=total cost for 3 giant dog pillows/number of dog pillows purchased
cost per dog pillow=$53.85/3
cost per dog pillow=$17.95
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complete the equation of the line whose slope is -2 and y intercept is (0,3)
Write the equation of the line passing through the points (-4,5) and (-5,4)
Answer:
y=x+9
Step-by-step explanation:
The general equation for a straight line is y=mx+c
1. first we need to find the gradient (m) to do this we do
4-5/-5-(-4)
which gives the answer of 1. This means or gradient (m) is 1. we can substitute this in our general formula y=mx+c which gives
y=1x+c this can also be written as y=x+c
2. we need to find the value of c. to do this we can sub in any co-ordinates from the question in this case we will be using (-4,5)
-4 is the x co-ordinate
5 is the y co-ordinate
5= -4+c
to get c we add 4 on each side we get
9=c
we can sub this into the equation we produced with the gradient giving us
y=x+9
3. the final answer is y=x+9
- Write 1,340 in scientific notation. (1 pc
O1.34 x 104
O 1.34 x 10³
O 13.4 x 10³
O 1.34 x 10-
Answer:
1.34×10³Step-by-step explanation:
that is the answer
Write each expression in simplest form. ∛125 x⁶ - ∛27 x⁶
The simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .
The given expression is,
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to solve step wise,
[tex]\sqrt[3]{125}[/tex] = [tex]\sqrt[3]{25.25.25}[/tex] = 5
[tex]\sqrt[3]{27}[/tex] = [tex]\sqrt[3]{3.3.3}[/tex] = 3
Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 5[tex]x^{6}[/tex] - 3[tex]x^{6}[/tex]
On further simplifying, we will get
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 2[tex]x^{6}[/tex]
Thus we can write that the simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .
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Hattie had $1800 to invest and wants to earn 2.4% interest per year. She will put some of the money into an account that earns 2.3% per year and the rest into an account that earns 3.5% per year. How much money should she put into each account?
The amount invested in the account with 2.3% interest is $1650 whereas $150 was invested in the account whose interest rate is 3.5%
What is Hattie's annual earnings on the investment of $1,800?
The earnings that Hattie would receive every year on the investment is $1,800, the investment multiplied by the expected rate of return of 2.4%
annual earnings=$1,800*2.4%
annual earnings=$43.20
Let the amount invested at 2.3% to be x and the amount invested at 3.5% would be (1800-x), hence, the interest earnings are shown thus:
interest on 2.3% investment=x*2.3%=0.023x
interest on 3.5% investment=(1800-x)*3.5%
interest on 3.5% investment=63-0.035x
total interest=0.023x+63-0.035x
total interest=63-0.012x
43.20=63-0.012x
0.012x=63-43.20
0.012x=19.80
x=19.80/0.012
x=amount invested at 2.3%=$1650
amount invested at 3.5%=$1800-$1650
amount invested at 3.5%=$150
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5. 2 w+6 ≤ 10 this is for algebra
I need to find out if this is a horizontal or vertical compression/stretch and by what factor and also if it is a vertical, up or down, or horizontal, left to right, translation -4f(x)
The transformation rule f(x) → - 4 · f(x) is the consequence of combining a reflection about the x-axis and a vertical stretch.
What kind of rigid transformation is behind a transformation rule?
According to the statement, we must conclude what kind of rigid transformations are behind the transformation rule f(x) → - 4 · f(x). Rigid transformations are transformations applied on a function such that its form is not altered. The most common transformations are listed below:
Horizontal translation: f(x) → f(x - k), right when k > 0.Vertical translation: f(x) → f(x) + k, up when k > 0.Horizontal compression: f(x) → f(k · x), 0 < k < 1Horizontal stretch: f(x) → f(k · x), k > 1Vertical compression: f(x) → k · f(x), 0 < k < 1Vertical stretch: f(x) → k · f(x), k > 1Reflection about the x-axis: f(x) → - f(x)Reflection about the y-axis: f(x) → f(- x)Then, we find that the transformation rule f(x) → - 4 · f(x) is the consequence of combining a reflection about the x-axis and a vertical stretch.
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Tristan wants to build a square garden in his backyard that will cover an area of 75ft(squared). If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain
The 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.
We are given that:
Area of a square garden = 75 feet²
Let the side of the square garden be x
x² = 75
x = √ 75
x = 5 √3 feet
Perimeter of the square garden = 4 × x feet
Perimeter = 4 × 5 √ 3 feet
Perimeter = 20 √ 3 feet
P = 34.64 feet.
Now, Tristan only has 32 feet of material.
So, the material is not enough.
Therefore, we get that, the 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.
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plot the point in a coordinate plane then determine whether AB and CD are congruent A(-2, 1), B(2, 1), C(3, 2), D(3, -2).
For the given points, As the distance of AB and CD is same, So AB and CD are congruent.
What are congruent lines?If and only if their lengths are identical, any two line segments are congruent. The length of the line segment AB is identical to the length of the line segment CD in the aforementioned representations. Consequently, the two line segments AB and CD are similar.
length of AB = √(2+2)² + (1-1)² = 2
length of CD = √(3-3)² + (2+2)² = 2
As the value of AB = CD So, we can say that AB and CD are congruent.
Graph is attached at the end.
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What is the logarithmic form of each equation?
c. 1=3⁰
The logarithmic form of the given equation is log₃(1) = 0.
A logarithm is the degree to which a number must be raised in order to produce another number. For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 10² = 100.
The given equation is 1 = 3⁰
To convert this exponential form into logarithmic form, we are required.
Consider the given exponential form:1 = 3⁰
Taking logarithm on both sides with the base as 3, we get,⇒ log₃(1) = log₃(3⁰)
Now using the logarithmic rule logₐ(aⁿ) = n × logₐ(a) in the RHS of the above equation, we get
⇒ log₃(1) = 0 × log₃(3)
⇒ log₃(1) = 0 (Because 0 multiplied by any number equals zero,)
Therefore, the value of 1 = 3⁰ is given by log₃(1) = 0.
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earle bailey has 20 songs to choose from but can play only 7 in the next half‑hour on siriusxm classic vinyl. how many different (ordered) playlists are possible? (use decimal notation. give your answer as an exact number.)
The answer is 77520.
What is meant by decimal notation?Decimal notation is an alternative way to represent fractional values in mathematics. This indicates that base 10 is being used for the fractional representation. Both the fractions and decimals can be transformed. For instance, the decimal representation of the fraction 5/10 is 0.5.Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is considered standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 108.Because they represent a portion of a whole number, decimals are equivalent. The distinction is that fractions and decimals are written using different notations. We can visually estimate how much of a full number we are working with thanks to decimal notation.How many different (ordered) playlists are possible?
Number of possible playlists = 77520
Explanation:
Total number of songs = 20
Songs in the playlist = 7
So, we need to select 7 songs out of 20. This can be done using combinations.
n = 20 , r=7
C( n , r ) = ?
C( n , r ) = C (20 , 7)
= 20! / ( 7! (20-7)!)
= 20! / ( 7! × 13! )
= 77520
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estimate 1624 divided by 23 using compatible numbers
The estimate of the quotient 1624 divided by 23 using compatible numbers is 81
How to estimate the quotient of the numbers using compatible numbersThe quotient of numbers is the result of dividing the numbers
The statement is given as
1624 divided by 23 using compatible numbers
The expression can be represented as:
1624 ÷ 23
Using compatible numbers, 1624 can be estimated as 1620, while 23 can be estimated as 200:
So, the expression becomes
1624 ÷ 23 = 1620 ÷ 20
Next, we divide the estimated numbers
So, we have
1624 ÷ 23 = 81
Hence, the estimate of the quotient 1624 divided by 23 using compatible numbers is 81
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For each function, identify the transformation from the parent function y=b x . y=7 (x-5)
Transformation of y= bx into y=7(x-5) will take place by by horizontal translation by 5 units to the right, vertical dilation by a scale factor of 7 .
A parent function is the simplest form of a particular family of functions. A family of functions is a group of functions that have the same highest degree and therefore the same graph shape. Function transformations "move" or "resize" or "mirror" the graph of the parent function. Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means it is a reflection here, 'a' stands for vertical stretch , 'b' stands for horizontal stretch , 'c' stands for horizontal movement , 'd' stands for vertical movementWe have given two function y=b x and y=7 (x-5) which means that first y changes into (x -5 ). i.e., horizontal translation by 5 units to the right. Then it changes into 7 (x - 5). i.e., vertical dilation by a scale factor of 7.
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A department store purchases logo shirts at a cost of $10 per shirt. They mark up the price 100% and put them on the sales floor. Every month that a shirt doesn’t sell, the store reduces the selling price by 25%. After three monthly markdowns, the final shirt from the shipment is sold. There is a 5% sales tax on the selling price. What is the total cost to the customer?
The total cost to the customer is $8.86.
What Are Taxes?Taxes are mandatory contributions levied on individuals or corporations by a government entity—whether local, regional, or national.
Given:
Logo shirts at a cost of $10 per shirt.
Every month that a shirt doesn’t sell, the store reduces the selling price by 25%.
There is a 5% sales tax on the selling price.
According to given question we have
Cost of shirt = $10
Cost of the shirt after 100% increase
=100% of 10
= $10
Price of shirt after 100% increase
= $10 + $10
= $20
if shirt does not sell, price reduces by 25%. It means remaining value is 75% after every reduction.
So after 3 reductions, remaining value is 75% after every reduction
So, final price will be
$20 * 0.75 * 0.75 * 0.75
= $8.4375
There is a sales tax of 5% which customer will pay on the final price.
So, price for customer will be
$8.4375 + (5% of 8.4375)
= 8.4375 + 0.421875
= $8.859375≈ $8.86
Therefore, the total cost to the customer is $8.86.
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Write the equation of the line in point-slope form:
(-8, 2) (-6, 8)
The equation of the line in point-slope form is:
y - 8 = 3(x + 6) or y - 2 = 3(x + 8).
What is the Equation of a Line in Point-Slope Form?The equation, y - b = m(x - a), represents the equation of a line in point-slope form, where:
(a, b) is a point on the linem is the slope of the line.Given two points, (-8, 2) and (-6, 8), find the slope (m) of the line that passes through the two points:
Slope (m) = change in y / change in x = (8 - 2)/(-6 -(-8))
Slope (m) = 6/2
Slope (m) = 3
Substitute m = 3 and (-6, 8) into y - b = m(x - a):
y - 8 = 3(x - (-6))
y - 8 = 3(x + 6)
Or substitute m = 3 and (-8, 2) into y - b = m(x - a):
y - 2 = 3(x - (-8))
y - 2 = 3(x + 8)
Therefore, the equation of the line in point-slope form is:
y - 8 = 3(x + 6) or y - 2 = 3(x + 8).
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if there are "n" packets of Jelly tots. The chocolates are three more than 4 times the Jelly Tots Write down an algebraic expression for the number of chocolates.
Answer:
3+(4x)
Step-by-step explanation:
The algebraic expression will be written as:
x=jelly tots
The number of chocolates=3+(4×x)
=3+(4x)
The algebraic expression for the number of chocolates is 4n + 3 where n is number of packets of Jelly Tots.
Let's use variables to represent the number of Jelly Tots and chocolates:
Let "n" be the number of packets of Jelly Tots.
Now, the number of chocolates is three more than 4 times the number of Jelly Tots.
So, represent the number of chocolates as:
Number of chocolates = 4 * n + 3
4 * n represents 4 times the number of Jelly Tots.
Multiplying the number of Jelly Tots by 4 gives us the chocolates without the additional 3.
- +3 represents the additional chocolates.
Thus, the algebraic expression is 4n + 3.
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6x^2-5xy-6y^2
factor it
Step-by-step explanation:
Answer:
(3x + 2y) (2x - 3y)
Step-by-step explanation:
Check it using the FOIL method - first times first, outer times outer, inner times inner, last times last
the quotient of 2 and a numbe x times 3
Answer:
Step-by-step explanation:
2x
Simplify each radical expression. Use absolute value symbols when needed. 5√0.00032 x⁵
The value of radical expression 5√0.00032 x⁵ is (6.4e-5)x.
By considering the given radical expression
5√0.00032 x⁵
=(0.00032 x⁵ )^1/5
=(6.4e-5)x
A y-intercept, a horizontal asymptote, a domain (the range of x values at which the function exists), and a constant growth factor, b, are the four main characteristics of exponential functions.
An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.
The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression a^b.
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For what positive integers n are the domain and range of y=n√x the set of real numbers? Assume that x is a real number.
The domain and range will be a set of all real numbers for all the odd positive integers.
In its simplest form the domain is all the values that go into a function, that is the values for which function is defined and the range is all the values that come out that is the result obtained by putting all the domain valuesWe can write given equation as y² =n²x
if we Put even value of n then we get function similar to y²=x which does not match with the given question
If we put the odd value of n then we get function similar to y³ = x which match with the given question.
Hence the domain and range will be a set of all real numbers for all the odd positive integers.
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Helppp MEEEEE PLSSSSSS ⁉️⁉️❓❓❓❓❓❓
A) a
B) 0
C) 1
D)2
E)c
======================================================
Explanation:
The general quadratic ax^2+bx+c = 0 has these properties
sum of the roots = -b/aproduct of the roots = c/aFor more information, check out Vieta's formulas.
If we flip the bx term to -bx, thereby getting ax^2-bx+c = 0, then we have these properties
sum of the roots = b/aproduct of the roots = c/aWe're told the sum and product of the roots are the same
b/a = c/a
b = c
Example:
The equation x^2-10x+10=0 has the sum of the roots equal to 10, and the product of the roots is also 10. You can use the quadratic formula to confirm this.
Answer:
12
Step-by-step explanation:
good right? if not then your question was wrong
1. In some lion prides, the ratio of female to
male lions is 3: 1. What percent of the lions
are male? (Example 1)
Plssss help
Answer:
25%
Step-by-step explanation:
Based on the given conditions, formulate
Calculate the sum or difference:
Multiply a number to both the numerator and the denominator
: Write as a single fraction:
Calculate the product or quotient:
Rewrite a fraction with denominator equals 100 to a percentage:
What is the solution of √x+2=x ?
After the solution, the value of x for the equation √x+2 = x is 2.
What, accurately, is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation would be 3x - 5 = 16.After solving this equation, we get the value for the variable x as x = 7.So,
Given the equation: √x+2 = x
Then,
To get a quadratic, square it:
x+2=x²x²-x-2=0Quadratic formula:
x=1/2(1±√1+8)x=1/2(1±3)x=-1, 2However, when we square in our work, we must ensure that we haven't accidentally introduced extra roots.
In this case, -1 is not a solution to the original equation, whereas 2 is.
Therefore, after the solution, the value of x for the equation √x+2 = x is 2.
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