Multiply. (4+2√3)(6-3√3)
After multiplying, the answer of (4+2√3)(6-3√3) is 15.
How do we multiply square roots?1. Divide the radicands by two. Under the radical sign, there is a number called a radicand. 2. Multiple the integers as though they were whole numbers in order to multiply radicands. Keep the product under a single radical sign at all times.
3. Remove any perfect squares from the radicand by factoring. Check to determine whether the radicand is a factor of any perfect squares to do this.
4. Before the radical sign, place the square root of the ideal square. Keep the second element in the radical sign.
5. Square the root of a square. A square root may occasionally need to be multiplied by itself.
(4+2√3)(6-3√3)
⇒ 4 ×6 + 4 × -3√3 + 2√3 × 6 - 2√3 × 3√3
⇒ 24 - 12√3 + 12√3 - 9
⇒ 15
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Mrs johnson just purchased a total of 12 books and magazines for her office. the total bill was $112. she spent $16 on magazines, and the books cost $12 each. how many magazines did she buy
The number of books that Mrs. Johnson bought is 8 books.
What is formulated in math?A formula in mathematics is an assertion of a fact, rule, or principle using mathematical symbols.Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulae.Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another.We'll use the most well-known equation of all for our first. Elegant and initially illogical, Albert Einstein's 1905 equation connecting mass and energy is a masterpiece. According to this definition, energy is equal to an object's mass in its resting frame times the square root of the speed of light.How many magazines did she buy:
Let x represent the number of books she bought
The first step is to formulate an equation
12x + 16 = 112 dollars
The second step is to transpose
12x=112-16
12x = 96
The third step is to divide both sides by 12
x=96/12
x = 8
In conclusion, the number of books that Mrs. Johnson bought is eight books.
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rewrite 19+7÷2×6+1 using 2 pairs of brakets making the total equal to 2
5. square EFGH
Ay
O
H(1,-3)
G(3,-1)
X
F(5,-3)
E(3,-5)
The area of the square is found as -8 unit².
What exactly is the distance formula?We get a list of distance formulas in coordinate geometry that can be used to find the distance between two points, the distance between such a point and a line, this same distances between two parallel lines, the distances between two parallel planes, and so on.The distance between two points, for example, is the length of a line segment linking them.Distance between two coordinates (x₁, y₁) and (x₂, y₂) are-
d = √[(x₁ - x₂)² + (y₁ - y₂)²]
Consider two given coordinates;
(x₁, y₁) = H(1,-3) and
(x₂, y₂) = G(3,-1)
Put the values in the given distance formula;
d = √[(1 - 3)² + (-3 + 1)²]
d = √[(-2)² + (-2)²]
On solving,
d = 2√2 unit
Thus, one side of the square is found as 2√2 unit.
The area of the square is given as;
Area = side²
Area = (2√2)²
Area = 8 unit²
Therefore, the area of the square given by the coordinates if found to be 8 unit².
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The complete question is-
The coordinates of square are given, find the area of the square-
H(1,-3)
G(3,-1)
F(5,-3)
E(3,-5)
Need help please help
The equation of the line in fully simplified slope-intercept form is y = -x + 3
From the question, we are to write the equation of the line in fully simplified slope-intercept form
The slope-intercept form of the equation of a straight line is given as
y = mx + b
Where m is the slope of the line
and b is the y-intercept
From the graph,
The y-intercept is 3
∴ b = 3
Now, we will determine the slope, m, of the line
Given any two points (x₁, y₁) and (x₂, y₂) on a line, the slope, m, of the line is
m = (y₂ - y₁)/(x₂ - x₁)
Picking the points, (0, 3) and (2, 1)
m = (1 - 3)/(2 - 0)
m = -2/2
m = -1
Putting in the slope, m, and the y-intercept, b into the equation of a line
y = mx + b
We get
y = -1(x) + 3
Simplify
y = -x + 3
Hence, the equation of the line in fully simplified slope-intercept form is y = -x + 3
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Which fraction is equivalent to 16.6¯¯¯%
(c) given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (round your answer to four decimal places.)
The probability is 0.357
Given that,
The system has at least one type of defect,
Suppose, A certain system can experience three different types of defects.
Let (i = 1,2,3) denote the event that the system has a defect of type i.
Suppose that the following probabilities are,
P(A1)=0.11
P(A2)=0.08
P(A3)=0.05
P(A1UA2)=0.13
P(A1UA3)=0.13
P(A2UA3)=0.11
P(A1nA2nA3)=0.01
P(A1nA2)=0.06
P(A1nA3)=0.03
P(A2nA3)=0.02
P(A1UA2UA3)=0.14
P= P(A1) + P(A2) + P(A3) - 2P(A1UA2) - 2P(A1UA3) - 2P(A2UA3) + 3P(A1nA2nA3) / P(A1UA2UA3)
P= 0.11 + 0.08 + 0.05 -2*0.06 -2*0.03 -2*0.02 +3*0.01 / 0.14
P=0.357
Hence, the probability is 0.357
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We need to calculate the probability that it has exactly one type of defect
Using given data
+ +
P =
Put the value into the formula
Hence, The probability is 0.357
find the numerical value of the expression
sin 45 cos 45 + sin 30 cos 60 -cos^{2} 30
Greetings from Brasil...
According to trigonometry, we have:
COS α = SIN (90 - α)
SIN α = COS(90 - α)
Then
(SIN 45).(COS 45) + [(SIN 30).(COS 60)] - COS² 30]
(√2/2).(√2/2) + [(1/2).(1/2)] - (√3/2)² = 0
Write each expression as a single logarithm. Identify any properties used. 3 log₄ x+2 log₄x
According to the given logarithm 3 log₄ x+2 log₄x written as a single logarithm 5 log₄(x).
What exactly is a condensed log form?When they urge you to "simplify" a log expression, it usually implies they've given you a bunch of log terms, each with a simple argument, and they'd like you to combine them all into one log with a sophisticated argument. In this sense, "simplifying" usually means the inverse of "growing."
According to the given information:3 log₄ x+2 log₄ x
Add similar elements:
So:
This expression can be written as:
3 log₄ (x)+2 log₄ (x) = 5 log₄(x)
According to the given logarithm 3 log₄ x+2 log₄x written as a single logarithm 5 log₄(x).
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Write an equation that is parallel to y = 1 2 x + 3 and passes through (0, 0).
Answer:
y = 12x
Step-by-step explanation:
For an equation to be parallel the slopes must be the same. The slope from the equation is 12.
y = mx + b is the slope-intercept form of a line'
y = 12x + 3. The m is the slope and that is 12 ion this equation.
We will use the slope (12), the x (0) and the y (0) to write the new equation. We need to find the y intercept. We can see from the ordered pair given that the y - intercept would be zero, but here is another way to check.
y = mx + b
0 = 12(0) + b
0 = 0 + b
0 = b
y = 12x + 0
or
y = 12x
Evaluate the function f(x) = x+4 when x=3
The value of function f(x) = x+4 when x=3 is 7.
By considering given function
f(x) = x+4
f(3)= 3+4
f(3)=7
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
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The value of function f(x) = x+4 by evaluating it when x = 3 will be 7.
A function is defined as anything from a set X to a set Y assigns to each element of X exactly one element of Y.
We are given a function:
f(x) = x + 4
We need to evaluate for x = 3.
We will do this by putting x = 3 in the function given to us.
So, we get that:
f ( 3 ) = 3 + 4
Adding the terms, we get that:
f ( 3 ) = 7
Therefore, value of function f(x) = x+4 by evaluating it when x = 3 will be 7.
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I need help and i will give lots of points
the slope of that equation is -3/5
pls pls help whoever gets it right gets a crown
Answer:
m=-1
Step-by-step explanation:
20m+5-2m=-13
18m=-18
m=-1
Answer:
[tex] \sf \: m=−1[/tex]
Step-by-step explanation:
5(4m+1)-2m=-13
Step 1: Simplify both sides of the equation.
5(4m+1)−2m=−13
(5)(4m)+(5)(1)+−2m=−13(Distribute)
20m+5+−2m=−13
(20m+−2m)+(5)=−13(Combine Like Terms)
18m+5=−13
18m+5=−13
Step 2: Subtract 5 from both sides.
18m+5−5=−13−5
18m=−18
Step 3: Divide both sides by 18.
18m/18 = −18/18
m=−1
Which of these situations can be represented with an integer that, when combined with the opposite of , makes 0?
If you climb up 5 flights of stairs it will give zero according to the given condition. The correct option is C.
What about expression?
Expression in maths is defined as the combination of numbers, variables, and functions by using operators like addition, subtraction, multiplication, and division.
Given some situations which of those can be represented with an integer that, when combined with the opposite of −5, makes 0?
If you climb up 5 flights of stairs means you move forward upwards then it will give the positive value of 5.
Now, when it is added to -5 then it will give zero.
= 5+(-5)
= 5-5
= 0
Therefore, If you climb up 5 flights of stairs it will give zero by combining the opposite of that according to the given question. The correct option is C.
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The question is incomplete.
Kindly, find the complete question below.
Which of these situations can be represented with an integer that, when combined with the opposite of −5, makes 0?
Select all that apply.
A. You earn $5 from your chores.
B. You walk down 5 flights of stairs.
C. You climb up 5 flights of stairs.
D. The temperature drops 5°F.
E. You spend $5 on a game.
reverse mean higher GCSE questions.
Pete has seven Shetland ponies. They have a mean height of 116cm.
Pete buys an eighth pony. The height of this pony is 128cm.
Find the mean height of all eight ponies.
Answer:
dat it
116cm times 7=812
128cm times 8=1024
1024-812=212cm
I suck at algebra and am stuck on this question
the linear equation such that it is parallel to the line:
y = -2x + 5
And that it passes through the point (-2, -4) is y = -2*x - 8
How to find the slope-intercept form of the line?Here we want to find a linear equation such that it is parallel to the line:
y = -2x + 5
And that it passes through the point (-2, -4)
Remember that two lines are parallel if and only if the lines have the same slope and different y-intercept.
Then our line is something like:
y = -2*x + b
To find the value of b, we replace the values of the given point:
-4 = -2*-2 + b
-4 = 4 + b
-4 - 4 = b = -8
We conclude that the linear equation is y = -2*x - 8
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Determine whether the statement is true or false. if it is false, rewrite it as a true statement. data at the ordinal level are quantitative only.
According to the given statement;
The statement is False. Data at the ordinal level can be qualitative or quantitative.
What is Ordinal level?Ordinal data is a form of categorical statistical data where the distances between the categories are unknown and the variables have naturally occurring, ordered categories.
Ordinal is the second of four levels of measurement in a hierarchy that also includes nominal , ordinal , interval , and ratio. The degrees of measurement show how well the data were recorded.
In contrast to nominal and ordinal variables, which are categorical, interval and ratio variables are quantitative.
According to the given data,
The statement is False.
Data at the ordinal level can be qualitative or quantitative.
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Domain:
Range:
Increasing:
Decreasing:
Positive:
Negative:
The answers are:
Domain: [-7, ∞)
Range: [-3, ∞)
Increasing: [-7, -2] U [4, ∞]
Decreasing: [-2, 4]
Positive: [-5, 2] U [6, ∞)
Negative: [-7, -5] U [2, 6]
How to find the domain and the range of the function?The domain is the set of the possible inputs of the function, by looking at the graph we can see that the graph starts at x = -7 and keeps going to the right, so the domain is:
D: [-7, ∞)
The range is the set of the outputs, in this case, the minimum value is y = -3 and then it keeps going up.
R: [-3, ∞)
Now, the graph increases when it goes upwards, in this case the graph increases in:
[-7, -2] U [4, ∞]
And decreases on:[-2, 4]
And it is negative on the intervals where the function is below the horizontal axis: [-7, -5] U [2, 6]
And it is positive on the intervals: [-5, 2] U [6, ∞)
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Fully simplify 8x + 3y - 6x + 4y
8x+3y-6x+4y
=8x-6x+3y+4y
=2x+7y
i need help what's the answer?
Answer:
53°
Step-by-step explanation:
Corresponding angles are congruent
1. What is −12 + |−3| − |−14|?
2. The depth of a local river averages 25 ft, which is represented as |−25|. In January, it measured 5 ft deep, or |−5|, and in July, it was 27 ft, or |−27|. What is the difference between depths in January and July?
3. What is the value of −3 + |−17|?
Answer:
1. -1 2. -22 i think may be wrong 3. -20
Step-by-step explanation:
good ol integers payin off
If p(x) = x² + 5x - 3, find the following:
p (0) =
Answer:
-3
Step-by-step explanation:
p(0) = (0^2) + 5(0) - 3
p(0) = 0 + 0 - 3
p(0) = -3
Answer the 3 question in the photo
[easy points]
Answer:
if i am looking at this correct then number 4 is 6 faces number 5 is 5 and number 6 is 5
Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 2%?.
If scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score you would need to be in the top 2% is equal to 88.929.
A problem of this type in mathematics can be characterized as a normal distribution problem. We can use the z-score to solve it by using the formula;
Z = x - μ / σ
In this formula the standard score is represented by Z, the observed value is represented by x, the mean is represented by μ, and the standard deviation is represented by σ.
The p-value can be used to determine the z-score with the help of a standard table.
As we have to find the minimum score to be in the top 2%, p-value = 0.02
The z-score that is found to correspond with this p-value of 0.02 in the standard table is 2.054
Therefore,
2.054 = x - 76.4 ÷ 6.1
2.054 × 6.1 = x - 76.4
12.529 = x - 76.4
12.529 + 76.4 = x
x = 88.929
Hence 88.929 is calculated to be the lowest score required to be in the top 2%.
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Find the inverse of each function. Is the inverse a function? f(x)=1.2 x⁴
The inverse for the function f (x) = 1.2 x⁴ will be f ⁻¹ (x) = ⁴√ ( 5 x / 6).
We are given the function:
f (x) = 1.2 x⁴
we need to find the inverse of the function.
First we will write the function in the form of x.
y = 1.2 x⁴
y / 1.2 = x⁴
x = ⁴√ ( y / 1.2)
x = ⁴√ ( 5 y / 6)
So, the inverse function will be:
f ⁻¹ (x) = ⁴√ ( 5 x / 6)
Therefore, the inverse for the function f (x) = 1.2 x⁴ will be f ⁻¹ (x) = ⁴√ ( 5 x / 6).
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A carpenter sales nightstands at a local store the table shows the number of nightstands sold in the amount of profit earned what is the missing value in the table
Answer:
The missing value of the table is 1,800 .
For Hakeem's lemonade recipe, 18 lemons are required to make 15 cups of lemonade.
At what rate are lemons being used in lemons per cup of lemonade?
The rate of lemon used in lemons per cup of lemonade is 120%
Based on the given conditions,
18/15 = 6/5
Cross out the common factor: 6/5 x 20/20
Multiply a number to both the numerator and the denominator,
6 x 20/ 5 x 20.
Write as a single fraction, 120/100
Rewrite a fraction with denominator equals 100 to a percentage which is 120%.
part of a whole expressed in hundredths a high percentage of students attended. b : the result obtained by multiplying a number by a percent the percentage equals the rate times the base. 2a : a share of winnings or profits.5 percent is one half of 10 percent. To calculate 5 percent of a number, simply divide 10 percent of the number by 2. For example, 5 percent of 230 is 23 divided by 2, or 11.5.
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A square floor has a side length of (9/2) units. A square tile has a side length of (3/2)² units. The square tiles will be placed ro tile the square floor. How many full tiles will it take to cover the floor?
The square tiles needed to cover the floor will be 9.
How to calculate the value?From the information, the square floor has a side length of (9/2) units and the square tile has a side length of (3/2)² units.
Therefore, the square tiles needed to cover the floor will be:
= Area of floor / Area of one tile
= (9/2)² / (3/2)²
= (9 × 9)/(3 × 3)
= 81 / 9.
= 9
Therefore, the square tiles needed to cover the floor will be 9.
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The perimeter of a square picture frame is to be at most 35 inches but no less than 12 inches. Find all possible values for the length of its sides.
Considering the definition of an inequality, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Definition of perimeterThe perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.
The perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure.
Perimeter of a squareA square is a flat geometric figure that has four equal sides, so the expression to calculate the perimeter of a square is:
Perimeter= 4× length of the sides
Possible values for the lengthIn this case, you know that the perimeter of a square picture frame is to be at most 35 inches but no less than 12 inches.
Being "S" the length of the sides of the square picture, the inequality that expresses the previous relationship is
12 inches< 4×S ≤35 inches
Solving:
12 inches ÷4< S ≤35 inches ÷4
3 inches <S≤ 8.75 inches
Finally, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.
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what is 10,000 less of 84.562 and what is 10,000 more? how would i show my work?
Answer: 10,000 less of 84.562 = −
9915.438 | 10000 more of 84.562 = 10084.562
Step-by-step explanation:
10000 less:
Just subtract 10000 from 84.562.
10000 More:
Just add 10000 to 84.562