[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LM=\sqrt{(~~-2 - 7~~)^2 + (~~4 - (-1)~~)^2} \implies LM=\sqrt{(-2 -7)^2 + (4 +1)^2} \\\\\\ LM=\sqrt{( -9 )^2 + ( 5 )^2} \implies LM=\sqrt{ 81 + 25 } \implies LM=\sqrt{ 106 }[/tex]
Solve for X
x-9.8/-2.2=9.7
The value of x in the equation is 5. 25
What are algebraic expressions?
Algebraic expressions are defined as expressions comprising of terms, variables, coefficients, factors, and constants.
They are also made up of mathematical operations such as addition, multiplication, division, bracket, etc
Given the expression;
x - 9.8 / -2.2 = 9.7
Find the quotient
x - (-4. 45) = 9. 7
expand the bracket
x + 4. 45 = 9. 7
collect like terms
x = 9. 7 - 4. 45
Subtract like terms
x = 5. 25
Thus, the value of x in the equation is 5. 25
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Carlos was having a house.The blueprints are shown below
Kindly check if any file is attached.
The actual width of the entire building is 28 feet and the length of the entire building is 84 feet.
Step-by-step explanation:The scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object. The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.Now, width = 8 inches in feet is 4 × 7 =28 feetLength = 14+10 =24 inches in feet is 12 × 7 = 84 feetTherefore, the actual width of the entire building is 28 feet and the length of the entire building is 84 feet.f(x)=[tex]f(x)=3\sqrt{3} x-3[/tex]
The domain is all real numbers of x that makes the expression defined.
Set-builder notation: { x| x ≥ 0 }.
Interval notation: [0,∞).
What is the domain of the given function?Given the function in the question;
f(x) = 3√3x - 3
To determine the domain, we find where the expression is defined by setting the radicand √3x to be greater than or equal to zero and solve for x.
3x ≥ 0
Divide both sides by 3
3x ≥ 0
3x/3 ≥ 0/3
x ≥ 0/3
x ≥ 0
The domain is all real numbers of x that makes the expression defined.
Set-builder notation: { x| x ≥ 0 }.
Interval notation: [0,∞).
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Use the formula below to solve the given problem. In the formula, d
represents the distance an object falls, in meters, and t represents the time
that an object falls, in seconds. Do not include units in your answer.
A rock dropped down a well takes 3 seconds to fall to the bottom of the well.
What is the depth of the well?
√d=t•√49
Answer here
Answer:
[tex]d = 441[/tex]
Step-by-step explanation:
We know that [tex]d = 49t^2[/tex].
We also know that it takes 3 seconds to reach the bottom of the well, meaning that if we substituted [tex]t = 3s[/tex] in the formula, we'd get the height of the well.
[tex]d = 49 \times 3^2 \to 49 \times 9 \to 441[/tex]
What is 5+18÷6 step by step
we may use BODMAS in answering this question you divide 18 by 6 and your answer will be 3 you then add 5 to the 3 to obtain your answer which is 8
A cube has six sides that are numbered 1 to 6. The sides numbered 1, 3, and 5 are yellow, and the sides numbered 2, 4, and 6 are orange. What is the probability of rolling the cube and getting a yellow and even number?
Answer:
0.
Step-by-step explanation:
None of the sides colored yellow (1, 3, 5) have an even number that corresponds.
Which value of kkk makes 5-k+12=165−k+12=165, minus, k, plus, 12, equals, 16 a true statement? Choose 1 answer:
The value of k that makes the statement true is: k = -4.
How to Find the Value of a Variable in an Equation?If we are given an equation that has an unknown variable, to find the value of the variable, solve to isolate the variable. The value of the variable is what will make the equation a true statement.
Given the equation:
-k + 12 = 16
Subtract 12 from both sides
-k + 12 - 12 = 16 - 12 [subtraction property]
-k = 4
Divide both sides by -1
-k/-1 = 4/-1 [division property]
k = -4
Check: substitute k = -4 into the equation
-k + 12 = 16
-(-4) + 12 = 16
4 + 12 = 16
16 = 16 [true]
Therefore, the value of k that makes the statement true is: k = -4.
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Please help with this algebra 1 question, it's in the attachments
The graph of the piecewise function is given at the end of the answer. From the graph, and from it's concepts, we have that:
The domain is all real numbers.The range is (-∞,-2) U [0, ∞).What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, the function has two definitions, as follows:
f(x) = -x - 2 to the right of x = 0.f(x) = -x to the left of x = 0.Both are decreasing linear functions, with the definition opening a space at x = 0, between y = 0 and y = -2, as shown in the graph. The closed interval, due to the equal sign, is at x = 0.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph, the domain and the range are found as follows:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, for the function in this problem, we have that:
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The measure of a side of a square is x units. A new square is formed with each side 6 units longer than the original square's side. Write a simplified expression to represent the area of the new square.
Answer:
[tex]A = x^2 + 12x + 36[/tex]
Step-by-step explanation:
The new square's side can be algebraically expressed as [tex]x + 6[/tex], as we know it's 6 units longer than the previous square with side length [tex]x[/tex].
Therefore, its area would be:
[tex]A = (x + 6)^2 \text{ // Remember: } (a + b)^2 = a^2 + 2ab + b^2\\\to A = x^2 + 12x + 36[/tex]
Solve the equation r³ = 125.
het ont to able rose à pne
Answer:
[tex]r = 5[/tex]
Step-by-step explanation:
[tex]r^3 = 125 \text{ // Take the 3rd sqrt of both sides}\\\to \sqrt[3]{r^3} = \sqrt[3]{125}\\\to r = 5[/tex]
Answer:
Brainleast Answer
Step-by-step explanation:
r=5
hopebit helps
Bro how do so you do this I’m slow ash and they kno this
Answer:
9. 5/10
12. 4/10
15. 1/2
Step-by-step explanation:
1/2 = 5/10 --> 10 ÷ 5 = 2 --> 5+5 = 10 || Basically half
4/10 = 40/100 --> Multiply 10 more
6/12 = 1/2 --> 6+6 = 12 || Half again
what is the formula for arithmetic mean
Answer:
A = arithmetic mean
n = number of values
a_i = data set values
Step-by-step explanation:
Hope it helps! =D
In january of 2019, the american midwest experienced record-breaking freezing temperatures. A certain metropolitan area in wisconsin, with a residential population of over 1. 15 million, experienced daily average temperatures as low as minus 28 degrees fahrenheit. Hospitals saw a steady stream of patients reporting symptoms of frostbite. In the aftermath, a survey was conducted in order to estimate the true proportions of individuals afflicted by frostbite during the extreme weather. 289 residents were selected via simple random sampling and 273 reported not having any symptoms. What was the sample proportion obtained by the survey? give your answer to 3 decimal places. For help on how to input a numeric answer, please see instructions for inputting a numeric response.
The proportion of the sample obtained from the survey is 0.055
What is a percentage?
The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.
It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.
To solve this problem, we use a simple rule of three to find the percentage value of the sample.
289 -------- 100%
273 --------- x
x = (273 * 100%) / 289
x = 94.46%
100% - 94.46% = 5.53%
The ratio in propotion with 3 decimals is
5.53/100 = 0.055
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5) Find LM
K
K
9
-4+4x
x-1
L
M
According to the solving the line segment LM of line KM = 3.
What is line segment?A line segment is defined as the area between two different points on a line. A line segment is a section of a line that links two points. A line has no endpoints and stretches in both directions indefinitely, but a line segment includes two fixed or definite endpoints.
What exactly is a line segment?In general, if both end points of a line segment are vertices of such a polygon or polyhedron, the line segment has to be either the edge (of that polygon or polyhedron) if they are both adjacent vertices, or a diagonal. A chord is a line segment whose end points are both on a curve (such as a circle) (of that curve).
According to the given data:KL = 9
LM = x - 1
KM = -4 + 4x
So
KL + LM = KM
Substituting the value we get:
9 + x - 1 = -4 + 4x
8 + x = -4 + 4x
8 + 4 = 4x - x
12 = 3x
x = 4
The value of x = 4 putting the value in the (LM = x - 1):
We get:
LM = x - 1
LM = 4 - 1
= 3
LM = 3
According to the solving the line segment LM of line KM = 3.
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Lily has 76 stars brandon has 100 times more how many stars does Brandon have
Put the reasons in the correct order that will justify the statements given
The reasons arranged in the order that correctly completes the two column table to prove that ‹2 and ‹3 are supplementary is as follows;
Given(‹1 and ‹2 form a linear pair)Supplementary theorem Definition of supplementary angles Given (‹1 and ‹3 are congruent)Definition of congruency Substitution Definition of supplementary angles What are supplementary angles?Supplementary angles are angles that have a sum of 180°.
The completed table is presented as follows;
Statements Reasons
1. ‹1 and ‹2 form a linear pair; Given(‹1 and ‹2 form a linear pair)
2. ‹1 and ‹2 are supplementary; Supplementary theorem
3. m‹1 and m‹2 = 180°; Definition of supplementary angles
4. ‹1 congruent ‹3;Given (‹1 and ‹3 are congruent)
5. m‹1 = m‹3; Definition of congruency
6. m‹3 + m‹2 = 180°; Substitution
7. ‹2 and ‹3 are supplementary; Definition of supplementary angles
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what is the solution to 3 + 8.2 = 26.2
Answer:
Your answer is 26.2 but there is also no solution.
Step-by-step explanation:
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Can someone help me find the radius of the circle
In 2009,the population of brazil was 191.5 million. this represented a decrease in population of $3.7%from 2000 .what was the population of brazil in 2000 round to the nearest tenth of a million
Population in the year 2000= 198.85million
From the question, we get to know that the population in 2009 was 191.5 million.
And we have to find the population of the year 2000 which is 3.7%more than the 2009 population.
So let us take the population of the year 2000 to be x.
From the above, we can form an equation:
(population of year 2000 * ( 100-3.7 /100) = (population of year 2009)
i.e., x * 100-3.7/ 100 = 191.5
x * 96.3 = 191.5
x = 198.85
So 198.85 is the population of 2000.
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It's Max's birthday and his grandfather just signed over his Social Security check to him for $625.95. Max wants to buy as many new PS 4 Mine craft video games with the money as he can at $32.10 a piece to sell them on Betsy. If he wants to keep one, how many can he have left over?
The number of video games that Max will have left when he keeps one is 18 games.
How to illustrate the information?It should be noted that the total amount that he has is $625.95.
Cost of each video game = $32.10
Therefore, the number of games that he can buy will be:
= Amount / Cost of game
= $625.95 / $32.10
= 19.5
= He can buy 19 games.
Therefore, if he keeps one, the number left will be:
= 19 - 1 = 18
He I'll have 18 left.
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define product give an example of two whole number factors with a product of 9
Answer:
"6a = 9"
"x × y = 9"
→ Variables can also be factors in the instance that they are multiplied by a number or another variable.
Using the Completing the Square method, what are the zeros of the quadratic function f(x) = 2x2² +8x-3? O x=-2- O x=-2- O x=2- Ox=2- 11 72 11 F and x = -2 + and x = -2 + and x = 2 + and x = 2 + 7 - 2 Jul 12 LL 72 11 11 2
the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.
We are given a function:
f (x) = 2 x² + 8 x - 3
We need to use the completing the square method to find the zeroes.
f (x) = 2 x² + 8 x - 3
f (x) = x² + 4 x - 3 / 2
f (x) = ( x )² + 2 (2) (x) + (2)² - (2)² - 3 / 2
f (x) = ( x + 2 )² - 4 - 3 / 2
f (x) = ( x + 2 )² - 11 / 2
(x + 2)² = 11 / 2
x + 2 = ± √ 11 / 2
x = - 2 ± √ 11 / 2
Therefore, the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.
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Write 0.2777 as a fraction in lowest terms:
Answer:
27.77
Step-by-step explanation:
To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right).
0.2777 × 100 = 27.77
Let z and y be positive integers and x > y. Which expression in equivalent to 19^z/19^y
Answer:
[tex]19^{z-y}[/tex]
Step-by-step explanation:
assuming you meant z > y
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex] ( m > n ) , then
[tex]\frac{19^{z} }{19^{y} }[/tex] = [tex]19^{z-y}[/tex]
5. a bag of chocolates is labeled to contain 0.384 pounds of chocolates. the actual weight of the chocolates is 0.3798 pounds. a. are the chocolates heavier or lighter than the weight stated on the label? explain how you know. b. how much heavier or lighter are the chocolates than stated on the label? show your
Comparing the values by subtraction, the chocolates are lighter than the weight stated on the label by 0.0042 pounds.
When comparing two values whether which is greater, compare the digits from left to right.
Comparing 0.384 to 0.3798, where the first digits are both 0, and the digit after the decimal are also the same, compare the hundredth's place.
8 > 7
Hence, the actual weight of the chocolates is less than or lighter than the weight stated on the label.
Using subtraction, two values can also be compared by getting how much one exceeds the other.
Subtracting the two values,
0.384 - 0.3798 = 0.0042 pounds
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What is (7g+3) (-g-3) =
The distance AB = [?]
Round to the nearest tenth.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~-1 - (-3)~~)^2 + (~~-1 - 1~~)^2} \implies AB=\sqrt{(-1 +3)^2 + (-1 -1)^2} \\\\\\ AB=\sqrt{( 2 )^2 + ( -2 )^2} \implies AB=\sqrt{ 4 + 4 } \implies AB=\sqrt{ 8 }\implies AB\approx 2.8[/tex]
Suppose you plan to purchase 10 items that each cost $4.95. How much will it cost for the ten items using mental math? Group of answer choices
It will cost $49.5 for the ten items.
What is arithmetic operation?Arithmetic operation is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Now it is given that,
Total items purchased = 10
Each item cost = $4.95
Thus, Cost of 10 items = 10*Each item cost
Putting the value we get,
Cost of 10 items = 10*4.95
Solving we get,
Cost of 10 items = $49.5
this is the required cost for the ten items.
Thus, It will cost $49.5 for the ten items.
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Kali made cookies for her study group. The recipe bakes 61 cookies, and there are 5 people in her study group. How many cookies does each student get? Use the space below to solve, then interpret the quotient and the remainder in a sentence. (In your own words, what does your solution and remainder represent for this tasty problem?)
Answer: Each person can get 12 cookies, or 12.2
Step-by-step explanation:
All you have to do is divide 61 by 5, your answer would 12 remainder 1, you would then divide 1 by 5 to get 0.2 . Add 12 and .2 to get your answer. The quotient would be 12 and the remainder 1.
Larry drove from San Francisco to San Jose.
The graph shows the distance he traveled during his drive.
Use the drop-down menus to complete the statements based on the graph.
The labeled point means that in
In 1 hour, Larry traveled
miles.
His distance changed at a unit rate of
hours, Larry traveled
miles.
miles per hour, so Larry's speed was
If Larry had driven more slowly, the slope of the graph would be
Distance Larry Traveled
60
y
50
40+
30+
20+
8 10+
Distance (miles)
miles per hour.
0
1
Time (hours)
(1.5,45)
CLEAR
CHECK
Using a proportional relationship, it is found that:
Point (1.5, 45) means that the 1.5 hours, he traveled 45 miles.In one hour, Larry traveled 30 miles.His distance changed at a unit rate of 30 miles per hour, so Larry's speed was of 30 miles per hour.If Larry had driven more slowly, the slope of the graph would be less than 30.What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx
From point (1.5, 45) on the graph, the constant is given as follows:
k = 45/1.5
k = 30.
Hence the equation is:
y = 30x.
In which:
x is the number of hours.y is the distance traveled.Hence, point (1.5, 45) means that the 1.5 hours, he traveled 45 miles.
From the constant k = 30, we have that in one hour, Larry traveled 30 miles, also meaning that:
His distance changed at a unit rate of 30 miles per hour, so Larry's speed was of 30 miles per hour.
The slope of the graph is the velocity, hence:
If Larry had driven more slowly, the slope of the graph would be less than 30.
What is the missing information?
For this problem, the graph is missing, and is given by the image at the end of the answer.
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