To find:
The midpoint of the line segment with the endpoints P1(11/2,3/8) and P2 (-7/2,5/8).
Solution:
The midpoint formula is:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Put the values:
[tex]\begin{gathered} (\frac{\frac{11}{2}-\frac{7}{2}}{2},\frac{\frac{3}{8}+\frac{5}{8}}{2})=(\frac{\frac{4}{2}}{2},\frac{\frac{8}{8}}{2}) \\ =(\frac{2}{2},\frac{1}{2}) \\ =(1,\frac{1}{2}) \end{gathered}[/tex]Thus, the midpoint is (1, 1/2).
The data show the number of pieces of mail delivered to a single home address each day for three weeks.
4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2
Which statement is true about a graph representing the data? Select two options.
The number line of a dot plot would start at 1.
A dot plot would show 7 points for numbers greater than 2.
The intervals on a histogram should be 0 to 2, 3 to 4, and 5 to 6.
A histogram would have a maximum of 7 bars.
A histogram should not show a bar that includes 0 pieces of mail
For the above question, statement 2 and 4 are true for the given data and after plotting the dot plot and histogram.
As per the question statement, data is showing the number of pieces of mail delivered to a single home address each day for three weeks.
Which is as follows: 4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2
10 for 3 days, 1 for 4 days, 2 for 4 days, 3 for 2 days, 4 for 3 days, 5 for 1 day and 6 for 1 day.
Statement 1: False because the number line of a dot plot would start at 0.
Statement 2: True
Statement 3: False as it should be 0, 1, 2, 3, 4, 5 and 6
Statement 4: True
Statement 5: False as it should show 3 bars at 0 in histogram
Dot plot: An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)Histogram: A histogram is a graph that use rectangles to display the frequency of numerical data.To learn more about dot plot and histogram, click on the link given below:
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Answer:
b,d
Step-by-step explanation:
Once a large pink ribbon, the sign of the fight against breast cancer, was erected out of pink post-it notes on a billboard. If the area of the rectangular billboard covered by the ribbon was approximately
3705 square feet, and the width of the billboard was approximately 57 feet, what was the height of this billboard?
Answer:
65 feet
Step-by-step explanation:
[tex]3705=57h \\ \\ h=\frac{3705}{57}=65[/tex]
In AJKL, JL is extended through point L to point M,
m/JKL = (3x – 16)°, m/LJK = (2x + 15)°, and
m/KLM = (8x – 19)°. Find m/LJK.
The value of x is 6 and the measure of angle LJK is 27°.
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
We have the measure of the following angles,
m∠JKL = ( 3x - 16 )°
m∠LJK = ( 2x + 15 )°
m∠KLM = ( 8x - 19)°
In ΔJKL, JL is extended through point L to point M.
At point L, the measure of angle JLK will be as,
m∠KLM + m∠JLK = 180°
m∠JLK = 180° - m∠KLM
m∠JLK = 180° - ( 8x - 19)°
m∠JLK = ( 199 - 8x )°
Now,
In triangle JKL,
By angle sum property:
m∠JKL + m∠LJK + m∠JLK = 180°
(3x – 16)° + (2x + 15)° + ( 199 - 8x )° = 180°
- 3x + 198 = 180
- 3x = - 18
x = 6°
Therefore,
m∠LJK = ( 2x + 15 )°
m∠LJK = ( 2(6) + 15 )°
m∠LJK = ( 12 + 15 )°
m∠LJK = 27°
The measure of angle LJK is 27°.
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A line with a slope of – 1/6 passes through the points (1,3) and (7,f). What is the value of f?
Answer:
[tex]{ \tt{ - \frac{1}{6} = \frac{f - 3}{7 - 1} }} \\ \\ { \tt{6(f - 3) = - 6 }} \\ \\ { \tt{f - 3 = - 1}} \\ \\{ \tt{f = 2}}[/tex]
Answer:-2
Step-by-step explanation:
Complete the table by classifying the polynomials by degree and number of terms. binomial quadratic monomial Polynominal 2002 3x 55 -3x²2 - 6x + 9 constant exponential Name Using Degree linear Name Using Number of Terms trinomial
The given expression -3x²-6x+9 is quadratic expression and it is trinomial.
Classification of polynomials are given below:
A) 2x²
Degree = 2, so it is quadratic expression
Name using number of terms=monomial
B) -2
Degree = 0, it is constant
Name using number of terms=monomial
3) 3x-9
Degree = 1, so it is linear expression
Name using number of terms=monomial
4) -3x²-6x+9
Degree = 2, so it is quadratic expression
Name using number of terms=trinomial
Therefore, the given expression -3x²-6x+9 is quadratic expression and it is trinomial.
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Bronze is an alloy made of copper and tin. the ratio of copper to tin is 23 to 2, if a bronze statue weighs 50kg what is the mass of copper in the statue
STEP BY STEP AND URGENT
Answer:46kg
Step-by-step explanation:
23+2=25
50/25=2
2x23=46kg
Answer:
46 kg
Step-by-step explanation:
Ratio of copper to tin in the bronze alloy is 23:2
That means, as a ratio of the entire brass mass, the copper content is in the ratio of 23/(23 + 2) = 23/25
Since the mass of the bronze statue is 50 kg, the mass of copper in it must be 50 x 23/25 = 46 kg
The remaining kg (2/25 of 50 kg) is tin
give this answer please
Answer:
<KLC
Step-by-step explanation:
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Both are obtuse angles and are on the opposite side of the transversal line
Answer:
∠KLC is the alternate angle of ∠BKL
Step-by-step explanation:
Alternate angles are angles that are opposite of one another and on two different parallel lines created by an intersecting line (also known as a transverse line).
In this case, the parallel lines are lines A↔B and C↔D, and the transverse line is M↔N. Therefore, the alternate angle from ∠BKL is ∠KLC.
Need help!!! ASAP!!!!
g(x)×h(x) means we will have to multiply the two functions.
[tex]g(x) \times (h(x) = (3 {x}^{2} - 1)( {x}^{2} - x) \\ = 3 {x}^{2} ( {x}^{2} - x) - 1( {x}^{2} - x) \\ = 3 {x}^{4} - 3 {x}^{3} - {x}^{2} + x \\ g(x) \times h(x) = 3{x}^{4} - {x}^{3} - {x}^{2} + x[/tex]
ATTACHED IS THE SOLUTION
1.the difference of six and two divided by four
2.eighteen divided by the sum of two and seven
3.the difference of eleven and four times five
4.the sum of two and four and six times eight
Answer:
1. 4
2. 2
3. 35
4. 96
Step-by-step explanation:
1. (6-2)÷4=4
2. 18÷(2+7)=2
3. (11-4)×5= 35
4.(4+2+6)×8= 96
Answer:
1. 1
2. 2
3. 35
4. 96
If 1/4 gallon of paint covers 1/3 of a wall in Luna's bedroom, how many gallons of paint does she need to cover 1 wall?
Answer: 3/4 of a gallon
Step-by-step explanation:
1/4 times 1/3 is 3/4 so she would need to buy a gallon of paint
evaluate 3x - 2 when x =
a) 0
b) +3
c) -2
Answer:
- 2, 7 , - 8
Step-by-step explanation:
substitute the given values of x into the expression
(a)
x = 0 : 3(0) - 2 = 0 - 2 = - 2
(b)
x = 3 : 3(3) - 2 = 9 - 2 = 7
(c)
x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8
WILL GIVE BRAINLIEST
Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4).
y equals negative one-fourth times x minus 7
y equals negative one-fourth times x plus 2
y = 4x + 24
y = 4x + 36
Answer:
[tex]y=-\frac{1}{4}x+2[/tex]
Step-by-step explanation:
Perpendicular lines have slopes thst are negative reciprocals, so the slope of the line to be found is -1/4.
Substituting into point-slope form, the equation is [tex]y-4=-\frac{1}{4}(x+8)[/tex].
Rearranging into slope-intercept form,
[tex]y-4=-\frac{1}{4}(x+8) \\ \\ y-4=-\frac{1}{4}x-2 \\ \\ y=-\frac{1}{4}x+2[/tex]
could i get some help
last one got deleted
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 4^{\frac{2}{5}} \right)^{\frac{1}{4}}\implies 4^{\frac{2}{5}\cdot \frac{1}{4}}\implies 4^{\frac{1}{10}}\implies \sqrt[10]{4^1}\implies {\Large \begin{array}{llll} \sqrt[10]{4} \end{array}}[/tex]
9.
Katy fills some gift boxes.
Each gift box will contain one toy and one keyring.
Katy buys toys in bags of 8.
Katy buys keyrings in bags of 14.
She wants to use all the toys and all the keyrings she buys.
What is the smallest number of gift boxes Katy can fill?
Anyone
The most appropriate choice for LCM will be given by
Smallest number of gift boxes Katy can fill is 56
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
Katy buys toys in bags of 8.
Katy buys keyrings in bags of 14.
Each gift box will contain one toy and one keyring.
Number of gift boxes Katy can fill has to be a common multiple of 8 and 14
Smallest number of gift boxes Katy can fill is the least common multiple of 8 and 14
Now,
8 = 2 x 2 x 2
14 = 2 x 7
LCM of 8 and 14 = 2 x 2 x 2 x 7
= 56
Smallest number of gift boxes Katy can fill is 56
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write the equation in slope intercept form of the line that passes through the points (-4,8) and (4,6)
The equation of the line in the slope-intercept form is y = -1/4x + 9
Equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points.
The given points are (-4, 8) and (4, 6)
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
x₁ = -4
y₁ = 8
x₂ = 4
y₂ = 6
Thus,
(y - 8)/(x - -4) = (6 - 8)/(4 - -4)
(y - 8)/(x + 4) = -2 / (4 + 4)
(y - 8)/(x + 4) = -2 / 8
(y - 8)/(x + 4) = -1/4
4(y - 8) = -1(x + 4)
4(y - 8) = -x + 4
y - 8 = -1/4x + 1
y = -1/4x + 1 + 8
y = -1/4x + 9
Therefore,
The equation is y = -1/4x + 9
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Solve the system by graphing.check your solution
3x-y=3
-3x-y=-9
The equation intercept at (2,3) in the graph given in the question.
solve ?
Given two equations are ,
3 x - y = 3
-3 x - y = -9
to solve the equations, substract both equations ,
(3 x - y = 3) - (-3x -y = -9)
we get, 6x =12
x = 2
by substituting value of x in any of the equation we get ,
3 x 2 -y =3
6 -y =3
-y = -3
y = 3
so x = 2 , y = 3
the points on the graph is (2,3)
Both equations are in slope intercept form.
The graph of y = mx +b, where m is the slope and b is the y intercept, is shown below.
They have the same y intercept, so they cross at (2,3).
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Show the relationship between -5/6 and -7/10. Use an inequality symbol
[repost]
The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.
What is the relationship between two rational numbers?
Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.
First, find the least common multiple of the two denominators:
6 = 2 × 3
10 = 2 × 5
L.C.M. = 2 × 3 × 5 = 30
Second, amplify each rational number:
- (5 × 5) / (6 × 5) = - 25 / 30
- (7 × 3) / (10 × 3) = - 21 / 30
Third, compare the numerators of the fraction found in the previous step:
Since - 25 < - 21, then - 5 / 6 < - 7 / 10.
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Pretty please help. I'm going to be grounded if I dont get this answered
A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?
A) Yes, because 4 + 5 > 8
B) Yes, because 5 + 8 > 4
C) No, because 4 + 5 > 8
D) No, because 5 + 8 > 4
Answer: Yes, because 4 + 5 > 8
Step-by-step explanation: The sum of 4 + 5 must be more than 8 to be a triangle
Answer:
The answer is A) Yes, because 4 + 5 > 8
Step-by-step explanation:
I got it right loves <3
Determine the slope of the function as a unit rate for the linear situation. y = − 4 4/5x + 13 1/2
The slope of the function as a unit rate for the linear situation. y = [tex]-4\frac{4}{5}[/tex]x + [tex]13\frac{1}{2}[/tex] can be viewed as [tex]-4\frac{4}{5}[/tex] by taking the derivative of the first term of the equation.
What is the slope of a function?The slope m=y/x of a straight-line y=mx+b quantifies the change in y for every unit change in x. This can also be interpreted as a kind of measure of "sensitivity''.
Finding the slope of a function is like finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable).
How to find the slope of a function?To find the slope of a line that is given with the equation of the line, first you have to write the equation of the line in a slope-intercept form.
Then use inverse operations in order to solve for y so that it is written as y=mx+b. Thereafter you can easily spot the slope since the slope is the coefficient of the x variable, or in other words, the number in front of x.
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Help again :').. sorry for the spam of questions lol
29 points will b givin
Answer:
A
Step-by-step explanation:
Do long division. See the attached image for work.
Answer:
B
Step-by-step explanation:
[tex]\frac{56}{90}[/tex]
= 56 ÷ 90
= 0.6222222..
= 0.62 ( with a bar above the 2 , indicating the 2 is repeating )
Find three equivalent rational numbers for 81/24 PLEASE ...
Answer:
3.375
3[tex]\frac{375}{1000}[/tex]
[tex]\frac{27}{8}[/tex]
Step-by-step explanation:
The first answer divide 81 by 24 and you will get the decimal answer of 3.375.
0.375 is [tex]\frac{375}{1000}[/tex]
[tex]\frac{81}{24}[/tex] Divide the top and the bottom by 3 to get [tex]\frac{27}{8}[/tex]
which of the following options result in a graph that shows expoential decay
The option that results in a graph that shows exponential decay is Option(b) f(x) = 3(0.7)ˣ.
What is the Exponential Decay Formula?The exponential decay formula helps to determine the rapid decline over time or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.The exponential decay formula is f(x) = abˣ, where a is the initial amount, b is the decay factor and x is the time interval.According to the question, we have to determine the function that results in a graph that shows exponential decay.
The function will show an exponential decay if the value of b was less than 1 and greater than 0.
As we can notice in the second option, f(x) = 3(0.7)ˣ, where b is equal to 0.7 which is less than one.
So, f(x) = 3(0.7)ˣ shows exponential decay.
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The complete question is: "Which of the following options results in a graph that shows exponential decay?
a. f(x) = 0.6(2)ˣ
b. f(x) = 3(0.7)ˣ
c. f(x) = 0.4(1.6)ˣ
d. f(x) = 20(3)ˣ."
A students cost for last semester was 2000 she spent 320 on books. What percent of last semester was cost in books
The percentage of money spent on books to that of cost for last semester is 16%
The cost for last semester was 2000.
The cost books was 320.
The percentage formula = part/whole × 100
Part = 320
Whole = 2000
Equation = 320/2000× 100
= 32/20
= 16%
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find one seventh of the sum of 19 and the product of 4 and 11
Answer: One seventh of the sum of 19: 2.714
Product of 4 and 11: 44
Step-by-step explanation:
4x11=44
One seventh times 19 equal 2.714.
1/7 x 19/1 = 19/7
Simpified 2 5/7
2 5/2 as decimals is 2.714
|-2+2|-2
Wouldn’t this be -2
Answer:
yes correct ^ ^
Step-by-step explanation:
This question is a bit confusing
Carlos is moving to a new city and looking for a new job. He wants to rent an apartment, and he is willing to use half of his monthly paycheck for rent and apartment-related fees that he knows will be 200$. He doesn’t know exactly how much he’ll make at his new job yet, but he knows it will be somewhere between $3000 and $4000. Write an inequality and solve an inequality to show the price range David’s apartment will have to be in.
Answer: The price of the apartment lies in the range of $1300 to $1800
Step-by-step explanation: Because Carlos doesn't exactly know how much he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.
Let the rent on the new apartment = r
let monthly pay of Carlos = x
Given, apartment related fees = 200$
Given he is willing to use half of his monthly pay for rent and apartment related fees combined.
∴rent + apartment related fees = Monthly pay / 2
⇒[tex]r + 200 = \frac{x}{2}[/tex]
⇒[tex]x=2*(r+200)[/tex]
⇒[tex]x=2r+400[/tex] (1)
Given Carlos' monthly pay is in the range of $3000 to $4000
∴[tex]3000\leq x\leq 4000[/tex]
⇒[tex]3000\leq (2r+400)\leq 4000[/tex] (from equation (1))
⇒[tex]3000-400\leq 2r+400-400\leq 4000-400[/tex] (subtracting 400)
⇒[tex]2600\leq 2r\leq 3600[/tex]
⇒[tex]\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}[/tex] (dividing by 2)
⇒[tex]1300\leq r\leq 1800[/tex] (2)
ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)
here is a problem solved using inequality
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In a recent year, 32.2% of all registered doctors were female. If there were 53,600 female registered doctors that year, what was the total number of registered
doctors?
Round your answer to the nearest whole number.
Answer:
166,460 doctors registered.
Step-by-step explanation:
32.2% -------- 53,600 female doctors
100% -------- X
X * 32.2% = 100% * 53,600
X = (100% * 53,600) / 32.2%
X = 166,460 doctors
help me please help me
Step-by-step explanation:
we sadly need to do all the multiplications for the whole polynomial in standard form.
the other 3 things we get out of the given form :
we multiply 3 terms, each in x. the result will be x³.
so, we have the 3rd degree.
the leading coefficient is 1, as for the x³ term we get x×x×x = x³. no other number is involved.
the constant term is the extreme on the other end. it is 4×2×1 = 8.
so, now for the full multiplications, that should also show you, why I could make the conclusions above.
(x+4)(x-2)(x+1)
we do this by multiplying first 2 terms with each other, and then we multiply that result by the third term.
remember, we need to multiply every item of one term with every item in the other term.
(x+4)(x-2) = x² -2x + 4x - 8 = x² + 2x - 8
now
(x² + 2x - 8)(x+1) = x³ + x² + 2x² + 2x - 8x - 8 =
= x³ + 3x² - 6x - 8
so, that is already the standard form
f(x) = x³ + 3x² - 6x - 8
Drag each object to show whether distance is proportional to time in the situation represented.
The table with the situations that represent or not proportional relationships of distance and time is given at the end of the answer.
Which situation models a proportional relationship?A situation represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
One example, in the context of this problem, is the relation between velocity, distance and time, as velocity is distance divided by time, hence:
v = d/t.
The relation between distance and time is given as follows:
distance = velocity x time
distance = v x t.
Hence it will only be proportional if the velocity is constant, that is, if the acceleration is of zero.
Examples of non-proportional situations in the context of this problem are:
A touchdown, as when the play starts the player is stopped then he accelerates and the velocity is not constant.The horse running around the race track, same logic, different velocities.The distance and time table (4 - 15, 8 - 30, 12 - 45) does not show enough information, we need to know if the initial point was of (0,0).
What is the missing information?The objects are missing, and have been dragged to their correct situation on the table.
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