7. Each set of numbers below represents the lengths of three line segments.
Which set represents line segments that could be connected to form a triangle:
A. (1, 2, 3)
B. (3, 4, 5)
C. (1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)
Please don't just give a letter choice as an answer. There are more questions like this one and I'd like to understand how to do it : )
Answer:
B: (3, 4, 5)
Step-by-step explanation:
You want to know which segment lengths could be used to form a triangle.
Triangle inequalityThe triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.
A: 1+2 = 3 . . . not a triangle
B: 3+4 > 5 . . . forms a triangle
C: 1+10 < 100 . . . not a triangle
D: 1+2 < 5 . . . not a triangle
E: 1+3 = 4 . . . not a triangle
F: 1+20 < 100 . . . not a triangle
__
Additional comment
The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.
The triangle inequality can also be seen to be expressed as ...
a + b ≥ c . . . . . . where a, b, c are side lengths in any order
The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."
Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2D) y = 2
Answer
B) y = 3
Step-by-step explanation
Given the system of equations:
[tex]\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}[/tex]Isolating x from equation 1:
[tex]\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ \frac{3x}{3}=\frac{12-2y}{3} \\ x=\frac{12}{3}-\frac{2}{3}y \\ x=4-\frac{2}{3}y\text{ \lparen eq. 3\rparen} \end{gathered}[/tex]Substituting equation 3 into equation 2 and solving for y:
[tex]\begin{gathered} 5(4-\frac{2}{3}y)-y=7 \\ 5\cdot4-5\cdot\frac{2}{3}y-y=7 \\ 20-\frac{10}{3}y-y=7 \\ 20-\frac{13}{3}y=7 \\ 20-\frac{13}{3}y-20=7-20 \\ -\frac{13}{3}y=-13 \\ (-\frac{3}{13})\cdot-\frac{13}{3}y=(-\frac{3}{13})\cdot-13 \\ y=3 \end{gathered}[/tex]
Answer:
y=3
Step-by-step explanation:
Got it right :/
Question at position 3
Write the expression as a sum and/or difference of logarithms with all variables to the first degree
[tex]ln\sqrt{8t^{4} v^{2}[/tex]
The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Given,
Write the expression as a sum and/or difference of logarithms with all variables to the first degree.
[tex]In\sqrt{8t^4v^2}[/tex]
Convert to exponential form
= [tex]In(8t^4v^2)^\frac{1}{2}[/tex]
Simplify using exponent rule with same exponent [tex](ab)^n = a^n . b^n[/tex]
= [tex]In (8^\frac{1}{2} . (t^4)^\frac{1}{2}(v^2)^\frac{1}{2} )[/tex]
Apply laws of logarithms to simplify the expression.
= [tex]In 8^\frac{1}{2} + In(t^4)^\frac{1}{2} + In(v^2)^\frac{1}{2}[/tex]
Express the logarithm of a power of an expression as the power times the logarithm of the expression.
= [tex]\frac{1}{2} . In8 + In(t^4)^\frac{1}{2} + In(v^2)\frac{1}{2}[/tex]
=[tex]\frac{1}{2} . In8 + \frac{1}{2} . In(t^4) + \frac{1}{2} .In(v^2)[/tex]
Multiply the monomials
[tex]\frac{In8}{2} + \frac{1}{2} . 4 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Hence, The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
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QuestRecently, More Money 4U offered an annuity that pays 6.6% compounded monthly. If $1,504 is deposited into this annuity every month, how much is in the account after 11 years? How much of this is interest?Type the amount in the account: $(Round to the nearest dollar.)
ANSWER
Amount = $3102.75
Interest = $1598.75
EXPLANATION
The annuity pays 6.6% compounded monthly.
The formula for an Amount compounded at a rate of r after t years is given as:
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where P = principal (amount deposited) = $1,504
r = rate = 6.6% = 0.066
n = 12 (12 months in a year)
t = number of years = 11 years
Therefore, the amount in the account after 11 years is:
[tex]A\text{ = 1504(1 +}\frac{0.066}{12})^{12\cdot\text{ 11}}[/tex][tex]\begin{gathered} A=1504(1+0.0055)^{132} \\ A\text{ = 1504(}1.0055)^{132} \\ A\text{ = 1504 }\cdot\text{ 2.063} \\ A\text{ = \$3102.75} \end{gathered}[/tex]That's the amount in the account after 11 years.
This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:
Interest = 3102.75 - 1504
Interest = $1598.75
Help me please, it’s due in 10 minutes!
Answer: x<2 or (−∞,2)
Step-by-step explanation:
Now move the red distribution at the top to the right so that its mean is approximately 375 and then look at the middle and bottom distributions. Based on the location of 0 in the bottom distribution (meaning no difference in the means) what is the best conclusion?
Based on the location of 0 in the bottom distribution (meaning no difference in the means), the best conclusion is:
A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.
What is a distribution?In mathematics, distribution describes the probability that a system or a data set will take on a specific value or set of values.
Probability distribution shows how data values are distributed. It is also known as statistical distribution because it demarcates values into common and uncommon (left and right), making a bell-shaped normal distribution.
Thus, when there is no difference in the means, the best conclusion of the statistical distribution is Option A.
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Question Completion with Answer Options:A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.
B- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different.
C- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different.
D- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different.
what is the price of a line jacket at discount Heaven?
The price of the lined jacket at discount heaven is 32.
To find the price of the lined jacket at the house of denim we use the rule of three.
[tex]\begin{gathered} 35.25\rightarrow100 \\ x\rightarrow10 \end{gathered}[/tex]Then the discount is:
[tex]x=\frac{10\cdot35.25}{100}=3.525[/tex]Hence, the price of the lined jacket at house of denim is:
[tex]35.25-\text{3}.525=31.725=\text{31}.73[/tex]Therefore, the price of the lined jacket at house of denin is $31.73.
The following table shows a proportional relationship between wand z.318z 2. 545819Write an equation to describe the relationship between w and z.
when w = 18 then z =2
take ratio,
k = 18/2
k = 9
when w =45 then z = 5
take ratio
k = 45/5
k = 9
now it is clear that the constant of proportionality is k = 2
so, the relation between w and z is
w = k z
put k = 9
w = 9z
so, the relation between w and z is w = 9z
8 Write the equation of the line in standard form, point-slope form, and slope-intercept form. 4 -2 DELL
step 1
Find the slope
we need two points
take the points (0,3) and (1,0)
m=(0-3)/(1-0)
m=-3
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-3
b=3
substitute
y=-3x+3step 3
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-3
point (0,3)
y-3=-3(x-0)
y-3=-3xstep 4
standard form
AX+By=C
we have
y=-3x+3
3x+y=3 -----> standard formUse the graph below for this question: graph of parabola going through negative 3, negative 1 and 5, negative 1. What is the average rate of change from x = −3 to x = 5? (1 point) A) −1
B) 0
C) 1
D) 8
The average rate of change of the function at the interval x = -3 to x = 5 has a value of (b) 0
How to calculate the average rate of change f?From the question, we have the following points
Parabola going through (-3, -1) and (5, -1).
Also from the question, the interval is given as
x = −3 to x = 5
This interval can also be represented as
(a, b) = (-3, 5)
The points in the question can be expressed as
f(a) = f(-3) = -1
f(b) = f(5) = -1
The value of the average rate of change of the graph at the interval is then calculated as
Rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have the following equation
Rate = [f(5) - f(-3)]/[5 + 3]
So, we have the following equation
Rate = [-1 + 1]/[5 + 3]
Evaluate the above quotient
Rate = 0
Hence, the average rate of change of function f is (b) 0
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Leonard is 68 years less than quadruple Sheldon's age. In 12 years, Leonard's age will be 24 years less than two times Sheldon's age. What are their 2 ages?
Sheldon is 16 4/7 years old, while Leonard is 21 1/7.
We are given the correlations between two numbers in this sort of query, specifically the data when their ages are contrasted now and in the future.
Let x represent Leonard's age.
We can infer Sheldon's age from the question as being 4x - 68.
The following equation results from the question:
x + 12 = 2((4x - 68) + 12) - 24
Fix x,
=> x + 12 = 2(4x - 68 + 12) - 24
x + 12 = 2(4x - 56) - 24
x + 12 = 8x - 112 - 24
x - 8x = -136 - 12
-7x = - 148
x = 148 / 7 or 21 1/7
Now, simply multiply 4x by 68 to get Sheldon's age.
=> 4x - 68
=> 4 * 148/7 - 68
=> 592/7 - 68
=> 116/7 or 16 4/7
Leonard is therefore 21 1/7 years old, while Sheldon is 16 4/7.
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A sample of 342 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according tomajor ("blology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.Biology Business Engineering Mathematics Computer scienceFemale4623501837Male4815461544What is the relative frequency of male students in the sample?Round your answer to two decimal places.0Х5.?
The relative frequency of an event is the quotient of the division between the event and the total number of the sample
From the given table
Add the numbers of males to find their total
[tex]48+15+46+15+44=168[/tex]Then add the numbers of females and males to find the total of the sample
[tex]168+46+23+50+18+37=342[/tex]Now, divide the number of males by the total to find the relative frequency
[tex]\begin{gathered} R\mathrm{}F=\frac{168}{342} \\ R\mathrm{}F=0.4912280702 \end{gathered}[/tex]Round it to 2 decimal places, then
The relative frequency of the male students = 0.49
Someone help me out pls!
Answer:
look my photo. hope it can help
Passes through the coordinates -2,2 parallel to the line whose slope is -1
The equation of the line is y-2x= 6.
Here the problem we are dealing with is related to the slope of the line, where, a slope of a line is the alter in the y coordinate about the alter in the x coordinate. The net change in the y-coordinate is spoken to by Δy and the net change in the x-coordinate is spoken to by Δx. The equation for the slope of a straight line is given by y − y1 = m(x − x1), where m is the slope and (x1,y1) are the points that pass through it,whereas the slope-intercept form of the line is given by y = mx + b, where b is the y-intercept. Since if two lines are parallel at that point it said the slope of both those lines are equal i.e m₁= m₂
Since it is given that the coordinates (-2,2) and the slope of the parallel to it, m=2
so the equation for the line is
=>y − y1 = m(x − x1)
=>y − 2 = 2(x +2)
=>y − 2 = 2x+4
=>y-2x= 6
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Find the eqaution of the line that passes through the coordinates -2,2 parallel to the line whose slope is -1.
PLS HELP ( geometry) and please explain the steps tyy
Answer: The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
Step-by-step explanation:
consider functions f and g. f(x) = -x^3g(x) = | 1/8x-1| what is the value of ( g • f)(4)a: -9b: -1/8 c: 9 d: 1/8
The solution:
Given the functions:
[tex]\begin{gathered} f(x)-x^3 \\ \\ g(x)=|\frac{1}{8}x-1| \end{gathered}[/tex]Required:
To find the value of g(f(4))
Step 1:
Substitute 4 for x in f(x).
[tex]f(4)=-(4)^3=-64[/tex]Step 2:
Substitute -64 for x in g(x).
[tex]\begin{gathered} g(-64)=|\frac{1}{8}(-64)-1| \\ \\ g(-64)=|(1\times-8)-1| \\ \\ g(-64)=|-8-1|=|-9|=9 \end{gathered}[/tex]Therefore, the correct answer is 9 [option C]
Describe the
transformation from the
graph of of to the graph
of g.
In the picture, there is table with functions. g(x)=-f(x)
The graph of g is negative 1 times of graph of f.
Given that,
In the picture, there is table with functions.
We have to find the transformation from the graph of f to the graph g.
The table has functions with the numbers.
x values as -2,-2,0,1
Function f(x) as 4,1,0,1
Function g(x) as -4,-1,0,-1
The f(x) function we can write as
f(x)=x²
And the g(x) function we can write as
g(x)=-x²
Therefore, g(x)=-f(x)
The graph of g is negative 1 times of graph of f.
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A cosine function has an amplitude of 1/4 , period of pi/2, horizontal shift of 2pi, and vertical shift of -4.
What is the y-value of the positive function when x = 2π?
y = ?
The value of y when y = y = 0.25sin(4(x+2π))-4. and x = 2pi is -4.
Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.The Amplitude is the height from the center line to the peak (or to the trough).The Phase Shift is how far the function is shifted horizontally from the usual position.The Vertical Shift is how far the function is shifted vertically from the usual position.
We can have all of them in one equation:
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
So, for the given question we have amplitude is 0.25, period is 2π/4, phase shift is 2π, vertical shift is -4
So,
y = 0.25sin(4(x+2π))-4.
when x = 2π
y = 0.25sin(16π)-4
y = 0-4
y = - 4
Therefore, y = 0.25sin(4(x+2π))-4, and its y - value when x = 2π is -4.
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Sequence: 0, 4, 8, 12,...
Find the 18th term.
Answer:
68
Step-by-step explanation:
Bryant measured a house and made a scale drawing the scale he used was 1 inch = 1 foot what scale factor does the drawing use?
The scale factor which is being used by this drawing is 1 : 12.
What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.
Mathematically, the scale factor of a geometric figure can be calculated by using tis formula:
Scale factor = Dimension of image/Dimension of original figure
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 inch = 1 foot
12 inches = 1 foot
Therefore, the scale factor for this drawing is 1 : 12.
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write an equation of a line m= -7 b= -11
Answer:
y= -7x-11
Step-by-step explanation:
m= -7 (gradient)
b= -11 (y-intercept)
write in the form of y=mx+b
y=-7x-11
A regular polygon is shown.
15 sided regular polygon
Determine the measure of one of its angles.
156°
168°
2,340°
2,700°
The measure of the given polygon's angle is 2340°
Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.
In an n-sided polygon, there are n inner angles.
The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.
the formula is ;
Sₙ = ( n - 2 ) 180°
Here in question n is given as 15
Thus Sₙ = ( n - 2 ) 180° becomes
Sₙ = ( 15 - 2) 180
13 × 180
= 2340 °
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Answer:
it is really A 156 i took the test and got an 100%
Step-by-step explanation:
Jared sells jewelry online. He can make 25 necklaces from 375 beads. Yesterday he made 21 necklaces. How many beads did Jared use to make necklaces yesterday
The number of beads he used to make 21 necklaces is 315 beads.
How to find the number of beads Jared use to make necklaces?He sells jewellery online. He can make 25 necklaces from 375 beads.
This means Jared uses 375 beads to make 25 necklaces.
Yesterday he made 21 necklaces.
Therefore, the number of beads he used to make the 21 jewellery can be calculated as follows:
Hence,
25 necklaces = 375 beads
21 necklaces = ?
cross multiply
number of beads used to make the necklaces = 21 × 375 / 25
number of beads used to make the necklaces = 7875 / 25
Therefore,
number of beads used to make the necklaces = 315
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11A family went out to dinner. The cost of their meal was $689, before sales tax and tip.A sales tax of 8% was added.(a)The family then tipped 20% on the amount after the sales tax was added,Part AWhat was the amount, rounded to the nearest cent, of just the sales tax?Show all of your work and record your final answer in the space below.Click the box below to type your math work and answer.On the right side of the box, click thebutton to start a new line.
The cost of the meal before the sales tax and tip= $689
Sales tax = 8%
The family then tipped 20% on the ammount after the sales was added
PART A
The amount of the sales tax can be calculated as follows
Amount of sales tax = sales tax * the amount of the meal
Amount of sales tax = 8% x $689
Amount of sales tax = 8/100 x 689
Amount of sales tax = 0.08 x 689
Amount of sales tax = $55.12
Therefore, the amount of sales tax is $55.12
PART B
What is the total amount paid by the family after adding the tax sales and 20% tipping
The cost of the meal = $689
Amount of sales tax = $55. 12
20% tipping on the amount after the sales tax was added
Amount of the meal after the sales has been added = $689 + $55.12
Amount of the meal after the sales tax has been added = $744. 12
20% tipping of the total amount = 20% x 744.12
= 20/100 x 744.12
= 0.2 x 744.12
= $148.82
The total amount paid by the family = 689 + 55.12 + 148.82
The total amount = $892.94
Therefore, the family paid a total amount of $892.94
Assume that all interest is simple interestBerger Car rental borrow $8500 at 4% interest to cover the increase cost of the auto insurance find the term of the loan if the interest is $170.
we know that
The formula of simple interest is equal to
[tex]I=P(rt)[/tex]In this problem
we have
I=$170
P=$8,500
r=4%=4/100=0.04
t=?
substitute given values in the formula
[tex]\begin{gathered} 170=8,500(0.04t) \\ Solve\text{ for t} \\ t=\frac{170}{8,500*0.04} \\ t=0.5\text{ years} \end{gathered}[/tex]therefore
0.5 years=6 months
The answer is 6 months. Find the slope and y-intercept of the line shown below.to10-8--10-8-6-4-2.co6-4-2---2--4--6--8--10-yX4 6 8 10
Solution:
Given the graph:
Using two points on the line to find the slope, m:
[tex]\begin{gathered} (0,-1),(5,-2) \\ \\ x_1=0,y_1=-1,x_2=5,y_2=-2 \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-2-(-1)}{5-0} \\ \\ m=-\frac{1}{5} \end{gathered}[/tex]Thus, the y-intercept and slope, m of the line respectively are:
[tex][/tex]Can someone please help me with this problem? I’ll give brainliest
Answer:
Step-by-step explanation:
gee girls generation
Please asnwer corrrectly and if you could explain or not
Answer:
y = 4·0.5^x
Step-by-step explanation:
If x is increased by 1, y is multiplied by 0.5.
x | y
0 | 4
1 | 4·0.5
2 | 4·0.5·0.5
3 | 4·0.5·0.5·0.5
Please Help . I'm Running Out Of Time!
-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.
Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps
If this is wrong I am deeply sorry.
Omar and Zina Aboud found that the dealers cost of the base price was $16.558.16 and the dealer's options cost was $611.60. The consumer paid the $476.00 destination charge. If the percent of the dealer's cost is 92% and the percent of dealer's options cost is 88%, find the car's sticker price.
We want to calculate the sticker price. The sticker price is given by the formula
[tex]\text{sticker price = base }price+\text{ options + destination charge}[/tex]We are told that the destination charge is 476. We should determine the base price and the options to find the price sticker.
We are told that the dealer's cost of the base price is 92% of the pase price. So we have the equation
[tex]16558.16=\frac{92}{100}\cdot\text{base price}[/tex]so if we divide both sides by 92 and multiply by 100 we get
[tex]\text{base price = }16558.16\cdot\frac{100}{92}=17998[/tex]Now, applying the same principal for the options, we have
[tex]611.60=\frac{88}{100}\text{options}[/tex]which means that
[tex]\text{options}=611.6\cdot\frac{100}{88}=695[/tex]Replacing these values in the original equation we have that
[tex]\text{sticker price = }17998+695+476=19169[/tex]so the sticker price would be 19169