Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
Answers
The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
Related Questions
What is the starting value of the exponential function below?
Answers
The starting value of an exponential function is the value that it takes when x=1.
In this case, we can see that y=3 when x=1.
Then, the starting value is equal to 3.
Find two positive numbers whose difference is 14 and whose product is 1976
Answers
The positive numbers that the difference is 14 and the product is 1976 are 38 and 52.
How to find the positive numbers?The difference of the positive numbers is 14 and the products of the positive numbers is 1976.
The positive numbers are the numbers that are greater than zero.
Positive numbers includes fractions, In general, positive numbers are natural counting numbers.
Therefore,
let the numbers be x and y
Hence, the difference of the positive numbers is 14.
x - y = 14
The product of the positive numbers is 1976. Therefore,
xy = 1976
Make x the subject of the formula in equation(ii)
x = 1976 / y
Substitute the value of x in equation(i)
1976 / y - y = 14
14y = 1976 - y²
solve the quadratic equation formed.
y² + 14y - 1976 = 0
Hence,
y² - 38y + 52y - 1976
y(y - 38) + 52(y - 38)
(y - 38)(y + 52)
Therefore,
y = 38 and y = -52
The number is positive .
Therefore, we can only use 38.
y = 38
Substitute the value of y in equation(i)
x - 38 = 14
x = 14 + 38
x = 52
Therefore, the positive numbers are 38 and 52.
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If a2 -2ab + b2 = 9 and a
Answers
If a2 -2ab + b2 = 9 and a[tex]\begin{gathered} a^2-2ab+b^2=9 \\ a
Step 1
factorize
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]then
[tex]\begin{gathered} (a-b)^2=9 \\ \sqrt{(a-b)^2}=\sqrt{9} \\ a-b=\pm3 \\ \\ aa-b=-3Skis are listed by a manufacturer for $850, less trade discounts of 35% and 18%. What further rate of discount should be given to bring the net price to $446?
Answers
The Solution:
The listing price of the Skis by a manufacturer is $850.
A trade discount of 35% was allowed.
[tex]\begin{gathered} 35\text{ \% of \$850=0.35}\times850=\text{ \$297.50} \\ \text{Price}=850-297.50=\text{ \$552.50} \end{gathered}[/tex]Allowing an extra discount of 18%, we get
[tex]\begin{gathered} 18\text{ \% of \$}552.50=0.18\times552.50=\text{ \$99.45} \\ \text{Price}=552.50-99.45=\text{ \$453.05} \end{gathered}[/tex]We are required to find what further rate of discount should be given to bring the net price to $446.00
[tex]\begin{gathered} 453.05-446.00=7.05 \\ To\text{ find the required percentage of discount, we have} \\ \frac{7.05}{453.05}\times100=0.0155612\times100=1.55612\approx1.56\text{\%} \end{gathered}[/tex]Therefore, the correct answer is 1.56%
x + 4y = 4 2x + 4y = 8x=4y=-2
Answers
x + 4y = 4
2x + 4y = 8
x=4
y=-2
we know that
If a ordered pair is a solution of a equation, then the ordered pair must satisfy the equation
we have the ordered pair (4,-2)
Verify if the ordered pair is a solution of the given equations
Equation 1
x+4y=4
substitute the value of x and the value of y in the given equation
(4)+4(-2)=4
4-8=4
-4=4 ------> is not true
the ordered pair is not a solution of the equation
Equation 2
2x + 4y = 8
substitute the value of x and the value of y in the given equation
2(4)+4(-2)=8
8-8=8
0=8 -----> is not true
the ordered pair is not a solution of the equation
Hurry Will give 75 points
(Score for Question 3: of 4 points)
3. The equation y = 14x describes the amount of money Louis earns, where x is the number of hours he works
and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl's Earnings
Time (h)
Money earned
($)
Hours 3 5 8 10
Money 54 90 144 180
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.
Answer:
Carl earns 18 dollars an hour, we can get this by dividing the money earned by time which gets your answer.
Answers
Part a: Carl earning per hour is $18.
Part b: More Money is earned by Carl.
Part c: The graph that represents Carl's earnings is drawn.
What is termed as the equation?A mathematical statement consisting of two expressions joined by an equal sign is known as an equation. 3x - 5 = 46 is an example of an equation. We have the value for the variable x as x = 17 after solving this equation.For the given question,
The amount of the money Louis have is defined by the equation.
y = 14xx is the number of hours.y is the amount of money.Carl's Earnings
Time (h) Hours 3 5 8 10
Money earned($) 54 90 144 180
Part a: Carl earning per hour.
For 3 hours Carl earns $54.
For one hour-$54/3 = $ 18.
Part b: More Money is earned by-
For 1 hours Carl earns $8.
For 1 hour Louis earning is y = 14×1 = $14.
Thus, Carl earns more.
Part c: The graph that represents Carl's earnings over time in hours is drawn.
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Type your response in the box.Use the information in the table to determine some similarities and differences between linear and exponentialequations. Include observations about the forms of both equations and the placement of the independent variablein the equations.f(3) = 5(3)s() = 2x+55057121192
Answers
Ok let's talk about some similarities and differences between linear and exponential equations.
In the linear functions the rate of change is constant. While in the exponential fuctions the rate of change is not constant.
In linear function the graph is a straight line. in the exponential fuctions graph is an exponential curve.
In linear functions the placement of the independent variable is is multiplying a coefficient. In the exponential fuctions the placement of the independent variable is as the power of a coefficient.
Find fractional notation of 87.5%
Answers
To find the fractional notation, we have to transform 87.5% into a fraction. To do that, we just have to divide the percentage by 100.
[tex]\frac{87.5}{100}[/tex]Then, we multiply each part by 10.
[tex]\frac{87.5\times10}{100\times10}=\frac{875}{1000}[/tex]At last, we simplify the fraction by 125 to get 7/8.
[tex]\begin{gathered} \frac{875}{125}=7 \\ \frac{1000}{125}=8 \end{gathered}[/tex]Hence, the given percent, in fractional notation, is 7/8.10 i You spin the spinner and flip a coin. Find the probability of the compound event. 3 LD t The probability of spinning a number less than 3 and flipping tails is
Answers
Compound probability = probability of first event * probability of second event
Let the spinning of the spinner be event A(First event)
Recall,
Probability = number of favourable outcomes/total number of outcomes
The numbers lesser than 3 are 1 and 2. thus, favourable outcomes = 2
total outcomes = 5
P(A) = 2/5
For event B(second event)
The coin has only head and tail
P(B) = 1/2
Thus, the probability of spinning a number less than 3 and flipping tails is
2/5 * 1/2
= 1/5
Examine this lable of points, which are all on a certain line. 8 What is the slope of this line? Enter your answer as a number, like this 42 Or, if the slope is undefined. enter a lowercase letter "u. like this. u
Answers
The formula for determining slope, m is expressed as
slope, m = (y2 - y1)/(x2 - x1)
y1 represents initial value of y
y2 represents final value of y
x1 represents initial value of x
x2 represents final value of x
From the table,
y2 = - 8
y1 = 0
x2 = - 1
x1 = - 5
Slope, m = (0 - - 8)/(- 1 - - 5)
Slope, m = (0 + 8)/(- 1 + 5)
Slope, m = 8/4
Slope = 2
f(x) = 4x - 2 for x = 0
Answers
Substituting x = 0 into the function we get:
f(0) = 4(0) - 2
f(0) = 0 - 2
f(0) = -2
Find the distance between the two points. 16.) (-4,2), (5,1)
Answers
distance is 9.055
Explanation:Given:
Two points; (-4, 2) and (5, 1)
To find:
the distance between two points
We will apply the formula for distance between two points:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} x_1=-4,y_1=2,\text{ }x_2=5,\text{ }y_2\text{ = 1} \\ distance\text{ = }\sqrt{(1-2)^2+(5-(-4))^2} \\ distance\text{ = }\sqrt{1\text{ + 9}^2} \\ distance\text{ = }\sqrt{82} \\ distance\text{ = 9.055} \end{gathered}[/tex]Daniel ate 3 pieces of pizza. Jeremy ate 2 times that much. How many pieces of (p) did Jeremy eat?
Answers
Let:
x = pieces of pizza eaten by Daniel
y = Pieces of pizza eaten by Jeremy
Daniel ate 3 pieces of pizza. so:
[tex]x=3[/tex]Jeremy ate 2 times that much, so:
[tex]\begin{gathered} y=2x \\ so\colon \\ y=2(3) \\ y=6 \end{gathered}[/tex]Jeremy ate 6 pieces of pizza
Kaylee read 1 book in 4 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
If Kaylee read 1 book in 4 months, this means that in 1 month, she read 1/4 of the book. We can see this in the following figure:
Vocabulary Are 23 and 24 adjacent angles? Explain. 1. 2. 3. 4 Reasoning Does every angle have a complement? Explain.
Answers
We will have the following:
1. We have that 3 & 4 are not adjacent angles.
2. We have that 3 and 4 are adjacent angles.
3. We have that 3 and 4 are not adjacent angles.
4. Not every angle has a complement. A complement is when two angles add up to 90°, so any angle greater than 90° won't have a complement.
***Explainations***
1- 3 & 4 in order to be adjacent have to share the same vertex [They do] and have to be one right next to the other [They are not, there is another angle between them].
2. 3 & 4 are adjacent since they share the same vertex and are one next to the other.
3. 3 & 4 are not adjacent since they do not share a vertex.
I got this connected from the tutor I need to know how to do the factorial in this formula to bio normal distribution formula The symbol that looks like an!
Answers
Binomial distribution formula:
[tex]P(x)=\frac{n!}{(n-x)!x!}*p^{`x}*q^{n-x}[/tex]For the gien situations:
* n=15, p=0.4, find P(4 successes)
[tex]\begin{gathered} n=15 \\ p=0.4 \\ q=1-p=1-0.4=0.6 \\ x=4 \end{gathered}[/tex][tex]P(4)=\frac{15!}{(15-4)!4!}*0.4^4*0.6^{15-4}[/tex][tex][/tex]I need help to do these composition of functions. I have a photo if needed.h(a)=4a+1g(a)=2a-5Find (h×g)(-9)
Answers
The composition of two functions is defined as follows:
[tex](h\circ g)(x)=h(g(x))[/tex]Use the given rules of correspondence of h and g to find the composition of those two functions. Then, evaluate the composition at -9:
[tex]\begin{gathered} h(a)=4a+1 \\ \Rightarrow h(g(a))=4\cdot g(a)+1 \end{gathered}[/tex][tex]\begin{gathered} g(a)=2a-5 \\ \Rightarrow4\cdot g(a)+1=4\cdot(2a-5)+1 \\ =8a-20+1 \\ =8a-19 \end{gathered}[/tex]Then:
[tex]\begin{gathered} (h\circ g)(a)=h(g(a)) \\ =4\cdot g(a)+1 \\ =8a-19 \\ \\ \therefore(h\circ g)(a)=8a-19 \end{gathered}[/tex]Evaluate the composition of h and g at a=-9:
[tex]\begin{gathered} (h\circ g)(-9)=8(-9)-19 \\ =-72-19 \\ =-91 \end{gathered}[/tex]Therefore:
[tex](h\circ g)(-9)=-91[/tex]If sine= 2/3, which of the following are possible for the same value of ?
Answers
Given
[tex]\sin\theta=\frac{2}{3}[/tex]Find
which of the following are possible?
Explanation
as we know ,
[tex]\begin{gathered} \sin\theta=\frac{P}{H} \\ \end{gathered}[/tex]so , H = 3 , P = 2
then
[tex]\begin{gathered} B=\sqrt{H^2-P^2} \\ B=\sqrt{9-4} \\ B=\sqrt{5} \end{gathered}[/tex]so ,
[tex]\begin{gathered} \cos\theta=\frac{B}{H}=\frac{\sqrt{5}}{3} \\ \\ \tan\theta=\frac{P}{B}=\frac{2}{\sqrt{5}} \\ \\ sec\theta=\frac{1}{\cos\theta}=\frac{3}{\sqrt{5}} \end{gathered}[/tex]Final Answer
Hence , the correct options are B and C
Show that Polygon ZSCH
is a Scaled copy of
Polygon XJYN.
Answers
As ratio is not given, we cannot prove that they are scaled copy.
Define scaled copy.Corresponding portions, or parts that are at the same location in relation to the remainder of each figure, exist in both the original figure and its scaled copy. These components could be angles, points, or segments. Polygon 2, for instance, is a scaled-down version of Polygon 1. There is a point in Polygon 2 for each point in Polygon 1.
Given,
Polygon ZSCH is a Scaled copy of Polygon XJYN.
We simply calculate the ratio of the lengths of the two corresponding sides of two polygons to determine the scale factor. The scaling factor is known as such and the polygons are similar if the ratio is the same for all matching sides.
As ratio is not given, we cannot prove that they are scaled copy.
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A car's cooling system has a capacity of 20 quarts. Initially, the system contains a mixture of 7 quarts of antifreeze and 13 quarts of water. Water runs into the system at the rate of 1 gal min , then the homogeneous mixture runs out at the same rate. In quarts, how much antifreeze is in the system at the end of 5 minutes? (Round your answer to two decimal places.)
Answers
After 5 minutes there will be 2.29376 quarts of antifreeze in the system.
Given,
The capacity of the cooling system of a car = 20 quarts
The mixture in the system is 7 quarts of antifreeze and 13 quarts of water.
The running rate of water = 1 gal/min
Homogenous mixture also runs 1 gal/min
We have to find the antifreeze in the system at the end of 5 minutes;
Here,
1 quart = 0.25 gallons
7 x 0.25 = 1.75 gallons of antifreeze
13 x 0.25 = 3.25 gallons of water
1 = 0.2 of 5
Minute 1 = 1.75 x 0.8 = 1.4Minute 2 = 1.4 x 0.8 = 1.12Minute 3 = 1.12 x 0.8 = 0.896Minute 4 = 0.896 x 0.8 = 0.7168Minute 5 = 0.7168 x 0.8 = 0.573440.57344 gallons = 2.29376 quarts
After 5 minutes there will be 2.29376 quarts of antifreeze in the system.
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what is the most important piece of the software in a computer
Answers
Answer:
Step-by-step explanation:
the operating system
Answer:
An operating system is the most important software that runs on a computer. It manages the computer's memory and processes, as well as all of its software and hardware. It also allows you to communicate with the computer without knowing how to speak the computer's language.
Brainliest please?
Hope this helps
Write the following ratio using two other notations: 1/3
Answers
Given:
[tex]\frac{1}{3}[/tex]To write the given fraction into two other notations, we use "to" for word notation while ":" for number notation.
Therefore, the answers are:
1 to 3
1:3
What is the slope of the line shown in the graph
Answers
Step by step
We have the coordinate pairs of
(0, 3) and (-3, 5) as shown on the attachment
Slope is found by
y2 - y1 over x2 - x1
5 - 3 over -3 - 0
2 over -3
Slope is -2/3
You can also count from point to point y over x
Here we have -2 down and +3 over for a slope of -2/3
Remember if your line going left to right goes at a downward angle, it is a negative slope.
What is the image of (-5,1) after a dilation by a scale factor of 5 centered at the origin?
Answers
Explanation
Step 1
when you have a coordinate (x,y) and you want to get the image after a dilationi, make
[tex]\text{new image=(coordinate)}\cdot factor[/tex]then
let
coordinate=(-5,1)
dilation scale=5
now, replace
[tex]\begin{gathered} \text{new image=(coordinate)}\cdot factor \\ \text{new image=(-5,1)}\cdot5 \\ \text{new image=(}-25,5) \end{gathered}[/tex]I hope this helps you
what is 9=-1/4x+4 in standard form
Answers
The standard form in which the equation must be written is -1/4x = 5
Standard Equation FormStandard form is just another way to write a linear equation equation along with slope intercept form and point slope form.
Standard form appears in the form ax + by = c
Where a, b and c are integers and a must be positive
In the given equation 9 = -1/4x + 4, we can rewrite this into standard equation of line by
-1/4x + 4 = 9
-1/4x + 4 - 9 = 0
-1/4x - 5 = 0
-1/4x = 5
The standard form of the equation is -1/4x = 5
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A plumber charges $14 for transportation and $30 per hour for repairs. Complete the expression that can be used to find the cost in dollars for a repair that takes h hours.An expression that can be used to find the cost in dollars for a repair that takes h hours is ____ + ____h.
Answers
A plumber charges $14 for transportation and $30 per hour for repairs.
Complete the expression that can be used to find the cost in dollars for a repair that takes h hours.
An expression that can be used to find the cost in dollars for a repair that takes h hours is ____ + ____h.
_______________________________________________________________________
Charges
14 + 30* h
________________________________
Answer
An expression that can be used to find the cost in dollars for a repair that takes h hours is _14___ + _30___h.
____________________________________________
30 per hour, if it's two hours then 60 for example
For each set of points below determine the distance between them using the distance formula. Express each answer in simplest radical form.
Answers
Given data:
The given points are (5, 4) and (-1, 14).
The distance between the given points is,
[tex]\begin{gathered} d=\sqrt[]{(-1-5)^2+(14-4)^2} \\ =\sqrt[]{36+100} \\ =\sqrt[]{136} \\ =2\sqrt[]{34} \end{gathered}[/tex]Thus, the distance between the given points is 2√(34).
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, …
a9
a10
a11
a12
Answers
The term that is the −20,155,392 in the sequence is a₁₀.
How to solve sequence?The sequence below is a geometric sequence.
Therefore, a geometric sequence can be represented as follows:
nth term = arⁿ⁻¹
where
a = first termn = number of termsr = common ratioTherefore, let's find which term is −20,155,392 for the sequence.
2, -12, 72, -432
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Hence,
nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Therefore, it's the 10th term.
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The term −20,155,392 is the tenth in the given geometric sequence.
The given sequence is below which is in a geometric pattern
2, -12, 72, -432
Here first term (a) = 2
The common ratio (r) = -12 / 2
The common ratio (r) = -6
We know that the nth term of the geometric sequence is
Tₙ = arⁿ⁻¹
Here Tₙ = −20,155,392
⇒ −20,155,392 = arⁿ⁻¹
Substitute the values of a and r in the above equation,
⇒ −20,155,392 = 2 × -6ⁿ⁻¹
⇒ −20,155,392 / 2 = -6ⁿ⁻¹
Apply the division operation,
⇒ - 10077696 = -6ⁿ⁻¹
⇒ 6ⁿ⁻¹ = 10077696
⇒ 6ⁿ⁻¹ = 6⁹
Equating exponents of the base
⇒ n - 1 = 9
⇒ n = 10
Therefore, the term −20,155,392 would be the tenth in the given sequence.
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It takes 2000 bees 1 year to make 7 jars of honey. How long will it take 5000 bees to make 70 jars of honey?
Answers
If the bees are working at the same rate, the number of years taken to make 70 jars is 4 years.
What is the rate of jar making by a bee?
The rate at which a bee makes a jar is calculated as follows;
rate = 2000 bees / 7 Jars
rate = 285.71 b/J
The later of rate of the bees is calculated as follows;
rate = 5000 bees / 70 jars
rate = 71.42 b/J
If the bees were to maintain the first rate, the number of years taken to make 70 jars is calculated as follows;
number of years = (285.71) / (71.42) = 4 years
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help meee pleaseeee pleasee
Answers
Answer:
f(4) = (16/7)
f(0) = -12
f(-5) = (-7/11)
Step-by-step explanation:
x + 12
f(x) = -----------
2x - 1
(4) + 12 16
f(4) = ----------- = ---------
2(4) - 1 7
(0) + 12 12
f(0) = ----------- = ------- = -12
2(0) - 1 -1
(-5) + 12 7 -7
f(-5) = ------------ = ----------- = -------
2(-5) - 1 -11 11
I hope this helps!