No, The sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to Pythagorean theorem.
What is the Pythagorean theorem?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
a right triangle needs to follow the Pythagorean theorem, that is,
a2 + b2 = c2
where c is the length of the hypotenuse and a and b are the lengths of the other sides of the right triangle. We can check to see if this property holds for the given triangle. Since
5² + 10² = 15²
25 + 100 = 225
the Pythagorean theorem does not hold for the given triangle, meaning that it can not be a right triangle.
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A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation
C(x)=0.00048(x-200)³ + 311,040
100≤x≤ 1,000
where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x)=
(A) Write the equation for the average cost function C.
The equation for the average cost function C [tex]= \frac{0.00048(x - 200)^{3} + 246840 }{x}[/tex]
When a company creates products or services, it is required to pay production-related expenses. Some of these expenses are cyclical and alter as the output does. Expenditures that alter when production changes include things like raw materials, labor, and utility costs. These are referred to as variables. Other expenses are set, such as rent and insurance payments. These fixed expenses do not alter with changes in output.
The sum of the fixed and variable costs is the total cost.
Total Cost = Variable Cost + Fixed Cost
Now as per the question the cost equation is :
[tex]= \frac{C(x)}{x} = \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]
Therefore, the equation for the average cost function :[tex]= \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]
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Solve the following equation. 2x/5 + 1 = 7Then place the correct number in the box provided.
Answer:
[tex] \sf \large \: x=15[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
2x/5+1=7
Step 1: Simplify both sides of the equation.
2/5x+1=7
Step 2: Subtract 1 from both sides.
2/5x+1−1=7−1
2/5x=6
Step 3: Multiply both sides by 5/2.
(5/2)*(2/5x)=(5/2)*(6)
x=15
Brian opens a new savings account, with an interest rate of 3.5% compounded annually. If his
initial deposit is GBP 3000, how many years will it take for his money to grow to GBP 9000?
If initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.
Given that the initial deposit is GBP 3000 and the rate is 3.5%.
We are required to find the number of years after which the amount will reach to GBP 9000.
Compound interest is basically the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Amount after compounding=P[tex](1+r)^{n}[/tex], where P is principal ,r is rate of interest and n is number of years.
The number of years can be calculated as under:
9000=3000[tex](1+0.035)^{n}[/tex]
3=[tex](1.035)^{n}[/tex]
[tex](1.035)^{32}[/tex]=[tex](1.035)^{n}[/tex]
By comparing both sides,we will get n=32.
Hence if initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.
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Evaluate the function
f(x) = -2x^2 - 4x + 13
Find f(-7)
Answer:
g(-7) = 57
Step-by-step explanation:
note: the editor will not let me use eff of x. I have to use g(x)
Equation
g(x) = -2x^2 -4x + 13
Comment
y is the same thing as g(x) so you are really being asked to find y,
Given
x = - 7
g(-7) means that x is -7
Solution
g(x) = -2(-7)^2 - 4(-7) + 13 Substitute x = - 7 on the right
g(x) = -2*49 + 28 + 13 Combine
g(x) = -98 + 28 + 13
g(-7) = -57
(-4/9) divided by (5/8) = (-4/9) x ?
A. 9/4
B. -8/5
C. 8/5
D. -9/4
Answer:
-4/9 * 8/5 = (- 4/9) x
-32/45= - 4x /9
-288 = 180x
-8/5
please help
maths midpoint theorem
Step-by-step explanation:
10.
the various sides and line segments have been marked as equal already.
so, SSS proves that both triangles are congruent.
but to reprove things with the midpoint theorem :
remember
the line segment in a triangle connecting the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
so,
D, F are the midpoints of BA and BC.
so, AC is parallel to DF and twice as long as DF.
D, E are the midpoints of BA and AC.
so, BC is parallel to DE and twice as long as DE.
E, F are the midpoints of AC and BC.
so, BA is parallel to EF and twice as long as EF.
so, DF = AE = EC
DE = BF = FC
EF = BD = DA
so, the EF of DEF corresponds to DA of ADE.
DF corresponds to AE.
and DE is shared between both triangles.
so, again, all 3 sides correspond 1:1 to sides in the other triangle. and SSS proves they are congruent.
11.
equilateral means all 3 sides are equal :
PS = PT = ST
TSR can only be isoceles (both legs are equal) when
ST = SR
because PM = MQ, M is the midpoint of PQ.
and because of MS || QR, S is the midpoint of PR.
that means PS = SR.
and because PS = ST, ST = SR
therefore, TSR is isoceles.
Given the following values, find the perimeter of the figure shown below:
AB = 7 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
Answer:
26
Step-by-step explanation:
First, split the figure into 3 rectangles and label the sides so that it is easier to work with.
Then you have to find the unknown values: HG and AH.
HG: Since AB=7 and AB is the longest horizontal side; we know that HG+EF+CD=AB=7. Plugging in the known values: HG+3+1=7 => HG+4=7. Therefore, HG=3 because 3+4=7.
AH: BC and FG are the corresponding sides to AH so AH+FG=BC. Plugging in the known values: AH+1=3. Therefore, AH is 2 because 2+1=3.
Now you have to use the perimeter of rectangle formula which is P=2(L+w) for the 3 rectangles.
Rectangle 1: 2(3+2)=10
Rectangle 2: 2(3+1)=8
Rectangle 3: 2(3+1)=8
Add them all up to find the total perimeter: 10+8+8=26.
Coordinates will be fine PLs ASAP cause I need this rn
13 POINTS!!!
If the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)
Given,
The vertices of the triangle = J(-3,-5), K(-2,2) and L(1,-4)
We know,
In reflection in y axis (x,y) will become (-x,y)
Then the vertices of the reflection in y axis = J(3,-5), K(2,2) and L(-1,-4)
Draw the triangle using the vertices.
Hence, if the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)
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A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points)
Part B:Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)
Part C: In January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
The inequality that represents the temperatures at which the gas in the truck will remain in liquid form is; -40°F < x < 140°F
How to solve Inequality Word Problems?
A) x is the temperature, and the temperature can't go down to -40°F and so x is greater than -40°F so that the gas doesn't freeze. Finally, x can't go higher than 140°F because the gas will evaporate. Thus, the inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;
-40°F < x < 140°F
B) Open interval of the graph would mean that the interval is from -40°F to < 140°F. However, not equal to means that the gas in the truck can't stay liquid and as such means the coordinate is (-40°F, 140°F)
C) The gas will freeze because it has been said in the question the gas freezes at -40°F and as such if it goes -49°F, then it will freeze because the gas is supposed to stay higher than -40°F.
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WILL MARK BRAINIEST ANG GIVE POUNTS!! Pls solve the check mark problems (105,107,103)
Answer: 103. h<=2 or h>=12
105. No solution
107. -6<x<1
Step-by-step explanation:
103. |h-7|>=5
h-7>=5
h>=12
h-7<=-5
h<=2
h<=2 or h>=12
105. |2x-8|<-10 ==> No solution since absolute value functions are always positive.
107. |10+4x|<14
10+4x<14
4x<4
x<1
10+4x>-14
4x>-24
x>-6
-6<x<1
Data were collected from a typing class with 45 students. The class had an average of 56 words per minute (WPM)
with a standard deviation of 7 WPM. The teacher realized that the data from one student who typed 55 WPM was
not entered. If this student's results were included in the data set, what effect would it have on the standard
deviation?
O The standard deviation would be noticeably larger.
O The standard deviation would be noticeably smaller.
O The standard deviation would be about the same, perhaps a little larger.
O The standard deviation would be about the same, perhaps a little smaller.
The correct option regarding the standard deviation of the data-set adding observation 55 is:
The standard deviation would be about the same, perhaps a little smaller.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this problem, we have that an observation of 55 has a difference squared of 1 with the mean, which is less than the variance of 7² = 49, hence the mean of the differences squared would suffer a small decay(small due to the sample size), and would the standard deviation, hence the correct option is given by:
The standard deviation would be about the same, perhaps a little smaller.
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Answer:
No, its A: The standard deviation would be noticeably larger. I swearrr, these "verified" accounts are so useless bru
Is 17.305 greater or less than 17.066
Answer: greater than
Step-by-step explanation:17.305[tex]\geq[/tex]17.066
Answer:
Yes
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
The sum of three consecutive even integers is 50 more than the third integer.find the integers
Answer: 24, 26, 28
Step-by-step explanation:
a=even integer one.
b=even integer two.
c=even integer three.
a=b-2
b=c-2
a=c-2-2
a=c-4
a+b+c=50+c
c-4+c-2+c=50+c
c+c+c-4-2=50+c
3c-6=c+50
2c-6=50
2c=56
c=28
b=c-2
b=28-2
b=26
a=26-2
a=24
24, 26, 28
At the end of last year, teachers were rated by their students on a 0-10 scale. Two of the teachers' ratings are given. Whose class would you register for? Explain your reasoning.
spellings are incorect
Write 44.259 in word form
Answer:
Forty-four and two-hundred fifty-nine thousandths.
please help!!!
use the diagram to determine x
Answer:i think its like 40 or sum like that mb-
Step-by-step explanation:
Scaling a Rectangle
A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.
Scale factor back to original size = 1/7
The transform object is a mathematical mapping from one coordinate system to another. The coordinate system can differ in position (i.e. origin), scale, axis orientation, and relative axis orientation. We are told that the rectangle has been scaled by a factor of 7. This means that if the length and width are x and y respectively, the new scaled measurements will be;7x and 7 years.
Now, to get us back to the original size, all we have to do is divide the new scale measure by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Hence, the scale factor will be 1/7 back to the original size.
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what’s the distance between (2,8) and (-6,-2)
Answer:
Root
Step-by-step explanation:
Answer:
The distance between (2,8) and (-6,-2)
is √100+64
Step-by-step explanation:
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
63,16
Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate.
f(x) = 6x²; x = 0
y=
The equation of the tangent line to the graph is equal to y = 0.
What is the equation of the tangent line of a curve at a given location?
A line is tangent to a function if and only if the function meets the curve only in one point. The slope of the tangent line can be found by using the first derivative of the curve and the y-intercept is determined from the slope-intercept form of the equation of the line. First, determine the slope of the tangent line:
f'(x) = 12 · x
f'(0) = 12 · 0
f'(0) = 0
Second, find the intercept of the equation of the line:
y = 6 · 0²
y = 0
b = y - m · x
b = 0 - 0 · 0
b = 0
Then, the equation of the tangent line to the graph is equal to y = 0.
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if 3 of a dozen eggs are broken, what part of the dozen is broken? unbroken?
Answer:
1/4 of the dozen is broken
Step-by-step explanation:
If universal set U = { 1, 2, 3.......10 } A = {factor of 6} B = {factor of 8} and C= {factor of 9} then show (A intersection B intersection C (colon ) in Venn diagram by Shading
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a cyclist competing in a race rides past a water station. The graph of the function d(t) - 1/3 |t-60| represents her distance in kilometers from the water station in t minutes. What does the graoh of the function tell you about her race.
From the given absolute value function, we have that:
The cyclist starts 20 kilometers from the station.The cyclist reaches the station in 60 minutes.What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
For this problem, the function is:
d(t) = 1/3|t - 60|.
The d-intercept is given by:
d(0) = 1/3|-60| = 20.
Hence: The cyclist starts 20 kilometers from the station.
The t-intercept is found as follows:
1/3|t - 60| = 0
t - 60 = 0
t = 60.
Hence: The cyclist reaches the station in 60 minutes.
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Identify the property used in each step of solving the inequality
,,,,step ,,,,,,,,,,,,,,,, justification
3x – 2 > –4. |||||||1. given
3x > -2. |||||||||||||||| 2. _____
x>- 2/3 ||||||||||\|||||3. _____
The algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.
What is the algebraic property used?
We are given the inequality;
3x – 2 > –4
Step 2;
Using Addition Property of Equality, add 2 to both sides;
3x – 2 + 2 > –4 + 2
3x > –2
Step 3;
Using Division Property of Equality, divide both sides by 3 to get;
3x/3 > –2/3
x > –2/3
Thus, we conclude that the algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.
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Nose como se hace esto
Answer: 8, 13, 6, 12, 4, 13, 5, 13, 11, 19, 12, 17, 9, 16, 10, 13, 7, 14, 11, 20, 10, 18, 9, 16, 7, 15.
Step-by-step explanation:
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¡Espero que esto te ayude!
1Carla participates in competitive archery. Each competition allows a
maximum of 90 points. Carla's results for the last 8 competitions are (76, 78, 81, 75,
80, 80, 76, 77). Find and interpret the standard deviation of the data.
Answer:
76
Step-by-step explanation:
76 occurs multiple times in the set, thus deviating from it.
An intermediate algebra student drives a car at 45 miles per hour. Let d be the distance (in miles) that the student travels in 1 hours.
a. Is there a linear relationship between t and d? Explain. If the relationship is linear, find the slope and describe what it means in this situation.
b. Find an equation of the model
There is no linear relationship between t and d.
What do we mean by linear relationship?A linear relationship (or linear association) is a statistical term that describes a two-variable relationship that follows a straight line. Linear relationships can be represented graphically or mathematically as the equation y = mx + b. In everyday life, linear relationships are fairly common.So, the student drives a car at 45 miles per hour, so travels 45 miles in an hour.
Since the linear relationship equation is in the form y = mx + b but the t and d are just the same.So, there is no linear relationship between t and d.Therefore, there is no linear relationship between t and d.
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The pie chart describes the distribution of favorite school subject for 300 high school students. How many students reported that “Math” is their favorite subject?
The number of students whose best subject is Maths is 78.
How many students best subject is Maths?A pie chart is a graph that displays information in a circle. The circle is divided into sections which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees. A pie chart is equal to 100%.
The first step is to determine the percentage of the section allocated to mathematics: 100% - (8% + 15% + 8% + 32% + 11%)
100% - 74% = 26%
Number of students whose best subject is Maths = (26/100) x 300 = 78
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list the factors of 12
Answer:
2·2·3 or {1, 2, 3, 4, 6, 12} depending on what you mean
Step-by-step explanation:
You want the factors of 12.
Prime factorsThe prime factors of 12 are ...
12 = 2·2·3 = 2²·3
DivisorsThe product of exponents of the prime factors, each increased by 1, is the number of divisors of 12:
(2+1)(1+1) = 3·2 = 6 . . . . number of divisors of 12.
Those are ...
1, 2, 3, 4, 6, 12
__
Additional comment
The word "factors" is often used when "divisors" is intended. An expression is factored when it is expressed as a product of prime factors.
Timothy deposited $2,780.20 in a savings account that earns 4.3% simple interest. What will Timothy's account balance be in 7 months?
Total balance in the account after 7 months is 2849.737$
It is given that Timothy deposits $2780.20 in a savings account
It is given that rate of interest is 4.3 % and it of the simple interest nature.
We are required to find the account balance of Timothy's account in 7 months
We know that formula of simple interest is given by
(principal x rate x time)/100
where principal is the amount put for investing
rate is the rate at which the person is going to earn
time is the time for which the amount is to be invested
Now the time that is given to us in the form of months and hence we must convert it into years form
1 year =12 months
therefore, 7 months = 7/12 years
Now applying this value to calculate the simple interest earned
Let the simple interest be 'SI'
principal = $2780.20
rate = 4.3%
time = 7/12 years
SI= (2780.20x 4.3 x 7)/100 x 12
= 69.737$
The balance in Timothy's account will be original amount + the simple interest
Total balance after 7 months = 2780.20+69.737
=2849.937$
Hence total balance in the account after 7 months is 2849.737$
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