A student is not correct when he stated that a triangle can be formed with side lengths 3 in, 5 in, and 9 in because 3 + 5 < 9.
A triangle is a polygon with three sides and three vertices.
To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 3, b = 5, and c = 9
a + b > c : 3 + 5 > 9 8 > 9 False
a + c > b : 3 + 9 > 5 12 > 5 True
b + c > a : 5 + 9 > 3 14 > 3 True
If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.
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A candle is 20 in. tall after burning for 3 hours. After 5 hours, it is 19 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.
[tex]\begin{array}{ccll} \stackrel{hours}{t}&\stackrel{height}{h}\\ \cline{1-2} 3&20\\ 5&19 \end{array}[/tex] with those values provided from the table, let's get its equation
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{19}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{19}-\stackrel{y1}{20}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{19 -20}{5 -3} \implies -\cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{-\cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{3}) \implies y-20=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2} \\\\\\ y=-\cfrac{ 1 }{ 2 }x+\cfrac{3}{2}+20\implies y=-\cfrac{ 1 }{ 2 }x+\cfrac{43}{2}\implies \LARGE \begin{array}{llll} h=-\cfrac{ 1 }{ 2 }t+\cfrac{43}{2} \end{array}[/tex]
how talll will the candle be after 8 hours? namely when t = 8.
[tex]h=-\cfrac{ 1 }{ 2 }(8)+\cfrac{43}{2}\implies h=-4+\cfrac{43}{2}\implies h=\cfrac{35}{2}\implies \LARGE \begin{array}{llll} h=17\frac{1}{2} \end{array}[/tex]
Simplify (3.7 × 10−9) − (8.2 × 10−8). Write the final answer in scientific notation.
−7.83 × 10−8
−7.83 × 10−9
−4.5 × 101
−4.5 × 10−1
Answer:
The first answer is correct. See the picture below
Step-by-step explanation:
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line in simplest form is: 1.
How to Find the Slope of a Line?The slope (m) of a line is calculated as:
Slope (m) = rise/run = change in y / change in x.
The horizontal distance across the line is the run, while the vertical distance is the rise.
The blue line shows the rise of the line = 2 units
The red line shows the run of the line = 2 units
Slope (m) = rise/run = 2 units/2 units
Slope (m) = 1
Therefore, the slope of the line in simplest form is: 1.
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2x² + 12x + 16
what is it
Answer:
2(x+2)(x+4)
Step-by-step explanation:
A student claimed that 0.036 m and 0.0036 m have the same number of significant digits. Do you agree or disagree?
Disagree
Agree
someone help please<3
Answer:
subduction zones <3333
Practice
6. Fill in each blank with the correct symbol >,<, or =
(a) 6.5
6.5 x 1
The correct symbol will be (equal to) 6.5 = 6.5
Use the greater than and less than symbols to compare values and expressions. > is the symbol for more than. 6.5 is commonly thought to mean 6.5 "6.5 is the same as 6.5. " "= "is the sign of equality. Two more comparison expressions are "greater than" and "equal to" (less than or equal to).
Two values are equal when the "equals" sign is used to indicate this. (=)
When two values are obviously not equal, the "not equal to" signal is used. (≠)
To show that one value is smaller than another, we use the "less than" sign. (<)
To show that one value is greater than another, we use the "greater than" symbol. (>)
The answer to the left-hand question is 6.5, whereas the answer to the right is 6.5 * 1 is equal to 6.5.
Therefore, 6.5 = 6.5
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What are
2 sixths in the lowest term
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{6}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{1}{3}[/tex] ← in simplest form
a fraction is in simplest form when no other value but 1 can divide into the numerator/ denominator.
You believe that water boils at 100 degrees Celsius.
Rate each statement below on a scale from best to worst.
a. Your cousin said that he tested the temperature of boiling water and found that it was 100°C.
b. Most people you know believe that water boils at 100°C.
c. You used a thermometer to measure the temperature at which water boiled. You repeated the experiment 3 times. Each time the thermometer read 100°C.
d. You read an article in a science journal from 50 different labs around the world that have tested the temperature of water and found that it boils at 100°C in every location.
BEST EVIDENCE _____, _____, ______, _____ WORST EVIDENCE
Rating each statement below on a scale from best to worst will be:
1. You read an article in a science journal from 50 different labs around the world that have tested the temperature of water and found that it boils at 100°C in every location.
2. You used a thermometer to measure the temperature at which water boiled. You repeated the experiment 3 times. Each time the thermometer read 100°C.
3. Your cousin said that he tested the temperature of boiling water and found that it was 100°C.
4. Most people you know believe that water boils at 100°C.
How to illustrate the information?It should be noted that the science journal will give the most accurate information. Therefore, it's the best.
It should be noted that the fact that most people you know believe that water boils at 100°C doesn't necessarily mean it's correct. It wasn't tested. Therefore, it's the worst.
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Try Again
Your answer is incorrect.
Pablo reads a book at a rate of 16 chapters per hour.
How many chapters does he read in 4 hours?
4 chapters
8 08
X
Ś
Answer:
64
Step-by-step explanation:
16 chapters per hour times 4 hours is 64 chapters
Which ordered pair, when graphed, would be on the same line as
(
1
,
3
)
and
(
4
,
9
)
?
Multiple choice question.
cross out
A)
(
−
1
,
−
3
)
cross out
B)
(
−
2
,
−
3
)
cross out
C)
(
2
,
4
)
cross out
D)
(
3
,
6
)
The required ordered pair, when graphed, would be on the same line as (1,3) and (4,9) is (-2,-3).
Option (B) is correct.
What is co-ordinate geometry?
Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.
Given:
The given points is
(1,3) and (4,9)
According to given question we have
The points is
(1,3) and (4,9)
Plot the ordered pairs Draw a line through the points to indicate all of the points on the line.
The points lie on the given point is (-2,-3).
Therefore, the required ordered pair, when graphed, would be on the same line as (1,3) and (4,9) is (-2,-3).
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The angle below is the image formed when a figure containing nop is dilated by a scale factor of 2. what is the measure of nop?
The measurement of the actual angle NOP is 56° when it is being dilated by the scale factor of 2 to form the dilated angle NOP as 112° .
We are given the dilated angle as:
∠ NOP = 112°
The scale factor for dilation is given as 2.
Now, we need to find the value of actual angle NOP.
For this, we will divide the dilated angle NOP with the scale factor of dilation.
So, we will get the result as:
Actual ∠ NOP = 112° / 2
Actual ∠ NOP = 56°
Therefore, we get that, the measurement of the actual angle NOP is 56° when it is being dilated by the scale factor of 2 to form the dilated angle NOP as 112° .
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Determine whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and/or 10. Then,
explain why.
1. 450
2. 168
Explain why
Find the value of c in the equation c3 = 1,728
Answer:
c = 576
Step-by-step explanation:
3 c = 1728
divide both sides by 3
c = 576
What is 1 2/3 minus -5 2/3?
Please do it fast!
Answer:
7 1/3
Step-by-step explanation:
1 2/3 - (-5 2/3)
1 2/3 + 5 2/3
7 1/3
I'll give brainliest!!!
Answer in the picture !!!
PLEASE HELP‼️For each direct variation, find the constant of variation. Then find the
value of y when x = -5.
y = -5 when x = 3
Answer: For each direct variation, find the constant of variation. Then find the value of $y$ when $x=-5 .$
$y=-\frac{2}{3}$ when $x=-\frac{1}{3}$
Step-by-step explanation:
the length of an arc of a circle is 269πcentimeters and the measure of the corresponding central angle is 65∘. what is the length of the circle's radius?
The length of the circle's radius = 744.92 cm
Given the length of arc of a circle, arc length = 269π cm
Central angle of a circle is the angle made between the radius through the arc length at the center of the circle.
The corresponding central angle = 65°
To find the corresponding central angle in radians = 65° x π/180 = 13π/36 radians
We have, arc length of a circle = radius x central angle
Therefore, radius of the circle = arc length / central angle
= 269π /(13π/36)
= 744.92 cm
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the surface of a solid is 50,682,000 square milliliters. Is the surface area greater than 50 square meters
Answer:
Step-by-step explanation:
One square millimeter converted into square meter equals = 0.0000010 m2 , sq m
1 mm2 , sq mm = 0.0000010 m2 , sq m
Answer:
I think 50,682,000 square milliliters
Step-by-step explanation:
mei has written 250 pages of her novel. if she is able to write at a rate of 6 pages per day for the next 30 days, how many pages will mei have written at the end of the 30 days?
Mei will have written a total of 430 pages at the end of the 30 days.
The range of already written pages by Mei is 250.the speed of Mei is 6 pages in keeping with day.the entire time is 30 days.The variety of pages written in 30 days by means of Mei is 30*6.Mei's range of pages written in 30 days is 180.Mei's general variety of pages that she will have written on the end of 30 days is 250 + 180.the total range of pages that Mei will have written at the stop of 30 days is 430.To learn more about speed, visit :
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In the figure below, m44 = 79°. Find m1, m2, and m 3
The angle of m1, angle of m2 and angle of m3 is 101°, 79° and 101° respectively.
It is given that the angle of m4 is 79°.
To find angles m1, m2 and m3 :
As we know that angle m4 is equal to angle m2 (because they are vertically off opposite angle).
So, angle m2 = 79º
In the same manner the angle of m1will be equal to angle m3.
Now, we can see that in the figure the angles m2 and m1 is lying on one plane, and a plane line makes a angle of 180º
So,
m2+m1 = 180º
79º+m1 = 180º
m1 = 180º-79º
Angle m1 = 101º
And, as we can see that the angles m1 and m3 are vertically of opposite angle.
So, m1= m3= 101º
Hence, angle m1=101º,
angle m2= 79º,
And, angle m3=101º.
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Choose a linear function for the line represented by the point-slope equation y - 5= 3(x - 2).
f(x) = 3x + 1
f(x) = 3x - 1
f(x) = 8x + 10
f(x) = 8x - 10
through: (0, -5), slope: 7/3
Which of the following pairs consists of equivalent fractions?
Answer:
the second pair
Step-by-step explanation:
the first pair can't be equivalent because to check whether two fractions are equivalent we have to use the criss-cross method so.....
1.3*4=12 and 12*3=36....so not equal
2.6*15=90 and 9*10=90.....it matches:)) so this is the answer
What is the purpose of the list of grievances?
to list the reasons the colonists are abolishing their government
to explain the purpose of natural rights to the king
to declare that the United States of America is a free and independent state
to show that the colonists understand the importance of their actions
The purpose of the list of grievances is to declare that the United States of America is a free and independent state.
The colonists' complaints against King George's treatment of them were listed in the list of grievances. It was essentially a list of justifications for their declaration of independence.
A list of complaints that Thomas Jefferson thought George III, the king of Great Britain, had made against the colonists is included in the Declaration of Independence. The primary justifications for the Colonists' involvement in the American Revolution were described in these grievances. Taxation without representation, or as Thomas Jefferson more elegantly puts it, "for imposing Taxes on us without our Consent," is arguably the most significant of them.
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Succotash is made by combining corn with lima beans and costs $1.00 per pound.
If lima beans cost $1.10 per pound and corn costs $.60 per pound, how many pounds of each should be used to make 5 lb of succotash?
Answer:
1 lb corn and 4 lb lima beans
Step-by-step explanation:
Let x = weight of corn.
Let y = weight of lima beans.
x + y = 5
0.6x + 1.1y = 5
x = 5 - y
0.6(5 - y) + 1.1y = 5
3 - 0.6y + 1.1y = 5
0.5y = 2
y = 4
x + y = 5
x + 4 = 5
x = 1
Answer: 1 lb corn and 4 lb lima beans
Richard wants to paint the top and sides of the block column. What is the surface area he needs to cover?
The Surface area to be painted = 512 ft²
What is the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(w × l + h× l + h × w). Where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
The block column has a shape of rectangular prism. Therefore, the surface area that Richard needs to paint which excludes the bottom of the block = 2(w × l + h× l + h × w) - l × w.
l = 10 fth = 12 ftw = 8 ftPlug in the values
Surface area to be painted = 2(8 × 10 + 12 × 10 + 12 × 8) - 10 × 8
Surface area to be painted = 592 - 80
Surface area to be painted = 512 ft²
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Write 28 as a product of primes.
Use index notation when giving your answer.
HELP
Answer:
28 = 2² × 7
Step-by-step explanation:
28 = 4 × 7 = 2² × 7
Approximate when the function is positive, negative, increasing, or decreasing.
From the graph of the function, we have that:
Positive: -1 < x < 1.Negative: x < -1 and x > 1.Increasing: x < 1.Decreasing: x > 1.When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.Hence:
Positive: -1 < x < 1.Negative: x < -1 and x > 1.When a function is increasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y decreases.
When a function is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
Hence:
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in infant's Tylenol, 5 ml contains 160 mg of Acetaminophen. If you child's pediatrician says that your child can take 48 mg of Acetaminophen, how many milliliters (ml) should you give the child?
The amount of milliliters (ml) you should give the child is 1.5 ml
How to determine how many milliliters (ml) you should give the child?The given parameters are:
infant's Tylenol, 5 ml = 160 mg
This can be represented as
5 ml = 160 mg
Let the number of ml to give a child that requires 48 mg be x
So, we have:
5 ml = 160 mg
x = 48 mg
Cross multiply
x * 160 = 48 * 5 ml
Divide both sides by 160
x = 1.5 ml
Hence, the amount of milliliters (ml) you should give the child is 1.5 ml
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