The following set of numbers 15, 20, and 24 can be the measures of the sides of an acute triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number 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 = 15, b = 20, and c = 24
a + b > c 15 + 20 > 24 35 > 24 True
a + c > b 15 + 24 > 20 39 > 20 True
b + c > a 20 + 24 > 15 44 > 15 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
15^2 + 20^2 = 625
2. Compare it to the square of the largest side.
24^2 = 576
625 > 576
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 15, 20, and 24 can be the measure of the sides of an acute triangle.
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54 x 10 to the power of 4
Answer: 54*10^4=540000
Step-by-step explanation:
can someone please help me I don’t understand and it’s a really important homework
Answer: Large number: 36
Smaller number: 9
Step-by-step explanation:
name all the sets of numbers to which each real number belongs.
1. 12
2. -15
3. 1 1/2
4. 3.18
5. square root 48
6. 9.3
7. -2 7/9
8. square root 25
9. square root 3
10. negative square root 64
11. negative square root 12
12. 8/4
These are the description of the real numbers.
According to the statement
We have to explain all about the real numbers.
So, For this purpose, we know that the
Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.
From the given information:
Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.
• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.
• Whole numbers include all positive integer values including 0.
• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)
• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)
Using the definitions above :
• 12 = Natural, integer , integer and rational (12/1)
• -15 = Integer, rational (-15/1)
• 1 1/2 = 3/2 = Rational
• 3.18 = rational (terminating decimal)
• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)
• 9.3 = rational (terminating decimal)
• -2 7/9 = -25/9 = rational (a/b)
• root 25 = √25 = ±5 = integer, rational (5/1)
• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .
• negative root 64 = - √64 = - 8 = integer, rational (-8/1)
• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)
• 8/4 = 2 = natural, number, rational, integer
So, These are the description of the real numbers.
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me i don't now this help please
Frequency is measured in Hertz, which is one per second. If the wave vibrated 10 times in 10 seconds, it would have a frequency of 1Hz According to the graph, the frequency is increasing to 2Hz then 3Hz.
This is further explained below.
What is Frequency?Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.
In conclusion, Hertz is the unit of measurement for frequency, and one Hertz equals one second. If the wave vibrated once per second for a whole minute, its frequency would be one hertz (Hz).
The graph indicates that the frequency will reach 2Hz, and eventually 3Hz, in the near future.
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Solve the following problem for x. If there is more than one solution include all solutions in your answer.
|3z-6|=9
X=
X=
Answer:
z = - 1 , z = 5
Step-by-step explanation:
| 3z - 6 | = 9
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
3z - 6 = 9 ( add 6 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
or
- (3z - 6) = 9
- 3z + 6 = 9 ( subtract 6 from both sides )
- 3z = 3 ( divide both sides by - 3 )
z = - 1
As a check
substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 5
| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side
x = - 1
| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side
then solutions are z = - 1 , z = 5
Suppose you pull a card from a standard 52-card deck. Find the probability of following event. The card is a face card.
3/13 is the probability of following event. The card is a face card.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Total no.of cards = 52
Let A be the event of taking face card.
No.of face cards = 4×3 = 12
Now n(S)= 52C1 = 52, n(A) = 12C1 = 12
So P(A) = n(A)/n(S) = 12/52 = 3/13
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a boy has a metal of density 14000kg/m3 .He intends to use it to make a rectangular pipe with external dimension of 18 cm by 10 cm and internal dimension of 15 cm by 8 cm .The length of the pipe is150 cm .Calculate the mass of the pipe in kg
Mass of the pipe= 100.8kgs
Mass is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force.
mass= density x volume
given that, the area of cross- section of the pipe is rectangular ring with area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
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Answer:
The pipe weighs 100.8 kg.
Step-by-step explanation:
Mass is essentially a body of matter's resistance to having its speed or position change when a force is applied. The change caused by an applied force is smaller the more mass a body has.
density x volume equals mass.
Considering that the pipe's cross-section is a rectangular ring of area,
A=(10x10) - (15x8)
=180-120
=60 cm²=0.006 m²
length of the pipe = 150 cm=h
volume= A. h
= 0.006x150x10⁻²
= 0.720x10⁻²
= 0.0072 m³
Density =14000kg/m³
mass= density x volume
= 14000 x 0.0072
= 14 x 7.2
= 100.8 kg
we got that the mass of the pipe in kgs is = 100.8kgs
Kevin needs to order some new supplies for the restraunt where he works. the restraunt needs at least 492 glasses. there are currently 333 glasses. if each set on sale contains 18 glasses
Answer:
Step-by-step explanation:492 is needed right,and Kevin has 333 glass.So you need 159 glasses,but you need to find out how many sets you need to get 492 glasses.If 18 glasses comes in a set you'll need to divide 159 by 18 and get 8.83333333333. Then simplefiy the number to 8.8
i need 3.234 minus 3.234 written out
need help please find the height of a cylinder with a volume of 500 cubic meters
Answer:
height = 20 cm
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here r = 5 and V = 500π , then
π × 5² × h = 500π
25πh = 500π ( isolate h by dividing both sides by 25π )
h = [tex]\frac{500\pi }{25\pi }[/tex] = 20 cm
Write an equation for the line on the graph below:
Answer:
y= - 6
Step-by-step explanation:
the coordinate- y of every point on the line will be - 6
Which is an equivalent expression for (5^2 • 3^4)^3?
15^18
5^6 • 3^12
5^2 • 3^12
5^5 • 3^7
Answer:
answer 2
Step-by-step explanation:
3*4=12
Answer:
B. 5^6 x 3^12
Step-by-step explanation:
(5^2 x 3^4)^3 =
5 x 5 x 3 x 3 x 3 x 3 =
25 x 81 =
2025
2025^3 =
8,303,765,625
Option B is correct because,
5^6 x 3^12 =
5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =
15,625 x 531,441 =
8,303,765,625
Three integers have a mean of 8, a median of 8 and a range of 4.
Answer:
The 3 integers are 6 8 and 10
Step-by-step explanation:
Comment
Start with the median. That's the middle number of an ordered set of numbers.
a 8 b is what you have so far.
Now the range between a and b is 4 which means that a and b differ by 4.
a + 4 = b
The mean will solve this quickly. Put a + 4 for b
[(a + 8 + a + 4)]/3 = 8 Combine like terms
(2a + 12)/3 = 8 Multiply both sides by 3
3 (2a + 12)/3 = 8 *3
2a+12 = 24 Subtract 12 from both sides
2a + 12 - 12 = 24-12 Combine
2a = 12
a = 6
but we know that the range between a (which is 6 ) and b is a + 4 = 10
So b must equal 10
43 43. The area of a circle is 100 cm². Calculate its radius.
Answer:
About 5.6 cm
Step-by-step explanation:
The formula for the radius of a circle (based on the area) is [tex]\sqrt{\frac{A}{\pi } }[/tex], where [tex]A[/tex] is the area of the circle?
Solve each equation. (m-2)-5=8-2(m-4)
The solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
According to the given question.
We have a linear equation in one variable
(m-2)-5=8-2(m-4)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable (m-2)-5=8-2(m-4) is given by
(m -2) -5 = 8 -2(m -4)
⇒ m -2 - 5 = 8 -2m + 8 (by distributive rule)
⇒ m -7 = 16 - 2m (adding and subtracting the line terms)
⇒ m + 2m = 16 + 7
⇒ 3m = 23
⇒ m = 23/3
Hence, the solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
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→
List all the 4-digit even numbers
that can be created by
rearranging
these number tiles.
3472
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 21+19+17+ . . . ; n=8
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
The given series is 21+19+17+ . . .
On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.
So the formula will be (-2n +/- something).
Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.
So if n=0, our first term is 21
If n=1, our second term is 19
If n=2, our third term is 17
and so on.
So, we have the expression (21 - 2n).
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
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Evaluate each algebraic expression for x=3 and (y=-2).
2x-3y
The result of the algebraic expression 2x-3y for x=3 and y=-2 is 12
Given,
The algebraic expression = 2x-3y
x= 3
y= -2
Substitute the values in the expression
2x-3y= 2(3)-3(-2)
=6+6
=12
Hence, the result of the algebraic expression 2x-3y for x=3 and y=-2 is 12.
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how can changing fractions to decimals make them easier to compare?
Answer:
They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.
Step-by-step explanation:
5
y≥--x-3
2
how do i graph this?
The given inequality can be graphed by solving the inequation first.
What is an inequality?
Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.
The given inequality can be solved as
[tex]5y\geq -x-32[/tex]
[tex]for, x=1, 5y\geq -1-32[/tex]
[tex]or, 5y\geq -33[/tex]
[tex]or, y=\frac{33}{5}[/tex]
Solve for two more values of x and then plot the inequality on the graph
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Can someone provide a justification?
The piecewise function that best models her weekly pay h(t) is given by:
h(t) = 12t, 0 ≤ t ≤ 40.h(t) = 480 + 18t.What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, we have that:
The input is the number of hours worked.The output is the weekly pay.Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:
Standard hours: t ≤ 40.Overtime hours: t > 40.For up to 40 hours, she receives the standard wage of $12, hence:
h(t) = 12t, 0 ≤ t ≤ 40.
For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:
h(t) = 480 + 18t.
Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:
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PLS HELP I NEED TO FINISH THES IN ORDER TO PASS MY GRADE
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 2, 3 comma 3, 2 comma negative 5
Determine the coordinates of triangle A′B′C′ if triangle ABC is rotated 270° clockwise.
A′(−2, 2), B′(3, −3), C′(−5, −2)
A′(2, −2), B′(−3, 3), C′(5, 2)
A′(2, 2), B′(−3, −3), C′(5, −2)
A′(2, −2), B′(−3, 3), C′(2, 5)
Answer:
A′(2, −2), B′(−3, 3), C′(5, 2) (2nd choice)
Step-by-step explanation:
Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°
In either case, the coordinates of any point (x, y) become new coordinates (-y, x)
I will summarize the original and rotated points,.
Original Rotated
Point(x, y) Point(-y, x) Remarks
-------------- -------------- -------------
A(-2, -2) A'(2, -2) eliminates 1st and 3rd choices
B( 3, 3) B'(-3, 3) no luck, both 2nd and 4th choices have this
C(2, -5) C'( 5, -2) only the 2nd choice fits all three
Answer: A′(2, −2), B′(−3, 3), C′(5, 2)
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
The correct answer is (A).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
To rotate a point (x,y) 270° clockwise about the origin,
We can use the formulas:
x' = y and y' = -x.
So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:
A' = (-2, 2) rotated 270° = (2, -2)
B' = (3, 3) rotated 270° = (-3, 3)
C' = (2, -5) rotated 270° = (5, 2)
Therefore,
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
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The trail mix that you are making requires 4 cups of raisins for every 10 cups total of trail mix. If you use 24 cups of peanuts (the other ingredient), how many total cups will you have?
Answer:
40 cups
Step-by-step explanation:
4/10 is raisin
6/10 is peanuts
24/40 is peanuts
Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
The statement given is true.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
What is acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.
According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.
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2.
lons that are made of more than
one atom are called
A ionic compounds
B crystals
C polyatomic atoms
D ionic bonds
Answer:
C polyatomic atoms
Step-by-step explanation:
The path is 8,000 meters. How long
is the path in kilometers?
kilometers
Answer:
8 kilometers
Step-by-step explanation:
8000/1000
= 8 kilometers.
Enter the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating
decimal.
4/5
If each student in the class drinks
1 cups of juice during the party
and there are 9 students in the
class, how many cups of juice will
be needed?
Answer:9
Step-by-step explanation:
find the interest rate if $13400 has a final value of $17829 in 4 years give your answer to 1dp
Answer: It is $4429 (interest combined) or $1107.25 (interest annually)
Step-by-step explanation:
1. Subtract 13400 from 17829:
17829 - 13400 = 4429
2. Now, we know that 4429 is the accumulated interest in 4 years, now divide 4429 by 4:
4429/4 = 1107.25
3. Now we know that 1107.25 is the interest accumulated every year.
A refrigerator that originally costs $ 1,200 it's on sale for 15% off. Tax is 8%. What would be the sale price of this refrigerator be including tax
The sale price of this refrigerator be including tax $1101.6 .
The value on the label of associate article/product is termed the marked price or asking price. this is often the worth at that product is meant to be sold-out. However, there will be some discount given on this value and therefore the actualof the merchandise could also be but the marked price. it's typically denoted by MP.When Discount is obtainable, M.P. > S.P.When Discount isn't offered, M.P. < S.P.Discount is outlined because the quantity of rebate given on the label value (marked price) of a piece. it's given by merchants/shopkeepers for attracting customers for increasing their sales.Discount = Marked value – priceIt is given that a refrigerator that originally costs $ 1,200 it's on sale for 15% off.
Discount percentage = [(Discount)/(Marked price)]× 100
15 = Discount / 1200 × 100
15 = Discount / 12
Discount = 15 × 12
= $ 180
Selling price = marked price - discount
= 1200 - 180
= $ 1020
The selling tax is given by = 8% 1020
= 8 / 100 ×1020
= $ 81.6
The total amount one has to pay to buy a refrigerator is = 1020 + 81.6
= $ 1101.6
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