Only Set 3 forms a right triangle as it satisfies the Pythagorean theorem, with side lengths matching the equation (√3)^2 + 4^2 = (√5)^2.
The question is about determining which set of side lengths will form a right triangle. To form a right triangle, the side lengths must satisfy the Pythagorean theorem, where the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
Let's check each set of side lengths:
Set 1: 62 + 72
eq (√12)2 (Not a right triangle)
Set 2: 82 + (√29)2
eq (√35)2 (Not a right triangle)
Set 3: (√3)2 + 42 = (√5)2 (Right triangle)
Set 4: 92 + (√26)2
eq 62 (Not a right triangle)
Therefore, only Set 3 forms a right triangle because it is the only set that satisfies the Pythagorean theorem.
Kelly combines 6.54 ounces of strawberries with 6.09 ounces of blueberries to make fruit bowls.She pours the fruit equally into three bowls, and has 1.68 ounces of fruit left over. How many ounces of fruit are in each bowl?
Answer:
3.65 ounces in each bowl
Step-by-step explanation:
Strawberry=6.54 ounces
Blueberry=6.09 ounces
If Kelly combines the two fruits to make fruits bowls
Then,
6.54 ounces of strawberry + 6.09 ounces of blueberry=12.63 ounces of fruits.
She pours the fruits equally in each bowl and has a leftover of 1.68 ounces.
Let quantity in each bowl = x
There are 3 bowls
Total quantity in three bowls=3x
Leftover=1.68
Total fruits = 12.63
We have the equation
3x+1.68=12.63
Subtract 1.68 from both sides
3x=12.63-1.68
3x= 10.95
Divide both sides by 3
x=10.95/3
x=3.65
Answer:
3.65 ounces of fruit in each bowl
Step-by-step explanation:
If the combination was made with 6.54 ounces of strawberries and 6.09 ounces of blueberries, the total ounces of fruit used is 6.54 + 6.09 = 12.63 ounces.
The remaining after dividing in three bowls is 1.68, so the amount used is 12.63 - 1.68 = 10.95 ounces
If we divide this amount of fruit by three bowls, we have:
Amount of fruit per bowl = 10.95 / 3 = 3.65 ounces
David loves his dog Thor and he wants to create a rectangular enclosure that has an area of 1600ft² for the dog to stay in while no one is home. David has a total of 120 feet of fencing available and he wants to use the wall of his garage as one of the sides of the enclosure. What are the dimensions of the enclosure?
Make a Sketch of the rectangular enclosure and label the sides using variable(s).
Write and solve an equation(s) that model this situation.
What are the dimensions of the rectangular enclosure?
Answer:
80 feet by 20 feet
Step-by-step explanation:
Area of the rectangular enclosure = 1600ft²
Area, lw=1600
w=1600/l
Perimeter, 2w+l=120 feet
Substituting w=1600/l into the perimeter
2(1600/l)+l=120
3200/l+l=120
[tex]\dfrac{3200+l^2}{l}=120\\ 3200+l^2=120l\\l^2-120l+3200=0\\l^2-40l-80l+3200=0\\l(l-40)-80(l-40)=0\\(l-40)(l-80)=0\\l-40=0\:or\:l-80=0\\l=40\:or\:l=80[/tex]
When l=40, w=1600/40=40 feet
When l=80, w=1600/80=20 feet
Since the enclosure is rectangular, the acceptable dimensions are:
Length =80 feet
Width =20 feet
The amount a money in the bank account can be expressed by the exponential equation A=300(1.005)^12t where A is the amount in dollars and t is the time in years. About how many years will it take for the amount in the account to be more than $900?
Answer:
It will take more than 18.35 years for the amount in the account to be more than $900
Step-by-step explanation:
The amount in the bank account can be expressed by the exponential equation :
[tex]A=300(1.005)^{12t}[/tex]
Where A is the amount in dollars
t is the time
We are supposed to find About how many years will it take for the amount in the account to be more than $900
So, [tex]300(1.005)^{12t} >900[/tex]
[tex](1.005)^{12t} > \frac{900}{300}[/tex]
[tex](1.005)^{12t} > 3[/tex]
t>18.35
Hence It will take more than 18.35 years for the amount in the account to be more than $900
Answer:
19th year
Step-by-step explanation:
19th year
peter and marie worked the same number of days and earned equal amounts of money. peter earned a rate of $45 per day. Marie earned a rate of $30 per day and received a bonus of $60. how many days did each of them work.
The common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280.
What is the first term of the series?
Answer:
The first term of the geometric series is 1
Step-by-step explanation:
In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.
Mathematically, the sum of terms in a geometric series can be calculated as;
S = a(r^n-1)/( r-1)
where a is the first term that we are looking for
r is the common ratio which is 3 according to the question
n is the number of terms which is 8
S is the sum of the number of terms which is 3280 according to the question
Plugging these values, we have
3280 = a(3^8 -1)/(3-1)
3280 = a( 6561-1)/2
3280 = a(6560)/2
3280 = 3280a
a = 3280/3280
a = 1
Final answer:
To find the first term of a geometric series with a common ratio of 3 and a sum of the first 8 terms being 3280, we use the sum formula for a geometric series and isolate the first term 'a'. After plugging in the values and simplifying, we find that the first term 'a' is equal to 1.
Explanation:
The student is asking about the first term of a geometric series with a known common ratio and the sum of the first 8 terms. The common ratio for this series is 3, and the sum of the first 8 terms (S8) is 3280. To find the first term (a), we'll use the following formula for the sum of the first N terms of a geometric series:
S_N = a * (1 - x^N)/(1 - x),
where 'SN' is the sum of the first N terms, 'a' is the first term, 'x' is the common ratio, and 'N' is the number of terms. In this case, x=3 and S_8=3280.
Solving for 'a' gives us:
3280 = a * (1 - 3^8)/(1 - 3)
The first term (a) can now be calculated by isolating 'a' on one side of the equation.
a = 3280 / ((1 - 3^8)/(1 - 3))
a = 3280 / (1 - 6561)/(-2)
a = 3280 / (6560/2)
a = 3280 / 3280
a = 1.
Therefore, the first term of the geometric series is 1.
What is the solution to this equation?
4x - 6 + 2 x = 18
Answer:
x = 4
Step-by-step explanation:
4x + 2x = 18 + 6 (6 goes to the other side and changes its sign)
6x = 24
x = 4 (divide 24 by 6)
Answer:
x = 4
Step-by-step explanation:
4x - 6 + 2x = 18
4x + 2x = 18 + 6 collect like terms
6x = 24 divide both sides by the coefficient of x
x = 4
24 divided by 10 to the power of 4
Answer: 0.0024
Step-by-step explanation: To get the answer, all we have to do is...
24 ÷ 10 ⁴ = 0.0024
We have to push 24 to the right 4 times...
24 ⇒ 2.4 ⇒ 0.24 ⇒ 0.024 ⇒ 0.0024
I hope this helps!
Easy Question
Topic: Volume
Focus on question 10
Answer:
a 120 cm^3
b 70 cm^3
Step-by-step explanation:
The volume of a right rectangular prism is given by
V = l*w*h
10 a V = 12*2*5
=120 cm^3
10 b V = 2.5 *8 *3.5
=70 cm^3
Answer:
120 cm^3;70 cm^3
Step-by-step explanation:
Volume = l * w * h
That means...
a) Volume = 12cm * 2cm * 5cm = 120 cm^3
b) Volume = 2.5cm * 8cm * 3.5cm = 70 cm^3
Which correctly describes the consistency of the speeds of the cars in the two races? The speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near to 165 mph. The speeds in race A are likely to be near 153 mph and the speeds in race B are likely to be near to 145 mph. The speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near to 125 mph. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
This question is not complete.
Complete question
The box plots show the average speeds, in miles per hour, for the race cars in two different races.
Average Speeds of Cars in Race A
120.
125
130
135
140
145
150
155
160
165
170
Find attached to this question, the picture of the box plots.
Which correctly describes the consistency of the speeds of the cars in the two races?
a. The speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near to 165 mph.
b. The speeds in race A are likely to be near 153 mph and the speeds in race B are likely to be near to 145 mph.
c. The speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near to 125 mph.
d. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
Answer:
d. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
Step-by-step explanation:
For the boxplot for Race A, the following is obtained from the attached diagram
The range of speed of the race is= Highest - Lowest
170 - 120= 50
The 1st Quartile is = 142
The 2nd Quartile is = 153
The 3rd Quartile is = 165
The Inter quartile range = 3rd quartile - 1st quartile = 165-142= 23
For the boxplot for Race B
The following values is obtained from the attached image.
The range of speed of the race is
Highest speed - Lowest speed
165 - 125= 40
The 1st Quartile is = 139
The 2nd Quartile is = 145
The 3rd Quartile is 150
The Inter quartile range = 3rd quartile- 1st quartile = 150 - 139 = 11
From the values above, we can see that ,
The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
how do I solve this question??
y = 30e is the equation (no y-intercept)
Therefore, plugging in 4 and 6 enables us to fill in the chart.
4 x 30 = 120
6 x 30 = 180
4,120
6,180
If Jason weighs 227 and can lose 3 pounds a month what will be his weight after 7 months
Answer:
206
Step-by-step explanation:
Answer:
206 pounds
Step-by-step explanation:
Somebody help me!!!
What is the area of the rectangle in the coordinate plane?
Answer:
The answer is 5 x 13. Google it bruh
Step-by-step explanation:
What kind of symmetry does the given isosceles trapezoidal prism have? The prism has both rotational and reflectional symmetry. The prism only has rotational symmetry. The prism has only reflectional symmetry. The prism has no symmetry.
Answer:the prism has both rotational and reflections symmetry.
Step-by-step explanation:
if g =-3, h =-4, and j = -4
what's the answer to this?
2gh + j
Answer:
20
Step-by-step explanation:
Substitute all the known values into the expression.
2 (-3) (-4) + (-4)
Then solve using pemdas
24 + (-4)
= 20
2plus2 equals 2222222222222222222222222222222222222222
Answer:
ur mum
Step-by-step explanation:
What is the value of ?
2
3
4
5
Answer:
4
Step-by-step explanation:
The actual question is "what is the value of log₃81" in which, your answer would be 4 on edge 2020
What are the domain and range of the function f(x)= 4 - 2x^2-4
A.) domain: all real numbers
range: all real numbers greater than or equal to –5
B.) domain: all real numbers
range: all real numbers greater than or equal to –4
C.) domain: all real numbers between –2.5 and 2.5
range: all real numbers
D.) domain: all real numbers between –2.5 and 2.5
range: all real numbers greater than or equal to –5
Answer:
If you meant to type f(x) = (4 - 2x)^2 - 4, then choose choice B.) domain: all real numbers
range: all real numbers greater than or equal to –4
----
With your typo... the choices narrow down to choice B and A. . The domain is definitely all real numbers for a quadratic function.
Step-by-step explanation:
We have a quadratic function
f(x) =4 -2*x^2 - 4
I assume there is a typo here.
check y >= -5 and y >= -4...
what if f(x) = (4 - 2x)^2 - 4
then f(x) = 4*(x - 2)^2 - 4 with vertex at (2, -4) which makes sense with the answer choice B.)
f(x) = 4*(xx - 4x + 4) - 4 = 4xx - 16x + 16 -4 = 4xx - 16x +12 ...
The domain of the function is all real numbers, and the range is all real numbers greater than or equal to -4.
The correct answer is option B.
Certainly, let's discuss the domain and range of the function f(x) = 4 - 2x^2 - 4 :
Domain (Possible x-values):
The domain of a function represents all the possible input values (x-values) for which the function is defined. In this case, f(x) is a polynomial function, and polynomial functions are defined for all real numbers. Therefore, the domain is all real numbers. So, options (A) and (B) are incorrect because they limit the domain.
Range (Possible y-values):
To determine the range, we need to analyze how the function behaves. The function f(x) = 4 - 2x^2 - 4 is a quadratic function with a leading coefficient of -2. It opens downward, and its vertex is at the point (0, 0). As x moves away from the vertex in either direction, the function value decreases without bound. Therefore, the range is all real numbers less than or equal to -4 because the function never goes above -4. So, options (C) and (D) are incorrect because they indicate that the range includes positive values.
Based on the analysis, the correct answer is:
B.) domain: all real numbers
range: all real numbers greater than or equal to -4
For more such information on: domain
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A full water tank holds 500 litres.
The tank begins to leak water and is losing 14% of its contents every hour. Find how much water is left in the tank after 8 hours.
Answer:
0 Litres
Step-by-step explanation:
If the tank holds 500 litres and its loosing 14% every hour, just multiply
14%x8h=112%
This means the tank has lost all of its water.
You can also do 500/100=5 <- 1% of the tank, then multiply it by 14 and it gives you 70 litres. Then, multiply this by 8 and its gonna be 560 litres. So this means the tanks is going to have 0 litres left at the end.
The quantity of water present in the tank after 8 hours will be 123.94 liters.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
Given that a full water tank holds 500 liters. The tank begins to leak water and is losing 14% of its contents every hour.
The quantity of water present in the tank will be,
W = 500 x ( 0.86)⁸
W = 500 x ( 0.2478)
W = 123.94 liters
Therefore, the quantity of water present in the tank after 8 hours will be 123.94 liters.
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Please help I don’t know the answer :(
Answer:
When x=8, y=-6. When x=10, y=0
Step-by-step explanation:
[tex]y=3x-30\\x^2+y^2=100[/tex]
You can plug the given y value into the second equation to get:
[tex]x^2+(3x-30)^2=100\\x^2+9x^2-180x+900=100\\10x^2-180x+800=0\\10(x^2-18x+80)=0\\10(x-8)(x+10)=0\\x= 8, 10\\y= -6, 0[/tex]
Hope this helps!
How many times does 2/3 go into 2?
Answer: 3 times
Step-by-step explanation:
2/(2/3)=3
Answer: 3 times.
Step-by-step explanation:
To find how many times 2/3 goes into 2, convert 2 to a fraction with the same denominator as 2/3.
You can do this by multiplying the fraction 2/1 by 3/3 to make the denominator equal 3:
[tex]\frac{2}{1}*\frac{3}{3} =\frac{6}{3}[/tex]
Then, you can divide the fractions. Because 6/3 and 2/3 have the same denominator, you can simply divide 6 by 2.
2/3 goes into 2 three times.
The areas of the squares adjacent to two sides of a right triangle are 32units^2 and 32 units^2. Find the length, x, of the third side of the triangle.
Answer:
The length of the third side of the triangle is 8 units
Step-by-step explanation:
Here, since the two sides are adjacent a square, what this means is that the length of the square equals the length of the sides of the triangle adjacent to it.
Mathematically, the formula for the area of a square is L^2
With an area of 32 square units, the length of the side of this triangle is thus √(32) =
4√2 units
So we have two sides of the right triangle with length 4√2 units
Now we should know that this right triangle is an isosceles right triangle since the lengths of the adjacent and the opposite are equal.
Now to calculate the length of the third side which is the hypotenuse, we make use of the pythagoras’ theorem which states that the square of the longest side of a right triangle which is the hypotenuse is equal to the sum of the squares of the other two sides
Thus mathematically, the square of the hypotenuse length is 32 + 32 = 64
Let’s call the hypotenuse h for documentation purposes
h^2 = 64
h = √64
h = 8 units
Answer:
8
Step-by-step explanation:
khan is never wrong :3
Each side length is tripled. Describe the change in the area. What is the
new area?
6.4 cm
4 cm
5 cm
please help mehbraaa
Answer:
(a) Choice 1, 2
(b) Choice 3, 4
Step-by-step explanation:
The negative can be out front, on the top or on the bottom
-2/5 = - 2/5 or 2 / -5
The negative can be out front, on the top or on the bottom
- 4/7 = -4/ -7 or -4/7
Step-by-step explanation:
Step 1: Find the correct options for (a)
The only correct choices for (a) is option A and B. Since there is only one negative sign in the given fraction, the other fractions must only have one also. Therefore, the correct options are A and B.
Step 2: Find the correct options for (b)
The only correct choices for (B) is option C and D. Since there is only one negative sign in the given fraction, the other fractions must only have one also. Therefore, the correct options are C and D.
What is a segment with its endpoints on the planes of
the bases that is perpendicular to the planes
of the bases?
Answer:
Altitude of a Cylinder
Step-by-step explanation:
Altitude of a Cylinder can be seen as a form of segment between the plane of a base to the plane of another base in which the height of the cylinder can be said to also be the length of the altitude meaning both the height and the length of the cylinder can be said to be equal which is why the axis of a cylinder is the segment which contains the centers of the two bases.
ALTITUDE OF A CYLINDER can also be seen as the distance between the bases of a cylinder which is the shortest line segment that occur between the possibly extended bases which is why ALTITUDE OF A BASE is a segment with its endpoints on the planes of
the bases that is perpendicular to the planes
of the bases.
The base lengths of a trapezoidal coffee table are 6 feet and 8 feet. The height is 5 feet. What is the area of the coffee table?
A = (a+b)h/2
A = 6
B = 8
H = 5
A = (6+8)5/2
A = 14(2.5)
A = 35
The area of the coffee table is 35 sq. feet.
Answer:
35!
Step-by-step explanation:
formula= a+b/2 h
6+8/2 = 7.
7*5= 35!
What is 60% of 60 minutes?
Answer:
36 minutes
Step-by-step explanation:
60(.6)= 36
The volume of a sphere is 4,186.67 cm cubed. To the nearest centimeter, what is the radius of the sphere? Use 3.14 for π.
A.8
B.5
C.10
Using the volume formula for a sphere (V = (4/3)πr3), the radius for the given volume of 4,186.67 cm3 is calculated to be 10 cm, making option C correct.
Explanation:The volume of a sphere is given by the formula V = (4/3)πr3. To find the radius of a sphere with a volume of 4,186.67 cm3, we rearrange the formula to solve for r:
r = ∛((3V) / (4π))
Substituting the given volume and 3.14 for π:
r = ∛[(3×4,186.67 cm3) / (4×3.14)]
r = ∛[(12,560.01 cm3) / (12.56)]
r = ∛(1,000)
r = 10 cm
So, to the nearest centimeter, the radius of the sphere is 10 centimeters, making option C the correct answer.
Which statements about the hyperbola are accurate? check all that apply. there is a focus at (–9, 1). there is a focus at (0, 1). there is a focus at (–8, 1). there is a directrix at x = –5.8. there is a directrix at y = 1. there is a directrix at x = –2.2?
Answer: A D F
Step by step equation
Answer:
1 4 and 6 option
Step-by-step explanation:
A shoebox in the shape of a right rectangular prism has a base that measures 7 inches by 12 inches and is 5 inches high. What is the volume of the shoe box, in cubic inches?
35 a
84 b
245 c
420 d
Answer:
D. 420
Step-by-step explanation:
The volume of a right rectangular prism is given as:
V = L * W * H
where L = length
W = width
H = height
The shoebox has dimensions 7 inches by 12 inches and is 5 inches. Therefore, its volume is:
V = 7 * 12 * 5 = 420 cubic inches
The volume of the shoebox in cubic inches is 420.
Which value should be added to this data set to produce a mean of 13?
________ should be added to the data set to produce a mean of 13.
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation: