The diameter of the base of a cylindrical can is 4 in. The height of the can is 6.5 in. Find the can’s surface area to the nearest tenth.
Answer:
106.8 in2
Step-by-step explanation:
Write a sentence representing the equation x+56/7=11
Antoine wants to convert millimeters into kilometers. Which operation should he choose?
The area of a rectangle is 300 square centimeters. If the sides of the rectangle are given as 5 centimeters and [tex] \sqrt{x+2600} [/tex] centimeters, then find the value of x and the other side of the rectangle.
Assume that triangle GHI is congruent to LMN. Which of the following congruence statement are correct? check all that apply
The congruence statements that are correct for the given scenario are △GHI ≅ △LMN, △IHG ≅ △NML, and △GIH ≅ △NML.
Explanation:The correct congruence statements for the given scenario are:
△GHI ≅ △LMN (by definition of congruence)△IHG ≅ △NML (by symmetry of congruence)△GIH ≅ △NML (by transitive property of congruence)These congruence statements indicate that the corresponding sides and angles of the triangles are equal, leading to overall congruence.
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simplfy 5(9)
will give brainlest
Kirstie is testing values that would make triangle klm a right triangle when ln is an altitude, and km = 16, as shown below. which lengths would make triangle klm a right triangle? 1) lm = 13 and kn = 6 2) lm = 12 and nm = 9 3) kl = 11 and kn = 7 4) ln = 8 and nm = 10
Answer: Option (2) is correct.
Step-by-step explanation:
Since we have given that
KLM is a right triangle, in which KM = 15, and ln is an altitude.
As we know that for right angled triangle, there are 3 conditions :
[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]
So, According to the options ,
Put LM = 12, NM = 9,
[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]
Since, it satisfies that KLM is a right triangle.
Hence, Option (2) is correct.
Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].
[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].
We will check each given option to see if the Pythagorean theorem holds.
Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:
[tex]\[ x = 16 - 6 = 10 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]
[tex]\[ 169 = LN^2 + 100 \][/tex]
[tex]\[ LN^2 = 69 \][/tex]
[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 69 \][/tex]
[tex]\[ KL^2 = 36 + 69 \][/tex]
[tex]\[ KL^2 = 105 \][/tex]
[tex]\[ KL \approx 10.2 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 9 = 7 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]
[tex]\[ 144 = LN^2 + 81 \][/tex]
[tex]\[ LN^2 = 63 \][/tex]
[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]
For [tex]\( \triangle KNL \):[/tex]
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 7^2 + 63 \][/tex]
[tex]\[ KL^2 = 49 + 63 \][/tex]
[tex]\[ KL^2 = 112 \][/tex]
[tex]\[ KL \approx 10.6 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:
[tex]\[ x = 16 - 7 = 9 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]
[tex]\[ 121 = 49 + LN^2 \][/tex]
[tex]\[ LN^2 = 72 \][/tex]
[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 72 + 9^2 \][/tex]
[tex]\[ LM^2 = 72 + 81 \][/tex]
[tex]\[ LM^2 = 153 \][/tex]
[tex]\[ LM \approx 12.4 \][/tex]
These calculations do not match the given [tex]\(LM\)[/tex] value.
Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 10 = 6 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]
[tex]\[ LM^2 = 64 + 100 \][/tex]
[tex]\[ LM^2 = 164 \][/tex]
[tex]\[ LM \approx 12.8 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]
[tex]\[ KL^2 = 36 + 64 \][/tex]
[tex]\[ KL^2 = 100 \][/tex]
[tex]\[ KL = 10 \][/tex]
These calculations match the given lengths.
Thus, the correct answer is:
D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]
The correct question is given below:
If F(x)=x-5 and G(x)=x^2, what is F(F(x))?
Answer:
(A)[tex]G(F(x))=(x-5)^2[/tex]
Step-by-step explanation:
Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].
To find: [tex]G(F(x))[/tex]
Solution:
It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:
[tex]G(F(x))=G(x-5)[/tex]
⇒[tex]G(F(x))=(x-5)^2[/tex]
Thus, it matches with the option A of the given options.
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Burt & ernie went to the toy store & saw a total of 51 rubber duckies. they saw twice as many yellow as orange. let y = the # of yellow duckies & r = the # of orange duckies. write a system that could be used to find the total of each color & then solve.
Phil received a prize of x dollars from a poker tournament. The tournament cost him 100 dollars to enter. What were Phil's net winnings from the tournament? Write your answer as an expression.
Answer: [tex]x-100[/tex]
Step-by-step explanation:
Given : Phil received a prize of x dollars from a poker tournament.
The tournament cost him 100 dollars to enter.
To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.
Thus, the expression to show Phil's net winnings from the tournament :-
[tex]x-100[/tex]
A speech pathologist had a gross income of 62,650 last year. if 18.9% of her income got withheld for federal income tax how much of the pay got withheld for federal income tax last year
Answer:
$11,840.85
Step-by-step explanation:
The length of a rectangular park is 20 feet longer than the width of the park. If the length of the park is 36 feet, what is the width of the park? 4 feet 16 feet 42 feet 56 feet
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
The result of the sum of the three numbers is: [tex]\frac{-767}{60}[/tex]
The numbers are given as:
Number 1: 1 1/5Number 2: -8 3/4Number 3: -2 5/6Start by calculating the sum of numbers 2 and 3 as follows:
[tex]Sum = -8\frac 34 -2\frac 56[/tex]
Express the numbers as improper fraction
[tex]Sum = -\frac{35}4 -\frac{17}6[/tex]
Take LCM
[tex]Sum = \frac{-3 \times 35 - 2 \times 17}{12}[/tex]
[tex]Sum = \frac{-139}{12}[/tex]
The opposite of number 1 is: -1 1/5
So, the overall sum is:
[tex]Sum = -1\frac 15 - \frac{139}{12}[/tex]
Express as improper fraction
[tex]Sum = -\frac 65 - \frac{139}{12}[/tex]
Take LCM
[tex]Sum = \frac{-72 - 695}{60}[/tex]
[tex]Sum = \frac{-767}{60}[/tex]
Hence, the result of the sum is: [tex]\frac{-767}{60}[/tex]
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Ali must choose a number between 61 and 107 that is a multiple of , 2, 4 and 5 . Write all the numbers that he could choose.
The numbers between 61 and 100 are given as 80 and 100.
How to find the LCM of two numbers?The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.
The required numbers between 61 and 107 are given as follows,
The LCM of 2,4 and 5 is 20.
Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.
Now, the multiples of 20 are 20, 40, 60, 80 and 100.
80 and 100 lies between 61 and 107.
Hence, the numbers that Ali can choose are given as 80 and 100.
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Eight subtracted from the product of
5
and a number is at most
30
.
Use the variable
c
for the unknown number.
WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the value of x.
Which of the following is a solution of y - x > -3?
(6, 2)
(2, 6)
(2, -1)
y - x > -3
(6, 2) → x = 6, y = 2
substitute
2 - 6 = - 4 < -3 NOT
(2, 6) → x = 2, y = 6
substitute
6 - 2 = 4 > -3 CORRECT
(2, -1) → x = 2, y = -1
substitute
-1 - 2 = -3 NOT
Answer: (2, 6)
Jen picked 3/4 of a gallon of strawberries in half an hour. If she keeps picking strawberries at the same rate, how many gallons will she have picked in 2 hours.
Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.
Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.
The sum of the first and second of three consecutive even integers is 158. find the three even integers.
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Which describes how to calculate the range of this data set?
4, 5, 6, 8, 11, 12
A. Subtract 11- 5
B. Subtract 12- 4
C. Add 11+ 5
D. Add 12+ 4
The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.
What is a data set?A data set is a set of information that corresponds to one or more database tables in the case of tabular data,
The maximum value is 12
The minimum value is 4
The range of the data set will be;
R = M-m
R=12-4
R=8
Hence the range of this data set will be 8.
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For the following figure, complete the statement about the points. If U lies on the same line as R and N, what terms describe the relationship the three points must have?
The term that describes the relationship the three points must have is known as: collinear.
What are collinear points?Collinear points are points positioned on a shared straight line, forming a linear arrangement.
In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.
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What is the volume of the cone with diameter 7in and height 9in? Round to the nearest cubic inch
Danes puppy weighed 8 ounces when it was born.Now the puppy weighs 18 times as much as it did when it was born. How many pounds does Danes puppy weigh now.
nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. if the angle of elevation from nick's mom to nick is 73 degrees, how far off the ground is nick?
A. 118.2 ft
B. 120.9 ft
C. 124.3 ft
D. 126.5 ft
E. 128.1 ft
Answer:
C. 124.3 ft
Step-by-step explanation:
Let h represent Nick's distance from ground.
We have been given that Nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. The angle of elevation from nick's mom to nick is 73 degrees.
Nick, his mother and angle of elevation forms a right triangle with respect to ground, where, h is opposite side and 38 feet is adjacent side.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{tan}(73^{\circ})=\frac{h}{38}[/tex]
[tex]\text{tan}(73^{\circ})*38=\frac{h}{38}*38[/tex]
[tex]3.270852618484*38=h[/tex]
[tex]h=3.270852618484*38[/tex]
[tex]h=124.292399502392[/tex]
[tex]h\approx 124.3[/tex]
Therefore, Nick is 124.3 feet above the ground.
evaluate -x+4y when -x=-4/5 and y= 1/3 write your anwser as a fraction or mixed number
The value of expression with the given x and y value is 8/15.
The given expression is -x+4y, -x=-4/5 and y=1/3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, put x=4/5 and y=1/3 in the given expression and simplify
That is, -4/5 + 4(1/3)
=-4/5 + 4/3
Take LCM of denominators 5 and 3 is 15
Now, -12/15 + 20/15
=(-12+20)/15
=8/15
Therefore, the value of expression with the given x and y value is 8/15.
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Why is circle 1 similar to circle 2?
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
.
A) Circle 1 is a dilation of circle 2 with a scale factor of 2.
.
B) Circle 1 is a dilation of circle 2 with a scale factor of 7.
.
C) Circle 1 is a translation of circle 2.
.
D) Circle 1 and circle 2 have the same center.
We have a golden rule about similarity of figures. It is "All circle are always similar to each other".
In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.
The ratio of radii of two circles is called the scale factor of dilation between them.
Given are two circles with following information :-
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
Finding the ratio of their radii :-
[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]
So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.
Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.
solve f(1) for f(x)=1-5x
f(1)= [?]