A helium tank shaped like a cylinder has 2,401π in³ of space inside the tank. If the diameter of the helium tank is 14 inches, its height is 1 inch.
What is Volume?
Volume is a measure of the amount of space occupied by a three-dimensional object or a region of space. It is usually measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or liters (L).
For a solid object, such as a cube, cylinder, or sphere, volume is calculated by measuring the length, width, and height of the object and using a formula that is specific to that shape. For irregularly shaped objects, such as rocks or trees, volume can be determined by using techniques such as water displacement.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, we are given the diameter of the cylinder, which is 14 inches. The radius of the cylinder is half of the diameter, so r = 7 inches.
We are also given the volume of the cylinder, which is 2,401π cubic inches.
Using the formula for the volume of a cylinder, we can set up the following equation:
2,401π = π(7)²h
Simplifying this equation, we get:
2,401 = 49h
Dividing both sides by 49, we get:
h = 49/49 = 1
Therefore, the height of the helium tank is 1 inch.
However, this answer seems unlikely since the height of the tank should be greater than its radius. Therefore, there may be an error in the given volume or diameter of the tank.
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the answer is A its height is 49
It is a point that divides a segment into two congruent segments.
A.Point
B.Midpoint
C.Bisector
D.Ray​
The point that divides a segment into two congruent segments is called the midpoint. Therefore, the answer is B) midpoint.
In geometry, a midpoint is a point that divides a line segment into two equal parts. It is the point on the line segment that is equidistant from both endpoints. The midpoint is important in geometry as it can be used to construct other geometric figures, such as perpendicular bisectors, which are lines that pass through the midpoint of a line segment and are perpendicular to it. For example, if we have a line segment AB, the midpoint M is the point that is exactly halfway between A and B, such that AM = MB. This can be found by drawing a perpendicular bisector of AB, which is a line that passes through the midpoint M and is perpendicular to AB. The perpendicular bisector will intersect AB at the midpoint M. It is important to note that the midpoint is not a bisector, ray, or point on a line. A bisector is a line, segment, or ray that divides an object into two congruent parts, while a ray is a part of a line that extends infinitely in one direction. The midpoint is simply the point that divides a line segment into two equal parts, and it is denoted by a symbol, such as a small vertical line with a hat on top, or by labeling the midpoint as a letter, such as M in the example above
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Write the equation of the line shown on the coordinate plane below?
4
3
لا
2
1
-8-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
2 3 4 5 6 7 8
The equation of line shown on the coordinate plane is,
⇒ y = - 1/4x
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, 0) and (4, -1).
Now,
Since, The equation of line passes through the points (0, 0) and (4, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - 0) / (4 - 0)
m = - 1 / 4
Thus, The equation of line with slope - 1/4 is,
⇒ y - 0 = - 1/4 (x - 0)
⇒ y = - 1/4x
Therefore, The equation of line passes through the points (0, 0) and
(4, -1) will be;
⇒ y = - 1/4x
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How do I do this? I need all these problems solved pls I really need help and don't care about the process as much but when you put the answers please just put the numbered question they go to
The missing sides of right triangles are, respectively:
Case 1: x = 18.910
Case 2: x = 23.584
Case 3: x = 15.890
Case 4: x = 16.659
Case 5: x = 24.111
And the angles of the right triangles are, respectively:
Case 6: 32°
Case 7: 31°
Case 8: 71°
Case 9: 71°
Case 10: 32°
The exact values of trigonometric functions:
Case 11: cos A = 12 / 13
Case 12: tan C = 3 / 4
Case 13: tan A = 3 / 4
And the trigonometric ratios of right triangles are:
Case 14: tan X = 1.3333
Case 15: sin A = 0.6000
Case 16: cos C = 0.3243
How to analyze right triangles by trigonometric functions
In this question we find 16 cases of right triangles that must be analyzed by trigonometric functions. Trigonometric functions is an important tool to determine missing sides and angles and relationships with sides. Most important trigonometric functions are described below:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Where:
x, y - Legsr - Hypotenuse.Please notice that hypotenuse is the longest side of a right triangle.
The first five cases implies the determination of missing lengths in five right triangles:
Case 1
x = 20 · cos 19°
x = 18.910
Case 2
x = 20 / cos 32°
x = 23.584
Case 3
x = 10 / cos 51°
x = 15.890
Case 4
x = 15 / tan 42°
x = 16.659
Case 5
x = 19 / sin 52°
x = 24.111
The following five cases implies the determination of angles by means of direct and inverse trigonometric functions:
Case 6
tan θ = 16 / 26
tan θ = 8 / 13
θ = 31.608° (32°)
Case 7
tan θ = 6 / 10
θ = 30.964° (31°)
Case 8
tan θ = 76 / 26
θ = 71.114° (71°)
Case 9
tan θ = 67 / 23
θ = 71.053° (71°)
Case 10
tan θ = 26 / 42
θ = 31.759° (32°)
The next three cases implies the computation of the exact values of trigonometric functions:
Case 11
cos A = 24 / 26
cos A = 12 / 13
Case 12
tan C = 24 / 32
tan C = 3 / 4
Case 13
tan A = 27 / 36
tan A = 3 / 4
And the last three triangles implies the values of trigonometric ratios:
Case 14
tan X = 36 / 27
tan X = 4 / 3 (1.3333)
Case 15
sin A = 30 / 50
sin A = 3 / 5 (0.6000)
Case 16
cos C = 12 / 37 (0.3243)
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The lengths of the sides, measures of the angles and the values of the trigonometric ratios are as follows;
1) x ≈ 18.9
2) x ≈ 23.1
3) x ≈ 15.9
4) x ≈ 16.7
5) x ≈ 23.1
6) x ≈ 32°
7) x ≈ 31°
8) x ≈ 71°
9) x ≈ 71°
10) x ≈ 32°
11) cos(A) ≈ 0.9
What are trigonometric ratios?Trigonometric ratios are expressions that specify the relationships between two sides of a right triangle and an interior angle of the triangle.
1) The opposite side = 20 × sin(19°) ≈ 6.5
The adjacent side = 20 × cos(19°) ≈ 18.91
2) cos(30°) = 20/x
cos(30°) = (√3)/2, therefore;
(√3)/2 = 20/x
x = 20/((√3)/2) = 40·√3/3 ≈ 23.1
x ≈ 23.1
3) cos(51°) = 10/x
Therefore;
x = 10/(cos(51°)) ≈ 15.9
4) tan(42°) = 15/x
Therefore;
x = 15/(tan(42°)) ≈ 16.7
x ≈ 16.7
5) sin(52°) = 19/x
Therefore;
x = 19/(tan(52°))
x = 20/(cos(30°)) ≈ 23.1
x ≈ 23.1
6) tan(x) = 16/26
tan(x) = 16/26 = 8/13
x = arctan(8/13) ≈ 32°
7) tan(x) = 6/10
tan(x) = 6/10 = 3/5
x = arctan(3/5) ≈ 31°
8) tan(x) = 76/26
tan(x) = 76/26 = 38/13
x = arctan(38/13) ≈ 71°
9) tan(x) = 67/23
x = arctan(67/23) ≈ 71°
x ≈ 71°
10) tan(x) = 26/42
tan(x) = 26/42 = 13/21
tan(x) = 13/21
x = arctan(13/21) ≈ 32°
11) The trigonometric ratios for cosine indicates that we get;
cos(A) = 24/26 ≈ 0.9
12) Trigonometric ratio for tangent indicates that we get;
tan(C) = 24/32 = 0.75
13) tan(A) = 27/36
27/36 = 3/4
Therefore; tan(A) = 3/4 = 0.75
14) tan(x) = 36/27 = 4/3
tan(x) = 4/3 = 1 1/3
15) sin(A) = 30/50 = 3/5
sin(A) = 3/5 = 0.6
16) cos(C) = 12/37 ≈ 0.32
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QuestionIntermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the intervalATrueBFalse
The given statement about the intermediate value theorem is false
The given statement is
"Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"
But according to Intermediate value theorem "if a continuous function f with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"
So if we takes discontinuous function the given statement will be wrong
Therefore, the statement is false
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Find the distance between the two points
rounding to the nearest tenth (if
necessary).
(3,-4) and (9,-9)
The distance between the given pair of points (3,-4) and (9,-9) is 7.8 unit.
What is the distance between the given pair of points?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1 ( 3,-4 )
x₁ = 3y₁ = -4Point 2 ( 9,-9 )
x₂ = 9y₂ = -9Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 9 - 3 )² + ( -9 - (-4) )² )
D = √( ( 9 - 3 )² + ( -9 + 4 )² )
D = √( ( 6 )² + ( -5 )² )
D = √( 36 + 25 )
D = √( 61 )
D = 7.8 units
Therefore, the distance between the of points is 7.8 units.
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consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. explain how you would use this variable to describe something about the states.
Option b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.
The variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college can provide insights into students' preferences for attending college in their home state. A large proportion of students who attend college in their home state indicates that students prefer to stay close to home for higher education, while a small proportion suggests that they are more likely to attend college in a different state. This information can be useful for policymakers and educators to better understand the higher education preferences of their state's students and to develop policies and programs to encourage more students to attend college within their home state.
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Complete question:
The U.S. Census Bureau collects a large amount of information concerning higher education. For example, the bureau provides a table that includes the following variables: state, number of students from the state who attend college, number of students who attend college in their home state.
Consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. Explain how you would use this variable to describe something about the states.
a. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that less of the state’s population attend college while a small proportion means that more of the state’s population attend college.
b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.
c. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college outside their home state and a small proportion means that students prefer to attend college in their home state.
d. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that more of the state’s population attend college while a small proportion means that less of the state’s population attend college.
Which equation is true?
O 6 ÷ 10 60
O 6 ÷ 100 = 60
O 6 ÷ 100.6
100
O 6100 = 0.6
of the value than the 6 in 25 division
Answer:sry
Step-by-step explanation:i need points
The equation which is true is 6 ÷ 100 = 0.06
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 6
Let the second number be q = 100
Substituting the values in the equation , we get
A = p/q
A = 6/100
The value of A = 0.06
Hence , the equation is A = 0.06 and is true
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PLS HELP I HAVE TO SUBMIT IN LESS THAN AN HOUR
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x)=0.9x²-180x+20,985. How many machines must be made to
minimize the unit cost?
Do not round your answer.
At 100 machines the unit cost will be minimum and the minimum cost is 11985.
Finding the maximum and minimum on parabolas:The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.
The formula for the minimum value is given by -b/2a
Here we have
The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.
Compare given C(x) with the standard equation ax² + bx + c
=> a = 0.9, b = -180 and c = 20,985
We can find the x - coordinate where the minimum value occurs using the formula -b/2a
The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)
= (180)/1.8 = 100
Hence at x = 100, the unit cost will be minimum
The unit cost can be calculated as follows
C(100) = 0.9(100)²-180(100)+20,985
= 0.9(10000) -18000 + 20,985
= 9000 - 18000 + 20985
= 11985
Therefore,
At 100 machines the unit cost will be minimum and the minimum cost is 11985.
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Зу = 4х+5
4y = 4х +7
Answer:
y = 2; x = 1/4
Step-by-step explanation:
We can solve for y then x using elimination. We can multiply the first equation by -4 to cancel out the xs:
[tex]-1(3y=4x+5)\\\\4y=4x+7\\-3y=-4x-5\\\\y=2\\\\[/tex]
Now, we can plug in this 2 for y in any of two equations to find x:
[tex]3(2)=4x+5\\6=4x+5\\1=4x\\1/4=x[/tex]
Parallel lines s and t are cut by a transversal, r.
(image)
A) If the measure of angle 7 is 52°, what is the measure of angle 1? ____________
B) If the measure of angle 8 is 112°, what is the measure of angle 3? ___________
help!
Answer:
a the answer for angle 1 is also 52
b the answer for angle 3 is 180- 112= 68
3. A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150
yards from the center of the green. Whilestanding on the marker facing the green, the golfer turns
110 toward his ball. He then paces off 35 yards to hit his ball. See figure. How far is the ball from the
center of the green? Round to the nearest yard
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.
Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:
x = 35 * cos(110)
y = 35 * sin(110)
Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:
d^2 = x^2 + (y + 150)^2
Plugging in the values for x and y, we get:
d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2
d^2 = 1225 + (150 + 35 * sin(110))^2
Using a calculator, we can find that sin(110) = 0.939, so:
d^2 = 1225 + (150 + 31.65)^2
d^2 = 1225 + (181.65)^2
d^2 = 1225 + 32762.7225
Taking the square root of both sides:
d = sqrt(1225 + 32762.7225)
d = sqrt(33987.7225)
d = 183.83
Rounding to the nearest yard:
d = 184 yards
So, the ball is 184 yards from the center of the green.
What is the cube of 4?
Answer:
64
Step-by-step explanation:
How much is 5$? please I need help because I just dont know how much is it im so confused!!!!
5 dollars equals 500 pennies, once 5 dollars times 100 equals 500. What's 5 dollars in cents? 5 dollars equals 500 cents, once 5 dollars times 100 equals 500.
Mr Jacobs travels for 2 hours by car and covers a distance of 220 km Jong (in hours and minutes will it take Mr Jaces to cover a distance of 352 km at the same average speed?
At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.
To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:
Time = (Distance / Average Speed) * 60
Time = (352 km / 220 km/h) * 60
Time = (1.6) * 60
Time = 96 minutes
Time = 1 hour and 36 minutes
Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.
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if the test in problem 1 had been performed in a primary care setting (instead of a hospital) with a baseline cervical cancer prevalence of 15%, what would have been the test performance? for this, you need to use the same sensitivity and specificity values obtained in the study, but apply them to a different population with 15% prevalence of cervical cancer. use the blank tables given below. assume that the same number of patients is screened (3,300). round to the nearest whole number when making calculations.
In a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.
To calculate the test performance of the screening test in a primary care setting with a 15% baseline cervical cancer prevalence,
we can use the same sensitivity and specificity values obtained in the study, but apply them to a different population.
Given that the prevalence of cervical cancer is 15%, the number of true positives (TP) and false negatives (FN) in the screened population would be:
TP = Prevalence x Sensitivity x Number screened
TP = 0.15 x 0.91 x 3300
TP = 449.19, rounded to 449.
FN = Number with disease - TP
FN = 0.15 x 3300 - 449
FN = 26.5, rounded to 27.
Similarly, the number of true negatives (TN) and false positives (FP) in the screened population would be:
TN = (1 - Prevalence) x Specificity x Number screened
TN = 0.85 x 0.85 x 3300
TN = 2382.75, rounded to 2383.
FP = Number without disease - TN
FP = 0.85 x 3300 - 2383
FP = 396.5, rounded to 397.
Using these values, we can construct the following 2x2 contingency table for the primary care setting:
Actual condition:-
Test outcome Positive (P) Negative (N)
Disease (D) True positive (TP = 449) False negative (FN = 27)
No disease (ND) False positive (FP = 397) True negative (TN = 2383)
Using this contingency table, we can calculate the following test performance measures:
Sensitivity = TP / (TP + FN) = 449 / (449 + 27) = 0.943, or 94.3%.
Specificity = TN / (FP + TN) = 2383 / (397 + 2383) = 0.857, or 85.7%.
Positive predictive value (PPV) = TP / (TP + FP) = 449 / (449 + 397) = 0.531, or 53.1%.
Negative predictive value (NPV) = TN / (FN + TN) = 2383 / (27 + 2383) = 0.988, or 98.8%.
Therefore, in a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.
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4
Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 70 feet. His back yard has a length of 10 feet and a width of 40 feet. How many square feet of sod does Jayden need to purchase?
Jayden needs to purchase 3900 square feet of sod to cover his front and back yards.
The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then multiplying or dividing to find the value of the whole. In this case, the unit we will use is square feet.
To calculate the area of the front yard, we need to multiply its length by its width. So, we have:
Area of front yard = Length x Width = 50 ft x 70 ft = 3500 sq ft
To find the area of the back yard, we use the same formula:
Area of back yard = Length x Width = 10 ft x 40 ft = 400 sq ft
Now, we need to add the two areas to find the total area that requires sod. So, we have:
Total area = Area of front yard + Area of back yard
=> 3500 sq ft + 400 sq ft = 3900 sq ft
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Find the nth term of this number sequence 1, 7, 13, 19, .. .
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
7 - 1 = 13 - 7 = 19 - 13 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 6 , then
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
2 Paul is exactly 6 years older than Jane. The ratio of their ages is 5: 3. How old is Paul?
The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years,
given the household's annual income, ›
Approximately how much would it cost to raise a child from birth to
17 years in a household with an annual income of $64,000?
•
$209,619
$186,302
S164.219
$99.200
Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
Explanation:
To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:
y = 1.55x + 110,419
y = 1.55 * 64,000 + 110,419
y = 101,600 + 110,419
y = $212,019
So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
Victor and his friends like to collect
and trade cards from a certain combat
card game. Victor used his allowance
to purchase 9 booster packs and 4
premade decks, which included a total
of 266 cards. For his birthday, he
received 10 booster packs and 5
premade decks, which included a total
of 320 cards. How many cards come in
every booster pack and every
premade deck?
The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
What is a system of equation?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.
Let the number of booster pack and premade deck be x and y,
Establishing the system of equations,
9x + 4y = 266....(i)
10x + 5y = 320
2x + y = 64...(ii)
Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)
(9x + 4y = 266) - (8x + 4y = 256)
x = 10
Put x = 10 in eq(ii)
20 + y = 64
y = 44
Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
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For some reason, Brainly keeps saying that the question I'm asking hurts their feelings though I am just typing out the question from the screenshot. please take a look
There is part A and Part B.
Based on the information in the graph, we can infer that the area of the three triangles is the same. In this case the area would be 45 cm².
How to calculate the area of triangles?To calculate the area of the triangles we must calculate the area of one of them taking into account that all three have the same dimensions. According to the above, we must apply the following formula:
a = b * h / 2Then we must replace the values of the base and the height:
a = 9 * 10 / 2a = 90 / 2a = 45So the area of the triangles would be 45cm.
Note: This question is incomplete. Here is the complete information:
question
What is the area of the triangles?
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PLS HELP ITS A TESTTTT
Answer:
14)37
15)16
16)38
17)C
Step-by-step explanation:
14)7*4+9=28+9=37
15)42/7+10=6+10=16
16)-5*(-6)+8=30+8=38
Question 15 (5 points)
Anthony's teacher told him that he needed to read more than 20 minutes each day.
Which inequality represents the amount of time he needs to read daily if m
represents the number of minutes?
Om > 20
m < 20
Om > 20
Om ≤ 20
Answer:
m<20
Step-by-step explanation:
Karen,Sam, and Hector order a pizza.
Karen eats 1/3 of the pizza, Sam eats 1/3 of
what is left after Karen is done, and Hector
eats 1/3 of what is left after Sam is done.
What part of the pie is left after Hector is
done?
the surface area of a cuboid whose 6 faces have 10cm
The surface area of a cuboid is 600 cm².
What is surface area of a cuboid?The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.
Given that, a cuboid whose 6 faces have 10 cm.
We know that, surface area of a cuboid = 2(lb+bh+hl)
= 2(10×10+10×10+10×10)
= 2(100+100+100)
= 2(300)
= 600 cm²
Therefore, the surface area of a cuboid is 600 cm².
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Robert tutors two students, Andy and Sue. Andy pays robert $70 per month. Sue pays $50 per month how many months will Robert have to tutor until he earns $600?
Answer: 5 Months
Step-by-step explanation:
Alright, we know he will make $120 a month (since 50 + 70 = 120)
(Let's have months=m)
So now we need to figure out for how many months (m) will he need to get to $600.
We know 120 a month so we can get the equation: 120m=600
Now all we have to do is solve for m
Divide both sides by two to get m=5
Checking Answers
70(5)=350
50(5)=250
250+350=600
So this solution works.
Answer: 5 months
Step-by-step explanation: so, what you have to do is add up 120 5 times so in total you will have 600 so the answer is 5 months.
(-2,6)(-4,3)(3,-2)(8,6) is the relation a function
The given relation (-2,6)(-4,3)(3,-2)(8,6) is a function as every input has a single output.
A relation is set to be a function when every input has a single output.
In the given relation, -2,-4,3,8 has single output. Therefore, it is a function.
So, -2,-4,3 and 8 are the elements of the domain of the given
relation.
Here domain ={-2,-4,3,8} and range ={6,3,-3}
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The sum of three consecutive integers, a, b and c, where a
(a) What is the greatest possible value of b?
(b) Find the square root of the largest possible value of c.
The values of a, b and c based on the information will be 2, 3, 4.
The square root of c which is 4 will be 2.
How to calculate the valuesFrom the information, it was stated that the sum of the three consecutive integers, a, b and c, is 9.
This can be Illustrated as:
a + a + 1 + a + 2 = 9
3a + 3 = 9
3a = 9 - 3
a = 6 / 3
a = 2
b will be 2 + 1 = 3
c will be 2 + 2 = 4
The square root of c which is 4 will be:
= ✓4
= 2
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The sum of three consecutive integers, a, b and c, is 9.
(a) What is the greatest possible value of b?
(b) Find the square root of the largest possible value of c.
State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
SSS
Step-by-step explanation:
Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.
16. 220 fans travel to a rugby match in minibuses.
Each minibus holds 18 fans.
How many minibuses are needed?
Answer:
13 buses are required.
Step-by-step explanation:
To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.
220 /18
12 2/9
We need to round up to make sure all the fans get on a bus.
13 buses are required.
