The width of the mural (in feet) when it is finished is equal to 12.25 feet.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Scale factor = 2/5
For the width of the mural (in feet), we have:
2/5 = 4.9/x
x = (5 × 4.9)/2
x = 24.5/2
x = 12.25 feet.
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the long leg of a right triangle is 71 feet longer than the short leg. the hypotenuse is 85 feet long. how long are the legs of the right triangle?
The right triangle Short leg: 14 feet and Long leg: 85 feet.
Because you have a right triangle, and you know the hypotenuse, you can use the Pythagorean Theorem:
x2 + y2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now you have 2 equations. Use the expression for x in the 2nd equation, and substitute into the first:
(y + 71)2 + y2 = 852
Originally known as a rectangle triangle , a right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., It has two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
The hypotenuse is the side that is opposite the right angle (side c in the figure). Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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The value of the short leg of the right angle triangle is 14 feet while the value of the long leg will be 85 feet.
You may apply the Pythagorean Theorem since you have a right triangle and know the hypotenuse:
x^2 + y^2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now we have 2 equations.
Now, we will use the expression for x in the 2nd equation, and substitute into the first:
Thus we will get it as:
(y + 71)^2+y^2=852
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., it has two perpendicular sides.
The connection between the sides and angles of a right triangle is the basis of trigonometry.
The hypotenuse is the opposite side of the right angle.
Legs are the sides that are nearly at the right angle
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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Calcula la fuerza resultante de un avión que viaja 24 km al sur y 17 km al oeste.
La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.
¿Cómo determinar la fuerza resultante de un avión?
Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:
R = F · cos θ i + F · sin θ j
Donde:
F - Magnitud de la fuerza, en newtons. θ - Dirección del vector con respecto a la dirección este, en grados.La dirección del vector se determina mediante la siguiente función trigonométrica inversa:
θ = tan⁻¹ (Fy / Fx)
Donde:
Fx - Componente horizontal, en kilómetros. Fy - Componente vertical, en kilómetros.Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:
θ ≈ 234.689°
R = F · cos 234.689° i + F · sin 234.689° j
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PLEASE HELP!! GIVING 50 POINTS. NEED DONE ASAP
Answer:
1. T, W, E, G
2. C, B, D, A
Step-by-step explanation:
For question 1:
G passes through (2, 3) and (0, -1). So, the slope is [tex]\frac{-1-3}{0-2}[/tex] = 2.
T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = [tex]\frac{1}{4}[/tex].
E has a slope of [tex]\frac{5}{3}[/tex] because the equation is y = mx+b where m is the slope.
W has a slope of [tex]\frac{1}{3}[/tex] since slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{3}[/tex], [tex]\frac{5}{3}[/tex], and 2.
Therefore, the answer is T, W, E, G.
For question 2:
A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = [tex]\frac{3}{2}[/tex].
B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = [tex]\frac{1}{2}[/tex].
C has a slope of [tex]\frac{1}{4}[/tex] since the equation is y=mx+b where m is the slope.
D has a slope of [tex]\frac{3}{4}[/tex] since the slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex], and [tex]\frac{3}{2}[/tex].
Therefore, the answer is C, B, D, A.
I hope this helps! :)
Didn't understand something? Some important formulas/things to remember that I used:
The equation of a linear function can be written as y=mx+b. m represents the slope.
The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.
The formula for the slope is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex], where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.
Given the measure of arc(ABC) = 7x + 20 and arc(AC) = 4x + 10, find x.
Answer:
Step-by-step explanation:
Ahh hell nah
Trina must spend at least 45 minutes, m, studying for her test
The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.
How to write the inequality ?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.
Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.
The inequality for this is therefore:
x ≥ 45
Assuming that the minutes she spends studying is x.
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Full question is:
Trina must spend at least 45 minutes studying for her math test. (find the inequality)
if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer. a) statement (1) alone is sufficient, but statement (2) alone is not sufficient. b) statement (2) alone is sufficient, but statement (1) alone is not sufficient. c) both statements together are sufficient, but neither statement alone is sufficient. d) each statement alone is sufficient. e) statements (1) and (2) together are not sufficient.
c) both statements together are sufficient, but neither statement alone is sufficient.
According to the question
The query asks if statements (1) and (2) by themselves are sufficient to determine whether x is an even number. The answer is that neither assertion by itself is adequate to ascertain what x is worth. However, when both claims are taken into account, they are adequate to decide whether or not x is an even number. This is due to the fact that if xyz is even and yz is odd, x must be even. If x were odd, both xy xz and y xz would be strange as well. Due to this, the proper response is "c) neither statement is adequate when read alone, but both assertions taken together are sufficient."
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Solve by using a proportion. Round answer to the nearest hundredth of necessary.
A map scale designates 0.75 inch = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive
to go from the first town to the second town?
Answer:
miles
To go from the first town to the second town, you must drive 137.5 miles.
What is an proportion?
A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.
We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:
0.75 inch / 50 miles = x / distance
where x is the actual distance we want to find.
We can cross-multiply and solve for x:
0.75 inch * distance = 2.75 inches * 50 miles
x = (2.75 inches * 50 miles) / 0.75 inch
x = (137.5 miles)
To go from the first town to the second town, you must drive 137.5 miles.
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find an equation of a plane containing the three points (3, -1, -2), (1, -6, -4), (1, -5, -2) in which the coefficient of is -8.
I think of a number. I halve it and multiply it by 4. my answer is 40. What is the number? pls it's needed urgently due in 10mins
Answer:
The number is 20
Step-by-step explanation:
First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.
Answer:
20
Step-by-step explanation:
Find the Area of the figure below.
Answer:
Your answer is 9x^6*y^2π
Step-by-step explanation:
The formula for a circle is πr^2, with r as the radius.
Since 3x^3*y is the radius, you put that value in to get the equation:
(3x^3*y)^2*π
Once simplified, you get 9x^6*y^2π.
You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.
I hope this was helpful.
Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
The answer is the fourth one: Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Convert 36 pounds to kilograms. (1 pound = 0.454 kilogram)
79 kilograms
7.9 kilograms
163.44 kilograms
16.344 kilograms
36 pounds is equal to 16.344 kilograms.
Given that we need to convert 36 pounds to kilograms.
We have 1 pound = 0.454 kilogram,
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.454 kilogram.
Given that we have 36 pounds, we can multiply this value by the conversion factor to find the equivalent weight in kilograms:
36 pounds x 0.454 kilogram/pound = 16.344 kilograms
Therefore, 36 pounds is equal to 16.344 kilograms.
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A 2-column table with 3 rows. The first column is labeled time (t) with entries negative 2, 3.5, 30. The second column is labeled Elevation(e) with entries a, b, c.
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?
a =
b =
c =
Answer:
a = not viable
b = 265
c = 0
good?
Answer: a = not viable b= 265 c = 0
Step-by-step explanation:
6/7 of a number is 5400. find 7/9 of the same money
Answer:
7/9 of the same money is 4900
Step-by-step explanation:
If 6/7 of a number is 5400, we can set up an equation to find the value of the number:
(6/7)x = 5400
To solve for x, we can multiply both sides by 7/6:
x = 5400 * (7/6)
x = 6000
Now that we know the number is 6000, we can find 7/9 of that value:
(7/9) * 6000 = 4900
So 7/9 of the same money is 4900.
Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and used to obtain the regression equation ŷ = –0. 227x + 50. 455, where x represents the price of bobbleheads (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). What is the predicted demand of a bobblehead that has price of $6. 00?
–1. 362 units
49. 093 units
51. 817 units
195. 837 units
The predicted demand of a bobblehead that has price of $6.00 is given as follows:
49.093 units.
What is the function?The function in the context of this problem is defined as follows:
y = -0.227x + 50.445.
In which:
x is the price of the bobblehead.y is the predicted demand.For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:
y = -0.227(6) + 50.445
y = 49.093 units.
Meaning that the second option is the correct option.
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Suppose you spend $500. 00 on an oven to bake bread. Each loaf of bread costs 0. 20 to bake. You sell the loaves for 1. 00 each. How many loaves of bread must you sell for you to break even? (Use a system of equations to model each situation. Solve by any method. ) (PLEASE SHOW ANSWER AND WORK. SERIOUS APPLICANTS ONLY, THIS IS A MATH TEST, I FAILED THE LAST ONE. )
We must sell 625 loaves of bread to break even.
If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.
Let N be the number of loaves you sell.
Your cost would be,
C = 500 + 0.2N
Your revenue would be,
R = 1. N
Now, find out when is C = R
⇒500 + 0.2N = N
⇒500 = 0. 8 N
⇒N = 500/0. 8
⇒N = 625
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Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?
Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C.
Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.
Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C.
Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.
( the answer is not B )
The triangle pairs that can be mapped to one another using both a translation and a reflection across the line containing AB will be A based on the provided information. Triangles A B C and X Y Z are similar. Triangle A is created by reflecting triangle X, Y, and Z across a line. The correct option is A.
What is the Triangles about?The first triangle pair is a pair that can be mapped to one another using both translation and reflection across a line containing AB.
The first figure is made up of the coordinates XYZ and ABC, which are translations and reflections of one another across the line AB.
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Answer: it is A
Step-by-step explanation: just took the test
In which number does the digit 8 have a value that is 1/10 10 1 start fraction, 1, divided by, 10, end fraction times as great as the digit 888 in the number 2{,}980. 72,980. 72, comma, 980, point, 7?
The digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.7 will be 548
The 8 in our number, 2,980.7, is in the tens place and hence represents an 80.
The value of the digit 8 is equal to 1/10 of 10 divided by 1, which is 10 times greater than the value of the digit 888.
We need a number that contains an 8 and has a value that is 1/10 of the previous number, hence we need:
1/10*80 = 8
So, the number we're seeking has an 8 in the position of the one.
Option C: 548 would be this.
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A large school district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer: To find the number of students, you can multiply the number of teachers by the number of students per teacher.
3,461 teachers * 28 students/teacher = 96,668 students
So, there are 96,668 students in the school district.
Step-by-step explanation:
Help I need the answer
Answer:
9
Step-by-step explanation:
make them equal to each other
15x = 14x + 9
x = 9
A linear function passes through the points (-3, 14)
and (2, -1). What is the rate of change of the
function?
The rate of change of the linear function is the third option which is -3.
The linear function runs through the points (-3,14) and is specified in question (2,-1).
The function's rate of change must be determined.
Having said that,
The slope of a linear function determines how quickly it changes.
A line's slope
By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
In light of this, the slope of a line passing through the points (-3,14) and (2,-1) is
(-1-14)/(2-(-3)) = -15/5 = -3.
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15. Death Valley's Badwater Basin has an elevation of 284 feet below sea level, the lowest
elevation in the United States. Mount McKinley has an elevation of 2,500 feet above sea
level, the highest elevation in the United States. What is the difference between the
elevation of Badwater Basin and Mount McKinley?
Answer:2216 feet
Step-by-step explanation:
Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).
Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.
Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.
Hope this helps you!
I drive 378 miles in 3.5 hours. How many miles per hour am I driving
Answer: 108 mph
Step-by-step explanation: 378 divided by 3.5= 108mph
Answer: 108mph
Step-by-step explanation: 378 divided by 3.5= 108mph
Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the northbound car has traveled 4 kilometers, and the eastbound car has traveled 4 kilometers. Measured in a straight line, how far apart are the two cars? If necessary, round to the nearest tenth
The straight line distance between the northbound and eastbound cars is 5.7 kilometres.
The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.
Distance between the two cars = ✓4² + 4²
Taking square of the numbers
Distance between the two cars = ✓16 + 16
Performing addition
Distance between the two cars = ✓32
Taking square root
Distance between the two cars = 5.66
Round to nearest tenth = 5.7
Thus, the distance is 5.7 kilometres.
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Louis bought 8 2/5 oranges for the soccer team. The team ate 4 5/8 pounds of the oranges. How many are left?
0.3 pounds of oranges are left and this can be calculated by following steps :
Convert the 8 2/5 oranges to pounds.
8 2/5 oranges = 8.4 oranges
1 orange = 0.5 pounds
8.4 oranges x 0.5 pounds = 4.2 pounds
Subtract the amount of oranges eaten (4 5/8 pounds) from the total amount of oranges (4.2 pounds).
4.2 pounds - 4 5/8 pounds = 0.3 pounds
Answer: 0.3 pounds of oranges are left.
One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction.
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At Sneaky Pete’ chool, the teacher-tudent ratio i 1:30. If the chool ha 900 tudent,
how many additional teacher need to be hired to have a 1:18 ratio?
The school need to hire additional teacher to get 1:18 ratio is 20.
The teacher and student ratio in a school is 1:30,
let the number of teachers in a school=x,
then the number of students in school=30x,
total number of students in school=900
So, the number of teachers in school x=900÷30
x=30.
We want to take ratio of students and teachers =1:18
So, according to this ratio number of students=18x
and the number of required teachers x= 900 ÷ 18
x=50,
the school required 50 teachers,
Hence, the school need to hired teachers = 50-30=20
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The group of linear function is shown on the coordinate grid. What is the slope of the line?
Answer:
what grid
Step-by-step explanation:
Kaitlin's fish tank has 15 liters of water in it. She plans to add 6 liters per minute until the tank has at least 63 liters. What are the possible numbers of minutes
Kaitlin could add water?
User for the number of minutes.
Write your answer as an inequality solved for t.
15 + 6t >= 63
t >= (63 - 15) / 6
t >= 4.5
t >= 5 (since t must be a whole number of minutes)
So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.
the nine horizontal and nine vertical lines on an $8 \times 8$ checkerboard form $r$ rectangles, of which $s$ are squares. the number $s/r$ can be written in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
By using the combination theorem, it can be concluded that the value of m + n = 125
Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
nCr = n! / (n - r)! r!
Let's denote the number of rectangles as r, and the number of squares as s:
r = ⁹C₂ x ⁹C₂
= (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)
= (9! / 7! 2!) x (9! / 7! 2!)
= 36 x 36
= 1296 rectangles
s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²
= 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64
= 204 squares
Then we get the ratio of s : r as follows:
s / r = 204 / 1296
= 17 / 108
Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.
Thus, it can be concluded that the value of m + n = 125
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Evin is modeling the temperture of water heating on the stove. She find the fahrenheit temperture can be modeling by the linear function F(m)= 15. 2m + 58, where m is the number of minutes the water has been heating. Give a physical interpretation of the parameters 15. 2 and 58 in the linear model. Use appropiate units in your explaination
The last temperature will be 73.2 degrees Fahrenheit.
The parameter f(m) 15.2m+58 in the straight capability addresses the rate at which the water temperature increments over the long haul. In particular, it addresses the number of degrees Fahrenheit that the water temperature increments for each 1 moment of warming. So assuming the water has been warming for 2 minutes, its temperature will have expanded by 2 * 15.2 = 30.4 degrees Fahrenheit.
Parameter 58 in the linear function addresses the underlying temperature of the water when it begins warming. It is estimated in degrees Fahrenheit. So on the off chance that the water begins at a temperature of 58 degrees Fahrenheit and is warmed for 1 moment, its last temperature will be 15.2 + 58 = 73.2 degrees Fahrenheit.
Subsequently, The last temperature will be 73.2 degrees Fahrenheit.
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