The area of a triangle is equal to
\(A=\frac{1}{2}\cdot b\cdot h\)we have
b=12 ft
h=3.6 ft
Remember that
1 yd = 3ft
so
Convert feet to yards
12 ft=12/3=4 yd
3.6 ft=3.6/3=1.2 yd
substitute in the formula of area
\(\begin{gathered} A=\frac{1}{2}\cdot4\cdot1.2 \\ A=2.4\text{ yd2} \end{gathered}\)The area is 2.4 square yardsA triangle has an area of 37.5 inches the height of the triangle is 20 inches what is the length of the base of the triangle?
Answer:
base = 3.75 inches
Step-by-step explanation:
37.5 = 20b/2
37.5 = 10b
b = 3.75
What the meaning of statement this?
This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.
The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:
∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))
The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.
The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.
The statement can be interpreted as follows:
"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."
In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.
It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.
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The following are the temperatures in °C for the first 14 days of January:
7
,
−
4.5
,
−
2
,
0
,
2.5
,
1
,
−
5
,
−
0.5
,
3
,
−
5.5
,
4
,
2
,
−
3
,
4.5
What is the median temperature for those 14 days?
Give your answer as a decimal.
Answer:
Hey! First you will put the numbers in order least to greatest. So it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0! Hope this helped.
Step-by-step explanation:
a. Which segments are parallel to RU?
b. Which segments are skew to SW?
c. What are two pairs of parallel planes?
d. What are two segments parallel to plane RUYV?
Answer:
a. VY, WX, ST
b. RU, UT, VY, YX
c. (RSWV, UTXY), (STXW, RUYV)
d. TX, SW
HOPE THIS HELPS YOU
Follw me = 10 thanks
Mark as brainliest = 10 thanks
1 thanks to me = 2 thanks
How do you find the area of a regular polygon.
Answer:
Step-by-step explanation:
1/2(apothem)(perimeter)
QUESTION; 01. A sarveyor standing 25°SW of a tower measure the angle of elevation of the top of the tower as 46°30' from a position 23°SE from the tower the elevation of the top is 37°15'. Determine the height of the tower if the distance between the two observations is 75m.
When you know the tower's height, you may calculate your distance from it.The answer is 92.54 feet .
Determine the height of the tower ?When you know the tower's height, you may calculate your distance from it.The tangent of the angle of elevation multiplied by the horizontal distance, or doing the calculation, is all that is required to manually determine the height.
30° vertical angle from A to the tower's summit
50 + x is the horizontal separation between A and the tower's base.
Call h to get the tower's height.
tan 30 = h / (50 + x) => 50 + x = h / tan 30 => x = h / tan 30 - 50 (1)
40° vertical angle from B to the tower's summit
The tower's base is x feet away from B in a horizontal direction.
ratio: x = h / tan40; tan40 = h / tan40 (2)
Consequently, (1) and (2) are equivalent.
Tan40 = Tan30 - 50 =
30 - 40 = 50 h/tan
1,7321h - 1,1918h = 50
0.5403h = 50
h = 50/0.5403 = 92.54
Response: 92.54 feet
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please help!!!!! What is the surface area of the right cone below?
slanted hight: 15
radius: 8
A. 1847 units2
B. 304 units2
C. 2487 units2
D. 4967 units
Answer:
Total surface area of cone = 578.28 unit²
Step-by-step explanation:
Given:
Slanted Hight of cone = 15 unit
Radius of cone = 8 units
Find:
Total surface area of cone
Computation:
Total surface area of cone = πr[l + r]
Total surface area of cone = (22/7)(8)[15 + 8]
Total surface area of cone = (22/7)(8)[23]
Total surface area of cone = (22/7)(184)
Total surface area of cone = 4,048 / 7
Total surface area of cone = 578.28 unit²
Kyle submits a design for the contest, but his explanation was misplaced. How can figure A be mapped onto figure B? Can any other transformation be used to map figure A onto figure B
Answer:
A
Step-by-step explanation:
ita a bc i know its I did this before
The function F is given in 3 equivalent forms.
Which form most quickly reveals the y intercept?
Look at image below
Part 2: what is the y intercept?
The form that most quickly reveals the y intercept is
B f(x) = 1/2 x² - 5x + 21/2The y intercept is (0, 21/2)
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
In the form, f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept
hence we can easily say that the y intercept is (0, 21/2)
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a 16 foot piece of wood was cut into two pieces. the longer of is 3 feet less than twice the shorter piece. what is the length of the longer piece of wood?
Explanation
Step 1
Let
total length(purple line)= 16 feet
shorter piece= x
twice the shorter piece=2x
the longer piece= y
the longer is 3 feet less than twice the shorter piece.( in other words you have to add 3 to the longer pice to obtain twice the shorter piece)
\(\begin{gathered} y+3=2x \\ y=2x-3\text{ Equation (1)} \end{gathered}\)Also
shorter piece+longer piece = full wood piece
replacing
\(x+y=16\text{ Equation (2)}\)Step 2
fin x and y , using Equation (1) and (2)
i)repace equation (1) in equation (2)
\(\begin{gathered} y=2x-3\text{ Equation (1)} \\ x+y=16\text{ Equation (2)} \\ repplace \\ x+2x-3=16 \\ 3x-3=16 \\ 3x=16+3 \\ x=\frac{19}{3} \end{gathered}\)ii)
replace the value of x in equation (1) to find y
\(\begin{gathered} y=2x-3\text{ Equation (1)} \\ y=2\cdot\frac{19}{3}-3 \\ y=\frac{38}{3}-3 \\ y=\frac{29}{3} \end{gathered}\)I hope this helps you
Write the slip-intercept form of the equation of the line described
- through: (4,1), parallel to y = 5/6x - 3
- through: (3,3), perp. to y= -3/8x + 2
Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
Point-slope form:
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= \( \frac{5}{6} \)
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
\(1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} \)
Thus the equation of the line is \(y = \frac{5}{6} x - 2 \frac{1}{3} \).
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= \( \frac{8}{3} \)
\(y = \frac{8}{3} x + c\)
When x=3, y=3,
\(3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5\)
Thus the equation of the line is \(y = \frac{8}{3} x - 5\).
The coldest temperature
recorded in Buffalo was-39°F. This was 12°F
warmer than the coldest temperature recorded
in Chicago. Which equation can be used to find
the coldest temperature recorded in Chicago?
What is the coldest temperature recorded in
Chicago?
A. C-12-39; -51°
B. C+12=-39; -27°
C. C-12-39; -27°
D. C+12=-39; -51°
Based on the coldest temperature in Buffalo and the difference in the temperature of Chicago, the equation that can be used to find the coldest temperature in Chicago is C. C - 12 = -39; -27°
What is the temperature at its coldest in Chicago?When temperatures are warmer, it means that they are higher. This means that to find the coldest temperature in Chicago, you need to add 12°F to the temperature of Buffalo.
The formula would therefore be:
C = -39 + 12
Making the Buffalo temperature the subject gives;
C - 12 = -39
The coldest temperature in Chicago is:
= -39 + 12
= -27°F
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
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A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect. Describe a Type I error and a Type II error in this setting, and give a possible consequence of each.
Type I error: Reject the null hypothesis H₀, when H₀ is true.
Failure to reject the null hypothesis H₀, when H₀ is untrue is a Type II mistake.
Define hypothesisA hypothesis is a proposed explanation or prediction for a phenomenon or observed phenomenon. It is a statement that suggests an explanation for an observed fact or set of facts and provides a basis for further investigation or experimentation.
Given Information
Determine the hypothesis:
Hₐ: p₁>p₂
Type I error: Reject the null hypothesis H₀, when H₀ is true.
Although being ineffectual, the adjustment gives the impression of being effective.
As a result, more vehicles than anticipated have brake problems, which might result in additional expenses for the company.
Failure to reject the null hypothesis H₀, when H₀ is untrue is a Type II mistake.
Interpretation: The adjustment is successful even though it appears to be ineffective.
As a consequence, fewer automobiles than anticipated have brake issues, which might result in financial savings for the corporation.
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Explain how the sum and difference formula can be useful.
Answer: The formula can be useful because we can use the sum and difference formulas to identify the sum or difference of angles when the ratio of sine, cosine, or tangent is provided for each of the individual angles.
How much paint is needed to cover silo with radius of 3 and height of 12
The amount of paint needed to cover silo with radius of 3 and height of 12 is 0.64π
How to calculate how much paint is needed to cover silo with radius of 3 and height of 12To calculate the amount of paint needed to cover the silo, we need to find the surface area of the silo first.
The surface area of the curved part of the silo (excluding the top and bottom) can be calculated using the formula:
A = 2πrh
where:
r is the radius of the silo and
h is the height of the silo.
Plugging in the values, we get:
A = 2π(3)(12)
A = 72π
The surface area of the top and bottom of the silo can be calculated using the formula for the area of a circle:
A = πr^2
Plugging in the value of the radius, we get:
A = π(3)^2
A = 9π
To get the total surface area of the silo, we need to add the surface area of the curved part and the surface area of the top and bottom:
Total surface area = 72π + 9π = 81π
To calculate the amount of paint needed, we need to divide the total surface area by the coverage area of one gallon of paint. Let's assume that one gallon of paint can cover 400 square feet.
Amount of paint needed = Total surface area / Coverage area per gallon
Amount of paint needed = (81π) / 400
Amount of paint needed = 0.64π
Therefore, approximately 0.64π gallons of paint are needed to cover the silo.
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PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80
PLS Answer these questions! I have a test!
Answer:
ZDM is not a name for the angle, 6 square units is the area, A the cylindar, 26 degrees
Step-by-step explanation:
Area of triangle is 1/2 base x height
116-90 = 26 degrees to angle ABC
11% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?
HELPPPP
Answer:
0.11
Step-by-step explanation:
Write down the percent divided by 100 like this:percent 100
Then if the percent is not a whole number then multiply both top and bottom by 10 for ever
Allen traveled 6 kilometers in 2 hours How many hours does it take Alan to travel 1 kilometer?
Answer:
1/3
Step-by-step explanation:
6x=2
x= 1/3
Answer:
1 kilo takes 20 minutes
Step-by-step explanation:
6kilo in 2hrs
3kilo in 1 hr
1hr = 60min
3kilo/3 = 1 kilo
60min/ 3 = 20 min
1 kilo * 6 = 6kilo
20min * 6 = 120min ( 2 hours )
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Answer: your wasting my time
Step-by-step explanation: stop wasting peoples time thank you
CAN SOMEONE PLZ HELP?????
The length of the longer leg of a right triangle is 16 cm more than four times the length of the shorter leg. The length of the hypotenuse is
17 cm more than four times the length of the shorter leg. Find the side lengths of the triangle.
The side lengths of the triangle are 12 cm, 64 cm, and 65 cm.
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let's denote the length of the shorter leg as "x". Then, according to the problem statement, the length of the longer leg is "16 cm more than four times the length of the shorter leg", which can be expressed as 4x + 16.
Also, the length of the hypotenuse is "17 cm more than four times the length of the shorter leg", which can be expressed as 4x + 17.
Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse.
So, we can write an equation as follows:
x² + (4x + 16)² = (4x + 17)²
Simplifying this equation, we get:
x² + 16x² + 128x + 256 = 16x² + 136x + 289
Bringing all the terms to one side, we get:
x² - 8x - 33 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = -8, and c = -33.
Plugging in these values, we get:
x = (8 ± √(8^2 - 4(1)(-33))) / 2(1)
x = (8 ± √(256)) / 2
x = 4 ± 8
Therefore, we have two possible values for x: x = -4 or x = 12. Since the length of a side of a triangle cannot be negative, we reject x = -4 and conclude that x = 12.
Substituting this value of x into the expressions we derived earlier, we get:
Length of shorter leg: x = 12 cm
Length of longer leg: 4x + 16 = 4(12) + 16 = 64 cm
Length of hypotenuse: 4x + 17 = 4(12) + 17 = 65 cm
Hence , the triangle is solved
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What is the first step in solving the equation 9m - 2 = 16?
Add 2 to each side.
Subtract 2 from each side.
Divide each side by 9.
Multiply each side by 9.
Answer: Add 2 to each side
Step-by-step explanation:
9m-2=16
+2 +2
9m=18
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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The area of a circle of radius 1 is T units squared. Use scaling to explain why the area of a circle of radius r is T/p? units squared.
Given a figure with an area A, if we use a scale factor of b on its dimensions, the new area A' will be:
\(A^{\prime}=b^2\cdot A\)Now, if we have a unitary circle (radius = 1) of area A, the scale factor to go to a circle of radius r will be r, because 1*r = r. Then, using the equation above:
\(A^{\prime}=r^2\cdot A\)Additionally, we know that the area of the unitary circle is:
\(A=\pi\text{ units squared}\)Finally, we conclude:
\(A^{\prime}=\pi\cdot r^2\text{ units squared}\)
Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
1. f : R → R defined by f(x) = 3x^3
2. g : R+ → R defined by g(x) = ln(x).
3. h : R → R defined by h(x) = x − 9
a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
b. The inverse image of g(x) is \(g^{-1}(x) = e^{x}\)
c. The inverse image of h(x) is h⁻¹(x) = x + 9
The domain of TSince T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0
⇒ x² ≥ 25
⇒ x ≥ ±5
⇒ -5 ≤ x ≤ 5.
Inverse image of f(x)
The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
f : R → R defined by f(x) = 3x³
Let f(x) = y.
So, y = 3x³
Dividing through by 3, we have
y/3 = x³
Taking cube root of both sides, we have
x = ∛(y/3)
Replacing y with x we have
y = ∛(x/3)
Replacing y with f⁻¹(x), we have
So, the inverse image of f(x) is f⁻¹(x) = ∛(x/3)
Inverse image of g(x)
The inverse image of g(x) is \(g^{-1}(x) = e^{x}\)
g : R+ → R defined by g(x) = ln(x).
Let g(x) = y
y = ln(x)
Taking exponents of both sides, we have
\(e^{y} = e^{lnx} \\e^{y} = x\)
Replacing x with y, we have
\(y = e^{x}\)
Replacing y with g⁻¹(x), we have
So, the inverse image of g(x) is \(g^{-1}(x) = e^{x}\)
Inverse image of h(x)The inverse image of h(x) is h⁻¹(x) = x + 9
h : R → R defined by h(x) = x − 9
Let y = h(x)
y = x - 9
Adding 9 to both sides, we have
y + 9 = x
Replacing x with y, we have
x + 9 = y
Replacing y with h⁻¹(x), we have
So, the inverse image of h(x) is h⁻¹(x) = x + 9
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Which number(s) have a 5 that is 10 times the value of the 13,725 in ?
Answer:
I will give you three, but the answer is the number that has a 50
Step-by-step explanation:
52
654
7657
50 is the numbers that have a 5 in 10 times the value of the 13,725.
What is place value?Place value is the value of each digit in a number.
For example, the 5 in 350 represents 5 tens, or 50; however the 5 in 5006 represents 5 thousands, or 5000.
Now the given number is,
13,725
10 times of the number is givens as,
13,725*10
or, 137,250
here place value of 5 in 137,250 is 5 tens or 50.
Therefore, 50 is the numbers that have a 5 in 10 times the value of the 13,725.
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What is the prime factorization of 28 and 50?
Explain if possible.
Answer:
prime factorization of 28
28 = 2 × 2 × 7
prime factorization of 50
50 = 2 × 5 × 5
Step-by-step explanation:
GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2
pls thats the answer have a nice day
PLS HELP ASAP
What is (f-g)(3})?
Answer:
442
Step-by-step explanation:
you can download g a u t h m a t h for questions like this, good luck :D