Answer:
The angle of elevation of the pile is 30°
Step-by-step explanation:
Given that;
Height = 15 ft
Diameter = 52 ft
so radius r = D/2 = 52/2 = 26 ft
Now, to get the angle of elevation.
given the details in the question,
we can say; the given height is the opposite which is 15 ft.
Also the radius is adjacent which is 26 ft
using SOH CAH TOA
TOA; Tan = Opposite / Adjacent
so
tan∅ = 15 ft / 26 ft
tan∅ = 0.5769
∅ = tan⁻¹( 0.5769 )
∅ = 29.98° ≈ 30°
Therefore, The angle of elevation of the pile is 30°
PLEASE HELP I WILL GIVE BRAINLIEST
9514 1404 393
Answer:
48
Step-by-step explanation:
Evaluate each of the functions by putting the number where x is.
[tex]g(x)=x^2-4\\\\g(-7)=(-7)^2-4=49-4\\\\\boxed{g(-7)=45}\\\\f(x)=x+4\\\\f(-7)=-7+4\\\\\boxed{f(-7)=-3}[/tex]
Then the difference is ...
g(-7) -f(-7) = 45 -(-3) = 45 +3 = 48
Answer:
solution given;
g(x)=x²-4
f(x)=x+4
Now
g(-7)-f(-7)=(-7)²-4-(-7+4)=49-4+3=48
48 is a required answer.
180 miles in 4 hours at what rate how long will it take to drive 270 miles
Answer:
6
Step-by-step explanation:
180 / 4 = 45
45mi = 1hr
270 / 6 = 45
Jackie has $250 in her bank account and makes $25 every time she babysits. Write an expression in simplest form representing how much Jackie has in her account after babysitting t times
Step-by-step explanation:
y = 25t + 250
y is the total amount
t is number of times babysitting
what is 473.2608 rounded to the nearest tenth
Answer:
473.2608 rounded to the nearest tenth Is 473.3
Step-by-step explanation:
You start driving north for 24 miles, turn right, and drive east for another 10 miles. At
the end of driving, what is your straight line distance from your starting point?
Answer:
26 miles.
Step-by-step explanation:
To solve this problem, the Pythagorean theorem must be applied, which states that the hypotenuse squared of every right triangle is equal to the sum of its squared legs, that is, A^2 + B^2 = C^2 .
Therefore, applying this formula, to determine the distance in a straight line from the starting point to the driving end point, the following calculation must be performed:
24^2 + 10^2 = X^2
576 + 100 = X^2
√676 = X
26 = X
Thus, the distance between the two points is 26 miles.
Shape p is translated to shape Q using vector (a b).
Please find A.
Photo attached.
Answer:
-7
Step-by-step explanation:
you basically just move across and because its moving to the left its a negative
Shape P is translated to shape Q using b[tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex]..
What is translation of a graph?In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are congruent with one another.
Given:
The shape P is mentioned on the graph is translated to shape Q.
So, the shape shifted 7 units to left.
and, the shape needs to shift downwards 4 places.
Hence, the required vector is [tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex].
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f(x)=x-7 and g(x)=2x-3
find f(g(4))
Answer:
f(g(4)) = -2
Step-by-step explanation:
First, find g(4) by plugging in 4 as x into the function:
g(x) = 2x - 3
g(4) = 2(4) - 3
g(4) = 8 - 3
g(4) = 5
f(g(4)) can be found by finding f(5), since g(4) = 5
Find f(5) by plugging in 5 into the function:
f(x)= x - 7
f(5) = 5 - 7
f(5) = -2
So, f(g(4)) = -2
Adult tickets to the fall play cost $6 and student tickets cost $3. The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected $660 from ticket sales, how many student tickets were sold?
The drama class sold how many tickets?
The solution is?
9514 1404 393
Answer:
90 student tickets65 adult ticketsStep-by-step explanation:
For many "mixture" problems, it is convenient to use a variable for the quantity of the highest contributor. Here, we can use 'a' to represent the number of adult tickets, because adult tickets cost the most. Then the number of student tickets is (a+25), and the total revenue is ...
6a +3(a+25) = 660
9a +75 = 660
9a = 585
a = 65
(a+25) = 90
The drama class sold 90 student tickets and 65 adult tickets.
given that angle one is approximately equal to angle two, and angle three is approximately equal to angle one, prove line xy is parallel to line wv (using the statements and reasons columns)
Answer :
Statements :-
1. Segment XY is parallel to segment WV.
2. Angle 1 is congruent to angle 2.
3. Angle 3 is congruent to angle 1.
4. Angle XMY is congruent to angle VMW.
Reasons :-
1. Given
2. Given
3. Given
4. SSS (Side-Side-Side)
Hope this helps, thank you !!
Work out the value of 3 \times(3^2 + 4) - 83×(32+4)−8
Answer:Conversion a mixed number 8 1/
4
to a improper fraction: 8 1/4 = 8 1/
4
= 8 · 4 + 1/
4
= 32 + 1/
4
= 33/
4
To find new numerator:
a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/
4
= 32/
4
b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 4.
Eight and one quarter is thirty-three quarters
Conversion a mixed number 3 2/
5
to a improper fraction: 3 2/5 = 3 2/
5
= 3 · 5 + 2/
5
= 15 + 2/
5
= 17/
5
To find new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/
5
= 15/
5
b) Add the answer from previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
c) Write a previous answer (new numerator 17) over the denominator 5.
Three and two fifths is seventeen fifths
Subtract: 33/
4
- 17/
5
= 33 · 5/
4 · 5
- 17 · 4/
5 · 4
= 165/
20
- 68/
20
= 165 - 68/
20
= 97/
20
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - thirty-three quarters minus seventeen fifths = ninety-seven twentieths.
Conversion a mixed number 2 1/
3
to a improper fraction: 2 1/3 = 2 1/
3
= 2 · 3 + 1/
3
= 6 + 1/
3
= 7/
3
To find new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/
3
= 6/
3
b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.
Two and one third is seven thirds
Subtract: 7/
3
- 1/
4
= 7 · 4/
3 · 4
- 1 · 3/
4 · 3
= 28/
12
- 3/
12
= 28 - 3/
12
= 25/
12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - seven thirds minus one quarter = twenty-five twelfths.
Subtract: the result of step No. 3 - the result of step No. 5 = 97/
20
- 25/
12
= 97 · 3/
20 · 3
- 25 · 5/
12 · 5
= 291/
60
- 125/
60
= 291 - 125/
60
= 166/
60
= 2 · 83/
2 · 30
= 83/
30
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(20, 12) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 12 = 240. In the next intermediate step , cancel by a common factor of 2 gives 83/
30
.
In words - ninety-seven twentieths minus twenty-five twelfths = eighty-three thirtieths.
Step-by-step explanation:took a lot of time brainliest plz
Simplify
(5 - 4x) (6 + 7x)
Answer:
30+11x−28x2
Step-by-step explanation:
it is 30+11x-28x2
cos(2x) + sin^2(x) = 0
cos(2θ) + sin²(θ) = 0
Half-angle identity:
cos(2θ) + (1 - cos(2θ))/2 = 0
Simplify:
2 cos(2θ) + 1 - cos(2θ) = 0
cos(2θ) = -1
Solve for θ :
2θ = arccos(-1) + 2nπ
2θ = π + 2nπ
θ = π/2 + nπ
where n is any integer.
Which of the following statements about this function's domain is true?
A.) Domain: 0≤x≤16 and 0
The domain represents all of the values that were measured in this problem.
B.) Domain: 0≤y≤16
The domain represents the set of all possible inputs - the times when depth was measured.
C.) Domain: 0
The domain represents the set of all possible outputs - the various depths of the pool.
D.) Domain: 0≤x≤16
The domain represents the set of all possible inputs - the times when depth was measured.
Answer:
D.) Domain: 0≤x≤16
The domain represents the set of all possible inputs - the times when depth was measured
Step-by-step explanation:
Domain of a function is the possible set of inputs which are usually plotted on the x-axis, while range are corresponding outputs plotted on the y-axis.
In this case, the domain is the set of all possible inputs (x-values), which represents the times the depth was measured.
Domain ranges from 0 to 16. Thus:
Domain: 0 ≤ x ≤ 16
Need help with math who is up points and brainlest for you !!
Answer:
8ft
Step-by-step explanation:
Use similarity and congruence
AB/ED=AC/EF
3/6=4/X
CROSS MULTIPLICATION
3X=6*4
3X=24
X=8ft
Katie uses 12 cups of flour and sugar to make cookies. The amount of flour is four more than three times the amount of sugar. How many cups of flour are in this recipe?
The solution is?
Answer:
146
Step-by-step explanation:
because 3times the cups is 36
so four times more 36
There are 13 cups of flour in this recipe when Katie uses 12 cups of flour and sugar to make cookies. The amount of flour is four more than three times the amount of sugar.
Let's assume the amount of sugar used in the recipe is represented by the variable "s."
According to the given information, the amount of flour used is four more than three times the amount of sugar. In mathematical terms, this can be expressed as:
Flour = 3s + 4
Now, we know that Katie uses 12 cups of flour in the recipe. We can set up an equation to solve for the amount of sugar:
12 = 3s + 4
Subtracting 4 from both sides of the equation:
12 - 4 = 3s
8 = 3s
Dividing both sides by 3:
8/3 = s
s = 2.67
Since the number of cups of sugar must be a whole number, we can round the value to the nearest whole number. Thus, s ≈ 3.
Now, we can find the amount of flour by substituting the value of sugar into the equation:
Flour = 3s + 4
Flour = 3(3) + 4
Flour = 9 + 4
Flour = 13
Therefore, there are 13 cups of flour in this recipe.
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The power, P (watts), of a car engine is proportional to the square of its speed, s (m/s).
When s = 35, P = 1760.
Work out the power (to 1 DP) when the speed is 40 m/s
Answer:
P = 2288 W
Step-by-step explanation:
The power, P (watts), of a car engine is proportional to the square of its speed i.e.
[tex]P\propto s^2[/tex]
or
[tex]P=ks^2[/tex]
Put s = 35, P = 1760 to find k.
[tex]k=\dfrac{P}{s^2}\\\\k=\dfrac{1760}{35^2}\\\\k=1.43[/tex]
Now put k = 1.43 and s = 40. So,
[tex]P=1.43\times (40)^2\\\\P=2288\ W[/tex]
So, the new power is 2288 W when the speed is 40 m/s.
Which of the following are mathematical sentences? Check all that apply.
A. 144 +7
B. X-49
c. 4
D. 5g=31
E. 3>2
F. 1+12 = x
Find an equation of the straight line that is perpendicular to y=2x+1 and passes through the point (-2,5)
Answer:
y = -1/2x + 4
Step-by-step explanation:
to answer this question you need to find the slope and the y-intercept
to find the slope of a line that is perpendicular to another line you take the opposite and reciprocal of the slope of the first line
in this case the slope of the initial line is 2; therefore, the opposite reciprocal is -1/2
knowing slope ('m') = -1/2 and having the point (-2, 5) can give us the y-intercept of the new line; we start with:
y = mx + b and then plug the values in so find the y-intercept ('b')
5 = (-1/2)(-2) + b
5 = 1 + b
b = 4
put it all together: y = -1/2x + 4
QUESTION: A survey of students in a homeroom class explored the
relationship between gender and participation in the school band. What
is a reasonable conclusion to draw from the data?*
Answer:
ill say its c but im not that sure
Step-by-step explanation:
Rewrite the following polynomial in standard form
Answer:
-7x³ - ⅑x - 1
Step-by-step explanation:
A polynomial written in standard form would be written in such a way that the term with the highest degree comes first, followed by the second highest and so on, then what comes last is the constant.
Given the polynomial -7x³ - 1 - ⅑x, -7x³ with the highest degree comes first, followed by -⅑x, and then the constant, -1, comes last.
Thus, we would have:
✅-7x³ - ⅑x - 1
What are the domain restrictions of q^2-3q-4/q^2-7q-8
Solve the system of linear equations by substitution.
−5x+y=−7
−3x−2y=−12
Please help I'm having panic attacks about failing this test and failing the class this is my last test and I have a C please help
Answer:
[tex]x = 2 \\ y = 3[/tex]
[tex] - 5x + y = - 7.......(1) \\ - 3x - 2y = - 12......(2) \\ from \: (1) \\ y = - 7 + 5x \\ substitute \: in \: (2) \\ - 3x - 2( - 7 + 5x) = - 12 \\ - 3x + 14 - 10x = - 12 \\ [/tex]
[tex] - 13x = - 26 \\ x = \frac{ 26}{13} \\ x = 2[/tex]
[tex]y = - 7 + 5x \\ = - 7 + 5 \times 2 \\ = - 7 + 10 \\ y= 3[/tex]
What is 23% over a 100
Answer:
0.0023 or 23 / 10000
Step-by-step explanation:
23% = 0.23
0.23 / 100 = 0.0023
Answer:
23
Step-by-step explanation:
anything over 100 s a percent
like 15/100 is 15%
A number x is three times the value of number y. A number z is eight times the value of y. The sum of
the three numbers is 528. What are the 3 numbers (HINT: This problem requires 3 equations to solve!!
Step-by-step explanation:
y=a
x= 3a
z=8a
3a+8a+a=524
12a=528
a=44
X=3×44=132
z=8×44= 352
Answer:
y=a
x= 3a
z=8a
3a+8a+a=524
12a=528
a=44
X=3×44=132
z=8×44= 35
2
Step-by-step explanation:
The Miller family likes to paddle along the North River.
1. They paddled the same distance each day throughout the course of 3 days, traveling a total of 14 miles. How many miles did they travel each day ?
write the mixed number you got
4 2/3 think of how many time you can put 3 into 14 the section out the rest
Answer:
4 2/3
Step-by-step explanation:
the millers travled 4 2/3
Solve each equation.
40 = -8(x + 2)
Answer:
x = -7
Step-by-step explanation:
it’s right!
Write the following rate in simplest forms.
1. 333 calories burned in 55 minutes.
2. 4 million hits on a website in 16 months.
3. 279 points in 27 games.
4. $49 for 448 photos.
5. 6 pounds of zucchini for 24 servings.
What is the cos A? ....
Answer:
4/5
Step-by-step explanation:
The area of a circle is 9πft^2. What is the circumference in feet?
Answer:
98
Step-by-step explanation:
Answer:
6π ftStep-by-step explanation:
Area:
A = πr²Circumference:
C = 2πrSubstitute values in area:
πr² = 9πr² = 9r = 3 ftCircumference is:
C = 2π*3 = 6πSegment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?
Answer choices:
A. 1/2
B. 2
C. 3
D.4
Given:
Endpoint of segment AB are A(0,2), B(2,3).
Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).
To find:
The scale factor of dilation.
Solution:
If a figure is dilated about the origin with factor k, then
[tex](x,y)\to (kx,ky)[/tex]
Using this rule, we get
[tex]A(0,2)\to A'(k(0),k(2))[/tex]
[tex]A(0,2)\to A'(0,2k)[/tex]
So, the image of A is A'(0,2k).
It is given that image of A is A'(0,4). So,
[tex]A'(0,2k)=A'(0,4)[/tex]
On comparing the y-coordinates from both sides, we get
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2 and the correct option is B.
Dilation involves changing the size of a line
The scale factor is 2.
From the graph, the coordinates of AB are:
[tex]\mathbf{A = (0,2)}[/tex]
[tex]\mathbf{B = (2,3)}[/tex]
The coordinates of AB are:
[tex]\mathbf{A' = (0,4)}[/tex]
[tex]\mathbf{B' = (4,6)}[/tex]
Divide A' by A or B' by B to calculate the scale ratio (k)
[tex]\mathbf{k = \frac{A'}{A}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]
Expand
[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]
Divide
[tex]\mathbf{k = 2}\\\\\\\\[/tex]
Hence, the scale factor is 2.
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