a) The vertical rise per step is of 18.1 feet.
b) The number of steps needed to climb from road level to the 2nd floor is of: 3 steps.
How to obtain the rise?The rise is obtained applying the slope concept, as follows:
Rise = Total elevation x Tangent of Angle.
The parameters are given as follows:
Total elevation = 24 feet.Angle: 37 degrees.Then the rise per step is calculated as follows:
Rise = 24 x tangent of 37 degrees = 18.1 feet.
The total vertical elevation needed to reach the second floor is given as follows:
24 + 24 = 48 feet.
Then the total number of steps needed to climb to the 2nd floor is found applying the proportion, as follows:
48/18.1 = 2.65 steps.
Rounding up, 3 steps are needed.
More can be learned about the slope concept at https://brainly.com/question/8062156
#SPJ1
i need help asap please! 100 points
f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.
f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.
f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.
How to calculate Functions and values?Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:
f(x)=(x+2)²+250.
If the domain value of the function is -4, then;
f(-4)=(-4+2)²+250
f(-4) = 4 + 250
f(-4) = 254
f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem
If the domain value of the function is -4, then;
f(2)=(2+2)²+250
f(2) = 16 + 250
f(2) = 266
f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem
If the domain value of the function is 2.5, then;
f(2.5)=(2.5+2)²+250
f(2.5) = 20.25 + 250
f(2.5) = 270.25
f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem
Determining the domain
The domain exist for the value of (x+2)² ≥ 0
x + 2 ≥ 0
x ≥ - 2
Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2
Learn more about domain, functions and values at:
brainly.com/question/1942755
#SPJ1
Does dilation change the shape of the image?
No, The dilation doesn't change the shape of the image
Dilation is a type of a transform where an image size either increase or decrease but has the same shape as the original. In other words, the dilation is similar to the original.
All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing)
Scale factor tells us how much the figure stretches or shrinks. A scale factor is typically labeled "k" and is always greater than zero. It is the ratio of the sizes of the original figure with the dilated figure
The only change in the dilation process is that the distance between the points changes. It means that the length of the sides of the original image and the dilated image may vary.
Therefore , Dilation doesn't changes the shape
To know more about Dilation here
https://brainly.com/question/4000812
#SPJ4
find the component form of vector v
By using the concept of vector, it can be calculated that
Component form of vector v = (-4 , 5)
What is a vector?
Vector is anything that has magnitude and direction and follow the vector addition law. Vector is a very important tool in mathematics and physics.
Here,
The initial point of vector v is (1, -4) and the terminal point of vector v is (-3, 1)
Component form of vector v = (-3 - 1, 1 - (-4)) = (-4 , 5)
Second option is correct
To learn more about vector, refer to the link-
https://brainly.com/question/15519257
#SPJ1
Pls help rn!
There were 110 people at the concert. If 55% of the seats were filled, how many seats are in the auditorium?
There are seats in the auditorium.
Answer:61
Step-by-step explanation:
Answer:
200
Step-by-step explanation:
Because there were 110 people at the concert, that means only 110 seats were filled. So we can think of the problem as its own equation if we word it like this:
110 is 55% of how many seats
110 = 0.55 x ?
Now to solve by dividing 110 by 0.55
110/0.55 = 200
determine the intervals on which the function is increasing decreasing and constant
The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively.
There is no interval where the function is constant.
In order to solve this question we need to study the graph attached,
From the graph, we could see that the plotting of the graph is starting from the negative axes and we could observe an increasing slope in the function, and the increment stopped after reaching point B(3,0), we can also observe that the value of the y-axis increases with that of the x-axis.
The interval at B(0,3) must be wrote down as ( -∞,3]
Again we could see a sudden drop in the slope of the function of the graph as the slope of the graph this time starts decreasing and moves to infinity and again we could observe that the value of the x-axis starts decreasing with the decrease in the value of the y-axis.
The function was constant at a null interval.
Therefore, The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively and there is no interval where the function is constant.
To know more about Graphical questions,
https://brainly.com/question/28757585
#SPJ4
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. while making oatmeal cookies, angela needs to add 12 cup of milk to her dough. however, she has only a 14-cup measuring cup. how many times does she need to fill the measuring cup to pour 12 cup of milk? the number of times angela needs to fill the 14-cup measuring cup to pour 12 cup of milk is
Therefore , Angela needs to fill this cup 6/7 times.
What is fraction ?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.
Here,
To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.
Thus, the number of times angela needs to fill cup are = 12/14 times
thus ,
=> 12/14 =6/7
Therefore , Angela needs to fill this cup 6/7 times.
To know more about fraction , visit
https://brainly.com/question/10354322
#SPJ4
You deposit $500 into a savings account. You will earn 3% interest per year. If you are earning simple interest, how much money will you have in your bank account after 5 years?
Answer:
$575 after 5 years
Step-by-step explanation
3% of 500= 15
15 × 5= 75
500 + 75= $575
Choose all of the values that are equivalent to
Answer:
A and B
Step-by-step explanation:
-(5/3) = -1.67
-5/3 = -1.67
5/-3 = -1.67
5/3 ≠ -1.67
-5/-3 ≠ -1.67
-(-5/3) ≠ -1.67
what is 3.50 divided by 3
Answer:
1.1667
Step-by-step explanation:
Brainliest please!
What’s the value of x?
Answer:
a value that is not yet known
Hi I need help which is the answer ??
Answer:
[tex]b) 5^{\frac{1}{12} }[/tex]
Step-by-step explanation:
∛5 = 5^1/3
⁴√5 = 5^1/4
Then:
∛5 / ⁴√5 = (5^1/3) / (5^1/4)
= 5^(1/3 - 1/4)
1/3 - 1/4 = 4/12 - 3/12 = 1/12
Then:
5^(1/3 - 1/4) = 5^1/12
= [tex]5^{\frac{1}{12} }[/tex]
**** The symbol ^ means that the expression on the right is an exponent.
Example:
5^1/3
means 1/3 is an exponent,
Factorise completely 12 p 2 + 10 p
Answer:
2p(6p + 5)
Step-by-step explanation:
12p² + 10p ← factor out 2p from each term
= 2p(6p + 5)
Which is an example of AAS congruence theorem?
Given ▲ ABC and ▲DEF are the examples of AAS congruence theorem.
According to the AAS, or Angle Angle Side congruence rule, two triangles are said to be congruent if two pairs of corresponding angles and the opposite or non-included sides are equal to one another.
The sides are not included between the angles but rather run in either direction of the angles, whereas the angles are sequential and corresponding in nature.
let's consider 2 triangles ▲ ABC , ▲DEF.
A at top B left C right . D at top E left F right side
∠B = ∠E
∠C = ∠F
AB = DE.
We can see that ∠B = E and ∠C = F if we superimpose the two triangles on top of one another. The lengths of the excluded sides, AB and DE, are also equal. As a result, we can state that ABC ≅ DEF.
To know more about congruence theorem here
https://brainly.com/question/19258025
#SPJ4
sarah used 2.5 cups of cheese in a dish that serves 10 people. what constant of proportionality relates the number of servings to cups of cheese?
The constant of proportionality that relates the number of servings to cups of cheese is 0.25.
According to the question,
Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :
let the c be the cups of cheese : c = 2.5 cups of cheese
let n be the number of the people that is been served
Then the equation can be written as :
c ∝ n
then we can bring in the proportionality constant sign as ;
then c = kn
then we can introduce the given figures into the equation as ;
=> 2.5=k (10)
the we can determine the value of the constant as :
=> k=2.5/10 = 0.25
Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25
To know more about proportionality here
brainly.com/question/29126727
#SPJ4
Find missing side with trigometry
The measure of the perpendicular of the right-angle triangle will be 16.728 units.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The sine of the angle is the ratio of perpendicular to the hypotenuse.
sin θ = Perpendicular / Hypotenuse
The angle is 42° and the measure of Hypotenuse is 25. Then the measure of the side 'x' will be given as,
sin θ = Perpendicular / Hypotenuse
sin 42° = Perpendicular / 25
Perpendicular = 25 x sin 42°
Perpendicular = 16.728
The measure of the perpendicular of the right-angle triangle will be 16.728 units.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
Please help asap
Triangle ABC has the following angle measures:
m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°
What is m∠C?
17°
23°
36°
121°
Answer:
121°
Step-by-step explanation:
x + 6 + 3x -15 + 5x + 36 = 180
9x + 27= 180
9x = 180 - 27
9x = 153
9/9 x = 153/9
x = 17
mC = 5·17 + 36
85 + 36
121°
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?
Perimeter of Rectangle is 44m
What is Perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.
According to the given information
Area of Rectangle = l × b
Area of Rectangle = 105 [tex]m^{2}[/tex]
Length of one side = 7 m
Let the length of the adjacent side = b
Area of Rectangle given = 7 × b
105 = 7 × b
b = [tex]\frac{105}{7}[/tex]
b = 15 m
Perimeter of Rectangle given = 2( l + b )
= 2 ( 7 + 15 )
= 2 × 22
= 44m
Perimeter of Rectangle is 44m
To know more about Perimeter
https://brainly.com/question/15271274
#SPJ4
Write the coordinates for the center of the hyperbola: (x-2)^2/36 - (y+1)^2/64 = 1
The reasoning above makes it very evident that the hyperbola's coordinate is (8, -1)
How does hyperbola work?The hyperbola is open upward and downward because the expression 'y' has a positive leading coefficient. In comparison to the usual equation, the hyperbola's center is found to be at (2, -1) and its 'a' point, 6, and 'b' point is 8. A smooth curve that lies in a plane and is classified as a hyperbola in mathematics by either its geometric characteristics or by equations for which it is the solution set. Two parts of a hyperbola, referred to as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
Given,
((x-2)²/36)-((y+1)²/64)=1
We know that the standard form of a parabola is:
((x-k)²/a²)-((y-h)²/b²)=1
Center for the given hyperbola is (2, -1)
And a=6, b=8
And the coordinates for the center of the hyperbola are x=8, y= -1
Therefore, (x, y)=(8, -1)
The reasoning above makes it very evident that the hyperbola's coordinate is
(8, -1)
To know more about hyperbola, visit:
https://brainly.com/question/27799190
#SPJ1
Solve the system by substitution.
y = -2x + 16
y = 2x
Answer: y = 8 , x = 4
Step-by-step explanation:
gosh darn i haven done this since algebra 1 !!
since both equations equal y, we can make them equal to each other since y = y
-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)
x = 4 (this is the first answer)
now we can plug in x to find y
y = 2(4)
y = 8 (second answer)
im sorry if the grammar is horrid its 3 am
After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Round the answer to the nearest penny. $8,103.08 $5,256.41 $12,500.75 $12,530.37
The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.
What is continuous compounding?
There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.
We have,
9 years in an account with a 3.9% annual interest rate compounded continuously,
an investment is worth a total of $17,757.16.
First, convert R as a percent to r as a decimal
r = R/100
r = 3.9/100
r = 0.039 per year,
Then, solve the equation for P
P = A / ert
P = 17,757.16 / e(0.039*9)
P = $12,500.75
Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.
To learn more about the continuous compounding visit,
https://brainly.com/question/14303868
#SPJ1
Answer:
$12,500.75
Step-by-step explanation:
I got it right.
a family of four went out to dinner. the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal. what is the total amount they will pay
The total amount they will pay would be $95.557
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.
Cost of meal = $75.99
The tax amount = 6.75% of 75.99
= ( 6.75/100 ) x 75.99
= $5.129
Tip amount = 19% of 75.99
= (19/100) x 75.99
= $14.438
Thus, the Total amount they will pay
= $75.99 + $5.129 + $14.438 = $95.557
To Learn more about the percentage form the link:
brainly.com/question/8011401
#SPJ1
Help me please raise my grade
Answer:
20% = 20 out of 10080% = 80 out of 10080th percentile = 80% of all the values in the data set are less than or equal to this quantity.20th percentile = 20% of all the values in the data set are less than or equal to this quantity.solve the following equation: x/7-6=-x/6+5
By solving the given equation x/7 - 6 = - x/6 + 5 we get x value = 462/13.
What is called the equation?
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.Given that :
x/7 - 6 = - x/6 + 5
Multiply the denominators with numerator on both sides
x / 7 - 6(7) = - x / 6 + 5(6)
x - 42 / 7 = - x + 30 / 6
Multiply both denominators with numerator on both sides
6 (x - 42) = 7 (- x + 30)
Multiply 6 and 7 inside the bracket
6x - 252 = - 7x + 210
Separate x terms and constant terms
6x + 7x = 210 + 252
13x = 462
x = 462 / 13
Therefore, x = 462 /13
To learn more about equation check the given link
brainly.com/question/17145398
#SPJ1
If f(x) = -x² - 1, and g(x) = x + 5, then f(g(x)) = [? ]x² + [ ]x + [ ] +[
explanation please
Answer:
-x² -10x -26
Step-by-step explanation:
Substitute x in f(x) with x + 5:
f(g(x)) = - (x+5)² - 1
= - (x² + 10x + 25) -1
= -x² -10x -25 -1
= -x² -10x -26
What happens when the scale factor is negative 1?
What is the inverse of the function f (x)=19/x^3
Answer:
Below
Step-by-step explanation:
y = 19/x^3 <===== solve for 'x'
x = cube rt (19/y) < ====now switch the x and y's
y = cube rt ( 19/x)
Answer: f^-1(x) = 19^3/x
Step-by-step explanation:
Given that : f(x) = y = 19/x^3
x^3 = 19/y
y = (19)^3/x = f^-1(x)
What does dilating an image do?
After dilation, the size of the image will change and the shape of the image will be same
Dilating an image means the changing the size of the image, but the shape of the image will be same
Dilation is the process of changing the size of the image without changing the shape of the image
The image after the dilation is called as the pre image.
The dilation can be done by using the scale factor or normally increase or decrease the size,
If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases
Therefore, size of the image will change after the dilation
Learn more about dilation here
brainly.com/question/13176891
#SPJ4
graph equation of y = 3.5x after a translation 2 units up. what are the pairs?
The given equation after a translation by 2 units upwards is y = 3.5x + 2.
What is the rule for translation?The rules for translating an equation in both vertical and horizontal directions are:
The equation of the graph is y = f(x). Then its translation along the vertical direction is either upwards or downwards.The equations after upward and downward translations are y = f(x) + m and y = f(x) - m.When the translation is along the horizontal direction (i.e., left or right), the equations after the left and right translations are y = f(x+m) and y = f(x - m).Calculation:The given equation is y = 3.5x
The equation after translation by 2 units upward is obtained by using the rule we have y = f(x) + m.
⇒ y = 3.5x + 2
The graphs for the given equation and the translated equation are shown in the graph below.
For the pair that show translation in both equations, substituting x = 0, we get
y = 3.5x ⇒ y = 3.5(0) = 0; So, the point is (0,0)
and
y = 3.5x + 2 ⇒ y = 3.5(0) +2 = y = 2; So, the point (0,2)
Therefore, the required pair is (0,0) and (0,2).
Learn more about the translation of a graph here:
https://brainly.com/question/15123583
#SPJ1
Can we use standard deviation on a curve that is not normal
Answer:Use it as it is or fit non-normal distribution
Step-by-step explanation:
Look at this set of data:
3, 7, 4, 6, 3, 5, 9, 40, 6, 3
What is the mode?
6
4
2
3
5
Answer:
mode = 3
Step-by-step explanation:
the mode is the value that occurs most often in the data set
3, 7, 4, 6, 3, 5, 9, 40, 6, 3
the value 3 occurs most often , 3 times
then mode of data set = 3