Answer:
Q1. Answer: According to the guidelines, the ratio of the rise (height) to the run (length) of a wheelchair ramp should be no greater than 1:12.
Option A: A ramp with a length of 30 feet and a height of 3 feet. The ratio of the rise to the run is 3/30 = 1/10, which is less than 1:12, so this ramp follows the guidelines.
Option B: A ramp with a length of 20 meters and a height of 0.5 meters. The ratio of the rise to the run is 0.5/20 = 1/40, which is less than 1:12, so this ramp follows the guidelines.
Option C: A ramp with a length of 384 inches and a height of 32 inches. The ratio of the rise to the run is 32/384 = 8/96 = 2/24, which is less than 1:12, so this ramp follows the guidelines.
Option D: A ramp with a length of 1 feet and a height of 12 feet. The ratio of the rise to the run is 12/1 = 12, which is not less than 1:12, so this ramp does not follow the guidelines.
Therefore, the ramps that follow the guidelines are options A, B, and C.
Q2. Answer: The guidelines for a wheelchair ramp suggest that the ratio of the rise (height) to the run (length) of the ramp should be no greater than 1:12. In this case, the rise is 2.5 feet and the run is the length of the ramp (x feet). The ratio of the rise to the run is 2.5/x.
To follow the guidelines, the ratio of the rise to the run should be no greater than 1:12, or 1/12. Therefore, the length of the ramp (x) should be greater than or equal to 2.5/1/12 = 30 feet.
Therefore, the correct answer is C: X ≥ 30.
Step-by-step explanation:
Rewrite (2x+v)^2 without parentheses and simplify
Answer:
[tex]4x^2+4vx + v^2[/tex]
Step-by-step explanation:
[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]
Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]
Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
the image point using the translation (x,y) (x + 4, y -1) for the point (3,3) is?
The image of the point (3, 3) after a translation 4 units right and one unit down is (7, 2)
What is transformation?Transformation involves moving an object from its original position to a new position on the coordinate plane. This can be a translation, dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size. Other types of rigid transformation are reflection, and rotation
The translation using the rule (x, y) ⇒ (x + 4, y -1) is a translation 4 units right and 1 unit down.
The image of the point (3, 3) using the rule (x, y) ⇒ (x + 4, y -1) is (7, 2)
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Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.
g(t) = t^2 - 27/t
The coordinates of the inflection points are (3, 0) and it concave upwards
How to determine the coordinates of the inflection points.From the question, we have the following parameters that can be used in our computation:
g(t) = t^2 - 27/t
Express properly
So, we have
g(t) = t² - 27/t
Calculate the second derivative
So, we have
g''(t) = 2 - 54/t³
Set the differentiated equation to 0
2 - 54/t³ = 0
So, we have
2t³ = 54
Divide by 2
t³ = 27
Take the cube roots
t = 3
Substitute t = 3 in g(t) = t² - 27/t
g(3) = 3² - 27/3
g(3) = 0
This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)
How to determine the point of concave upward and concave downwardRecall that
g''(t) = 2 - 54/t³
Next, we check if the second derivative exist at t = 0,
g''(0) = 2 - 54/0³
g(0) = undefined
The undefined value implies that the graph has a vertical inflection point at t = 0
And as such, the graph of the function is concave upward
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a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
Step-by-Step:5 cars and 14 bikes
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°
The measurement of three angles in the triangle are 43°, 81°, 56°.
What are the angles of a triangle?A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.
Given three angles,
∠A = (5x - 17)°
∠B = (7x - 3)°
∠C = 56°
We know that in a triangle ∠A + ∠B + ∠C = 180°
By substituting values,
(5x - 17) + (7x - 3) + 56 = 180
12x -20 + 56 = 180
12 x + 36 = 180
12x = 180 - 36
12x = 144
x = 144/12
x = 12
By substituting values of x we get,
∠A = (5x - 17)°
= 5 x 12 - 17
= 60 - 17
= 43
∠A = 43°
∠B = (7x - 3)°
= 7 x 12 - 3
= 84 - 3
= 81
∠B = 81°
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A store buys 14 sweaters for $84 and sells them for $504. How much profit does the store make per sweater?
Answer:
$30 per sweater is how much profit the store will make
Step-by-step explanation:
The cost of 1 sweater (for the store) is $6.
The store sells the sweater for $36 (504/14).
The store is making $30 per sweater.
There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league
Answer:
54
Step-by-step explanation:
Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.
9 times 6 = 54
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30)≥20 tell you?
The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Greater than (>).Less than (<).Less than or equal to (≤).How to determine the required function?Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;
g(x) ≥ x
when x = 30, we have;
g(30) ≥ 20
Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.
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Complete Question:
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30) ≥ 20 tell you?
It took at least 20 minutes for Mona to find 30 seashells.
Mona found at least 20 seashells in the first 30 minutes.
It took at least 30 minutes for Mona to find 20 seashells.
Mona found no more than 20 seashells in the first 30 minutes.
Write an equation
Y=|x| 10 units down
To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .
Write an equation Y=|x| 10 units down?y=|x-10|-3
Inside, is opposite. So therefore, to move it right 10 units, you subtract ten. However, outside of the absolute value, it is normal, so to move it down 3 units, you subtract 3.The number –45.3 is 45.3 units away from zero and the number 10 is 10 units away from zero. Therefore, the absolute value of any number is really a positive number (or zero).As we know that absolute value means remove the negative sign from the number and make it positive. So we get the absolute value of -10 as 10. So we get the absolute value of 10 as 10. Hence absolute value of -10 and 10 is 10 and 10 respectivelyTo know more about units visit:
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What is the domain of f(x)=[1/2]*
Here we need to find the domain of the given function.
We will see that the domain is the set of all real numbers.
The first thing we need to do is to define the domain of a function.
For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.
Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.
Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.
Particularly, in our function: f(x) = (1/2)^x
We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).
Concluding, because there is no problem with any real value, we can see that the domain is the set of all real numbers
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3p-3p+2s-6s+2q-3q+8r-7r
Is it ok to not put the p in this equation as the 3p is minus
Answer:
- 4s - q + r
Step-by-step explanation:
that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-
⇒3p-3p+2s-6s+2q-3q+8r-7r
add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q
⇒0 - 4s - 1q + 1r
⇒- 4s - q + r Answer
hope that helps...
When is it best to solve a system of equations using substitution?
Answer:
It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.
Step-by-step explanation:
This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution
Answer:
Answer Below
Step-by-step explanation:
It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.
I need to know the first and last one
The lines FE and GH are parallel to each orther.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given that
ΔPEI = ΔGHI
here ∠pie = ∠gih
PI =HI
GI=EI
So both triangles are congruent
So the FE║GH.
Hence the lines FE and GH are parallel to each orther.
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Is the relation shown in the table a function?
Input: 4,8,4,8
Output: 1,3,5,4
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
100 points please answer
The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C
What are trigonometric identities?Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.
These involve certain functions of one, two or more angles.
They also are different from triangle identities, which involves angles and side lengths of a triangle.
To verify a trigonometric identity, we take the following steps;
Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.Hence, the best option is C
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Simplify to a single trig function
On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)
=| -cos(t)+2cosec(t) |
= -cos(t)+2cosec(t)
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Write the equation of the line shown on graph (-1,-5) and (2,1)
Answer:
y = 2x -3
Step-by-step explanation:
You want the equation of the line through the points (-1, -5) and (2, 1).
SlopeThe slope of the line is given by ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-1)) = 6/3 = 2
Y-interceptThe y-intercept of the line can be found from ...
b = y -mx
y = -5 -2(-1) = -3
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . . line with slope m and y-intercept b
Using our found values, the equation is ...
y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3
Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!
Polynomial in standard form
1.
7-3x^3+6x^2
2.
2y-3-8y^2
Answer:
[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]Step-by-step explanation:
The terms are ordered from greatest to least degree.
TEXT ANSWER
How can you use the unit price to find the cost of 10
pounds of tomatoes? Please help
To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.
What is the unit cost?
The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.
Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The unitary method is used to find the unit cost of an object.
To find the cost of a unit object, multiply a by unit cost.
Given that, the unit cost of a unit pound of tomatoes.
The cost of 10 pounds of tomatoes is 10 × unit price of tomatoes.
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2. What number is a common multiple of
5 and 9?
i have been trying to figure this out for hours-
answer choices:
SSS
SAS
ASA
AAS
HL
Not Congruent
Answer: The answer is SAS
Help please! How do I write an equation in standard form using the information on the graph?
Answer:
3x -y = 2
Step-by-step explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
SlopeThe slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
InterceptThe point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equationWith this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard formThe standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.
Mental Math In a toy store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240 dolls, how many teddy bears are in the store? Use pencil and paper. Describe the mental math steps you use to solve this problem.
Answer:
Step-by-step explanation:
Dolls:240 Teddy Bears:120
120:240
Please Describe the fraction If Possible.
Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2
System of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are
a. y = 5x + 11 and y = 5x
Substitute the y value in first equation
5x=5x+11
So the system of equations y = 5x + 11 and y = 5x has no solution.
b. y = 6x + 3 and y = 3x
Substitute the y value in first equation
3x=6x+3
-3x=3
x=-1
y=-3
The system of equations has one solution
c. x + 4y = 8 and y = -1/4x + 2
x+4(-1/4x + 2)=8
x-x+2=8
The system of equations has one solution has no solution
Hence, system of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
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Which of the following tables represents a linear relationship that is also proportional?
x y
0 3
3 6
6 9
x y
0 4
2 6
4 8
x y
0 0
6 3
12 6
x y
0 3
5 5
10 7
The solution is Option A. , Option C.
The equations which are also proportional is y = 3x and x = 2y
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the values of x = { 0 , 3 , 6 }
Let the values of y = { 3 , 6 , 9 }
Now , the proportional equation is y = 3x
So , the proportionality constant is k = 3
b)
Let the values of x = { 0 , 6 , 12 }
Let the values of y = { 0 , 3 , 6 }
Now , the proportional equation is x = 2y
So , the proportionality constant is k = 2
Hence , the equations are y = 3x and x = 2y
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Answer: The solution is Option A. , Option C.
Step-by-step explanation:
The equations which are also proportional is y = 3x and x = 2y
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the values of x = { 0 , 3 , 6 }
Let the values of y = { 3 , 6 , 9 }
Now , the proportional equation is y = 3x
So , the proportionality constant is k = 3
b)
Let the values of x = { 0 , 6 , 12 }
Let the values of y = { 0 , 3 , 6 }
Now , the proportional equation is x = 2y
So , the proportionality constant is k = 2
Hence , the equations are y = 3x and x = 2y
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Find the measurement of the angle I dictated for each trapezoid.
The measures of missing angles in trapezoids are listed below:
Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°
How to determine the measures of missing angles
In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:
Any pair of angles along one of the two parallel lines and between the other two congruent sides have the same measure. Any pair of angles between two parallel lines are supplementary angles. Two angles are supplementary when the sum of their measures equals 180°.Now we proceed to determine the missing angles in every trapezoid:
Case 5
m ∠ K + m ∠ J = 180°
21 · x + 15 · x = 180°
36 · x = 180°
x = 5
m ∠ J = 15 · x
m ∠ J = 15 · 5
m ∠ J = 75°
Case 7
m ∠ U = m ∠ T
m ∠ T = m ∠ U
m ∠ T = 118°
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1/3m = 12-m
Please explain step by step to get marked as brainliest.
Step-by-step explanation:
cross multiply
12-m(3m)= 1
12-3m²-1=0
multiply by -1
3m²+1-12=0
3m²= 11
m²= 11/3
m=√11/3.
True or False: 10, 8, 6, 4, … is a geometric sequence.
Answer:
False
Step-by-step explanation:
You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.
Geometric sequenceA geometric sequence has a common ratio between adjacent terms. Here the ratios are ...
8/10 = 0.8
6/8 = 0.75
These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)