Answer:
It is nonlinear
Step-by-step explanation:
A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees. How high does the ladder reach on the building?
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.
Let h represent the height of the building, hence:
sin(72) = h/20
h = 19.02 feet
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
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The height reached by the ladder of height 20-ft. inclined at 72° is approximately 19.02-ft.
How can the height reached by the ladder be found?Length of the ladder = 20 feet
Angle between the ground and ladder = 72°
Height reached by the ladder = Required
Solution:
From the definition of the sine of an angle, we have;
[tex]sin (\theta) = \mathbf{ \frac{opposite \: side}{hypotenuse}} [/tex]
The length of the ladder = The hypotenuse side = 20 ft.
The opposite side to the angle 72° = The height reached by the ladder
Which gives;
[tex]sin (72 ^ {\circ})= \frac{height \: reached}{20} [/tex]
Height = 20 × sin(72°) = 19.02
The height reached by the ladder on the building ≈ 19.02-ft.Learn more about the sine of angles here:
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Can someone help please
Answer:
35.3
Step-by-step explanation:
please mark brainliest
Answer:
35.3
Step-by-step explanation:
f is an even function. a = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries 4, 5, a, 7. g is an odd function b = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries b, 0, negative 3, negative 4.
The values of a and b are 4 and -3
How to solve for (a) and (b)?To solve for a, we make use of the function f(x).
x f(x)
2 4
0 5
2 a
3 7
Remove the x values 0 and 3
x f(x)
2 4
2 a
The above table implies that:
f(2) = 4 and f(2) = a
Substitute 4 for f(2) in f(2) = a
4 = a
Rewrite as:
a = 4
To solve for b, we make use of the function g(x).
x g(x)
2 b
0 0
2 -3
3 -4
Remove the x values 0 and 3
x g(x)
2 b
2 -3
The above table implies that:
f(2) = b and f(2) = -3
Substitute -3 for f(2) in f(2) = b
-3 = b
Rewrite as:
b = -3
Hence, the values of a and b are 4 and -3
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Complete question
Use the Symmetry of a Function to Find Coordinates
f is an even function g is an odd function
x f(x) x g(x)
2 4 2 b
0 5 0 0
2 a 2 -3
3 7 3 -4
Find a and b
Answer:
4, 3
Step-by-step explanation:
In the rhombus below, if NL = 7 and KM = 8 find JL.
Answer:
JL = 14
Step-by-step explanation:
N represents the center of the rhombus
Then
N is the midpoint of the diagonal (line segment) JL
Then
JL = 2 × NL
= 2 × 7
= 14
Tara makes donut topping by mixing sugar and 12 g of cinnamon. The tape diagram shows the ratio of sugar to
cinnamon.
Complete the table.
Here is the completed table:
Original Ratio Amount (g)
Sugar 3 18
Cinnamon 2 12
Total topping 5 30
How should the table be filled?Original ratio of Cinnamon = total topping - original ratio of sugar
5 - 3 = 2
Amount of Sugar = (12 x 3) / 2 =18g
Total toppings = 18 + 12 = 30g
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Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x . Leave your answer in the form y = m x + c
Answer:
[tex]y = \frac{1}{2} x + \frac{5}{2} [/tex]
Step-by-step explanation:
Since the line with equation y = 1 - 2x has slope -2, we need to find the equation of the line with slope 1/2.
[tex]3 = \frac{1}{2} (1) + b[/tex]
[tex]3 = \frac{1}{2} + b[/tex]
[tex]b = \frac{5}{2} [/tex]
[tex]y = \frac{1}{2}x + \frac{5}{2} [/tex]
what would be 12% of 40
Hello,
Answer:
4,8
Step-by-step explanation:
what would be 12% of 40 ?
12% × 40 = 12/100 × 40 = 0,12 × 40 = 4,8
A bag contains 75 marbles some red some blue the ratio of red marbles to blue marbles is 3 to 2 how many red marbles are there
Answer: 45 red marbles
Step-by-step explanation:
Using the ratios, we can create a fraction for the number of marbles.
3/5 of the bag would be red marbles, and 2/5 of the bag would be blue marbles.
(you get the 5 from adding 3+2 together)
If you take 3/5 of 75, you would get 45 red marbles.
How long should the ladder be if they want to use all the cable they have? Use the law of sines to find the length
Answer:
Step-by-step explanation:
Which function is graphed below?
The graphed rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
Which function is graphed below?Here we can see that we have a rational function of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.
Then q(x) is a constant, let's say:
q(x) = k
We also can see that we have a vertical asymptote at x = -2, then:
p(x) = (x + 2)
So the rational function is:
[tex]f(x) = \frac{K}{x + 2}[/tex]
Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:
[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]
Then the rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
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can someone please help me
Answer: A
Step-by-step explanation:
Answer:
A
I solved on paper it took me 45 mins
Solve for Y
V = −4y + 4x
Answer:
Y=−4y/v +4x/v
Step-by-step explanation:
Divide each term in by v and simplify.
An urn contains two red and three yellow balls. Two balls are selected randomly without replacement. What is the probability that both are yellow
The probability that both are yellow is 3/10.
Using the probability method, we get
P(y1 and y2) = P(y1) P(y2|y1)
= 3/5 x 2/4
= 6 / 20
= 3 / 10
The probability that both are yellow is 3/10.
Probability is sincerely how in all likelihood something is to manifest. each time we're uncertain approximately the final results of an occasion, we will speak about the possibilities of sure effects—how probably they're. The analysis of activities ruled by using possibility is known as statistics.
A series of actions where the outcomes are continually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a dice. occasion. It is a single final result of an experiment.
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A moving company sells boxes for packing items. the large box has a volume of 6x^2+2x+3 cubic units. the medium box has a volume of 2x^2-5 cubic units. a customer purchases two large boxes and one medium box. what is the total volume of the purchased boxes?
The total volume of the purchased boxes is 14x^2+4x+1
Sum of polynomialsGiven the following parameters
Volume of a large box = 6x^2+2x+3 cubic units
Volume of medium = 2x^2-5 cubic units.
If a customer purchases two large boxes and one medium box, the total volume is expressed as:
Total volume = 2(6x^2+2x+3) + 2x^2-5
Expand
Total volume = 12x^2+4x+6+2x^2-5
Total volume = 14x^2+4x+1
Hence the total volume of the purchased boxes is 14x^2+4x+1
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If
1 ƒ (x) = 3x + 5/x, what is f(a + 2)?
Answer: [tex]3a+6+\frac{5}[a+2}[/tex]
Step-by-step explanation:
[tex]f(a+2)=3(a+2)+\frac{5}{a+2}=3a+6+\frac{5}[a+2}[/tex]
using addition rules ,show how to add the two real numbers 7+(-14)
Answer:
Step-by-step explanation:
14+(−7)+7
Now −7 is the idea or the construct that is the complete opposite of 7, when it comes to additive regions. So, they would cancel out.
And we are left with
14.
someone please help me slove this its due tmrw somebody help, i will give brainlisest answer please
Answer:
Question 5:
a) 65 degrees
b) 11
Question 6:
a) 15.6
b) 6.4
Question 7:
a) 10
b) 20
Question 8:
a) EF = 14.4
Question 9:
a) x = 6
b) y = 22.5
Step-by-step explanation:
47. A car travels at a constant speed of 50 miles per hour.
The distance the car travels in miles is a function of
time, t, in hours given by d(t) = 50t. Find the inverse
function by expressing the time of travel in terms of
the distance traveled. Call this function t(d). Find
t(180) and interpret its meaning.
Answer:
The inverse of the given function is [tex]$t(d)=\frac{d}{50}$[/tex]. The time taken to travel 180 miles is 3.6 hours.
Step-by-step explanation:
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
[tex]$$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$$[/tex]
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
[tex]$$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$$[/tex]
The time taken to travel 180 miles is 3.6 hours.
prime factorization of 90
On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
The statement which is true about the end behavior of the graphed function is third option that is as the x-values go to negative infinity, the function's values are equal to zero.
A coordinate plane is a two dimensional plane formed by the intersection of two number lines . One of these number lines is a horizontal number lines called the x-axis and the other number line is a vertical number line called the y-axis.
The exact answer is third option that is as the x-values go to negative infinity, the function's values are equal to zero.
Step by step explanation:
Minimum value (negative 1.25, negative 3.25)
Maximum value of (0.25, negative 1.75)
The x intercepts where the graph crosses the x axis.
Value of x when y=0 crosses x axis at (negative 2.25, 0)
The y intercept are where the graph crosses the y axis.
Value of y when x=0 crosses y axis at (0, negative 2)
The line exits the plane at (negative 2.75, 6) and (1.5, 6).
It can be seen from the coordinates that as the x-values go to negative infinity, the function's values are equal to zero, the coordinates of y approaches zero.
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Answer:
D
Step-by-step explanation:
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
Answer:
y < 3x + 2
Step-by-step explanation:
We will be solving this in slope-intercept form, which is a form that gives us the slope and the y-intercept of the graph explicitly:
[tex]y=mx+b[/tex], m is the slope and b is the y-intercept
We are given that everything to the left of the resulting line is shaded, so we know that the inequality sign will be < (less than). That already eliminates the second and fourth options. We also know the y-intercept, or the point where the graph crosses the y-axis and x is 0. because it is given to us (2, which comes from the point (0,2)). To figure out the slope, we can use the formula since we are given two points [(-3, -7) and (0, 2)] the line passes through. The formula, which is mapped out below, tells us that the slope is just the difference in rise (vertical movement) divided by the difference in run (horizontal movement).
[tex]m=\frac{-7-2}{-3-0} =\frac{-9}{-3} =3[/tex]
Now we have all the information we need to find the inequality. The slope is 3, the y-intercept is 2, and the sign is <. The first inequality fits these criteria, meaning the correct linear inequality is y < 3x + 2
look at image.........
Answer:
first of all its not d since the y intercept is negitive
then its not b since its sloping down
so the slop is either 7/5 or 5/7
since rise/run it has to be 7/5
Hope This Helps!!!
Sec6A - tan6A = 1+3tan2A.sec2A
sec ^6 A−tan ^6A=(1+tan ^2A−tan ^2 A)(1+tan ^4
A+2tan ^2 A+tan ^2 A+tan ^4 A+tan ^4 A)
sec ^6 A−tan ^6 A=1+3tan ^2 A+3tan ^4A
L.H.S. = R.H.S.
Hence proved
Step-by-step explanation:
♡´･ᴗ･`♡
Help me asap find the area for each letter and find the surface area
Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.
S.A of the box = 460 square inches.
What is a cuboid?A cuboid is a three dimensional solid shape made of 6 rectangles.
Analysis:
surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches
surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches
surface area of B = surface area of F = 10 x 12 = 120 square inches
surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.
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Angelica Reardon received a 4-year non-subsidized student loan of $17,000 at an annual interest rate of 6.1%. What are Angelica's monthly loan payments for this loan after she graduates in 4 years? (Round your answer to the nearest cent.) $
Answer:
$1503.08 per month
Step-by-step explanation:
Hi! having a bit of trouble with this one problem that I can't seem to solve correctly. This is an exponential and logarithmic equation problem, but I keep getting 1.74036... and apparently that isn't the answer. I'd appreciate the help!
The value of x from the given expression is 0.7558
Solving exponential equationsThe standard exponential equation is expressed as y = ab^x
Given the equation below
10^x +5 = 60
Subtract 5 from both sides
10^x = 60 - 5
10^x = 55
Take the log of both sides
log10^x = log55
x = log55/log10
x = 0.7558
Hence the value of x from the given expression is 0.7558
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4. Verbal
Explain how to find a line parallel to a linear function that passes through a given point.
Answer:
The required line can be found by substituting the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.
Step-by-step explanation:
In the given question, it is given that a linear function passes through a given point.It is required to find a line parallel to the function.When two functions are parallel, their slopes are equal.Thus, substitute the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.The equation of a parallel line to a linear function that passes through a point can be explained using the examples below.
We have,
The parallel line to a linear function that passes through a point can be explained using the examples below.
Example:
Let's find a line parallel to the linear function y = 3x - 2 that passes through the point (2, 5).
Step 1: Given linear function and point
Linear function: y = 3x - 2
Point: (2, 5)
Step 2: Determine the slope of the given linear function
The slope (m) of the given function y = 3x - 2 is 3.
Step 3: Use the slope to find the equation of the parallel line
Since the parallel line has the same slope (3), its equation will be
y = 3x + b, where "b" is the y-intercept that we need to find.
Step 4: Substitute the coordinates of the given point into the equation of the parallel line
Using the coordinates (2, 5) of the given point, we can solve for "b":
5 = 3(2) + b
5 = 6 + b
b = 5 - 6
b = -1
So, the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5) is:
y = 3x - 1.
Thus,
The equation of a parallel line to a linear function that passes through a point can be explained using the examples above.
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Help Me Asap Please And Thank You!
In this case using the elimination method is actually easier, but the question asks you to use substitution method so....
2x+y= -10
3x-y=0
1st equation: It is better to isolate 2x on both sides because the y is going to be positive no matter what, 2x+y=-10 => y=-2x-10
If you isolated 3x for the 2nd equation, the y will be negative, and you have to divide the whole equation by -1 to make it positive
Now we got y=-2x-10, lets substitute it in the 2nd equation and solve for x:
3x-(-2x-10) = 0
5x+10=0
5x=-10
x=-2
Now lets solve for y:
3(-2)-y=0
-6-y=0
y=-6
Lets see if the same is applicable for 1st equation
2(-2)+(-6)=-10
-10=-10
Yess!!
(-2,-6) is the solution
The answer to the question is explained at the beginning
Hope it helps!
Jon's bathtub is rectangular and its base is 16 ft2. How fast is the water level rising if Jon is filling the tub at a rate of 0.5 ft3/min
Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.
If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:
Volume (V) = length × breadth × height
where;
the base = length × breadth = 16ft²
∴ the volume of the rectangular bathtub = 16h --- (1)
Using differentiation to differentiate 16h with respect to t implicitly, then:
dV/ dT = 16 dH /dT
When the rate of rising of the volume is 0.5 ft³/min
Then:
0.5 = 16 dH /dT
dH /dT = 1 / 16 * 0.5
dH /dT = 0.3125.
Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.
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Jim has 10 used books and 12 used DVD's to sell at a garage sale for $1.50 and $5.00 each respectively.
Let x be the number of books and y be the number of DVD's Jim ends up selling.
Which of the following systems of linear inequalities represents this situation if Jim wants to make at least $40.00?
a.)
x ≥ 10
y ≥ 12
1.5x + 5y ≥ 40
b.)
x ≤ 10
y ≤ 12
1.5x + 5y ≥ 40
c.)
x ≥ 1.5
y ≥ 5
10x + 12y ≥ 40
d.)
x ≤ 1.5
y ≤ 5
10x + 12y ≥ 40
Answer:
The correct system of inequalities is b.