The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.
Let:
x be the distance from the bottom of the ladder to the base of the wall
y be the distance from the top of the ladder to the bottom of the wall
When the ladder is still, apply the Pythagorean Theorem,
x² + y² = 13²
5² + y² = 13²
y² = 169 - 25 = 144
y = 12 ft
When the ladder slides, apply the differential equation:
x² + y² = 13²
2x . dx/dt + 2y . dy/dt = 0
Substitute x = 5, dx/dt = 1, y = 12
2 . 5 . 1 + 2 . 12 . dy/dt = 0
24 dy/dt = -10
dy/dt = -5/12 = - 0.417 ft/s
The minus sign indicates that the ladder is sliding downward.
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What is the slope of y = -5x - 11
Answer:
0
Step-by-step explanation:
Let g(x) be the transformation, vertical translation 5 units down, of f(x)= 3x+9. Write the rule for g(x).
We can see the next function:
[tex]f(x)=3x+9[/tex]And we need to translate this function 5 units down, which results in the function g(x).
To find the rule for g(x), we can follow the next steps:
1. We know that the general rule for a function translated k units down is given by:
[tex]f(x)-k\rightarrow\text{ f\lparen x\rparen has been translated by k units down \lparen where k > 0\rparen.}[/tex]2. Then if we translate the original function by 5 units down, we will have that:
[tex]\begin{gathered} f(x)=3x+9 \\ \\ \\ f(x)-5=3x+9-5\rightarrow g(x) \\ \\ \end{gathered}[/tex]3. Therefore, g(x) will be:
[tex]\begin{gathered} g(x)=3x+9-5=3x+4 \\ \\ g(x)=3x+4 \end{gathered}[/tex]Hence, in summary, we have that the rule for g(x) is g(x) = 3x + 4 (option A).
Julia has a mask collection consisting of 255 masks she keeps on the wall and 45 she keeps in a display case. What percentage of Julias mask collection does she keep on her wall?
We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is
[tex]255+45=300\text{masks}[/tex]The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is
[tex]\frac{255}{300}\times100[/tex][tex]=85.\text{ }[/tex]Hence, Julia keeps 85% of her mask collection on her wall.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = Negative one-thirdx − One-third y = Negative one-thirdx − Five-thirds y = 3x − 3 y = 3x − 7
1st , 3rd & 5th choices
Step-by-step explanation:
perpendicular line would have a slope that is a
negative reciprocal
so if the slope is 3 then a perpendicular line would have a slope of -1/3
y - 1 = 1/3 (x + 2)
make the line look like y = mx + b
y = 1/3 (x + 2) + 1
y = 1/3 (x + 2) + 3/3
y = 1/3x + 2/3 + 3/3
y = 1/3x + 5/3
m = 1/3
perpendicular line has a slope of
m = -3
Find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4. A6x−2B12x−4C8x^2+4x−24D12x^2+20
The perimeter of a rectangular garden with width w = 4x - 6 and length l = 2x + 4 is given by: 2w + 2l = 2(4x - 6) + 2(2x + 4) = 8x - 12 + 4x + 8 = 12x - 4
Answer: option B
If F(x) = 5x + 4, which of the following is the inverse of F(x)? A. F-1(x) = 4 – 5x B. F-1(x) = C. F-1(x) = D. F-1(x) = 5x – 4
Answer:
5x-4
Step-by-step explanation:
Select all the intervals where f is decreasing.(Choice A)-5
Looking at the graph
we have that
Decreasing intervals are
(-infinite, -2.5) and (1.75, infinite)
so
Verify each option
A ----> is true
B ---> is not true
C ---> is true
D ---> is not true
The answer is A and CIs the function positive or negative over the interval (–8, –6)?
Answer:negative
Step-by-step explanation:
Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.
a bicycle path and a road cross at right angles. a police woman stands on the road 70 meters south of the crossing and watches an eastbound cyclist traveling at 6 meters per second. at how many meters per second is the cyclist moving away from the police woman 4 seconds after passing the intersection?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, or, in standard algebraic notation, a² + b² = c².
What is meant by Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b² = c².
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
First use the Pythagorean theorem. a² + b² = c²
then take the first derivative of it to get
2a(a') + 2b(b') = 2c(c')
Now figure out how far the train is after 4 seconds
6(4)=24
70² + 24² = c²
c = 74
Now plug in the variables you know
2(70)0 + 2(24)6 = 2(74)c' and solve for c' or the rate of change of c.
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Translate and solve: negative eighty times r is less than 80
r > -1
Explanations:Negative eighty times r is less than 80 is expressed mathematically as;
[tex]-80r<80[/tex]Divide both sides by -80.
[tex]\begin{gathered} \frac{-80r}{-80}<-\frac{80}{80} \\ r>-1 \end{gathered}[/tex]Note the change in sign when divided by a negative value
27, 18, 12, 8 explicit formula for the sequence
The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]
Given,
The first four terms are 27, 18, 12, 8.
Find the common ratio:
To do this, let that ratio = r,
and write and solve 27r = 18. Thus, r = 2/3.
The general explicit formula for this sequence is:
a(n) = a(1)*(2/3)^(n - 1),
or, since a(1) = 27,
a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]
Hence, The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]
What is Explicit formula For sequence?
The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.
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A wholesaler sells a guitar for $1,396.20. What is the percent markup based on cost if the wholesaler paid $780 for the guitar?
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
Given,
The cost price of the guitar = $780
The selling price of the guitar = $1396.20
We have to find the markup percent based on the cost;
Markup percentage;
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.
Markup percent = (Selling price - cost price) / cost price x 100
= (1396.20 - 780) / 780 x 100
= 616.20 / 780 x 100
= 0.79 x 100
= 79%
That is,
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
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Find g'(x) for g(x) = 2x√x² +7
Answer:
[tex] {2x}^{2} + 7[/tex]
so hope it helps
Please help soon thanks
Answer:
x = -7
Step-by-step explanation:
Hi!
Ok we know a few things here :
x + 37 + x + 67 + 90 = 180
2x + 104 = 90
2x = -14
x = -7
Hope this helps!
Have a great day! :)
any given season, a soccer team plays 65 % of their games at home.
When the team plays at home, they win 83 % of their games.
When they play away from home, they win 26 % of their games.
find the probability the team wins with explanation
Based on the percentage of games played at home by the team, and the percentage win rate, the probability that the team wins is 63.05%
How to find the probability the team wins?First, find the probability that the team wins playing at home:
= Percentage win rate at home x Percentage played at home
= 83% x 65%
= 53.95%
Then find the probability of winning away:
= Percentage win rate away x Percentage played away
= 26% x (1 - 65%)
= 9.1%
The probability the team wins is:
= 53.95 + 9.1
= 63.05%
In conclusion, the probability of the team winning at home and the probability of them winning away, can be summed up to find the probability of the team winning which is 63.05%.
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Find the measures of the interior angles of the triangle.
The value of interior angle is 60.
What is triangle?
A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.
What is interior angle?
In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.
The sum of interior angle is 180
Given angles is 30, 90, x.
Therefore, sum is given by
90 + 30 + x = 180
120 + x = 180
x = 180-120
x = 60
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A rectangular prism is 9 inches long, 3 inches wide, and _____ inches high.
The volume of the box is 324 in.
What is the height of the box?
Answer:
height = 12
Step-by-step explanation:
try and use the formula to plug it in and solve for x.
SHOW YOUR WORK
2 x 1/4 =
Answer:
2 times 1/4 = 1/2 or 0.5
Step-by-step explanation:
Step 1: Setup
First of all, note that 2 is the same as 2/1 since 2 divided by 1 is 2. Therefore, start by setting up the problem like this:
2/1 x 1/4
Step 2: Multiply
Multiply the numerators together (2 x 1 = 2) and multiply the denominators together (1 x 4 = 4) and make it into one fraction like so:
2/4
Step 3: Minimize
The greatest common factor of 2 and 4 is 2. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get the answer as follows:
1/2
Write the system of linear equations represented by the augmented matrix to the right use WXY and Z for the variables Write the equation for all the rows
Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :
Solution:
An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:
-1 w - 3x +5y +2z = 13
0w + 1x + 3y + 0z = 10
0w + 0x +y - 1z = 3
1w - 3x + 0y + 0z = -2
this is equivalent to:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
So that, the correct answer is:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
Here are 5 lines on a coordinate grid: Write equations for lines a,b,c,d and e a: b: c: d: e:
The equations of each of the given lines are:
Line a is: x = -4
Line b is: x = 4
Line c is: y = 4
Line d is: y = -2
Line e is: y = -¾x + 1
How to Write the Equation of a Line?If we determine the slope value, m, and the y-intercept value, b, the equation of a line can be written as y = mx + b in slope-intercept form by plugging in the values of the determined variables.
For a vertical line, the equation is expressed as x = b, where b is the x-intercept of the line.
For a horizontal line, the equation would be y = b, where b is the line's y-intercept value.
Equation of line a (vertical line):
The x-intercept is -4. This means that, the equation of line a is: x = -4
Equation of line b (vertical line):
The line's x-intercept is 4. To write the equation of the line, substitute the value of the x-intercept into x = b.
Therefore, the equation of line b is: x = 4
Equation of line c (horizontal line):
The y-intercept (b) = 4. Substitute the b = 4 into y = b.
The equation of line c is: y = 4
Equation of line d (horizontal line):
y-intercept (b) = -2. Substitute b = -2 into y = b.
Equation of line d is: y = -2
Equation of line e:
Slope (m) = rise/run = -3/4
y-intercept (b) = 1
To write the equation of the line, substitute m = -¾, and b = 1 in the equation y = mx + b
y = -¾x + 1
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Dog food comes in two different sized bags. The 40 lb bag sells for $24 while the 10 lb
bag sells for $7. Which is cheaper and by how much? (compare unit rates)
Answer:
The 40 lb bag is cheaper by $4
Step-by-step explanation:
10 x 4 = 40
7 x 4 = 28
If you bought the 10 lb bag 4 times, you'd spend more money than just buying the 40 lb bag once.
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Triangles and angles worksheet
The △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.
What do we mean by the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.So, △ABE ≅ △CDE:
AB || CD (Given)∠ABE ≅ ∠CDE, ∠BAE ≅ ∠DCE (Diagonal bisects the angles)AB || CD (Given)E is the midpoint of AC and BD (Given)Point E (Definition of midpoint)∠AEB ≅ ∠CED (Inversilly opposite angles)△ABE ≅ △CDE (AAA condition, ASA condition, SSS condition, and SAS condition)Therefore, the △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.
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what is the slope of any line parallel to the line 8x+9x=3 in the standard (x,y) coordinate plane ?
The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.
What is the Slope of Parallel lines?If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.
Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:
8x + 9y = 3
8x + 9y - 8x = -8x + 3 [subtraction property of equality]
9y = -8x + 3
9y/9 = -8x/9 + 3/9 [division property of equality]
y = -8/9x + 1/3
The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.
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please help me ! please
Answer:
[tex] \sf {\large{4\pi }}[/tex]
Step-by-step explanation:
Circumference of a circle ⭕ = [tex] 2 \pi r [/tex]
Where,
r = d/2
d means diameter
r = 4/2 = 2
So, substitute to equation C = 2πr
C = 2πr
C = (2r)π
C = (2•2)π
C = 4π
Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure. Now write the slope of the line of reflection and any dotted line. 10 -9 -8 7 -6 5 4 3 2 y 10 2 8 2 73 6 -8 10 Slope of one of the dotted lines: Slope of the line of reflection:
Slope of one of the dotted lines: -1/3
Slope of the line of reflection: 3
From given figure, we can observe that the line of reflection passes through points (2, 8) and (0, 2)
We need to find the slope of the line of reflection and any dotted line.
Using the formula of slope, the slope of the line of reflection would be,
m1 = (y2 - y1)/(x2 - x1)
m1 = (2 - 8)/(0 - 2)
m1 = -6 / (-2)
m1 = 3
The dotted lines are perpendicular to the line of reflection.
Let m2 be the slope of any dotted line.
We know that the product of slopes of any perpendicular lines is -1.
so, m1 * m2 = -1
3 * m2 = -1
m2 = -1/3
So, the slope of dotted any line = - 1/3
Therefore, Slope of one of the dotted lines: -1/3
Slope of the line of reflection: 3
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MTR
3 MAINTAIN ACCURACY In Exercises 27-30, determine
whether the statement uses the word function in a way
that is mathematically correct. Explain your reasoning.
27. The selling price of an item is a function of the cost of
making the item.
28. The sales tax on a purchased item in a given state is a
function of the selling price.
29. A function pairs each student in your school with a
homeroom teacher.
30. A function pairs each chaperone on a school trip
with 10 students.
Please just do 28 and 30
Answer:
28. Correctly used
30. Incorrectly used
Step-by-step explanation:
You want to know if the word "function" is correctly used in the following cases:
28. The sales tax on a purchased item in a given state is a function of the selling price.
30. A function pairs each chaperone on a school trip with 10 students.
28. Sales taxThere is exactly one value of sales tax associated with any given selling price. This means the ordered pair (selling price, sales tax) will be unique for any given selling price. Hence, the relation between selling price and sales tax is a function. The word function is used correctly in describing this relation.
29. ChaperonesThere are 10 different students associated with any given chaperone. This means there will be multiple (chaperone, student) ordered pairs for any given chaperone: (c1, s1), (c1, s2), ..., (c1, s10), (c2, s11), (c2, s12), ..., (c2, s20), .... The relation between chaperones and students is not a function. The word function is used incorrectly in describing this relation.
I need help 9th grade math
Answer:
D
Step-by-step explanation:
Please answer quick! i'm stuck on th is and it is due today! (equation is on the bottom on the picture)
4 - 1/3x = x + 2x
help please!! Which of the following functions is graphed below? brainly and 100
The absolute value function graphed in this problem is given as follows:
A. y = |x - 5| - 4.
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
The leading coefficient a does not influence the vertex of the absolute value function.
The vertex of the graph is the turning point, hence it is given as follows:
(5, -4).
Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:
y = |x - 5| - 4.
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A painter has three partially filled paint cans.1 7/8 gallonsthe second contains 1 1/5 gallonsand the third contains 1 3/4which anwer is closet to the total amount of paint?A.2B.3C.4D.5
A painter has three partially filled paint cans.
The first contains 1 7/8 gallons
The second contains 1 1/5 gallons
The third contains 1 3/4 gallons
The total amount of paint is the sum of these paint cans.
[tex]total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4}[/tex]Now let us add these mixed fraction numbers
[tex]\begin{gathered} total=1\frac{7}{8}+1\frac{1}{5}+1\frac{3}{4} \\ total=(1+1+1)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(\frac{7}{8}+\frac{1}{5}+\frac{3}{4}) \\ total=(3)+(1.825) \\ total=4.825 \end{gathered}[/tex]As you can see, 4.825 is closest to 5.
Therefore, the correct option would be D