Answer:
The rate of change of the top of the ladder with respect to x is -x/y
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 ft.
The horizontal distance of the bottom of the ladder from the wall = x
The distance of the top of the ladder from the floor = y
By Pythagoras's theorem, we have;
10 = y² + x²
Therefore, we have;
x² = 10 - y²
d(x²)/dx = 2·x = d(10 - y²)/dx = -2·y·dy/dx
∴ 2·x = -2·y·dy/dx
dy/dx = 2·x/(-2·y) = -x/y
Therefore, the rate of change of the top of the ladder with respect to x, dy/dx = -x/y.
Three-eighths of the teachers at Naran's school are math teachers, and 30 of the teachers are not math teachers.
How many teachers are there at Naran's school??
Answer:
48 teachers
Step-by-step explanation:
Here's two solutions:
Solution 1: Build an equation.
Let $T$ be the number of teachers. The number of math teachers is $\frac{3}{8}T$, and the number of non-math teachers is $30$. Since each teacher is either a math teacher or not a math teacher, we have
$$\frac{3}{8}T + 30 = T.$$Multiplying each side of this equation by $8$ gives us
$$3T + 240 = 8T.$$Subtracting $3T$ from each side gives us $240 = 5T$, and dividing both sides by $5$ gives us $48=T$. Therefore, there are $48$ teachers at Naran's school.
Solution 2: Think proportionally.
Since three-eighths of the teachers are math teachers, the other five-eighths are not math teachers. So, these $30$ non-math teachers are five-eighths of the total number of teachers. Therefore, $\dfrac{30}{5} = 6$ teachers are one-eighth of the total. So, there are $6\cdot 8 = \boxed{48}$ teachers in all.
If your not busy mind helping me on this
Answer:
F
Step-by-step explanation:
add all the numbers and divide them by how many numbers there is(in this case 15) to find the average of the prices
please help me answer this math question, it is really important
Answer:
3 three point baskets
9 two point baskets
4 one point baskets
Step-by-step explanation:
Since you cannot have a 1/3 or 2/3 of a three point basket, finding multiples of threes for the initial two point baskets is the easiest way to start.
Simplify: (3p-4)^2+8(3p-2)
Answer:
3p^2 - 12p - 12p + 16 + 24p - 16
3p^2 -24p +24
p^2 -8p +8
I need help to find the value of x. Round to the nearest tenth
Answer:
17.1
Step-by-step explanation:
tan(35)=12/x, x=17.1
Answer:
x ≈ 17.1
Step-by-step explanation:
The angle is 35 degrees, so we do tan(35)
Which equals the side divided by x.
tan(35) = 12 / x
So x ≈ 17.1
What is the volume of the cone? Round to the nearest cubic cm.
Answer:
the answer will be
184.31
A real estate agent receives a 3%
commission for selling a house. Find the
commission that the agent earned for
selling a house for $131,000.
you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,
131000/100 = 1310 x 3 = 3930
the commission is $3930.00
hope it helps :)
Myles has calculated that 1/2 a box of tile will cover 1/6 of his kitchen floor. How many boxes of tile will he need to cover the entire kitchen?
Answer: He need 3 boxes.
Step-by-step explanation:
Every 1/6 of his floor needs 1/2 of the tile box.Split his floor into 6 parts, each part needing 1/2 of the tile box:
[tex]6*\frac{1}{2} =\frac{6}{2} =3[/tex]
Or you can add 1/2 six times for each 1/6 of the floor:
[tex]\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} +\frac{1}{2} =\frac{6}{2}=3[/tex]
The scatter plot below shows the relationship between years of education and income for a representative sample of adults.
Which of the following is the best estimate of the average change in a person's income that is associated with going to school for an additional year?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
$
1
$1dollar sign, 1
(Choice B)
B
$
2
$2dollar sign, 2
(Choice C)
C
$
3000
$3000dollar sign, 3000
(Choice D)
D
$
7000
$7000dollar sign, 7000
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20
22
22
24
24
20000
20000
40000
40000
60000
60000
80000
80000Annual income (dollars)Years of education
Answer:
A
Step-by-step explanation:
khan
Connie the fruiterer sells two fruit packs.
Pack 1 : 10 apples and 5 mangoes ($12)
Pack 2 : 15 apples and 4 mangoes ($14.15)
Determine the cost of 1 apple and 5 mangoes.
A brick is in the shape of a rectangular prism with a length of 6 inches, a width of 3 inches, and a height of 5.5 inches. The brick has a density of 2.7 grams per cubic centimeter. Find the mass of the brick to the nearest gram.
pls pls pls help
y............. xnxnxnxnxnccncncncnnncncjcjnf
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
(N)0.05 + (17-N)0.1 = M; M = amount of money I have.
Or 1.7-0.05N = M.
Step-by-step explanation:
Based on information from a large insurance company, 68% of all damage liability claims are made by single people under the age of 25. A random sample of 53 claims showed that 41 were made by single people under the age of 25. Does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company
Answer:
No, it doesn't indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company
Step-by-step explanation:
Let's first state the hypotheses.
Null hypothesis; H0: p = 0.68
Alternative hypothesis; Ha: p > 0.68
A random sample of 53 claims showed that 41 were made by single people under the age of 25.
Thus; p^ = 41/53 = 0.7736
Let's find the test statistic from the formula;
z = (p^ - p_o)/√(p_o(1 - p_o)/n)
z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)
z = 0.0936/0.07285
z = 1.28
From online p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;
P(z > 1.28) = 0.100273
The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.
Construct a function with a rate of change of 1/3 and an initial value of -3.
(put your equation in slope-intercept form y = mx +b)
So you pretty much have all you need. 1/3 represents slope, and slope is m. Initial value would be your y intercept which is b.
y=1/3x-3
Answer:
y = x/3 - 3
Step-by-step explanation:
x/3 is the equivalent of 1/3(x)
write an equation of the function in the form y=a(b)^x -c that has a y intercept of -6, asymptote of y= -2 and goes through (2,-18)
Step-by-step explanation:
Asymptote: y = 2 y-intercept: (0,8)
Step-by-step explanation:
The given function is
f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)
x
+2
This function is of the form:
f(x) = a {b}^{x} + cf(x)=ab
x
+c
where y=c is the horizontal asymptote.
By comparing , we have c=2 hence the horizontal asymptote is
y = 2y=2
To find the y-intercept, we put x=0 into the function to get:
f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)
0
+2=6+2=8
Therefore the y-intercept is (0,8).
Can u help solve this problem
Answer:
45in³
Step-by-step explanation:
6 x 5 x 3 = 90/2 = 45in³
(x^2+2x+1)+(-x^2+x+3)
Answer:
3x+4
Step-by-step explanation:
You have to combine like terms to get 3x+4.
If 75% is 10 days, how many days is the remaining 25%?
Answer:
10/3 days or 3 1/3 days
Step-by-step explanation:
Let d = number of days total
75% of the days is 10
.75 d = 10
d = 10/.75
d = 40/3 days
We want to know how man is 25% of d
d * 25%
(40/3) *.25
10/3 days
Please help me. Taylor pays $5.25 for 5 yard of frabric.Whats the cost per yard?
Thank you!
Answer:
$1.05 per yard
Step-by-step explanation:
5.25 ÷ 5 = 1.05
Answer:
$1.05 per yard.
Step-by-step explanation:
find unit rate; (cost / quantity)
5.25 / 5 = 1.05
ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.
Answer: About 6.321 cm
Step-by-step explanation:
[tex]tan(x)=\frac{opposite}{adjacent}[/tex]
[tex]tan(36)=\frac{x}{8.7} \\\\x=8.7*tan(36)=6.3209...[/tex]
If a sine curve has a vertical shift down 19 units with an amplitude of 21, what will the minimum and maximum values be? (i.e. how high and low will the graph go?)
Min Value:
Max Value:
Given:
Amplitude = 21
Vertical shift = 19 units down
To find:
The maximum and the minimum value.
Solution:
The general form of sine function is:
[tex]y=A\sin (Bx+C)+D[/tex]
Where, |A| is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is the vertical shift.
Here,
[tex]Maximum=D+A[/tex]
[tex]Minimum=D-A[/tex]
We have,
Amplitude: [tex]A = 21[/tex]
Vertical shift: [tex]D=-19[/tex]
Negative sign means shifts downwards.
Now,
[tex]Maximum=D+A[/tex]
[tex]Maximum=-19+21[/tex]
[tex]Maximum=2[/tex]
And,
[tex]Minimum=D-A[/tex]
[tex]Minimum=-19-21[/tex]
[tex]Minimum=-40[/tex]
Therefore, the minimum value is -40 and the maximum value is 2.
What is the area of this triangle? Enter your answer in the box.
Answer:
A =27 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 (9) (6)
A =27 cm^2
Answer:
I assure you the person above is perfectly right. The area of a triangle is:
A = 1/2bh
Step-by-step explanation:
Have a good day.
The sum of two numbers is 78. Their difference is 32. Write a system of equations that describes this situation. Solve by elimination to find the two numbers. x + y = 32 y – x = 78 50 and 24 x – y = 78 x + y = 32 54 and 24 x + y = 78 x – y = 32 55 and 23
Answer:
55, 23, x+y =78; x-y =32
Step-by-step explanation:
-the system of equation
x+y = 78
x-y = 32
-solve by elimination
x-y = 32, add y to both sides
x= y+32
x +y =78, substitute x= y+32
y+32+y = 78, subtract 32 from both sides
y+y = 78-32, combine like terms
2y = 46, divide both sides by 2
y = 23
x +y =78, substitute y = 23
x+ 23 =78, subtract 23 from both sides
x = 78-23, combine like terms
x = 55
Answer:
The equation:
x + y = 78
x - y = 32
The answers:
x= 55
y = 23
Step-by-step explanation:
Call the first number (x) and the second number (y). Take is as a given that (x) is larger than (y). One is given the following information:
"The sum of two numbers is 78"
"Their difference is 32"
Rewrite this in numerical terms:
x + y = 78
x - y = 32
The process of elimination is a way of solving a system of equations. First one manipulates one of the equations such that one variable has an inverse coefficient of its like term in the other equation. This step one does not need to be performed, as the coefficients of the term (y) are inverses in the equations. Next, one adds the equations. Then one uses inverse operations to solve for the remaining variable. Finally, one back solves for the value of the eliminated variable by substituting the value of the solved variable into one of the equations, and simplifying.
Add the equations,
x + y = 78
x - y = 32
____________
2x = 110
Inverse operations,
2x = 110
x = 55
Back solve,
x + y = 78
x = 55
55 + y = 78
y = 23
Part A
The poll report includes a table titled, “Americans Using Cash Now Versus Five Years Ago, by Age.” The age intervals are not equal. Why do you think the Gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results?
Answer:
These are the intervals of the people who are at least adults and are mature enough to take the survey seriously and answer correctly
Step-by-step explanation:
Simplify the expression:
4m + 5 - 3m
Answer:
m+5
Step-by-step explanation:
4m + 5 - 3m
Combine like terms
4m-3m +5
m+5
Answer:
This equation simplified is [tex]m+5[/tex]
Step-by-step explanation:
To simplify this expression subtract 3m from 4m to get 1m or m.
State the domain and range of the graph below:
Answer:
domain [-1, ∞)
range [ -3, ∞)
Step-by-step explanation:
change the following to grams only
a. 7kg 85g
b. 6kg 346g
c. 5kg 342g
Answer:
a) 7085g
b) 6346g
c) 5342g
Step-by-step explanation:
1kg = 1000g
9) Three times a number added to 12 gives -6. Find the number.
Answer:
The number is -6.
Step-by-step explanation:
Variable x = a number
Set up an equation:
3x + 12 = -6
Isolate variable x:
3x = -18
x = -6
Check your work:
3(-6) + 12 = -6
-18 + 12 = -6
-6 = -6
Correct!
Answer:
3x +12=-6
3x=-6-12
3x=-18
x=-18/3
x=-6
Alice stand at point A and looks at the top of a 17.8 m tree TB, such that her line of sight makes an angle 38° with the horizontal. The height of her eye level is 1.5 m. Find the horizontal distance AB between Alice and the tree.
Answer:
Step-by-step explanation:
let the horizontal distance be x
(17.8-1.5)/x = tan 38
or x = 16.3/tan38
or x = 20.863
if the ratio a to b is 4:5 and the ratio of a to c os 2:7 what is the ratio of c to b
Answer:
G. 14:5 is the correct answer.
Step-by-step explanation:
a:b = 4:5
a:c = 2:7
so,
here in first ratio a = 4
in second ratio a = 2
making them equal:
Taking LCM of 2 and 4 = 4
so
a:c = 2/7 = (2×2)/(7×2) = 4/14
so,
a = 4
c = 14
b = 5
so ratio c : b = 14:5
