Answer:
9-3
Subtract 3 from 9 and you get 6
The top of a ladder slides down a vertical wall at a rate of 2 feet per second. At the moment when the bottom of the ladder is 4 feet from the wall, it slides away from the wall at a rate of 3 feet per second. How long is the ladder
Answer:
The length of the ladder is 7.21 feet
Step-by-step explanation:
Let
y = Height of the wall
x = Distance between the wall and the ladder (bottom)
L = Length of the ladder
So, the given parameters are:
[tex]\frac{dy}{dt} = -2ft/s[/tex]
When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:
[tex]L^2 = x^2 + y^2[/tex]
Differentiate with respect to time
[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
The length of the ladder does not change with time. So:
[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Rewrite as:
[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]
Divide both sides by 2
[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]
Recall that:
[tex]\frac{dy}{dt} = -2ft/s[/tex] and [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]
So:
[tex]4 * 3 = -y * -2[/tex]
[tex]12 = 2y[/tex]
[tex]6 = y[/tex]
[tex]y = 6[/tex]
Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]
[tex]L^2 =4^2 + 6^2[/tex]
[tex]L^2 =52[/tex]
[tex]L = \sqrt{52[/tex]
[tex]L = 7.21ft[/tex]
If the critic rates a total of 100 movies, what is the best prediction for the number of movies she gives exactly 3 stars?
А
27
B
47
50
D
35
Answer:
I think its gonna be 35 I'm not sure
8+8+8=24 as multiplecation sentence
Answer
Hola la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
PLS HELP ASAP!its due very soon so tysm if u help me :)
Answer:
23
Step-by-step explanation:
Use the part/whole = %/100.
You have that whole = 115 and % = 20, so that would be:
[tex]part/115=20/100[/tex]
simplify & solve:
[tex]part/115=1/5[/tex]
multiply both sides by 115
[tex]part=115/5\\part = 23[/tex]
how many different ways can you find for 7 coins totaling 95 cents?
Answer:
one way
Step-by-step explanation:
2 quarters
4 dimes
1 nickel
Zander found these coins in his Couch
Answer:
91 cents
Step-by-step explanation:
3 quarters+3 nickel+1 penny=91 cents
Answer:
91 cents
Step-by-step explanation:
3 quarters=75c
3 nickels=15c
1 penny=1c
75c+15c+1c=91 cents
The following expression represents the profit made by John as he mows
lawns: P = 20L - 100
Which description correctly interprets each part of the expression?
Answer:
P is price per lawn, 20 is the money made per lawn, L is the number of lawns mowed, 100 is his initial cost.
Step-by-step explanation:
Which line has the same slope as the line passing through (-4, -1) and (-1, -7) ?
Answer:
D
Step-by-step explanation:
Answer:
athe correct answer of this question is 6x + 3y = 5
Juice is on sale with the rule "buy one, get one half-off.” Write an expression two different ways to represent the cost of buying two containers of juice, j, on sale. Enter the correct answers in the boxes.
Answer:
34
24
Step-by-step explanation:
divide 25 by 3
Memorial Day Spending The National Retail Federation conducted a national randomly-selected survey of 8,526 consumers on September 1-9, 2009 asking households how much they plan to spend on Memorial Day. I would like to know if the average amount households planned to spend on Memorial Day is less than $57. What are the observational units
Answer:
households
Step-by-step explanation:
An observational units are defined as the entity for which the information is received and the statistics are compiled of in the process of collecting the statistical data. It is also known as the statistical unit.
In the context, National Retail Federation is conducting a survey asking various households how much they are planning to spend on the memorial day. So the observational units in this study are the household because the information are collected on the basis of each household going to spend on the Memorial day.
The observational units in this will be households.
What will be the observational unit?An observational unit is defined as the entity for which the data is received and the statistics are collected in the process of collecting the statistical data. It is also known as the statistical unit.
In this context, National Retail Federation is executing a survey asking various households how much they are planning to spend on memorial day.
So the observational units in this study are the household because the information is gathered on the basis of each household going to expend on Memorial day.
Thus the observational units in this will be households.
To know more about Observation follow
https://brainly.com/question/25843544
What is the slope of the line ?(khan academy)
Answer:
The slope of the line is 2.
Step-by-step explanation:
Slope of a line:
Suppose that we have two points. The slope of the line is given by the change in y divided by the change in x.
In this question:
Points (0,0) and (1,2)
Change in y: 2 - 0 = 2
Change in x: 1 - 0 = 1
Slope: [tex]m = \frac{2}{1} = 2[/tex]
The slope of the line is 2.
Find the inverse of the function.
f(x) = -3x + 7
taka is playing a game of darts. she scores 52 points. in the game she is playing, she gets a -3 score each time she misses the board. her final point total is 37. write and solve an equation to find out how many times she missed the board
Answer:
5
Step-by-step explanation:
52-37 is 15 . divide by 3 and u get five
The local park has a circular pond with a radius of 9 feet. What is the pond's circumference?
Answer:
Using 3.14 as pi, the answer would be 56.52, and using just pi (as in the input on a calculator) would be 56.54867.
Step-by-step explanation:
The equation for circumference of a circle is C = πd, C representing the circumference and d representing the diameter. Since the equation shows the radius, the equation can also be C = 2πr, since the radius is half of the diameter. Multiply nine by two to get eighteen. 18 times 3.14 = 56.52.
This is Adeles solution for the equation x^2+8x- 9 = 0 Step 1 x^2 +8x = 9 Step 2 x^2 +8x + 16 = 9 + 16 Step 3 ( x + 4 ) ^2 = 25 Step 4 x + 4 = 25 or x + 4 = - 25 Step 5 x = 21 or x = - 29. Where did Adele make her mistake? What are the solutions to this equation? Show all of your work. 2. Which would be the best method to use to solve the following equation. Explain your reasoning. A x^2 - 49 = 0 B. x^2 - 3x - 4 = 0 C. x^2 - 2x - 6 = 0
Answer:
Adeles forgot to square root 25 in step 4 therefore the solutions would be 1 and -9
Step-by-step explanation:
Equation : x² + 8x - 9 = 0
Step 1 : x² + 8x = 9
Step 2 : x² + 8x + 16 = 9 + 16
Step 3 : ( x + 4 )² = 25
Step 4 : x + 4 = 25 or x + 4 = - 25
Step 5 : x = 21 or x = - 29.
4) An arithmetic sequence has a 7th term of 54 and a 13th term of 94. Find the common difference
Please answer!!
Answer:
20/3
Step-by-step explanation:
Every nth term takes the form of a + n*d, where a is the first term.
So 7th term = (54 = a + 7d), 13th term = (94 = a + 13d).
equate them both:
94 - 13d = 54 - 7d
40 = 6d
d = 40/6
PLS HELP WILL GIVE BRAINLESS
Answer:
1a. 3/8
1b. 4/12-1/3
Step-by-step explanation:
to get the answers you have to find a common denominator and then add them
Answer:
The answer would be
a) 3/8
b) 1/3
Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant
Answer:
[tex]\mathbf{ \dfrac{128}{3}}[/tex]
Step-by-step explanation:
Given that:
[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]
[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]
[tex]Then;[/tex]
[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]
[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]
∴
[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]
[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]
∴
[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]
[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]
[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]
∴
[tex]\mathbf{V = \dfrac{128}{3}}[/tex]
Paul owns a gym and needs to replace the carpeting on the floor. The gym's floor plan is shown.
8 yd
3 yd
4 yd
المة
How many square yards of carpeting is needed to cover the entire gym?
O 18 square yards
O 24 square yards
O 36 square yards
44 square yards
Answer:
24 square yards
Step-by-step explanation:
Find the diagram attached.
The area of the diagram = Area of rectangle + Area of triangle
Area of rectangle = 3 * 4
Area of rectangle = 12 square yards
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 6 * 4
Area of triangle = 12 square yards
Area of the diagram = 12 + 12
Area of diagram = 24 square yards
Hence 24 square yards of carpeting is needed
Information collected from runner 3# is in the table below
The constant proportionality for runner 3 is..?
Answer:
the constant of proportionality would be 9
I need help the question is what is the are of the composite figure
Answer:
Option 4
Step-by-step explanation:
Area of a trapezoid = [tex]\frac{1}{2}(b_1+b_2)h[/tex]
Here, [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and 'h' is the height between the bases.
Area of the composite figure = Area of two trapezoids given
= [tex]\frac{1}{2}(12+12)14+\frac{1}{2}(25+31)11[/tex]
= [tex]\frac{1}{2}(24)(14)+\frac{1}{2}(56)(11)[/tex]
= 168 + 308
= 476 square ft
Option 4 is the answer.
Expand (2x - 5)4 with the help of Pascal's triangle
Answer:
8x-20
Step-by-step explanation:
8x-20
(2x-5)4 2x*4
8x- 4*5
8x-20
Answer:
Answer:(2x-5)4
Answer:(2x-5)42x=20
Answer:(2x-5)42x=20or,x=20/2
°°°x=10
change improper fractions: 6 × 1/4 =
Answer:
[tex]1 \frac{1}{2}[/tex]
Old Navy charges $30 for 4 t-shirts and $45 two pairs of pants. If Unique’s mom orders 9 t-shirts and 6 pairs of pants, how much will Unique’s mom spend?
PLS HELP ME!!! i’ll give you a brainliest answer :)
Answer:
B is the correct answer
What is the area of the triangle at the right?
Answer:
13.16
Step-by-step explanation:
formula= (absin∅)/2
= (4×9×sin47)/2
= 13.16
What is the solution to the system of equations
Y=x+6
Y= -0.5x+3
Answer:
[tex]y = 4 \\ x = - 2[/tex]
Please help ASAP
I’ll mark Brainliest
What’s the total and lateral surface area for the figure?
Answer:
The total is 20 and the lateral surface is 1008 I think
aiko is biulding a tower out of paper she starts by making 2 congruent circular bases she then makes 1 curved surface sor the body of the tower what 3 dimensional figure does aiko biuld
cylinder
Step-by-step explanation:
the basses is top and bottom so if there circular on top and bottom and curved surface for the body its a cylinder
explain the answer to 481.5÷45
Answer:
10.7
Step-by-step explanation:
10.7
- 45
31
-00
315
-315
00