Given :
A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall.
By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec.
To Find :
How fast is the top of the ladder sliding down the wall.
Solution :
By, Pythagoras theorem, distance of ladder from horizontal to wall is 5 feet.
Now, [tex]x^2 + y^2 = 13^2[/tex]
Differentiating both sides, we get :
[tex]2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0\\\\(2\times 12\times 5) + (2\times 5 \times \dfrac{dy}{dt})=0\\\\\dfrac{dy}{dt}= -12 \ feet/sec[/tex]
Solve the function algebraically. -8|3 - 8x| = 40
Answer: x =1
Distribute
add 24 to each side
simplify
divide both sides by the same term
simplify
A boat goes 24 miles at a constant speed in 4 hours against a river current.
It takes the boat 3 hours to go the same distance at the same speed with the
current of the river. What is the speed of the boat and what is the current of
the river?
The speed of the boat is 7 miles/hour and the current of the river is 1 mile/hour.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
A boat goes 24 miles at a constant speed in 4 hours against a river current.
It takes the boat 3 hours to go the same distance at the same speed with the current of the river.
Let's suppose the speed of the boat is x miles/hour and the current of the river is y
x- y = 24/4
x - y = 6 ..(1)
x + y = 24/3
x + y = 8 ..(2)
Adding equation (1) and (2):
2x = 14
x = 7 miles/hour
y = 8 - 7 = 1 miles/hour
Thus, the speed of the boat is 7 miles/hour and the current of the river is 1 mile/hour.
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A circle has a diameter of 6 meters. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determined.
The numerical value of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
The numerical value of the circumference is greater than the numerical value of the area.
Step-by-step explanation:
This has already been answered
The numerical value of the circumference is less than the numerical value of the area.
Which statement is true?For a circle of radius R, remember that the diameter is twice the radius, we have:
area = pi*R^2
And the circumference is:
C = 2*pi*R
In this case, we have:
D = 6m
R = 6m/2 = 3m
The circumference is:
C = 2*3.14*3m = 18.84m
And the area:
A = 3.14*(3m)² = 28.26 m^2
So the area is larger than the perimeter, the true statement is:
"The numerical value of the circumference is less than the numerical value of the area."
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5у - 4х = -7
2y + 4x = - 14
PLEASE HELP ME :) 20 points
Answer:
its d thats the right anwsers
Step-by-step explanation:
8(x – 3) – (6 – 2x) = 2(x + 2) – 5(5 – 2)
Answer:
x= [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
8(x−3)−(6−2x)=2(x+2)−5(5−2)
Step 1: Simplify both sides of the equation.
8(x−3)−(6−2x)=2(x+2)−5(5−2)
8(x−3)+−1(6−2x)=2(x+2)−5(5−2)(Distribute the Negative Sign)
8(x−3)+(−1)(6)+−1(−2x)=2(x+2)−5(5−2)
8(x−3)+−6+2x=2(x+2)−5(5−2)
(8)(x)+(8)(−3)+−6+2x=(2)(x)+(2)(2)+−5(5−2)(Distribute)
8x+−24+−6+2x=2x+4+−15
(8x+2x)+(−24+−6)=(2x)+(4+−15)(Combine Like Terms)
10x+−30=2x+−11
10x−30=2x−11
Step 2: Subtract 2x from both sides.
10x−30−2x=2x−11−2x
8x−30=−11
Step 3: Add 30 to both sides.
8x−30+30=−11+30
8x=19
Step 4: Divide both sides by 8.
8x/8=19/8
Answer: x=[tex]\frac{19}{8}[/tex]
8(x - 3) - (6 - 2x) = 2(x + 2) - 5(5 - 2)
8*x - 8*3 - 6 + 2x = 2*x + 2*2 - 5*3
8x - 24 - 6 + 2x = 2x + 4 - 15 ( Cancel equal terms on both sides of the equation)
8x - 24 - 6 = 4 - 15
8x - 30 = -11
8x = -11 + 30
8x = 19
x = 19/8
(4+x) divided by 12.
im stuck heree :(
Steps:
See attachment.
Description:
The first step is to simplify the equation step by step and to simplify an equation you can first multiplying the factors and use the exponent rules to remove the parentheses. After that you need to combine it a terms. Then you will get your answer.
For more steps and graph see the attachment.
Answer: 1/12 x + 1/3
Hope this helps.
A truck is 180 inches long. A car is 30% shorter than the truck. How long is the car?
Rewrite the sum of 75+18 as a product of a number and another sum
Answer:
(2)(9) + 75 = 75+18
Step-by-step explanation:
(2)(9) + 75 = 75+18
The expression written as a product of a number and another sum is 3(25 + 8)
Given the expression 75 + 18, we are to write as a product of a number and another sum.
First we need to find the GCF of 75 and 18
75 = 3 * 25
18 = 3 * 6
Since 3 is common to both D+GCF, we can factor it out from the expression to have:
75 + 18 = 3(25 + 8)
Hence the expression written as a product of a number and another sum is 3(25 + 8)
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Find the measure of each side indicated. Round to the nearest tenth.
Answer:
Step-by-step explanation:
to find x we can use tangent function
tan 31= x/9
0.60=x/9
x=0.60*9=5.4 choice B
The measure of x side.
We have given a right angle triangle whose angle A=31 degrees and two sides that is x and 9.
We have to determine the value of x.
Therefore we use here the trigonometric ratio
What is the tan ratio?[tex]tan\theta=\frac{opposite side}{adjacent side}[/tex]
Therefore we get
tan 31= x/9
tan(31)=0.60
0.60=x/9
Isolate the x
x=0.60*9
x=5.4
Therefore option B is correct.
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0.9 to the 2 power =
Answer:
0.81
Step-by-step explanation:
MAKE ME BRAINLIEST PLEASEE <333
Answer:
0.81
Step-by-step explanation:
the answer is 0.81
0.9×0.9=0.81
On a map with a scale of 0.25 inch = 30 miles the distance between two cities is 8.3 inches
Answer:
Step-by-step explanation:
8.3÷0.25
Multiply that by 30 and you get 996
The actual distance between the two cities will be 996 miles.
What is the distance?Distance is defined as the product of speed and time.
Scale is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
The given scale is 0.25 inches on the map representing 30 miles.
If the distance between two cities is 8.3 inches
As per the given scale, the actual distance between the two cities will be as:
⇒ 8.3 × 30/0.25
⇒ 83/10 × 3000/25
⇒ 249,000/250
Apply the division operation, and we get
⇒ 996 miles
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The question seems to be incomplete the correct question would be:
On a map with a scale of 0.25 inch = 30 miles the distance between two cities is 8.3 inches. find the actual distance between two cities?
WILL GIVE BRAINLIEST
This table represents a linear function.
x y
0 5
5 15
This graph represents another function.
The greater unit rate of the two functions is ____. The greater y-intercept of the two functions is _____.
Given:
One linear function represented by the table.
Another linear function represented by the graph.
To find:
The greater unit rate and greater y-intercept.
Solution:
Formula for slope (unit rate):
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table it is clear that the linear function passes through (0,5) and (5,15). The function intersect the y-axis at (0,15), so the y-intercept is 15.
[tex]m_1=\dfrac{15-5}{5-0}[/tex]
[tex]m_1=\dfrac{10}{5}[/tex]
[tex]m_1=2[/tex]
So, the unit rate of first function is 2.
From the given graph it is clear that the linear function passes through (0,6) and (-4,0). The function intersect the y-axis at (0,6), so the y-intercept is 6.
[tex]m_2=\dfrac{0-6}{-4-0}[/tex]
[tex]m_2=\dfrac{-6}{-4}[/tex]
[tex]m_2=\dfrac{3}{2}[/tex]
So, the unit rate of first function is [tex]\dfrac{3}{2}[/tex].
Now,
[tex]2>\dfrac{3}{2}[/tex]
[tex]m_1>m_2[/tex]
And,
[tex]15>6[/tex]
Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of the two functions is 15.
Answer:
The greater unit rate of the two functions is 2.
The greater y-intercept of the two functions is 6.
Step-by-step explanation:
yay!
9÷45 plz help someone
Answer: 0.2
Step-by-step explanation:
please please help
The rectangular patio shown in the diagram below is enclosed on three sides by a fence.
Patio
w
House
The area of this patio is no more than 400 square feet. The total length of the three sides of
this fence is no more than 60 feet. Which system of inequalities can be used to find values of
1, the patio's length, and w, the patio's width, that will satisfy these conditions?
Answer: A
i had looked up another question on my quiz thing and an old staar test popped up and this was one of the questions with the answer, i also had this question on my quiz.
Rogelio's pay for working part-time at his father's
shop was $24.25, $26.25, $23.50, $32.55, $28.35,
$30.80 and $27.50. What is the median of his
νησος 2 ?
Answer:
The Median of all these numbers is $32.55
Step-by-step explanation:
What is fourty three hundredths as a decimal
Answer:
0.043
Step-by-step explanation:
0.0 is tenths
0.00 is 100ths
On a field trip, there are 3 adults for every 45 students. Which graph models a relationship
with the same unit rate?
10
9
8
7
6
10
9
8
F
H
0
30 60 90 120 150*
0
30 60
90
120 156
10
9
10
8
6
3
6
5
4
3
2
0
30 60 90 120 150
0
30
60 90 120 150
Answer:
H (the second graph)
Step-by-step explanation:
246.8 is what percent of 128? Round to the nearest thousandth.
Answer:
60%
Step-by-step explanation:
Answer:
Most 193%
Step-by-step explanation:
246.8/128= 1.928
Is this correct ? Please answer asap !
Answer:
Yes that formula is right, and the y- intercept is where the line intersects with the y- axis on the graph.
A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should be used with 2 cups of sugar? Type your answerin
Answer
6 cups!
Step-by-step explanation:
8. Gisele spins a spinner that has equally
sized yellow, green, blue and red
sections. What is the probability that
Gisele spins orange?
Answer:
0
Step-by-step explanation:
it was never stated that there was orange on the spinner
Plz help!!
Will give brainliest
WHICH OF THE FOLLOWING REPRESENTS A NON LINEAR EQUATION
Answer:
y = 3/x
Step-by-step explanation:
if a=1 b=2 c=3 find the value of 4a3b2
Answer:
14
Step-by-step explanation:
a4=4
3b=2 x 3=6
2c=2 x 3=6
Answer:
48
Step-by-step explanation:
We just need to put in the values of a and b.
4a3b² = 4(1) × 3(2)²
= 4 × 3(4)
= 4 × 12
= 48
Hereeeeeee helllllllpp lol
3(2x + 4) + 2(x-2)
Match the equivalent expressions
Answer:
3(2x+4)+2(x-2)
6x+12+2x-4
6x+2x+12-4
8x+8
I am from grade 9 from which grade are you
8 + 3m = 26 what is thissssss
Answer:
m=6
Step-by-step explanation:
Subtract 8 from both sides.
then divide both sides by 3 to get 6.
Hope this helps!
PLS HELP LAST ONE I NEED ILL MARK U BRAINLIEST
Which of the following is the lowest cost per can?
A. 3 cans of juice for $3.80
B.
5 cans of juice for $6.15
C.
8 cans of juice for $9.52
D.
12 cans of juice for $14.58
Answer:
The answer is C. 8 cans of juice for $9.52
Step-by-step explanation:
A. About $1.27 per can
B. $1.23 per can
C. $1.19 per can
D. About $1.22 per can
According to the calculations, 8 cans of juice for $9.52 is the lowest cost out of the four answer choices.
