Answer: the answer is 3 3/4
The base of a triangle is shrinking at a rate of 5 cm/s and the height of the triangle is increasing at a rate of 9 cm/s. Find the rate at which the area of the triangle changes when the height is 12 cm and the base is 4 cm.
Provide your answer below:
The rate of change of the area of the triangle is ___ cm²/s.
Answer:
Step-by-step explanation
Area of a triangle
A = ½bh
dA/dt = ½(b(dh/dt) + h(db/dt)
dA/dt = ½(4(9) + 12(-5))
dA/dt = ½(36 - 60)
dA/dt = ½(-24)
dA/dt = -12 cm²/s
The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to an area of an open surface or even the boundary of a three-dimensional object, whereas the area of a plane region as well as plane area refers to a area of a shape or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of a curve's length.
A shape's area can be calculated by contrasting it with squares of a known size.
[tex]\frac{\mathrm{d} b(t)}{\mathrm{d} t}=-5cm/s[/tex]
[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t}=9 cm/s[/tex]
[tex]\frac{\mathrm{d}A }{\mathrm{d} t}=\frac{1}{2}\left (b\frac{\mathrm{d} h}{\mathrm{d} t} +h\frac{\mathrm{d} b}{\mathrm{d} t}\right )[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=-12 cm^{2}/s[/tex]
Hence, The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].
Learn more about area from link
https://brainly.com/question/25292087
#SPJ2
triangle abc was dilated from the orgin by a scale factor of 2 to create triangle A’B’C’ which statement explains why the triangles are similar ?
Answer:ABC was dilated from the origin by a scale factor of 2 to create Delta A'B'C' . Which statement explains why the triangles are similar? Dilations preserve side length; therefore, the corresponding sides of Delta ABC and Delta A'B'C' are congruent.
Step-by-step explanation:Googel
What is the value of x if the side length of Terrarium A is four times the side length of Terrarium B?
The value of x if the side length of Terrarium A is four times the side length of Terrarium B is 3.6
Since we are both given the required length, we can assume the side length of Terrarium A and B and solve it in a general way.
Let;
Side length of Terrarium A = x - 6Side length of Terrarium B = x + 3If the side length of Terrarium A is four times the side length of Terrarium B, then;
x - 6 = 4(x + 3)
x - 6 = 4x + 12
x + 4x = 12 + 6
5x = 18
x = 3.6
Hence the value of x if the side length of Terrarium A is four times the side length of Terrarium B is 3.6
Learn more on linaer equation here: https://brainly.com/question/13738662
Mr. White has 2 suits, 5 dress shirts, and
6 ties. How many different clothing combinations can he make?
Answer:
60
Step-by-step explanation:
Use the counting principle.
2 × 5 × 6 = 60
Answer: 60
A researcher is interested in testing the perceived effort (PE) of runners under three different terrains. PE is measured on a scale that ranges from 0 to 15, where higher scores indicate greater effort. The three terrains were a running track (i.e. the control), a mostly flat sidewalk, and a hilly neighborhood. Participants were randomly assigned to only one type of terrain. What type of analysis should the researcher conduct
113-5.[ 2 3-( 2 3+(6))]
Answer:
143 should be correct
Step-by-step explanation:
hope this helps
I need help with math
[tex] \frac{1}{5} + \frac{3}{4} \times \frac{3}{5} = \\ [/tex]
[tex] \frac{1}{5} + \frac{9}{20} = \\ [/tex]
[tex] \frac{4}{20} + \frac{9}{20} = \\ [/tex]
[tex] \frac{13}{20} \\ [/tex]
Ernie’s bakery sells pastries for $.75 each. A customer purchased 112 pastries, and Ernie gave him an 8.375% discount. How much did that customer pay for the pastries he purchased?
Answer:
$7.6965 or $7.70
Step-by-step explanation:
We multiply the price by the amout he bought.
0.75 x 112 = 84 or $8.40
This is how much he would have paid without a discount. To find the discount we multiply the initial amount by the discount percent in decimal form.
8.4 x 0.08375 = 0.7035
This is the amount thay will be subtracted from the initial price.
8.4 - 0.7035 = 7.6965 or $7.70
Please help me in this 4th grader question, its a homework and i was sick over the weekend
Answer:
what is your question ask then I shall answer you
QUESTION 4
Round the following number to two significant digits: 137,426.9
The coordinates of a square are (3,2), (8,2), (8,7), and (?,?)
Answer:
i don't know can u solve plz
Answer:
(3, 8)
Step-by-step explanation:
For this, draw a graph and locate the points. Then you can determine where the missing point should be to draw a square. Check out the graph I sent to understand what I'm talking about.
Help me solve this please, im really bad at stuff like this
Answer:
given
Step-by-step explanation:
Answer:
statement - reason
BC||AD, <BAD is congruent to <DCB - given
<CBD is congruent to <ADB - alternate interior angles
BD is congruent to BD - reflexive (?)
triangle ADB is congruent to triangle CBD - AAS
AB is congruent to CD - CPCTC (corresponding parts of congruent triangles are congruent)
if Jenny buys 2 8-inch di|dos for 8$ then what is the total price
Answer:
$16
Step-by-step explanation 2 x 8 to 8 + 8 =16
Mary works at a local Burger King restaurant. Her regular hourly wage is $14.70. If she works overtime, she
receives an hourly rate of 14 times her regular hourly rate. If she regularly works 40 hours per week with no
overtime, what is her regular weekly pay?
$882
$2.94
$588
$294
Answer:
I’m pretty sure it’s 588
Step-by-step explanation:
14.70 * 40 = 588
Find the perimeter of the figure.
[tex]perimeter = 17 + 19 + 7 + 11 + 10 + 8 \\ [/tex]
[tex]perimeter = 72 \: \: cm[/tex]
Joe lost his part-time job, which reduced the net family income by 20%. His wife Janice decided to work overtime to compensate for the lost income. Other things being equal, by what percentage must her net salary increase in order to arrive at the same net family income as they had before Joe lost his job?
The percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the salary of Joe be represented by x, while the salary of Janice is represented by y.
Since the sum of the salary of Joe and Janice is the net income of the family. Therefore, the net salary when Joe had a job will be,
x + y₁ = 100%
Now, it is known that Joe lost his job, which reduced the net family income by 20%. Therefore, the net salary now will be only 80% which will be equal to the salary of Janice. Thus, we can write,
y₁ = 80%
Further, Janice decided to work overtime to compensate for the lost income. Therefore, we can write,
y₂ = 100%
Furthermore, the percentage change in salary of Janice can be written as,
Percentage Change = [(100% - 80%)/80% ] × 100%
= 20/80 × 100%
= 25%
Hence, the percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
Learn more about Percentages:
https://brainly.com/question/6972121
#SPJ2
Um yeah so ignore the blue circles. I need your helpp ty <3
Answer:
where is the diagram u there is must must graphic of this or diagram
Answer:
15, 6,0, 11, 7
I'm not sure but hope it helps
Step-by-step explanation:
y=8+7
=15
y=-1+7
=6
y=-7+7
=0
y=4+7
=11
y=0+7
=7
LESSON 3
WHATS MORE
Translate each English phrase/sentance into Mathematical phrase/sentance
1. The sum of 4 and number________
2. Six less than a number_________
3. The product of 8 and a number______
4. The quotient of x and 7 ______
5. Five more than a number is equal to 15_____
Answer:
1. 4+x
2. x-6
3. 8x
4. x/7
5. x+5=15
Step-by-step explanation:
Solve for x. Round to the nearest hundredth. 10^x = 42
Answer: The answer is 1.62.
Explanation: It is in the image.
A rectangle has a length of 25 meters less than 6 times it’s width. If the are of the rectangle is 261 square meters, find the length of the triangle
List all the factors of 19. Tell whether 19 is prime or composite.
Answer:
19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)
Step-by-step explanation:
What is the correct unit rate?And what is Jessie's likely error?
Answer:
4
Step-by-step explanation:
1[tex]\frac{1}{2} / \frac{1}{8} = \frac{1}{2} * \frac{8}{1} = \frac{8}{2} = 4[/tex]
she forget that fraction will reverse if it move below or up side, I think
What is 1 1/2 divided by 8
Answer:
3/16
Step-by-step explanation:
start by converting 1 1/2 to an improper fraction by multiplying the 1 by the denomerator and then adding the 1 from teh numerator. Then place that all over the denomantor two. so you get 3/2
then set up your equation:
3/2 x 1/8
you do the resipricol of one of the numbers so instead of 8/1 we do 1/8
3 times 1= 3
2 times 8 is 16
3/16 does not simplify so thats your answer
Answer:
3/16
Step-by-step explanation:
((1 1/2)/8)=(3/2)/8
8 times 2(demoninator)=16
numerator stays same so the answer is 3/16
Which of the number line graphs shows the solution set of |x – 2| > 3?
Answer:
I have it!
Step-by-step explanation:
Jennifer’s bill for lunch was $15.00 If Jennifer left a 20% tip, which proportion would BEST represent how to find how much tip she should leave?
Answer: $3
Step-by-step explanation:
15 times .20 then subtract that from 15
Answer:
$3
Step-by-step explanation:
because other people said it and especially your MOTHER SAID IT TOO HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAH
What is the equation of the line that passes through the point (8,6) and has a slope of
{3}{2}
What does y= -3x+3 equal
Answer:
Solving for x, the answer is x = 1 - y/3
Hope this helps :D
Answer:
Step-by-step explanation:
y= -3x+3 is the equation of a straight line with slope -3 and y-intercept 3. The x-intercept is found by letting y = 0 and solving for x: x = 1.
y= -3x+3 can be re-written in "standard form:" 3x + y = 3.
Lincln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 688 cans have been collected. Write and solve an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal. Which two-step inequality represents this situation?
Is the inequality 5-x^2<4 true for x=1?
5 - x² < 4
- x² < 4 - 5
- x² < - 1
=》x² < 1
Now, let's check with x = 1
x² < 1
(1)² < 1
1 < 1
1 is not less than or greater than 1. They are equals. So, the inequality 5 - x² < 4 is NOT true for x = 1.
_____
Hope it helps ⚜
Need help!! timed, and will give brainlist
Answer: 90
Step-by-step explanation: