D varies as R and S, and inversely as t. D=12, R=3, S=20, and t=5, find D when R=15, S=4 and t=8.
Given:
D varies as R and S, and inversely as t.
D=12, R=3, S=20, and t=5
To find:
The value of D when R=15, S=4 and t=8.
Solution:
It is given that D varies as R and S, and inversely as t. So,
[tex]D\propto \dfrac{RS}{t}[/tex]
[tex]D=\dfrac{kRS}{t}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get
[tex]12=\dfrac{k(3)(20)}{5}[/tex]
[tex]12=12k[/tex]
[tex]\dfrac{12}{12}=k[/tex]
[tex]1=k[/tex]
Substituting [tex]k=1[/tex] in (i), we get the required equation.
[tex]D=\dfrac{(1)RS}{t}[/tex]
[tex]D=\dfrac{RS}{t}[/tex]
We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get
[tex]D=\dfrac{(15)(4)}{8}[/tex]
[tex]D=\dfrac{60}{8}[/tex]
[tex]D=7.5[/tex]
Therefore, the required value of D is 7.5.
Solve the following quadratic equation for all values of xx in simplest form.
4(x^2-5)-1=
4(x
2
−5)−1=
\,\,3
3
The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
Find and interpret the average rate of change.
Time (in months)
Balance
0 1 2 3 4 5 6
$250 $234 $220 $202 $189 $171 $157
3. The table shows the balance
in Sonia's bank account over
6 months. Find and interpret
the average rate of change
during this time period.
Could someone help me
1. P=2.625
2. variable= p
3. operator= subtraction
4. constants= -10, 32
5. coefficients= 16p
6. 5w + 50 = 150 w=20
Help me please 35 points on the line
Answer shown in bold
401924109147The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.
========================================================
Explanations:
Add up all of the values in the Venn diagram to find the total. Therefore, 9+10+14+7 = 40 students were surveyed.We add the values in the "social interaction activities" circle only. There are 9+10 = 19 students here.This time add up the values in the "technology driven activities" to get 10+14 = 24 students.The answer is 10 because this value is in the overlapped region between the two circles. The answer is 9 since this value is in the "social interaction activities" circle, but outside the other circle. The answer is 14 as this value is in the "technology driven activities" circle, but outside the other circle.The answer is 7 because this value is outside both circles.Let me know if you have any questions.
An octagon has a perimeter of 27 feet. If the sides of the octagon shrink by a scale factor of 8/9, what will the perimeter of the new octagon be
The perimeter of the new octagon be 24 feet.
What is the perimeter of octagon?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.
The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.
Given that the perimeter of an octagon is 27 feet
so the length of its side is 27/8 feet
if the side of the octagon shrink by a scale factor of 8/9
The side of new octagon is (27/8) * (8/9)
The side of new octagon is 3 feet.
So the perimeter of new octagon is 8 * side
⇒ the perimeter of new octagon = 8 * 3 feet
⇒ the perimeter of new octagon = 24 feet
To learn more about perimeter visit:
brainly.com/question/6465134
#SPJ1
2 copies of 1/10 write fraction for each statement
2 copies of 1/10 can be written as 2/10
What is a fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here 2 copies of 1/10 thus 2×1/10=2/10
=1/5
Hence, 2 copies of 1/10 can be written as 2/10
Learn more about mixed fractions here:
https://brainly.com/question/29264210
#SPJ1
Q1
0.06 million = 6.2 thousand =
Give your answer to two de
Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).
Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:
F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)
We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:
105 = (R + F) * 3
Now we can substitute the first equation into the second equation:
105 = (R + (R + 5)) * 3
Simplifying and solving for R, we get:
R = 20 mph
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).
Learn more about velocity through:
https://brainly.com/question/18084516
#SPJ1
Find RS, WILL GIVE BRAINLIEST!!!! Due Today!
Answer:
RS = 6
Step-by-step explanation:
RS² = SU*ST (secant-tangent rule)
Substitute
(x + 6)² = (x + 4 + 5)(x + 4)
(x + 6)(x + 6) = (x + 9)(x + 4)
x(x + 6) +6(x + 6) = x(x + 4) + 9(x + 4)
x² + 6x + 6x + 36 = x² + 4x + 9x + 36
x² + 12x + 36 = x² + 13x + 36
Collect like terms
x² - x² + 12x - 13x = -36 + 36
-x = 0
x = 0
✔️RS = x + 6
Plug in the value of x
RS = 0 + 6
RS = 6
Calculating the median
The following data points represent the number of attendees at each of the private dance events hosted by
Fenel Arrangements.
Sort the data from least to greatest.
49
48
33
51
38
47
42 34
Find the median number of attendees.
attendees
Repon a problems
Stuck? Watch a video or use a hint.
Answer:
Okay so!
Step-by-step explanation:
33, 34, 38, 42, 47, 47, 48, 49, 51.
The median is 47 because it turns up twice.
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
Define volume.Volume, which is expressed in cubic units, is a unit of measurement for the 3-dimensional space occupied by matter or encircled by a surface. The SI unit of volume = area * height is the cubic metre (m3), which is a derived unit. A "litre" (L) is the name given to the cubic decimeter (dm3).
Here,
The volume of cylinder = πr²h
Given : Diameter = 12 inches
radius = 12/2 = 6 inches
Height = 8 inches
Thus ,
To find the volume we put the all the above values in the formula:
=> V = πr²h
=> V = 22/7 * 6² * 8
=> V =355/113 * (6)² * 8
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
To know more about volume , visit
brainly.com/question/13338592
#SPJ1
Answer:
V equals 355 over 113 times 6 squared times 8.
Step-by-step explanation:
What are the exact values of a and b?
CORRECT ANSWER
WITH EXPLANATION
Step-by-step explanation:
TRY WITH SOME Trigonometric FUNCTION.
IF SOMETHING IS Wrong . I AM STILL A STUDENT
4. The Jerico family went ice skating on the
frozen lake. The 2 parents and 4 children each
had ice skates. They brought an extra pair of
ice skates in case anyone else wanted to join
them. How many ice skates did the family
bring?
Answer:
10
I wish you luck in your assignments.
When the function f(x) is divided by x + 2, the quotient is x² - 5x + 8 and the
remainder is 8. Find the function f(x) and write the result in standard form.
Step-by-step explanation:
this means :
f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)
f(x) = (x + 2)(x² - 5x + 8) + 8 =
= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =
= x³ - 3x² - 2x + 24
Express The Ratio 36 : 42 In it's Simplest Form ?
Answer:
6/7
Step-by-step explanation:
36/42 = 36:6/42:6 = 6/7
What is the surface area? 5 mm 4 mm 5 mm 6 mm 6 mm square millimeters
Answer:
184
Step-by-step explanation:
A triangular prism has 2 triangular faces and 3 rectangular faces.
solve
Find the area of each face 1/2x6x4=12 do twice for the two sides so its 24 with them both added then 5x10=50 do it twice for the other 2 sides then you got the bottom 6x10=60 only one time because the top is not a side
Surface area
12 + 12 + 50 + 50 + 60= 184 hope it helps
The surface area of the prism is 104 mm^2.
What is a triangular prism?Connect three rectangles edge to edge. Now close their triangular mouths from both ends. That shape is called a triangular prism.
We are given that;
Height=4mm, Base=6mm, sides=5mm, 5mm and 6mm
Now,
Plug in the values into the formula for surface area and simplify:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base area)
Surface area = (16 × 5) + (2 × 12)
Surface area = 80 + 24
Surface area = 104 mm^2
Therefore, by the area of the triangular prism answer will be 104 mm^2.
Learn more about triangular prisms here:
https://brainly.com/question/16261758
#SPJ2
I need some answers please like I really don’t know how to do these problems at all
Answer:
EVALUATE THE FUCTION WHEN: f (1/2 % 32)////////21+×_37- 4 = 37.2
EVALUATE THE FUNCTION WHEN f(3+38 x + formula of angle are = _1/2 decimals point 78.32)*/% =3( 92.03
Step-by-step explanation:
HOPE IT HELPS A LOT!!
Solve for the missing side indícate Round any answers to the nearest tenth
Answer:
do 180-36-90 and then what you get add a ° and it should be 53°
You have a 1/3 -teaspoon measuring spoon and a 1/2-teaspoon measuring spoon. What are two ways you can measure 3 1/6 teaspoons of salt?
Answer: One way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:
the 1/2 teaspoon measuring spoon 3 times to measure 3/2 = 1 1/2 teaspoons
and use the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons
3 1/2 + 2/3 = 3 1/6
Another way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:
the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons
and use the 1/2 teaspoon measuring spoon 6 times to measure 6 * 1/2 = 3 teaspoons
3 + 2/3 = 3 1/6
So, there are two ways to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2-teaspoon measuring spoon, one is by using 3 times 1/2 teaspoon measuring spoon and 6 times 1/3 teaspoon measuring spoon and the second one is by using 6 times 1/3 teaspoon measuring spoon and 3 times 1/2 teaspoon measuring spoon.
Step-by-step explanation:
What's the area of the triangle with 9mm 76mm 100mm
9514 1404 393
Answer:
342 mm²
Step-by-step explanation:
The triangle shown has a base of 9 mm and a height of 76 mm. Its area is ...
A = 1/2bh
A = (1/2)(9 mm)(76 mm) = 342 mm²
The triangle shown has an area of 342 mm².
_____
Additional comment
The other leg of the right triangle with one leg 76 mm and hypotenuse 100 mm will be about 65 mm. The base shown is 9 mm, so any triangle with the dimensions shown will be a fairly skinny obtuse triangle, not the acute triangle in the picture. (This makes us suspect an error: the 9 mm dimension maybe should be 90 mm.)
6y2 + 3y - 1 4 for y = 1
The value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]
Why use the vertex form?In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.
In the equation we are given the value of y as: 1
[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]
Therefore, we can say that the value of the given polynomial is: 8
To know more about polynomial equations visit :-
brainly.com/question/30127172
#SPJ1
Complete question is: Find 6y2 + 3y - 1 4 for y = 1
what is the volume of a prism if the length is 11ft the width is 8ft and the height is 9ft
Answer:
792ft
Step-by-step explanation:
V=LxWxH, so all you do is do 11 times 8 times 9 to get the answer to that question
In the figure, d || m. What is the value of x?
I WILL MARK BRAINLIEST!!
|
———— | ————
(2x - 20°)|
| 86°
———— | ———-
|
Answer: 53
Step-by-step explanation:
2x-20=86 [alternate interior angles theorem]2x=106 [add 20 to both sides]x = 53 [divide both sides by 2]draw the graph y = 2x + 1
Answer:
are there any other information
15. Given a triangle with angle measures 35º and 25°. Find the measure of the third angle and classify
the triangle.
A. 30°, Right
B. 90°, Right
C. 120°, Obtuse
D. 30°, Acute
Answer: 120° obtuse.
Step-by-step explanation:
The sum of the angles in a triangle is 180°. Since two of the angles given are 35° and 25°, the third angle will be:
= 180° - (35° + 25°)
= 180° - 60°
= 120°
This is an obtuse angle since it's greater than 90° but less than 180°
PLEASE ANSWER
Write an equation in point-slope form passing through the given point and parallel to the given line:
(- 4, 4)
y = - 7/4x + 2
Answer:
y-4=-7/4(x+4)
Step-by-step explanation:
Point Slope Form: y-y*sub*1=m(x-x*sub*1)
Parallel lines have the same slope as the line to which they are parallel.
y-4=-7/4(x+4)
Hope this helps :)
PLEASE HELP MEEEE!!!
Answer:
x= 9
y= 3 root 3
Step-by-step explanation:
to find the shorter leg length you have: hypotenuse/2
[tex] \frac{6 \sqrt{3} }{2} = 3 \sqrt{3} [/tex]
to find the longer leg length you have: shorter leg × root 3
[tex]3 \sqrt{3} \times \sqrt{3} = 3 \sqrt{9 } = 3(3) = 9[/tex]
What is the value of c in the equation below?
24.22=abc
0 -4
0 -2
O
1
64
O
1
4
Answer:
are the values of a or b given?
Step-by-step explanation:
Select ALL composite numbers with their correct prime factors(I need help)
Answer:
The answer would be the second and fourth options.
Step-by-step explanation:
This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!