Answer:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]
u = ( x + 1 )
v = ( 2x + 5 )²
[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]
2/5(1/3x-15/8)-1/3(1/2-2/3x)
Answer:
[tex]\frac{16}{45}x-\frac{11}{12}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]
We have to find the equivalent expression.
[tex]\frac{2}{5}(\frac{1}{3}x-\frac{15}{8})-\frac{1}{3}(\frac{1}{2}-\frac{2}{3}x)[/tex]
[tex]\frac{2}{5}\times \frac{1}{3}x-\frac{2}{5}\times \frac{15}{8}-\frac{1}{3}\times \frac{1}{2}-\frac{1}{3}\times (-\frac{2}{3}x)[/tex]
Using the the property
[tex]a\cdot (c-b)=a\cdot c-a\cdot b[/tex]
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]
[tex]=\frac{2}{15}x-\frac{3}{4}-\frac{1}{6}+\frac{2}{9}x[/tex]
[tex]=\frac{6x+10x}{45}+\frac{-9-2}{12}[/tex]
[tex]=\frac{16}{45}x-\frac{11}{12}[/tex]
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)=\frac{16}{45}x-\frac{11}{12}[/tex]
Given that PQ/ST = QR/TU= RS/US, select the postulate or theorem that you can use to conclude that the triangles are similar.
Answer: SSS Similarity Theorem (Choice A)
This is because we have three pairs of corresponding sides that form the same ratio, as shown by the given equation PQ/ST = QR/TU = RS/US.
That equation is basically the shorthand version of PQ/ST = QR/TU and QR/TU = RS/US combined together as one.
Logan was going to go to
Disneyland in America so he got
$450 from the bank. Then he
changed my travel plans, to go to
Eurodisney in Paris. How many
Euros will he have to spend?
Exchange Rate
GBP to Dollars £1: $1.50
GBP to Euros £1: €1.38
At a coffee shop, the first 100 customers'
orders were as follows.
Small
Large
Medium
Hot
un
48
22
Cold
8
12
5
5
What is the probability that a customer ordered
a large given that he or she ordered a cold
drink?
Rounded to the nearest percent, [? ]%
Answer:
people who ordered a cold drink=
[tex]8+12+5=25[/tex]
people who ordered a large cold drink= 5
[tex]probability= \frac{5}{25}[/tex] [tex]=\frac{1}{5}[/tex]
[tex]=\frac{1}{5} \times100=20~\%[/tex]
[tex]Answer: 20\%[/tex]
-----------------------
Hope it helps...
Have a great day!!
The probability that the customer ordered a large given that he or she ordered a cold drink is 5%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the order of the first 100 customers in a coffee shop.
Number of customers who ordered a large which is also a cold drink = 5
Total number of customers = 100
Probability = Number of desired outcomes / Total number of outcomes
Substituting,
Probability = 5 / 100 = 0.05 = 5%
Hence the required percent is 5%.
Learn more about Probability here :
https://brainly.com/question/30034780
#SPJ7
y = -4(x + 6)(x - 8)
How do you write this in standard form?
Answer:
[tex]y = -4x^2 + 8x + 192[/tex]
Step-by-step explanation:
Hi there!
Standard form: [tex]y=ax^2+bx+c[/tex]
[tex]y = -4(x + 6)(x - 8)[/tex]
Use the distributive property to multiply (x+6) and (x-8)
[tex]y = -4(x(x - 8) + 6(x - 8))\\y = -4(x^2 - 8x + 6x - 48)\\y = -4(x^2 - 2x - 48)[/tex]
Multiply the parentheses by -4
[tex]y = -4x^2 + 8x + 192[/tex]
I hope this helps!
A 12-member jury is to be selected from 15 men and 13 women. Find the probability that this jury has 6 or 7 males.
Answer:
The right solution is "0.5545".
Step-by-step explanation:
According to the question,
The probability of having 6 or 7 males will be:
= [tex]P(6 \ males)+ P(7 \ males)[/tex]
= [tex]\frac{15_C_6\times 13_C_6}{28_C_{12}} + \frac{15_C_7\times 13_C_5}{28_C_{12}}[/tex]
= [tex]\frac{5005\times 1716+6435\times 1287}{30421755}[/tex]
= [tex]\frac{16870425}{30421755}[/tex]
= [tex]0.5545[/tex]
Match the number with its opposite -5.4
To the nearest tenth of a second, the ball is in the air for s.
Answer:
2.4
Step-by-step explanation:
Took the assignment
Answer:
2.4 seconds is the correct answer.
Step-by-step explanation:
Just completed it.
Independent Practice
x
0
1
2
3
4
y
2
1.5
1
0.5
0
Which kind of function best models the data in the table? Write an equation to model the data.
A.
linear; y= 1 2 x+2
B.
quadratic; y=− x 2
C.
quadratic; y=− 1 2 x 2
D.
linear; y=− 1 2 x+2
Answer:
D. linear; y = - 1/2x + 2
Step-by-step explanation:
As the values of x increase by 1, the values of y decrease by 0.5. This means that we have a negative linear relationship of 1/2. In other words, the slope is -1/2. Our y-intercept is 2 since when x = 0, y = 2. So, D is the correct choice.
Type the correct answer in each box. Use numerals instead of words.
The domain of this function is {-12, -6, 3, 15}.
y = -2/3x + 7
Complete the table based on the given domain.
Answer:
hope it helps plz mark me brainliest!
Step-by-step explanation:
4x² - 3, x less than/equal to 0
Step-by-step explanation:
y = (-1/2)[(x+3)^½]
(x+3)^½ = -2y
Square both sides,
(x+3) = (-2y)²
x+3 = 4y²
x = 4y²-3
Interswitch x and y
Inverse is 4x²-3
Domain of inverse is the range of f.
The range of f is less than/equal to 0
Because at x = -3, f(x) = 0
For x > -3, f(x) is negative
Domain of inverse is x less than/equal to 0
Use the ordered pairs to give a function rule. Give the rule in slope intercept form {(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)}
Answer:
[tex]y = -0.25x -1.5[/tex]
Step-by-step explanation:
Given
[tex](x,y) = \{(-12,1.5)(-1,-1.25),(5,-2.75),(8,-3.5)\}[/tex]
Required
The function rule (in slope intercept)
First, we calculate the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{-1.25 -1.5}{-1 - -12}[/tex]
[tex]m = \frac{-2.75}{11}[/tex]
[tex]m = -\frac{2.75}{11}[/tex]
[tex]m = -0.25[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -0.25(x - -12) + 1.5[/tex]
[tex]y = -0.25(x +12) + 1.5[/tex]
Open bracket
[tex]y = -0.25x -3 + 1.5[/tex]
[tex]y = -0.25x -1.5[/tex]
Givenl || m | n, find the value of x.
m
44°
n
Submit Answer
PLS HELP
Answer:
x=136
Step-by-step explanation:
Show all work when answering the question for full credit. Do it as best as you can.
Solve the equation: 7(2x + 3) = 12x - 13
Answer:
x = -17
Step-by-step explanation:
7(2x + 3) = 12x - 13
Distribute
7*2x +7*3 = 12x-13
14x +21 = 12x-13
Subtract 12x from each side
14x-12x+21 = 12x-12x-13
2x+21 = -13
Subtract 21 from each side
2x+21-21 = -13-21
2x = -34
Divide by 2
2x/2 = -34/2
x = -17
IF B=
3 4 8
4 2 1
find b12, b21, b22 and b23
Answer:
since b is 348421 and we are looking for b21 it is 348421(12)
find the cost of four score of plate at 50k each and three dozens of spoon at 20k each
A farmer needs to cross the river with his fox, his chicken and a bag of corn. However, the boat can only fit the farmer and one other thing at a time. The problem is, the fox and the chicken are both hungry, so if he leaves the fox and chicken together, the fox might eat the chicken. If he leaves the chicken and corn together, the chicken might eat the corn. So how can the farmer get everyone across the river safely
first send the fox alone to the other side then send the corn, the fox wont eat the corn so that should be fine then lastly go with the farmer and the chicken, hope this helps!
Algebra 1 proportional relationships
Answer:
It always pass through the origin.(0,0)
Im not exactly understanding this question. Can someone please help me and possibly explain this to me?
Answer:
From the graph, when x=-6, y=1
so, your answer is A) f(x)=∛(x-6)+1
OAmalOHopeO
Help this is due in 10 mins
Answer:
Only A is true
for sure
....................
A polynomial p is graphed. What could be the equation of p? Choose 1 answer:
A. p(x) = x( x + 2)(2x + 7)
B. p(x) = x(x - 2)(2x - 7)
C. p(x) = x(2x) (7/2x)
D. p(x) = x(-2x)(- 7/2x)
Answer:
[tex]\text{B. }p(x)=x(x-2)(2x-7)[/tex]
Step-by-step explanation:
The zeroes of a function occur when the function crosses the x-axis. The function shown crossed the x-axis at [tex]x=0[/tex], [tex]x=2[/tex], and [tex]x=3.5[/tex]. These values of [tex]x[/tex] should produce an output of 0 when plugged into the function.
Therefore, the equation of the function graphed is [tex]\boxed{\text{B. }p(x)=x(x-2)(2x-7)}[/tex]
PLS HELP 10 POINTS!!!
Identify the term whose coefficient is -12 in the expression:
98x – 12xy2 - 15xy2
Answer:
[tex] - 12xy {}^{2} [/tex]
Step-by-step explanation:
A coefficient is a rational number in front of multiple consecutive terms.
If 4 over 7 ton of concrete covers 7 over 8 of a bridge, how many tons of concrete are required to cover the entire bridge?
Answer:
Your answer would be 32/49.
Step-by-step explanation:
4/7 tons = 7/8 x
4/7 / 7/8
32/49
The tons of concrete are required to cover the entire bridge is 32/49 tons.
What are fractions?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/7.
How many tons is needed to cover the whole bridge?To determine this value, divide 4/7 by 7/8
4/7 ÷ 7/8
4/7 x 8/7 = 32/49 tons
To learn more about the division of fractions, please check: https://brainly.com/question/25779356
The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.
[ x + y = 90 ; x = 14 + 3y ]
Answer:
fourteen times six equals eighty-four, eighty-four plus six equals 90
PLEASE HELP WILL GIVE BRAINSLIST
Answer: 3. 55° 2. 225° 1. 125°
Step-by-step explanation: don't want brainliest
solve
[tex]100 {5}^{2} - 500 {5}^{6} [/tex]
Please help before 9:00 pm
Urgent i need help!!…….
Answer:
Step-by-step explanation:
These are similar triangles. We know that because we know that all right triangles are similar. The height of the red one is 8 and the height of the blue one is 4; that means that the red one is twice the size of the blue one; likewise, the blue one is half the size of the red one. That means that ALL the measurements of these triangles exist in that ratio...even the base of the blue one. If the base of the red one is 3, and the red one is twice the size of the blue one, then the base of the blue one is 3/2 or 1.5. I can't see your choices because they are too small.
what is the quotient
Answer:
The quotient is 4x+5 and the remainder is -13
Step-by-step explanation:
Using synthetic division
-5 4 25 12
Bringing down the 4 and multiplying
-5 4 25 12
↓ -20 -25
----------------------
4 5 -13
The quotient is 4x+5 and the remainder is -13
Answer:
4x +5 [tex]\frac{-13}{x+5}[/tex]
Step-by-step explanation:
. 4x +5 [tex]\frac{-13}{x+5}[/tex]
x + 5 | 4x^2 + 25x + 12
- 4x^2 + 20x
5x + 12
5x + 25
-13
Keith used the following steps to find the inverse of f, but he thinks he made a error
f(x) = 7x + 5
Answer:
Step-by-step explanation:
[tex]\Large \boldsymbol{} f(x) \ \ inverse \ \ function \ \ (f(x))^{-1} \\\\ y=7x+5 \\\\x=7y+5 \\\\ y=\dfrac{x-5}{7} \ \ or \ \ f(x)^{-1}= \dfrac{x-5}{7}[/tex]
*Please Help!*
What is the volume of water, to the nearest tenth of a cubic metre, that would fill this spa tub?
First cylinder= 0.75m diameter, 0.80m height
Cylinder Underneath= 1.25m diameter, 0.70m height
Semi Sphere that holds both cylinders= 3m long
Answer:
The volume of water that will fill the spa tub is 5.9 cubic meters.
Step-by-step explanation:
Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)
i. volume of first cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius and h is the height of the cylinder.
r = [tex]\frac{0.75}{2}[/tex] = [tex]\frac{3}{8}[/tex]
= 0.375 m
h = 0.80 m
volume of the first cylinder = [tex]\frac{22}{7}[/tex] x [tex](\frac{3}{8} )^{2}[/tex] x 0.8
= 0.3536 cubic meters
ii. volume of the cylinder underneath = [tex]\pi[/tex][tex]r^{2}[/tex]h
r = [tex]\frac{1.25}{2}[/tex] = [tex]\frac{5}{8}[/tex]
= 0.625
h = 0.70 m
volume of the cylinder underneath = [tex]\frac{22}{7}[/tex] x [tex](\frac{5}{8}) ^{2}[/tex] x 0.7
= 0.8594 cubic meters
iii. volume of the semi sphere = [tex]\frac{2}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius = 1.5 m
volume of the semi sphere = [tex]\frac{2}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]
= 7.0714 cubic meters
Thus,
volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)
= 5.8584
The volume of water that will fill the spa tub is 5.9 cubic meters.
Explain how to solve 5^(x-2)= 8 using the change of base formula
Answer:
x = 3.3
Step-by-step explanation:
A equation is given to us and we need to solve out for x. The given equation is ,
[tex]\sf\longrightarrow 5^{x -2}= 8 [/tex]
Take log on both sides with base as " 10" . We have ,
[tex]\sf\longrightarrow log_{10} 5^{x-2}= log_{10}\ 8[/tex]
Simplify using the property of log , [tex]\sf log a^m = m log a [/tex] , we have ,
[tex]\sf\longrightarrow ( x -2) log_{10} 5 = log_{10} 8 [/tex]
Simplify ,
[tex]\sf\longrightarrow ( x -2 ) log_{10}5 = log_{10} 2^3[/tex]
Again simplify using the property of log ,
[tex]\sf\longrightarrow (x-2) log 5 = 3 log 2[/tex]
We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,
[tex]\sf\longrightarrow ( x - 2 ) = \dfrac{ 3\times 0.301}{0.69}[/tex]
Simplify the RHS ,
[tex]\sf\longrightarrow x - 2 = 1.30 [/tex]
Add 2 both sides ,
[tex]\sf\longrightarrow \boxed{\blue{\sf x = 3.30}}[/tex]
Hence the Value of x is 3.30 .
Answer:
its actually 3.292 because we round to the nearest thousandth and thats not even the equation you use above
Step-by-step explanation:
For this equation we use the formula log a^m=m (log a) so the equation will be written as log 5 (5^x-2) = log 5 (8). You use the base, which is 5, and use log to base 5 on both sides of the equation. Then you take the exponent " x-2" and write( x-2) log 5 (5) = log 5(8). Since log a =1, you multiply that 1 by x-2, which keeps it x-2. Making the equation x-2 = log 5 (8). Next, we use the change of the base properties with the formula log b^y= log y/ log b. The equation will be written as x-2 = log 8/ log 5, since 5 is the base it stays in the bottom or basement. We then add +2 to both sides of x-2 and log 8/ log 5. To solve this equation, you can find out what log 8 and log 5 are and divide those and add +2 to solve. So log 8 = 0.903 and log 5 = 0.698970 and divide those to get 1.29190 +2 and you get the answer rounded as 3.292.
