Answer:
49.5
Step-by-step explanation:
you multiply the height and base then divide that awnser by 2
Which of the following is in standard form of quadratic?
if f(x)= x²+x(2a+2b)+4ab-x. f'(x)=....
DON'T COPY PASTE!!! please use the methods and steps
[tex]f(x) = x^2 +x (2a+2b) +4ab-x\\\\f'(x) = 2x+x \cdot 0 + 2a+2b + 0 -1\\\\~~~~~~~~=2x+0+2a+2b-1\\\\~~~~~~~~=2x+2a+2b-1[/tex]
From the definition of the derivative,
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]
We have
[tex]f(x) = x^2 + x(2a+2b) + 4ab - x = x^2 + (2a+2b-1)x + 4ab[/tex]
and so
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{\left((x+h)^2 + (2a+2b-1)(x+h) + 4ab\right) - \left(x^2 + (2a+2b-1)x + 4ab\right)}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{x^2 + 2xh + h^2 + (2a+2b-1)x + (2a+2b-1)h + 4ab - x^2 - (2a+2b-1)x - 4ab}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{2xh + h^2 + (2a+2b-1)h}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} (2x + h + 2a+2b-1)[/tex]
[tex]\displaystyle f'(x) = \boxed{2x + 2a + 2b - 1}[/tex]
Please help with question with explanations. Ty.
Answer:
last option is correct answer
Step-by-step explanation:
[tex]perimeter = 2(l + w) \\ = 2( \frac{5x + 10}{2x + 5} + \frac{x - 2}{2x + 5} ) \\ = 2( \frac{5x + 10 + x - 2}{2x + 5} ) \\ = 2( \frac{6x + 8}{2x + 5} ) \\ = \frac{12x + 16}{2x + 16} [/tex]
A mouse climbs up a well of 86 meters. It advances 14 meters during the night, but during the day it retreats 2. The mouse will reach the surface on the day:
Step-by-step explanation:
we assume day and night are equally long.
and the mouse will start at night of day 1.
then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).
so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).
with a starting value of 14 (the first night).
so, we are getting an arithmetic sequence
an = an-1 + c
c = 12 in our case.
a1 = 14
a2 = a1 + 12 = 14+12 = 26
a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38
an = a1 + (n-1)×12 = 14 + 12(n-1)
at what n will it reach 86 ?
86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n
84 = 12n
n = 7
so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).
Can i have some Help Please I Will Give Brainlest If your Right And i need you to show your work
Perpendicular Line: y = 3x - 10
Explanation:[tex]\sf {Given:} \ y = -\dfrac{1}{3} x-4[/tex]
Comparing it with slope intercept formula: [tex]\bf y = mx + b[/tex]
where m is the slope, b is y interceptIdentify the slope for this particular function:
[tex]\star \ \ \sf slope = -\dfrac{1}{3}[/tex]
Now given that the line passes perpendicularly, then the slope shall be negatively inverse of the parallel slope.
[tex]\implies \sf \ perpendicular \ slope : \ -(\dfrac{1}{m} ) \ = \ -(\dfrac{1}{-1/3} ) \ = \ 3[/tex]
Now, find the equation:
[tex]y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex] given points : (6, 8)
equation:
[tex]\rightarrow \sf y - 8 = 3(x-6)[/tex]
[tex]\rightarrow \sf y = 3x-18+8[/tex]
[tex]\rightarrow \sf y = 3x-10[/tex]
On comparing to y=mX+b
Slope =m=-1/3Perpendicular lines have slopes negative reciprocal to each other
Slope of perpendicular line
3Equation in point slope form
y-8=3(x-6)y-8=3x-18y=3x-10Select the correct answer from each drop-down menu.
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of
sources. For each water source, he has sample with no treatment and a sample treated with the recommended amount of the water softener
salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is
v because the sample is
v . In this instance, an
v study was
performed.
The conclusion drawn from the study is valid because the sample is homogenous. In this instance, an experimental study was performed.
What is an experimental study?An experimental study can be defined as a quantitative research method that is used by a researcher to determine and show the effects of changes in the dependent variable, while placing other relevant independent variables under control.
Based on the experimental study conducted by using water from a variety of sources, the conclusion which can be drawn from this study is valid because the sample is homogenous.
In this instance, we can infer and logically deduce that an experimental study was performed.
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On a test that has a normal distribution, a score of 49 falls two standard deviations
below the mean, and a score of 61 falls one standard deviation above the mean.
Determine the mean of this test.
Answer:
57 mean
Step-by-step explanation:
x = mean
(x - 49 ) = 2 ( 61 -x)
x = 57
What is the diameter of the circle (x + 25/4)² + y² = 25?
Answer:
10 units
Step-by-step explanation:
Compare the given equation to the standard-form equation for a circle to identify the relevant dimension.
The equation of a circle is written in standard form as ...
(x -h)² +(y -k)² = r² . . . . . . . centered at (h, k) with radius r
__
Comparing this to what you are given, you see that ...
h = -25/4
k = 0
r² = 25
The radius is ...
r = √25 = 5
The diameter is twice the radius, so is ...
d = 2r = 2(5)
d = 10
The diameter of the circle is 10 units.
1/2 + 1/4 = how many quarters
Answer:
3
Step-by-step explanation:
1/2 = 0.5
1/4 = 0.25
1/2 + 1/4
= 0.5 + 0.25
= 0.75
= 75/100
= 3/4
Quarter is 1/4.
3/4 can be written as 3 x 1/4
Hence,
1/2 + 1/4 is 3 times 1/4
1/2 + 1/4 = 3 quarters.
Answer:
3/4
Step-by-step explanation:
1*(1/2)= (2/2)*(1/2)= (2*1)/(2*2)=2/4
1/2+1/4=2/4+1/4=3/4
How many more pairs of parallel sides does a regular octogon have then a regular hexagon
Answer:
1 more.
Step-by-step explanation:
A regular octagon has 4 pairs.
A regular hexagon has 3 pairs.
Hope this helped. :)
A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
We will see that there are 156,000 different combinations, so the correct option is C.
How many possibilities are there?
First, we need to find the selections, here we have:
First letter.Second letter.Third letter.Number.Now we need to find the number of options for each of these selections.
First letter. (26 options)Second letter. (25 options, because we can't repeat letters)Third letter. (24 options)Number. (10 options).We assumed that the number can be any integer from 0 to 9.
The total number of possibilities is equal to the product between the numbers of options, we will have:
P = 26*25*24*10 = 156,000
So, the correct option is C.
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I already answered one please answer the rest
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
The correlation coefficient is 0.92
What is Correlation Coefficient ?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
In other words, it reflects how similar the measurements of two or more variables are across a dataset.
When one variable changes, the other variables change in the same direction or opposite direction.
Perfect positive correlation :When one variable changes, the other variables change in the same direction.
Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.
[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]
After calculation we get
r = 0.92
Therefore it is a Perfect positive correlation
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Question 3 :
Find the value of 3x3 - 4x2 + x - 5 when x = -3
(A) -54 (B) -71 (C) -32
Todd bought g boxes of granola bars. There are 12 granola bars in each box. Write an expression that shows how many granola bars Todd bought.
The expression that shows the granola bars Todd bought is 12g.
What is an algebraic expression?The algebraic expression stands for the mixture of variables, coefficient, constant, or all three in a mathematical form where both sides are set equivalent to each other.
Given: Todd bought g boxes of granola bars.
There are 12 granola bars in each box.
Let g be the boxes of granola bars.
Therefore, the expression that shows the granola bars Todd bought is 12g.
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factor 6x(x + 12) – 15(x + 12)
Need help please answer ASAP!
Let's see
3x²-9x3x(x-3)3x is one factor
Other one is x-3#2
Mass of 1000 protons
1000×Mass of one proton1.67×10^{-24}×10³1.67×10^{-21}gAnswer:
22. (3) x - 3
23. (4) [tex]1.67 \times 10^{-21}\: \sf g[/tex]
Step-by-step explanation:
Question 22Given expression:
[tex]3x^2-9x[/tex]
Factor out common term [tex]3x[/tex]:
[tex]\implies 3x \cdot x - 3 \cdot 3x[/tex]
[tex]\implies 3x(x-3)[/tex]
Therefore, the two factors are [tex]3x[/tex] and [tex]x-3[/tex]
Question 23[tex]\textsf{Mass of 1 proton}=1.67 \times 10^{-24}\: \sf g[/tex]
[tex]1000=10 \times 10 \times 10=10^3[/tex]
[tex]\begin{aligned}\implies \textsf{Mass of 1000 protons} & = \textsf{mass of 1 proton} \times 1000\\& =(1.67 \times 10^{-24}) \times 1000\\& =1.67 \times 10^{-24}\times 10^3\\ & =1.67 \times 10^{-24+3}\\ & = 1.67 \times 10^{-21}\: \sf g\end{aligned}[/tex]
Paula has a client who wants to invest into an account that earns 4% interest, compounded annually. The client opens the account with an initial deposit of $4,000, and deposits an additional $4,000 into the account each year thereafter.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the eighth deposit is __________.
The balance of the account after the eighth deposit will be $36857 if an account that earns 4% interest, compounded annually.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
P = 4000, r = 4% = 0.04 and an additional $4,000 into the account each year thereafter.
The balance of the account after the eighth deposit;
[tex]A = \rm 4000\times \dfrac{1\times (1+0.04)^8}{1-(1+0.04)}[/tex]
A = 36856.90 ≈ $36857
Thus, the balance of the account after the eighth deposit will be $36857 if an account that earns 4% interest, compounded annually.
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Aaron flips a coin three times, what is the probability of getting only one head?
3/8
1/8
1/2
3/7
What is the Parent Function?
What Are The Transformations?
Answer:
Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15
The zeroes of the function are___
Answer:
The zeros are x = -2, x = 0, x = 4.
Step-by-step explanation:
The zeros describe where the function crosses the x-axis, or where the y-value is zero. In this case, the zeros are x = -2, x = 0, x = 4.
What point can be found by taking the average of the endpoints of a line
segment?
O A. Endpoint
O B. Vertex
O C. Midpoint
O D. Center
Step-by-step explanation:
C. Midpoint
The average is the distance of the line divided by 2
I need help quickly, I'm preparing for a test! Help is appreciated!
Solve each triangle. Round your answers to the nearest tenth. (#4)
The measure of angle ∠A and angle ∠C will be 65.37° and 17.63°. And the measure of the length of CA will be 29.48 inches.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
In triangle ABC, the side AB is 9 in, the side BC is 27 in, and the angle B is 97 degrees.
Then the other two angles and the side CA will be
The side CA is given by the cosine rule. Then we have
[tex]\rm CA^2 = AB ^2+ BC^2 - 2 \times AB \times BC \cos B\\\\\\CA^2 = 9^2 + 27^2 - 2 \times 9 \times 27 \cos 97^o\\\\\\CA^2 = 810 + 59.23\\\\\\CA ^2 = 869.23\\\\\\CA \ = 29.48 \ in[/tex]
Then angle A will be given by the sine rule. Then we have
[tex]\dfrac{27}{\sin A} = \dfrac{29.48}{\sin 97^0}\\\\\\\sin A = \dfrac{27 \sin 97^0}{29.48}\\\\\\\sin A = 0.9090\\\\\\A \ \ \ \ = 65.37^0[/tex]
Then the angle C will be
∠A + ∠B + ∠C = 180°
65.37° + 97° + ∠C = 180°
∠C = 17.63°
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I need some help with these please :')
Step-by-step explanation:
problem 1.
1. 6y = 30
2. y = 5
3. 3x + 2(5) = 16
4. 3x+10=16
5. 3x=6
6. x=2
solution: (2,5)
problem 2.
1. x=7
2. 4(2)-2y=18
3. 28-2y=18
4. -2y= -10
5. y=5
solution (7,5)
problem 3
10x=10
x=1
7(1) +y =-2
y=-9
(1,9)
problem 4
0= -6
no solution
problem 5
0=0
Infinite many
What is the approximate Volume of the cone below?
Answer:
B - 183 cm3
Step-by-step explanation:
volume of a cone is 1/3 x pi x r^2 x H
Answer:Your answer is going to be D
Step-by-step explanation:
1/3 x 3.14 x 10^2 x 7 =732.66
If you help me you have a special place in my heart forever I swear .
Answer:
x = 9
y = 116
Step-by-step explanation:
116 and y are vertically opposite angles.
Vertically opposite angles are equal.
So,
y = 116
116 and ( 13x - 53 ) are linear pair angles.
Sum of linear pair angles is 180,
13x - 53 + 116 = 180
13x + 63 = 180
Subtract 63 on both sides,
13x = 180 - 63
13x = 117
Divide 13 on both the sides,
x = 117 / 13
x = 9
a piece of string measures 2 16/20 meters which of the following is equivalent to the length of the string in meters
The equivalent to the length of the string in meters is 14 / 5 meters
How to find the equivalent length of a string?The length of the string is expressed in a mixed fraction form.
length of the string = 2 16 / 20
let's express it in a simplified form. This is usually in an improper fraction form.
Therefore,
2 16 / 20 = 56 / 20
Hence,
56 / 20 = 14 / 5 meters
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A classroom floor is 20 metres wide.
If the total area of the floor is 300 square metres, how long is it?
Answer:
It is 15 m long.
Step-by-step explanation:
Given
width (b) = 20 m
Area of the floor (A) = 300 m^2
Length (L) = ?
we know
A = L * b
300 = L * 20
L = 15 m
Hope it will help :)
PLSSS HELP ASAP!
(Will give brainliest)
Answer:
Question 3: D, 90°
Question 2: D, 84°
Step-by-step explanation:
Answer:
2. d. 84°
3. d. 90°
Step-by-step explanation:
Q2
32 + 64 + x = 180x + 96 = 180x = 84°Q3
20 + 70 + x = 180x + 90 = 180x = 90°1. 2x - 12 = 6
2. 2x + 6= 8
3. 12 = 12s - 12
4. 14s + 6 = 35
5. 3s - 12 = 6
6. 18t + 9 = 34
7. 21x + 7 = 28
8. 105 = 50y + 5
9. 1/4x - 6 = 24
10. 13x + 2 = 18
11. 6 - 3x = 18
12. 14 + s = 21
13. 28 = 16x - 4
14. 19x + 2 = 40
15. 10t = 194
16. 400x + 100 = 1100
17. - 3x + 43 = 113
1. x=9
2. x=1
3. s=2
4. s= 2.5
5. s=6
6. T=5/6
7. x=1
8. y=2
9. x=120
10. x=16/13
11. x=-4
12. s=7
13. x=2
14. x=2
15. t=97/5
16. x=5/2
17. x=-70/3
