Hey there!☺
[tex]Answer:\boxed{-(b-6)(b+5)}[/tex]
[tex]Explanation:[/tex]
[tex]30+b-b^2[/tex]
Factor 30+b-b^2 by grouping.
[tex]-(b-6)(b+5)[/tex]
Hope this helps!☺
Demi traveled 480 miles in 6 hours. What was her average speed in miles per hour?
choose the congruent angles on the triangle shown below
Answer:
I think it would be angles A and B.
Hope this helps!
Use integration by parts to evaluate the indefinite integral
[ 2x sin(c) dx
Answer:
-2x cos x + 2 sin x + C
Step-by-step explanation:
∫ (2x sin x) dx
If u = 2x, then du = 2 dx.
If dv = sin dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 2x (-cos x) − ∫ (-cos x) (2 dx)
= -2x cos x + 2 ∫ cos x dx
= -2x cos x + 2 sin x + C
Answer:
[tex]\displaystyle \large{2 \sin x - 2x \cos x + C}[/tex]
Step-by-step explanation:
We are given the indefinite integral:
[tex]\displaystyle \large{\int {2x \sin x} \ dx }[/tex]
Using by-part method, we have to substitute u-term and dv appropriately.
By-part is an integration of product rules, when integrated the product rules of differentiation, we’ll obtain:
[tex]\displaystyle \large{\int {u} \ dv = uv - \int {v} \ du}[/tex]
Above is by-part method/formula.
Where 4 terms are presented:
ududvvOur main terms to substitute are u and dv which mean u-term has to be a function that’s differentiatable and dv has to be a function that’s integratable.
The main concept of by-part is to understand how to substitute appropriately which you can simply follow below:
LIATE
Stands for Logarithm, Inverse (Trigonometry), Algebraic, Trigonometric and Exponential.
These are in orders from first to last on what to let u-term first. That means logarithm functions must be the first to substitute themselves as u-term, so if you encounter a logarithmic function and a polynomial function, you must let u = logarithmic function while dv = polynomial.
In this case, we have 2x which is polynomial and sin(x) which is trigonometric. According to LIATE, we have to let Algebraic or Polynomial 2x be first to substitute as u-term, that means our dv is trigonometric sin(x).
Therefore, we have:
u = 2xdu = 2dx dv = sin(x)dxv = -cos(x)Now, substitute these terms in accordingly to formula of by-part.
[tex]\displaystyle \large{\int {2x \sin x} \ dx = 2x \cdot (-\cos x) - \int {-\cos x \cdot 2 \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + \int {2 \cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \int {\cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \cdot \sin x + C}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \sin x + C}[/tex]
__________________________________________________
Summary
Property
[tex]\displaystyle \large{ \int {k f(x)} \ dx = k \int{f(x)} \ dx \ \ \ \ \tt{(k \ \ \ is \ \ \ a \ \ \ constant.)}\\[/tex]
Only shown in explanation.
By-Part
[tex]\displaystyle \large{\int u \ dv = uv- \int v \ du}[/tex]
LIATE
The functions in order that should be u-term from first to last.
Logarithm Inverse TrigonometricThese functions above do not have integration formula by default.
Polynomial (Algebraic)TrigonometricExponential (Last since it’s the easiest to integrate, especially natural exponential)Indefinite Integral
Make sure to always add + C after evaluating the integral, regardless what multiplies or attempts to affect + C, we must always add + C.
__________________________________________________
Find the value of n so that the line perpendicular to y = (-1/4)x-1 passes through the points (n, 3) and (4,11).
Answer:
2
Step-by-step explanation:
You'll need to find the reciprocal of m. -1/4 is your is your m and when you find the reciprocal you flip the number to 4/1 or 4 and change the negative to a positive. Then graph (4,11), you don't need to worry about your y intercept, b, or -1. On your graph go down 4 and over one to the left because it's positive the line should be going like " / " <-- that. Keep going down until your y is three and whatever your x is, is your answer. Ex: (4,11) (3,7) (2,3). Hopefully, you understand :)
Cricket match Australia v England begins 10:00 UK time. Australian time is 11 hours ahead of UK time. What time will the game start in Australia (24 hr clock)
Answer:
21:00 AST
Step-by-step explanation:
10:00 uk time
Australia time is 11 hours ahead of UK time then
10:00 + 11 hours
21:00 AUSTRALIA TIME
OR 9:00 PM Australia time
Javon and Ivy are both given the equation 5-2x-1/3=4, Javon thinks the first step is -2x-1/3=9. Ivy thinks the first step is -2x-1/3=-1. Who is incorrect and why?
Answer:
Javon is incorrect
Step-by-step explanation:
You have to subtract 5 both sides to move it to the other side:
5 -2x -1/3 = 4
5 - 5 - 2x - 1/3 = 4 -5
-2x - 1/3 = -1
Answer:
Javon is incorrect because he didnt subtract 5 from both sides, or add -5
Step-by-step explanation:
I had this question
Given f(x)=10(3−x)+6, what is the value of f(−1)?
Answer: 46
Step-by-step explanation:
10 (3 +1) + 6
30 + 10 + 6
46
What number is 40% of 30?
Input only whole numbers.
Numerical Answers Expected!
Answer for Blank 1:
Answer:
12
Step-by-step explanation:
40/100*30
=12
Answer:
12..
Step-by-step explanation:
off topic but broski i think we're in the same school program?
What is the distance between the following points?
Y
7
10-
9+
8+
7+
6+
5+
4+
3 |
2+
1+
+++++++
1 2 3 4 5 6 7
A++
-3-2
Answer:
+1 is the distanse of the following point
17. Identify the explicit formula for the arithmetic sequence 12, 14, 16, 18, . . . . options: A) f(n) = 12 + 2(n − 1) B) f(n) = 12 + 2(n + 1) C) f(n) = 2 + 12(n + 1) D) f(n) = 2 + 12(n − 1)
Answer:
A) f(n) = 12 + 2(n-1)
Step-by-step explanation:
Arithmetic Sequence Formula:
a(n) = a(1) + (n-1)d
d = 2
a(1) = 12
a(n) = 12 + 2(n-1)
Answer:
Step-by-step explanation:
A) f(n) = 12 + 2(n-1)
The midpoint of PQ is at (6,5) and point P is at (4,9).
What are the coordinates of point Q?
Answer:
B. (8, 1)
Step-by-step explanation:
Given M(6, 5) as midpoint of PQ, and P(4, 9),
let [tex] P(4, 9) = (x_2, y_2) [/tex]
[tex] Q(?, ?) = (x_1, y_1) [/tex]
[tex] M(6, 5) = (\frac{x_1 + 4}{2}, \frac{y_1 + 9}{2}) [/tex]
Rewrite the equation to find the coordinates of Q (x1, y1):
[tex] 6 = \frac{x_1 + 4}{2} [/tex] and [tex] 5 = \frac{y_1 + 9}{2} [/tex]
Solve for each:
[tex] 6 = \frac{x_1 + 4}{2} [/tex]
Multiply both sides by 2
[tex] 6*2 = \frac{x_1 + 4}{2}*2 [/tex]
[tex] 12 = x_1 + 4 [/tex]
Subtract 4 from both sides
[tex] 12 - 4 = x_1 + 4 - 4 [/tex]
[tex] 8 = x_1 [/tex]
[tex] x_1 = 8 [/tex]
[tex] 5 = \frac{y_1 + 9}{2} [/tex]
Multiply both sides by 2
[tex] 5*2 = \frac{y_1 + 9}{2}*2 [/tex]
[tex] 10 = y_1 + 9 [/tex]
Subtract 9 from both sides
[tex] 10 - 9 = y_1 + 9 - 9 [/tex]
[tex] 1 = y_1 [/tex]
[tex] y_1 = 1 [/tex]
Coordinates of Q is (8, 1)
Rewrite the expression 7 to the -2 power
Answer:
1/49
Step-by-step explanation:
7^-2
1/49
7^2 is usually 49 for negative exponents just flip it
Answer:
(7)^-2
Step-by-step explanation:
hope this helps
Why did I get this question wrong?
Step-by-step explanation:
∫ 9 arctan(1/x) dx
If u = 9 arctan(1/x), then:
du = 9 / (1 + (1/x)²) (-1/x²) dx
du = -9 dx (1/x²) / (1 + (1/x²))
du = -9 dx / (x² + 1)
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ln(x² + 1)
Evaluate from x=1 to x=√3.
[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]
[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]
(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)
(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)
(6π√3 − 9π)/4 + 9/2 ln(2)
Answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Step-by-step explanation:
We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].
Now let's say that u = arctan(1/x). The value of 'du' would be as follows:
du = - x / (1 + x²) * dx
If we apply integration by parts, v = 1, and of course u = arctan(1/x):
=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]
Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':
=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx
=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du
=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du
=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )
=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |
So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;
[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]
Now computing the boundaries we have the following answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Question 4
Subtract.
-20 - 10
Help:(
Answer:
-20 - 10 = -30
Answer: -30
Step-by-step explanation: basically -20 + -10 = -30
please help me solve it
Answer:
I SUGHESTED THE ANSWER IS AWhat value of x that satisfies the equation 7/n=8/7
what is the reciprocal of 15 1/4
The reciprocal of 15 1/4 is 4/61
Step-by-step explanation:
15 1/4 multiply 15 by 4 and then add 1 it will give you 61/4 then you change into reciprocal which will be 4/61
A. B. 4 x +1 x+4 =−3 =−12 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Rewrite one side (or both) using the distributive property (Choice B) B Rewrite one side (or both) by combining like terms (Choice C) C Multiply/divide only one side by a non-zero constant (Choice D) D Multiply/divide both sides by the same non-zero constant 2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Answer:
D. Multiply/divide both sides by the same non-zero constant
A. Yes
Just Did It On Khan Academy
Step-by-step explanation:
What number multiplied by itself 3 times equals 10
Answer:
2.1544
Step-by-step explanation:
[tex]\sqrt[3]{10}[/tex] = 2.1544
check: 2.1544^3
What is the greatest common factor of 80 and 16?
Answer:
16
Step-by-step explanation:
did the calculation
Answer:
Therefore the highest common factor of 80 and 16 = 8
wish of the following is most likely the next step in the series? A4a,b8B,C12c,d16D
Simplify 7^8 divided by 7^4
Answer:
2401 is your answer hope this helps
Two similar triangles are shown below: Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle. Which two sets of angles are corresponding angles? (4 points) a ∠w and ∠v; ∠x and ∠y b ∠w and ∠y; ∠x and ∠v c ∠w and ∠z; ∠x and ∠v d ∠w and ∠z; ∠x and ∠y
Answer:
a. ∠w and ∠v; ∠x and ∠yStep-by-step explanation:
We can see that the scale factor is 2
Corresponding sides have length of:
6 and 3; 4 and 2; 3 and 1.5Therefore corresponding angles, opposite to corresponding sides are:
∠x and ∠y; ∠w and ∠vCorrect answer option:
a. ∠w and ∠v; ∠x and ∠yAnswer:
His answer is correct!
Step-by-step explanation:
Got it right
If a side of a square is 10 what the other sides will be
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
all sides are equal
Identities in maths 4sin30°cos45° What is the answer?
Answer:
[tex]4*1/2*\sqrt{2} /2=\sqrt{2}[/tex]
Step-by-step explanation:
The sum of prime number
less than x is 58
find an integer value for x
Answer:
58
Step-by-step explanation:
Prime Numbers = 2+3+5+7+11+13+17
= 58
Given two independent random samples with the following results:n1=13x‾1=186s1=33 n2=13x‾2=171s2=23Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Complete Question
Given two independent random samples with the following results:
[tex]n_2=13\ , \= x_2=171\ s_1=23[/tex]
Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.
Answer:
Step 1 of 3:
[tex]\= x_p = 15[/tex]
Step 2 of 3:
[tex]E =7.79[/tex]
Step 3 of 3:
[tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]
Step-by-step explanation:
Now considering the Step 1 of 3, the point estimate that should be used in constructing the confidence interval is mathematically represented as
[tex]\= x_p = \= x_1 - \= x_2[/tex]
=> [tex]\= x_p = 186 - 171[/tex]
=> [tex]\= x_p = 15[/tex]
Now considering the Step 2 of 3
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100-90)\%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
=> [tex]df = 13 + 13 - 2[/tex]
=> [tex]df = 24[/tex]
From the student t-distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24 \ is \ \ t_{\frac{\alpha }{2} ,df} = 1.711[/tex]
Generally the pooled variance is mathematically represented as
[tex]s_p^2 = \frac{ (13 -1 ) 33^2 + (13 -1 ) 23^2 }{(13 - 1 )(13 - 1)}[/tex]
[tex]s_p^2 = 134.83 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} ,df } * \sqrt{\frac{s_p^2}{n_1} +\frac{s_p^2}{n_2} }[/tex]
=> [tex]E = 1.711* \sqrt{\frac{134.83}{13} +\frac{134.83}{13}}[/tex]
=> [tex]E =7.79[/tex]
Now considering the Step 3 of 3
Generally the 90% confidence interval is mathematically represented as
[tex]\= x_p -E < \mu_1 - \mu_2 < \= x_p +E[/tex]
=> [tex] 15 -7.79 < \mu_1 - \mu_2 < 15 +7.79[/tex]
=> [tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]
If 15 books cost $90, what is the unit price?
Answer:
$6/ book
Step-by-step explanation:
Unit price = Total cost/ total number of items
= 90/15
=$6 per book
Solve the formula C = πd for d
Answer:
[tex]d = \frac{C}{\pi}[/tex]
Step-by-step explanation:
[tex]C= \pi d\\[/tex]
Isolate d ; Divide both sides of the equation by [tex]\pi[/tex]
[tex]\frac{C}{\pi} = \frac{\pi d}{\pi }[/tex]
Simplify
[tex]\frac{C}{\pi} = d\\\\d = \frac{C}{\pi}[/tex]
Note; Another formula for d(diameter) =
[tex]2\times radius[/tex]
A basketball player has a 60% accuracy rate for making free throws. During practice, this player fails to make a free throw three times in a row, but is finally successful on the fourth attempt. P (X equals k )equals (1 minus p )to the power of k minus 1 end exponent p Using the geometric distribution formula, what is the probability of this player successfully making a free throw on the fourth attempt
This question is incomplete, the complete question is;
A basketball player has a 60% accuracy rate for making free throws. During practice, this player fails to make a free throw three times in a row, but is finally successful on the fourth attempt.
p(x=k) = p^k (1-p)^k-1
Using the geometric distribution formula, what is the probability of this player successfully making a free throw on the fourth attempt? Each attempt is independent of each other and answer choices are rounded to the hundredths place.
a.) 0.04
b.) 0.60
c.) 0.40
d.) 0.10
Answer: a.) 0.04
Step-by-step explanation:
Given that;
The basketball player has 60% accuracy of free throws
Now the probability of the player successfully making a free throw on the fourth attempt.
probability of success p = 0.60
number of failure k = 3
the given p.d.f of geometric distribution p(x=k) = p^k (1-p)^k-1
{ 0 <p<= 1 , k=0,1,2,3... }
we substitute our given data
p(x=3) = 0.60^3 (1-0.6)^3-1
= (0.60)^3 (0.40)^2
= 0.216 * 0.16
= 0.035 = 0.04 ( OPTION A)