Answer:
13
Step-by-step explanation:
the formula for distance is √(X2-X1)^2 + (y2-y1)^2
=√(5-0)^2 + (12-0)^2
=√5^2 + 12^2
=√25+144
=√169
=13
What is a1
of the arithmetic sequence for which a3=126
and a64=3,725
a
64
=
3
,
725
?
In an arithmetic sequence, every pair of consecutive terms differs by a fixed number c, so that the n-th term [tex]a_n[/tex] is given recursively by
[tex]a_n=a_{n-1}+c[/tex]
Then for n ≥ 2, we have
[tex]a_2=a_1+c[/tex]
[tex]a_3=a_2+c = (a_1+c)+c = a_1 + 2c[/tex]
[tex]a_4=a_3+c = (a_1 + 2c) + c = a_1 + 3c[/tex]
and so on, up to
[tex]a_n=a_1+(n-1)c[/tex]
Given that [tex]a_3=126[/tex] and [tex]a_{64}=3725[/tex], we can solve for [tex]a_1[/tex]:
[tex]\begin{cases}a_1+2c=126\\a_1+63c=3725\end{cases}[/tex]
[tex]\implies(a_1+63c)-(a_1+2c)=3725-126[/tex]
[tex]\implies 61c = 3599[/tex]
[tex]\implies c=59[/tex]
[tex]\implies a_1+2\times59=126[/tex]
[tex]\implies a_1+118 = 126[/tex]
[tex]\implies \boxed{a_1=8}[/tex]
An arc of 10 meters is formed by a central angle A on a circle radius 4. The measure of A In degrees (to two decimal places) is___.
A. 143.24
B. 36.76
C. 2.50
D. 216.76
Answer:
arc length = circumference • [central angle (degrees) ÷ 360]
central angle (degrees) = 360 * arc length / circumference
circumference = PI * 2 * 4 = 25.1327412287
central angle (degrees) = 360 * 10 / 25.1327412287
central angle (degrees) = 143.2394487828
answer is A--------
Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Therefore, the coordinates of vertex S are (2,0,-2).
a gym class has 10 boys and 12 girls. how many ways can a team of 6 be selected if the team must have the same number of boys and girls
Answer:
The number of ways of selecting the team is 26,400 ways.
Step-by-step explanation:
Given;
total number boys in the gym, b = 10 boys
total number of girls in the gym, g = 12 girls
number of team to be selected, n = 6
If there must equal number of boys and girls in the team, then the team must consist of 3 boys and 3 girls.
Number of ways of choosing 3 boys from the total of 10 = [tex]10_C_3[/tex]
Number of ways of choosing 3 girls from a total of 12 = [tex]12_C_3[/tex]
The number of ways of combining the two possibilities;
[tex]n = 10_C_3 \times 12_C_3\\\\n = \frac{10!}{7!3!} \ \times \ \frac{12!}{9!3!} \\\\n = \frac{10\times 9 \times 8}{3\times 2} \ \times \ \frac{12\times 11 \times 10}{3\times 2} \\\\n = 120 \times 220\\\\n = 26,400 \ ways[/tex]
Therefore, the number of ways of selecting the team is 26,400 ways.
Can someone help me with this problem
Answer:
3/11
Step-by-step explanation:
3w2 – 21w = 0
Need some help.
Answer:
The solutions are w=0 ,7
Step-by-step explanation:
3w^2 – 21w = 0
Factor out 3w
3w(w-7) =0
Using the zero product property
3w=0 w-7=0
w =0 w=7
The solutions are w=0 ,7
URGENT HELP
The gradient of the tangent to the curve y = ax + bx^3 at the point (2, -4) is 6.
Determine the unknowns a and b.
a=?
b=?
Answer:
a = -6
b = 1
Step-by-step explanation:
The gradient of the tangent to the curve y = ax + bx^3, will be:
dy/dx = a + 3bx²
at (2, -4)
dy/dx = a+3b(2)²
dy/dx = a+12b
Since the gradient at the point is 6, then;
a+12b = 6 ....1
Substitute x = 2 and y = -4 into the original expression
-4 = 2a + 8b
a + 4b = -2 ...2
a+12b = 6 ....1
Subtract
4b - 12b = -2-6
-8b = -8
b = -8/-8
b = 1
Substitute b = 1 into equation 1
Recall from 1 that a+12b = 6
a+12(1) = 6
a = 6 - 12
a = -6
Hence a = -6, b = 1
Open the graphing tool one last time. Compare the graphs of y=log (x-k) and y=log x+k in relation to their domain, range, and asymptotes. Describe what you see.
Answer:
sorry I don't know the answer
Answer:
For the equation y=log(x-k), the domain depends on the value of K. Sliding K moves the left bound of the domain interval. The range and the right end behavior stay the same. For the equation y=log x+k, the domain is fixed, starting at an x-value of 0. The vertical asymptote is also fixed. The range of the equation depends on K.
Step-by-step explanation:
A man owns 3/4 of the share of a business and sells 1/3 of his
shares for Birr 10,000. What is the value of the business in Bir?
Given:
A man owns 3/4 of the share of a business and sells 1/3 of his shares for Bir 10,000.
To find:
The value of the business in Bir.
Solution:
Let x be the value of the business.
It is given that a man owns 3/4 of the share of a business and sells 1/3 of his shares for Bir 10,000.
[tex]x\times \dfrac{3}{4}\times \dfrac{1}{3}=10000[/tex]
[tex]x\times \dfrac{1}{4}=10000[/tex]
Multiply both sides by 4.
[tex]x=4\times 10000[/tex]
[tex]x=40000[/tex]
Therefore, the value of the business is 40,000 Bir.
6
1
10 points
Find the probability that a randomly selected person's birthday is not in May. Ignore leap years.
31
334
31
365
334
365
11
2
3
12
Previous
Answer:
c. [tex]\frac{334}{365}[/tex]
Step-by-step explanation:
May has 31 days and a normal year is 365 days, so the probability is [tex]\frac{31}{365}[/tex]
The probability that isn't in May is: 1 - [tex]\frac{31}{365}[/tex] = [tex]\frac{334}{365}[/tex]
Which graph shows the solution to the given system of inequalities? [y<6x+1 y<-3.2x-4
Answer:
VERY NICE RACK U HAVE MAM
Step-by-step explanation:
Answer:
Its a
Step-by-step explanation:
found on another thing and im taking test
the coefficients corresponding to k=0,1,2,5 in the expression (x+y)^5 are
Answer:
Step-by-step explanation: you got trolded
HELP ASAP!!!!!!
Thank you so much
We know
[tex]\boxed{\sf P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]
[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]
[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]
[tex]\\ \sf\longmapsto p(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]
m:n=3:5
We know
[tex]\boxed{\sf M(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]
[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]
[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]
[tex]\\ \sf\longmapsto M(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]
The sum of two binomials is 12x2 − 5x. If one of the binomials is x2 − 2x, the other binomial is:
1. 11x2 − 7x.
2. 12x2 − 3x.
3. 11x2 − 3x.
4. None of these choices are correct.
Answer:
C. 11x² - 3x
Step-by-step explanation:
(12x² - 5x) - (x² - 2x)
12x² - 5x - x² + 2x
12x - x² - 5x + 2x
11x² - 3x
distance between 4, -4 and -7, -4
Step-by-step explanation:
here's the answer to your question
Answer: Distance = 11
Step-by-step explanation:
Concept:
Here, we need to know the idea of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Find the distance between A and B, where:
A (4, -4)B (-7, -4)[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance=\sqrt{(4+7)^2+(-4+4)^2}[/tex]
[tex]Distance=\sqrt{(11)^2+(0)^2}[/tex]
[tex]Distance=\sqrt{121+0}[/tex]
[tex]Distance=\sqrt{121}[/tex]
[tex]Distance=11[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which expression is equivalent to -6(-2/3 + 2x)?
Answer:
4-12x
Step-by-step explanation:
-6 ×(-2/3 + 2x)
2 × 2-12x=
4-12x
Question 7 of 13
Find the solution to the system of equations,
5x - 3y - Z= 6
-4x + 5y + z = 6
Х
+ 3z = 10
Answer:
D. x = 4, y = 4, z = 2
Step-by-step explanation
Plugged in given answers as trying to substitute is impossible, already tried all combinations
А _______ equation can be written in the form ax2 + bx+c=0 where a, b, and c are real numbers, and a is a nonzero number.
Fill in the blank.
A) quadratic
B) quartic
C) linear
D) cubic
Wrong answers WILL be reported. Thanks!
Answer:
A) quadratic
Step-by-step explanation:
ax2 + bx+c=0
Since the highest power of the equation is 2
A) quadratic -2
B) quartic- 4
C) linear- 1
D) cubic-3
please help me with this on the image
Answer:
ik only 1 of them and i dont even know if this is correct...
a) A
I don’t know how to do this
Answer:
8 = h
Step-by-step explanation:
see attached photo for explanation
If the length is 10 cm and the width of a rectangle is 3cm , what is the area
Answer: 30cm
Step-by-step explanation:
The area of a rectangle is determined by length times width
Equation: A=LW
10cm×3cm = 30cm
The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
[tex][(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ][/tex]
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
[tex]X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401[/tex]
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.
Look at the figure. Find the value of x.
K
x + 5
J
L
2X-7
M
JK=JM
[tex] \\ \sf \longmapsto \: x + 5 = 2x - 7 \\ \\ \sf \longmapsto \: x - 2x = - 7 - 5 \\ \\ \sf \longmapsto \: - x = - 12 \\ \\ \sf \longmapsto \: x = 12[/tex]
Help I don’t get this
Answer:
Step-by-step explanation:
5t² + 4t = 5t² + 4 if and only if t=1.
A zero coefficient makes the value of the term equal to zero.
Answer: 5t to the second power and 5t to the second power. I don't know the answer to b.
Step-by-step explanation:
Select the correct answer. Which graph represents this inequality? y ≥ 4x − 3
Step-by-step explanation:
You didn't put the graph, but you can compare between your graphs and the picture.
Brainliest please
The graph that represents this inequality y ≥ 4x − 3 is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that the inequality is;
y ≥ 4x − 3
The slope of the inequality is 4.
The equation of the red line is y = 4x − 3
The shading is above the line and the line is solid, that means y is greater than or equal 4x − 3
The graph of this inequality y ≥ 4x − 3 is attached below.
Learn more about inequalities here:
https://brainly.com/question/27425770
#SPJ2
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
PLEASE HELP ME AND BE CORRECT
Answer:
please someone help me with my latest question
Answer:
41 units
Step-by-step explanation:
Its the reflection the length are same
https://www.drfrostmaths.com/util-generatekeyskillpic.php?name=AnglePoint4&width=400¶ms=%5B61%2C0%2C%22y%22%2C4%5D
Answer:
Complementary angle
<y+61° =90°
<y = 90°- 61°
<y =29°
I Hope this helps.
Foot Locker is having a 60% off sale on shorts. John paid $18 for a pair of shorts that were on sale. What was the original price of the shorts?
Answer:
=$45
Step-by-step explanation:
$18=40%
18÷4=4.5
$4.5=10%
4.5×10=45
$45=100%
Find the volume of a cone whose height is 12 and whose radius is 4. Use 3.14 for Pi and round your final answer to one decimal place.
Answer:
201.088 cubic units
Step-by-step explanation:
Given data
height= 12 units
radius= 4 units
The expression for the volume of a cone is given as
Volume = 1/3*πr^2h
Substitute the given data to find the volume of the cone
Volunme= 1/3* 3.142* 4^2* 12
Volume = 1/3* 3.142* 16*12
Volume= 1/3* 603.264
Volume= 201.088 cubic units
