Answer:
[tex]\displaystyle m = \frac{22}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (1, 3)
Point (10, 25)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{25 - 3}{10 - 1}[/tex]Subtract: [tex]\displaystyle m = \frac{22}{9}[/tex]Answer:
c
Step-by-step explanation:
The number of booker borrowed from a library each week follows a normal distribution. When sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30
Answer:
2.5%
Step-by-step explanation:
Given :
Mean, μ = 190
Standard deviation, σ = 30
Probability that more than 250 books are borrowed ;
x = 250
P(Z > z)
Z = (x - μ) / σ
P[Z > (x - μ) / σ] = P[Z > (250 - 190) / 30]
P(Z > z) = P(Z > 2)
P(Z > 2) = 1 - P(Z < 2) = 1 - 0.97725
P(Z > 2) = 1 - P(Z < 2) = 0.02275
(0.02275 * 100)% = 2.275%
2.5% is closest to 2.275%
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).
Answer:
[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]
[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]
[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]
[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x-10[/tex]
[tex]OAmalOHopeO[/tex]
Find the slope.
Directions: For problems 1 through 3, graph the line by using the given X values and find its slope.
Answer:
Answer is in the picture.
If a point is chosen inside the square, what is the probability that it will also be inside the circle?
Answer:
[tex]79\%[/tex]
Step-by-step explanation:
The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.
Formulas used:
Area of a square with side length [tex]s[/tex] is given by [tex]A=s^2[/tex] Area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:
Area of square: [tex]A=2^2=4[/tex]
Area of circle:
[tex]A=1^2\pi=\pi[/tex]
Therefore, the probability that the point will be inside the circle is:
[tex]\frac{\pi}{4}=0.78539816339\approx \boxed{79\%}[/tex]
Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]Can someone help me with this please
Answer:
.574
Step-by-step explanation:
This can be inputted in a calculator to achieve .57357643
To three decimal places that is .574
The robotics team purchased 3 androids for the purpose of programming. Each of the robots was $398, which included tax. If the tax rate is 8%, what is the TOTAL TAX to be paid?
Answer:
$95.52
Step-by-step explanation:
Number of robots = 3
Cost of each robots = $398
Tax rate = 8%
Amount of tax of each robots = 8% of $398
= 8/100 × $398
= 0.08 × $398
= $31.84
TOTAL TAX to be paid = Amount of tax of each robots × Number of robots
= $31.84 × 3
= $95.52
TOTAL TAX to be paid = $95.52
find the midpoint between this pair of points (-4,10) and (14,0)
Explanation:
The x coordinates are -4 and 14. They add up to -4+14 = 10. Then this cuts in half to get 10/2 = 5. This is the x coordinate of the midpoint.
We'll follow this same idea for the y coordinates as well.
10+0 = 10 which cuts in half to 10/2 = 5, and this is the y coordinate of the midpoint.
Therefore, the midpoint is (5,5).
Coincidentally, the x and y coordinates are the same for the midpoint (both are 5). This won't always happen.
HELP
Line CD passes through points C(3, -5) and D(6,0). What is the equation of line CD in standard form?
60
O 5x + 3y = 18
O 5x - 3y = 30
O 5x - y = 30
O 5x + y = 18
Answer:
Hello the answer is 5x - y = 30!
Step-by-step explanation:
m = (0 (-5))/(6 - 3) = (0 + 5)/(3) = 5/3
y = mx + b
O = (5/3)(6) + b
O = (30/3) + b
O = 10 + b
-10 = b
3y = 5x - 30
3y + 30 = 5x
5x - 3y = 30
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
The diagram shows a square with side length 5cm.
The length of the diagonal is y cm.
Find the exact value of y.
Answer:
5sqrt2
Step-by-step explanation:
Using the pythagorean theorem, we get 5^2+5^2=c^2. C is the diagonal here. 25+25=c^2, c^2=50. c=sqrt50. Simplifying it, we get the diagonal as 5sqrt2.
What is Index Law 2?
please give definition
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.
Answer:
The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.
On a world , the distance between city A and city B is 5,625 inches. The two cities are actually 1688 miles apart. On the same , what would be the distance between city C and city D, two cities that are actually 1296 miles apart? Use a proportion to solve this problem.
Answer:
The distance between C and D is 4.2768 inches.
Step-by-step explanation:
As from A to B the distance is 5.625 inches and actual is 1688 miles
so,
1 mile = 5.625/1688 = 0.0033 inches
So, the distance between C and D is 1296 miles
= 1296 x 0.0033 inches = 4.2768 inches
match the absolute value functions with their vertices
factor x^2-3x-28 using the x method
Answer:
[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]
i need help ASAP please
Answer:
reflection over Y axis
Step-by-step explanation:
Answer:
I believe it is D) a reflection over the Y-axis
Step-by-step explanation
it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)
What type of line is PQ¯¯¯¯¯¯¯¯?
A. median
B. angle bisector
C. side bisector
D. altitude
Answer:
angle bisector
Step-by-step explanation:
Since the line divided the top angle into two equal pieces we call this an angle bisector.
Please help!!!!!!!!!!!!!!
Answer:
choice A is the answer
Step-by-step explanation:
[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]
but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
please help me solve the equations, I re-wrote the question under each of them so you can read it better. Ty
Answer:
45:13/36
46:86/63
47:19/42
48:9/10
49:1/12
Can someone please help me with this I’m struggling
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
What’s the answer? I don’t understand the question and I came to see if you all can help
Answer:
15/2 that is the answer man
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
https://brainly.com/question/22213822
The graph of a relation is shown.
Which of these values could be the slope of the line?
Select two options.
-2
-8/5
0
7/4
3
Answer:
4th option, 7/4 and
5th option, 3
Step-by-step explanation:
The line seems like it will have a positive slope and will not be 0 since it's not passing through the origin
so, possible values are 7/4 and 3
Answered by GAUTHMATH
Answer: The answer would be 7/4, 3
Step-by-step explanation:
When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number
Answer:
a) 1/4
b) 1/6
c) 1/12
Step-by-step explanation:
Let S be the sample space.
S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}
n(s) =12
Events
A: coin with head and die with prime number .
B:coin with head and die with composite number.
C:coin with tail and die with even prime number.
a) A={H2,H3,H5}
n(A) = 3
P(A) =n(A)/n(S)
=3/12
= 1/4
b) B={H4,H6}
n(B)= 2
P(B) = n(B)/n(S)
= 2/12
= 1/6
c) C ={T2}
n(C) = 1
P(C) = n(C)/n(S)
= 1/12
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
