Answer:
[tex]\boxed{\text{The slope is -8.}}[/tex]Step-by-step explanation:
To find the slope of the line, you have to use a slope formula.
Slope formula:
[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
⇒ y2=(-15)
⇒ y1=1
⇒ x2=1
⇒ x1=(-1)
Rewrite the whole problem down.
[tex]\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}[/tex]
So, the slope is -8, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Find the hourly wage for a person with an income of $60376, who works 57 hours a week for 44 weeks.
Answer:
$24.07
Step-by-step explanation:
57×44=2508 hrs
60376÷2508=$24.07 per hr
What is the surface area of this prism?
Answer:
Step-by-step explanation:
front side: 6x3 = 18
back : 6x3 = 18
right:6x2 = 12
left:6x2 = 12
top: 3x2 =6
bottom: 3x2 =6
18 + 18 + 12 + 12 + 6 + 6
= 72
which equation is equivalent to 3(2x - 5) = 4 (x + 3) ?
Step-by-step explanation:
3(2x - 5) = 4(x+3)
Distribute. Multiply 3 by 2x so the product keeps the variable, multiply 3 by 5 and keep the subtraction symbol. Multiply 4 by x so it would be 4x, multiply 4 by 3
(6x-5=4x+12) Answer
A spherical ball has a radius of 2 ft what is the volume in cubic feet of the ball
The Formula for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]
r --> length of radius --> 2ft
Volume = [tex]\frac{4}{3} \pi (2)^3 = \frac{4*8}{3} \pi =33.510[/tex]
The volume is 33.51 cubic feet
Hope that helps!
A pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces. How many different recital programs are possible?
The different recital programs that are possible is 80,730 ways
Combination and permutationPermutation has to do with arrangement while combination has to do with the selection.
According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.
The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]
Hence the different recital programs that are possible is 80,730 ways
Learn more on combination here: https://brainly.com/question/11732255
6. If 2 cards are drawn from a standard deck with replacement, find the probability of drawing a face card and an even number.
Answer:
15/169
Step-by-step explanation:
There are 52 cards in a standard deck. Of those 52 cards, 12 are face cards and 20 are even numbered. To find the probabily in this situation, we multiply 12/52 by 20/52. This gives us 240/2704. This can be reduced to 15/169.
How many ways can you place the letters in the word "PASTURE" into groups of four letters without repetition?
Using the permutation formula, it is found that there are 840 ways to place the letters.
The order in which the letters are placed is important, as PAST is a different arrangement that PTAS, for example, hence the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 letters are taken from a set of 7, hence:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
There are 840 ways to place the letters.
More can be learned about the permutation formula at https://brainly.com/question/25925367
#SPJ1
Answer:35
Step-by-step explanation:
5. The perimeter of a rectangular poultry farm is 38m. If 3 meters are subtracted from its length and 2 meters from its breadth, the length will be two times the breadth. Find the area of the farm?
By solving a system of equations we will find the dimensions of the rectangle, and with these, we will see that the area is equal to 82.31 m^2
How to find the area of the farm?For a rectangle of length L and width W, the perimeter is:
P = 2*L + 2*W
In this case, we know that the perimeter is equal to 38m, then:
38m = 2*L + 2*W
We also know that if we subtract 3 meters from the length and 2 meters from the breadth, the length will e 2 times the breadth.
This is written as:
(L - 3m) = 2*(W - 2m)
Then we have a system of equations:
38m = 2*L + 2*W
(L - 3m) = 2*(W - 2m)
To solve this, we isolate one of the variables in one of the equations, I will isolate L on the second equation:
L = 2*(W - 2m) + 3m
Replacing that on the other equation we get:
38m = 2*(2*(W - 2m) + 3m) + 2*W
Now we can solve this for W.
38m = 4*(W - 2m) + 6m + 2*W
38m = 4*W - 2m + 2*W
38m + 2m = 6*W
40m = 6*W
40m/6 = W = 6.67m
Then the length is:
L = 2*( 6.67m - 2m) + 3m = 12.34 m
So the area of the rectangle is:
A = L*W = 12.34m*6.67m = 82.31 m^2
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
Simplify the expression: 4(− + 7) < 40 *
a > −11.75
b < −11.75
c < −3
d > −3
Answer:x=70
Step-by-step explanation:
STEP
1
:
40
Simplify ——
x
Equation at the end of step
1
:
4 40
— - —— = 0
7 x
STEP
2
:
4
Simplify —
7
Equation at the end of step
2
:
4 40
— - —— = 0
7 x
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 7
The right denominator is : x
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
7 1 0 1
Product of all
Prime Factors 7 1 7
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 0 1 1
Least Common Multiple:
7x
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = x
Right_M = L.C.M / R_Deno = 7
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 4 • x
—————————————————— = —————
L.C.M 7x
R. Mult. • R. Num. 40 • 7
—————————————————— = ——————
L.C.M 7x
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
4 • x - (40 • 7) 4x - 280
———————————————— = ————————
7x 7x
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
4x - 280 = 4 • (x - 70)
Equation at the end of step
4
:
4 • (x - 70)
———————————— = 0
7x
STEP
5
:
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
4•(x-70)
———————— • 7x = 0 • 7x
7x
Now, on the left hand side, the 7x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
4 • (x-70) = 0
Equations which are never true:
5.2 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.3 Solve : x-70 = 0
Add 70 to both sides of the equation :
x = 70
One solution was found :
x = 70
Select the best answer for the question.
15. If the following fractions were converted to decimals, which one would result in
O A.314
O B.5111
O C.317
OD. 1/9
Upon asking I got the rest of the information needed to answer this question.
-> Which one becomes a repeating decimal?
Your answer is D. 1/9.
1/9 = 0.111111111111111111111111111111111 ... or 0.1 repeating. It can be written with a line over the 1 asyou can see in the attached.
This means that D is the answer to your question.
The distance between 2 cities is 7200 miles. How long will it take a plan that flies 600 miles/h to travel between the 2 cities?
Statistics 1
You are buying uniforms for young male military recruits. You know the mean chest size and the standard deviation of the chest size. About what proportion of the chest sizes of the recruits would you expect to be within one standard deviation of the mean chest size? Choose the best answer below
A. 50%, if the mean chest size is Normally distributed
B. 2/3
C. 50%, if the chest sizes are Normally distributed
D. 68%, if the chest sizes are Normally distributed
E. 95%
[tex]$a+a r+a r^{2}+\ldots \infty=15$$a^{2}+(a r)^{2}+\left(a r^{2}\right)^{2}+\ldots \infty=150$. Find $a r^{3}+a r^{4}+a r^{6}+\ldots \infty$[/tex]
Options:
[tex](a) $\frac{1}{2}$\\(b) $\frac{2}{5}$[/tex]
Let
[tex]S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n[/tex]
where we assume |r| < 1. Multiplying on both sides by r gives
[tex]r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}[/tex]
and subtracting this from [tex]S_n[/tex] gives
[tex](1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}[/tex]
As n → ∞, the exponential term will converge to 0, and the partial sums [tex]S_n[/tex] will converge to
[tex]\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}[/tex]
Now, we're given
[tex]a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a[/tex]
[tex]a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}[/tex]
We must have |r| < 1 since both sums converge, so
[tex]\dfrac{15}a = \dfrac1{1-r}[/tex]
[tex]\dfrac{150}{a^2} = \dfrac1{1-r^2}[/tex]
Solving for r by substitution, we have
[tex]\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)[/tex]
[tex]\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}[/tex]
Recalling the difference of squares identity, we have
[tex]\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}[/tex]
We've already confirmed r ≠ 1, so we can simplify this to
[tex]\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15[/tex]
It follows that
[tex]\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12[/tex]
and so the sum we want is
[tex]ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}[/tex]
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Help plssssssssssssssssssss I NEED THIS TODAY!! PLS
Answer:
The first 1 is the answer (a)
Step-by-step explanation:
The sum of three numbers is 10. The sum of twice the first number, 4 times the second number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 28. Find the three numbers.
Answer:
5 2 3Step-by-step explanation:
The given relations allow us to write three equations in the three unknown values. We can let x, y, z represent the three numbers, in order.
__
x +y +z = 10 . . . . . . . the sum of the three numbers is 10
2x +4y +5z = 33 . . . . . designated sum is 33
6x -y = 28 . . . . . . . . 6 times the first is 28 more than the second
__
There are many ways to solve a system of equations like this. Perhaps one of the easiest is to enter the equations as an augmented matrix in your calculator, and let it do the work. (Some calculators will solve the equations directly.)
The three numbers are 5, 2, and 3.
_____
Additional comment
The third equation lets you write an expression for y in terms of x:
y = 6x -28
Substituting this into the first two equations, we get ...
x +(6x -28) +z = 10 ⇒ 7x +z = 38
2x +4(6x -28) +5z = 33 ⇒ 26x +5z = 145
Subtracting the second from 5 times the first of these equations gives ...
5(7x +z) -(26x +5z) = 5(38) -(145)
9x = 45 . . . . . the y-variable is eliminated
x = 5
Use equations from above to find z and y.
z = 38 -7x = 3
y = 6(5) -28 = 2
IM CONFUSED CAN SOMEBODY HELP ME SOLVE THE EQUATION
Answer:
y = - ½(x - 2)² + 3
Step-by-step explanation:
What is the name of the Platonic solid shown below?
A. Hexahedron
B. Dodecahedron
C. Tetrahedron
D. Octahedron
Answer: c
Step-by-step explanation: The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe
The name of the platonic solid shown is hexahedron.
What are different types of solids?Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.
Hexahedron - Any polyhedron with six faces is called a hexahedron.
Octahedron - An octahedron is a polyhedron with eight faces in geometry.
Dodecahedron - In geometry, a dodecahedron or duo decahedron is any polyhedron with twelve flat faces.
The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.
Learn more about shapes on:
brainly.com/question/303508
#SPJ7
The complete question is attached.
find the range of the data.
133,117,152,127,168,146,174
133, 117, 152, 127, 168, 146, 174.
to find:range.
solution:first arrange the numbers in order, which gives you:
= 117, 127, 133, 146, 152, 168, 174
then subtract the lowest number from the highest, which gives you:
174 - 117
= 57
range= 57.
When fully charged, Jaylin's
computer works for 20 hours.
She uses her computer for about
1.5 hours each day. A low battery
warning comes on when there is
hours of use or less remaining
Answer:
The battery seems to be charging at a rate of 1 percentage point per minute. So the battery should be fully charged at 10:11 AM.
Step-by-step explanation:
! PLS HELP ! In a raffle, one thousand tickets are sold. There
is a grand prize of $4000, a second prize of
$500, and a third prize of $100. What ticket
price would make this game fair?
Answer:
$4.60
Step-by-step explanation:
Guys please help me!!!
Answer:
p = 2
q = -1
k = -1
Step-by-step explanation:
Cosine functions always start above or below 0. So, the one that starts at (0, 1) is f(x) = (p)cosx + q. Sine functions always start at 0. So, the one that starts at (0, 0) is g(x) = (k)sinx.
Using the help image attached, we know that:
p and k = amplitude (top to midline)
Negative when cosx/sinx starts at the bottomq = vertical shift (movement of midline)
For f(x) = (p)cosx + q:
p = 2
q = -1
For g(x) = (k)sinx:
k = -1
Hope this helps!
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written??
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \sf \dashrightarrow \:y =a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6
[distance between any successive Crest or trough]
a = - 4 (flipped)
b = 2π/p = 2π/6 = π/3
k = -2
Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \sf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]
There is not crest given so use distance between troughs
Period (T):-
Distance between two troughs|3-(-3)|6Frequency:-
[tex]\\ \rm\dashrightarrow \dfrac{1}{T}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{1}{6}[/tex]
[tex]\\ \rm\dashrightarrow 0.17Hz[/tex]
Please help me solve these problems
From the dots the parabola’s are the same size just transitioned to different locations.
blue = y = x^2 + 3
Green = y = (x-4)^2
Orange = y = x^2 - 3
Purple = y = (x+4)^2
What is the value of the expression shown below?
−(−4)(-6) − (10 + 15)
-
1|3
Answer:
-27.3 is the ans without decimal its -27-1/3
Answer:
-49 and 1/3
Step-by-step explanation:
− (-4 x -6) − (10 + 15) − 1/3
− (24) − (25) − 1/3
− 24 − 25 − 1/3
−49 − 1/3
-49 and 1/3
BRAINLIEST please if this helped!I need help finding the surface area of this shape
Answer:
1030 [tex]yd^{2}[/tex]
Step-by-step explanation:
split it into 2 different rectangular prisms
first one is 27 yd by 8 yd by 9 yd
second is 10yd by 8 yd by 12 yd
Answer:
1494 [yd²].
Step-by-step explanation:
1) the required area can be calculated as (see the attached picture):
A=A1+A2+A3+A4+A5+A6+2*A7;
2) finally,
A=9*8+17*8+8*12+10*8+(12+9)*8+27*8+2*(27*9+12*10);
A=1494 [yd²].
Note, the suggested solution is not the shortest one.
What is the axis of symmetry for the function f(x)=7−4x+x2?
Answer:
The axis of symmetry is x=2
Step-by-step explanation:
If the probability of receiving a message on the internet today is 8/9, what is the probability of not receiving a message?
[Give the answer as a fraction in simplest form.]
Answer:
The probability is 1/9
Step-by-step explanation:
1 - 8/9 = 1/9
Cos2A + cosec4A = cot A-cot 4A
Answer:
no solution
Step-by-step explanation:
A graphing calculator shows the left-side expression is never equal to the right-side expression for any real-number value of A.
The equation is not an identity, and has no solution.
__
Additional comment
By subtracting the right-side expression from the left-side expression, we get an equation of the form f(A)=0. Any solutions will be x-intercepts of the graph. The graph for this equation never comes close to crossing the x-axis.
A regular octagon with side length = 5.3 meters. What is the total area of the shape? Round to two
decimal places at the end of your calculation.
Answer:
97.31 [tex]m^2[/tex]
Step-by-step explanation:
The area of the octagon is:
[tex]\frac{8 * 5.3 * 2.65\sqrt{3} }{2}[/tex] ~97.31 m^2
Enter the values needed to find the
length AB. (Simplify your answer.)
A(-3a, b)
F
В(3a, b)
AB = ([?])2
✓([?])2 + (0)2
Distance Formula: d = x)2 + (92-y)
C-a Sb)
Enter
Answer:
The missing value is 6a
Step-by-step explanation:
Given:
[tex]\displaystyle \large{A(-3a,b)}\\\displaystyle \large{B(3a,b)}[/tex]
Find:
Missing Value
Distance Formula:
[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
Determine:
[tex]\displaystyle \large{(x_2,y_2)=(3a,b)}\\\displaystyle \large{(x_1,y_1)=(-3a,b)}[/tex]
Input given information above in the formula:
[tex]\displaystyle \large{AB=\sqrt{(3a-(-3a))^2+(b-b)^2}}\\\displaystyle \large{AB=\sqrt{(3a+3a)^2+(0)^2}}\\\displaystyle \large{AB=\sqrt{(6a)^2}}\\\displaystyle \large{AB=6a}[/tex]
The length is 6a but since we want to find the value in the square root then the answer is still 6a
