Step-by-step explanation:
Bob's salary : $35000 per year plus 10% after one year
100% = 35000
1% = 100%/100 = 35000/100 = $350
10% = 10×1% = 10×350 = $3500
so in total, his salary will be $35000+$3500 = $38500 after one year.
Sam's salary : $3842.42 per month plus 5% after one year.
100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.
so, 100% 12×3842.42 = $46109.04
1% = 100%/100 = 46109.04/100 = $461.09
5% = 5×1% = 5×461.09 = $2305.45
so, in total, his salary will be $46109.04+$2305.45 = $
How do I solve this?
Answer:
y = 0.8x – 2
Step-by-step explanation:
Slope (m) =
ΔY/ ΔX = 4 /5 = 0.8
y=.8x+b
plug in point
b=-2
Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-intercept of (0,9).
Answer:
f(x) = -3(x+3)(x-1)
Step-by-step explanation:
x = -3 & 1; f(x) = 9
f(x) = a(x-r1)(x-r2)
f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)
9 = a(3)(-1); 9 = a(-3)
a = -3
f(x) = -3(x+3)(x-1)
Answer:
f(x) = -3x^2 - 6x + 9.
Step-by-step explanation:
As the x intercepts are - 3 and 1 we can write it as:
f(x) = a(x - 1)(x + 3) where a is a constant to be found.
As the - intercept is at (0, 9), x =0 when f(x) = 9 so we can also write:
a( 0 - 1)(0 + 3) = 9
(-1)(3)a = 9
a = 9 / -3
= -3.
So the equation is f(x) = -3(x - 1)(x + 3)
In expanded form it is
-3(x^2 + 2x - 3)
= -3x^2 - 6x + 9.
the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.
Answer:
Smaller factor/larger figure = 3/6 = ½
Step-by-step explanation:
Scale factor of similar figures is usually the ratio of one to the other.
In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.
Length of smaller figure = 3
Corresponding length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = ½
Corine needs 4 pieces
each a foot long to make one
friendship bracelet. She has a total of 144 inches of string. How many friendship bracelets can Corina make?
[?]friendship bracelets
Answer:
Corina can make 3 friendship bracelets.
Step-by-step explanation:
Solve for how much string is needed for one friendship bracelet:
4 pieces × 1 foot
4 feet
Convert feet into inches (1 foot = 12 inches):
4 feet × 12 inches
48 inches
Divide the total string by each bracelet's string:
144 inches ÷ 48 inches
3 friendship bracelets
Answer:лаксдкннйд
Step-by-step explanation:
Which is enough information to prove that U|| V?
Answer:
∠4 = ∠8
Step-by-step explanation:
the lines are parallel if a pair of corresponding angles are congruent
Evaluate in 7
0.51
1.95
0.85
1.61
Answer:
We may log in directly in our scientific calculator the given value ln 7 and get an answer of 1.9459. On the other hand, we can rewrite the expression as,
log to the base e or 7 = x
which can be written as,
e^x = 7
The value of x from this is still equal to 1.9459.
Step-by-step explanation:
a.) Where does the turning point of the curve Y= 6- 4x - x^2 occur?
b.) Differentiate with respect to x, [tex]\frac{cos x}{sin 2x}[/tex]
Answer:
Have you gotten the answer. if yes Hmu... Aihs I sit beside you
Step-by-step explanation:
HELPPPPP
A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?
Answer is : 2,8, and 32
Please show steps because I'm very confused
Let x be the first term in the geometric sequence. Then the next two terms in the sequence are xr and xr ², where r is some constant. (This is the defining characteristic of geometric sequences.)
The sum of the first three terms is 42, so
x + xr + xr ² = 42
x (1 + r + r ²) = 42
The third term is 3.2 times the sum of the other two, so that
xr ² = 3.2 (x + xr )
Solve the second equation for r :
xr ² = 3.2 x (1 + r )
We can divide both sides by x since x ≠ 0. (This is obvious, since if x was zero, then all three terms in the sequence would be 0.)
r ² = 3.2 (1 + r )
r ² = 3.2 + 3.2r
r ² - 3.2r - 3.2 = 0
r ² - 16/5 r - 16/5 = 0
5r ² - 16r - 16 = 0
(5r + 4) (r - 4) = 0
==> r = -4/5 or r = 4
Since there are two possible values of r that might work, there are two possible sequences that meet the criteria.
Plug either of these solutions into the first equation:
r = -4/5 ==> x (1 + (-4/5) + (-4/5)²) = 42
… … … … … … 21/25 x = 42
… … … … … … x = 50
r = 4 ==> x (1 + 4 + 4²) = 42
… … … … … 21x = 42
… … … … … x = 2
Then the two possible answers would be
• if r = -4/5, then the three terms are {50, -40, 32}
• if r = 4, then they are {2, 8, 32}
Answer:
Step-by-step explanation:
A geometric series means that we multiply one number by a common ratio to get the second number. Let's say our first number is x, and our common ratio is y. We can write the first term is x, and to get the second number, we multiply x by our common ratio, y. For example, if 5 was the first number and 2 was the common ratio, the second number would be 5*2 = 10, and the third would be 10 * 2 = 20.
For our question, the first number is x, the second is x*y, and the third is x*y*y = x*y²
The sum of these three terms is 42, so we can say
x + x*y + x*y² = 42
Next, the third term is equal to 3.2 times the sum of the other two. First, we have 3.2 times something. That something is the sum of the other two, so we must prioritize calculating the sum of the first two numbers, and then multiply that by 3.2 to get the third. We can write this as
(x + x*y) * 3.2 = x*y²
factor out x
x * 3.2(1 +y) = x*y²
divide both sides by x
3.2(1+y) = y²
expand
3.2 + 3.2y = y²
subtract (3.2 + 3.2y) from both sides to make this a quadratic equation
y²-3.2y-3.2 = 0
use the quadratic formula to solve for y (note that +- here stands for "plus or minus")
[tex]y = \frac{-(-3.2) +- \sqrt{3.2^{2}-4(-3.2)(1)} }{2} \\= \frac{3.2+-\sqrt{10.24+12.8} }{2} \\= \frac{3.2+- 4.8}{2}[/tex]
= -0.8 or 4
With these two possibilities, we can try each in our other equation to see what works.
x + x*y + x*y² = 42
for y = -0.8
x + -0.8x + 0.64x = 42
x - 0.16x = 42
0.84x = 42
multiply both sides by 1/0.84 to isolate the x
x=50
This works, with x (the first number) =50, the second number being 50 * -0.8 = -40, and the third being -40 * -0.8 = 32. 50+(-40) = 10, 10*3.2=32, and 50-40+32 = 42
Next, for y=4, we have
x+4x + 16x= 42
21x = 42
divide both sides by 21 to isolate the x
This works as well, with x=2, the second value being 2*4 = 8, and the third value being 8*4 =32. 2+8=10, 10*3.2 = 32, and 2+8+32 = 42
Find the measure of angle BAC.
Answer:
[tex]\angle 72=BC-86/2[/tex]
[tex]144+86=BC[/tex]
[tex]BC=230[/tex]
[tex]BC=230/2[/tex]
[tex]\angle BAC= 115[/tex]°
~OAmalOHopeO
please help me out i need this answer very fast! 20points!!!!
Graph the system of equations on graph paper to answer the question.
{y=2/5x+4
y=2x+12
What is the solution for this system of equations?
Enter your answer in the boxes.
Translate sentence into equation
nine more than a product of a number and 4 is 8
Answer:
If x is the required number, equation will be 9+4x=8
3y^4/3y^2-6=10 please help I will.mark it as the brainliest answer!
Answer:
y=4
Step-by-step explanation:
you multiply through by 3y^2
3y^4 - 18y^2 =30y^2
Collect like terms
3y^4=48y^2
divide through by y^2
3y^2=48
divide through by 3
y^2=16
take the square root of both sides
y=4
Helppppp please
What is the slope of the line shown below?
Answer:
A.
[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]
please me in math
[tex] \frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1} [/tex]
Step-by-step explanation:
hope this helps you thank you
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]
Use the algebraic identities ⟶
[tex]{\sf(a - b)(a + b) = {a}^{2} - b ^{2}} [/tex][tex]{\sf(a + b) {}^{2} = {a}^{2} + 2ab - {b}^{2}} [/tex][tex]{\sf(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}} [/tex]Squaring on both the sides
[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]
[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]
[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
A mixture of jellybeans is to contain twice as many red as yellow, three times as many green as yellow, and twice as many pink as red. Red jelly beans cost $1.50 per pound, yellow cost $3.00 per pound, green cost $4.00 per pound, and pink only costs $1.00 per pound. How many pounds of each color jellybean should be in a 10 pound canister that costs $2.20 per pound?
Which of the following equations correctly represents the law of sines?
Answer:
Option c is correct
Step-by-step explanation:
From the screenshot I attached.
sinA/a=SinC/c
a/c=SinA/SinC
Thus a=cSinA/SinC
1.Find the first five terms of the recursive sequence.
Answer:
4.5, - 27, 162, - 972, 5832
Step-by-step explanation:
Using the recursive rule and a₁ = 4.5 , then
a₂ = - 6a₁ = - 6 × 4.5 = - 27
a₃ = - 6a₂ = - 6 × - 27 = 162
a₄ = - 6a₃ = - 6 × 162 = - 972
a₅ = - 6a₄ = - 6 × - 972 = 5832
The first 5 terms are 4.5, - 27, 162, - 972, 5832
Polygon D is a scaled copy of Polygon C using a scale factor of 6.
How many times as large is the area of Polygon D compared to the area Polygon C?
Answer:
The area of D is 36 times bigger than C
Step-by-step explanation:
The scale factor is 1:6
We know the ratio of the areas is the ratio of the scale factor squared
1^2 : 6^2
1:36
The area of D is 36 times bigger than C
What is the range of 58, 59, 57, 59, 55
Answer:
4
Step-by-step explanation:
Hi there!
Range = largest number from data given - smallest number from data given
From the given data, 58, 59, 57, 59, 55,
59 is the largest number and 55 is the smallest number
So the range = 59 - 55 = 4
Which function has a domain of all real numbers?
Answer:
c part ....
please mark brainlest
If b = -1, which one is the value of b^3?
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
Express as a trinomial (2x-10)(2x+6)
Answer:
4x² - 8x - 60
Step-by-step explanation:
Given :-
(2x - 10 )(2x + 6)Simplify ,
2x ( 2x + 6) -10(2x +6) 4x² + 12x - 20x -60 4x² -8x -60Trinomial expression :-
4x² - 8x - 60The polynomial function [tex](2x-10)(2x+6)[/tex] expressed as a trinomial is [tex]4x^2 - 8x - 60[/tex].
Given data:
The polynomial function is represented as A.
Now, the value of [tex]A=(2x-10)(2x+6)[/tex].
On simplifying the equation:
From distributive property to multiply the terms:
[tex]A=2x * 2x + 2x * 6 - 10 * 2x - 10 * 6[/tex]
[tex]A=4x^2 + 12x - 20x - 60[/tex]
On simplifying the equation:
[tex]A=4x^2 - 8x - 60[/tex]
Hence, the trinomial is [tex]4x^2 - 8x - 60[/tex].
To learn more about polynomial equations, refer:
https://brainly.com/question/13199883
#SPJ6
if x=(a+4 and y=(a-4),show that xy=a square -16
(a+4) (a-4)
according to formula,
x square - y square : (x+y) (x-y)
(a+4) (a-4)
xy : a square - 4
Find the value of z such that 0.04 of the area lies to the left of z. Round your answer to two decimal places.
Answer: The value of z is -1.75.
Step-by-step explanation:
Given: P(Z<z)=0.04
To find the value of z such that 0.04 of the area lies to the left of z.
We will use z-score table to get the value of z here.
IN z-score table, we have
For P(Z<-1.7507)=0.04
Hence, the value of z is -1.7507.
Its approximate value is -1.75
So the final answer is z=-1.75.
50 points. Please explain each step
Solution given:
Cos[tex]\theta_{1}=\frac{10}{17}[/tex]
[tex]\frac{adjacent}{hypotenuse}=\frac{10}{17}[/tex]
equating corresponding value
we get
adjacent=10
hypotenuse=17
perpendicular=x
now
by using Pythagoras law
Hypotenuse ²=perpendicular²+adjacent ²
substituting value
17²=x²+10²
17²-10²=x²
x²=17²-10²
x²=189
doing square root
[tex]\sqrt{x²}=\sqrt{189}[/tex]
x=[tex]3\sqrt{21}[/tex]
now
In I Quadrant sin angle is positive
Sin[tex]\theta_{1}=\frac{perpendicular}{hypotenuse}[/tex]
Sin[tex]\theta_{1}=\frac{3\sqrt{21}}{17}[/tex]Answer:
sin theta = 3 sqrt(21)/17
Step-by-step explanation:
cos theta = adj / hyp
We can find the opp by using the Pythagorean theorem
adj^2 + opp ^2 = hyp^2
10^2 +opp^2 = 17^2
100 + opp^2 = 289
opp^2 = 289-100
opp^2 = 189
Taking the square root
opp = sqrt(189)
opp = 3 sqrt(21)
Since we are in the first quad, opp is positive
sin theta = opp /hyp
sin theta = 3 sqrt(21)/17
answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
7/6
Step-by-step explanation:
(7x/12)/(x/2)
=7/6
Help!!!!!!!!!!!!!!!!
502.5 = -502.5
Now
x = -502.5
= -5025/10
= -1005/2 feet
Answered by Gauthmath must click thanks and mark brainliest
6.7.35
Question Help
As(t)
800-
A toy rocket is launched from the top of a building 360
feet tall at an initial velocity of 112 feet/second. The
height of the rocket t seconds after launch is given by
the equation s(t)= - 16t2 + 112t+ 360. When does the
rocket reach its greatest height? What is the greatest
height?
600-
400-
200-
0-
0 1
8 9 10
The rocket reaches its greatest height at
feet after
second(s)
Answer:
Step-by-step explanation:
This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!
The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.
If:
[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:
v(t) = -32t + 112 and solve for t:
-112 = -32t so
t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.
Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:
[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and
s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.
please help me with this question <3
9514 1404 393
Answer:
a) 30.7 million
b) 1.5% per year
c) 42.0 million
d) 2017
Step-by-step explanation:
a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.
__
b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.
The population is growing by 1.5% per year.
__
c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.
P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0
The population in Canada in 2021 is predicted to be 42.0 million.
__
d) For this we need to solve for t when P(t) = 40.
40 = 30.7·1.015^t
40/30.7 = 1.015^t
Taking logarithms gives ...
log(40/30.7) = t·log(1.015)
t = log(40/30.7)/log(1.015) ≈ 17.773
In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.
_____
Additional comment
The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.
3. Given the graph below, determine whether each statement is true or false.
Answers:
TrueTrueTrueFalseFalse======================================
Explanation:
In this context, a zero is another term for x intercept or root. This is where the graph either touches or crosses the x axis. This occurs in three locations: x = -3, x = 2, and x = 0. So those are the three roots. That makes the first three statements true, while the remaining two others are false.
Side note: x = 0 doesn't always have to be involved. Its quite possible to have x = 0 not be an x intercept. The term "zero" is a bit misleading in that regard. I prefer either "root" or "x intercept" instead.
