Answer:
A) x + 5y = 20
B) x + 3y = 14
Multiplying A) by -1
A) -x -5y = -20 then adding B)
B) x + 3y = 14
-2y = -6
y = 3
x = 5
Step-by-step explanation:
how do i calculate an enlargement
Answer: The formula involves the dimension of the space available divided by the size of the original. In this case, that is 94 divided by 72. The answer is 1.31. Move the decimal point and that is a 131 percent enlargement.
Step-by-step explanation:
The factors of x cube -10x square -53x-42
Answer:
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
Step-by-step explanation:
[tex]x^3 - 10x^2 -53x - 42[/tex]
The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
Using trial and error method we will find the first root of the polynomial.
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
Now by long division or by using synthetic division we can find other factors.
Synthetic Division :
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)[/tex] ------ ( 1 )
Next further factorize x² - 11x - 42
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
What is the general equation for direct
variation?
Answer:
☆ y=kx
Example: if we have x= 3 and y= 15
Find y?
y= kx
*We know that y= 15 and x= 3
So,
15=k(3)
15=3k
*divide 3 from both sides
K=5
y=5x
y=5(5)=25
☆▪☆▪☆▪☆▪☆
Hope it helps..
Have a great day!!
help meeeeeeeeeeee (25 points)
Answer:
239 mm^2
Step-by-step explanation:
We will split the figure into 3 pieces
The bottom rectangle
A = l*w = 7*3 = 21 mm^2
The top rectangle
A = l*w = 5*10 = 50 mm^2
The right triangle
A = 1/2 b*h = 1/2 ( 16) * (16+5) = 8 * (21) = 168 mm^2
The total area is 21+50+168 =239
what is (x+2)(x-2) equal ?
Answer:
x^2 - 4
Step-by-step explanation:
since it is in the form of
a^2 - b^2 = (a + b)(a - b)
u can directly write x^2 - 2^2
=x^2 - 4
process :
(x + 2)(x - 2)
=x(x - 2) + 2(x - 2)
=x^2 - 2x + 2x - 4
=-2x and plus 2x gets cancel
=x^2 - 4
Classify the following triangle. Check all that apply.
Answer:
A, E, F
Step-by-step explanation:
A: the angles are less than 90 degrees
E: all sides have equal lengths
F: has at least 2 sides equivalent in length
I wil Mark BRANLIEST!! HELP!!!! Consider the graphs of linear function f(x) = 3x, quadratic function g(x) = 3x2, and exponential function h(x) = 2x. Which statement about the functions f, g, and h is correct?
A. As x increases, the value of f(x) will eventually exceed the values of g(x) and h(x).
B. As x increases, the value of g(x) will eventually exceed the values of f(x) and h(x).
C. As x increases, the value of h(x) will eventually exceed the values of f(x) and g(x).
D. As x increases, the values of both f(x) and g(x) will eventually exceed the value of h(x).
Here the Graph: https://www.savvasrealize.com/community/proxy/assessment/68bd51a0599744be92849bd2e08be180/images/bdbcc6b2-8670-4ddc-95a2-a48b6d6da348
Answer:
option C
Step-by-step explanation:
Given :
[tex]f(x) = 3x \\\\g(x) = 3x^2\\\\h(x) = 2^x[/tex]
We will just put values for x and check the function :
Let x = 1
f(x) = 3
g(x) = 3
h(x) = 2
Let x = 10,
f(x) = 30
g(x) = 300
h(x) = 1024
Let x = 100
f(x) = 300
g(x) = 30000
h(x) = [tex]1.27 \times 10^{30}[/tex]
Clearly , as x increases value of h(x) exceeds the value of f(x) and g(x).
80 PTS PLS ANSWER WILL AWARD BRAINLIEST
Answer:
I think it’s A B B A and the last one is D is believe
Step-by-step explanation:
Answer:
2. A
3. A
4. D
5. A
6.
a) 180-n = m
b) 180-40 = 140
7. a) 161-(38+80)=a
b)38+80=118
b)161-118 = 43, a = 43
8. a) NMQ, and NQR
b) NMR and NPR
Step-by-step explanation:
Remember, two vertical angles are always congruent or the same. Complimentary angles equal 90 degrees and supplementary angles equal 180 degrees.
Pls help me I don’t understand how they got 6 on the first one let alone the rest of the questions. -due tomorrow- will give brainliest—thanks
Answer:
(x, y)
-2, 0
-1, -4
1, -6
2, -4
3, 0
Work:
x^2 - x - 6
(-3)^2 -(-3) - 6
9 + 3 - 6 = 9 - 3 = 6
Just substitute the x values, and solve for y
Answer:
Step-by-step explanation:
[tex]substitute x=-3\\ x^{2} -x-6=(-3)^{2} -(-3)-6=9+3-6=12-6=6[/tex]
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
Complete Question
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
a) Determine the total amount they will pay for their house
b) How much of the cost will be interest?
c) How much of the first payment on the mortgage is applied to the principal?
Answer:
a) [tex]X=\$289800[/tex]
b) [tex]I=\$169800[/tex]
c) [tex]Y=\$116[/tex]
Step-by-step explanation:
From the question we are told that:
Time [tex]T=25years =>300 months[/tex]
Initial Mortgage [tex]N=140,000[/tex]
Mortgage [tex]N'=120,000[/tex]
Rate [tex]r=8.5\%=>0.085[/tex]
Monthly Mortgage payment P=\%966
a)
The total amount Payable X is mathematically given as
[tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]
[tex]X=966*300[/tex]
[tex]X=\$289800[/tex]
b)
Generally the equation for Interest I is mathematically given by
[tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]
[tex]I=289800-120000[/tex]
[tex]I=\$169800[/tex]
c)
Generally the equation for Interest I is mathematically given by
[tex]I=Ptr[/tex]
Where
[tex]t= Month +.1month=>1/12[/tex]
Therefore
[tex]I=120000*1/12*0.085[/tex]
[tex]I=850[/tex]
Therefore the first payment on the mortgage is applied to the principal is
[tex]Y=\$966-850[/tex]
[tex]Y=\$116[/tex]
CAN ANYONE HELP ME WITH THIS QUICKKKKK!
Step-by-step explanation:
You can mention the main values like N = 50 , Efm= 2640 in the answer box and put the formula for calculating mean Efm/N and simply show the answer. Goodluck
tìm các giá trị của tham số m để hàm số y = (m-1)x^3 - 3(m-1)x^2 + 3(2m-3)x + m nghịch biến trên R
Answer:
3
Step-by-step explanation:
Anyone know this answer?
Answer:
56 degrees
Step-by-step explanation:
The tangent of any angle in a right triangle is equal to its opposite side divided by its adjacent side.
Therefore, we have the equation:
[tex]\tan x^{\circ}=\frac{15}{10}[/tex]
To isolate [tex]x[/tex], take the inverse tangent of both sides:
[tex]\tan^{-1}(\tan (x^{\circ}))=\tan^{-1}(\frac{15}{10}),\\x^{\circ}=\arctan(\frac{15}{10})=56.30993247\approx \boxed{56^{\circ}}[/tex]
*Recall [tex]\tan^{-1}(\tan x)=x, x\in (-\frac{\pi}{2}, \frac{\pi}{2})[/tex]
What is the area of a circle with a radius of 3.5cm
Answer:
A≈38.48cm²
Step-by-step explanation:
Answer:
38.48 cm²
Step-by-step explanation:
Area of a circle goes by the formula πr²
Substitute in the value of r;
area = π(3.5)²
= 38.48451 cm²
~ 38.48 cm² (2 d.p.)
2 consecutive postive nos are such that the sum of their squares is 113. Find the 2 numbers
Answer:
7,8
Step-by-step explanation:
n^2+(n+1)^2=113; this is the information we are provided in the question.
n^2+n^2+2n+1=113 ; just expanding the numbers
2n^2+2n-112=0 ; moving everything to the same side
n^2+n - 56= 0 ; divide everything by two
(n-7)(n+8)=0 : factor the polynomial
so answers for n are: 7 and -8. since the questions asks for positive numbers -8 cannot be correct.
so n=7
n+1 = 8
Each pair of figures is similar find the missing sie
Answer:
x = 3
Step-by-step explanation:
since they are similar use these ratios
x/9 = 1/3
do cross multiplication
9*1 = 3*x
9/3 = x
3 = x
need help asap!!!!!! Marcel is performing the first test on his company’s new electric car. During the test, the electric car reaches a maximum speed of 81 mph.
The performance test results of the electric car can be modeled by the following table, where x represents time, in seconds at the start of the test, and y represents the speed, in miles per hour.
For this case we have the following variables:
x: represents time, in seconds at the start of the test.
y: represents the speed, in miles per hour.
We have then that:
x = 0 ---> y = 0
x = 12 ---> y = 0
Answer:
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
Find the value of (2x-1) -(y+3) when x=3 and y=1
Answer:
1
Step-by-step explanation:
(2*3-1)-(1+3)
(6-1)-4
5-4
1
If this helps you mark as brainlist
Answer:
putting the Given values in equation
(3*3-1)-(1+3)
=8-4
=4
A car travels at a speed of s miles per hour. It covers 126 miles in 3 hours.
The equation that can be used to find the value of s is
× s = ??
The speed of the car is ??
miles per hour.
PLEASE HELP (also thanks for the answers on the last couple of questions yall)
Answer:
Step-by-step explanation:
This is a distance = rate times time problem where you are calling the rate "speed" instead. So our formula for distance then is distance = speed times time which is
d = st
The distance traveled in 126 miles and the time it took to do this was 3 hours. Filling in those values gives us
126 = s3 or
126 = 3s since multiplication is commutative. Solve for s by dividing both sides by 3 to get
s = 126/3 which is
s = 42 miles per hour
Cho hình chóp SABCD. Lấy I thuộc SA, J thuộc SB sao cho IJ không song song với AB. Lấy điểm K trong miền tứ giác ABCD. Tìm đường cao tuyến của I, J, K với các mặt sau đây: ABCD, SBC, SAD, SCD
Answer:
Step-by-step explanation:
Nina and Jo both ran an 8 km race. Nina took 55 minutes to run the whole race. Jo started the race 3 minutes later than Nina but caught up when they had both travelled 6 km. If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
Answer:
Step-by-step explanation:
First we figure out how fast Nina can run. If Nina can run 8 km in 55 minutes, then her rate is
[tex]\frac{8km}{55min}=.145\frac{km}{min}[/tex] and we can use that in a d = rt table:
d = r * t
Nina .145
Jo
Now we can fill in the distance which is 6 for both, since that is the distance where they met:
d = r * t
Nina 6 = .145
Jo 6 =
Now we go to the info given about the time. If Jo started the race 3 minutes after Nina, that means that Nina is running 3 minutes longer than Jo. Filling in the time info:
d = r * t
Nina 6 = .145 * t + 3
Jo 6 = r * t
As you can see, right now we have 2 unknowns in Jo's row. But we don't have to! We will go to Nina's row where the only unknown is time and solve for t. If d = rt, then
6 = .145(t + 3) and
6 = .145t + .435 and
5.55 = .145t so
t = 38.379 minutes. This means that Jo was running 38.379 minutes when she caught up to Nina (it took Nina 3 minutes longer than that to go 6 km since she was already running for 3 minutes when Jo started the race). If Jo's time is 38.379, we can use that in her row for t and solve for r. If d = rt, then
6 = r(38.379) and
r = .16 km/min
Let's check it without the rounding (rounding takes away from the accuracy). If 6 = .145(t + 3) and Nina's rate not rounded is .145454545 and t = 38.37931034, then, rewriting without rounding:
6 should equal .145454545( 38.37931034 + 3)
6 ?=? .145454545(41.37931034)
6 ?=? 6.0 so
Jo's rate is .16 km/min rounded
rewrite the following linear equations in general form
can someone help explain how to do this?
Answer:
5y = x +15
Step-by-step explanation:
here you have to multiply both sides with 5 to make it a general form ,
5(y) = 5(1/5x) + 5(3)
5y = x + 15
Got a little help from app called Gauthmath. It got concept videos and tutors. You can check it on Play Store and App Store. Really good app in my opinion.
Hope this helps. :)
(125^2 +25^2) (5^2-1) is divisible by 3
Answer:
See Below.
Step-by-step explanation:
We want to prove that the expression:
[tex](125^2+25^2)(5^2-1)[/tex]
Is divisible by three.
We can simplify the second factor:
[tex]=(125^2+25^2)(25-1)\\\\ = (125^2+25^2)(24) \\\\ = (125^2+25^2)(8\cdot 3)[/tex]
Since the second factor is being multiplied by three, we can conclude that the entire expression is divisible by three.
Answer:
It is divisible by 3.
Step-by-step explanation:
(125² + 25²)(5² - 1) ÷ 3
(15625 + 625)(25 - 1) ÷ 3
(16250)(24) ÷ 3
390000 ÷ 3
130000
URGENT: Click on the graph to choose the correct answer to the equation.
x > 2
(Choose one of the pictures as the answer)
Answer:
The first graph.
Step-by-step explanation:
The equation is x is greater than 2. Therefore, the graph needs to shade anything greater than 2, but not 2.
ABCD is a square. Square A B C D is shown. The length of A B is x + 6 and the length of B C is 2 x minus 1. What is the length of line segment DC? 5 units 7 units 11 units 13 units
Answer:
DC = 13units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13units
Hence the length of DC is 13units
Answer: 13 units
Step-by-step explanation:
DC = 13 units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13 units
Hence the length of DC is 13 units
please answer this !!!
You toss a coin 83 times. The coin lands 40 times on heads and 43 times on tails. If you define a fails as a success, what is the relative frequency of tails?
Answer:
to do this we have to divide 43 by 83
0.51807228915
so the frequency is about 51.8%
Expand and simplify (x - 1)(x + 2)(x - 1)
Answer:
[tex](x - 1)(x + 2)(x - 1)=(x-1)^{2}(x+2)[/tex]
Step-by-step explanation:
Use the product rule [tex]x^{a} x^{b}=x^{a+b}[/tex]
Answer:
x^3 -3x + 2
Step-by-step explanation:
(x - 1)(x - 1) =
x^2 -2x + 1 (x+2) =
x^3 + 2x^2
-2x^ - 4x
x + 2
----------------------------
x^3 -3x + 2
harlie is a hotel manager. Their responsibilities include renting rooms for conferences. The hotel charges $250 per day plus $15 per person for the grand ballroom.
Create a formula for the cost, C, in dollars, to rent the ballroom for any number of people for 1 day.
Hint: Use C for cost and n for the number of people. C = ________
How much should Charlie charge to rent the hall for 50 people? What about 100 people?
Rearrange your formula to express n in terms of C (rewrite your formula to solve for n)
How many people could attend a wedding reception if the planners have a budget of:
$4000
$2000
Answer:
Formula: C= $15n + $250
50 People: $1000
100 People: $1750
Formula: n= (C- $250)/ 15
$4000 Budget: 250 Guests
$2000 Budget: 116.67 Guests
Step-by-step explanation:
Since the rental is $250 with an additional charge of $15 per person, we write this as C = $250 + $15n.
With the given equation, simply substitute n for the amount of guests.
C = $250 + $15(50) = $1000
C = $250 + $15(100) = $1750
To solve for n, everything would need to be moved to isolate n. This can be achieved by first subtracting $250 from each side: C- 250= 15n
Then divide both sides by 15, making the new equation: (C-250)/15 = n
Again, substitute C with allowed cost to find the amount of guests allowed.
n = ($4000- 250)/ 15 = 250 People
n = ($2000-250)/15 = 116.67 People
what is 65 divded by 487
Answer:
0.13347022587
Step-by-step explanation:
Answer:
7 R 32
Step-by-step explanation:
0 0 7
6 5 4 8 7
− 0
4 8
− 0
4 8 7
− 4 5 5
3 2
During a game of pool near hit a ball and it follow the path from B to C and then to de- the angles formed by the path of congruent to the nearest 10th of an inch which of the following represents the total distance the ball travels before it stopped at point D
Answer:
please mark me as brainleast