Step-by-step explanation:
so, it is a quadratic equation :
-3x² + 30x - 90 = 0
the first thing we can do is divide by 3
-x² + 10x - 30 = 0
remember, the formula to solve and find the 2 solutions is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here
a = -1
b = 10
c = -30
x = (-10 ± sqrt(100 - 4×-1×-30))/-2 =
= (-10 ± sqrt(100 - 120))/-2 = (-10 ± sqrt(-20))/-2 =
= (-10 ± sqrt(4×5)i)/-2 = (-10 ± 2×sqrt(5)i)/-2 =
= 5 ± -sqrt(5)i
x1 = 5 - sqrt(5)i
x2 = 5 + sqrt(5)i
remember, i = sqrt(-1), a complex number.
Solve: (4x^2-3x+7)-(x^2+8x-5)
Given polynomial:
(4x²-3x+7) - (x²+8x-5)
⇛ 4x²-3x+7-x²-8x+5
⇛ (4x²-x²) +(-3x-8x)+(7+5)
⇛ (4-1)x²+(-3-8)x+12
⇛ 3x²+(-11)x+12
⇛ 3x²-11x+12
(4x²-3x+7) - (x²+8x-5) = 3x²-11x+12Note:-
When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.
Read more:
Similar Questions
Simplify: (2n-3)/(6n-9) A) 3 B) 1 C) 1/3 D) 1/3n 2. Multiply: (4x+12)/(x^2-2x) × x/(6x+18) A) 2/(3(x-2)) B) 2/(x-2) C) 2/3 D) 4/x 3. Subtract: 8x/(x+1)- 3/(x+1)...
https://brainly.com/question/3597437?referrer
. 8x2 - 50 A) 2(4x - 5)(x - 5) B) 2(2x - 5)(2x - 5) C) 2(2x + 5)(2x + 5) D) 2(2x - 5)(2x + 5) 4) Which binomial is a factor of the polynomial? 3x2 + 7x + 2 A) (...
https://brainly.com/question/15823865?referrer
Answer:
[tex]3x^2-11x+12[/tex]
Step-by-step explanation:
First, distribute the negative:
[tex]4x^2-3x+7-x^2-8x+5[/tex]
Then combine like terms:
[tex]3x^2-11x+12[/tex]
Find the slope of the line that passes through the following points E(4,1 2/3) and F (-2, 2/3)
is a function f(x)= 1/x odd or even?
Answer:
the function is odd.
Step-by-step explanation:
f(x) is even if f(−x)=f(x) . f(x) is odd if f(−x)=−f(x) . Since −1x=−f(x).
Answer:
Odd
Step-by-step explanation:
There are two ways a function can be determined even or odd.
1. Graph
If the line of symmetry is the y=axis, the function is even.
If it can be rotated 180˚ about the origin and lines up with the original equation, it is odd.
If none of the cases above are satisfied, the function is neither.
2. f(-x)
If you substitute -x for x and you get the equation to be the same as before, the function is even.
If you substitute -x for x and you get the previous equation * -1, the function is odd.
If none of the cases above are satisfied, the function is neither.
Moneysaver's Bank offers a savings account that earns 5% interest compounded continuously. If Ravi deposits $3200, how much will he have in the account
after six years, assuming he makes no withdrawals?
Do not round any intermediate computations, and round your answer to the nearest cent
x
5
?
the answer is 4160$
After 6 years of investment of $3200 compounded continuously, final amount in the account will be $4319.55.
Moneysaver's Bank offers a saving account with the features as,
Rate of interest = 5% annualTime of investment = 6 yearsPrincipal amount = $3200Expression to calculate the final amount when compounded continuously,
Final amount = [tex]P.e^{rt}[/tex]
Here, P = Principal amount
r = Rate of interest
t = Duration of investment
By substituting the values in the expression,
Final amount = [tex]3200.e^{0.05\times 6}[/tex]
= 3200(1.3498588)
= 4319.548
≈ $4319.55
Therefore, after 6 years of investment of $3200, final amount in the account will be $4319.55.
Learn more,
https://brainly.com/question/2141828
NEED RATIONAL
G borrowed $15,000 to buy a business. The interest
rate was 11%. If G paid all the interest and the amount
borrowed with a single payment at the end of 16
months, what is the amount of this payment?
Camilla invests $5,000 into an account with a 1.8% interest rate that is compounded monthly. How much money will be in this account after 4 years?
Round your answer to the nearest cent.
Answer:
There would be $5,372.99 in Camilla's account after 4 years.
Step-by-step explanation:
Total Principal $5,000.00
Total Interest $372.99
* interest rate of 1.8% compound monthly is equivalent to annual rate of 1.815%
Camilla will have approximately $5,454.41 in her account after 4 years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Camilla invests $5,000 into an account with a 1.8% interest rate that is compounded monthly.
Now, After 4 years, the investment will grow to:
= $5,000 (1 + (1.8%/12))¹²ˣ⁴
= $5,000 (1 + (1.8%/12))⁴⁸
= $5,454.41
Hence, Rounding this to the nearest cent gives us a final answer of $5,454.41.
So, Camilla will have approximately $5,454.41 in her account after 4 years.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Find the equation of the line through (−8,1) which is perpendicular to the line y=−x/2−6.
Give your answer in the form y=mx+b.
Linear equations can represent parallel lines, perpendicular lines and lines with no relationship at all.
The equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]
The equation is given as:
[tex]\mathbf{y =-\frac x2 - 6}[/tex]
For a linear equation y = mx + b, the slope of the equation is m
So, by comparison:
[tex]\mathbf{m =-\frac 12}[/tex]
The relationship between the slopes of perpendicular lines is:
[tex]\mathbf{m_2 =-\frac 1{m_1}}[/tex]
So, we have:
[tex]\mathbf{m_2 =-\frac 1{-1/2}}[/tex]
[tex]\mathbf{m_2 =2 }[/tex]
This means that, the slope of the line that passes through point (-8,1) is 2
The line equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = 2(x + 8) + 1}[/tex]
Open brackets
[tex]\mathbf{y = 2x + 16 + 1}[/tex]
Simplify
[tex]\mathbf{y = 2x + 17}[/tex]
Hence, the equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]
Read more about linear equations at:
https://brainly.com/question/11897796
what is the area of the rectangle below?
Answer:
B. 120sq. unitsStep-by-step explanation:
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
so
8 * 15 = 120sq. units
one added to the square root of the sum of a number and one is equal to four. find the number
[tex]\stackrel{\textit{one added to the }\sqrt{\qquad }}{1+\sqrt{\quad }}~~,~~ \stackrel{\sqrt{~~}\textit{ of a number and one}}{\sqrt{x+1}}\implies 1+\sqrt{x+1}\stackrel{\textit{equals}}{=}4 \\\\\\ \sqrt{x+1}=3\implies \left( \sqrt{x+1} \right)^2=3^2\implies x+1=9\implies \boxed{x=8}[/tex]
Does Timmy really brush his teeth before bedtime?
Remember when you were a kid and you were told to brush your teeth before
going to bed? How many of us pretended to brush our teeth thinking that no one
would notice? (It probably took more time to pretend than it would have been to
just brush our teeth in the first place.)
Here we have a null hypothesis, an alternative hypothesis, and the data (evidence).
Null the
Were Hypothesis
They rushed
His Teeth
Teled Not truth
e Tea
The Data
Dry Toothbrush
• What level of significance would you choose, 0.1 or 0.01? Explain.
. Would you reject or not reject the null hypothesis based on the data (a dry
toothbrush)? Explain.
Is there anything that could go wrong with your decision? Explain.
• If something could go wrong, what type of error would that be?
Answer:
no he doesnt brush his teeth
Step-by-step explanation:
Find two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum.
The two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
Let the two variables be x and y
If the product of the numbers is 300, hence
xy = 300
x = 300/y ........ 1
If the sum of the first and four times the second is a minimum, then;
P(x, y) = x + 4y .................. 2
Substitute equation 1 into equation 2:
P(x, y) = x + 4y
P(y) = 300/y + 4y
If this function is at mimimum, hence dP/dy = 0
dP/dy = -300/y² + 4 = 0
-300/y² + 4 = 0
-300 + 4y² = 0
4y² = 300
y² = 300/4
y²= 75
y = 7.66
Since xy = 300
x = 300/7.66
x = 39.16
Hence the two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
Learn more here: https://brainly.com/question/19531412
can someone PLEASE help me with this!? I’ve been trying to find the answer but I just couldn’t find it. I’m behind in math and this was due four days ago!!
Answer:
{-2}
Step-by-step explanation:
Answer:
B)-2
Step-by-step explanation:
In functions, X is your input. Y is the output unless specifically stated otherwise :P
Brainliest? <3
Does anyone know this?
Answer:
i think 36???
Step-by-step explanation:
3 x 2 is 6 and 6 x 6 is 36
Im going to be honest, I don't know what I'm doing
Check the picture below.
Simplify (-9k+12k+9)-(10k+3k+4K-8)
Answer:
-14k+17
Step-by-step explanation:
Evaluate each expression if x = 7, y = 1, and z = 8.
=
19. x + y + 2
20. x + 2z
21. 4y
22. 4x – 3z
23. 4x – 17
24. 62 – 52
shto The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
25. 9y + (2x + 1)
26. 14 + 2z
27. 2 : 2
28. xz
29. y - x
30. 24y - 2
31. x2 – 2y + 8
32. 2xz
33. 30y - 40x – 1,000
19, 15.5
20, 25
21, 1/16
22, 4
23, 11
24, 8
25, 19.5
26, 30
27, 4
28, 56
29, 6.5
30, 4
31, 21
32, 112
33, 3,200
here are they
7-2×8+1 evaluate each of the following
Answer:
-8
Step-by-step explanation:
u just do the 2x8 first
Hi! So in equations similar to this, you will need to use PEMDAS.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Now that you know this, reevaluate your equation.
7-2x8+1
Firstly, you must multiply -2 and 8. Leaving you with -16.
7-16+1
Next, subtract 16 from 7.
-9 + 1
Finally, add -9 and 1.
-8
Your final answer is -8.
if i get 45/50 in a test how much percentage is it
Answer:
the answer to your questions is 90%
Suppose all counting numbers are arranged in columns as shown below. Under what letter will the number 2019 appear?
Answer: b
Step-by-step explanation:
In my town, gas prices are always listed to the thousandth place. Since the smallest coin we have is the penny, we have to round them to the hundredth place. If the price of gas is $8.162, what will the price be when we round it to the hundredth place?
3x-9=3
solve if you can
Finding the value of x,
→ 3x - 9 = 3
→ 3x = 3 + 9
→ x = 12/3
→ [ x = 4 ]
Thus, the value of x is 4.
Tim bought 3 pens and 5 pencils at the school store. The pens and pencils
were the same price. He also bought 2 erasers for 50¢ each. He spent $5 total
at the school store. How much is a pen or pencil at the school store?
Answer:
The answer to " How much is a pen or pencil at the school store?" is $0.5
Step-by-step explanation:
3+5=8
-1.00 for erasers
total cost now =4
4/8= $0.5
total cost of everthing =5
Jiro uses fabric to make costumes for a show choir
Answer:
Print it
Step-by-step explanation:
A ___ is a way of expressing a number as a fraction of 100
grade 5
Answer:
Percentage is the answer
Solve
-14 - 7
A. -21
B. -7
C. 7
D. 21
Answer:
since negative and negative are plus we add it but not
change the sign
Step-by-step explanation:
so the answer is -21
hope I helped
Identify the given quadrilateral
Can anyone tell me if these are correct?
Please help me please!!!!!!!!!
Step-by-step explanation:
the radius is diameter divided by 2
7/2/2 =1 .75
circumference of a circle is 2πr
2*22/7*1.75=11
3.14*11 =34.54
which matrix multiplication is defined?
What is the equation of the line shown in this graph?
Answer:
y=1
Step-by-step explanation:
the y values r 1 n even using the calculation it will give 1 as y
Does anyone know how to solve this:
22 - 6x > 4
Answer:
x<3
Step-by-step explanation:
22-6x > 4
solve like a regular equation for x
subtract 22 on both sides
-6x>-18
divide -6
x>3
and since 6 is negative you switch the sign
so
x<3
Willie stands on one side of a cart and pushes with a force of 100 Newtons. Jenny stands on the others side of a filing cabinet and pushes with a force of 100 Newtons. If Willie wants to help Jenny demonstrate balanced forces, what does Willie need to do?
Willie needs to keep same force acting by him on the cart inorder to balance the force.
Let's check how?
F_1=100NF_2=-100N[tex]\\ \sf\longmapsto F_{net}=100-100=0N[/tex]
.Hence verified