Answers
Answer:
Rewriting the equation in the form (x+c)²=d by completing the square
[tex]\left(x+5\right)^2=16[/tex]The solutions to the quadratic equation are:
[tex]x=-1,\:x=-9[/tex]Step-by-step explanation:
Given the equation
[tex]x^2+10x+22=13[/tex]
subtract 22 from both sides
[tex]x^2+10x+22-22=13-22[/tex]
simplify
[tex]x^2+10x=-9[/tex]
Rewriting the equation in the form (x+c)²=d by completing the square
[tex]x^2+10x+5^2=-9+5^2[/tex]
[tex]x^2+10x+5^2=16[/tex]
[tex]\left(x+5\right)^2=16[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solve
[tex]x+5=\sqrt{16}[/tex]
[tex]x+5=\sqrt{4^2}[/tex]
[tex]x+5=4[/tex]
[tex]x=-1[/tex]
also solving
[tex]x+5=-\sqrt{16}[/tex]
[tex]x+5=-4[/tex]
[tex]x=-9[/tex]
Therefore, the solutions to the quadratic equation are:
[tex]x=-1,\:x=-9[/tex]
Related Questions
idk how to do this! Pls help me! I need to hurry!
Answers
Answer:
Step-by-step explanation:
What would this be ?
Answers
Answer:
-8,1 mabey I don't really know
The function P gives the numbers of people in millions who own a smart phone t years after year 2000. What does P(17)=2320 tell us about smartphone ownership?
Answers
Answer:
2320 smartphone owners exists in the year 2017
Step-by-step explanation:
Given that:
P is a function ; which gives the number of people who own a smartphone t years after year 2000
If P(17) = 2320
Then the function stated above represents the number of people who own a smartphone 17 years after year 2000
17 years after year 2000 equals ;
2000 + 17 = 2017
Hence, according to the function 2320 smartphone owners exists in the year 2017
The Observatory charges a $100 trip fee, plus $6.50 per student. Identify the rate of change.
Answers
Answer:
i deepends on how many students but if you have 5 kids then its 100$ plus 6.50 each kid
Step-by-step explanation:
Answer: Maybe I agree with the student, deepends on how many students but if you have 5 kids then its 100$ plus 6.50 each kid.
Step-by-step explanation:
3(x + 5) this question must be at least 20 characters long so yeah
Answers
Answer: 3x + 15
Step-by-step explanation:
Distribute the 3 to each of the values within the paranthesis:
3 * x = 3x and 3 * 5 = 15
Combine and the solution is 3x + 15
1/5 - 3/4
im giving 95 points for this so plz give me right answer
Answers
1/5 = 4/20
-3/4 = -15/20
4/20 - 15/20 = -11/20
The answer is -11/20
which equation represents the relationship between x values and y values in the table
y=4x+6
y=2x+4
y=x+4
2x+12
x y
0 4
2 16
4 28
6 40
10 64
Answers
HELP PLZ GUYS I BEG YOU 15 PTS ITS EASYYYYYYY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Jennifer received many pieces of candy for Halloween. She decided to limit herself to only eating 4 pieces every day. On the 14th day after this decision, she had 67 pieces of candy left.
1) Write a linear equation in point-slope form based on the situation above.
2) Define each of your variables based on your equation above.
3) Determine how many pieces of candy Jennifer received on Halloween.
Answers
Answer:
1) The linear equation in point and slope form is y - 67 = -4 × (x - 14)
2) The variables are;
a) The number of candies available = y
b) The number of days Jennifer eats the candies =
c) The slope, m = -4
3) Jennifer received 123 pieces of candies on Halloween
Step-by-step explanation:
The given parameters are;
The number of candies Jennifer eats everyday = 4 pieces
The number of days for which Jennifer eats the daily 4 candies = 14
The number of candies left at the end of the 14th day = 67 candies
1) We note that the rate of decrease in the number of candies = 4 candies/day
Therefore, the slope of the linear equation is m = -4
The y-intercept = The initial amount of candies Jennifer has = c = 67 + 14× 4 = 123 candies
The linear equation in point and slope form is given as follows;
y - 67 = -4 × (x - 14)
2) The variables are;
a) The y-value represents the number of candies available on a specific day
b) The x value represents the number of days Jennifer eats the candies'
c) The slope = The rate of decrease in the number of candies per day = -4
3) The number of candies Jennifer receives on Halloween is given by the y-intercept of the straight line equation as follows;
y - 67 = -4 × (x - 14)
y - 67 = -4·x + 56
y = -4·x + 56 + 67 = -4·x + 123
y = -4·x + 123
Comparing the above equation, with the general form of the straight line equation, y = m·x + c, where, the constant term, c = The y-intercept, we have;
The y-intercept of the equation y = -4·x + 123 = 123 = The initial amount of candies Jennifer received on Halloween.
Who ran further elena or tyler in ten minutes
Answers
Answer:
depends who the faster person is
Answer:
need more information
Divide. Reduce the answer to lowest terms.
1/5 ÷ 3/4
Answers
Answer:
4/15
Step-by-step explanation:
1/5÷3/4 is the same as 1/5•4/3 by using same, change, reciprocal.1/5•4/3=4/15.4/15 cannot be simplified any more so the answer is 4/15.Answer:
4/15 Is the answer
Step-by-step explanation:
I just need to know the answers for number 3. I don’t understand how to do it. Thank u sm!
Answers
Answer:
Step-by-step explanation:
solve the system of equations 8x+2y=6
y= -4x+3
Answers
negative 3 times negative x equals?
Answers
Answer: 3x
Step-by-step explanation:
What is the value of 6(g+2)h when g = 6 and h = 4?
Answers
Answer:
6(6+2)4
6×8×4 = 192
Answer is 192
Answer:
12
Step-by-step explanation:
6(g+2)h=6(6+2)4=6(8)4=484=12
(4x + 13x2 +27x+6) = (4x + 1)
Answers
Answer:
x=-5/53
Step-by-step explanation:
1. Add similar elements: 4x+27x=31x
2. Multiply 13 times 2 to get 26
3. Once again add the similar elements: 31x+26x=57x
4. Expand!!: Originally (4x+1) take away the Parentheses!!
5. 57x+6=4x+1
6. Subtract 6 from both sides: 57x+6-6=4x+1-6
7. Simplify: 57x=4x-5
8. Subtract 4x from both sides: 57x-4x=4x-5-4x
9. Simplify: 53x=-5
10. Divide both sides by 53: 53x/53= -5/53
11. x= -5/53
Need help with this thanks
Answers
Answer:
126/420
Step-by-step explanation:
you cross multipy 3/10 and x/420 then you get 1260=10x, then you divide by 10 and get 126
25 POINTS!! State the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family you used in part a. Then, explain how to calculate the hourly wage based on the monthly income and state the hourly wage. Assume that each full-time worker works four 40-hour work weeks per month, and each part-time worker works two 40-hour weeks per month.
Answers
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Step-by-step explanation:
1. Let's review the information given to answer the question correctly:
Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 7,846
Full-time worker = 4 weeks of 40-hour per month
Part-time worker = 2 weeks of 40-hour per month
2. Let's calculate the minimum monthly income and hourly wage per worker
Full-time worker hourly wage = Monthly costs/160
Part-time worker hourly wage = Monthly costs/80
Full-time worker hourly wage = 7,846/160
Part-time worker hourly wage = 7,846/80
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Full-time worker minimum monthly income = Hourly wage * 160
Part-time worker minimum monthly income = Hourly wage * 80
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Let f (x) = 8x^2 + 4 and g(x) = -x^2+ 12x + 10. Which statements below are true for f (x) · g(x)? Select all that apply.
The constant term is 40.
The leading term is 8x^4.
The x term has a coefficient of 12.
The x^2 term has a coefficient of -76.
The x^3 term has a coefficient of 96.
The resulting polynomial has degree 4.
Answers
LCM: 16r⁴+36r²s²+81s⁴,8r³–27s³,8r²–22rs+15s²
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many students are boys?
Answers
Answer: 20 boys
Step-by-step explanation:
4+3 = 7 total parts
let x be one part
7x=35
x=5
4x=20
Find the equation of the line that
- is perpendicular to the line y=3x-1
and
-passes through the point (7,4)
Answers
Answer:
y = -1/3x + 19/3
Step-by-step explanation:
let the equation of the line be y = mx + b
since it is perpendicular to y = 3x - 1, these two lines's gradient when producted gives -1.
hence, 3 x m = -1
m = -1/3
sub m = -1/3 and (7, 4):
4 = -1/3(7) + b
b = 19/3
therefore, equation of the line is y = -1/3x + 19/3
Topic: coordinate geometry
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
show any calculations, including 180 degrees, go step by step pls.
Answers
Answer:
120°, 120°, 60°, 60°
Step-by-step explanation:
m∠1 = 180° - 60° = 120°
m∠1 = m ∠2 (alternate interior)
m∠3 = 60° (vertical to given angle)
m∠4 = m∠3 (alternate exterior)
which is incorrect rounding for 53.864?
Please help me!
Answers
Answer:
52
Step-by-step explanation: This would be incorrect because 53.864 must round up.
Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?
6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
Answers
Answer:
A: 6 + 2(x + 4) = 1/2(3 - x)
Jennifer earns $7.60 per hour working after school. She wants to buy a musical instrument and she needs at least $500. Write an inequality that describes how many hours she must work to buy the instrument.
Answers
Answer: 7.60x ≥ 500, where x represents the numbers of hours worked.
Step-by-step explanation:
What is the ratio 15 to 35 written as a fraction in lowest terms? 13 37 35 57
Answers
Answer:
Step-by-step explanation:
15:35 should be 3/7
a positive number multiplied by a negative number equal a positive number. True or False
Answers
Answer: False
Step-by-step explanation:
Example 3 times -3= -9
Answer: False
Step-by-step explanation:
Positive * Positive = Positive
Negative * Positive = Negative
Negative * Negative = Positive
Calculate surface area of a sphere with a radius of 13.
Answers
Answer:
2123.72
Step-by-step explanation:
A=4πr2=4·π·132≈2123.71663
Answer:
2120 (rounded off to 3 s.f.)
Formula:
Surface area of sphere = 4×pi×r²
Step-by-step explanation:
Apply the formula with the radius as 13:
4×pi×13² = 4×pi×169
= 676pi
= 2120 (rounded off to 3 s.f.)
I need help please )):
Answers
Christina biked 36 miles in 6 hours. If she biked at a constant speed, how many miles did she ride in one hour?
Answers
Answer:
6
Step-by-step explanation:
because you divided the amount of mile by the amount of time it took to get your answer
Find the vertical horizontal and slant asymptotes if any for f(x)=2x^3+24x^2+35x-175/x^2+14x+45
Answers
Answer:
A on edge
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
took test