Answers
Answer:
[tex]x = -1[/tex]
Step-by-step explanation:
To do the last question using the quadratic formula, you first need the equation in standard form.
ax² + bx + c = 0.
To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.
2(x - 2)(x + 1) = x² - 4x - 5 Expand brackets first using FOIL
2(x² + x - 2x - 2) = x² - 4x - 5 Collect like terms in brackets (x - 2x = -x)
2(x² - x - 2) = x² - 4x - 5 Distribute, multiply bracket numbers by "2"
2x² - 2x - 4 = x² - 4x - 5 Now make the equation equal 0
2x² - 2x - 4 - x² = x² - 4x - 5 - x² Subtract x² from both sides
x² - 2x - 4 = -4x - 5 "x²" eliminated from the right side. Simplify left side.
x² - 2x - 4 + 4x = -4x - 5 + 4x Add 4x to both sides.
x² + 2x - 4 = -5 "4x" eliminated from right side. Simplify left side.
x² + 2x - 4 + 5 = -5 + 5 Add 5 to both sides to eliminate it on the right.
x² + 2x + 1 = 0 Simplified left side.
This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.
a = 1; b = 2; c = 1
Substitute into the quadratic formula
[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex] (Please ignore the Â, it's a formatting error)
[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex] Simplify the square root
[tex]x = \frac{-2±\sqrt{0} }{2}[/tex] The square root of 0 is 0.
[tex]x = \frac{-2}{2}[/tex] The numerator can only be -2. Simplify the fraction
[tex]x = -1[/tex] Only one answer for "x".
Whenever the square root equals "0", there will only be one answer for "x".
Related Questions
a food truck sells salad for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads ans drinks in one day was $836.50. How many salads were sold that day?
Answers
Answer:
93
Step-by-step explanation:
s= salads d= drinks
$6.5s + $2d = $836.5
s + d =209
s = 209-d
6.5 (209-d) + 2d = 836.5
1358.5 - 6.5d + 2d = 836.5
-4.5d = -522
d = 116
s = 209 - 116 = 93
T=42-0.7t how fast did the temperature drop?
Answers
The given equation describes a linear relationship between temperature and time. The slope, -0.7, indicates that the temperature is dropping at a rate of 0.7 degrees per unit of time.
Explanation:The equation given, T=42-0.7t, is in the form of a linear equation, y=mx+b, where T is the temperature in degrees Celsius, t is the time, 42 represents an initial temperature, and -0.7 is the slope representing the rate of temperature change over time.
In this equation, the slope, -0.7, tells us that the temperature is decreasing or dropping at a rate of 0.7 degrees per unit of time. This could be per minute, per hour, etc., depending on the context given.
Note that because the '-0.7' is negative, we know that the temperature is decreasing, or dropping, rather than increasing. If it were positive, it would mean the temperature is rising. Thus, when you're asked how fast the temperature is dropping, the answer based on this equation is that it's dropping at a rate of 0.7 degrees per unit of time.
Learn more about Rate of Temperature Change here:https://brainly.com/question/11482539
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The temperature drops at a rate of 0.7 degrees per time unit, as indicated by the coefficient of t in the equation T = 42 - 0.7t.
The equation given, T = 42 - 0.7t, suggests a relationship between temperature (T) and time (t), where the temperature drops over time due to some cooling process, such as a cold front arriving. To determine how fast the temperature is dropping, we look at the coefficient of t in the equation, which is -0.7. This means that for every unit of time that passes, the temperature drops by 0.7 units. Thus, the rate of temperature drop is 0.7 degrees per time unit, assuming the temperature is measured in degrees and time in matching time units (likely minutes or seconds).
What is the range of the equation ?
Answers
Option D:
all real numbers
Solution:
Definition of domain:
The domain of the function is the set of all possible
x-values (independent variable).
Definition of range:
The range of a function is the set of all possible resulting values
of y-values (dependent variable).
i.e The range of a function is the resulting y-values we get after substituting all the possible x-values.
Given function: [tex]y=\log_8x[/tex]
Domain of y: (0, ∞) (or) {x | x > 0}
Range of y: (–∞, ∞) (or) {y | y > R}
i.e all real numbers
Option D is the correct answer.
Hence the range of y is all real numbers.
The graph for the equation y=-2x+1 is shown below. If another equation is graphed so that the system has no solution, which equation could that be
Answers
This line is parallel to the original line so they never intersect
Therefore the answer is no solution
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
your welcome :) and sorry that I'm a bit late
total area of the trapezoid
meters. What is the length of
2 The trapezoid below is made up of a square and a triangle. The total area of the
is 57.5 square meters. The area of the triangle is 32.5 square meters. What is the
a side of the square?
A 5 meters
B 25 meters
C 90 meters
D Not enough information is given.
Answers
Answer:
A 5 meters
Step-by-step explanation:
57.5 - 32.5 = 25
25 cubed is 5
Find two consecutive even integers such that the sun of the larger and twice the smaller is 62.
Answers
Answer:
20 and 22.
Step-by-step explanation:
Let the consecutive integers be a and b
Then b = a + 2
a is the smaller integer.
[tex]\begin{array}{rcl}2a + b & = & 62\\2a + a + 2& = & 62\\3a + 2 & = & 62\\3a & = & 60\\a & = & \dfrac{60}{3}\\\\& = & \mathbf{20}\\\end{array}[/tex]
a = 20
b = 20 + 2 = 22
The two integers, in ascending order, are 20 and 22.
Check:
2(20) + 22 = 62
40 + 22 = 62
62 = 62
OK.
Find the 20th term of the arithmetic sequence 15, 9, 3, -3, ...
Answers
The 20th term is -106
15,9,3,-3,-9,-15,-21,-28,-35,-41,-46 (10) -6 x 10 = -60
-60 + -46
-106
You're just subtracting by 6.
Answer:
-99
Step-by-step explanation:
you subtract by 6 every number.....
-3-6=-9
-9-6=-15
so on and so on until you get to the 20th term.....
Widget Wonders produces widgets. They
have found that the cost, o(x), of making x
widgets is a quadratic function in terms of x.
The company also discovered that it costs
$20.50 to produce 3 widgets. $60.50 to
produce 7 widgets, and $133 to produce 12
widgets.
What is the total cost of producing nine widgets
Answers
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50
In a class room of 30 students, 18 are female and 12 are male. If you randomly select one person, what is the probability you will select a female
Answers
18/30 = 0.60 .
If 2y + 6 = 1 −3y, then y = −−−−−−
Answers
Answer:
y = -1
Step-by-step explanation:
Add 3y to both sides:
2y + 3y + 6 = 1 - 3y + 3y
Simplify:
5y + 6 = 1
Subtract 6 from both sides to isolate the y value:
5y + 6 - 6 = 1 - 6
Simplify:
5y = -5
Divide by 5 on both sides to solve:
5y/5 = -5/5
Simplify:
y = -1
The Indian Ocean is 2/10 of the area of the world’s oceans. What fraction represents the area of the remaining oceans that make up the world’s ocean? Wrote in simplest form
Answers
Answer I believe it would just be 8/10
Step-by-step explanation:
You have 2/10 of the worlds ocean which = Indian Ocean
So Your remaining ocean (10-2 = 8)
Also known as 8/10
The remaining oceans make up 4/5 of the world's oceans after subtracting the 1/5 that represents the Indian Ocean.
If the Indian Ocean covers 2/10 (or 1/5 when simplified) of the world's oceans, then the fraction representing the remaining oceans is found by subtracting this fraction from the whole (1, as the whole represents all of the world's oceans).
So, the calculation to find the fraction of the area of the remaining oceans would be:
1 - 2/10 = 1 - 1/5 = 5/5 - 1/5 = 4/5
Therefore, the remaining oceans make up 4/5 of the area of the world's oceans.
Help help help help
Answers
Answer:
b=[tex]\frac{t-5}{4}[/tex]Step-by-step explanation:
4b+5=t
First, you must get the variable alone! Substract 5 from both sides!
4b+5=t
-5 -5
The 5 cancels out because 5-5=0
The new equation is 4b=t-5
You must divide by 4 to get the variable alone since your solving for b!
4b=t-5
4 4
b= [tex]\frac{t-5}{4} \\[/tex]
This is your answer!
Shawn's father gave him $168. Shawn bought 10 books, each of which cost $10. How much money does Shawn have left?
will make brainliest
Answers
Answer:
68$
Step-by-step explanation:
cost of 10 book= 10$ * 10= 100$
now,
Remaining money= 168$-100$
=68$
Answer:
$68
Step-by-step explanation:
If each of the 10 books costs $10, you must multiply $10 x 10 to get $100. Then, you do $168 - $100 and get $68.
You invested into a content management company that specializes in peer to peer networks four years ago with a stock value
of $56.30 a share. Today, a single share of the company is worth $32.21. Given this information, determine the decay factor
for the four year period and round your answer to the hundredth place.
a 57.0
C. 570
b. 0.57
d. 1.57
Answers
Answer:
0.57
Step-by-step explanation:
56.30 divided by 1.57=32.21
The school that Julia goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 5 adult tickets and 13 child tickets for a total of $159. The school
took in $51 on the second day by selling 1 adult ticket and 5 child tickets. What is the price each
of one adult ticket and one child ticket?!
Answers
We have a system of equations in two variables, namely, a and c. Use the substitution to find a and c.
Answer:
The price of 1 adult ticket is $11, while the price of one child ticket is $8.
Step-by-step explanation:
Let's identify what we already know:
1) On the first day of ticket sales, the school sold $159 worth of tickets.
2) On the first day, they sold 5 adults tickets, and 13 adult tickets.
3) The school sold $51 worth of tickets on the second day.
4) The school sold 1 adult ticket, and 5 child tickets.
Let's create two formulas:
(5 times x) + (13 times y) = $159
(1 times x) + (5 times y) = $51
The sale price of a sweater is $48. The price is 20% less than the original price. What was the original price.
Answers
The original price of the sweater, before a 20% discount, was found to be $60. This was calculated by dividing the sale price of $48 by 0.80, as the sale price represents 80% of the original price.
Explanation:The student is asking how to find the original price of a sweater given that the sale price is $48 and this sale price represents a 20% discount from the original price.
To find the original price, we need to understand that the sale price is 80% of the original price (100% - 20% discount). Let's denote the original price as P. We can set up the equation P * 0.80 = $48. Solving for P, we get P = $48 / 0.80
The calculation will give us the original price which is $60. The original price of the sweater was $60 before the 20% discount was applied.
Final answer:
The original price of the sweater was $60.
Explanation:
Let x be the original price of the sweater.
According to the given information, the sale price of the sweater is $48, which is 20% less than the original price.
So, we can set up the equation as follows-
Original Price - Discount = Sales Price
x - 0.2x = $48
Simplifying:
0.8x = $48
Dividing both sides by 0.8, we get:
x = $60
Therefore, the original price of the sweater was $60.
3x^+7x-6 factor completely
Answers
The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
Step-by-step explanation:
To find the factors of the equation,
1) Multiply the coefficient of the [tex]x^2[/tex] and the constant value.
⇒3×(-6)= -18.
2) Now find two numbers that can result is in -18 while multiplying and 7 (middle term or coefficient of x) while adding.
⇒9 × (-2) = -18.
9+(-2)= 7.
Now spit the equation as[tex]3x^2+9x-2x-6[/tex].
=[tex](3x^2+9x)-(2x-6)[/tex].
=3x(x+3) - 2(x+3).
=(x+3)(3x-2). (by taking out the common term x+3)
∴ The factor for given equation [tex]3x^2+7x-6[/tex] is (3x-2) and (x+3).
Write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution. Solve your equation to show that the solution are the same.
Answers
Answer:
[tex]x = \frac{3}{5} \times \frac{5}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]
Step-by-step explanation:
We have to write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution.
Let the multiplication equation be, [tex]x = \frac{3}{5} \times \frac{5}{7}[/tex].
And the subtraction equation is, [tex]y = \frac{16}{21} - \frac{1}{3}[/tex]
Now, [tex]x = \frac{3}{5} \times \frac{5}{7} = \frac{3}{7}[/tex] and [tex]y = \frac{16}{21} - \frac{1}{3} = \frac{16 - 7}{21} = \frac{9}{21} = \frac{3}{7}[/tex]
Therefore, in both the equations the solution is [tex]\frac{3}{7}[/tex]. (Answer)
Final answer:
Both a multiplication equation (½ * 2 = 1) and a subtraction equation (1 - ½ = ½) can be constructed to have the same solution, where the multiplication involves doubling the fraction and the subtraction involves a whole number minus the fraction.
Explanation:
Creating a multiplication equation and a subtraction equation with the same solution involves finding a common value that the operations can share. Here's a simple example:
Let's say we have the fraction ½. If we want a multiplication equation, we could multiply this fraction by 2 to get 1 (since ½ * 2 = 1).
Multiplication equation: ½ * x = 1, where x = 2.
For the subtraction equation, we consider the fact that subtracting 0 from any number leaves it unchanged. We can use this to our advantage by creating an equation where we subtract a fraction from itself:
Subtraction equation: y - ½ = ½, where y = 1.
By solving these equations, we can see they have the same solution:
½ * 2 = 11 - ½ = ½Both equations simplify to the same value, demonstrating that multiplication and subtraction can indeed share the same result when formulated correctly.
Suppose a population has a doubling time of 25 years. By what factor will it grow in 25 years? 50 years? In 100 years?
Answers
A population with a doubling time of 25 years will grow by a factor of 2 in 25 years, by a factor of 4 in 50 years, and by a factor of 16 in 100 years, based on the exponential growth rule.
Explanation:If a population has a doubling time of 25 years, by what factor will it grow in various timeframes? Let's calculate this using the rule of exponential growth.
In 25 years, the factor by which the population will grow is 2, because the definition of doubling time implies that the population doubles every 25 years.
In 50 years, which is two doubling periods, the population will grow by a factor of 2^2 (2 raised to the power of 2), which is 4.
In 100 years, which is four doubling periods, the population growth factor will be 2^4 (2 raised to the power of 4), which equals 16.
Thus:
After 25 years, growth factor = 2After 50 years, growth factor = 4After 100 years, growth factor = 16which inequality is equivalent to -m>_15
Answers
Answer:
m<=-15
Step-by-step explanation:
7x + 2(6x + 9) = 170
Answers
Answer:
x = 8
Step-by-step explanation:
7x + 2(6x + 9) = 170
2(6x + 9) = 12x + 18
7x + 12x + 18 = 170
19x = 152
152/19 = 8
x = 8
Kendra is three times her daughter's age plus seven years Kendra is 49 years old write an equation to find her daughter's age
Answers
Answer: [tex]49 = 3x + 7[/tex]
Step-by-step explanation:
Let the daughter's age be x and Kendra's age be y , then from the first statement;
[tex]y = 3x + 7[/tex]
Since Kendra's age is 49 , substitute it into the equation , we have
[tex]49 = 3x + 7[/tex]
subtract t from both sides
[tex]49 - 7 = 3x[/tex]
[tex]42 = 3x[/tex]
divide through by 3
[tex]x = 14[/tex]
Therefore : the daughter's age is 14
Answer:
3x+7=49
Step-by-step explanation:
start time 1:20 pm end time 2:00pm elapsed time
Answers
Answer:
40 minutes
Step-by-step explanation:
Elapsed time = end time - start time
Elapsed time = 2:00 - 1: 20
Elapsed time = 40 minutes
sixteen and two-tenth subtracted from two times a number
Answers
Step-by-step explanation:
Let the required number = x
To find, the required number = ?
According to question,
∴ 2x - 16 - 2 × 10 = 0
⇒ 2x - 16 - 20 = 0
⇒ 2x - 36 = 0
⇒ 2x = 36
⇒ x = 18
∴ The required number = 18
Thus, the required number is 18.
Answer: x=18
Explanation:
if ABCD is a rombus with side length 15 mm and if BD=24 mm, then find the length of the other diagonal, AC. Draw a diagram and show work.
Answers
Answer:
AC = 18 mm
Step-by-step explanation:
See the attachment for a diagram.
Since length BD = 24 mm, length BO = 12 mm. Then ΔBOC is a right triangle with one leg 12 and hypotenuse 15. The other leg (OC) is given by the Pythagorean theorem:
OC² +OB² = BC²
OC = √(BC² -OB²) = √(225 -144) = √81
OC = 9
Diagonal AC is twice the length of OC, so is ...
AC = 2·9 = 18 . . . . mm
_____
It can save a little time if you recognize that the given sides of triangle BOC have the ratio 4:5. This suggests you're dealing with a 3:4:5 right triangle, and that side OC is (3/5)·(15 mm) = 9 mm.
Find a pair of numbers that is a member of both y=-3x-27 and y=5+x
Answers
Answer:
(x, y) = (-8, -3)
Step-by-step explanation:
If all you want is a quick solution, I find a graphing calculator to be very handy. The one used in the attachment shows the solution to be (x, y) = (-8, -3).
_____
You can use one equation to substitute for y in the other equation:
-3x -27 = 5 +x
-32 = 4x . . . . . . add 3x-5 to both sides
-8 = x . . . . . . . . divide by 4
y = 5 +(-8) = -3 . . . . . use the second equation to find y
The pair of numbers that satisfies both equations is ...
(x, y) = (-8, -3)
Is 0,3 a solution to 2x-y=-3
Answers
Answer:
Yes, (x, y) = (0, 3) is a solution
Step-by-step explanation:
You can determine whether a given ordered pair is a solution by substituting those values into the equation, then checking to see if the resulting statement is true.
For x=0 and y=3, the equation becomes ...
2·0 -3 = -3 . . . . . a true statement
(0, 3) is a solution to the equation
Please Help !
TRYING TO MAKE HONOR ROLL
Which point represents the solution to the system of equations below ?
Answers
Answer:
I think its c. but i could be wrong
Evaluate the expression when x=3 and y= -2
Answers
Answer:
-11
Step-by-step explanation:
To evaluate an expression with variables, replace the variables with what the question tells you to.
Replace "x" with 3. Replace "y" with -2.
-x + 4y
= -(3) + 4(-2) Multiply 4 and -2 first to get -8
= (-3) + (-8) Add normally. -3 + (-8) is the same as (-3) - 8.
= -11 Answer
Therefore the solution is -11.
The first mechanic charged $95 per hours, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2,000. How long did each mechanic work?
Answers
Answer:
Step-by-step explanation:
Let a represent the hours put in my mechanic 1 and b represent that of mechanic 2.
a + b = 25, i.e. a = 25 - b
95a + 70b = 2000
Let's substitute the value of a in the second equation
95(25 - b) + 70b = 2000
2375 - 95b + 70b = 2000
2375 - 25b = 2000
-25b = 2000 - 2375
-25b = -375
b = 375/25
b = 15hrs
If b = 15hrs,
a + 15 = 25
a = 10hrs