Answer: f(x) = -3| x - 1 | is really just f(x) = -3| x - 1 | + 0.
now, what value of "x" makes the absolute value expression to 0?
well, let's just set it to 0 and check,
x - 1 = 0
x = 1
so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at
f(x) = -3| (1) - 1 | + 0 --------------> ( 1, 0 )
mr morton sold bird houses to stores. he started the week with 60. he sold 10 to one store and divided the rest between 5 other stores. how many birdhouses did he sell to each of the other 5 stores?
Answer:
10
Step-by-step explanation:
Mr morton initially had 60 bird houses.
He sold 10 to one store.
So left number of birdhouses = 60 - 10 = 50.
He sold them equally to 5 stores,
So, each of them will get [tex]\frac{50}{5}[/tex] = 10 bird houses.
So,
He sold 10 birdhouses to each of the other 5 stores.
Mrs. William shops at a store that has an annual membership fee of $30. today she paid her annual membership and bought several fruit baskets costing $15 each as gifts for her co-workers. her total was $105. solve the equation 15b+ 30=105 to find the number of fruit baskets mrs. Williams purchased.
Number of fruit baskets purchased by Mrs. William is 5
Solution:Given that
Annual membership fee of store where Mrs. William shops = $30
Cost of one fruit basket which Mrs. William as gifts for her co-workers = $15
Total amount spent by Mrs. William = $150
Given that "b" represents number of basket purchased
Equation which models the above scenario is as follows
15b+ 30=105 ------ (1)
Where b represents number of fruit basket purchased by Mrs. William
Need to calculate number of fruit basket purchased by Mrs. William
For which we need to solve equation (1) for b
On solving we get
15b+ 30 = 105
On Subtracting 30 from both sides we get
15b + 30 – 30 = 105 – 30
=> 15b = 75
On dividing both sides by 15 we get
[tex]\begin{array}{l}{\frac{15 b}{15}=\frac{75}{15}} \\\\ {=>b=5}\end{array}[/tex]
As variable "b" represents number of basket purchased, hence we can conclude that number of fruit baskets purchased by Mrs. William is 5
What number would x be for 2x+1/3 and 2x be the same equation
Answer:
No solution.
Step-by-step explanation:
2x+1/3=2x
1/3=2x-2x
1/3=0
no solution
if f(x)=4/x+2 and g is the inverse of f, then g'(10)=
Answer:
The value of g'(10)=[tex]\frac{(-1)}{16}[/tex]
Step-by-step explanation:
Given function is f(x)=[tex]\frac{4}{x} + 2[/tex]
Take f(x)=y
y=[tex]\frac{4}{x} + 2[/tex]
Subtract 2 from both side.
y-2=[tex]\frac{4}{x}[/tex]
x=[tex]\frac{4}{y-2}[/tex]
The inverse of f(x) is written as [tex] \frac{4}{y-2}[/tex]
It is said as g is inverse of f
g(y)=\frac{4}{y-2}[/tex]
g(y)=[tex]\frac{4}{y-2}[/tex]
g(10)=[tex]\frac{4}{10-2}[/tex]
g(10)=[tex]\frac{1}{2}[/tex]
Differentiating both sides we get,
g'(y)=[tex]\frac{4(-1)}{(y-2)^{2}}+0[/tex]
g'(y)=[tex]\frac{(-4)}{(y-2)^{2}}[/tex]
To find g'(10)=[tex]\frac{(-4)}{(10-2)^{2}}[/tex]
g'(10)=[tex]\frac{(-1)}{16}[/tex]
One day, the high temperature was 84 degrees and the low temperature was 68 degrees. Write a compound inequality to represent the day’s temperatures
Answer:
x > 68 and x < 84
Step-by-step explanation:
The area of a rectangle is 28 square meters. The length is 7 meters.
What is the width of the rectangle?
meters
To find the width of the rectangle, use the formula Width = Area ÷ Length. Given an area of 28 square meters and a length of 7 meters, the width is 4 meters.
The area of a rectangle is calculated using the formula:
Area = Length × Width
Given that the area is 28 square meters and the length is 7 meters, we can find the width by rearranging the formula:
Width = Area ÷ Length
Substitute the given values into the formula:
Width = 28 square meters ÷ 7 meters = 4 meters
Therefore, the width of the rectangle is 4 meters.
Which of the following problems can be solved by finding 4 divided by 2/3?
A. 4 people equally share 2/3 of a pizza. How much of the pizza does each person eat?
B. How many 2/3 cup servings of soup are in 4 cups of soup?
C. A pie recipe requires 2/3 pounds of apples. How many apples are needed for 4 pies?
D A family ate 2/3 of a 4 foot sandwich. How much did he they eat?
Arthur chose A as the correct answer. How did he get that answer?
Step-by-step explanation:
Arthur got because a pizza is shared by 4 people. however only
2/3 of the pizza is there so it is divided by the four people.
The correct option is b.
The correct problem that can be solved by calculating 4 divided by 2/3 is determining the number of 2/3 cup servings of soup in 4 cups. By understanding how division of fractions work, we can see that there are 6 such servings in 4 cups.
Explanation:The subject matter of the question is related to basic division and fractions. Specifically, it's asking about when we would need to find the result of 4 divided by 2/3. Given the answer choices, option B is the correct one. The question here is not about sharing a pizza or calculating the quantity of apples for pies, or the amount of sandwich eaten. It's rather about how many 2/3 cup servings fit within 4 cups of soup. When we do the division 4 ÷ 2/3, we're essentially figuring out how many 2/3s there are in 4. This concept can be a bit tricky because dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 2/3 is 3/2, so 4 × 3/2 = 6. Hence, there are 6 servings of 2/3 cup soup in 4 cups.
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Solve the problem.
6. John bought three cups of root beer. Two of the cups were smalls and the last
was a large. All the cups together add up to 52 fl. oz. of root beer. If the large can hold 36 fl. oz.
of root beer, how much root beer can a small cup hold.
Answer:
the small cup of root beer can hold 8 fl. oz
Step-by-step explanation:
52-36=16
16/2=8
Each small cup holds 8 fl. oz. Together they hold 16 fl. oz. Plus 36 fl. oz. Which equals 52 fl. oz.
if my grade is a 49.1 F and i get 90 points on a test what will my grade go to
Answer:
A I think
Step-by-step explanation:
49.1+ 90
Answer:
C
Step-by-step explanation:
Find the average of the two test scores.
(49.1 + 90)/2
139.1/2
69.55 ⇒ which is grade C
What is y+2=⅞(x-3) in standard form?
Answer:
7x - 8y = 37
Explanation:
y+2 = ⅞(x-3) (distribute ⅞ -- x times 7/8, -3 times 7/8)
y+2 = ⅞x - 21/8 (subtract ⅞x from both sides)
y+2-⅞x = -21/8 (subtract 2 from both sides)
y-⅞x = -37/8 <--- result of -21/8 - 2
Multiply both sides by 8 to get ride of fractions
8y - 7x = -37 (rearrange)
-7x + 8y = -37
It's better to have a positive coefficient for x if you can. So multiply both sides by -1. That just means changing the sign of every term on both sides, you get
7x - 8y = 37
A wooden beam is left parenthesis 6 y squared plus 5 y plus 1 right parenthesis6y2+5y+1 meters long. If a piece of length left parenthesis y squared minus 12 right parenthesisy2−12 meters is cut off, express the length of the remaining piece of beam as a polynomial in y.
Answer:
5y² + 5y - 11
Step-by-step explanation:
The length of a wooden beam is as a function of y
L(y) = 6y² + 5y + 1
and a piece of length y² - 12 is cut off the remaining piece is
6y² + 5y + 1 - y² - 12 = 5y² + 5y - 11
To find the remaining length of the wooden beam, subtract the length of the cut-off piece from the original polynomial. Simplify the expression to get the final answer: 5y² + 5y + 13 meters. This represents the remaining length of the beam.
Finding the Remaining Length of the Wooden Beam:
We start with the original length of the wooden beam given by the polynomial 6y² + 5y + 1 meters.
We need to subtract the length of the piece that was cut off, which is given by the polynomial y² - 12 meters.
First, write down the original length of the beam:
6y² + 5y + 1
Next, identify the length of the piece cut off:
y² - 12
Subtract the second polynomial from the first:
(6y² + 5y + 1) - (y² - 12)
Simplify the expression by combining like terms:
6y² - y² = 5y²
5y remains unchanged.
1 - (-12) = 1 + 12 = 13
So, the remaining length of the beam is:
5y² + 5y + 13
The remaining length of the wooden beam, expressed as a polynomial in y, is 5y² + 5y + 13 meters.
Thank you! Please do both
Answer:
my 12 inch pito that pito good
What’s 333x333 please I need to know
Answer:
110889
Step-by-step explanation:
Answer:
110,889 is the answer dude..
What is the solution to this equation x - 12 = - 4
Answer:
x = 8Step-by-step explanation:
x - 12 = -4 add 12 to both sides
x - 12 + 12 = -4 + 12
x = 8
you miss3 out of 7 on a science quiz and 9 out of 23 on math quiz which quiz has a higher percent of correct answers
Science Quiz: 42.8571429%
Math Quiz: 39.1304348%
Take the amount of answers correct out of the total, divide it, and then multiply by 100. In this case, Science has a higher score.
The percentage of correct answers for the science quiz is 57.14%, while for the math quiz it's 60.87%. Therefore, the student had a higher percentage of correct answers on the math quiz.
Explanation:You determine the percentage of correct answers on each quiz by dividing the number of correct answers by the total number of questions on each quiz respectively.
For the science quiz, you answered 4 out of 7 questions correctly since you missed 3 out of 7. The percentage of correct answers for the science quiz is thus (4/7)*100 = 57.14%.
For the math quiz, you answered 14 out of 23 questions correctly since you missed 9 out of 23. The percentage of correct answers for the math quiz is thus (14/23)*100 = 60.87%.
Therefore, you had a higher percentage of correct answers on the math quiz than on the science quiz.
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Given: △AKM, KD ⊥ AM , AK = 6, KM = 10, m∠AKM = 93º Find: KD
The length of KD in triangle △AKM, with AK = 6 and KM = 10, and m∠AKM = 93° is 10, since KD is the height of a right triangle and KM is the hypotenuse.
The question asks to find the length of KD in triangle △AKM where KD is perpendicular to AM. Given AK = 6, KM = 10, and m∠AKM = 93º, we can solve for KD using trigonometric ratios.
Since KD ⊥ AM, we have a right triangle △KDM.
We know the hypotenuse KM and angle AKM, so we can use the sine function, where sin(AKM) = opposite/hypotenuse, to find the length of KD. The sine of angle AKM (which is slightly adjusted from 93º to 90º since we are looking for the height in a right triangle) gives us:
sin(90º) = KD/ KM
We know sin(90º) = 1 and KM = 10, so:
1 = KD / 10
Therefore, KD = 10.
294 rounded to the nearest hundred
Answer:
300
Step-by-step explanation:
9 rounds it up
Over the course of a year, a company goes from 115 employees to 124 employees.
Use the drop-down menus to build an equation that could be used to find the percent change, p, in the number of employees
Answer:
on the top is 124 - 115 whille in the bottom is 115
Step-by-step explanation:
To calculate the percent change in the number of employees, use the formula (Change in Quantity / Original Quantity) × 100. The original number of employees is 115, and it increased to 124, resulting in a change of 9. The percent change is approximately 7.83%.
Explanation:To find the percent change in the number of employees, you can use the following formula:
Percent Change (p) = (Change in Quantity / Original Quantity) × 100
In this case, the Original Quantity is the number of employees at the start of the year (115) and the Change in Quantity is the difference between the number at the end of the year (124) and the number at the start of the year (115).
So, we calculate Change in Quantity as 124 - 115 = 9.
Now, using the formula:
p = (9 / 115) × 100
Calculating this gives us the percentage change:
p = (9 / 115) × 100 ≈ 7.83%
The percent change in the number of employees is approximately 7.83%.
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2kilogram convert into g
Answer:
The answer is 2000 g
Step-by-step explanation:
We use the following equivalence:
1 kg-------1000g
2kg----- X = (2kgx1000g)/1kg= 2000g
The football team scored 28 points in the
first game. 35 points in their second game,
and 17 points in the third game About how
many points were scored in all three
games?
Answer:
80 points
Step-by-step explanation:
28+35=63.
63+17=80.
Hope this is addition.
That simple
By adding the points scored in each game, we find that the football team scored a total of 80 points in all three games.
Explanation:To find the total number of points the football team scored in all three games, we simply have to add the points scored in each game together. So, in the first game the team scored 28 points, in the second game they scored 35 points, and in the third game they scored 17 points. If we add these scores together (28 + 35 + 17), we get a total of 80 points. Therefore, the football team scored 80 points in all three games.
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Solving systems by substitution
X=y-11
2x+3y=8
Answer:
x=-5, y=6. (-5, 6).
Step-by-step explanation:
x=y-11
2x+3y=8
--------------
2(y-11)+3y=8
2y-22+3y=8
5y-22=8
5y=8+22
5y=30
y=30/5=6
x=6-11=-5
It took a car 5 days to travel 1459 miles. What was this car average speed in miles per hour ?
Answer:
12.1583333333 miles/hr.
Step-by-step explanation:
24 * 5 = 120 hrs
1459/120 = 12.1583333333
Answer:
12.158 miles/hour
Step-by-step explanation:
[tex]\frac{1459 miles}{5 days} = 291.8 miles/day\\\frac{291.8 miles}{1 day} x \frac{1 day}{24 hours} = 12.158 miles/hour[/tex]
Shawn hikes up a mountain, back down the other side, then around the front of the mountain back to his truck. How far did he go if n = 5 and m = 6?
Answer:
The distance Shawn went is 40.
Step-by-step explanation:
Given:
N= 5 and M =6
Mountain hike = N = 5
Back down the other side = 2N+1 = 2×5 + 1 = 10 + 1 =11
From Mountain back to truck = 4M = 4×6 = 24
We need to find the total distance he went and can be calculate by adding Mountain hike with back down the other side and then from Mountain back to truck.
Total distance Shawn went = Mountain hike+ Back down the other side + From Mountain back to truck = 5 + 11 + 24 = 40
Hence Shawn went the distance of 40.
please help. If you answer correctly and give an explanation I'll give you 5 stars, thanks, and brainliest.
solve the equation:
2x + 1-x/4 = 3
or
[tex]2x + \frac{1-x}{4} = 3[/tex]
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
Step-by-step explanation:
To simplify an equation of x
Simplify each side of the equationCollect x in side and the numerical terms in the other sideFind the value of x∵ The equation is [tex]2x + \frac{1-x}{4}=3[/tex]
- Multiply all terms of the equation by 4 to cancel the denominator
of the 2nd term in the left hand side
∵ The equation is [tex]4(2x) +4 (\frac{1-x}{4})=4(3)[/tex]
∴ 8x + (1 - x) = 12
∴ 8x + 1 - x = 12
- Add like terms
∴ (8x - x) + 1 = 12
∴ 7x + 1 = 12
- Subtract 1 from both sides
∴ 7x = 11
- Divide both sides by 7
∴ [tex]x=\frac{11}{7}[/tex]
The solution of the equation is [tex]x=\frac{11}{7}[/tex]
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INEQUALITIES-PLEASE HELP! Tricia receives a $5 allowance every week. She also earns $6.50 for every hour that she baby-sits. Next week she wants to earn at least $21.25 to buy a present. Please write an inequality to math this equation.
Answer:
6.50x + 5 = 21.25 is the answer
Step-by-step explanation:
x=2.5
The inequality that represents Tricia's goal to earn at least $21.25 through her $5 allowance and $6.50 per hour from babysitting is E = 5 + 6.50h ≥ 21.25, where h represents the number of hours she babysits.
The student's question asks for an inequality to represent the situation where Tricia receives a $5 weekly allowance and earns $6.50 for each hour she babysits. The goal is to earn at least $21.25 to buy a present.
Let's denote the number of hours Tricia babysits as h. The inequality representing her total earnings E from both her allowance and babysitting will be:
E = 5 + 6.50h ≥ 21.25
This inequality implies that the sum of Tricia's weekly allowance ($5) and her babysitting earnings ($6.50 per hour multiplied by the number of hours h) should be at least $21.25.
2. One of the most common mutagens in
our environment, that we are exposed
to everyday we are outside in the
sunlight, is
O UV radiation
infrared radiation
Answer:
Ultraviolet (UV) radiation.
Step-by-step explanation:
Mutagen is part of genetics, it is chemical or physical agent which are present in atmosphere and causes changes or mutation in the genetic materials i.e. in DNA (these changes can be permanent as well). Example of mutagen are radioactive substances, ultraviolet radiation, etc.
UV radiation is an electromagnetic radiation which is present in sunlight. It is a strong mutagen which is when absorbed by DNA can cause extreme damage, for example, uncontrolled division of skin cell can cause skin cancer, that's the reason why UV radiation is the most common mutagen to which we are exposed to when we are outside in the sunlight.
Factor −1/2 out of −1/2x+6.
The factored expression is
Final answer:
To factor −1/2 out of −1/2x+6, we identify the common factor, divide each term by −1/2, and write the expression as −1/2 times the simplified expression. The result is −1/2(x − 12).
Explanation:
To factor −1/2 out of −1/2x+6, we can think of pulling out the −1/2 as a common factor from both terms in the expression. Here's a step-by-step breakdown:
Identify the common factor in both terms. In this case, the common factor is −1/2.Divide each term by −1/2 (which is the same as multiplying by −2).Write the original expression as the product of the common factor and the simplified expression.Applying these steps, we get:
−1/2x divided by −1/2 equals x.6 divided by −1/2 equals −12.The factored expression is then −1/2(x − 12).So, −1/2x+6 factored with −1/2 taken out is −1/2(x − 12).
Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches
cost $1.20 per pound, and a gallon of milk costs $3.60.
The inequality 1.20x+ 3.60 39.60 models this situation, where x is the
number of pounds of peaches.
HEF
Solve the inequality. How many pounds of peaches can Rammy buy?
Answer:
[tex]\large \boxed{\text{5.00 lb}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}[/tex]
Check:
[tex]\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}[/tex]
OK.
The number of pounds of peaches that Rammy can buy is 5 pounds.
Based on the information given in the question, the equation to solve the question will be:
1.20x + 3.60 ≤ 9.60
Collect like terms
1.20x ≤ 9.60 - 3.60
1.20x ≤ 6.00
Divide both side by 1.20
1.20x/1.20 ≤ 6.00/1.20
x ≤ 5.00
Therefore, the number of pounds of peaches that Rammy can buy is 5 pounds
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Which expression is equivalent to the expression (-18) - 64n?
A -2(9 - 32n)
B 2(9 - 32n)
C -2(9 + 32n)
D 2(9 + 32n)
Answer:
C) -2(9+32n)
Step-by-step explanation:
(-18)-64n=-18-64n
---------------------------
A) -2(9-32n)=-18+64n
B) 2(9-32n)=18-64n
C) -2(9+32n)=-18-64n
D) 2(9+32n)=18+64n
-----------------------------------
The answer is C.
use the method of completing the square to solve y²+y-7=0
Answer:
y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Step-by-step explanation:
Solve for y:
y^2 + y - 7 = 0
Add 7 to both sides:
y^2 + y = 7
Add 1/4 to both sides:
y^2 + y + 1/4 = 29/4
Write the left hand side as a square:
(y + 1/2)^2 = 29/4
Take the square root of both sides:
y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2
Subtract 1/2 from both sides:
Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2
Answer:
y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2
Step-by-step explanation:
y^2+y-7=0
completing the square,
(b/2)^2=(1/2)^2=1/4
(y+1/2)^2=7+1/4
(y+1/2)^2=28/4+1/4
(y+1/2)^2=29/4
y+1/2=sqrt(29/4)
y=sqrt(29/4)-1/2
y=sqrt(29)/2-1/2
y=-sqrt(29)/2-1/2