Answer:
f(x)=2x^2+4x+6
f(x)=2(x^2+2x)+6
f(x)+?=2(x^2+2x+?)+6
f(x)+?=2(x^2+2x+1)+6
f(x)+2x1=2(x^2+2x+?)+6
f(x)+2=2(x^2+2x+1)+6
f(x)=2(x+1)^2+6-2
f(x)=2(x+1)^2+4
Answer:
f(x)=2(x+1)^2+4
A triangle has side lengths 25, 15x and 20x. The longest side is 25. What value for x proves that this triangle is a right triangle?
To prove that this triangle is a right triangle, we need to check the side lengths using pythogoras theorem.
Given:
Longest side = 25 unitsTriangle side lengths: 25, 15x, and 20xPutting the side lengths into pythogoras theorem:
⇒ [tex]25^{2} = 15^{2} + 20^{2}[/tex]⇒ [tex]625 = (10x + 5x)^{2} + (20x + 0x)^{2}[/tex]Using the formula "(a + b)² = a² + 2ab + b²
⇒ [tex]625 =[(10x)^{2} + 2(10x)(5x) + (5x)^{2} ] + [(20x)^{2} + 2(20x)(0) + (0)^{2} ][/tex]⇒ [tex]625 = [(10x)(10x) + 2(10x)(5x) + (5x)(5x)] + [(20x)(20x)][/tex]⇒ [tex]625 =[100x^{2} + 100x^{2} + 25x^{2} ] + [400x^{2} ][/tex]⇒ [tex]625 = 100x^{2} + 100x^{2} + 25x^{2} + 400x^{2}[/tex]⇒ [tex]625 = 625x^{2}[/tex]Divide both sides by 625:
⇒ [tex]\frac{625}{625} = \frac{625x^{2}}{625}[/tex]⇒ [tex]1 = x^{2}[/tex]⇒ [tex]\sqrt{1} = \sqrt{x^{2} }[/tex]⇒ [tex]\sqrt{1 \times 1} = \sqrt{x \times x }[/tex]⇒ [tex]1 = x[/tex]The value of x that proves this triangle a right triangle is 1.
x = 1
If it is a right angle triangle
→ (short side)² + (short side)² = (long side)²
given long side is 25====================================
(15x)² + (20x)² = 25²225x² + 400x² = 625625x² = 625x² = 1x = √1x = ±1as distance is positive
x = 1Refer to the graph representing the number of hybrid cars sold in January in the United States for the given years.
What is the difference between the January sales in 2008 and 2007?
The difference is _____ cars.
Answer:
First, let's find how many hybrid cars are sold during those two years.
2007 = 17,300 hybrid cars were sold
2008 = 22,600 hybrid cars were sold
Find the difference by subtracting the cars in 2007 from 2008.
22,600(2008) - 17,300(2007)
= 5,300
The difference is 5,300 cars.
The teacher’s bookshelf is 7 feet tall. She builds one more shelf on it that is ¾ of a foot tall. How tall is her bookshelf now?
Help. Parallelogram ABCD is shown with vertices A(−2, 3), B(3, 3), C(2, −3) and D(−3, −3)
The coordinates of the image of the parallelogram ABCD after the transformations are A''(-2,-3), B'(3, -3), C'(2, 3) and D'(-3, 3)
How to determine the final vertices?The coordinates of the parallelogram ABCD are given as:
A(−2, 3), B(3, 3), C(2, −3) and D(−3, −3)
When reflected across the y-axis, the rule of transformation is:
(x,y) -> (-x,y)
So, we have:
A'(2, 3), B'(-3, 3), C'(-2, -3) and D'(3, −3)
When rotated by 180 degrees, the rule of transformation is:
(x,y) -> (-x,-y)
So, we have:
A''(-2,-3), B'(3, -3), C'(2, 3) and D'(-3, 3)
Hence, the coordinates after the transformations are A''(-2,-3), B'(3, -3), C'(2, 3) and D'(-3, 3)
Read more about transformation at:
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Solve for y. 2y - 5 = 5y - 11
Answer:
y = 2
Step-by-step explanation:
Given equation:
[tex]2y - 5 = 5y - 11[/tex]
Subtract 5y both sides:
[tex]\implies 2y - 5 = 5y - 11[/tex]
[tex]\implies 2y - 5 - 5y = 5y - 5y - 11[/tex]
[tex]\implies -3y - 5 = -11[/tex]
Add 5 both sides:
[tex]\implies -3y - 5 = -11[/tex]
[tex]\implies -3y - 5 + 5 = -11 + 5[/tex]
[tex]\implies -3y = -6[/tex]
Multiply -1 both sides:
[tex]\implies -3y = -6[/tex]
[tex]\implies \dfrac{-3y}{-1} = \dfrac{-6}{-1}[/tex]
[tex]\implies 3y = 6[/tex]
Divide 3 both sides:
[tex]\implies 3y = 6[/tex]
[tex]\implies \dfrac{3y}{3} = \dfrac{6}{3}[/tex]
[tex]\implies \boxed{y = 2}[/tex]
please help!!!
A store is advertising a sale with 15% off all prices in the store. Sales
tax is 8%.
Which expressions represent the total cost of buying an item with
an original price of p, after the dischwunt and sales tax are included?
A. 1.08p - 0.15p
B. 1.15p + 0.08p
C. 1.08(0.85p)
D .85p + (0.08)(0.85p)
E. p - 0.15p + 0.08p
Answer:
The right answer is C
Step-by-step explanation:
1.08(0.85p)
Question 26 of 27
Find the value of x that makes ABCD a parallelogram.
Answer:
60°
Step-by-step explanation:
→ Find the sum of the angles
70 + 70 + x + 50 + x + 50 = 2x + 240
→ Equate the expression to 360
2x + 240 = 360
→ Minus 240 from both sides
2x = 120
→ Divide both sides by 2
x = 60
In 2010, a city’s population was 49,339 and it was declining at a rate of 1.06% each year.
Which is the best prediction for when the city’s population will first be below 35,000?
2036
2039
2042
2045
Answer: the answer is 2042 or C
Step-by-step explanation:
Answer:
2042
Step-by-step explanation:
took the test
The sum of two numbers is 143 and their difference is 7. What are the numbers?
Answer:
The numbers are 75,68
Step-by-step explanation:
Let the number be a ,b
The sum of two numbers is 143
⇒ x + y = 143 -------------(I)
Their difference is 7
⇒ x - y = 7 --------------(II)
Add the equation (I) & (II) and thus y will be eliminated and we can find the value of x
(I) x + y = 143
(II) x - y = 7 {Now add}
2x = 150
x = 150 ÷ 2
x = 75
Substitue x = 75 in equaion (I)
75 + y =143
y = 143 - 75
y = 68
please help me with this question
Answer:
119
Step-by-step explanation:
64 + 23 + 32
119 I think
A veterinarian collects a random sample of 40 cats that she has treated over the years and indicated the number of years each cat lived. Ten of the forty cats lived to be over 11 years old.
1. Use the Empirical Rule to construct a 99.7% confidence interval of the proportion (round to three decimal places) of all cats that will live to be more than 11 years old.
2. What sample size should the veterinarian use to achieve a margin of error of no more than 8% for the 99.7% confidence interval using the Empirical Rule? Use p=0.5 since we do not know the exact population proportion.
Answer:
1. 0.047, 0.453
2. 343
Step-by-step explanation:
The confidence interval regarding the veterinarian will be (0.045, 0.455).
How to depict the confidence interval?Sample success = 10
Sample size = 40
Pt estimate = 10/40 = 0.25
Standard error = 0.0685
The corresponding interval is (0.045, 0.455).
The sample size that the veterinarian should use to achieve a margin of error will be:
Margin of error = 0.08
Critical Z = 3.0
Estimated proportion = 0.5
Sample size = p × (1-p) × (z/e)²
= 0.5 × (1-0.5) × (3/0.08)²
= 352
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Priya's favorite singer has made 6 albums containing 75 songs in total. Priya wants to make a playlist of 10 of
those songs, and she won't repeat 1 of the 75 songs.
The permutation formula n Pr can be used to find the number of unique ways Priya can pick and arrange the
songs for the playlist
What are the appropriate values of n and r?
The appropriate values of n and r are illustrations of permutation.
The values of n and r are 75 and 10, respectively
How to determine the appropriate values of n and r?From the question, we have the following parameters:
Albums = 6Total songs = 75Songs to arrange in a album = 10The above means that:
n = 75
r = 10
This can be interpreted as:
Arrange 10 songs from a list of 75 songs
Hence, the appropriate values of n and r are 75 and 10, respectively
Read more about permutation at:
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Solve the equation below by factoring:
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
═════════════════════
Answer: =A.[tex]x = - 3[/tex] [tex]x = - 4[/tex]
Solution:
[tex]x ^ { 2 } +7x=-12[/tex]
[tex]x^{2}+7x+12=0 [/tex]
[tex]a+b=7 ab=12 [/tex]
[tex]1,12 2,6 3,4 [/tex]
[tex]1+12=13 2+6=8 3+4=7 [/tex]
[tex]a=3 b=4 [/tex]
[tex]\left(x+3\right)\left(x+4\right) [/tex]
[tex]x = -3[/tex] , [tex]x = -4[/tex]
so the answer is = A.════════════════════
Explanation:
#Carry on learning
Find the interest paid on a loan of $8,000 for 1 year at a simple interest rate of 8% per year.
O A. $720
O B. $64
C. $8.640
O D. $640
Answer:
The answer is $64.
Formula for simple Interest is P x R x T/100. Which is $8000 x 8 x 1/100 = $64
please help me with this graph problem. NO LINKS!!!
Step-by-step explanation:
a)
Eric runs for 4 min and walks for 8 min.
The distance covered is
4*200 + 8*80 = 800 + 640 = 1440The goal of 1600 m is not met, needs additional 160 m
b)
The equation of distance is
d = 200x + 80yc)
For d = 1600, the equation is
200x + 80y = 1600Simplified form of it
2.5x + y = 20Some combinations of x and y to make the equation right
x = 2, y = 15x = 4, y = 10x = 6, y = 5d)
See the attached graph for more combinations, where the first coordinate represents running time and the second coordinate - walking time
Answer:
Part (a)Given:
Average running speed = 200 m/minAverage walking speed = 80 m/minIf Eric runs for 4 minutes ⇒ 200 x 4 = 800 m
If Eric walks for 8 minutes ⇒ 80 x 8 = 640 m
Total distance covered = 800 + 640 = 1440 m
Therefore, he is 160 m away from his 1600 m goal.
Part (b)Let x = number of minutes Eric runs
Let y = number of minutes Eric walks
Let d = total distance Eric covers
Equation: d = 200x + 80y
Part (c)Set d = 1600, then rewrite to make y the subject:
200x + 80y = 1600
⇒ 5x + 2y = 40
⇒ 2y = 40 - 5x
⇒ y = 20 - 2.5x
Now find ordered pairs (points on the line):
x-intercept (y = 0): 20 - 2.5x = 0 ⇒ x = 8 ⇒ (8, 0)y-intercept (x = 0): 20 - 2.5(0) = 20 ⇒ (0, 20)when x = 4: 20 - 2.5(4) = 10 ⇒ (4, 10)Part (d)Plot (8, 0) (0, 20) and (4, 10) and connect with a straight line.
(see attached graph)
From inspection of the graph, other combinations of running and walking times for which Eric would cover 1600 meters are:
2 minutes running, 15 minutes walking6 minutes running, 5 minutes walkingSophie purchased a pair of Airpods that cost
$215. She used a coupon that offers 12% off.
How much did Sophie spend on the Airpods after
the discount?
Answer:
$189.20
Step-by-step explanation:
Since 12% off is the same thing as 88% of the original value, then you can simply multiply 215 by 0.88. This results in 189.2.
Answer:
$189.2
please make this answer brainliest If I helped you!
find the volume of the prism
[tex] \huge\fbox\orange{ANSWER} [/tex]
[tex] \mathsf \purple{v = l \times w \times h}[/tex]
[tex] \mathsf \pink{v = 8 \times 2 \times 5}[/tex]
[tex] \mathsf \purple{v = 80 \: cubic \: units} [/tex]
Answer:
80 cubic units
Step-by-step explanation:
Given
Height = 5 unitsLength = 8 unitsWidth = 2 unitsVolume = Length x Width x Height
V = 8 x 2 x 5V = 40 x 2V = 80 cubic unitsASAP . Solve and graph each inequality
Answer:
x less than or equal to -24
graph attached
Step-by-step explanation:
attached in image
Find the volume of the figure?
Answer:
Make two piece of this figure
Step-by-step explanation:
then use formula of v = l × b × h
Write an equation to find the value of x and solve it. Round your answer to the nearest tenth if necessary.
x =
Write your equation and explain how you came up with your equation and how you solved it. What concepts apply to this problem? How do you know your answer is correct?
Answer: x = 14
Step-by-step explanation:
4. In the figure below, rays KV and JP intersect at point M
K
Р
M
Which expression has a value that is equal to MPMV?
A 180° (MLKJM M JKM)
B 180° - (m_KJM
-
m/KMJ)
C 180°
(m. JMK)
D 180°
(m/JKM)
The intersection of the rays KV and JP would create vertical angles
The expressions that have the equal values as PMV are KMJ, 180 - JMV and 180 - PMK
How to determine the expression with equal value?The rays are given as:
Rays KV and JP
The point of intersection is given as:
Point M
When the rays KV and JP intersect at point M, the following angles are created
KMJ, JMV, PMV and PMK
Such that:
KMJ and PMV are vertical angles JMV and PMK are vertical anglesThe above means that angles KMJ and PMV are equal and
PMV = 180 - JMV
PMV = 180 - PMK
Hence, the expressions that have the equal values as PMV are KMJ, 180 - JMV and 180 - PMK
Read more about vertical angles at:
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four triangles are formed by joining the midpoints of three sides of an equilateral triangle
Answer:
all are congruent
Step-by-step explanation:
Four triangles are formed by joining the mid points of the three sides of a triangle then all are congruent as sides of all triangles will be same as they are formed by joining the mid points.
Please help on math.
I need help with this crazy Algebra 1a problem!
You have 14 coins in your pocket that are either quarters or nickels. The total value of the coins is $2.50.
A. Write a system of two equations that represents this situation. Let q represent the number of quarters and n represent the number of nickels.
B. Solve each equation for q.
D. What is the solution to the system?
E. Verify that the answer to part D is correct using the answer to part A.
F. How many of each coin are there?
Answer:
See below.
Step-by-step explanation:
A. First equation is
q + n = 14
then we have
0.25q + 0.05n = 2.5
Multiply last equation by -20
-5q - n = -50 Now add this to the first equation
-4q + 0 = -36
B. q = -36/-4 = 9.
D Substitute for q in the first equation
9 + n = 14
n = 14 - 9 = 5.
So the solution to the system is q = 9, n = 5.
E Verify this solution by substituting in the second equation:
0.25(9) + 0.05(5)
= 2.25 + 0.25 = 2.50.
- verified.
F. 9 quarters and 5 nickels.
what is the mode median mean and range of 4,5,0,2,3,1
Answer:
Mode = none, Median = 2.5, Mean= 2.5
Step-by-step explanation:
Hope this helps! :)
Step-by-step explanation:
the mode is the data item that occurres the most often.
but in 4, 5, 0, 2, 3, 1 every number appears only once. so, the mode is 0, 1, 2, 3, 4, 5 (as special case this average number can have more than one value - like in our case here).
the median is the value in the data set that lies directly in the middle between the other values (half of them are higher, the other half is lower).
if our data set has an even number of data points, or there is no unique middle value for other reasons, then the median is the mean value of the 2 middle values.
in our case 2 and 3 are the 2 middle values, so the median is (2+3)/2 = 2.5
the mean value is directly the average value across the whole data set : the sum of all values divided by the number of values.
(0+1+2+3+4+5)/6 = 15/6 = 2.5
the range is the difference between the highest and the lowest value in the data set : 5 - 0 = 0
Mai drank x oz of juice and Kiran
drank more than that.
Answer:
x≤k
Step-by-step explanation:
k= how many oz. Kiran drank. -Crispin
Question 1: Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive? Your response should include: The answer to how much money Trevon received AND your reasoning for your answer, with a focus on writing as complete of sentences as you can.
Question 2: Jenny wants to buy a game that costs $30.98. How much change does she receive if she gives the cashier $40?Your response should include: The answer to how much change Jenny will receive back AND your reasoning for your answer, with a focus on writing as complete of sentences as you can.
I WILL CHECK BEFORE GIVING POINTS, I REALLY NEED THIS THANK YOU :)
The amount of money Trevon had last Friday⇢$29
The total amount of money he has after cleaning the attic⇢$41
So,
The amount of money he received after cleaning the attic ⇢ Total money he has after cleaning the attic - The money he had last Friday
⇢ $41-$29⇢$12Thus ,he received $ 12 for cleaning up the attic.
Answer²↷$9.02Solution ↷The cost of the game ⇢$30.98
The amount of money she gave to the cashier ⇢$40
The amount she'll receive back⇢ the amount of money she gave to the cashier - the cost of the game
⇢$ 40 - $ 30.98⇢$ 9.02Hence , she'll receive $ 9.02 back from the cashier.
Answer:
Question 1Given:
Last Friday Trevon had $29He received money for cleaning the atticHe now has $41To calculate the money Trevon received for cleaning the attic over the weekend, we need to find the difference between the money he started with and the money he now has. To find the difference, subtract the smaller number from the bigger number:
⇒ Money Trevon received = Money he has now - money on Friday
= $41 - $29
= $12
Therefore, Trevon received $12 for cleaning the attic over the weekend.
Question 2Given:
Cost of game = $30.98Money gave the cashier = $40To calculate the change Jenny received from the cashier, we need to find the difference between the two amounts. To find the difference, subtract the cost of the game from the money Jenny gave to the cashier:
⇒ Change = money given - cost of game
= $40 - $30.98
= $9.02
Therefore, Jenny received $9.02 in change from the cashier after paying for a game that costs $30.98 with $40.
$35
130
b Bettieis Boutlque is having a 20% off sale
original price sale price
$15
$12
$25
120
$35
$28
Assuming we need to find out what 20% off of the prices listed is, we can set up equations for each of them, where x is the original price.
New price = [tex]\frac{8}{10} x[/tex] or simplified to [tex]\frac{4}{5} x[/tex]
So, putting the original prices through the formula, we get these values:
$15 --> $12
$12 --> $9.60
$25 --> $20
$120 --> $96
$35 --> $28
$28 --> $22.40
What are the zeros of this function?
5
O A. x = 0 and x = 2
O B. x = 0 and x = -4
O c. x= 0 and x = 4
O D. x = 2 and x = -4
PLEASE HELPPP
THANK YOUUU
Answer:
At origin x-axis and y-axis are Zeros and when the the will at x-axis then y-axis wil zero so,
C is the right answer
1) Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?
2) Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?
3) Carmen is trying to decide which jet ski rental plan to use. Plan A charges a one-time fee of $40 and $25 per hour. Plan B charges a one-time fee of $60 and $15 per hour. After how many hours will the plans cost the same?
4) Julie and Wendi purchased cell phones. Julie’s phone cost $50 and she pays $0.35 per minute. Wendi’s phone cost $70 and she pays $0.15 per minute. After how many minutes of use will Julie’s phone cost more than Wendi’s?
5) 78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
6) 168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
7) Christina spent $81.25 on books. Comic books cost $2.25 each and novels cost $7.00 each. If she bought 15 books, how many comic books did she buy?
8) Tina bought 8 pieces of clothing for a total of $164. Jeans cost $22 each and shirts cost $18 each. How many shirts did Tina buy?
9) Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?
10) Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?
What you need to do:
Please WRITE both equations for each problem, identify what your variables represent, and solve the system.
I don’t know what to do, so please help me understand by explaining how you got the answer.
I WANT TO LEARN FROM YOU! :)
- Will give BRAINLIEST if it gives me the option -
78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
Solution:Let the number of cars be "x" and the number of vans be "y".
According to question,
x + y = 10 5x + 12y = 78 -->(ii)
=> 5(x + y) = 10 × 5
=> 5x + 5y = 50 -->(i)
By Elimination method,
Equation (i) - (ii) we get,
(5x + 5y) - (5x + 12y) = 50 - 78
=> 5x + 5y - 5x - 12y = - 28
=> - 7y = - 28
=> 7y = 28
=> y = 28/7
=> y = 4
Putting the value of "y" in Equation (i)
5x + 5y = 50
=> 5x + 5 × 4 = 50
=> 5x + 20 = 50
=> 5x = 50 - 20
=> 5x = 30
=> x = 30/5
=> x = 6
Therefore,The total number of cars went = 6
The total number of vans went = 4
====================================================
Question no.6:168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
Solution:
Let the number of buses be "x" and the number of vans be "y".
According to question,
x + y = 10 42x + 6y = 168 -->(ii)
=> 42(x + y) = 10 × 42
=> 42x + 42y = 420 -->(i)
By Elimination method,
Equation (i) - (ii)
(42x + 42y) - (42x + 6y) = 420 - 168
=> 42x + 42y - 42x - 6y = 252
=> 36y = 252
=> y = 252/36
=> y = 7
Putting the value of "y" in Equation (ii)
42x + 6y = 168
=> 42x + 6 × 7 = 168
=> 42x + 42 = 168
=> 42x = 168 - 42
=>42x = 126
=> x = 126/42
=> x = 3
Therefore,Total number of buses went = 3
Total number of vans went = 7