Using substitution method, For the given equations, the value of x is 1/2 or x = -3
Describe substitution.A fundamental operation in computer algebra is substitution. In computer algebra systems, it is frequently abbreviated as "subs" or "subst."
When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.
Given,
y= 9 - x
y= 2x² + 4x + 6
Substituting the value of y from 1 equation to other.
⇒ 9 - x = 2x² + 4x + 6
Now factorizing the equation,
⇒ 2x² + 5x - 3 = 0
⇒ 2x² + 6x - 1x - 3
⇒ 2x(x + 3) -1 (x + 3)
⇒ (2x - 1) (x + 3)
x = 1/2 or x = -3
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Simplify this expression: 7 + 9x2-5= A. 27 B. 20 C.-48 D. 19 HELP ASAP
Answer:
the answer to the problem is A 27
Step-by-step explanation:
santi and vlado drove together from new york to new orleans. both drove the same amount of time, but santi drove 75% as quickly as vlado. if the drive took a total of 24 hours and new orleans is 1,304 miles from new york, approximately how many miles did santi drive?
If both Santi and Vlado drove for the same amount of time with Santi driving at 75% of Vlado's average speed, and they covered 1304 miles in 24 hours, then Santi had driven for approximately 559 miles.
As per the question statement, Santi and Vlado drove together from New York to New Orleans. Both of them drove for the same amount of time with Santi driving 75% as quickly as Vlado, and it took them 24 hours to complete the 1304 miles journey.
We are required to calculate the approximate number of miles, that Santi drove during their trip.
Since given that, Both of them drove for the same amount of time and it took them 24 hours to complete the 1304 miles journey, therefore, both Santi and Vlado drove for (24/2) = 12 hours each.
Now, let us consider that Vlado drove at an average speed of "v" miles/hour.
Then, Santi would have driven at a average speed of [(75/100)v] m/h
= (0.75v) m/h
= 0.75V miles/hour
[Since Santi drove 75% as quickly as Vlado]
Now as we know that, [(speed * time) = distance], applying the same formula to the velocities and driving times of Santi and Vlado, we get,
[{(12 * v) + (12 * 0.75v)} = 1304]
Or, [(12v + 9v) = 1304]
Or,(21v = 1304)
Or, v = [(1304/21)]
Or, (v = 62.095 miles/hour)
Or, (v ≈ 62.1 miles/hour)
That is, Vlado drove at an average speed of 62.1 miles per hour,
And, Santi drove at an average speed of (62.1 * 0.75) miles per hour
= (46.575) miles per hour.
Therefore, Santi drove a total of (46.575 * 12) = 558.9 miles ≈ 559 miles,
as he drove at an average speed of 46.575 miles per hour, for 12 hours.
Average Speed: In Mathematics as well as physics, the average speed of any travelling object is the total distance traveled by the object in a particular time interval. It is a scalar quantity, represented by the magnitude and does not have direction.To learn more about Average Speeds, click on the link below.
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Translate the sentence into an equation or formula.
25 less than the cube of x is equal to four times the sum of y and five
Answer:
x + y y added to 7. 7+ y. The sum of a and b a + b m more than n n + m ... y. 5 or y ÷ 5. The ratio of u to v u v or u ÷ v u separated into 4 equal parts.
Step-by-step explanation im just guessing so if its incorrect sorry:(
5 1/2 ÷3 3/8
hey umi, need it
because i have school in 26 well Thursday and it is a assignment and it is due today
Answer:
1 - 1.5
2 - 3.9375
3 - 3
4 - 1.62962963
5 - 2.83333
6 - 4.05555556
7 - 8
8 - 1.555555556
9 - 6.4
10 - 6
11 - 1.5
12 - 18
Fill in the blanks with the correct angle measure.
For example:
Measure of angle 1 = 110 degrees. You only need to type 110.
Answer:
1:110
2:70
3:110
4:70
5:110
6:70
7:110
8;70
Step-by-step explanation:
lol i think its pretty simple
RS has endpoints R(3, 5) and S(–3, –1). Which statement explains whether the midpoint M of lies on the y-axis?
M = = (4, –2) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (3, 3) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (2, 0) lies on the y-axis because the y-coordinate is zero.
M = = (0, 2) lies on the y-axis because the x-coordinate is zero.
Mark this and return
Step-by-step explanation:
M = (0, 2), and it lies on the y-axis, because the x-coordinate is 0.
by the way, the first 2 answer options are correct statements too, they are just not specifying the actual midpoint.
Answer:d
Step-by-step explanation:edge2023
Which of the following is equivalent to 2.68?
2.68%
two and seventeen twenty fifths
twenty five seventeenths
26.8%
The expression that is equivalent to the number 2.68 is (b) two and seventeen twenty fifths
How to determine the equivalent number/expression?From the question, we have the following parameters that can be used in our computation:
Number = 2.68
Expand the number using the addition operator
So, we have the following representation
Number = 2 + 0.68
Express 0.68 as a fraction
This gives
Number = 2 + 68/100
Simplify the fraction
So, we have the following representation
Number = 2 + 17/25
This implies that
Number = two and seventeen twenty fifths
Hence, the equivalent of 2.68 is (b) two and seventeen twenty fifths
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Given h(x) = − 4x − 4, solve for x when h(x) = −8.
Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
World Stationery
Pack of 25 stickers for £2.25
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Answer:
Buying from World Stationery shop would profit Gigi.
How to find the most profitable shop?Given,
Gigi is going to buy 100 stickers.
Stickers4u - Pack of 25 stickers for £2.25
World Stationery - Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Solution:
Cost of 1 sticker in Stickers4u = £2.25/25 stickers = £0.09
Cost of 1 sticker in World Stationery = £1.75/ 10 stickers = £0.175
Since it is mentioned, 'Buy 1 pack get 1 pack 1 free' in this shop, the total no of stickers one would get for the price would be doubled.
Hence,
Cost of 1 sticker in World Stationery would be = £1.75/ 20 stickers = £0.0875
On comparing the price per sticker of both the shops, we can say that
buying from World Stationery shop would profit Gigi.
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Find the slope and reduce,
P=(-5, 2) Q=(-3, 6)
Slope = [?]
Answer:
Slope m = 2
Step-by-step explanation:
find X. would love the help thank you
Answer:
120
Step-by-step explanation:
x + the angle = 180 because it makes a line
we know from the picture that the triangle is equilateral so the angle has to be 60
so 180 = x + 60 and solve for x
Solve the quadratic equation.
x² + 9x - 36 = 0
O A. x = 3 or 12
OB. x = 3 or -12
O C. x = 6 or -6
OD. no real solution
Answer:
B x = 3 or -12
Step-by-step explanation:
(btw this / is a fraction sign and this ^ is the power of sign)
Let's solve your equation step-by-step.
x^2+9x−36=0
For this equation: a=1, b=9, c=-36
1x^2+9x+−36=0
Step 1: Use quadratic formula with a=1, b=9, c=-36.
x= −b±√b^2−4ac/2a
x= −(9)±√(9)2−4(1)(−36)/2(1)
x= −9±√225/2
= x= 3 or x= -12
I need this answer as soon as possible
Note: This is grade 6 maths
10.
A gallon = 4 quarts
4 quarts = 4 x 2 = 8 pints.
8 pints = 8 x 16 = 128 (ounces)
So, a gallon equals 128 ounces.
11.
Generally, 2 cups = 1 pint.
-> 4 cups = 2 pint = 1 quart
So, he should (probably) use the entire quart.
12.
Convert all the mixed numbers to fractions, mk.
14(7/9) + 6(5/9)
= 14+6(7/9+5/9) = 20(12/9) = 64/3.
13. 15(11/16) + 21(9/16) = 36(11/16+9/16) = 36(20/16) = 149/4
14. 7(1/2) + 5(1/2) = 12(1/2+1/2) = 13( = 13/1)
15. 17(3/4) - 4(1/4) = 17-4(3/4-1/4) = 13(1/2) = 27/2
16. 23(5/8) - 12(3/8) = 23-12(5/8-3/8) = 11(2/8) = 45/4
17. 27 - 6/8 = 216/8 - 6/8 = 210/8 = 55/2.
Please recheck and if you spot anything wrong tell me.
help pls i don’t understand and don’t know which option topick
Answer: C
Explanation:
The range of a function is the set of all values of y that satisfy the function. On the graph, it is between the lowest value of y at the bottom and the highest value of y at the top. Looking at the graph, it extends to negative infinity at the bottom and the maximum value at the top y = 4
Thus, in interval notation,
Range = (- ∞, 4]
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 525 miles on 25 gallons of gas. How far could you drive on 40 gallons of gas? What is the car's gas mileage?
40 gallons
[tex]\frac{525}{25} \times 40=840[/tex] miles
Gas Mileage
[tex]\frac{525}{25}=21[/tex] miles per gallon
3) Each volume of an encyclopedia has two covers, each 1/4-inch thick, and 300 pages of text that are 2-inthick. The books are arranged in order on a shelf. How far does a bookworm travel who burrows his way from the first page of Volume I to the last page of Volume III?
Answer:
7 inches
Step-by-step explanation:
Volume 1 - 300 pages 2 inches
back cover 1/4 inch
Volume 2 - front cover 1/4 inch
300 pages 2 inches
back cover 1/4 inch
Volume 3 - front cover 1/4 inch
300 pages 2 inches
How many permutations can be formed from all of the letters of the word houston?.
The word "Houston" can have a maximum of 2520 permutations using all it's letters.
As per the question statement, we are provided with a word: HOUSTON.
And we are required to calculate the total number of permutations that can be formed using all the letters of it.
To solve this question, first we will need to determine the number of letters in our concerned word, which in this case is 7, and then number of repeated letters, which is 2, since the letter "O" is repeated once.
Therefore, the total number of permutations that can be formed using all the letters of the word HOUSTON = [(7!)/(2!)]
= (7 * 6 * 5 * 4 * 3)
= 2520
Permutation: In Mathematics, a permutation is a technique to determines the number of possible arrangements of the elements in a set, in a definite order.To learn more about Permutations, click on the link below.
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Charlie Brown and Linus are so excited for Halloween that they have planned trips to three different parks. They are willing to pay no more than $40 to go to all of them. Jones’ Corn Maze has an entry fee that is $4 less than double the amount of Tomilloso’s Pumpkin Patch entrance fee. King’s Haunted House has an entry fee that is $2 more than Tomilloso’s Pumpkin Patch. What is the maximum price Charlie and Linus are willing to pay to enter each park?
The maximum price Charlie and Linus are wiling to pay to enter each park is 10.5 dollars.
How to use inequality to represent a situation?Charlie Brown and Linus are so excited for Halloween that they have planned trips to three different parks.
They are willing to pay no more than $40 to go to all of them.
Jones’ Corn Maze has an entry fee that is $4 less than double the amount of Tomilloso’s Pumpkin Patch entrance fee.
King’s Haunted House has an entry fee that is $2 more than Tomilloso’s Pumpkin Patch.
let
x = amount of Tomilloso’s Pumpkin Patch entrance fee
Therefore, the inequality that represent the situation is as follows;
Jones’ Corn Maze an entry fee = 2x - 4
King’s Haunted House entry fee = 2 + x
Therefore,
2x - 4 + 2 + x + x ≤ 40
4x - 2 ≤ 40
add 2 to both sides of the inequality
4x - 2 + 2 ≤ 40 + 2
4x ≤ 42
divide both sides of the inequality by 4
4x / 4 ≤ 42 / 4
x ≤ 10.5
Therefore, the maximum price they can pay is 10.5 dollars
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1. The reduced fraction or mixed number for 375%
Answer:
the answer is shown below for the reduced fractional mixed number for 385 percentage
Step-by-step explanation:
Steps to Convert 375% to Fraction
Place the Percentage Value at the top over 100. The exact form of the fraction is 154. In the decimal form, the fraction can be written as 3.75. In the Mixed Number form, the fraction can be written as 3 .34.
(50 points) Show that x+2 is a factor of p(x)=[tex]x^4+2x^3+4x^2+x-14[/tex]. Then write p(x) as the product of x+2 and another factor. Please show work.
Answer:
Let p(x)=x
3
−4x
2
−2x+20
By factor theorem, (x+2) is a factor of p(x) if p(−2)=0.
∴ It is sufficient to show that (x+2) is a factor of p(x)
Now, p(x)=x
3
−4x
2
−2x+20
∴p(−2)=(−2)
3
−4(−2)
2
−2(−2)+20=−8−16+4+20=0
∴(x+2) is a factor of p(x)=x
3
−4x
2
−2x+20
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 868686 chocolate chip cookies and 424242 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
Camryn practiced both the trumpet and the flute today.
How many days until Camryn practices the trumpet and flute again in the same day
The greatest number of identical packages that Shaquira can make is 2.
Given data:
Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
To find:
The greatest number of identical packages that Shaquira can make
In order to find the greatest number of packages, we find the HCF of 86 and 42.
Write down this part from the attached image.
Here, 86 = 1 × 2 × 43, 42 = 1 × 2 × 21
Thus HCF = 1 × 2 = 2
So, Shaquira can make 2 identical packages the most.
Each package will have
(86 ÷ 2) = 43 chocolate chips and
(42 ÷ 2) = 21 sugar cookies.
For questions like these you would need to find out the Least Common Multiple, or L.C.M
If Camryn plays the trumpet and the flute today, and they both are in intervals of 11 and 3 days, you would need to find the LCM for 11 and 3.
LCM:
11 = 11, 1
3 = 3, 1
As they both have no common factors, and are prime numbers, multiply 11 x 3 = 33.
So, the least amount of days required for the trumpet and the flute to be played together is 33 days. And the interval between practising them both on the same day is 33 days.
Hence, the number of days until Camryn practices the trumpet and the flute on the same day is 33 days.
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Willie bought one package of basil for $3.
How many packages of basil can Julia buy
if she has $6?
please answer !!!!!!!!!!!!!!
Answer:
ST = 63
TU = 63
SU = 126
Step-by-step explanation:
Given that T is the midpoint...
Thus TS = ST and SU = 2ST =2TU
from equation...
9n = 5n + 28
9n - 5n = 28
4n = 28
n = 7
Put the value of n in the equation...
ST = 9n
= 9 x 7
= 63
SU = 9n + 5n + 28
= (9 x 7) + (5 x 7) + 28 = 126
Hope this helps!
Solve the system of linear equations using the substitution method.
2y + x = -15 and x = 3y
A. (-6, -3)
B. (-7, -6)
C. (-8, -6)
D. (-9, -3)
Answer:
the answer is D. (-9, -3)
[tex]{ \green{ \tt{option \: (d)}}}[/tex]
Step-by-step explanation:
Given,
[tex]{ \tt{2y + x = - 15}} \: { \to} \: { \tt {eq}^{n} (1)}[/tex]
[tex]{ \tt{x = 3y}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]
Substitute the value of eqⁿ (2) in (1) then,
[tex]{ \tt{2y}} \: + \: { \red{ \tt{3y}}} \: = - 15 [/tex]
[tex]{ \tt{5y = - 15}}[/tex]
Divide both sides by 5 then,
[tex]{ \tt{ \frac{5}{5}y = - \frac{15}{5}}} [/tex]
[tex]{ \red{ \boxed{ \tt{y = - 3}}}}[/tex]
Substitute the value of y in eqⁿ (2)
[tex]{ \tt{x = 3y}}[/tex]
[tex]{ \tt{x = 3( - 3)}}[/tex]
[tex]{ \red{ \boxed{ \tt{x = - 9}}}}[/tex]
Therefore, the value of (x,y) is (-9,-3)
Hence, option (d) is correct.
HELPPPPPP!!!!! PLEASEEEEE FAST!!!!!!!
Given the function f(x)=2.5xsquared+3, find the average rate of change over the interval 0 ≤ x ≤ 4. What does the average rate of change tell you about the function?
The average rate of change over the interval is 10 and it tells us about the slope
How to determine the average rate of changeThe definition of the function is given as
f(x) = 2.5xsquared + 3
Rewrite the function properly
So, we have the following equation
f(x) = 2.5x² + 3
The interval to calculate the average rate of change is given a
0 ≤ x ≤ 4
This can be represented as
[0, 4]
Further, rewrite as
[a, b] = [0, 4]
Where a = 0 and b = 4
Calculate f(a) and f(b)
So, we have
f(0) = 2.5(0)² + 3 = 3
f(4) = 2.5(4)² + 3 = 43
The average rate of change is then calculated as
Average rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have
Average rate = [43 - 3]/[4 - 0]
Evaluate
Average rate = 10
What the average rate tells usThe average rate is the slope of the function
This means that it represents the amount of change in the function with respect to the change in the input variables
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Cuanto es 3/8+-3/4
………..
PLS HELP ASAP!!!!
identify the type of transformation
Answer:
Reflection
Step-by-step explanation:
A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and form as the original, but it faces the opposite way. The opposing signs are created from the coordinates. Changes in posture during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
Write an equation involving absolute value for the graph if the points are located at -3.75 and 3.75.
The absolute value equation with the solutions -3.75 and 3.75 is:
|x| = 3.75
How to write the absolute value equation?The general absolute value equation can be written as:
|x+ a| = b
And this can be rewritten into two equations, which are:
x + a = b
x + a = -b
In this case, we want to get an absolute value function such that the two solutions are -3.75 and 3.75, this is ratter trivial to do, we can write the next absolute value function:
|x| = 3.75
If we decompose this, we will get the two equations:
x = 3.75
x = -3.75
Which are the two solutions we wanted.
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Which statement represents the simplified form of the given equation and correctly describes the solution? A. 6 ≠ 3; no real solution B. x = 6; exactly one real solution C. 6 = 6; infinite real solutions D. x = 1; exactly one real solution
Answer:infinite solution
Step-by-step explanation:
In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?
If In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. The probability that a student who has a sister also has a brother is: 3/10.
Determining the probabilityGiven data:
Total number of student = 30
Brother = 13
Sister = 8
Brother and sister = 3
Now let determine the probability that a student has brother and sister using this formula
P ( S n B ) = Brother and sister / Total number of student
Let plug in the formula
P ( S n B ) = 3/30
Therefore we can conclude that 3/30 is the probability.
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Answer:
3/8
Step-by-step explanation: