The positive solution to the equation 4x^2 + 12x = 135 is; x = 9/2
By quadratic formula;
x = {-b ±√(b² - 4ac)}/2awhere, a = 4, b = 12 and c = -135.
By solving the equation quadratically;
The solutions are;
x = 9/2. OR. x = -15/2In essence, the positive solution of the equation is; x = 9/2
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The positive solution to the equation 4x^2 + 12x = 135 is found using the quadratic formula, resulting in a positive root of approximately x ≈ 3.375.
Explanation:The positive solution to the equation 4x^2 + 12x = 135 can be found by first rearranging the equation into the standard quadratic form of ax^2 + bx + c = 0. Bringing all terms to one side gives us 4x^2 + 12x - 135 = 0. This equation can be solved by either factoring, completing the square or using the quadratic formula. Since the original equation does not easily factor into a product of binomials, and the instructions indicate a preference for recognizing a perfect square when possible, we should attempt to complete the square or use the quadratic formula.
To complete the square, we would add (b/2a)^2 to both sides of the equation after dividing the linear coefficient by 2 and squaring the result. However, in this case, it's more straightforward to employ the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values from our equation gives two roots, but since we are only interested in the positive root, we take the solution where the square root term is added to the negative b value.
After calculating, we find that the positive root is x ≈ 3.375, which is the solution to the equation in question.
Which graph shows a system of equations that solves - 2/(x - 1) = 4 , and the solution itself?
Answer:The answer is A
Step-by-step explanation:
The solution is x = -2/5.
How to solve the equation?The equation can be simplified by doing some algebra.
- 2/(x - 1) = 4
-2 = 4 (x-1)
-2 = 4x - 4
2 = 4x
x = 4/2
x= 0.5
What's an example of an equation?An equation is a mathematical announcement that is made up of expressions connected by way of an identical sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
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Solve for x (to the nearest tenth)
Step-by-step explanation:
By Geometric mean property:
[tex]x = \sqrt{5 \times 3} \\ = \sqrt{15} \\ = 3.87298335 \\ \huge\orange {\fbox{\therefore \: x \approx \: 3.9}} [/tex]
The circumference of a circle is 15 meters. Find the area. Use 3.14 for π.
Solve this system of linear equations: 4x-2y=8 Y=3/2x-2
The solution to the system of equations is x = 4 and Y = 4.
Explanation:To solve the system of linear equations, we can use substitution. Since we have the equation Y = 3/2x - 2, we can substitute this expression for Y in the first equation.
Substituting Y = 3/2x - 2 in 4x - 2y = 8:
4x - 2(3/2x - 2) = 8
Simplifying the expression:
4x - 3x + 4 = 8
x + 4 = 8
Solving for x:
x = 8 - 4
x = 4
Substituting the value of x into Y = 3/2x - 2:
Y = 3/2(4) - 2
Y = 6 - 2
Y = 4
Therefore, the solution to the system of equations is x = 4 and Y = 4.
Step-by-step explanation:
Got it right on edge. You can too
Which of the following expressions results in 0 when evaluated at x = 3?
Answer:
You need to provide the expressions you have to choose from.
Step-by-step explanation:
What is the solution to the inequality?
6x−5>−29
A.
x>−4
B.
x<4
C.
x<−4
D.
x>4
Prove algebraically what type of function this is (even, odd, or neither).
The given function is even.
Solution:
If f(-x) = f(x), then the function is even.
If f(-x) = -f(x), then the function is odd.
Given function:
[tex]f(x)=x^{6}-x^{4}[/tex]
Substitute x = -x
[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]
[tex]=x^{6}-x^{4}[/tex]
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
What is the volume, in cubic m, of a cube with an edge length of 11m?
the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .
Step-by-step explanation:
Here we have a side length of a cube as 11 m . We need to find the volume of cube . Let's find out:
We know that every side of a cube is identical and equal . And volume of cube is given by formula :
⇒ [tex]Volume = (side)^3[/tex] ...........(1)
According to question we have following parameters as
[tex]side = 11m[/tex]
Putting this in (1)
⇒ [tex]Volume = (11m)^3[/tex]
⇒ [tex]Volume = 11(11)(11)m^3[/tex]
⇒ [tex]Volume = (121)(11)m^3[/tex]
⇒ [tex]Volume = 1331m^3[/tex]
Therefore , the volume of cube with edge length 11 m is [tex]Volume = 1331m^3[/tex] .
The volume of the cube is 1331 m³
Explanation:
Given:
side of the cube, a = 11m
Volume of the cube, v = ?
we know:
Volume of the cube = (a)³
V = (11m)³
V = 1331 m³
Therefore, the volume of the cube is 1331 m³
What is an equation of the line that passes through the points (7, -6) and (3, -6)
Answer:
y=-6
Step-by-step explanation:
A colony of 300,000 bacteria doubles in size every 35 minutes what will the population be 70 minutes from now ?
Answer:
1,200,000
Step-by-step explanation:
300,000 x 4
It doubles every 35 minutes so you multiply by 4
Answer:
X=600000
Step-by-step explanation:
Let the unknown value for 70minutes be x
So let's solve the given question
300000 bacteria is double in every 35minutes
So to solve we will have
300000 bacteria=35minutes
X bacteria=70 minutes
So let's cross multiply
35x=300000×70
Let's make x the subject of formula by dividing both sides by 35
X=300000×70/35
X=300000×2
X=600000
Therefore the population in 70 minutes is 600000
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(f·g)(x) is x^5 - 5x^4 + 4x³ - x² + 5x - 4
Step-by-step explanation:
Step 1: Given, f(x) = x² - 5x + 4 and g(x) = x³ - 1 Find (f·g)(x)(f·g)(x) = f(x)·g(x) = (x² - 5x + 4)(x³ - 1)
= x^5 - 5x^4 + 4x³ - x² + 5x - 4
= x^5 - 5x^4 + 4x³ - x² + 5x - 4
how can something me nonlinear
A group of middle school boys have a mean height of 167 cm and a range of 164 cm to 169 cm. A group of high school boys have a mean height of 180 cm and a range of 175 cm to 183 cm. Which statement BEST compares the two groups of boys?
Answer:
C
Step-by-step explanation:
The high school boys vary in height more than the middle school boys.
middle school boys range = 169 − 164 = 5 cm
high school boys range = 183 − 175 = 8 cm
The range for both conditions is 5 cm and 8 cm respectively.
What is the range?The difference between the highest and lowest value data points of the provided data is known as the range in mathematics.
In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a given set of observations.
The high school boys vary in height more than the middle school boys.
Middle school boys range = 169 − 164 = 5 cm
High school boys range = 183 − 175 = 8 cm.
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Charlotte wants to swim 50 miles this school year she plans to swim 1/4 miles each day how many days Will it take her to swim 50 miles
Pls help me with this question
The solutions are £5575, £312.5 and £345 respectively.
Step-by-step explanation:
Step 1: Find the amount of Swedish kronor received by Theo in exchange for £500£1 = 11.15 kr
⇒ £500 = 500 × 11.15 = £5575
Step 2: Find the amount of Swiss francs received by Theo in exchange for £250£1 = 1.25 CHF
⇒ £250 = 250 × 1.25 = £312.5
Step 3: Find the pounds to get 407.10 euros.£1 = 1.18 euros
⇒ 407.10 euros = 407.10/1.18 = £345
The length of a rectangle is 3 centimeters less than twice the width. If the perimeter of the rectangle is 24 centimeters, find its dimensions.
Answer:
Width = 5 cm
Length = 7 cm
Step-by-step explanation:
Width = w
Length = 2w - 3
Perimeter = 24 cm
2* (length + width ) = 24
2*(2w-3 +w) = 24
2*(3w -3) = 24
3w - 3 = 24/2
3w - 3 = 12
3w = 12+ 3
3w = 15
w = 15/3
w = 5cm
Length = 2w - 3 = 2*5 - 3 = 10-3 = 7 cm
length = 7 cm
a group of rangers work 5 days per week. it takes them 4 days to plant trees on 1/2 acre.what is the unit rate per week
The unit rate at which the group of rangers plants trees is 5/8 of an acre per week, which is found by calculating the daily acreage planted and then multiplying by the number of workdays in a week.
Explanation:To determine the unit rate per week of the group of rangers planting trees, we need to calculate how much of an acre they can plant in a standard work week. As it takes them 4 days to plant trees on 1/2 acre, they will plant 1/2 acre in every 4 days of work. Since they work 5 days per week, we can adjust the ratio to calculate the weekly rate:
1/2 acre in 4 days is equivalent to (1/2 acre)/(4 days).Now, find out how much is planted in 1 day: (1/2 acre)/(4 days) = 1/8 acre in 1 day.Finally, multiply by 5 to get the weekly amount: (1/8 acre) * 5 days = 5/8 acre per week.Therefore, the unit rate at which the group of rangers plants trees is 5/8 of an acre per week.
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Carina spent a total of $5.27 buying a pineapple for $3.40 and some tomatoes that were on sale for $0.85 per pound. To determine the number of pounds of tomatoes that she bought, x, Carina wrote and solved the equation as shown below.
3.40 + 0.85 x = 5.27. 0.85 x = 8.67. x = 10.2 pounds.
Where, if anywhere, did Carina make an error?
Carina did not make any errors.
The initial equation that Carina wrote was incorrect.
Carina should have subtracted 3.40 from 5.27.
Carina should have divided 8.67 by 0.85.
Answer:
the correct answer is supposed to be 2.2 pounds.
So, C. Carina should have subtracted 3.40 from 5.27.
Step-by-step explanation:
Tip - look up on brainly or some sort of browser before waste points on asking....
Here:
5.27= 3.40+ 0.85x, we have our total our price of one pineapple and our variable
next I isolate the variable:
5.27-3.40=0.85x
next:
1.87=0.85x
Answer
x= 2.2
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Answer:
Option C, Carina should have subtracted 3.40 from 5.27.
Step-by-step explanation:
Step 1: Convert words into an equation
Carina spent a total of $5.27 buying a pineapple for $3.40 and some tomatoes that were on sale for $0.85 per pound.
3.40 + 0.85p = 5.27
Step 2: Solve for p
3.40 + 0.85p - 3.40 = 5.27 - 3.40
0.85p / 0.85 = 1.87 / 0.85
p = 2.2
The error was found when she add 3.40 to 5.27 instead of subtracting.
Answer: Option C, Carina should have subtracted 3.40 from 5.27.
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. Is it a right triangle
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters. It is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small side lengths and it can be determined by using the properties of the right triangle.
Given that,A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters.
We have to determine,Is it a right triangle?
According to the question,To determine the right triangle following all the steps given below.
A triangle has sides with lengths of 4 meters, 5 meters, and 7 meters.
The condition for the right triangle;The square of the largest side length is not equal to the sum of the square of the other two small side lengths then it is called the right triangle.
Then,
[tex]= (4)^2+(5)^2 = 7^2\\\\= 16 +25 = 49\\\\=41\neq 49[/tex]
Hence, Yes it is a right triangle because the square of the largest side length is not equal to the sum of the square of the other two small sides lengths.
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What is the probability of getting a head with the flip of a coin?
A) 0/2
B) 1/4
C) 1/2
D) 2/2
Answer:
1/2
Step-by-step explanation:
there is two side of a coin, so there is a 1/2 chance that you will head heads.
A coin has two sides, one side is heads, and the other is tails. Since there are 2 sides the probability of getting either heads or tails is 1/2. Therefore, the probability of flipping a coin and getting heads is C) 1/2.
Best of Luck!
54 months = _____ years 5.4 years 4 years 4.5 years 5 years
Answer:
C 4.5 years
Step-by-step explanation:
54 divided by 12 ( because 12 months is a single year) is 4 years and 6 months and since 6 months is half of twelve months your answer would be 4.5 years.
N x 23 = 8.05 solve for N
Answer:
0.35
Step-by-step explanation:
Just divide 8.05 by 23
The answer you are looking for is 0.35.
To solve for any variable (N in this case) you must get it by itself, by doing the opposite operation. To do so for this problem, divide 23 from both sides. In doing so, N will be by itself, and you'd then just divide 23 from 8.05. Thus getting 0.35 as an answer.
I hope this helps!
The graph shows the linear inequality y < x + 2.
Explain everything the line tells us. Why is it dashed?
Answer:
The reason why line is dashed because the inequality is indicating '<'.
Here, graphing a dashed line, then shading the area below the boundary line since y is less than x+2.
Step-by-step explanation:
Important things to observe when we graph the inequality.
Any inequality involving < or > will have a graph as a dotted line, whileAny inequality involving ≤ or ≥ will have a graph as a solid line.Given the inequality
[tex]y\:<\:x\:+\:2[/tex]
The reason why line is dashed because the inequality is indicating '<'.
Here, graphing a dashed line, then shading the area below the boundary line since y is less than x+2.
The graph is attached below.
PLEASE HELP IT'S SO IMPORTANT PLZ
create word problems that required multi-step mathematical thinking, such as the solution of the equation is then used to determine the actual solution of the question, and SOLVE IT.
Will this help?
Answers:
1. $8 left
2. 4 minutes
3. 9 balloons
Questions
1. Craig has a twenty dollar bill. He buys six squirt guns
for $2 each. How much money did Craig have left?
2. Lauren and Gina's mother told her daughters they can
swim in the pool for 20 minutes. First, they swam laps in
the pool for 7 minutes. Then they swam underwater for
one minute. Then they played water polo for 8 minutes.
How much longer can they stay in the pool?
3. Maria invited 4 of her friends over for a water balloon fight in
the backyard. At the start of the game, Maria gave each of
her friends 2 water balloons. She had one water balloon for
herself. How many water balloons did they have altogether?
HELP PLEASE BE QUICK
Answer:
Radius is 2 centimeters
Step-by-step explanation:
4π is the area of a circle
Area of a circle = πr^2
4π / π = πr^2 / π
sqrt(4) = sqrt(r^2)
2 = r
Answer: Radius is 2 centimeters
16 m, 21 m, 39 m in geometry tryna find out how to measure the side length that could form a triangle
Step-by-step explanation:
The given measurements are:
16 m, 21 m, 39 m
We know that, it is only possible to form a triangle if sum of the measures of any two lengths is always grater than the measure of third length.
[tex] \therefore \: 39 + 21 = 60 > 16 \\ \\ \: \: \: \: \: \: 16 + 39 = 55 > 21 \\ \\ \: \: \: \: \: \: 16 + 21 = 37 \ngtr39 \\ \\ \because \: last \: mathematical\: statement \: is \:\\ defying \: the \: above \: law \\ [/tex]
Therefore, it is not possible to form a triangle with given measurements.
The given lengths cannot form the sides of a triangle because they dont satisfy the sides of a triangle rule.
What is the sides of a triangle rule say?The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Given here, are the sides 16 m, 21 m , 39m
now if the two sides are 16, 21 then their sum is 16+21 = 37 but 37<39 thus combination of lengths cannot form a triangle
Hence, the lengths 16,21,39 cannot form the sides of a triangle
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Gohan earned scores of 95, 100, 65, 95, 75, 98, 100, 55, 100, 45 on his last ten quizzes. What is the mean of his quiz scores? What is the median of his quiz scores? What is the mode of his quiz scores?
Answer: Mean= 82.8
Median= 95
Mode=100
Step-by-step explanation:
Mean is the average of the scores
Mean= 95+100+65+95+75+98+100+55+100+45 =828/10= 82.8
To get the median, we rearrange the numbers in either ascending or descending order.
45,55,65,75,95,95,98,100,100,100
Median= 95
Mode is the number that occurs most which is 100
Answer:
Answer: Mean= 82.8
Median= 95
Mode=100
Step-by-step explanation:
I got this correct, hope this helps:)
Help I am confused i don’t remember how to answer this.
Answer:
5/6
Step-by-step explanation:
I hope this helps!
Answer:
5/6
Step-by-step explanation:
so for the first equation I would keep 1/3 the same
flip the division sign to multiplication
and turn the second fraction 4/10 upside down so it becomes 10/4
[tex]\frac{1}{3} *\frac{10}{4} =10/12[/tex]
10/12 can be simplified by dividing 2 on the numerator and denominator
10/2=5
12/2=6
5/6
for the second equation I know that each number in the first equation should be present in the second(since they are all the same numbers). However, 5/6 is not present in the second equation so that is the missing number
Hope this helps!
Quadrilateral ABCD was transformed to create A'B'C'D'. If A'B'C'D' is reflected over the y-axis, what will be the coordinates of D''?
Math item stem image
CLEAR CHECK
(-2, -3)
(-2, 3)
(2, -3)
(2, 3)
Answer: This question is impossible to answer if the original coordinate of D is not known
Step-by-step explanation: In order to answer this question you need to know what the coordinate of D is
The coordinates of D'' will be; (-2, 3)
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
We are given that Quadrilateral ABCD was transformed to create A'B'C'D'. If A'B'C'D' is reflected over the y-axis, then
A(-5,-3); B(-6,-1); C(-3,-1) ; D(-2,-3)
When a refection is done about x-axis, the values of the abscise x remain identical & the value of ordinate;
A(-5,-3); A'(-5,+3)
B(-6,-1); B'(-6,+1)
C(-3,-1); C'(-3,+1)
D(-2,-3); D'(-2,+3)
A'B'C'D' is translated 3 UNITS RIGHT, that means the ordinated of A'B'C'D' are the same but the abscises have been increased by 3 UNITS then the coordinates of D'' is (-2, 3)
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Each of the letters of the word ALABAMA are written on a piece of paper and then put into a bag. A piece of paper is drawn at random. What is the theoretical probability, as a decimal, of drawing an A? Round the decimal to the nearest hundredth.
The theoretical probability of drawing an 'A' from the word 'ALABAMA' is 0.57. This result arrives from dividing the number of 'A's (4) by the total number of letters in 'ALABAMA' (7).
Explanation:The question deals with a probability problem related to the selection of letters from the word 'ALABAMA'. The word 'ALABAMA' has 7 letters out of which 4 are 'A's. The theoretical probability is calculated as the number of successful outcomes divided by the total number of outcomes. Since we are interested in drawing an 'A', the successful outcomes are the number of 'A's which is 4, and the total outcomes are the total number of letters which is 7.
To calculate theoretical probability, you divide the number of successful outcomes by the total number of outcomes. In this case, the calculation will be 4 / 7 = 0.57 (rounded to the nearest hundredth).
So, the theoretical probability of drawing an A from the word 'ALABAMA' in decimal form, rounded to the nearest hundredth, is 0.57.
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