Hence, the value of x is:
[tex]x=\dfrac{1}{3}[/tex]
Step-by-step explanation:We have to solve for x i..e we have to find the value of 'x' by solving this equation.
The equation is given as:
[tex]-4(3x-2)=6x+2[/tex]
firstly we will solve the bracket term as:
[tex]-4\times 3x-4\times (-2)=6x+2\\\\-12x+8=6x+2[/tex]
Now we take like terms together i..e the variable term is taken to the right hand side of the equation and the constant term is kept on the left side of the equation as:
[tex]8-2=6x+12x\\\\\\6=18x[/tex]
on dividing both side of the equation by 18, we obtain:
[tex]x=\dfrac{6}{18}\\\\x=\dfrac{1}{3}[/tex]
Hence, the value of x is:
[tex]x=\dfrac{1}{3}[/tex]
Answer:
B
Step-by-step explanation:
how to write 2/5 as a decimal
Write 702,001 in Expanded Form. (No spaces in answer) ...?
The daily rainfall during a two week period in April was: 1, 0.5, 0.3, 0, 0 ,0, 1.2, 3, 0, 1.1, 0.7, 2, 1.3, 2 inches. What was the mode during this two week period?
Answer: 0.3 is the mode
Step-by-step explanation: The mode is what number shows up the most and 0.3 shows up 3 times.
0 shows up twice
How to find the product of rational expressions
A 16 ounce jar of peanut butter costs $1.98. What is the price per ounce, rounded to the nearest hundredths place?
The size S of a tumor in mm cubed is given by S=2^t, where t is the number of months since the tumor was discovered a: what is the total change in the size of the tumor during the first 6 months?
and b: what is the average rate of change in the size of the tumor during the first 6 months?
and c: estimate the rate at which the tumor is growing at t=6?
a. the total change in the size of the tumor during the first 6 months is 64 - 1 = 63 mm³.
b. the average rate of change in the size of the tumor during the first 6 months is 10.5 mm³ per month.
c. the estimated rate at which the tumor is growing at t = 6 is approximately 44.352 mm³ per month.
a) Total change in the size of the tumor during the first 6 months:
To find the total change in the size of the tumor, we need to subtract the initial size from the size after 6 months. Since [tex]\( S = 2^t \)[/tex], we can calculate the size at t = 6 by plugging in t = 6 into the equation. Then, we can subtract the initial size from this value.
[tex]\[ S(6) = 2^6 = 64 \][/tex]
The initial size is given by [tex]\( S(0) = 2^0 = 1 \).[/tex]
So, the total change in the size of the tumor during the first 6 months is 64 - 1 = 63 mm³.
b) Average rate of change in the size of the tumor during the first 6 months:
The average rate of change is given by the total change divided by the number of months. We already found the total change (63 mm³), and the number of months is 6.
[tex]\[ \text{Average rate of change} = \frac{\text{Total change}}{\text{Number of months}} = \frac{63}{6} = 10.5 \][/tex]
So, the average rate of change in the size of the tumor during the first 6 months is 10.5 mm³ per month.
c) Estimate the rate at which the tumor is growing at t = 6:
To estimate the rate at which the tumor is growing at t = 6, we can use calculus to find the derivative of the function [tex]\( S(t) = 2^t \)[/tex] with respect to t. The derivative represents the rate of change of S with respect to t at any given time.
[tex]\[ \frac{dS}{dt} = \frac{d}{dt} (2^t) = (\ln 2) \cdot (2^t) \][/tex]
Now, plug in t = 6 to find the rate of change at that specific time.
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} = (\ln 2) \cdot (2^6) \][/tex]
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} = (\ln 2) \cdot 64 \][/tex]
Since [tex]\( \ln 2 \approx 0.693 \)[/tex], we have:
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} \approx 0.693 \cdot 64 \approx 44.352 \][/tex]
So, the estimated rate at which the tumor is growing at t = 6 is approximately 44.352 mm³ per month.
help please.
What is the common difference d of the sequence?
−15, −4, 7, 18, 29, ...
d = ?
Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′.The slope of C'D' is
The slope doesn't change after dilation, it would still be 2.
Percent change 74 to 85
3 times a number divided by 2
Solve for x.
−5x−4(x−6)=−3
Enter your answer in the box.
x =
What is the equation in point-slope form of the line passing through (−1, 3) and (1, 7)
y − 7 = 4(x − 1)
y − 7 = 2(x − 1)
y − 3 = 2(x − 1)
y − 3 = 4(x + 1)
how do u right this Seven less than the quotient of x and 9
Answer:
(x÷9)−7 is your answer.
Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
The greatest common factor (GCF) of the expressions 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 · 5, or 40. This is determined by comparing the exponents of the common base terms in both expressions and selecting the lowest exponents.
Explanation:The student's question is about finding the greatest common factor (GCF) of two different mathematical expressions, namely: 2^5 · 5· 11 and 2^3· 5^2 · 7. In this context, 'GCF' refers to the greatest number that is a factor of two or more numbers. For these expressions, we will look at the shared factors of the two expressions.
Steps to find the GCF:
Compare the exponents of the common base terms in the two expressions. Here, the common base terms are '2' and '5'. In the first expression, '2' is raised to the power of '5' and '5' is raised to the power of '1'. In the second expression, '2' is raised to the power of '3' and '5' is raised to the power of '2'. For each base, select the lowest exponent. Therefore, for base '2', we select '3' as the exponent and for base '5', we select '1'. Therefore, the GCF of the two expressions is 2^3 · 5 or 40. Learn more about Greatest Common Factor here:
https://brainly.com/question/29584814
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Which answer is an equation in point-slope form for the given point and slope? Point: (1,9); Slope:5
y - 1 = 5(x + 9)
y + 9 = 5(x - 1)
y - 9 = 5(x - 1)
y - 9 = 5(x + 1)
Think the answer is C. DO NOT JUST AGREE WITH ME I think I'm wrong.
Thanks to whoever is going to answer. I will be marking the best answer the brainliest answer.
The answer is indeed C.
point slope form is: y - y1=m(x - x1)
we substitute the values in; y1= 9; x1=1
and of course, the slope is 5
which gives us
y-9=5(x - 1)
9x-3y=3; 3x+8y=-17
I want to know the steps and answers
You roll 1 red and 1 white dice. What is the probability that the number on the red die is larger than the number on the white die?
can anyone help me?:( ...?
You have $80 and your brother has $275 dollars. You save $10 of your allowance each week. Your brother spends his allowance plus $15 each week.
1. Write an equation to model this.
2. How long before you have as much money as your brother?
3. How much have you saved when you catch up to him?
Liana started to evaluate the function f(x) = 2x^2 – 3x + 7 for the input value 2.
f(x) = 2(2)2 – 3(2) + 7
= 2(4) – 3(2) + 7
What is the value of the function when x = 2?
a) 9
b) 10
c) 16
d) 17
Answer:
9 is the right answer on edge
Step-by-step explanation:
Jim Debt was reviewing the total accounts receivable. This month he received $80,000 from Credit customers. This represented 40 percent of all receivables due. The total amount of accounts receivable is ...?
40% = 80,000
20% = 40,000
x5 = 100% = 200,000
What is the length of the altitude of the equilateral triangle below
Answer
Find out the altitude of the equilateral triangle .
To proof
By using the trignometric identity.
[tex]tan\theta = \frac{Perpendicular}{base}[/tex]
As shown in the diagram
and putting the values of the angles , base and perpendicular
[tex]tan 60^{\circ} = \frac{a}{4\sqrt{3}}[/tex]
[tex]tan 60^{\circ} = \sqrt{3}[/tex]
solving
[tex]\sqrt{3} = \frac{a}{4\sqrt{3}}[/tex]
[tex]a = \sqrt{3}\times 4 \sqrt{3}[/tex]
As
[tex]\sqrt{3}\times \sqrt{3} = 3[/tex]
put in the above
a = 4 × 3
a = 12 units
The length of the altitude of the equilateral triangle is 12 units .
Option (F) is correct .
Hence proved
Answer:
F. 12
Step-by-step explanation:
We have been given an image of a triangle and we are asked to find the length of the altitude of our given triangle.
Since we know that altitude of an equilateral triangle splits it into two 30-60-90 triangle.
We will use Pythagoras theorem to solve for the altitude of our given triangle.
[tex]\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2[/tex]
Upon substituting our given values in above formula we will get,
[tex](4\sqrt{3})^2+a^2=(8\sqrt{3})^2[/tex]
[tex]16*3+a^2=64*3[/tex]
[tex]48+a^2=192[/tex]
[tex]48-48+a^2=192-48[/tex]
[tex]a^2=144[/tex]
Upon taking square root of both sides we will get,
[tex]a=\sqrt{144}[/tex]
[tex]a=12[/tex]
Therefore, the length of the altitude of our given equilateral triangle is 12 units and option F is the correct choice.
60 is 300% of what number
Let w represent the possible weights of boxes on a delivery truck. For this type of delivery, the weight of the box must be within 8 pounds of a standard lifting weight of 48 pounds. Write an inequality to describe the possible weights of boxes.
A. |w – 48| ≥ 8
B. |w – 48| ≤ 8
C. |w – 48| < –8
D. |w – 48| > –8
for each of the values of h given, when x is increased from 1 to 1+h, work out:
Differential equation: In solving equations involving x, y, and z, taking steps with various values of h optimizes the process.
Step size h: When h=0.5 over the interval 0 to 2, solutions can be calculated by incrementing x from 1 to 1+h.
Optimizing procedures: By choosing appropriate values for h, the iterative process can be streamlined for better efficiency.
Upvote
Which is a correct comparison of the fractions?
15/18 and 25/30
A.15/18 < 25/30
B.15/18 > 25/30
C.15/18 = 25/30
Therefore, the correct option is C. 15/18 = 25/30. The fractions 15/18 and 25/30 were simplified to 5/6, proving they are equal.
Comparison of Fractions 15/18 and 25/30
To compare the fractions 15/18 and 25/30, we can first simplify them to make the comparison easier. We simplify each fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
1. Simplify 15/18:
GCD of 15 and 18 is 3.
→ 15 ÷ 3 = 5
→ 18 ÷ 3 = 6
So, 15/18 = 5/6.
2. Simplify 25/30:
GCD of 25 and 30 is 5.
→ 25 ÷ 5 = 5
→ 30 ÷ 5 = 6
So, 25/30 = 5/6.
Therefore, 15/18 = 25/30. The correct comparison is:
C. 15/18 = 25/30
Expand 2x (3x+2y) Thanks
True or False? A secant is a line or segment that passes through a point on the circle and the center of the circle.
A. True
B. False
Answer:
B.False.
Step-by-step explanation:
A secant is a line or segment which passes through two points or more points and cut the curve at atleast two points.
We are talking about of secant of circle
Secant: A secant is a line that passe through two points of circle and it intersect the circle at two points.
Therefore,given definition of secant is
A secant is a line or segment that passes through a point on the circle and the cente rof the circle.
By definition of secant , we can say the given define in question is false.
Because that segment which passes through a point on circle and center of the circle is radius not secant.
Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.
y = –17(x)(x – 4)
y = –16(x)(x – 4)
y = –16(x – 2)^2 + 68
y = –17(x – 2)^2 + 68
Answer: C - Y = -16(x- 2)^2 + 68
Step-by-step explanation:
Edge 2023
Final answer:
The correct quadratic equation that models the ball's vertical motion is y = –16(x – 2)² + 68, since it reflects the ball reaching its maximum height at 2 seconds and the vertex of the parabola being the highest point of the ball's path.
Explanation:
The question involves finding an equation that models the height of a tennis ball thrown straight up into the air after a certain number of seconds. Given that the ball reaches its maximum height at 2 seconds, we can determine which equation best describes the ball's vertical motion. The correct equation will show the ball peaking at 2 seconds and then descending symmetrically in a parabolic path.
The equation that correctly models the motion of the ball in this context is y = –16(x – 2)² + 68. This quadratic equation is in the vertex form of a parabola, where the maximum height is represented by the vertex point (2, 68), and the vertex is the highest point of the parabola since the coefficient of the squared term is negative.
When x is 2 seconds, the equation simplifies to y = –16(0)²+ 68, which results in y = 68, demonstrating that the maximum height of 68 is indeed reached at 2 seconds after the ball is thrown, thus supporting that this is the correct quadratic equation for the scenario.
25% of what number is 17
The pilot of an airplane traveling 190 km/h wants to drop supplies to flood victims isolated on a patch of land 100 m below.
How many seconds before the plane is directly overhead should the supplies be dropped? ...?