Answer:
[tex]\implies \boxed{\red{\sf ( x +1)^2 = \dfrac{1}{4}}} [/tex]
Step-by-step explanation:
Given :-
A equation is given to usThe equation is 4x² + 8x + 3 = 0And we need to write the equation by completing the square. Here's the step by step explanation .
Step 1: Make the coefficient of x² as 1 :-
[tex]\implies \dfrac{4x^2}{4} + \dfrac{8x}{4} + \dfrac{3 }{4}= 0 [/tex]
Step 2: Rewrite the equation :-
[tex]\implies x^2 + 2x +\dfrac{3}{4}= 0 [/tex]
Step 3: Add 1² to both sides :-
[tex]\implies x^2 + 2x + 1^2+\dfrac{3}{4}= 0 + 1^2 [/tex]
Step 4: Rewriting in whole square form:-
[tex]\implies ( x +1)^2 = 1 - \dfrac{3}{4} [/tex]
Step 5: Simplify the RHS :-
[tex]\implies ( x +1)^2 = \dfrac{4- 3}{4} [/tex]
Step 6: The required form of equⁿ :-
[tex]\implies ( x +1)^2 = \dfrac{1}{4} [/tex]
Hence the equation by rewriting it by completing the square is ( x + 1)² = 1/4 .
(2h3 + 6h) + (3h3 - 7h - 3) standard form sum or difference.
Answer:
[tex]5h^3- h - 3[/tex]
Step-by-step explanation:
Given
[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]
Required
Standard form
We have:
[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]
Remove bracket
[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 6h + 3h^3 - 7h - 3[/tex]
Collect like terms
[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 3h^3+ 6h - 7h - 3[/tex]
[tex](2h^3 + 6h) + (3h^3 - 7h - 3) = 5h^3- h - 3[/tex]
Hence, the standard form is:
[tex]5h^3- h - 3[/tex]
Select all the polygons that would be used in a net of the solid figure shown.
A triangular pyramid. The base has all three sides equal in length. The pyramid is taller than the width of the base.
right triangle
equilateral triangle
isosceles triangle
rectangle
square
Answer:
C, definitely two sides are different in the triangle.
A, it looks as if the bottom is a right triangle if you look at it in a different way.
The polygons that would be used in a net isosceles triangle & right triangle
What is Pyramid?A pyramid is a structure whose outer surfaces are triangular and converge to a single step at the top,
As, we need a triangular pyramid whose base has all the three sides equal in length.
We can have a net in the form of isosceles triangle whose two are equal
i.e., two sides are different in the triangle.
and also, bottom with the right angle
i.e., the bottom is a right triangle if you look at it in a different way.
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Which equation describes a circle with center (4,−7) and radius 9? A (x−4)2+(y+7)2=81 B (x+4)2+(y−7)2=81 C (x−4)2+(y+7)2=9 D (x+4)2+(y−7)2=9
Answer:
A. (x - 4)² + (y + 7)² = 81
Step-by-step explanation:
The general equation for a circle is given by the formula;
x² + y² + 2hx + 2ky + c = 0 ......equation 1.
Where the center is C(-h, -k)
Also, the standard form of the equation of a circle is;
(x - h)² + (y - k)² = r² ......equation 2.
Where;
h and k represents the coordinates of the centre. r represents the radius of the circle.Given the following data;
h = 4
k = -7
r = 9
Substituting into eqn 2, we have;
(x - 4)² + (y - {-7})² = 9²
Simplifying further, we have;
(x - 4)² + (y + 7)² = 81
Solve the expression 8 + (9 x one third ) ÷ 3 using PEMDAS. (4 points)
Group of answer choices
4
7
8
9
Answer:
the answer is 9 hope this helps
Step-by-step explanation:
If the HCF is 5 and the product of the two numbers is 70, find the value of LCM.
If the HCF is 5 and the product of the two numbers is 70, then the value of LCM is 14.
Do two numbers make a product when they are the LCM of two numbers?The smallest number that can be divided by both numbers is known as the least common multiple, or LCM, of two numbers. The product of the two numbers is the LCM if their greatest common divisor is 1, in which case their product is 1.
Using the fundamental theorem of mathematics, how do you find the HCF and LCM?First, multiply both numbers by their prime factors to express them. Then, multiply the common factor with the highest power by the remaining factors to obtain the LCM. Take the common factors with the lowest power and multiply them to determine HCF.
To find the LCM of two numbers, you can use the formula: LCM = (a * b) / HCF.
In this case, we know that the HCF is 5, and the product of the two numbers is 70. Therefore, we can substitute these values into the formula:
LCM = (70) / 5 = 14.
So the LCM of the two numbers is 14.
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URGENT CLICK TO SEE LINKS WILL GET REPORTED PLS
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Complete the two-way frequency table below, which shows the relationship between adults' gender and whether these adults buy a truck or a car for their first new vehicle. From a sample of 88 adults, the following data are collected:
Truck Car Total
Female 5 35
Male 27 21
Total 88
What is the probability (rounded to the nearest whole percent) that an adult will buy a car, given that she is a female? Are the events being female and buying a car independent?
Answer:
Truck Car Total
Female 5 35 40
Male 27 21 48
Total 32 56 88
P(buying a car given a male ) = 21/88 = .238 ≈ 24%
Step-by-step explanation:
Let B = Probability of buying a car and being male 21/88
Let M = Probability of being a male = 48/88
P(B l M) = P(B and M) / P(M) = (21/88) / (48/88) = 21/48 = .4375 = 44%
Happy To Help!!!Jordan is 12 years older than Anna. The
sum of their ages is 50. Find the age of
each person.
First complete the equations below, where I stands for
Jordan's age and A stands for Anna's age.
J = [?] + A; J + A = []
Help
9514 1404 393
Answer:
J = [12] +AJ + A = [50]Step-by-step explanation:
If Anna's age is represented by A, then 12 more than Anna's age will be ...
12 + A
Jason's age is said to be 12 more than Anna's age, so ...
J = 12 + A
__
The sum of their ages will be J + A. That is said to be 50, so ...
J + A = 50
_____
These equations can be solved by using the first to substitute for J in the second.
(12 +A) +A = 50
2A = 38 . . . . . . . . subtract 12
A = 19 . . . . . . . . . . divide by 2
J = 12 +19 = 31 . . . find Jason's age
Jason is 31; Anna is 19.
MAth question:
A square pyramid has a height of 9 cm and a base length of 4 cm. Find the volume
Answer: 48
Step-by-step explanation:
Convert:
25 decimeters
=
Round to the tenths.
meters
Answer:
2.5
Step-by-step explanation:
Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.
Train A and Train B both leave the station at 9am. Train A stops every 15 minutes. Train B stops every 24 minutes. At what time do both Trains stop at the same time again?
Answer:
here
Step-by-step explanation:
180 minutes
helppppp
!NO LINKS, NO FILES!
please :)
Answer:
53
Step-by-step explanation:
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Instructions: Find the missing segment in the image below.
Help please
Answer:
9
Step-by-step explanation:
It’s a ratio.
5/30=x/54
reduce
1/6=x/54
cross multiply
54=6x
x=9
One pair of base angles of an isosceles trapezoid each have a measure of 2(x–10)°. The other pair of base angles of the trapezoid each have a measure of (4x+8)°. What is the value of x?
Answer:
x = 32
Step-by-step explanation:
• any lower base angle is supplementary to any upper base angle.
here base angle = 2(x - 10) and upper base angle = 4x + 8
supplementary angles sum to 180°
sum the base and upper base angles and equate to 180
2(x - 10) + 4x + 8 = 180
2x - 20 + 4x + 8 = 180
6x - 12 = 180 ( add 12 to both sides )
6x = 192 ( divide both sides by 6 )
x = 32
ABC is an equilateral triangle. A circle with radius 1 is tangent to the line
AB at the point B and to the line AC at point C. What is the side length of
ABC? Show your work?
The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.
How to evaluate for the side length of the triangleAn equilateral triangle have all its side lengths equal so;
line AB = line BC = line AC
At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle
Line BC form the diameter of the circle which is 2 radius of the circle so;
line BC = 2 × radius of the circle
line BC = 2 × 1
line BC = 2
Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.
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A __________ is a promise by a borrower to repay a loan at a specified rate of interest.
Select one:
a. Bond
b. Premium
c. Quoted Price
Find the value of x
Answer:
x = 30
Step-by-step explanation:
24(24 + x) = 36² => tangent-secant theorem
Open the bracket
24*24 + 24*x = 36²
576 + 24x = 1,296
24x = 1,296 - 576
24x = 720
Divide both sides by 24
24x/24 = 720/24
x = 30
The amount Y (in dollars) Of money in your savings account after X months is represented by the equation Y equals 12.5 X +100 a. graph the linear equation b. how many months will it take for you to save a total of $237.50[QUICK ITS HOMEWORK AND ITS LATE]
The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.
What is a saving account?
An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.
Given equation is
y = 12.5x + 100
To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:
y(0) = (12.5 × 0) + 100
y(0) = 100
y(1) = (12.5 × (1)) + 100
y(1) = 12.5 + 100
y(1) = 112.5
y(2) = (12.5 × 2) + 100
y(2) = 25 + 100
y(2) = 125.
The points on the linear equation are (0,100), (1, 112.5), (2,125).
Plot the points and join the points to draw the line to get graph the linear equation.
Putting y = 237.50 in the given equation y = 12.5x + 100:
237.50 = 12.5x + 100
Subtract 100 from both sides:
237.50 - 100 = 12.5x + 100 - 100
137.50 = 12.5x
Divide both sides by 12.5:
x = 137.50/12.5
x = 11
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1 18. You have a --cup 4 1 measuring cup and a --cup measuring 2 cup. What are two ways you can 3 measure 2 cups of water? - 4
In circle J with m
a. 46.5'
b.73'
c.292'
d.214'
Answer:
B. 73°
Step-by-step explanation:
mL HLK = ½ × mL HJK = ½×146=73°
ASAP PLZ HELP I WILL GIVE BRAINLIEST ALL QUESTIONS NO LINKS PLZZ
SOMEOINE HELP!!!
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. (1, 2), (2, 4), (3, 8), (4, 16) Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points) Part B: Write a function to represent the data. Show your work. (4 points) Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
Answer:
Part A:
This data is modeling an exponential function because the y-values are increasing at an increasing rate. For example, between station 1 and station 2, the time increased by 2 minutes, and between station 2 and station 3, the time increased by 4 minutes. The time between each station is increasing by a multiple of the time between the previous two stations. This indicates that the data follows an exponential curve.
Part B:
To represent this data as a function, we can use the formula y = ab^x, where a and b are constants and x is the input (station number).
Substituting in the values from the first data point, we get: 2 = ab^1
Substituting in the values from the second data point, we get: 4 = ab^2
We can then solve for a and b by dividing these equations:
4/2 = (ab^2)/(ab^1)
2 = b
Substituting this value back into the first equation, we get:
2 = a*2^1
1 = a
Therefore, the function that represents this data is y = 2^x.
Part C:
To find the average rate of change between station 2 and station 4, we can use the formula: (y2 - y1)/(x2 - x1).
Substituting in the values from the data, we get: (16 - 4)/(4 - 2) = 12/2 = 6.
Therefore, the average rate of change between station 2 and station 4 is 6.
1.) The acceleration of a particle moving along the x-axis at time t is given by a(t) = 6t-2. If the position is 10 when
t= 1, then which of the following could be the function for position x(t) = ?
The function for position x(t) could be x(t) = 3t^2 - 2t + 10.
What is function?In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.
This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.
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Divide. Round to the nearest tenth.
3.5/2.29
Answer:
The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.
A rhombus has a side length equal to one of the diagonals. The other diagonal is 4cm longer. Find the area of the rhombus.
Answer:
The area of the rhombus is 25.83 cm².
Step-by-step explanation:
The area of a rhombus is given by:
[tex] A = \frac{d_{1} \times d_{2}}{2} [/tex]
Where:
d₁: is one diagonal
d₂: is the other diagonal = d₁ + 4 cm
We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:
h: hypotenuse of the right triangle
a: one side of the right triangle
b: is the other side of the right triangle
From the above we know that:
h = d₁
[tex] a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2} [/tex]
[tex] b = \frac{d_{1}}{2} [/tex]
We can find d₁ with Pitagoras:
[tex] h^{2} = a^{2} + b^{2} [/tex]
[tex] d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2} [/tex]
[tex] d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2}) [/tex]
By solving the above quadratic equation for d₁ and taking the positive solution we have:
[tex] d_{1} = 5.46 cm [/tex]
So, d₂ is:
[tex] d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm [/tex]
Now, we can find the area:
[tex] A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2} [/tex]
Therefore, the area of the rhombus is 25.83 cm².
I hope it helps you!
Help
Write an equation and solve: A plumber charges a $65 fee for a visit plus $42 per hour of service. Trevor's bill was $233. Write and solve an equation to find how many hours of service the plumber charged?
Answer:
x=per hour
233=42x+65
Step-by-step explanation:
It takes Luke 2 h longer than it does Anna to clean a bathroom. If t represents the amount of time (in h) it takes for Luke to clean a bathroom, write an expression that represents the time (in h) it takes Anna to clean the bathroom.
please answer the following question, if you send me a link then you will be reported
Find the surface area of the triangular prism.
Answer:
16 x 12 = 192
192 x 2 = 384
10 x 8 = 80, 80 divided by 2 = 40
40 x 2 = 80
10 x 16 = 160
Add all given areas:
384 + 80 + 160 = 624 cm2 is your answer.
how many 2/5s are in 1 and 1/2
Answer:
4
Step-by-step explanation:
How many 2/5s are in 1 1/2? To make it easier and simpler , I would change these fractions into decimals . Our answer is there are ALMOST 4 of 2/5ths in 1 and a half .
Find the sum of the first 12 terms of the geometric series
2 + 4 + 8 +...
In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.
How can the sum of the initial terms in a geometric series be determined?the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.
What is a geometric series term?A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.
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