Answer:
[tex]\large\boxed{x^2+y^2+4x-2y+1=0}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
The general form of an equation of a circle:
[tex]x^2+y^2+Dx+Ey+F=0[/tex]
We have the center (-2, 1). Substitute to the equation in the standard form:
[tex](x-(-2))^2+(y-1)^2=r^2\\\\(x+2)^2+(y-1)^2=r^2[/tex]
Put thr coordinates of the point (-4, 1) to the equation and calculate a radius:
[tex](-4+2)^2+(1-1)^2=r^2\\\\r^2=(-2)^2+0^2\\\\r^2=4[/tex]
Therefore we have the equation:
[tex](x+2)^2+(y-1)^2=4[/tex]
Convert to the general form.
Use [tex](a\pm b)^2=a^2\pm 2ab+b^2[/tex]
[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\qquad\text{subtract 4 from both sides}\\\\x^2+y^2+4x-2y+1=0[/tex]
which do you think is greater , 4 x 3 2/5 or 3 x 4 2/5
Answer:
[tex]4(3\frac{2}{5})[/tex] is greater
Step-by-step explanation:
step 1
we have
[tex]4(3\frac{2}{5})[/tex]
convert to an improper fraction
[tex]3\frac{2}{5}=\frac{3*5+2}{5}=\frac{17}{5}[/tex]
so
[tex]4(3\frac{2}{5})=4(\frac{17}{5})=\frac{68}{5}[/tex]
step 2
we have
[tex]3(4\frac{2}{5})[/tex]
convert to an improper fraction
[tex]4\frac{2}{5}=\frac{4*5+2}{5}=\frac{22}{5}[/tex]
so
[tex]3(4\frac{2}{5})=3(\frac{22}{5})=\frac{66}{5}[/tex]
therefore
[tex]4(3\frac{2}{5})[/tex] is greater
Final answer:
After converting mixed numbers to improper fractions and multiplying, it is clear that 4 x [tex]3\frac{2}{5}[/tex] is greater than 3 x [tex]4\frac{2}{5}[/tex].
Explanation:
The question asks which is greater: 4 x [tex]3\frac{2}{5}[/tex] or 3 x [tex]4\frac{2}{5}[/tex]. Let's compare these two expressions
First, convert the mixed numbers to improper fractions:
[tex]3\frac{2}{5}[/tex] = (3x5 + 2)/5 = 17/5
[tex]4\frac{2}{5}[/tex] = (4x5 + 2)/5 = 22/5
Next, multiply each by the whole number:
4 x 17/5 = 68/5 = 13.6
3 x 22/5 = 66/5 = 13.2
Therefore, 4 x [tex]3\frac{2}{5}[/tex] is greater than 3 x [tex]4\frac{2}{5}[/tex].
7x-3/8=6x-5/8 what is x
7x - 3/8 = 6x -5/8
Subtract 6x from each side:
x - 3/8 = -5/8
Add 3/8 to each side:
x = -5/8 + 3/8
x = -2/8
x = -1/4
which quadratic equation is equivalent to (x^2-1)^2 -11(x^2-1)+24=0
A)u^2-11u+24=0 where u=(x^2-1)
B) (u^2)^2 -11(u^2) +24 where u = (x^2-1)
C)u^2+1-11u+24 =0 where u =(x^2-1)
D)(u^2-1)^2 -11(u^2-1) +24 where u =(x^2-1)
Answer:
[tex]\large\boxed{A)\ u^2-11u+24=0}[/tex]
Step-by-step explanation:
[tex](x^2-1)^2 -11(x^2-1)+24=0\\\\\text{Substitute}\ (x^2-1)=u\\\\\underbrace{(x^2-1)}_{u}\ ^2 -11\underbrace{(x^2-1)}_{u}+24=0\to u^2-11u+24=0[/tex]
Answer: The correct option is
(A) [tex]u^2-11u+24=0,~~\textup{where }u=(x^2-1).[/tex]
Step-by-step explanation: We are given to select the correct quadratic equation that is equivalent to the following equation :
[tex](x^2-1)^2-11(x^2-1)+24=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let us consider that
[tex]u=x^2-1.[/tex]
Substituting the value of u in equation (i), we get
[tex](x^2-1)^2-11(x^2-1)+24=0\\\\\Rightarrow u^2-11u+24=0.[/tex]
Thus, the required equivalent quadratic equation is
[tex]u^2-11u+24=0,~~\textup{where }u=(x^2-1).[/tex]
Option (A) is CORRECT.
What is the value of x in the equation 5(3x + 4) = 23?
[tex]\huge\text{$x=\boxed{\frac{1}{5}}$}[/tex]
Hey there! To solve this problem, we need to isolate [tex]x[/tex] on one side of the equation.
[tex]\begin{aligned}5(3x+4)&=23\\5\cdot3x+5\cdot4&=23&&\smash{\Big|}&&\text{Distribute the $5$.}\\15x+20&=23&&\smash{\Big|}&&\text{Multiply.}\\15x&=3&&\smash{\Big|}&&\text{Subtract $20$ from both sides.}\\x&=\frac{3}{15}&&\smash{\Big|}&&\text{Divide both sides by $15$.}\\x&=\boxed{\frac{1}{5}}&&\smash{\Big|}&&\text{Divide the numerator and denominator by $3$.}\end{aligned}[/tex]
Answer:
[tex] x = \frac { 1 } { 5 } [/tex]
Step-by-step explanation:
We are given the following equation and we are to find the value of x by making it the subject of the equation:
[tex] 5 ( 3 x + 4 ) = 23 [/tex]
We will start by opening the brackets and expanding the term by multiplying 5 with the terms inside the brackets to get:
[tex] 15 x + 20 = 23 [/tex]
[tex] 15 x = 23 - 20 [/tex]
[tex] 15 x = 3 [/tex]
[tex] x = \frac { 3 } { 15 } [/tex]
[tex] x = \frac { 1 } { 5 } [/tex]
Determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on, or below the x-axis.
Points "in common with the x-axis" are also known as the roots of the quadratic equation [tex]x^2-12x+12=0[/tex]. You can apply the quadratic root formula to determine the roots, and also to determine how many such roots there are. With a quadratic (whose graph is a parabola), there can be maximum of 2 roots. But under certain circumstances, there may be only one or no such root.
The root formula for a generic quadratic [tex]ax^2+bx+c[/tex] is as follows:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The expression [tex]b^2-4ac[/tex] under the square root is called the determinant. It is called so because it determines the number of real roots. If the determinant value is > 0, there will be 2 roots (and so the parabola will cross the x-axis in 2 points), if its value is =0, there will be only a single root (the the parabola will touch the x-axis in exactly one point), and, finally, if its value is < 0, the quadratic has no real root (andthe parabola will not have any x-intercepts).
So, let's take a look:
[tex]b^2-4ac= (-12)^2-4\cdot 1\cdot12=96[/tex]
This means the parabola will intercept the x-axis at 2 points, two real roots.
Since the coefficient of the quadratic term is positive (a=1), the parabola is oriented "open-up." But since we already know the parabola intercepts in two points, the fact that it is open-up implies now that the vertex must lie below the x-axis (otherwise it could not intercept it).
The number of common points between a parabola and the x-axis is determined by the discriminant of its equation, while the position of its vertex relative to the x-axis is determined by the value of y at the vertex. A positive discriminant yields two points of intersection, zero yields one, and negative yields none. The vertex's position can be above, on, or below the x-axis depending on whether k in its vertex form is positive, zero, or negative.
To determine how many points a parabola has in common with the x-axis, we look for the solutions to the parabolic equation when y is set to zero. The number of intersections corresponds to the number of real solutions to this equation. If the parabola's equation is given in the standard form y = ax2 + bx + c, we can use the discriminant (b2 - 4ac) to find out how many times the parabola touches the x-axis. If the discriminant is positive, the parabola intersects the x-axis at two distinct points; if it is zero, the parabola touches the x-axis at exactly one point (the vertex); and if it is negative, the parabola does not intersect the x-axis at all.
The vertex of the parabola lies above, on, or below the x-axis depending on the value of y at the vertex. In the vertex form of a parabola, y = a(x - h)2 + k, where (h, k) is the vertex, if k is positive, the vertex lies above the x-axis; if k is zero, the vertex is on the x-axis; and if k is negative, the vertex lies below the x-axis. Typically, the coefficient a determines the direction of the parabola opening—upwards if a is positive, and downwards if a is negative, but this does not affect the vertical placement of the vertex relative to the x-axis.
A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides. The exterior surface area of the trough is ________. The volume of the trough is _____. If a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be ______ cubic feet of water left in the trough.
Answer:
Part a) The exterior surface area is equal to [tex]160\ ft^{2}[/tex]
Part b) The volume is equal to [tex]240\ ft^{3}[/tex]
Part c) The volume water left in the trough will be [tex]84\ ft^{3}[/tex]
Step-by-step explanation:
Part a) we know that
The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles
so
Find the area of two rectangles
[tex]A=2[12*5]=120\ ft^{2}[/tex]
Find the area of two trapezoids
[tex]A=2[\frac{1}{2}(8+2)h][/tex]
Applying Pythagoras theorem calculate the height h
[tex]h^{2}=5^{2}-3^{2}\\h^{2}=16\\h=4\ ft[/tex]
substitute the value of h to find the area
[tex]A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}[/tex]
The exterior surface area is equal to
[tex]120\ ft^{2}+40\ ft^{2}=160\ ft^{2}[/tex]
Part b) Find the volume
we know that
The volume is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal face
L is the length of the trough
we have
[tex]B=20\ ft^{2}\\ L=12\ ft[/tex]
substitute
[tex]V=20(12)=240\ ft^{3}[/tex]
Part c)
step 1
Calculate the area of the trapezoid for h=2 ft (the half)
the length of the midsegment of the trapezoid is (8+2)/2=5 ft
[tex]A=\frac{1}{2}(5+2)(2)=7\ ft^{2}[/tex]
step 2
Find the volume
The volume is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal face
L is the length of the trough
we have
[tex]B=7\ ft^{2}\\ L=12\ ft[/tex]
substitute
[tex]V=7(12)=84\ ft^{3}[/tex]
(4,?) is on the line below. Find the other half of the coordinate. y=3/4x+3. Solve
Answer:
y = 6
Step-by-step explanation:
Given
y = [tex]\frac{3}{4}[/tex] x + 3 and (4, ? )
Substitute the x- coordinate x = 4 into the equation for corresponding value of the y- coordinate.
x = 4 : y = [tex]\frac{3}{4}[/tex] × 4 + 3 = 3 + 3 = 6
Hence the coordinate point is (4, 6)
Answer this for 20 pts and brainliest!!!!! (Please hurry up! "I am in a hurry!)
When there was no snow fall, the line would be flat ( horizontal).
There was no snow Between 3:30 pm and 2:00 pm.
Answer:
12:30 pm to 1:00 pm.
Step-by-step explanation:
Hope this helps you.
the product of c and 8 is greater than 21
Answer:
8c > 21
The solution is c > 21/8.
Step-by-step explanation:
Not all math problems have only one solution. Some math problems have multiple solutions such as set or group of solutions. These problems are called inequalities. Inequalities have solutions within a range using symbols such as >, <, ≤, and ≥. These are known as greater than, less than, less than or equal and greater than or equal. You can write any inequality expression from words into symbols using these signs.
The expression "the product of c and 8 is greater than 21" is translated into
8c > 21
since product is multiplication.
It can be solved by dividing both sides by 8.
The solution is c > 21/8.
Li rolls a pair of number cubes twice. On both rolls, the sum is 7. Are the rolls dependent or independent events?
Answer:
these are independent
Step-by-step explanation:
Mr. price drives 123 miles each day on his bus route he gets reimbursed .56 per every mile he drives. How much will mr. price reimbursed for 2 days of his bus route
he will be reimbursed 137.26 dollars for two days
Which equation represents the same proportional relationship as the graph
The slope of the given linear line is 3/5 thus the equation is y = 3/5 x so option (A) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
The slope of the line is 3/5
Since, the equation is y = mx + c where m is the slope and c is the y-intercept.
In the given line c = 0 and m = 3/5
y = 3/5 x
Hence "The slope of the given linear line is 3/5 thus the equation is y = 3/5 x".
For more about the linear function,
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The car owned by a person is part of his or her ____.
a.
investment assets
b.
liquid assets
c.
long term assets
d.
use assets
Please select the best answer from the choices provided
Answer:
The correct answer would be A
Step-by-step explanation:
The number of eggs in the refrigerator e decreased by 5 equals 18
Answer:
e=23
Step-by-step explanation:
The equation representing this scenario is e-5=18.
Add 5 to both sides and you get e=23 (eggs)
Answer:
e=23
Step-by-step explanation:
Ms. Franklin earns $ 15 an hour. For this year, she will be paid for 40 hours each week for 52 weeks. How much should Ms. Franklin expect to earn this year?
Answer:
About $31,200
Step-by-step explanation:
What is the value of 6X plus 7Y -5 when X = 2 and Y =3?
the answer is 28
have a good day!
Simplify the expressions. Show your work.
(X-2) (3x-4)
Please don’t guess
Answer: 3x^2-10x+8
Step-by-step explanation:
x*3x+x(-4)+(-2)*3x+(-2)(-4) Foil Method
3x^2-4x-6x+8 Add and subtract like factors
Answer:
3x² - 10x + 8Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](x-2)(3x-4)=(x)(3x)+(x)(-4)+(-2)(3x)+(-2)(-4)[/tex]
[tex]=3x^2-4x-6x+8[/tex] combine like terms
[tex]=3x^2+(-4x-6x)+8=3x^2-10x+8[/tex]
Use a calculator to find the standard deviation of this data set 8,14,12,9,16 round to the nearest tenth? NEED HELP ASAP THX
Answer:
3.3 apex
Step-by-step explanation:
Answer:
3.3
Step-by-step explanation:
The model represents an equation. What value of x makes the equation true?
when all goes wrong...choose c my friend.
All dogs are animals.
Some animals are pets.
------------------
Therefore, some dogs are pets.
Vaild or Invalid?
This is valid.
.
.
.
.
.
Is this the right answer
Answer:
V = 60
Step-by-step explanation:
Yes, it is
Best regards
Answer:
yes that is that is that is the right answer hope u get all your homework right
Step-by-step explanation:
24 students is _% of 43
Answer:
(24 / 43) * 100 = 55.81395349 %
which equals roughly 55.81 %
Step-by-step explanation:
What is an open line of credit? a. A line of credit which has no current balance. b. A line of credit with a variable interest rate. c. A line of credit against which additional debt may be drawn. d. A line of credit which has no credit history requirements. Please select the best answer from the choices provided A B
Answer: C
Step-by-step explanation: An open line of credit is a line of credit against which additional debt may be drawn. An open credit line allows you to borrow money against the credit line at different times. You can borrow against it up to the credit limit.
Solve the following equation by identifying all of its roots including any imaginary numbers and multiple roots.
(x2 - 1)(x2 + 2)(x + 3)(x - 4)(x + 1) = 0
Answer: x = {-1, 1, -i√2, i√2, -3, 4}
Step-by-step explanation:
(x² - 1)(x² + 2)(x + 3)(x - 4)(x+1)=0
Set each factor equal to zero and solve.
x² - 1 = 0 → x² = 1 → x = ±1
x² + 2 = 0 → x² = -2 → x = ± i√2
x + 3 = 0 → x = -3
x - 4 = 0 → x = 4
x + 1 = 0 → x = -1 (note that -1 is a duplicate - solved from the first factor)
Answer:
Answer: x = {-1, 1, -i√2, i√2, -3, 4}
Step-by-step explanation:
how many different ways can you arrange four pictures on a wall if you want them in a horizontal straight line
Answer:
You can do it four ways for horizontal straight line using a ruler.
Step-by-step explanation:
i did was make a 2x2 grid, and then arrange the four pictures inside.
Final answer:
There are 24 different ways to arrange four pictures on a wall in a horizontal straight line, calculated using the factorial of the number of pictures (4!).
Explanation:
The question of how many different ways you can arrange four pictures on a wall if you want them in a horizontal straight line is a problem of permutations, which is a concept in mathematics. To determine the number of different arrangements, we calculate the factorial of the number of pictures. The factorial, represented by an exclamation mark (!), means that you multiply the number by every number below it down to 1. For four pictures, the calculation is 4! (which is 4 x 3 x 2 x 1).
The result is:
4 x 3 x 2 x 1 = 24Therefore, there are 24 different ways to arrange four pictures on a wall in a horizontal straight line.
An egg is dropped from the window of a building. The height, in feet, of the egg t seconds after it is thrown is represented by d=-16t^2-7t+61. How many seconds after the egg is thrown will it be 10 feet from the ground?
Answer:
1.58
Step-by-step explanation:
Okay. We're solving for t because we need to know how many seconds. From the problem, we know the height (10), but we don't know when that height happens.
[tex]10 = -16tx^{2} -7t+61[/tex]
We can factor by multiplying -16 by 61 first to get -976 and see what multiplies to get -976 AND adds to get -7 at the same time. But we can also use the quadratic formula because, let's be honest, factoring can be a lot of extra work.
[tex]10 = -16t^{2} -7t+61\\\\0 = -16t^{2} -7t+51\\\\t=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a} \\=\frac{-(-7)\pm \sqrt{(-7)^{2}-4(-16)(51) } }{2(-16)} \\=\frac{7\pm \sqrt{49+64(51) } }{-32} \\=\frac{7\pm \sqrt{3313} }{-32}[/tex]
Plug both the plus and the minus versions into your calculator and...
[tex]t\approx -2.02, 1.58[/tex]
There's no such thing as negative time, so -2.02 is automatically disqualified, leaving 1.58 as the answer.
Hope this helps, let me know if I missed anything!
The time takes for the egg to reach the height 10 feet from the ground on the basis of the given quadratic equation will be 1.58 seconds.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.
As per the given quadratic equation,
d = - 16t² - 7t + 61
The time t in seconds at d = 10
-16t² - 7t + 61 = 10
16t² + 7t - 51 = 0
The roots of the above quadratic equation will be,
t = [-7 ± √(7² - 4 × 16 × -51 )] /(2 × 16)
t = (-7 ± 57.586)32
t = 1.58 or -2.02
Since, time is always positive thus, t = 1.58 seconds.
Hence "The time takes for the egg to reach the height 10 feet from the ground on the basis of the given quadratic equation will be 1.58 seconds".
For more about the quadratic equation,
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289.1 is 70% of what amount
70% × 413 =
(70 ÷ 100) × 413 =
(70 × 413) ÷ 100 =
28,910 ÷ 100 =
289.1
Proof
289.1 ÷ 413 =
0.7 =
0.7 × 100/100 =
0.7 × 100% =
(0.7 × 100)% =
70%
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Plz help!!!!!!!!!!!!!!!
Answer: b) (x - 2)(x + 1)(x + 3) = 0
Step-by-step explanation:
Look at the graph to find the x-intercepts (where the graph crosses the x-axis).
x = 2, x = -1, and x = -3
Rewrite them as factors:
x - 2 = 0, x + 1 = 0, and x + 3 = 0
Combine the factors through multiplication:
(x - 2) (x + 1) (x + 3) = 0
URGENT!!! WILL AWARD ALL POINTS Which expression is equivalent to sin(2β)sinβ for all values of β for which sin(2β)sinβ is defined?
Select the correct answer below:
2sin2β−tan2β
cot2β−2cos2β
1−tan2β
csc2β−2
2cosβ
Answer:
sin2b sin b
2 sin b cos b sin b
2 cos b sin^2 b
1−cos2b cos b
1- (2cos^2 b−1) cosb
2 cos beta
Answer:2sin =bahsyg=a=78sinb-7823sin= 1-tan2b
please help me answer this question.
Answer:
π/64
Step-by-step explanation:
assuming that c= circumference, and the circumference being 2πr(radius), then r=1/8 because 2π/8=π/4. to find the area, we use the formula πr^2, or π*1/8^2, or π/64