Answer:
x = 7/2 ±sqrt(65)/ 2
Step-by-step explanation:
x^2=7x+4
Subtract 7x from each side
x^2-7x=7x-7x+4
x^2 -7x =4
Complete the square
Take the coefficient of x and divide by 2
-7/2
Then square it
(-7/2)^2 = 49/4
Add this to each side
x^2 -7x +49/4 =4+49/4
(x-7/2)^2 = 4 +49/4
(x-7/2)^2 = 16/4 +49/4
(x-7/2)^2 =65/4
Take the square root of each side
sqrt((x-7/2)^2) =±sqrt(65/4)
x-7/2 = ±sqrt(65)/ sqrt(4)
x-7/2 = ±sqrt(65)/ 2
Add 7/2 to each side
x-7/2 +7/2=7/2 ±sqrt(65)/ 2
x = 7/2 ±sqrt(65)/ 2
The solutions to the quadratic equation x^2 = 7x + 4 are x = 3 and x = -7, found using the quadratic formula and verified by substitution into the original equation.
To solve the quadratic equation x^2 = 7x + 4, we first need to bring all terms to one side of the equation to get it into the standard form ax^2 + bx + c = 0. This gives us x^2 - 7x - 4 = 0. We can then apply the quadratic formula, which is x = (-b \/- sqrt(b^2 - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax^2 + bx + c = 0.
For our equation, a = 1, b = -7, and c = -4. Substituting these values into the quadratic formula gives us two solutions, which result in x = 3 and x = -7 as the solutions to the problem. To verify these solutions, we can substitute them back into the original equation and confirm they satisfy the equation, thus proving they are correct.
The equation y=mx+b is the slope-intercept form of a linear equation.
Solve y=mx+b for m
Answer:
[tex]\large\boxed{m=\dfrac{y-b}{x}}[/tex]
Step-by-step explanation:
[tex]y=mx+b\to mx+b=y\qquad\text{subtract}\ b\ \text{from both sides}\\\\mx+b-b=y-b\\\\mx=y-b\qquad\text{divide both sides by}\ x\neq0\\\\\dfrac{mx}{x}=\dfrac{y-b}{x}\\\\m=\dfrac{y-b}{x}[/tex]
Answer: [tex]m=\frac{y-b}{x}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Then, to solve for the slope "m", you can follow these steps:
- You need to subtract "b" from both sides of the equation:
[tex]y-b=mx+b-b\\\\y-b=mx[/tex]
- Finally, you can divide both sides of the equation by "x". Then:
[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]
Identify an equation in point-slope form for the line parallel to y = x-7 that
passes through (-3,-2).
Answer:
B. y + 2 = ½(x + 3)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].
I am joyous to assist you anytime.
write the names of these decimals 0.089 3.71 0.3 13.701 5.005
Answer:
0.089: eighty-nine thousandths, 3.71: three and 71 hundredths, 0.3: three tenths, 13.701: thirteen and 701 thousandths, 5.005: five and five thousandths
Step-by-step explanation:
The first place back is the tenths place (0.0), the second is the hundredths place (0.00), the third place is the thousandths (0.000).
4 more than the quotient of x squared and 3
An expression for the given statement is (x²/3)+4.
The given statement is 4 more than the quotient of x squared and 3.
We need to find an expression for the given statement.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be addition, subtraction, multiplication, or division.
The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
According to the question, we get (x²/3)+4.
Therefore, an expression for the given statement is (x²/3)+4.
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Solve by substitution. 3x+6y=21 -8x+y=63
What is the solution?
[tex]\bf \begin{cases} 3x+6y=21\\ \cline{1-1} -8x+y=63\\ \boxed{y}=63+8x \end{cases}~\hspace{7em}\stackrel{\textit{substituting on the 1st equation}}{3x+6\left( \boxed{63+8x} \right)}=21[/tex]
[tex]\bf 3x+378+48x=21\implies 51x+378=21\implies 51x=-357 \\\\\\ x=\cfrac{-357}{51}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=63+8x\implies }y=63+8(-7)\implies y=63-56\implies \blacktriangleright y=7 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-7,7)~\hfill[/tex]
A function in whitch each y value had only one corresponding x value is called a?
Answer:
See below.
Step-by-step explanation:
That is a one-to-one function.
Answer: One-to-One function.
Step-by-step explanation:
A One-to-One function (also written as 1-1) is that function for which every element of the Range corresponds to one and only one element of the Domain.
Given a Set A (Domain of a function) and a Set B (Range of the function), if [tex]If\ f(a) = f (b),\ then\ a = b[/tex] and it is a One-to-One function.
Given the graph of a function, you can determine if it is a One-to-One function if it passes the Horizontal Line Test.
The conclusion is: A function in which each y-value has only one corresponding x-value is called a One-to-One function.
Which angle is an exterior angle of the triangle?
PLEASE HELP!!
Answer:
4
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.
The exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].
Given that in the triangle [tex]\Delta LMN[/tex] marked with angles:
[tex]\angle MLN = \angle1\\\angle LMN = \angle2\\\angle LNM = \angle3[/tex]
And in the triangle, MN is extended to some point marked with angle [tex]\angle 4[/tex].
To find angle is an exterior angle of the triangle by using the definition of exterior angle:
Definition of exterior angle:
The exterior angle of the triangle is formed by extending one of its sides.
In the triangle, MN is extended to some point marked with angle [tex]\angle 4[/tex].
By using the definition implies:
exterior angle = [tex]\angle 4[/tex]
Therefore, the exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].
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BE is an angle bisector of ABE =2x+20 and mEBC=4x-6 determine m ABE
Answer:
46°
Step-by-step explanation:
BE is the bisector so abe is the same as ebc
2x+20=4x-6
26=2x
13=x
so now plug x back into abe to find its measure
2(13)+20
26+20
46
The answer is 46°.
How to find the length of ABE?BE is the bisector so abe is the same as ebc
2x+20=4x-6
26=2x
13=x
So now plug x back into abe to find its measure
2(13)+20
26+20
46
Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line. You will need a compass, pencil, and ruler.
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The number of fives is 3 more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives
Answer:
The required expression is f = 3+6t
Step-by-step explanation:
Let t represent number of tens
Let f represent number of fives
So, the expression for number of fives can be formed by using:
The number of fives is 3 more than six times the number of tens.
f = 3+6t
So, the required expression is f = 3+6t
Find the quotient of 2,196 ÷ 12.
For this case we must find the quotient of the following expression:
[tex]\frac {2196} {12}[/tex]
According to the attached figure, we must build a quotient that, when multiplied by the divisor, cancels the terms of the dividend, until we reach the remainder. In this case the division is exact and the quotient is 183.
Answer:
See attached image
The circle below is centered at the point (4, -3) and has a radius of length 3.
What is its equation?
А. (x-3)2 + (y+ 4)2 = 9
В. (x-3)2 + (у- 4)2 = 9
с. (х+4)2 + (у - 3)2 =
22
D. (x-4)2 + (y+ 3)2 =
32
The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2
where h and k is the center point and r is the radius.
Using the center point and radius given the equation becomes:
(x-4)^2 + (y+3)^2 = 3^2 or (x-4)^2 + (y+3)^2 = 9
If you answer yo get 20 points
When the square of a number is increased by one, the result is four times the original
number. Find the number.
Answer:
n = 2 + 2√3 and n = 2 - 2√3
Step-by-step explanation:
Let the number be n.
Then n² + 1 = 4n.
Rearranging this in proper quadratic format:
n² - 4n + 1
Here the coefficients are a = 1, b = -4 and c = 1.
Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.
By applying the quadratic formula, we find that the roots are:
- (-4) ± √12
n = ------------------
2
or n = 2 + 2√3 and n = 2 - 2√3
Answer:
3.732 or 0.268 to the nearest thousandth.
Exact values are 2 + √12/2 or 2 - √12/2.
Step-by-step explanation:
Let the original number be x, then:
x^2 + 1 = 4x
x^2 - 4x + 1 = 0
x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2
x = (4 + sqrt12)/ 2 , (4 - sqrt12) / 2
= 3.732, 0.268.
Given b(x) = X+41, what is b(-10)?
Answer:
your answer would be 6
Step-by-step explanation:
hope this helps
In a hospital parking lot, the rate is $1.50 for
the first 2 hours and $0.75 for each
additional hour or part of an hour. What
does it cost to park a car for 4 hours and 15
minutes?
Answer: $3.75
Step-by-step explanation
(This may not be the way teachers see it)
So take the $1.50 and multiply it by two and you get $3 for four hours
Then you would take the $0.75 and add it to the $3 to get $3.75
(would it be 0.75 for 15 min?)
What is the complete factorization of the polynomial below x^3+5x^2-x-5
Answer:
(x+5)(x-1)(x+1)
Step-by-step explanation:
Let's attempt factoring by grouping:
So what this means we first want to group the first two terms together and second two terms together, like so:
(x^3+5x^2)+(-x-5)
Now we factor what we can from each pair:
x^2(x+5)+1(-x-5)
Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:
x^2(x+5)-1(x+5)
You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:
(x+5)(x^2-1)
You can actually factor this more because x^2-1 is a difference of squares.
The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So the complete factored form of our expression we had initially is
(x+5)(x-1)(x+1).
Answer:
[tex]\large\boxed{x^3+5x^2-x-5=(x+5)(x-1)(x+1)}[/tex]
Step-by-step explanation:
[tex]x^3+5x^2-x-5\qquad\text{distributive}\\\\=x^2(x+5)-1(x+5)\\\\=(x+5)(x^2-1)\\\\=(x+5)(x^2-1^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+5)(x-1)(x+1)[/tex]
PLEASE HELP! I have three questions:
1. 4 students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.
2. Leslie has 7 books. There is enough space on a shelf for 3 books. In how many ways can 3 of the 7 books be arranged on the shelf? (For this one I keep getting the answer 35, but its coming up wrong on my assignment.)
3. Out of the 12 girls who tried out for the softball team, 10 will be chosen for the team. Find the number of different 10-person teams.
Thank you!!
Answer: 1. 3 can be made 2. i believe it is only one way to put three books on a shelf 3. 3 i believe, its been awhile since i studied this
Step-by-step explanation:
Chose the equation that represents the line that passes through the point (2,6) and has a slope of -5
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the slope m = -5, and the point (2, 6).
Substitute:
[tex]y-6=-5(x-2)[/tex]
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Convert:
[tex]y-6=-5(x-2)[/tex] use the distributive property a(b + c) = ab + ac
[tex]y-6=-5x+(-5)(-2)[/tex]
[tex]y-6=-5x+10[/tex] add 6 to both sides
[tex]y=-5x+16[/tex]
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
Convert:
[tex]y=-5x+16[/tex] add 5x to both sides
[tex]5x+y=16[/tex]
What is the equation of a line that is parallel to y=-6x +2 and passes through (-1, 2)
Answer:
y = - 6x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 6x + 2 ← is in this form with slope m = - 6
• Parallel lines have equal slopes, hence
y = - 6x + c ← is the partial equation of the parallel line.
To find c substitute (- 1, 2) into the partial equation
2 = 6 + c ⇒ c = 2 - 6 = - 4
y = - 6x - 4 ← equation of parallel line
Which set of statements about the angles is true?
Answer:
Answer choice 4
Step-by-step explanation:
Since alternate interior angles create congruent angles, angle 5 and 3 are congruent as well as 4 and 2, and since the only option that has these statements is answer choice 4, it is the correct answer.
Answer:
it is d
Step-by-step explanation:
HELP ME WITH THIS QUESTION THANKS!✔✔
Answer:
-1 9/18 and then -32/40 and then 1 8/20
Step-by-step explanation:
The largest negatives is the least , then the second to least and then non-negative should be the greatest or the last
If the perimeters of each shape are equal, which equation can be used to find the value of x?
Answer:
(x+2) + x + (x+4) = 2(1/2) + 2(x+3)
Step-by-step explanation:
They are equal to each other and the rectangle has 2x more perimeter
The triangle would be divided in half from that rectangle.
Sorry If this is confusing I am not very good at explaining things.
PLEASE HELP PLEASE
Which number is not divisible by either of the numbers 3 and 5?
A. 5000
B. 2374
C. 1203
D. 2505
Answer:
The answer is B. 2374
Answer:
B. 2374
Step-by-step explanation:
Division by 5: If a number ends in 0 or 5 it is divisible by 5.
A. 5000 is divisible by 5.
D. 2505 is divisible by 5.
Division by 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
B. 2374
Add the digits of 2374: 2 + 3 + 7 + 4 = 16. 16 is not divisible by 3, so 2374 is not divisible by 3. It is also not divisible by 5 since it does not end in 0 or 5.
C. 1203
Add the digits of 1203: 1 + 2 + 0 + 3 = 6. Since 6 is divisible by 3, 1203 is divisible by 3.
Answer: B. 2374
If you can draw one straight line through a polygon and cross more than two sides, the polygon is _______________.
A. concave
B. convex
C. regular
D. equiangular
Answer:
If you can draw one straight line through a polygon and cross more than two sides, the polygon is concave - A.
Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.
−b b2 − 4ac 2a
Use the part of the quadratic formula that you chose above and find its value, given the following quadratic equation:
4x2 + 6x + 2 = 0
Answer:
b^2-4ac, the value of the discriminant is 4
Step-by-step explanation:
The part b^2-4ac called the discriminant will tell you how many solutions a particular equation has, after plugging in the values you can tell how many solutions and what type of solutions that equation has by looking at whether the result is positive and a perfect square, positive, zero, or negative. If the result is a positive perfect square, there will be two rational solutions; if the result is positive there will be two real zeros; if the result is zero, there is one real zero; if the result is negative, there will be two complex conjugates or imaginary terms.
To find the value of the discriminant plug in the values of the equation.
6^2-4(4)(2)=4
The value of the discriminant in this particular equation is a perfect square, that means that there are two rational solutions. Put simply, this equation is factorable.
4x^2 + 6x + 2 = 0
(x+1)(4x+2)=0
x=-1 or -1/2
Answer:
The above explanation was correct.
To make it clear, just type 4 as the answer
wht equation describes a parabola that opens up or down and whos vertex is at the point (h,v)
Answer:
[tex]f(x)=a(x-h)^2+k[/tex]
Vertex form.
Step-by-step explanation:
You are talking about the vertex form for a parabola.
[tex]f(x)=a(x-h)^2+k[/tex] tells us:
A) The vertex is (h,k).
B) Open up (if a is positive) or open down (if a is negative)
C) a also tells us how much it is vertically stretched or compressed.
What is the approximate pH of a solution if the concentration of hydrogen ions is 5.0x10^-4 moles per liter
Answer:
it should be 3.3
Step-by-step explanation:
I did it with friend
Answer:
C) 3.3
Step-by-step explanation:
this is the correct answer on ed-genuity, hope this helps! :)
Consider the two triangles.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that....
PLEASE HELP.. extra coins
According to Side Angle Side theorem the correct option is d)
[tex]\rm \dfrac{AC}{GI}=\dfrac{BC}{HI}[/tex]
According to SAS theorem:
If an angle of one triangle is congruent to the corresponding angle of another triangle.And the lengths of the sides including these angles are in proportion, the triangles are similar.From the given triangles we can see that,
[tex]\rm \dfrac{AC}{BC}=\dfrac{GI}{HI}[/tex] ---- (according to SAS theorem)
Therefore, the correct option is D).
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Answer:
D !!!!!
Step-by-step explanation:
According to Side Angle Side theorem the correct option is d
AC / GI = BC / HI
-edge did the test
What is the square root of -1?
Т -
ОООО
Т -
Answer:
i
Step-by-step explanation:
The square root of -1 is i which is an imaginary number
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 3x - 4
x = 9
O A. (9,31)
O B. (1,-1)
O c. (0,-4)
O D. (9,23)
Answer:
D: (9, 23)
Step-by-step explanation:
Substitute the given value, 9, for x in y = 3x - 4. We get:
y = 3(9) - 4, or y = 23. Thus, the solution is (9, 23) (Answer D)
D. (9, 23) is the required ordered pair.
What is substitution method ?Substitution method is a mathematical method in which we have to pick one variable from one equation and substitute it to another equation.
How to solve the given problem ?Given equations are,
y = 3x - 4 .....(1) & x = 9 .....(2)
By using substitution method,
We have to put the value of x of (2) in (1),
i.e. we have to put x = 9 in (1),
∴ y = (3×9) - 4
= 27 - 4
= 23
So, the required ordered pair is (9, 23)
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Find the area of the shaded region.
Answer:
Area = 16
Step-by-step explanation:
The plan is to find the area of the large triangle (blue and white together) and subtract the white triangle's area.
Area of blue + white.
h = 8
b = 5 + 4
b = 9
Area = 1/2 * 8 * 9
Area = 1/2 * 72
Area = 36
===============
Area of white.
h = 8
b = 5
Area = 1/2 * 8 * 5
Area = 20
==============
Area of the shaded region (blue) = Area of both triangles - Area of the white
Shaded = 36 - 20
Shaded = 16