[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]
Explanation:
Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0
Here given:
a = abb = b² - acc = -bcApply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]
Insert values:
[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Apply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Help... will give you 20 points if you answer
Answer:
(-3,5) (-3,3) (-8,3)
Step-by-step explanation:
Answer:
(-3,5) , (-3,3) , (-8,3)
Step-by-step explanation:
bye, bye!!
the money in a bank account increased from $400 to $1000.
copy and complete these sentences.
a) $1000 is ........% of $400.
b) the money has increased by .......%
Answer:
a).1000/400*100
= (1000*100)/400
= 100000/400 = 250
b).600
Step-by-step explanation:
a). Percentage solution with steps:
Step 1: We make the assumption that 400 is 100 % since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: From step 1, it follows that 100 % = 400.
Step 4: In the same vein, x % = 1000 .
Step 5: This gives us a pair of simple equations:
100 % = 400(1).
x % = 1000(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100 % / x % = 400/1000
Step 7: Taking the inverse (or reciprocal) of both sides yields
x/100 = 1000/400
x = 250 %
Therefore, 1000 is 250 % of 400.
b) $1000-$400= 600
= $400+$600=$1000
If a person who is 5 feet tall throws a ball into the air, the path can be modeled using the table of values, where x represents the time in seconds and y is the height of the ball in feet. x y 0 5 1 6.75 2 8 3 8.75 4 9 5 8.75 which quadratic equation models the data in the table?
The quadratic equation is y = -0.15x² + 2x + 5.5 , Option D is the correct answer.
The complete question is
If a person who is 5.5 feet tall throws a baseball into the air, the path can be modelled using the table of values, where x represents the time in seconds and y is the height of the ball in feet.
(table is in the photo below)
Which quadratic equation models the data in the table?
y= −0.25x2 + 2x + 5.5
y= −0.35x2 + 2x + 5.5
y= −0.27x2 + 3x + 5.5
y= −0.15x2 + 2x + 5.5
The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5
What is an Equation ?When two algebraic expressions are linked with an equal sign , the expression formed is called an Equation.
The standard form of the Quadratic equation is
y = ax² + bx + c
here a, b and c are constants.
From the given data in the table
at point (0, 5.5)
5.5 = a(0)² + b(0) + c
at point (1, 7.35)
7.35 = a(1)² + b(1) + c
at point (2, 8.9)
8.9 = a(2)² + b(2) + c
The system of equations will be solved to determine the value of a,b and c
a= -0.15, b = 2, c = 5.5
Therefore , The quadratic equation is y = -0.15x² + 2x + 5.5 .
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Answer:
B) y= -0.25x^2 + 2x + 5
Step-by-step explanation:
I got it correct on test
PS: Can I have brainiest?
What is the domain and range of the following graph?
Answer:
Domain is all x-values and range is all y values. See all of the x values and y values that are touching the graph. Also, when there is a circle/ hole, use parenthesis for the interval notation. Hope it helps!
A square its diagonal length = 12cm then its area =
Answer:
72 sq cm
Step-by-step explanation:
For any rectangle, the diagonal is the hypotenuse of the right triangle formed by the base of the rectangle(b) and the height (h) of the rectangle
By the Pythogorean formula
[tex]d^{2} = b^{2} + h^{2}[/tex]
where d is the diagonal
For a square, all sides are equal so b = h = a and we get the formula
[tex]d^{2} = a^{2} + a^{2} = 2a^{2}[/tex]
[tex]a^{2} = d^{2} /2[/tex]
In this case we have d =12 so
[tex]a^{2} = 12^{2} /2 = 144/2 = 72[/tex]
But for a square of side a, the area is [tex]a^{2}[/tex] so 72 is the area
Answer:
72 square cm
Step-by-step explanation:
Area of square:[tex]\sf \boxed{\bf Area = \dfrac{d^{2}}{2}}[/tex] , here d is the length of the diagonal
[tex]\sf =\dfrac{12* 12 }{2}\\\\ = 6*2\\\\= 72 \ cm^2[/tex]
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A. 7
B. 5
C. 9
D. 4
E. 3
Considering the given histogram, the mean of the data-set is closest to:
B. 5.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
Hence, considering the histogram, the mean is given by:
M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.
Which is closest to 5, hence option B is correct.
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the vate rate of a country is 15% ,a woman bought an item with a price tag ghc 300 plus vat .what price did she pay for the item.
Answer:
i think 345 if not sorry
Step-by-step explanation:
The mean height of 20 boys and 14 girls is 161 cm. The mean height of 14 girls is 151 cm. Find the sum of the heights of 14 girls.
Answer: 2114
Step-by-step explanation:
m = sum of the terms / number of terms
151 = a/ 14
14 x 151 = a
2114 = a
Answer:
21.14 m
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
here mean is 151 cm and count = 14 , then
[tex]\frac{sum}{14}[/tex] = 151 ( multiply both sides by 14 to clear the fraction )
sum = 14 × 151 cm = 2114 cm = 2114 cm ÷ 100 = 21.14 m
the slope of the line is 4. which of the following is the point-slope form of the line
The point slope form of line is y+4 = -4( x+3)
What is point slope of form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
Given:
m=4
We know the general form is
y - b = -4(x - a)
So, from the graph attached below
b= -4, a= -3
So, y-(-4)= -4(x-(-3))
y+4 = -4( x+3)
Hence, point slope form of line is y+4 = -4( x+3).
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If T(x) = x + 0.14x, then find the value of T(290).
The value if T(290) is 330.6
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Given:
T(x) = x + 0.14x
T ( 290)= 290+ 0.14* 290
= 290+ 40.6
= 330.6
Hence, the value of T(290) is 330.6.
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In a group of 42 students, 9 study both Art and Biology.
10 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
help asap
\How could Brent use a rectangle to model the factors of x2 – 7x + 6?
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
Option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have a quadratic expression to model the area of the rectangle:
= x² – 7x + 6
[tex]\rm =\left(x^2-x\right)+\left(-6x+6\right)[/tex]
[tex]=\rm x\left(x-1\right)-6\left(x-1\right)[/tex]
= (x - 1)(x - 6)
Thus, option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.
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what is the solution to the system of equations below?
3x+y+2z=8
8y+6z=36
12y+2z=12
A. x=2, y=1, z=6
B. x=3, y=0, z=4
C. x=2, y=0, z=6
D. x=3, y=1, z=4
The solution to the system of equation are x=2, y=0, z=6
System of equationsSystem of equations are equations that contains unknown variables.
Given the equations
3x+y+2z=8
8y+6z=36
12y+2z=12
From equation 2 and 3
8y+6z=36 * 1
12y+2z=12 * 3
______________
8y+6z=36
36y+6z= 36
Subtract
8y - 36y = 36 - 36
-28y =0
y = 0
Substitute y = 0 into equation 2
8(0)+6z=36
6z = 36
z = 6
From equation 1
3x+y+2z =8
3x + 0 + 2(6) = 8
3x = 8 - 12
3x = 6
x = 2
Hence the solution to the system of equation are x=2, y=0, z=6
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-35÷6=
-350÷6-350-6=
350 - 60 =
Answer:
The first one is 5.83 or -5 5/6
The second one is -414 1/3
The last one is 290
How does simplifying a square root expression differ from simplifying a cube root expression?
The square root contains two same numbers and the cubic root contains three same numbers.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The square root contains two same numbers and the cubic root contains three same numbers.
For an example:-
√9 = [tex]\sqrt{3\times 3}[/tex] = 3 as we can see in the example the value of the square root of 9 is 3 it consists of two threes in the roots.
∛27 = [tex]\sqrt[3]{3\times 3\times 3}[/tex] = 3 here we have found that 27 contains 3 times 3 so the cube root of 27 will be equal to 3.
Therefore square root contains two same numbers and the cubic root contains three same numbers.
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in an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. can you find all angles of the triangles?
Answer:
all angles of the triangles is 60
Step-by-step explanation:
the perimeter = 2*side of an isosceles triangle + bottom edge
----> bottom edge = the perimeter - 2*side of an isosceles triangle =25
----> This is an equilateral triangle ----> all angles of the triangles is 60
what is 52 + 6 × (5 − 3) − 10⁄2 =
Answer: 59
Step-by-step explanation:
Order of operations.
52+6x(2)-5
52+12-5
64-5
59
Step-by-step explanation:
52+6×2-10/2
52+6×2-10÷2
52+6×2-5
52+12-5
64-5 =59
my answer is 59.
Which is the graph of the equation y-1=2/3(x-3)?
Answer:
The right graph
Step-by-step explanation:
Because the equation is in point slope form, we know it passes through (3,1) and has a slope of 2/3.
Question 3 of 10 A Assume EFG = JKL. If mLJ = 90°, mL K = 26°, and m< L = 64°, what is the measure of < E?
The measure of angle E will be 90 degrees as well.
Assume EFG = JKL.
If mLJ = 90°, mL K = 26°, and m< L = 64°,
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
We have been given an image of two congruent triangles.
Since, EFG = JKL
therefore, the corresponding angles will be congruent.
m < J = 90° = m< E = 90
By congruence measure of angle, J will be equal to the measure of angle E.
Hence, The measure of angle E will be 90 degrees as well.
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label the vertices and all the elements needed. find x
The value of x would be 30 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Let's consider an angle CAD be t.
In a triangle ABD
x + 90 + t = 180
t = 180 -x - 90
t = 90 - x ( by angle sum property)
Now, we know that the sum of the corresponding angle on a transversal is 180
So,
Angle A + angle D = 180
2x + t + x + x = 180
substitute the t value
2x + 90 - x + 2x = 180
3x + 90 = 180
3x = 90
x = 30 degree
Hence, the value of x would be 30 degrees.
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The sum of ten and eight times a number is 162. What is the number?
Answer:
9
Step-by-step explanation:
10x + 8x = 162
18x = 162
x = 9
A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
This assumes that the question was meant to read:
"A triangle has side lengths of (7x−4) centimeters, (x+3) centimeters, and (3x+2) centimeters." And not "A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters."
If the revision is correct, the perimeter is 11x + 1 cm
=============================================
If the question was correctly written, then answer is:
50x^2 - 50x + 9y^2 + 12 y + 29
===============
Step-by-step explanation:
(7x-4) cm
+ (x+3) cm
+ (3x+2) cm
11x + 1 cm
If the question was correctly written as is, then:
(7x-4)(7x−4) = 49x^2 - 56x + 16
+(x+3)(x+3) = + x^2 + 6x + 9
+(3y+2)(3y+2) = +9y^2 + 12 y + 4
50x^2 - 50x + 9y^2 + 12 y + 29 cm
The perimeter of triangle 8x+ 3y + 1.
What is Perimeter of Triangle?The complete length of a triangle's boundary is referred to as its perimeter. A triangle is a polygon with three sides, and there are various varieties of triangles depending on how big the sides and angles are.
The basic formula used to calculate the perimeter of a triangle is:
Perimeter = sum of the three sides
Given:
sides of triangle (7x-4) centimeters, (x+3) centimeters, and (3y+2).
Now, perimeter of triangle
= 7x-4 + x+ 3 + 3y+ 2
=8x + 3y + 5-4
=8x+ 3y + 1
Hence, the perimeter of triangle 8x+ 3y + 1.
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PLEASE ANSWER ASAP!!!!!!!
A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the cheesecake is 10 inches, and the area of the slice of blueberry cheesecake is 25π16 square inches.
How many slices does the cheesecake have?
A cheesecake has equally sized slices. Each slice is a different flavor. The cheesecake has 12 slices.
What is the area of the circle?
The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = πr²
In order to calculate the total area of the cheesecake, since it's a circle its area is given by:
cheesecake area = πr²
cheesecake area = π(10/2)² = π(5)²
cheesecake area = 25 π square inches
Therefore the number of slices is the ratio of the cheesecake total area by the area of each slice:
The number of slices = 25 π/(25 π/12)
The number of slices = 12
The cheesecake has 12 slices.
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Answer: 12 slices
Step-by-step explanation:
im a year late woo hoo
Simplify fully 4d2-6d2+5d2
Answer:
3d²
Step-by-step explanation:
Hello!
To simplify, we combine the like terms by adding them.
Like termsLike terms are terms with the same variable and degree. A degree is a power to which the term is raised. Like terms can have numerical coefficients. For example, a coefficient of 4 to x² would mean 4 times x².
We can see that the variable d² is common throughout the three terms, meaning they are like terms. We can simply add and subtract them.
Simplify4d² - 6d² + 5d²-2d² + 5d²3d²The simplified form is 3d².
Help needed
a hunid points :)
Answer:
the answer is C, 5a^6b
Step-by-step explanation:
Find the value of x ??
A. 31
B. 5
C. 11
D. 25
Which table represents a proportional relationship? A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 8, 18. Column 2 is labeled y with entries 6, 12, 26. A 2-column table with 3 rows. Column 1 is labeled x with entries 5, 20, 60. Column 2 is labeled y with entries 7, 28, 84. A 2-column table with 3 rows. Column 1 is labeled x with entries 12, 18, 26. Column 2 is labeled y with entries 5, 7, 9. A 2-column table with 3 rows. Column 1 is labeled x with entries 3, 9, 15. Column 2 is labeled y with entries 2, 8, 14.
Answer:
X Y
5 7
20 28
60 84
This table shows the proportional relationship.
Step-by-step explanation:
The equivalent ratios of two variables known as proportional relationship.
Table 1: X Y Table 3: X Y
4 6 12 5
8 12 18 7
18 26 26 9
Ratio = 4:6 = 8:12 ≠ 18:26 Ratio = 12:5 ≠ 18:7 ≠ 26:9
Table 2: X Y Table 4: X Y
5 7 3 2
20 28 9 8
60 84 15 14
Ratio = 5:7 =20:28=60:84 Ratio = 3:2 ≠ 9:8 ≠ 15:14
Here we see table 2 shows the proportional relationship.
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_3x_13 =_7x+15 what is the an
Answer:
x = -7Step-by-step explanation:
_3x_13 =_7x+15 what is the anSWER?
assuming that the underscore is a minus and you are looking for the x value.
-3x - 13 = -7 + 15
-3x = -7 + 15 + 13
-3x = 8 + 13
-3x = 21
x = -7
---------------
check
-3 * (-7) - 13 = -7 + 15
21 - 13 = 8
8 = 8
the answer is good
i need help asappppp
Answer:
a = 11, b = 7
Step-by-step explanation:
See picture
Find y in terms with x
Help me pleaseee thank uu:)
Answer:
y = 90 -5/2 x
Step-by-step explanation:
The angle on the left equals x+3x+x = 5x
The angle on the right equals 2y
The two angles are same side interior angles which are supplementary because the lines are parallel
5x+2y = 180
Solving for y
2y = 180-5x
Divide by 2
2y/2 = 180/2 -5x/2
y = 90 -5/2 x
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\tt y = 90 \degree - \cfrac{5x}{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The two lines are parallel, henceforth we can apply Angle pair rules.
[tex]\qquad \tt \rightarrow \:(x + 3x + x) + 2y = 180[/tex]
[ Co - interior angles ]
[tex]\qquad \tt \rightarrow \:5x + 2y = 180[/tex]
[tex]\qquad \tt \rightarrow \:2y = 180 - 5x[/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{180 - 5x}{2} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{180 }{2} - \cfrac{5x}{2} [/tex]
[tex]\qquad \tt \rightarrow \:y = 90 \degree - \cfrac{5x}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
