Answer:
Step-by-step explanation:
Solve each equation individually, using substitution or elimination.
A. x + 3y = 3
2x - y = -2
Substitute:
2(3-3y) - y = -2
6-6y-y = -2
6-7y = -2
y = 8/7
plug it back in to the first equation:
x + 24/7 = 3
x = -0.4285, approximately, and since this rounds to -0.4 and 8/7 approximately equals 1.1,
A is your answer.
The system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
To determine whether (-0.4, 1.1) is the solution of which equation,
So, put the solution in the equation of Option A,
x+3y = 3
-0.4 + 3(1.1) = 3
2.9 ≈ 3
And,
2x-y=-2
2(-0.4) - 1.1 = -2
-0.8 - 1.1 = -2
-1. 9 ≈ -2
Thus, the system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.
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Tell whether 4/2 and 14/7 form a proportion
Final answer:
Yes, 4/2 and 14/7 form a proportion because both ratios simplify to 2/1, which indicates they are equal and therefore proportional.
Explanation:
To determine if two ratios, 4/2 and 14/7, form a proportion, we need to compare the simplified forms of each ratio and see if they are equivalent. A proportion exists when two ratios are equal to each other. Simplifying both ratios, we get 4/2 = 2/1 and 14/7 = 2/1. Since both simplified ratios are equal to 2/1, we can conclude that 4/2 and 14/7 indeed form a proportion.
The figure shown is a composite figure. What is its volume?
2,622
2,109
3,648
1,387
Answer:
2622
Step-by-step explanation:
The answer can be found by adding up the volume of the two parts of the composite figure, which consists of a triangular prism and a rectangular prism
Volume of the rectangular prism=(Width)(Height)(Length)
=12*7*19
=1596
Volume of the triangular prism=(Base area)(Height)
If the triangle consisting of the sides 9, 12, 15 is a right angled triangle, 9²+12²=15²
The statement above is true
The triangle above is a right angled triangle, where 9 is the height and 12 is the base
Triangle area=(height)(base)(0.5)
=9*12*0.5
=54
Volume of triangular prism=54*19
=1026
Adding up both=1596+1026=2622
V = V1 + V2
V1 = 0.5 x 9 x 12 x 19
V1 = 1,026
V2 = 12 x 19 x 7
V2 = 1,596
V = V1 + V2
V = 1,026 + 1,596
V = 2,622
The answer is 2,622.
Find the quotient. (6x 2 - x - 40) ÷ (5 + 2x) 8 - 3x 3x + 8 3x - 8
Answer:
The quotient is 3x-8
Step-by-step explanation:
(6x^2-x-40)÷ (5 + 2x)
The above equation can be written as
(6x^2-x-40)÷ (2x + 5)
The division is shown in the figure below.
The quotient is 3x-8
Answer:
(6x^2-x-40)÷ (5 + 2x)
The above equation can be written as
(6x^2-x-40)÷ (2x + 5)
The division is shown in the figure below.
The quotient is 3x-8
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Consider the given table. x -2 2 5 9 f(x) 5 17 26 ?
The "?" in the table represents the number because the average rate of change on every interval of the function is .
The missing value in the table is 38, obtained by using the concept of average rate of change which is consistent across the given values, suggesting that the function is linear.
Explanation:In this question, the student needs to find the unknown value denoted by the "?" in the table of a function f(x), whose x-values are -2, 2, 5, 9, and the corresponding f(x)-values are 5, 17, 26, and unknown (?) respectively.
To predict the next value, we can use the concept of the average rate of change which is defined as the difference in the y-values divided by the difference in the x-values over the interval. This rate of change is the same between every pair of successive x-values in this table which suggests that the function might be linear.
We can calculate this using the formula, Average Rate of Change = Δf(x) / Δx. To illustrate, the average rate of change from x = -2 to x = 2 is (17-5) / (2 - (-2)) = 12 / 4 = 3. Similarly, the change from x = 2 to x = 5 is (26 - 17) / (5 - 2) = 9 / 3 = 3. Thus, the average rate of change is constant and equals 3.
If we follow the same pattern, then the missing f(x) value when x = 9 should be 26 (the last provided y-value) plus 4 (which is the next x interval) times 3 (the average rate of change) = 26 + 4*3 = 38. Hence, the missing value denoted by "?" is 38.
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Which best describes the transformation that occurs from
the graph of f(x) = x² to g(x) = (x - 2)2 + 3?
right 2, up 3
left 2 down 3
right 2, down 3
left 2, up 3
Answer:
right 2, up 3
Step-by-step explanation:
The original function is:
[tex]f(x) = x^2[/tex]
Translated to:
[tex]g(x)=(x-2)^2+3[/tex]
Lets look at the constants that are added or subtracted to determine the transformation.
As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.
As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.
So the correct answer is:
right 2, up 3 ..
Rationalize the denominator and simplify.
3 √6+5 √2/4 √6-3 √2
To rationalize the denominator and simplify the given expression, multiply both the numerator and denominator by the conjugate of the denominator. Simplify the resulting expression by applying the FOIL method and simplifying square roots. The final simplified expression is 72+24 √6+20 √12/84.
Explanation:To rationalize the denominator and simplify √6+5 √2/4 √6-3 √2, we need to eliminate the square root from the denominator. To do this, we can multiply both the numerator and denominator by the conjugate of the denominator, which in this case is 4 √6+3 √2. The conjugate of a binomial in the form a+b is a-b. So, we will multiply the numerator and denominator by 4 √6+3 √2:
(3 √6+5 √2)(4 √6+3 √2)/[(4 √6-3 √2)(4 √6+3 √2)]
Next, we can apply the FOIL method in the numerator and the difference of squares in the denominator to expand the expression:
(3*4*6+3*4*2 + 5*4 √6 √2 + 3* √2 √6)/ (16*6 - 9*2)
Simplifying further, we get:
(72+24 √6+20 √12)/102 - 18
The final simplified expression is:
72+24 √6+20 √12/84
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Solve the following system of equations using any method
2x+4y+1z=−35
3x+7y+7z=−34
2x+10y+6z=−64
Answer:
values of x,y and z are x = -2, y= -9 and z=5
Step-by-step explanation:
2x+4y+1z=−35 eq(1)
3x+7y+7z=−34 eq(2)
2x+10y+6z=−64 eq(3)
We can solve using elimination method
Subtracting eq (1) from eq(3)
2x + 10y +6z = -64
2x +4y +1z = -35
______________
6y + 5z = -29 eq(3)
Multiplying eq(2) with 2 and eq(3) with 3 and subtracting
6x + 14y +14z = -68
6x + 30y +18z = -192
- - - +
_________________
-16y -4z = 124 eq(4)
Multiply eq(3) with 4 and eq(4) with 5 and add both equations
24y + 20z = -116
-80y - 20z = 620
______________
-56y = 504
y = -504/56
y= -9
Putting value of y in equation(3)
6y + 5z = -29
6(-9) + 5z = -29
-54 + 5z = -29
5z = -29+54
5z = 25
z = 25/5
z =5
Now, putting value of y and z in eq(1)
2x + 4y +1z = -35
2x + 4(-9) +1(5) = -35
2x -36+5 = -35
2x -31 = -35
2x = -35+31
2x = -4
x= -4/2
x=-2
So, values of x,y and z are x = -2, y= -9 and z=5
which of the following shows the graphical representation of the solution for the one-variable linear equation 2x-1=3
For this case we have the following equation:
[tex]2x-1 = 3[/tex]
If we add 1 to both sides of the equation we have:
[tex]2x = 3 + 1\\2x = 4[/tex]
Dividing between 2 on both sides of the equation we have:
[tex]x = \frac {4} {2}\\x = 2[/tex]
The graph of the solution is shown in the attached figure.
Answer:
See attached image
If f(x) = -5% - 4 and g(x) = -3x - 2, find (f+ g)(x).
Need help !
Answer:
[tex]\large\boxed{(f+g)(x)=-8x-6}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-5x-4,\ g(x)=-3x-2\\\\\text{Substitute:}\\\\(f+g)(x)=(-5x-4)+(-3x-2)\\\\=-5x-4-3x-2\qquad\text{combine like terms}\\\\=(-5x-3x)+(-4-2)\\\\=-8x-6[/tex]
What is the value of m in the figure below? If necessary,round your answer to the nearest tenth of a unit
Answer:
D
Step-by-step explanation:
It turns out from similar triangles, that 7/BD = BD / 18. Use triangles ABD and BDC to show this relationship. Solving this equation will give you BD
BD^2 = 7*18
BD^2 = 126 Just leave it in this form. Do your rounding at the end.
Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m
m^2 = BD^2 + 7^2
m^2 = 126 + 49
m^2 = 175 Take the square root of both sides.
sqrt(m^2) = sqrt(175)
m = 13.22
so the answer is D
If f(x) = 4x + 3 and g(x) = 3x, evaluate for X = -1/2
Answer:
[tex]f(-\frac{1}{2}) = 1[/tex]
[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]
Step-by-step explanation:
Given the function [tex]f(x) = 4x + 3[/tex] and the function [tex]g(x) = 3x[/tex], to evaluate for [tex]x=-\frac{1}{2}[/tex], you need to substitute it into each function.
Then, for the function f(x), when [tex]x=-\frac{1}{2}[/tex], you get:
[tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]
[tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]
[tex]f(-\frac{1}{2}) = -\frac{4}{2}+ 3[/tex]
[tex]f(-\frac{1}{2}) = -2 + 3[/tex]
[tex]f(-\frac{1}{2}) = 1[/tex]
For the function g(x), when [tex]x=-\frac{1}{2}[/tex], you get:
[tex]g(-\frac{1}{2} ) = 3(-\frac{1}{2})[/tex]
[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]
Answer:
f(-1/2) = 1
g(-1/2) =-3/2
Step-by-step explanation:
f(x) = 4x+3
Let x = -1/2
f(-1/2) = 4(-1/2) +3
f(-1/2) = -2 +3
f(-1/2) =1
g(-1/2) = 3(-1/2)
= -3/2
Write a recursive formula for the sequence -2,4,-8, 16, ...
a = -2, a, = an - 1+6, n22
a = -2, an=-2an - 1, n > 2
19,5-2, a, = 24, -1, 122
aj = 16, an= -2an - 1, n > 2
Answer:
[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]
Step-by-step explanation:
The first number in the sequence, [tex] a_1 [/tex], is -2.
Each number after that is the previous number multiplied by -2.
[tex] a_1 = -2 [/tex]
[tex] a_2 = a_1 \times (-2) = -2 \times (-2) = 4 [/tex]
[tex] a_3 = a_2 \times (-2) = 4 \times (-2) = -8 [/tex]
etc.
[tex] a_n = -2a_{n - 1} [/tex]
We start by stating that [tex] a_1 = -2 [/tex].
Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.
[tex] a_n = -2a_{n - 1} [/tex]
Answer:
[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]
A recursive formula represents the relationship between each term and the ones before it. In the given geometric sequence (-2, 4, -8, 16,...), each term is -2 times the preceding term, hence the recursive formula is [tex]a_{n} = -2a_{n-1}[/tex] for n>1.
Explanation:The given sequence is -2, 4, -8, 16, ..., which is an example of a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'.
Looking at the pattern, we notice that each term is -2 multiplied by the prior term. Therefore, the recursive formula for this sequence is [tex]a_{n} = -2a_{n-1}[/tex] where 'an' represents the nth term and 'an-1' represents the previous term, and n > 1.
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a negative slope means that the line moves up from left to right
No the negative slope means the line moves down from left to right.
Hope this helps.
r3t40
Answer:
It slopes upwards from right to left.
Step-by-step explanation:
A negative slope means that a line rises from right to left. Like a back slash \.
find the interior angle of a regular polygon which has 6 sides
Answer:
120°.
Step-by-step explanation:
The sum of all interior angles in a polygon with [tex]n[/tex] sides ([tex]n\in \mathbb{Z}[/tex], [tex]n \ge 3[/tex]) is equal to [tex](n - 2) \cdot 180^{\circ}[/tex]. (Credit: Mathsisfun.)
The polygon here has 6 sides. [tex]n = 6[/tex]. Its interior angles shall add up to [tex](6 - 2) \times 180^{\circ} = 720^{\circ}[/tex].
Consider the properties of a regular polygon. (Credit: Mathsisfun.)
All sides in a regular polygon are equal in length. All angles in a regular polygon are also equal.There are six interior angles in a polygon with 6 sides. All six of them are equal. Thus, each of the six interior angle will be
[tex]\displaystyle \frac{1}{6}\times 720^{\circ} = 120^{\circ}[/tex].
help pleeesea!!!!!!!!!!!.Trina downloaded 3 music albums and 5 audio books one week at a cost of $49.60. The next week she downloaded 1 music album and 2 audio books at a cost of $20.50. Her mother wants to write a system of equations to determine the price of one music album and one audio book. She uses the variables x and y. She lets x represent the cost of one music album. What will y represent?
Y is the Audio Book.
"determine the price of one music album and one audio book"
"She lets x represent the cost of one music album."
According to this information "One Audio Book" should be the correct answer. Have a great day!
Answer:
y will represent the cost of one audio book.
Step-by-step explanation:
Here, the cost of 3 music albums and 5 audio books is $49.60 and 1 music album and 2 audio books is $20.50,
Since, there are two unknown values,
First one is the cost of one music album,
Second one is the cost of one audio book,
We know that, for finding an unknown value we take a variable,
If we have variables x and y in which x represent the cost of one music album, then y must represent the cost of one audio album.
How to write an equation of the line through the point (-2,1) that is perpendicular to the line 5x+9y=-9
Answer:
[tex]\large\boxed{y=\dfrac{5}{9}x+\dfrac{19}{9}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation i the standard form.}\\\text{ Convert it to the slope-intercept form}\ y=mx+b:\\\\5x+9y=-9\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\9y=-5x-9\qquad\text{divide both sides by 9}\\\\y=-\dfrac{5}{9}x-1\to m_1=-\dfrac{5}{9}\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{5}{9}}=\dfrac{9}{5}[/tex]
[tex]\text{We have the equation:}\\\\y=\dfrac{5}{9}x+b\\\\\text{Put the coordinates of the point (-2, 1) to the equation:}\\\\1=\dfrac{5}{9}(-2)+b\\\\1=-\dfrac{10}{9}+b\qquad\text{add}\ \dfrac{10}{5}\ \text{to both sides}\\\\\dfrac{19}{9}=b\to b=\dfrac{19}{9}[/tex]
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5?
A. 1/13
B.1/8
C. 5/13
D. 5/8
geometry archive find x simplify completely triangle with 16,25, and x
Answer:
x = 20
Step-by-step explanation:
see attached
From Pythagoras, [tex]\(z^2 - y^2 = 369\)[/tex]. Solving, z - y = 19, z + y = 19, yielding z = 19. Substituting, x = 17.
Given that Triangle A and Triangle B are right angle triangles with similar heights 'x' and different perpendicular (say 'y' and 'z' respectively).
From the Pythagoras theorem, we know that:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2[/tex]
Substituting the given values, we get:
[tex]y^2 = 16^2 + x^2[/tex]
[tex]z^2 = 25^2 + x^2[/tex]
Subtracting the two equations, we get:
[tex]z^2 - y^2 = 25^2 - 16^2[/tex]
(z - y)(z + y) = 625 - 256 = 369
z - y = 19
z + y = 369 / 19 = 19
Adding the two equations, we get:
2z = 38
z = 19
Substituting the value of 'z' in the equation:
[tex]z^2 = 25^2 + x^2[/tex]
[tex]19^2 = 25^2 + x^2[/tex]
[tex]x^2 = 19^2 - 25^2 = 289[/tex]
[tex]x = sqrt(289)[/tex] = 17
Therefore, the value of 'x' is 17.
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Which of the following equations will produce the graph shown below?
Answer:
The answer is the first one.
Step-by-step explanation:
What helped me figure this out was going to desmos.com which is a great site for graphing. If you put in the equations this should help you find the answer. I hope this helps love! :)
Answer: A. [tex]\dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]
Step-by-step explanation:
The equation of ellipse centered at origin is when the horizontal major axis (2a) and verticel minor axis (2b) is the major axis :-
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
From the given picture , [tex]a=10[/tex]
[tex]b=8[/tex]
Now, the equation of the given ellipse :-
[tex]\dfrac{x^2}{(10)^2}+\dfrac{y^2}{(8)^2}=1\\\\\Rightarrow\ \dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]
Quotient of 32 and -8
Answer:
-4
Step-by-step explanation:
mark branliest :))
Hello There!
The quotient of 32 and -8 is -8.
When dividing a positive number by a negative number, your final result will always end up with a negative number so 32 divided by 8 is 4 but it will be -4 instead of 4
edgar divided a five digit number by a two digit number.there was no remainder. what is the least possible quotient of the two numbers? A.100 B.102 C.111 D.1000
the least possible quotient of the two numbers would be C.) 111
please!!!!! ANSWERR!! HURRY ILL MARK YOU AS BRAINNN
Answer:
A=280in^2
Step-by-step explanation:
3*3=9
A=2LW+2WH+2LH
A=2(8*4)+2(4*9)+2(8*9)
A=2(32)+2(36)+2(72)
A=64+72+144
A=280in^2
help answer question 2
How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain
Answer:
If each linear function is given as a set of two ordered pairs, you need to use those points to find the equation of each line, and then solve the system of equations.
For example:
Let's say that f(x) has the following ordered pais: (a, b) and (c, d) and g(x) has the following ordered pais: (e, f) and (g, h). We know that the general equation of a line is the following:
(y - yo) = m(x-xo), where 'm' represents the slope and (xo, yo) any point from the line.
The slope will be given by: (y1 - yo)/(x1 - x0).
For example, the equation of the line of f(x) is:
f(x) = (y - b) = [(d - b)/(c - a)](x-a)
You do the same for the function g(x), and then you are all set to solve the system of equations!
Answer:
Sample response: Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.
If 32x+1 - 3^x+5, what is the value of x?
Answer:
x = 4
Step-by-step explanation:
hope this helps!!!
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Answer:
Part 1) The volume of pyramid A is two times the volume of pyramid B
Part 2) The new volume of pyramid B is equal to the volume of pyramid A
Step-by-step explanation:
we know that
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of pyramid
h is the height of the pyramid
Part 1
The heights of the pyramids are the same
Find the volume of pyramid A
Find the area of the base B
[tex]B=10*20=200\ m^{2}[/tex]
substitute
[tex]VA=\frac{1}{3}(200)h[/tex]
[tex]VA=\frac{200}{3}h\ m^{3}[/tex]
Find the volume of pyramid B
Find the area of the base B
[tex]B=10^{2}=100\ m^{2}[/tex]
substitute
[tex]VB=\frac{1}{3}(100)h[/tex]
[tex]VB=\frac{100}{3}h\ m^{3}[/tex]
Compare the volumes
[tex]VA=2VB[/tex]
The volume of pyramid A is two times the volume of pyramid B
Part 2)
If the height of pyramid B increases to twice that of pyramid A
we have that
[tex]VA=\frac{200}{3}h\ m^{3}[/tex]
Find the new volume of pyramid B
we have
[tex]B=100\ m^{2}[/tex]
[tex]h=2h\ m[/tex]
substitute
[tex]VB=\frac{1}{3}(100)(2h)[/tex]
[tex]VB=\frac{200}{3}h\ m^{3}[/tex]
Compare the volumes
[tex]VA=VB[/tex]
The new volume of pyramid B is equal to the volume of pyramid A
Answer:
The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
Step-by-step explanation:
Correct for plato :)
Solve the formula Ax+ By = C for x.
Answer:
x = (C-By)/A
Step-by-step explanation:
Ax+ By = C
We want to isolate x
Subtract By from both sides
Ax+ By-By = C-By
Ax = C - By
Now divide both sides by A
Ax/A = (C-By)/A
x = (C-By)/A
[tex]Ax+ By = C\\Ax=C-By\\x=\dfrac{C-By}{A}[/tex]
Rewrite without parentheses and simplify.
(6w+7)
Answer:
6w + 7
Step-by-step explanation:
There is nothing to simplify. Just remove the parentheses.
what are the approximate solutions of 2x^2+9x=8 to the nearest hundredth
Answer:
x=0.76 or -5.26
Step-by-step explanation:
You can apply the completing square method to solve this ;
[tex]2x^2+9x=8\\\\[/tex]
Rewrite the equation with a zero like below
[tex]2x^2+9x-8=0[/tex]
This is by taking 8 to the left side of the equation
Divide the terms by 2 in x²
[tex]\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}[/tex]
[tex]=x^2+4.5x-4=0[/tex]
Move the number term to the right side of the equation
[tex]x^2+4.5x=4[/tex]
complete square on the lefts side of the equation, how?
[tex]=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625[/tex]
balance the equation by adding this value to the right side , in this form
[tex]x^2+4.5x+5.0625=4+5.0625\\\\[/tex]
Factorize the left side
[tex](x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\[/tex]
Eliminate the square on the left side
[tex]x+2.25=\sqrt{9.0625}[/tex]
x+2.25= ± 3.010
Solve for x
x=+3.010-2.25=0.76
or
x=-3.010-2.25=-5.26
Answer:
x = 0.76 or x= -5.26
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation,
2x² + 9x = 8
⇒ 2x² + 9x - 8 = 0
To find the solution
Here a = 2, b = 9 and c = -8
x = [-b ± √(b² - 4ac)]/2a
= [-9 ± √(9² - 4*2*(-8))]/2*2
= [-9 ± √(81 +64)]/4
= [-9 ± √(145]/4
= [-9 ± 12.04]/4
x = [-9 + 12.04]/4 or x = [-9 - 12.04]/4
x = 0.76 or x= -5.26
A line passes through the point (8.-8) and has a slope of -5/4.
Write an equation in point-slope form for this line.
plz
[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-\cfrac{5}{4}(x-8)\implies y+8=-\cfrac{5}{4}(x-8)[/tex]
The equation in point-slope form for this line is 4y = -5x + 8.
What is point-slope form of equation of straight line ?The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the point-slope form. Here both the slope (m) and y-intercept (c) have real values. It is known as point-slope form as it gives the definition of both the slope, y-intercept and the points mentioned in the line.
How to form the given equation of straight line ?It is given that the line passes through the point (8.-8) and has a slope of -5/4.
The general representation for straight line is y = mx + c .
Here, m = -5/4 , x = 8 and y = -8 .
Thus we have ,
⇒ -8 = -5/4 * 8 + c
⇒ c = 10 - 8
∴ c = 2
The y-intercept is 2.
The equation of straight line becomes,
⇒ y = -(5/4)x + 2
∴ 4y = -5x + 8
Therefore, the equation in point-slope form for this line is 4y = -5x + 8.
To learn more about point-slope form, refer -
https://brainly.com/question/18617367
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