3x +11 = K
To solve for X, we need to isolate x on one side.
Subtract 11 from both sides:
3x = K -11
Divide both sides by 3:
x = (k-11)/3
Answer:
3x +11 = K
x = (k-11)/3
Step-by-step explanation:
Given the following functions f(x) and g(x), solve f over g (−5) and select the correct answer below:
f(x) = 2x − 20
g(x) = x − 1
−5
5
one sixth
30
=====================================================
Plug x = -5 into f(x)
f(x) = 2x-20
f(-5) = 2(-5) - 20
f(-5) = -10-20
f(-5) = -30
Then plug x = -5 into g(x)
g(x) = x-1
g(-5) = -5-1
g(-5) = -6
Divide the two results
(f/g)(-5) = f(-5)/g(-5)
(f/g)(-5) = (-30)/(-6)
(f/g)(-5) = -5
For this case we have the following functions:
[tex]f (x) = 2x-20\\g (x) = x-1[/tex]
We must find [tex]\frac {f (-5)} {g (-5)}[/tex], then:
We have in mind that:
[tex]+ * - = -[/tex]
Equal signs are added and the same sign is placed.
[tex]\frac {f (-5)} {g (-5)} = \frac {2 (-5) -20} {- 5-1} = \frac {-10-20} {- 6} = \frac {-30} {- 6} = 5[/tex]
Answer:
5
Please help me out brainiest and 30 points
Match each of the four lines with a line that is perpendicular to it.
Choices to pair with the equations are
y=74x+2
y=−65x+1
y=−74x+9
y=−56x−5
y=65x−5
y=−47x+2
y=47x+9
y=56x+1
Answer:
y = (5/6)x - 7
is with
y = - (6/5)x + 1
y = - (5/6)x - 8
is with
y = (6/5)x - 5
y = - (7/4)x - 1
is with
y = (4/7)x + 9
y = (7/4)x - 2
is with
y = - (4/7)x + 2
Step-by-step explanation:
You can double check by dividing -1 by the number before x. The answer from that calculation will be the number before the x of the perpendicular line's equation
pair with their perpendicular equations are
y = (5/6)x - 7y = - (6/5)x + 1
y = - (5/6)x - 8y = (6/5)x - 5
y = - (7/4)x - 1y = (4/7)x + 9
y = (7/4)x - 2y = - (4/7)x + 2
What is condition of perpendicular line?The given line is perpendicular to the required line under the condition of perpendicular lines m1×m2=–1.
As, m1*m2=-1
m1= -1/m2
For first equation
y = (5/6)x - 7
m1= 5/6
So, m2= -1/m2= -6/5
Hence, the equation of perpendicular line is y = - (6/5)x + 1.
Similarly,
y = (5/6)x - 7
m1= 5/6
So, m2= -1/m2= -6/5
Hence, the equation of perpendicular line is y = (6/5)x - 5.
again,
y = - (7/4)x - 1
m1=-7/4
So, m2= -1/m2= 7/4
Hence, the equation of perpendicular line is y = (4/7)x + 9
again,
y = (7/4)x - 2
m1= 7/4
So, m2= -1/m2= -4/7
Hence, the equation of perpendicular line is y = - (4/7)x + 2.
Learn more about perpendicular lines here:
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Solve for x in the equation X2 - 10x+ 25 = 35.
Answer:
x = 5 ± sqrt(35)
Step-by-step explanation:
X^2 - 10x+ 25 = 35.
Factor the left hand side. This is the difference of squares. a^2 -2ab - b^2 = (a-b)^2 where a = x and b = 5
(x-5) ^2 = 35
Take the square root of each side
sqrt((x-5) ^2) =± sqrt(35)
x-5 = ± sqrt(35)
Add 5 to each side
x-5+5 = 5 ± sqrt(35)
x = 5 ± sqrt(35)
The functions f(x) and g(x) are shown in the graph
f(x)=x^2
What is g(x) ?
Answer:
[tex]g(x)=-x^{2}-4[/tex]
Step-by-step explanation:
we know that
The function g(x) is a vertical parabola open downward with vertex at (0,-4)
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
I assume that g(x) is a reflection of the function f(x) over the line y=-2
so
a=-1 ---> because in the function f(x) the value of a is equal to 1
therefore
[tex]g(x)=-x^{2}-4[/tex]
In which figure is DE BC ? A. figure 1 B. figure 2 C. figure 3 D. figure 4
Answer:
figure 2
Step-by-step explanation:
Answer:
The answer is figure 4.
Which is the equation of the line with slope 0 passing through the point (-3,-1)?
When a line has a slope of zero it means that it is horizontal. This means that all the x values have the same y values. In this case it means that the y value is always -1.
The equation for this line is...
y = -1
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y= -1
Step-by-step explanation:
When we have a line with slope of 0, it means that the y value does not change, so our equation must be in the form y= something
The point has a y value of -1,
so our equation is
y= -1
What are the vertical asymptotes of the function f(x) =5x+5/x2 + x-2
let's recall that the vertical asymptotes for a rational expression occur when the denominator is at 0, so let's zero out this one and check.
[tex]\bf \cfrac{5x+5}{x^2+x-2}\qquad \stackrel{\textit{zeroing out the denominator}~\hfill }{x^2+x-2=0\implies (x+2)(x-1)=0}\implies \stackrel{\textit{vertical asymptotes}}{ \begin{cases} x=-2\\ x=1 \end{cases}}[/tex]
Final answer:
The vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2) occur where the denominator equals zero. Factoring the denominator, we find the vertical asymptotes to be at x = -2 and x = 1.
Explanation:
The student is asking about the vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2). To find the vertical asymptotes of a function, we look for values of x where the denominator is equal to zero, because these are the points where the function is undefined and the graph of the function will approach infinity.
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
x² + x - 2 = 0
Factoring the quadratic equation, we get:
(x+2)(x-1) = 0
Therefore, the vertical asymptotes are at x = -2 and x = 1, since these are the values of x for which the denominator becomes zero.
Paul's unmarried daughter, Candace, lived with him in his home for the entire year. Paul is divorced. He owns his own home and pays all of the costs of upkeep for the home. Paul paid over one-half of the cost of support for Candace. Paul may file as head of household if Candace is __________.
Answer:
Paul's unmarried daughter, Candace, lived with him in his home for the entire year. Paul is divorced. He owns his own home and pays all of the costs of upkeep for the home. Paul paid over one-half of the cost of support for Candace. Paul may file as head of household if Candace is under the age of 19 or permanently disabled.
If none of the conditions statetd above are met, then Candance won't be considered a dependent. If Candance is not a dependant, Paul can still file as a head of household given that he paid over one-half of the cost of support for Candance.
What is the height of a student who’s z score is 3? When the mean is 49 inches and the standard deviation is 2
Answer:
55 inches
Step-by-step explanation:
This question is on z-score for a sample
The general formula for finding z score for a sample is;
z=(x-μ)/δ...................where x is the sample is the height , μ is the mean and δ is the standard deviation
Given;
z=3 x=? μ=49 δ=2
Substitute values above in the general formulae
z=(x-μ)/δ
3=(x-49)/2
[tex]3=\frac{x-49}{2} \\\\\\3*2=x-49\\\\\\6=x-49\\\\\\6+49=x\\\\\\55=x[/tex]
Answer:
The student is 55 inches tall.Step-by-step explanation:
To solve this problem we need to use the following formula
[tex]Z=\frac{x- \mu}{\sigma}[/tex]
Where [tex]Z[/tex] is the z-value, [tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation and [tex]x[/tex] is the height of the student.
In this case, we have
[tex]Z=3\\\mu=49\\\sigma=2[/tex]
Replacing all these values, we have
[tex]3=\frac{x- 49}{2}\\6=x-49\\x=6+49\\x=55[/tex]
Therefore, the student is 55 inches tall.
When Quentin ordered a tennis racquet recently, he agreed to pay a 7% shipping and handling charge. If Quentin paid $9.45 in shipping and handling, bow much must the racquet have cost? Urgent!!!!!!!!!!!!!
Answer:
The cost of the racquet is [tex]\$135[/tex]
Step-by-step explanation:
Let
x-----> the cost of the racquet
we know that
The racquet represent the 100%
so
using proportion
[tex]x/100\%=\$9.45/7\%[/tex]
[tex]x=100\%*(\$9.45)/7\%[/tex]
[tex]x=\$135[/tex]
Estimate -12 4/9 · 5 7/8. please help asap!!!
Final answer:
To estimate the product -12 4/9 · 5 7/8, round each number to the nearest whole number and multiply. The estimated product is -72.
Explanation:
To estimate the product -12 4/9 · 5 7/8, we can round each number to the nearest whole number and then multiply.
Rounding -12 4/9 to the nearest whole number gives -12.
Rounding 5 7/8 to the nearest whole number gives 6.
Now, we can multiply -12 and 6: -12 · 6 = -72.
So, the estimated product is -72.
What is the slope-intercept equation of the line below?
T
Answer:
y = mx + b
Step-by-step explanation:
Since there is no illustration, that is all I can give you. I apologize.
Answer:
y=mx +b is the formula
Step-by-step explanation:
I think you are missing a part of the question.
What is the solution to the inequality below?
x2 < 49
I am going to assume that you mean:
x² < 49
To solve this you must do the opposite of squaring, which would be taking the square root. What you do to one side you must do to the other.
√x² < √49
x < 7
Hope this helped!
~Just a girl in love with Shawn Mendes
Final answer:
To solve the inequality x^2 < 49, we take the square root of both sides resulting in the solution -7 < x < 7, which means x can be any real number between -7 and 7.
Explanation:
The student's question is about solving an inequality involving a square of a variable, specifically x^2 < 49. To solve this inequality, we will first take the square root of both sides, keeping in mind that when we take the square root of a square inequality, we must consider both the positive and negative roots. Therefore, we can express the inequality as -7 < x < 7, since both positive and negative square roots of 49 are 7 and -7, respectively. This represents the range of values for x where the original inequality holds true.
The solution implies that x can take on any real value that is less than 7 and greater than -7. There's no need for tools like completing the square or the quadratic formula here, as the inequality is already in a solvable form.
Which translation transformed the parent function, f(x), to g(x)?
a translation right 2 units
a translation left 2 units
a translation up 2 units
a translation down 2 unit
Answer:
A. A translation right 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation right 2 units would be:
g(x) = f(x-2).
B. A translation left 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation left 2 units would be:
g(x) = f(x+2).
C. A translation up 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation up 2 units would be:
g(x) = f(x) + 2
D. A translation down 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation down 2 units would be:
g(x) = f(x) - 2
Final answer:
The function f(x) translated to g(x) via a translation right 2 units, which shifts the graph of the function 2 units to the right on the x-axis.
Explanation:
The transformation that transformed the parent function, f(x), to g(x) is a translation right 2 units. This is because when the argument of the function f(x) becomes f(x-2), the graph of f(x) is shifted to the right by 2 units along the x-axis. To understand this, let us consider the original function y = f(x).
The graph of the new function y = f(x-2) is the same as the original, but every point on the graph has been moved 2 units to the right. This can also be viewed as if the x-axis (and origin) has shifted 2 units to the left while the graph remains stationary.
what is the value of y
Answer:
B y=54 degrees
Step-by-step explanation:
Since a triangle's angles always add up to 180.
180-72=108
108/2=54
It must be divided by two because y is two angles not one.
A line passes through the points (−200,−4.03×10^4) and (50,9.7×10^3). Find the value of y when x=100. Write your answer in scientific notation.
Answer:
[tex]y=19.7*10^{3}[/tex]
Step-by-step explanation:
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](-200,-4.03*10^{4}), (50,9.7*10^{3})[/tex]
convert to
[tex](-200,-40.3*10^{3}), (50,9.7*10^{3})[/tex]
substitute in the formula
[tex]m=\frac{9.7*10^{3}+40.3*10^{3}}{50+200}[/tex]
[tex]m=\frac{50*10^{3}}{250}[/tex]
[tex]m=200[/tex]
step 2
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex](x1,y1)=(50,9.7*10^{3})[/tex]
[tex]m=200[/tex]
substitute
[tex]y-9.7*10^{3}=200(x-50)[/tex] ----> equation of the line into point slope form
step 3
Find the value of y when x=100
substitute in the equation the value of x
[tex]y-9.7*10^{3}=200(100-50)[/tex]
[tex]y=200(50)+9.7*10^{3}[/tex]
[tex]y=19,700[/tex]
[tex]y=19.7*10^{3}[/tex]
Miss Wilson has spent $6 on breakfast using her debit card 5 mornings per week for the past 8 weeks. What is the change in Miss Wilson’s account balance from buying breakfast during this time? Write a multiplication expression. Then find and interpret the product
Answer:
(6x5) • 8
Step-by-step explanation:
We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240
Answer:
Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240
Step-by-step explanation:
Given:
Amount spend on Breakfast using debit card = $6
Amount for breakfast spend for 5 mornings per week for past 8 weeks.
We need to write the multiplication expression for the given situation.
Amount spend on breakfast for a morning = $6
Amount spend on breakfast for 5 morning = 6 × 5
Amount spend on breakfast for 1 week = $ ( 6 × 5 )
Amount spend on breakfast for 8 week = ( 6 × 5 ) × 8
Required multiplication expression = ( 6 × 5 ) × 8
Answer of the multiplication = ( 6 × 5 ) × 8 = ( 30 ) × 8 = 240
Therefore, Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240
A sample data set has a mean of 122.3 and a standard deviation of 18.5. Convert a score of 168.4 to a z score and determine if the score is “usual” or “unusual.”
Answer:
[tex]Z=2.49[/tex] and this Z-score is “unusual.”
Step-by-step explanation:
To calculate the Z score use the following formula
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Where
μ is the average
[tex]\sigma[/tex] is the standard deviation
x is the data to which we will calculate the z-score
In this case
[tex]\mu = 122.3\\\\\sigma= 18.5\\\\x =168.4[/tex]
So
[tex]Z=\frac{168.4-122.3}{18.5}[/tex]
[tex]Z=2.49[/tex]
A z-score is unusual if [tex]Z> 2[/tex] or [tex]Z < -2[/tex]
Finally
[tex]Z=2.49[/tex] and this Z-score is “unusual.”
Answer: 2.49 unusual
Step-by-step explanation:
Identify an equation in point-slope form for the line perpendicular to
y= -4x - 1 that passes through (-2, 7).
O A. y-7 =-4(x+2)
O B. y+2 = 4(x-7)
O C. y+7--1(x-2)
O D. y-7 - 2(x+2)
Answer:
c is the correct answer
Step-by-step explanation:
the way I study
Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?
Quadratic formula: x =
For this case we have a quadratic equation given by:
[tex]4x ^ 2 + 2x-1 = 0[/tex]
The roots are found by means of the quadratic formula below:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = 2\\c = -1[/tex]
So, we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Or in an equivalent way we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2 + 4 (4) (1)}} {2 (4)}[/tex]
Answer:
The correct option will be:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Answer:
a = 4, b = 2 and c= -1
Step-by-step explanation:
Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a
Here quadratic equation is 4x2 + 2x – 1
a = 4, b = 2 and c= -1
x =[-b ± √(b² - 4ac)]/2a
= [-2 ± √(2² - 4*4*-1)]/2*4
= [-2 ± √(4 + 16)]/8
= [-2 ± √20)]/8
= [-2 ± 2√5)]/8
= [-1 ± √5)]/4
x = [-1 ± √5)]/4
Which value of n makes the following equation true?
3 sqrt n=8
a.2
b.16
c.24
d.512
Answer: d. 512
Step-by-step explanation:
You need to remember that:
[tex](\sqrt[3]{x})^3=x[/tex]
Then, given the equation:
[tex]\sqrt[3]{n}=8[/tex]
You can find the value of "n" that make the equation true, by solving for "n".
So, to solve for "n", you need to raise both side of the equation to power 3. Therefore, you get:
[tex]\sqrt[3]{n}=8[/tex]
[tex](\sqrt[3]{n})^3=(8)^3[/tex]
[tex]n=512[/tex]
Then, the value of "n" that makes the equation [tex]\sqrt[3]{n}=8[/tex] true is: 512 (You can observe that this matches with the option d).
Answer:
the answer is D
Step-by-step explanation:
Which statement is false ?
Answer:
B
Step-by-step explanation:
Guys please help!! Show your work! Any answers help
Answer:
I only know how to do the first and second one i'm not sure about the rest: V=Lwh
Step-by-step explanation:
so, (6)(6)(8)= 288ft^3
and (12)(16)(18)= 3456m^3
Hope i have helped you in some way!
Liesl grew 7/12 of a foot in one year. Her little sister grew 1/3 of a foot during that same year. How much more did Liesl grow than her little sister did
Answer:
The answer to this is 0.25
Step-by-step explanation:
7/12= 0.58333 repeating, and 1/3 is 0.3333 repeating. When you subtract 7/12 from 1/3 you get 0.25
Hope it helps
Answer:
0.25
Step-by-step explanation:
Henry is making a recipe for biscuits. A recipe calls for 5/10 kg and 9/100 kg. How can u write your answer as a decimal?
While flying at an altitude of 1.5 km, a plane measures angles or depression to opposite ends of a large crater, shown in the image below. Find the width of the crater
Check the picture below.
notice the alternate interior angles in the picture.
[tex]\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill[/tex]
The width of the crater is 1.61 km.
Given that:Plane is flying at altitude of 1.5 km
The angle of depressions to point A = 68 degrees/
The angle of depression to point B = 56 degrees.
Calculations:In the given diagram below, we can see:
Angle XPD is right angle and thus we have:
[tex]\angle APD + \angle APX = 90\\\angle APD = 180 - \angle APX = 90 - 68 = 22^\circ[/tex]
Similarly, Angle YPD is right angle and thus:
[tex]\angle DPB + \angle BPY = 90\\\angle DPB = 90 - \angle BPY = 90 - 56 = 34^\circ[/tex]
Since the triangle ADP and triangle PDB are right angled triangles, thus we have by trigonometric ratios:
[tex]tan(22) = \dfrac{AD}{PD}\\\\0.404 \times 1.5 = AD\\\\AD = 0.606\: \rm km[/tex]
Similarly,
[tex]tan(34) = \dfrac{BD}{PD}\\\\0.674 \times 1.5 = BD\\\\BD = 1.01 \: \rm km[/tex]
The width of the crater = AD + DB = 1.01 km + 0.606 km = 1.61 km
Thus, width of the crater is 1.61 km.
Learn more about angle of depression here:
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The equation (2x^2-1)(3x+2)=(2x^2)(3x)+(2x^2)(2)+(-1)(2) is an example of which method/property?
The answer is:
The equation is an example of the distributive property.
Why?To determine which method/property is the equation example, we need to remember the distributive property.
We can state the distributive property with the following example:
[tex](a+b)(c+d)=a*c+a*d+b*c*+b*d[/tex]
So, we are given the expression:
[tex](2x^{2}-1)(3x+2)[/tex]
Then, apllying the distributive property we have:
[tex](2x^{2}-1)(3x+2)=(2x^{2})*(3x)+(2x^{2})*2+(-1)*(3x)+(-1)*(2)[/tex]
Hence, the equation is an example of the distributive property.
Have a nice day!
What is the volume of the composite figure?
Answer: 372in³
Step-by-step explanation:
All we have to do is find the volume of the two separate rectangular prisms and add them up.
First we will find the volume of the standing prism:
5in * 3in * 12in = 180in³
Now the other prism:
12in * 4in * 4in = 192in³
Now add them up:
180in³ + 192in³ = 372in³
Answer:
372 [tex]inches^{3}[/tex]
Step-by-step explanation:
Imagine the figures are each separate. The top figure's dimensions would be L=12 in, W=4 in, and H=4 in. The bottom figure's dimensions would be L=5 in, W=3 in, and H=12 in. So, do the volume formula for each: L x W x H and then add them together.
12 x 4 x 4 = 192 inches^3
5 x 3 x 12 = 180 inches^3
192 + 180 = 372 inches^3
2(n-1)+4n=2(3n-1)
n=0
no solution
infinitely many solutions
n= - 4
HELP PLEASE!!!!!!!
Answer:
Infinitely many solutions.
Step-by-step explanation:
2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.
2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)
2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.
6n - 2 = 6n - 2 Add 2n + 4n.
-6n -6n Subtract 6n from both sides.
-2 = -2? Yes, -2 equals -2.
Therefore, the answer is infinitely many solutions, meaning that n can be any real number.
An equation can have no solution, one solution or infinitely many solutions.
The equation [tex]2(n -1) + 4n = 2(3n - 1)[/tex] has infinitely many solutions
Given that:
[tex]2(n -1) + 4n = 2(3n - 1)[/tex]
Open brackets
[tex]2n -2 + 4n = 6n - 2[/tex]
Collect like terms
[tex]2n + 4n - 6n= - 2+2[/tex]
[tex]0 = 0[/tex]
When the solution to an equation is 0 on both sides, the equation has infinitely many solutions
Read more about number of solutions at:
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Factor completely 5y^2-2y-3
Answer:
(5y+3)(y-1)
Step-by-step explanation:
5y^2-2y-3
I don't know if you like trial factors or not... but we can try that way
notice we have 5y^2
that can be written as 5y * 1y
Notice at the end we have -3
that can be written as -3*1
So possible answers could be:
(5y-3)(1y+1) =5y^2+5y-3y-3=5y^2+2y-3
So this was almost right.
If we just switch the signs the - and + there we will have got it
(5y+3)(1y-1)=5y^2-5y+3y-3=5y^2-2y-3 which is good
So the answer is (5y+3)(y-1)
To factor the quadratic equation 5y^2-2y-3 completely, find two numbers that multiply to -15 and add to -2, and use them to rewrite the middle term before factoring by grouping. The factors obtained are (5y - 3)(y + 1).
Explanation:The given quadratic equation to factor completely is 5y^2-2y-3. To achieve this, we are finding two numbers that multiply to the product of the coefficient of y^2 (which is 5) and the constant term (which is -3), and at the same time add up to the coefficient of the y term (which is -2).
The required pair of numbers is -3 and -1, because (-3)*(1) = -3 (the product of coefficient of y^2 and the constant term) and (-3)+(1) = -2 (the coefficient of the y term).
We rewrite the middle term and then factor by grouping:
Rewrite the equation: 5y^2 - 3y + y - 3Group the terms: (5y^2 - 3y) + (y - 3)Factor out the common terms: y(5y - 3) + 1(5y - 3)Since both terms have a common factor of (5y - 3), we can factor it out to get the final factored form: (5y - 3)(y + 1).Learn more about Factoring Quadratics here:https://brainly.com/question/30398551
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