Discriminant = 16
As 16>0, The roots will be real and unequal.
Step-by-step explanation:
The standard form of a quadratic equation is:
[tex]ax^2+bx+c = 0[/tex]
The discriminant is calculated as:
[tex]D=b^2-4ac[/tex]
Given equation is:
[tex]Y=-4x^2+2x+1[/tex]
Here
a = -4
b = 2
c = 1
Putting the values
[tex]D =(2)^2 - 4(-4)(1)\\=4+16\\=20[/tex]
The discriminant is 16 which is greater than zero so the roots of the equation will be real and unequal.
Keywords: Discriminant, Quadratic equation
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A point p in the first quadrant lies on the parabola y=x^2. Express the coordinates of p as a function of the angle of inclination of the line joining p to the origin
Answer:
The coordinates of the point p are: [tex](x,xtan\alpha )[/tex]
Explanation:
1. Name the angle of inclination of the line joining p to the origin α.
2. Find the relation between the coordinates of the point (x,y)
When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).
As per the definition of the tangent trigonometric ratio you have:
[tex]tan\alpha =\frac{y}{x}[/tex]From which you can clear y:
[tex]y=xtan\alpha =>(x,y)=(x,xtan\alpha )[/tex]Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.
20 points for this question
Find the least common multiple of x-1 and 1-x
Good evening ,
Step-by-step explanation:
we know that, x-1 = (-1)×(1-x) and 1-x=(-1)×(x-1)
then each of 1-x and x-1 is a multiple of the other one,
if x>1 then x-1>0 and 1-x<0 then x-1>1-x
therefore in this case the least common multiple of x-1 and 1-x is x-1.
if x<1 then x-1<0 and 1-x>0 Then 1-x>x-1
therefore in this case the least common multiple of x-1 and 1-x is 1-x.
:)
Choose all that are correct given the equation: y=1/4 x + 9
A.y=7.25 when x = -7
B.y=7 when x = -8
C.y=8.5 when x =-4
D.y=10.25 when x = 5
Answer: Option A, Option B, Option D.
Step-by-step explanation:
Let's check each option.
A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]
B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]
C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]
D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:
[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]
Then, the correct options are: Option A, Option B, Option D.
Ralph’s annual income is about $32,000. Based on his expenses illustrated in the graph below, roughly how much should Ralph expect to pay in taxes this year?
The answer is $11200.
Answer:
$11,200 or its D
Step-by-step explanation:
got it right on edge
find the equation of the line that has a slope of -1 and passes through the point (2,1)
Answer:
y-1=-x+2
Step-by-step explanation:
m=-1
y-1=-1(x-2)
y-1=-x+2
Find the inequality represented by the graph
Answer:
[tex]y\leq -\frac{1}{3}x+1[/tex]
Step-by-step explanation:
Given:
From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.
Now, for a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex], the slope is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)[/tex]. Therefore,
[tex]m=\frac{1-0}{0-3}=-\frac{1}{3}[/tex]
Now, y-intercept is [tex]b=1[/tex]
Therefore, the standard form of a line is of the form: [tex]y=mx+b[/tex]. So, the equation of the line on the graph is:
[tex]y=-\frac{1}{3}x+1[/tex]
Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,
[tex]y\leq -\frac{1}{3}x+1[/tex]
How much change does he need to receive back
Answer:
Damien will receive a change of [tex]\$4.69[/tex]
Step-by-step explanation:
Given:
Pair of jeans = $33
Sales tax = 7%
Money paid as Sales tax = 7% of sale done on pair of jeans = [tex]\frac{7}{100}\times \$33 = \$2.31[/tex]
Total amount paid = 40
We need to find the amount he will receive back
Amount receive back can be calculated by Total amount paid minus Amount for pair of jeans minus money paid as Sales Tax
Change amount received = Total amount paid - Amount for pair of jeans - money paid as Sales Tax = [tex]\$40 - \$33-\$2.31 = \$ 4.69[/tex]
Hence Damien will receive a change of [tex]\$4.69[/tex]
A) Miss Brown is reading two books every three weeks she has read 12 Books so far how many weeks has she been reading so far ? B) If Miss Brown wants to finish reading 12 books in 15 weeks what would you tell her to change?
Ms. Brown has been reading for 18 weeks so far.
To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.
Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:
[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]
Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.
Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:
[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]
Now, we can solve for ( x ) by cross-multiplying:
[tex]\[ 2 \times x = 3 \times 12 \][/tex]
[tex]\[ 2x = 36 \][/tex]
Divide both sides by 2 to solve for ( x ):
[tex]\[ x = \frac{36}{2} \][/tex]
[tex]\[ x = 18 \][/tex]
So, Ms. Brown has been reading for 18 weeks so far.
complete question given below:
Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?
3.6792mm+2×10
[tex]36792mm + .2mm + .0133mm[/tex]
Answer:
36792.2133
Step-by-step explanation:
36792+0.2+0.0133=36792.2133
I figured it out, its B A
If A = {4, 7, 10, 13, 17} and B = {3, 5, 7, 9}, then which of the following statements is false?
Ø A
B B
B A
Please help!!
In the triangle below, what is the cosine of 60°?
30
Ο
-
-
Ο
Ο
-
Ο
ω
Answer:
C. 1/2
Step-by-step explanation:
SOHCAHTOA
Cosine is adjacent over hypotenuse. For the angle that is 60 the adjacent is 1 and the hypotenuse is 2.
Dustin always takes the same route when he walks his dog. First, he walks 6 blocks to the park. Then he walks 4 blocks to the elementary school. Finally, he walks 7 blocks to get back home. Dustin walks his dog 3 times each day. How many blocks does Dustin's dog walk each day?
Answer:
51
Step-by-step explanation:
add them altogether then times by 3
What is the equation to this graph????
Answer:
y=3x
Step-by-step explanation:
The slope of this graph is 3.
What is the percent of 108 is 81
what are the constant of proportionality for these two tables
Please find the answer and explain how you got it
Answer:
m∠NQP=74°
Step-by-step explanation:
we know that
The measure of the interior angles in a triangle must be equal to 180 degrees
In this problem
In the triangle NPQ
m∠N+m∠P+m∠Q=180°
we have
m∠N=(2x)°
m∠P=(34)°
m∠Q=(2x+2)°
substitute the values
[tex](2x)\°+(34)\°+(2x+2)\°=180\°[/tex]
solve for x
[tex](4x+36)\°=180\°[/tex]
[tex]4x=180-36[/tex]
[tex]4x=144[/tex]
[tex]x=36[/tex]
Find the measure of angle NQP
we know that
m∠NQP=m∠Q=(2x+2)°
substitute the value of x
m∠NQP=(2(36)+2)=74°
20) What is the closed linear form of the sequence 3,4,5,6,7, ...?
A) a= 2n
B) a = 2-n
C) a=3+n
a, = 3-n
The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + n
Option C
Solution:
Given Sequence is 3, 4, 5, 6, 7, ...
Let us the check the each option which can form the above sequence
a) a= 2n
[tex]\begin{array}{l}{\text {For } n=0, a=2 \times(0)=0} \\\\ {\text {For } n=1, a=2 \times(1)=2} \\\\ {\text {For } n=2, a=2 \times(2)=4}\end{array}[/tex]
We get a sequence 0, 2, 4 which does not satisfy the given sequence
b) a= 2-n
[tex]\begin{array}{l}{\text {For } n=0, a=2-0=2} \\\\ {\text {For } n=1, a=2-1=1} \\\\ {\text {For } n=2, a=2-2=0}\end{array}[/tex]
We get a sequence 2, 1, 0 which does not satisfy the given sequence
c) a= 3+n
For n = 0, a = 3 + 0 = 3
For n = 1, a = 3 + 1 = 4
For n = 2, a = 3 + 2 = 5
For n = 3 , a = 3 + 3 = 6
For n = 4, a = 3 + 4 = 7
Which satisfy the given sequence
Hence, c) is the correct option
The closed linear form of the sequence 3, 4, 5, 6, 7, ... is a = 3 + n, which matches option C. The pattern in the sequence indicates that the nth term can be expressed as 3 + (n - 1). Therefore, the answer is option A: a = 2 + n.
To find the closed linear form, we identify the pattern in the sequence. The sequence starts at 3 and increments by 1 for each subsequent term. Hence, the nth term (an) can be expressed as:
an = 3 + (n - 1)
an = 2 + n
Therefore, the closed linear form of the given sequence is option A: a = 2 + n.
One number is 5 times another number the difference between the two numbers is 1460 what is the two numbers
Answer:
The two numbers are -365 and -1825.
Step-by-step explanation:
5x=y
x-y=1460
--------------
x-5x=1460
-4x=1460
x=1460/-4
x=-365
-365-y=1460
y=-365-1460=-1825
Finley's pumpkin had a mass of 6.56.56, point, 5 kilograms (\text{kg})(kg)left parenthesis, start text, k, g, end text, right parenthesis before he carved it. After carving it, the pumpkin had a mass of 3.9\,\text{kg}3.9kg3, point, 9, start text, k, g, end text.
What was the percent decrease in the mass of the pumpkin?
The percent decrease in the mass of Finley's pumpkin after carving is approximately 40.55%.
To calculate the percent decrease in the mass of Finley's pumpkin after carving, use the following formula:
Percent Decrease = ((Original Mass - New Mass) / Original Mass) 100%
First, let's find the decrease in mass.
Decrease in Mass = Original Mass - New Mass = 6.56 kg - 3.9 kg = 2.66 kg
Then, calculate the percent decrease:
Percent Decrease = (2.66 kg / 6.56 kg) 100% = 40.55%
The percent decrease in the mass of the pumpkin after carving is approximately 40.55%.
Shelly wanted to buy a shirt for $25 and a skirt for $20.When she got to the check out stand, they added 8% tax to her total. About how much tax did she pay?
Answer:
$3.60
Step-by-step explanation:
25+20=45 (because you need the tax of both)
0.8(45)=3.60 (finding the tax amount)
x-5y =30 and 10y=2x+90
Answer:
1. For x is x=5y+30 and for y is y=1/5x−6
2. For x is x=5y−45 and for y is y=1/5x+9
Step-by-step explanation:
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
E
o y- 48 (2)
y (43)
O ya 4036
The expression will be y =8*2 or y = (48/6)*2
Step-by-step explanation:
The direct proportion is given if y varied directly as x
y∝x
When the proprtionality symbol is removed, a proportionality constant is introduced.
y = kx
as we know y = 48 when x = 6
[tex]48 = k * 6\\k = \frac{48}{6}\\k = 8[/tex]
The equation will be:
y = 8x
So when x=2
y = 8*2
y = 16
Hence,
The expression will be y =8*2 or y = (48/6)*2
Keywords: Proportion, Direct proportion
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To find the value of y when x is 2 in a direct variation, use the constant of variation k found from the given values (y = 48 when x = 6), which is 8 in this case, and multiply it by 2 to get y = 16.
If y varies directly as x, this means that y can be expressed as y = kx, where k is the constant of variation. Given that y = 48 when x = 6, we can find the value of k by substituting these values into the direct variation equation:
k = y/x = 48/6 = 8
Now that we have k, we can find the value of y when x is 2:
y = kx = 8 x 2 = 16
Therefore, the expression to find the value of y when x is 2 is y = 8 x 2.
The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.If you have Plan 2 for 4 months and make 20 calls a month, how much will your total bill be?
Answer:
$79.20
Step-by-step explanation:
fixed charged of $19 x 4 months = $76.00
additional charged of $0.04 x 20 = $0.80 x 4 months = $3.20
Therefore, $76.00 + $3.20 = $79.20
Please it's urgent ans please
Write a division expression that is equivalent to 8/15 x (- 3/5)
Answer:
-8/15
Step-by-step explanation:
8*-3/15*5
=-24/75
= -8/15
Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the n^th term
5th term is 0;
50 term is - 135
What is 3y-12=4x+8 in Point-Slope form and graphed but the line needs to pass through (-2,4)
Answer:
The equation of the line in point slope form is equal to
[tex](y-4)=\frac{4}{3}(x+2)[/tex]
The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a line in point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]3y-12=4x+8[/tex]
Convert to point slope form
Factor 3 left side and factor 4 right side
[tex]3(y-4)=4(x+2)[/tex]
Divide by 3 both sides
[tex](y-4)=\frac{4}{3}(x+2)[/tex]
In this equation
the point is (-2,4)
the slope is [tex]m=\frac{4}{3}[/tex]
using a graphing tool
The graph in the attached figure
The first day of Alex's trip was a Monday. What was the day of the week on Alex's 39 day of his trip?
Answer: monday
Step-by-step explanation:
Jade normally leaves work at 5:00 pm, but she is leaving work 10 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel two times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late. Let x represent the number of minutes her normal commute takes when she leaves on time.
y equals one half times x minus ten
y = 2x − 10
y = 2x + 10
y equals one half times x plus ten
Answer:
It will be answer choice D.
Step-by-step explanation:
It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late.
The linear equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late is (y = 0.5x + 10).
Given :
Jade normally leaves work at 5:00 pm, but she is leaving work 10 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel two times faster by taking the toll road.Let x represent the number of minutes her normal commute takes when she leaves on time.According to the given, data x represent the number of minutes her normal commute takes when she leaves on time.
Let y be the total time taken by Jade after 5:00 pm to reach home. So, the linear equation that represents the given situation is:
[tex]\rm y = \dfrac{1}{2}x+10[/tex]
Therefore, the correct option is D).
For more information, refer to the link given below:
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Solve
2x + 3y =2/3
3x - 4y = 18
Answer:
[tex]\displaystyle [3\frac{1}{3}, -2][/tex]
Step-by-step explanation:
{2x + 3y = ⅔
{3x - 4y = 18
¾[3x - 4y = 18]
{2x + 3y = ⅔
{2¼x - 3y = 13½
____________
[tex]\displaystyle \frac{4\frac{1}{4}x}{4\frac{1}{4}} = \frac{14\frac{1}{6}}{4\frac{1}{4}} \\ \\[/tex]
[tex]\displaystyle x = 3\frac{1}{3}[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]-2 = y[/tex]
I am joyous to assist you anytime.
The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.
Explanation:To solve the system of equations:
2x + 3y = 2/33x - 4y = 18we can use the method of substitution or elimination. Let's use elimination in this case:
First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:
(4)(2x + 3y) = (4)(2/3) → 8x + 12y = 8/3(3)(3x - 4y) = (3)(18) → 9x - 12y = 54Next, we add the two equations together to eliminate y:
8x + 12y + 9x - 12y = 8/3 + 54
17x = 54 + 8/3
17x = 54 + 2.6667
17x = 56.6667
Now we divide both sides by 17 to solve for x:
x = 56.6667 / 17
x = 3.3333
With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:
2x + 3y = 2/3
Substitute x:
2(3.3333) + 3y = 2/3
6.6666 + 3y = 2/3
3y = 2/3 - 6.6666
3y = -6.0000
Now divide both sides by 3 to solve for y:
y = -6.0000 / 3
y = -2.0000
The solution to the system is x = 3.3333 and y = -2.0000.