Answer:
[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The solutions are, for a positive discriminant:
[tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]
Here, we have a = -21, b = -11, c = 40, so it gives:
[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]
So, we have two solutions:
[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]
We only want x > 0 so the solution is
[tex]\dfrac{8}{7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Sorry for the bad Angle, anyways if anyone could help me out that be great, I would do the question myself if I'd know how to do it, have a nice day
Answer:
210 students
Step-by-step explanation:
The total number of students surveyed was
19+14+30+23+14 = 100
The fraction that picked Yosemite is 14/100
Multiply that fraction by the total number of students
1500* 14/100 = 210
Answer:
210 students
Step-by-step explanation:
vote me brainliest plz
(a) Complete the statements below about the graphs of y = -x and y=x.
Compared to the graph of y=x, the graph of y=-x is Choose one
Compared to the graph of y=x, the graph of y = -x intersects the y-axis at Choose one
2
(b) Complete the statements below about the graphs of y=x+
and y=x.
3
2
Compared to the graph of y = x, the graph of y=x+ 5 is Choose one
2
Compared to the graph of y=x, the graph of y=x+
3
intersects the y-axis at Chonse one
a higher point
the same point.
a lower point
Х
?
Answer:
this. question is not clear please send clear question
We can conclude that -
Graphs pass through the origin. (y = x) has a slope of +1 while (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have the following two functions -
y = -x
AND
y = x
Refer to the graphs attached for both the functions -
y = - x and y = x
The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.
We can conclude that -
Graphs pass through the origin. (y = x) has a slope of +1 while (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.To solve more questions on straight line, visit the link below-
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Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.
Answer:
Step-by-step explanation:
Since we're given a time at which the height is maximum, we can use a cosine function for the model.
The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.
The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.
The period is given as 3 seconds, and the right shift is given as 1.31 seconds.
This gives us enough information to write the function as ...
H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)
H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm
It takes 4 people 2 days to paint a wall. How long would it take if we got 8 people to do it?
Answer:
if it takes 4 people for 2 days
4+4= 8
so it would only take 8 people for 1 day
Answer:
1 day
Step-by-step explanation:
4 people = 2 days
→ Work out how long 1 person takes
4 people = 2 days
( ÷ 4 ) ( × 4 )
1 person = 8 days
→ Work out how long 8 people can do it
1 person = 8 days
( × 8 ) ( ÷ 8 )
8 people = 1 day
On a coordinate plane, a line goes through (negative 4, negative 1) and (0, 1). Square a is around (negative 5, negative 2), square b is around (negative 1, 1), square c is around (1, 2), and square d is around (4, 4). The linear equation y = one-half x + 1 is represented by the graphed line. A second linear equation is represented by the data in the table. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 7, 6, 5, 4. In which square is the solution located?
Answer: D
Step-by-step explanation:
The solution of the two equations does not exist since they are parallel.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.
Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.
Given linear equation of a line in slope intercept form as,
y = 1/2 x + 1
Here slope = 1/2 and y intercept = 1
y intercept is the y value of a point where it touches the y axis.
A second linear equation is to be found by using the values in the table.
Taking two points (2, 7) and (0, 6).
Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2
Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.
y intercept = 6
Equation of the second line is,
y = 1/2 x + 6
Since the slopes of two lines are equal, they are parallel.
There is no solution for two parallel lines.
Hence there is no solution for the linear equations given.
To learn more about Slope, click on the link :
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Can someone help me with this problem?
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = 1
▹ Step-by-Step Explanation
y = mx + b
'm' represents the slope. since there is no number before the x, the coefficient will always be 1. therefore, the slope is 1.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
how many 4-digit numbers can be formed using only the digits 9, 8 and 7? :p
Answer: 81
Step-by-step explanation:
First digit and Second digit and Third digit and Fourth digit
3 choices x 3 choices x 3 choices x 3 choices = 81
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Answer:
The correct option is;
A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25
Please find attached the graphs of the table data
Step-by-step explanation:
Each of the given table data of in the tables are analysed to find direct variation;
Table 1
x, -3, -1, 2, 5, 10
y, -4.5, -3.0, -1.5, 0.0, 1.5
-4.5/-3 = 1.5 ≠ -3.0/-1 = 3
No direct variation
Table 2
x, -5.5, -4.5, -3.5, -2.5, -1.5
y, 10, 8, 6, 4, 2
10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9
However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2
Adjusted direct variation
Table 3
x, -5.5, -5.5, -5.5, -5.5, -5.5
y, -3, -1, 2, 5 , 10
-3/(-5.5) ≠ -1/-5.5
No direct variation
Table 4
x, -3, -1, 2, 5, 10
y, -7.5, -2.5, 5.0 , 12.5, 25
-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10
Direct variation exists
Answer:
so D
Step-by-step explanation:
Which table represents a function?
Answer:
Table 4 represents a function.
Step-by-step explanation:
Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.
The slope of the line below is -3 which is the following is the point - slope from the line ?
Answer:
D. y + 6 = -3(x - 2)
Step-by-step explanation:
To find the equation in point-slope form, you need to use the slope and a point from that line. The slope is -3 and the point given is (2, -6).
Point-slope form is y - y₁ = m(x - x₁). Plug in the slope and point.
y - (-6) = -3(x - 2)
y + 6 = -3(x - 2)
Answer:
D. [tex]y - 2 = -3(x+6 )[/tex]
Step-by-step explanation:
Well point slope form is,
[tex]y - y_{1} = m(x-x_{1} )[/tex]
So we already have slope meaning we can plug that in for m.
[tex]y - y_{1} = -3(x-x_{1} )[/tex]
And with the given point (2,-6),
we can create point slope form.
[tex]y - 2 = -3(x+6 )[/tex]
Therefore,
the answer is d. [tex]y - 2 = -3(x+6 )[/tex].
Hope this helps :)
You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.36 with a standard deviation of 0.96 You sample 60 day students, and the sample mean GPA is 2.19 with a standard deviation of 0.66 Calculate the test statistic, rounded to 2 decimal places
Answer:
Z = 0.87
Explanation:
Given the following data;
Sample 1:
n1 = 30
Mean, X = 2.36
Standard deviation, Ox = 0.96
Sample 2:
n2 = 60
Mean, Y = 2.19
Standard deviation, Oy = 0.66
The formula for test statistics for two population is;
[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]
Substituting the values, we have;
[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]
[tex]Z = \frac{0.17}{0.19488}[/tex]
Z = 0.8723
The test statistics to 2 d.p is 0.87
Therefore, Z = 0.87
50 Pts!!! Answer ASAP.
Answer:
0.8
Step-by-step explanation:
because the template should be axr^n-1
where r is the common ratio
r=0.8
Answer:
0.8
Step-by-step explanation:
Please help.. ty if you do
Answer:B
Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer
what is the measure of arc angle EG
Answer:
80 = EG
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
40 = 1/2 EG
Multiply each side by 2
80 = EG
Answer:
80 deg
Step-by-step explanation:
Theorem:
The measure of an inscribed angle is half the measure of the intercepted arc.
m<EFG = (1/2)m(arc)EG
40 deg = (1/2)m(arc)EG
m(arc)EG = 2 * 40 deg
m(arc)EG = 80 deg
A square and a regular heptagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of exterior angle $BAC$? Express your answer as a common fraction.
Answer:
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
Step-by-step explanation:
The interior angle of a regular heptagon = = 900/7° = 128.57°
Therefore, angle DAB = 128.57°
The interior angle of the square = 90°
Therefore, angle DAC = 90°
Therefore, we have
angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))
Angle BAC = 360° - angle DAB - angle DAC = 360° - 900/7° - 90° = 990/7°
Angle BAC = 141.43°
Expressing 141.43° as a common fraction gives;
[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]
[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]
The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]
Given, A square and a regular heptagon are coplanar as shown in below figure attached.
We have find the exterior angle of BAC.
We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,
[tex]\frac{180(n-2)}{n}[/tex] where n is the number of sides.
Since the heptagon has 7 no. of sides.
So regular heptagon's interior angle measures,
[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]
Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.
We know that a square's interior angle is 90 degrees and a heptagon's interior angle is 128.57 degrees. We will subtract those from 360 degrees to find angle BAC.
[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]
[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]
Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].
For more details on Exterior angle follow the link:
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A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 15, 5, 30, 50. The third column is labeled Y with entries 5, 8, 15, 28. The fourth column is labeled Z with entries 10, 7, 5, 22. The fifth column is labeled Total with entries 30, 20, 50, 100. Which two events are independent?
Answer:
hey! it's A and X on edge :)
Round the following numbers to 1 significant figure:
a) 25 637
b) £2.51
c)9877 m
Answer:
b
Step-by-step explanation:
you need to round 2.51 to 3 because it was the correct answer
What is the average length of a side in the shape made from the file datatest1.txt whose contents are shown below (just give to two decimal places)? -3,3 -4,-3 4,-2 6,5
Answer:
0.75
Step-by-step explanation:
The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).
Mathematically:
Average = (Sum of lengths) / frequency
The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.
The average is therefore:
Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8
Average = 0.75
Use multiplication to solve the proportion
w/4 = 42/24
Answer: w=5
Step-by-step explanation:
Solve and CHECK the following:
8−(5x−2)=6−2(3x+1)
Answer:
X=6/11
Step-by-step explanation:
8-(5x-2)=6-2(3x+1)
8-5x+2=6-6x-2
10-5x=4-6x
6=11x
x=6/11
Answer:
8-5x-2=6-6x+2
8-2-6-2=5x-6x
-10+8=-x
-2 =-x
x=2 ........×-1
x=2
Solve this problem n-6/-4=6
Answer:
N= 9/2
Step-by-step explanation:
Answer:
n = - 18Step-by-step explanation:
[tex] \frac{n - 6}{ - 4} = 6[/tex]
Cross multiply
We have
n - 6 = - 4 × 6
n - 6 = - 24
n = - 24 + 6
n = - 18Hope this helps you
The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?
Answer:
A.
Step-by-step explanation:
We need to find the equation where, if x is equal to 3, g(x) is equal to 1, because g(x) passes through the point (3,1)
Then, replacing x by 3 on every option we get:
[tex]g(x)=(\frac{1}{3}x)^2= (\frac{1}{3}3)^2=1\\g(x)=(\frac{1}{9}x)^2= (\frac{1}{9}3)^2=\frac{1}{9}\\g(x)= \frac{1}{3}x^2= \frac{1}{3}3^2=3\\g(x)=3x^2=3*3^2=27[/tex]
So, the answer is A. because g(x) is equal to 1
Which is a correct first step in solving 5 – 2x < 8x – 3? 5 < 6x – 3 3x < 8x – 3 5 < 10x – 3 2 – 2x < 8x
Answer:
5 < 10x – 3
Step-by-step explanation:
The inequality is 5 - 2x < 8x - 3.
5 < 6x – 3 is incorrect because 8x + 2x = 10x, not 6x.
3x < 8x – 3 is incorrect because 5 - 2x is not 3x, you can't subtract those terms as they are not like terms.
5 < 10x – 3 is correct because 8x + 2x = 10x.
2 – 2x < 8x is incorrect because 5 + 3 = 8, not 2.
Answer:
C on edg
Step-by-step explanation:
Plzzzzz Help I really need help
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
(1.5,-3) and (4.5,-3)
Step-by-step explanation:
Find the value of this expression if x=3 x^2 + 3/x-1
Answer: 9
Step-by-step explanation:
[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]
9/10 of the weight of a loaf of bread comes from the flour used in its baking. 2/9 of the weight is the protein what fraction of the weight is protein?
Answer:
1/5
Step-by-step explanation:
2/9 * 9/10 = 2/10 = 1/5
please help!!!!!!!!!!!
Answer:
The x value of the point 1/4 the distance from point C to point D is -0.25
Step-by-step explanation:
The given information are;
The location of point C = (1, 2)
The location of point D = (-4, -2)
The point 1/4 from point C to point D is the point 3/4 from point D to point C
Which gives;
The coordinate at point D + 3/4× The difference between the coordinates of point C and point D
Which is (-4 + 3/4×(1 - (-4), - 2 + 3/4×(2 - (-2))
Which gives;
(-4 + 3.75, -2 + 3) and (-0.25, 1)
The coordinates of the point 1/4 the distance from point C to point D is (-0.25, 1)
Therefore, the x value of the point 1/4 the distance from point C to point D = -0.25.
Mrs. Watson wants to buy some dresses for her trip to Houston. There are three boutiques, each offering a different deal.
Table
Lara's Boutique 4 dresses for $64
The Dress Shop 5 dresses for $75
Marge's Dresses 8 dresses for $160
Which boutique has the best deal for dresses?
A. Both Marge's Dresses and Lara Boutique
B. The Dress Shop
C. Lara's Boutique
D. Marge's Dresses
Answer:
B. The Dress Shop.
Step-by-step explanation:
To find the best deal, we want to find the cost for one dress.
Lara's Boutique: $64 for 4 dresses.
x / 1 = 64 / 4
x = 64 / 4
x = $16 per dress.
The Dress Shop: $75 for 5 dresses.
x / 1 = 75 / 5
x = 75 / 5
x = $15 per dress.
Marge's Dresses: $160 for 8 dresses.
x / 1 = 160 / 8
x = 160 / 8
x = $20 per dress.
The boutique with the best deal will have the cheapest dresses. So, the best deal would be at B. The Dress Shop.
Hope this helps!
if the denominator of a fraction is multiplied by 2,the value of the fraction is
Answer:
Half of its original
Step-by-step explanation:
When multiplying a denominator by a whole number, he value decreases accordingly, in other word, it changes inversely.
Examples:
In 1/2, if 2 is multiplied by 2, the value becomes 1/4, which is half of 1/2
In 1/4, if 4 is multiplied by 2, the value becomes 1/8 which is half of 1/4.
Hope this helps
Good luck
which ordered pair is a solution of the equation -3x+5y=2x+3y PLEASE HELP ASAP
Answer:
Every pair where y is equal x multiplied by 2.5for exapmle: (2, 5) {5=2•2.5}
(8, 20) {20=8•2.5}
(-5, -12.5} {-12.5=-5•2.5}
Step-by-step explanation:
-3x + 5y = 2x + 3y-3y+3x -3y+3x
2y = 5x÷2 ÷2
y = 2.5xAnswer:
neither
Step-by-step explanation: