Answer:
[tex]16x^{2} -42x+5[/tex]
Step-by-step explanation:
Sum of its zeroes=[tex]\alpha +\beta =\frac{21}{8} \\[/tex]
Product of its zeroes=[tex]\alpha \beta[/tex]=[tex]\frac{5}{16}[/tex]
Formula to form a quadratic polynomial:
[tex]p(x)=k[x^{2} -(\alpha +\beta )x+\alpha \beta ][/tex]
p(x)=[tex]k[x^{2} -(\frac{21}{8} )x+\frac{5}{16}][/tex]
p(x)=[tex]16[x^{2} -(\frac{21}{8} )x+\frac{5}{16}][/tex]
p(x)=[tex][16x^{2} -42x+5][/tex]
The quadratic polyniomial is [tex]16x^{2}-42x+5[/tex]
3x - y = 0
2x - y = 1
85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).
Answer:
[tex]\huge\boxed{\sf y = 2x -4}[/tex]
Step-by-step explanation:
The given equation is:
y = 2x + 3
Where Slope = m = 2 , Y-intercept = b = 3
Parallel lines have equal slopes
So, Slope of new line = m = 2
Now, Finding y-intercept:
Given Point = (x,y) = (1,-2)
So, x = 1 , y = -2
Putting m, x and y in standard form of equation to get b:
[tex]\sf y = mx+b[/tex]
[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]
Subtracting 2 to both sides
[tex]\sf b = -2-2\\[/tex]
b = -4
So, the standard form og equation for the new line is :
[tex]\sf y = mx+b[/tex]
[tex]\sf y = 2x -4[/tex]
Answer:
y = 2x - 4
Step-by-step explanation:
the problem is called (slope-intercept form)
the equation of the line is y = mx + b
the equation of a line is given as y = 2x + 3
slope = 2
b = y-intercept is where the line crosses the y-axis = 3
so point (x1, y1) = (1, -2)
by using the equation.
y = mx + b
-2 = 2 (1) + b
-2 -2 = b
therefore b = -4
writing the new equation using the slope intercept form
y = mx + b would be y = 2x + 4
so the equation parallel to the equation y = 2x + 3 is y = 2x - 4
Find a formula for the 4th term of the following G.P.S a) 1, 2,4......... b)50, 20, 8......... Pls explain very well.. Thank you.
Answer:
see below
Step-by-step explanation:
The formula for a geometric sequence is
an = a1 * r^ (n-1) where a1 is the first term and r is the common ratio
The common ratio is found by taking the second term and dividing it by the first term
a) 1, 2,4.........
a1 = 1
r = 2/1 = 2
an = 1 * ( 2) ^ (n-1)
Let n = 4
a4 = 1 * 2^ (4-1) = 1 * 2^3 = 8
b)50, 20, 8.........
a1 = 50
r = 50/20= 5/2
an = 50 * ( 5/2) ^ (n-1)
Let n = 4
a4 = 50 * (5/2)^ (4-1) = 50 * (5/2)^3 = 3125/4
Find the area of the triangle
Answer:
73.64 ft²
Step-by-step explanation:
bad at explaining but hope this helped <3
Evaluate. (-2 1/4)^2
Answer:
[tex]5 \frac{1}{16}[/tex]
Step-by-step explanation:
I did this before. Also sometimes once I look at the question I just find out the answer without steps.
What is the product of complex conjugates? (1 point)
the product of complex conjugates is a difference of two squares and is always a real number
the product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero
the product of complex conjugates is the same as the product of opposites
the product of complex conjugates is a sum of two squares and is always a real number
Answer:
A. the product of complex conjugates is a difference of two squares and is always a real number
Step-by-step explanation:
Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.
The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.
Taking the product of the complex number and its conjugate will give;
z1z2 = (x+iy)(x-iy)
z1z2 = x(x) - ixy + ixy - i²y²
z1z2 = x² - i²y²
.since i² = -1
z1z2 = x²-(-1)y²
z1z2 = x²+y²
The product gave a real function x²+y² since there is no presence of complex number 'i'
It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).
From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.
What is 164.362 rounded to 4, 3 and 1 significant figures
Answer:
4 sigfig is 164.4
3 sigfig is 164.
1 sigfig is 200
hope that answers your question
comment for more explanation
Translate this phrase into an algebraic expression.
the sum of 4 and twice a number is 12
Answer:
4+2x = 12
Step-by-step explanation:
sum means add an is means equal
4+2x = 12
Step-by-step explanation:
the sum of 4 and twice a number is 12:
Have a great day! I hope this helps!! :)20 POINTS! Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+10x−1 B. f(x)=−3x2+4x−1 C. f(x)=−2x2+5x−1 D. f(x)=−5x2+8x−1 3) Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13). A. y=−3(x−3)2+5 B. y=2(x−3)2+5 C. y=−2(x−3)2+5 D. y=2(x+3)2−5
Answer:
1) f(x) = 4·x² - 3·x + 6
2) f(x) = -2·x² + 5·x - 1
3) y = 2·(x - 3)² + 5
Step-by-step explanation:
1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows
The general form of a quadratic function is f(x) = a·x² + b·x + c
Where, in (x, y), f(x) = y, and x = x
Therefore for the point (0, 6), we have;
6 = 0·x² + 0·x + c
c = 6
We have c = 6
For the point (2, 16), we have;
16 = a·2² + b·2 + 6
10 = 4·a + 2·b.............................(1)
For the point (3, 33), we have;
33 = a·3² + b·3 + 6
27 = 9·a + 3·b............................(2)
Multiply equation (1) by 1.5 and subtract it from equation (2), we have;
1.5 × (10 = 4·a + 2·b)
15 = 6·a + 3·b
27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;
27 - 15 = 9·a - 6·a+ 3·b - 3·b
12 = 3·a
a = 12/3 = 4
a = 4
From equation (1), we have;
10 = 4·a + 2·b = 4×4 + 2·b
10 - 4×4 = 2·b
10 - 16 = 2·b
-6 = 2·b
b = -3
The function, f(x) = 4·x² - 3·x + 6
2) Where the points are (-1, -8), (0, -1), (1, 2), we have;
For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)
For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)
For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)
Adding equation (1) to equation (3) gives
-8 + 2 = a - b + c + a + b + c = 2·a + 2·c where, c = -1, we have
-8 + 2 = -6 = 2·a + 2
2·a = -6 + 2 = - 4
a = -8/2 = -2
From equation (3), we have;
2 = a + b + c
b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5
f(x) = -2·x² + 5·x - 1
3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola
The vertex equation of a parabola is y = a(x - h)² + k
Where;
(h, k) = Vertex (3, 5)
(x, y) = (1, 13)
We have
13 = a·(1 - 3)² + 5
13 = a·(-2)² + 5
13 - 5 = a·(-2)² = 4·a
4·a = 8
a = 8/4 = 2
The equation is y = 2·(x - 3)² + 5.
helppp, graph of function!!
The two liquids will have the same temperature at 10 units of time after the start of both processes.
Given: Graph showing changes of temperature of liquid A when it is heated and liquid B when it is cooled
To find: The time when the two liquids have the same temperature
The given graph is plotted such that 'P' representing the temperature of the liquid is taken on y-axis and 'x' representing the time is taken on x-axis.
The graphs of temperature change with respect to time, of both liquids A and B are plotted in the same answer space and it is implied that both processes (heating of liquid A and cooling of liquid B) occurs simultaneously.
The time when both liquids have the same temperature is represented by graphs of both liquids having the same 'P' value at the same 'x' value. In other words, it is represented by a point in the answer space at which the graphs of temperature of both liquids intersect.
As can be seen from the given figure, the graphs of temperature change of liquid A and B intersect at the point (10, 30), that is at 'x = 10'.
Since 'x' represents the time, this implies that the two liquids will have the same temperature at 10 units of time after the start of the experiment (x = 0).
Learn more about graphical analysis here:
https://brainly.com/question/21623345
Solve this problem... Really urgent
Answer:
[tex] \boxed{\sf Time \ taken = 15 \ minutes} [/tex]
Given:
Initial speed (u) = 65 km/h
Final speed (v) = 85 km/h
Acceleration (a) = 80 km/h²
To Find:
Time taken for car to achieve a speed of 85 km/h in minutes
Step-by-step explanation:
[tex]\sf From \ equation \ of \ motion:[/tex]
[tex] \boxed{ \bold{v = u + at}}[/tex]
By substituting value of v, u & a we get:
[tex] \sf \implies 85 = 65 + 80t[/tex]
Substract 65 from both sides:
[tex] \sf \implies 85 - 65 = 65 - 65 + 80t[/tex]
[tex] \sf \implies 20 = 80t[/tex]
[tex] \sf \implies 80t = 20[/tex]
Dividing both sides by 80:
[tex] \sf \implies \frac{ \cancel{80}t}{ \cancel{80}} = \frac{20}{80} [/tex]
[tex] \sf \implies t = \frac{2 \cancel{0}}{8 \cancel{0}} [/tex]
[tex] \sf \implies t = \frac{ \cancel{2}}{ \cancel{2} \times 4} [/tex]
[tex] \sf \implies t = \frac{1}{4} \: h[/tex]
[tex] \sf \implies t = \frac{1}{4} \times 60 \: minutes[/tex]
[tex] \sf \implies t = 15 \: minutes[/tex]
So,
Time taken for car to achieve a speed of 85 km/h in minutes = 15 minutes
The Tama, Japan, monorail carries 92,700 riders
each day. If the monorail usually carries
5,150 riders per hour, how many hours does
the monorail run each day?
Answer:
The monorail runs 18 hours runs every day.
Step-by-step explanation:
You know that the total number of riders the monorail carry each day is 92700 and the number of riders the monorail carry per hour is 5150.
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
A direct proportionality relationship is established between two quantities if:
The greater the quantity in one quantity, the greater the quantity in the other quantity, in the same proportion. The less quantity in the magnitude corresponds to the less quantity in the other magnitude, in the same proportion.If the relationship between the magnitudes is direct the direct rule of three must be applied and to solve a direct rule of three, the following formula must be followed:
a ⇒ b
c ⇒ x
Being
[tex]x=\frac{c*b}{a}[/tex]
In this case the rule of three can be applied in the following way: if the monorail carries 5,150 passengers in 1 hour, the monorail will transport 92,700 passengers in how many hours?
[tex]amount of hours=\frac{92,700 passengers*1hour}{5,150 passengers}[/tex]
amount of hours= 18 hours
So the monorail runs 18 hours runs every day.
In an examination ,80%examines passed in english,70%In mathematics and 60% in both subjects.if 45 examines failed in both subject.
1.draw a venn-diagram to represent the above information .
2.find the number of examines who passed only one subject.
3.find the number of student who failed in mathematics.
Answer:
1. Please refer to attached diagram.
2. 135
3. 135
Step-by-step explanation:
Given that
80%examines passed in English, n(E) = 80%
70%In mathematics, n(M) = 70%
and 60% in both subjects, n(E [tex]\cap[/tex] M) = 60%
45 examines failed in both subject.
1. Venn Diagram is attached in the answer area.
One circle represents the pass examines in Maths and
Other circle represents the pass examines in English.
Rectangle represents the total number of examines that appeared for the exam.
Rectangle minus the area of union of circles represent the number of students who failed in both subjects.
2. To find the number of examines who passed in only one subject.
i.e. n(E) - n(E [tex]\cap[/tex] M) + n(M) - n(E [tex]\cap[/tex] M) = (80 - 60 + 70 - 60)% = 30%
Let us find the number of students who passed in atleast one subject:
[tex]n(E\cup M) = n(E) +n(M)-n(E \cap M)\\\Rightarrow n(E\cup M) = (80 +70-60)\% = \bold{90\%}[/tex]
So, number of students who failed in both subjects = 100 - 90% = 10% of total students = 45
So, total number of students appeared = 450
So, number of examines who passed in only one subject = 450 [tex]\times[/tex] 30% = 135
3. Number of students who failed in mathematics.
100% - Passed in Mathematics = 100% - 70% = 30% of 450 = 135
Janice deposited $750 in a savings account that earns 3.5% simple interest. How much interest has Janice earned by the end of the first year? (1 point)
Answer:
$26.25
Step-by-step explanation:
We know that I = Prt where I = Interest, P = Principal, r = rate (as a decimal) and t = time (in years). Therefore:
I = 750 * 0.035 * 1 = $26.25
write the mixed numbers as fractions
1/1/2
Answer:
3/2
Step-by-step explanation:
230% of 99 hours is what?
Answer:
227.7 hours
Step-by-step explanation:
of means multiply and is means equals
230% * 99 = what
Change the percent to decimal form
2.30 * 99 = what
227.7= what
[tex]\\ \sf\longmapsto 230\%\:of\:99[/tex]
[tex]\\ \sf\longmapsto \dfrac{230}{100}\times 99[/tex]
[tex]\\ \sf\longmapsto \dfrac{230(99)}{100}[/tex]
[tex]\\ \sf\longmapsto \dfrac{22777}{100}[/tex]
[tex]\\ \sf\longmapsto 227.7hours[/tex]
Helppp please!! Thank you
Answer:
The answer is 4
Determine the sign of cos pi divided by three without using a calculator.
Answer:
positive
Step-by-step explanation:
To solve this, we can look at the unit circle (see attached photo), We know:
(0,1) = π/2
(-1, 0) = π
(0, -1) = 3π/2
(1, 0) = 0
Across the circle, we know that π/3 is between 0 and π/2. Therefore, as the unit circle line between that is positive in the x direction (cos), we can say that cos(π/3) is positive
Please help I did the first 2 already.
The answer to C is 1.5 or 3/2
Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2
show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x
Answer:
see explanation
Step-by-step explanation:
Given
(2x + 3)³
= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL
= (2x + 3)( 4x² + 12x + 9)
= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis
= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms
= 8x³ + 36x² + 54x + 27
26.
What is the solution to. y - 9 > 4 + 2y?
HELP. answer if you can!
Answer:
y<−13
y−9>4+2y
Simplify both sides of the inequality
y−9>2y+4
Subtract 2y from both sides
y−9−2y>2y+4−2y
−y−9>4
Add 9 to both sides.
−y−9+9>4+9
−y>13
The divide both sides by -1
Answer:
[tex]\boxed{y < -13}[/tex]
Step-by-step explanation:
Hey there!
To solve for y we‘ll combine like terms and use the communicative property.
y - 9 > 4 + 2y
+9 to both sides
y > 13 + 2y
-2y to both sides
-y > 13
Divide -1 by both sides
y < -13
Hope this helps :)
Can someone please help!! ****This problem is multiple choice!
Answer:
I believe it's A) 302.94
Step-by-step explanation:
There are 360 degrees in a circle. So I enetered 360/112 in a calculator and got 3.214.
Then I multiplied 3.214 by 30pi and got 302.939 AKA 302.94. I did this because I looked at it like a ratio problem but idk if thats correct.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The median of the lower half of the data set is the _____________.
A. Third quartile
B. First quartile
C. Fourth quartile
D. Second quartile
Answer:
B. First quartile
Step-by-step explanation:
The first quartile is the first 25% of a line graph, and the median of the lower half of a data set would be the median of the median, which means it would split the graph at 25%
20 points! Thank you :)
Answer:
[tex]\Large \boxed{x=-2 \ \mathrm{and} \ x=3}[/tex]
Step-by-step explanation:
The quadratic expression is given.
[tex]2x^2-2x-12=0[/tex]
Factor the left side of the equation.
[tex]2(x+2)(x-3)=0[/tex]
Set the factors equal to 0.
[tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x-3=0[/tex]
[tex]x=3[/tex]
The two solutions work in the original equation. The solutions make the equation true.
The quadratic expression:
[tex]2 {x}^{2} - 2x - 12[/tex]
★ By split middle term,we get
[tex]2 {x}^{2} - 6x + 4x - 12[/tex]
[tex]2x(x - 3) + 4( x - 3)[/tex]
[tex](2x + 4) (x - 3)[/tex]
[tex]2x + 4 = 0 \: \: and \: \: x - 3 = 0[/tex]
[tex]2 x = - 4 \: \: and \: \: x = 3[/tex]
[tex]x = - 2 \: \: and \: \: x = 3[/tex]
Therefore , the two solution of given quadratic equations is -2 and 3.
Using the box-and-whisker plot shown, find the maximum, minimum, and median values.
Hi, I'm happy to help!
for a box an whisker plot, maximum and minimum values on the edge of the lines. The maximum shown here is 8, because the line ends there. The minimum is -8 because the line ends there.
The median value is shown by the middle line, which is 4.
To sum it up: Maximum: 8, Minimum: -8, Median: 4\
I hope this was helpful, keep learning! :D
Duncan took a math quiz last week. There were 55 problems on the quiz and Duncan
answered 40% of them correctly. How many problems did Duncan get correct?
Answer: Duncan got 22 questions correct
Step-by-step explanation:
Total questions in quiz = 55
Total answered correctly by Duncan = 40% of 55
Total answers he got correct = 40% of 55
= 40/100×55
= 22
Therefore Duncan got 22 questions correct
please click thanks and mark brainliest if you like :)
I need help with 3 and 4
Answer:
Step-by-step explanation:
3) G
Step-by-step explanation:
Q(-1,-1) R(3,1) S(2,-4)
x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)
Q -1+2 -1+3 (1,2) (-1,-2)
R 3+2 1+3 (5,4) (-5,-4)
S 2+2 -4+3 (4,-1)
Help, Answer ASAP; will give brainliest
Answer:
The value of k is 16, the angle of OLN and MNL is 72° .
Step-by-step explanation:
Given that alternate interior angles are the same. So we can assume that ∠OLN and ∠MNL have the same angle. In order to find k, we have to let ∠OLN = ∠MNL :
[tex]4k + 8 = 5k - 8[/tex]
[tex]5k - 4k = 8 + 8[/tex]
[tex]k = 16[/tex]
Next, we have to find the angle of OLN and MNL :
[tex]OLN = 4k + 8 = 4(16) + 8 = 72[/tex]
[tex]MNL = 5k - 8 = 5(16) - 8 = 72[/tex]
Consider a triangle ABC like the one below. Suppose that a =53, b=18, and A=130º. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round
your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".
Answer:
B = 15.1°, C = 34.9°, c = 39.6
Step-by-step explanation:
law of sines
53/sin 130 = 18/sin B
sin B = .26; B = 15.1°
C = 180 - 15.1 - 130 = 34.9°
c/sin 34.9 = 53/sin 130
c = 39.6
A wheel turns through 90 revolutions per minute how many degrees does it turn through in 1 second
Answer:
540°
Step-by-step explanation:
90 revolutions = 360°×90 = 32400°
32400° in 60 sec or 1 min
so, in 1 sec 32400/60 = 540°
Answer:
540°
Step-by-step explanation:
90 revolutions = 360°×90 = 32400°
=> 32400° in 60 sec or 1 min
=> In 1 sec,
=> 32400/60 = 540°