Answers
Answer:
Your last step ( step 5 ) :
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{c}{a} + \frac{ {b}^{2} }{4 {a}^{2} } [/tex]
Step 6:
[tex]{ \boxed{x + ( \frac{b}{2a}) = ± \frac{ \sqrt{ {b}^{2} - 4ac } }{ \sqrt{4a^2} } }}[/tex]
Step-by-step explanation:
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{4ac}{4 {a}^{2} } + \frac{ {b}^{2} }{4 {a}^{2} } \\ \\ {x}^{2} + \frac{b}{a} x = \frac{4ac}{4a {}^{2} } \\ \\ {x} = \sqrt{ \frac{ - 4ac + b {}^{2} }{4a {}^{2} } } [/tex]
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Related Questions
Which graph represents the function f(x)=|x−1|−3 ?
Answers
In the equation $\frac{1}{j} + \frac{1}{k} = \frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$?
Answers
Answer:
Hello,
answer 22
Step-by-step explanation:
[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]
The sum of all possible values for k is 22.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
1/j + 1/k= 1/3
Simplifying the fraction
(k+ j)/ kj= 1/3
3k + 3j = kj
k(3- j) = -3j
k = -3j/ (3- j)
k= 3j/ (j-3)
k = 3j + 9 - 9 / (j-3)
k = 3 + 9/ (j-3)
Since (j-3) must be divisor of 9.
j- 3 = 1---> j=4, k= 3 +9 = 12
j- 3 = 3---> j=6, k= 3 +9/3 = 6
j- 3 = 9---> j=12, k= 3 +9/9 = 4
So, The sum is = 12+ 6 + 4 = 22
Learn more about Fraction here:
https://brainly.com/question/10354322
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HAI HELP ME ASAP PLEASE
Answers
Answer:
Y/X = 2/3 x^2 + 16/3
Y= 2/3 x^3 + 16/3 x
Just replace y with y/X and X with x^2
Please help explanation if possible
Answers
Answer:
y = 3x+6
Step-by-step explanation:
refer to the picture
Answer:
y = 3x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, so slope of parallel line is 3
Expressing the equation in point- slope form with m = 3 , (x₁, y₁ ) = (1, 9)
y - 9 = 3(x - 1)
y - 9 = 3x - 3 ( add 9 to both sides )
y = 3x + 6 ← in slope- intercept form
Identify the construction that the figure represents
Answers
Answer:
Not sure if this will help but that looks like a bisection of angles BAC and TSR.
What’s this topic called
Answers
Answer: MATH
Step-by-step explanation:
Answer:
answer for the question is
x = 1
y = 4
subject is math btw if you are asking about that
A payday loan store charges $25 for a one-month loan of $600. What annual interest rate is this equivalent to?
Answers
Answer:
50%
Step-by-step explanation:
1. determine the monthly interest rate
monthly interest rate = interest / loan amount
monthly interest = 25 / 600 = 4.17%
2, multiply the monthly interest rate by 12 to determine the annual interest rate
Annual interest = 4.17 x 12 = 0.5 = 50%
Solve by substitution:
y=x-12
8x+8y=-16
Answers
Answer:
[tex](x,y) = ( 5 , - 7)[/tex]
Step-by-step explanation:
we would like to solve the following system of linear equation by substitution:
[tex] \displaystyle \begin{cases} y = x - 12\\ 8x + 8y = - 16\end{cases}[/tex]
notice that, we're already given the value of y therefore simply substitute it to the II equation
[tex]8x + 8(x - 12) = - 16[/tex]
distribute:
[tex]8x + 8x - 96= - 16[/tex]
simplify addition:
[tex]16 x- 96= - 16[/tex]
isolate -96 to left hand side and change its sign:
[tex]16 x= - 16 + 96[/tex]
simplify addition:
[tex]16 x= 80[/tex]
divide both sides by 16 and that yields:
[tex] \boxed{x= 5}[/tex]
now substitute the got value of x to the first equation:
[tex]y = 5- 12[/tex]
simplify subtraction:
[tex]y = - 7[/tex]
hence,
the solution is (x,y)=(5,-7)
Solve by substitution :
y = x - 12
8x + 8y = -16
S O L U T I O N :y = x - 12 ------- eq(1)
8x + 8y = -16 ------- eq(2)
Finding x ⤵
Putting y = x - 12 in eq(2) we get
8x + 8(x - 12) = -168x + 8x - 96 = -1616x = 96 - 1616x = 80x = 80/16x = 5Finding y ⤵
Putting x = 5 in eq(1) we get
y = x - 12y = 5 - 12y = -7Hence, x is 5 and y is -7
Please help me anyone
Answers
Replace x with -11 and solve:
Y = (-11)^2 + 11
(-11)^2 = 121
Y = 121 + 11
Y = 132
Answer: 132
Answer:
132
Step-by-step explanation:
y = x^2 +11
Let x = -11
y = (-11)^2 +11
= 121+11
= 132
John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?
Answers
The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.
Answer:
Step-by-step explanation:
Given :
45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44
Using technology, the box and whisker plot generated for the data is attached below.
The 5 - number summary is also given below :
Minimum: 39
Median: 45
First quartile: 42
Third quartile: 47
Interquartile Range: 5
Maximum: 49
Outliers: none
Answer:
Step-by-step explanation:
The width of a rectangle is 9
inches less than the length. The
perimeter is 86 inches
Answers
Answer:
Below.
Step-by-step explanation:
If the length is x then the width is x-9 inches.
Perimeter
= 2L + 2W = 86
2x + 2(x - 9) = 86
4x - 18 = 86
4x = 104
x = 26
So the length is 26 inches and the width is 17 inches.
A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.
Answers
Answer: [tex]4004.76\ ft[/tex]
Step-by-step explanation:
Given
inclination is [tex]\theta=75^{\circ}[/tex]
Mountain is [tex]h=3900\ ft[/tex] high
Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain
From the figure, length of the shortest path is [tex]l[/tex]
It is given by using Pythagoras theorem
[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]
If the right angle triangle LMN.
L=30°, MN = 4cm and diagonal LM.
Find the LM and LN.
Answers
Find the length of the third side. If necessary, round to the nearest tenth. 5 10
Answers
Answer:
[tex]\boxed {\boxed {\sf 8.7}}[/tex]
Step-by-step explanation:
We are asked to find the length of the third side in a triangle, given the other 2 sides.
Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.
[tex]a^2 + b^2 =c^2[/tex]
In this theorem, a and b are the legs of the triangle and c is the hypotenuse.
We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.
b= 5 c= 10Substitute the values into the formula.
[tex]a^2 + (5)^2 = (10)^2[/tex]
Solve the exponents.
(5)²= 5*5 = 25 (10)²= 10*10= 100[tex]a^2 + 25=100[/tex]
We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.
[tex]a^2 +25-25=100-25[/tex]
[tex]a^2=100-25[/tex]
[tex]a^2 = 75[/tex]
a is being squared. The inverse of a square is the square root, so we take the square root of both sides.
[tex]\sqrt {a^2}= \sqrt{75}[/tex]
[tex]a= \sqrt{75}[/tex]
[tex]a= 8.660254038[/tex]
Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 up to a 7 in the tenth place.
[tex]a \approx 8.7[/tex]
The length of the third side is approximately 8.7
Using Pythagorean theorem
[tex]\boxed{\sf B^2=H^2-P^2}[/tex]
Putting values[tex]\\ \sf \longmapsto B^2=10^2-5^2[/tex]
[tex]\\ \sf \longmapsto B^2=100-25[/tex]
[tex]\\ \sf \longmapsto B^2=75[/tex]
[tex]\\ \sf \longmapsto B=\sqrt{75}[/tex]
[tex]\\ \sf \longmapsto B=\sqrt{25\times 3}[/tex]
[tex]\\ \sf \longmapsto B=5\sqrt{3}[/tex]
[tex]\\ \sf \longmapsto B=5\times 1.732[/tex]
[tex]\\ \sf \longmapsto B=8.66[/tex]
[tex]\\ \sf \longmapsto B\approx 8.7[/tex]
How to muilti step equation this problem
Answers
-5x-15=-4x-15
-5x+4x=-15+15
-1x=0 /-1
x = 0
find the value of x. give reasons to justify your answer NEED HELP ASAP!!!!
Answers
Answer:
[tex]x = 34^\circ[/tex]
Step-by-step explanation:
Note that ∠TSU and ∠PSR are vertical angles. Hence:
[tex]m\angle TSU = m\angle PSR[/tex]
∠PSR is the sum of ∠PSQ and ∠QSR. Hence:
[tex]\displaystyle m\angle TSU = m\angle PSQ + m\angle QSR[/tex]
We know that ∠TSU measures 4x and ∠QSR measures 3x. Thus:
[tex](4x) = m\angle PSQ + (3x)[/tex]
Solve for ∠PSQ:
[tex]m\angle PSQ = x[/tex]
Next, ∠PQS and ∠RQS form a linear pair. Thus:
[tex]m\angle PQS + m\angle RQS = 180^\circ[/tex]
∠RQS measures 68°. Thus:
[tex]m\angle PQS +(68^\circ) = 180^\circ[/tex]
Solve for ∠PQS:
[tex]m\angle PQS = 112^\circ[/tex]
The interior angles of a triangle must total 180°. So, for ΔPQS:
[tex]\displaystyle m\angle SPQ + m\angle PQS + m\angle PSQ = 180^\circ[/tex]
Substitute in the known values:
[tex](x) + (112^\circ) + (x) = 180^\circ[/tex]
Simplify:
[tex]2x = 68^\circ[/tex]
And divide. Hence:
[tex]x = 34^\circ[/tex]
The number of solutions of |x - 1| + |x - 3| = 2 is
Answers
Answer:
There are 3 intervals as following:
x ≤ 1
-(x - 1) - (x - 3) = 2-2x + 4 = 22x = 2x = 11 ≤ x ≤3
(x - 1) - (x - 3) = 22 = 2, any value of x in the same intervalx ≥ 3
(x - 1) + (x - 3) = 22x - 4 = 22x = 6x = 3Combining the all, we get:
1 ≤ x ≤3 or x = [1, 3]This is for geometry, please help ASAP
Answers
Answer:
Option C,
y² = 18x, since the graph opens right
Answered by GAUTHMATH
State the slope of the line shown below (help ASAP)
Is it a, b, c or d?
Answers
Answer:
D
Step-by-step explanation:
(the above graph depicts a horizontal line that intersects the y axis at -2)
(so, y = -2)
Answer:
0
Step-by-step explanation:
Horizontal line x axis is 0 while the vertical y axis is undefined.
Find the first three terms of the sequence below. 3n^2+5n−2
Answers
Answer:
-2, 6, 20 ,...
Step-by-step explanation:
3n² +5n -2
if n=0 , then 3*0² +5*0 -2= -2
if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6
if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20
The scale on a map is 1 inch = 10 miles.
What is the distance, in inches, on the map
between two towns that are m miles apart?
F.
m/10
G. M/5
H.5m
J.10m
K.m+10
Answers
Answer:
F. m/10.
Step-by-step explanation:
10 miles = 1 inch
1 mile = 1/10 of an inch so
m miles = m/10 inches.
1.
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.
A. exponential; y = –6 • 1.5x
B. quadratic; y = –x2
C. exponential; y = 6 • 2.5x
D. linear; y = –3x – 6
Answers
Answer:
D. linear; y = –3x – 6
B. quadratic; y = –x2
Step-by-step explanation:
Let
A (0,-2) B (1,-3) C (2,-4) D ( 3,-5) E (4,-6)
using a graph tool
see the attached figure N 1
case a) exponential
see the attached figure N 2
case b) quadratic
see the attached figure N 3
case c) linear
see the attached figure N 4
case d) linear
see the attached figure N 5
therefore
the answer is
the case c) linear
...............................................................................................................................................
Answer:
For the first part
What type of function best models the data in the graph?
✔ quadratic
y = 0.433x2 for the second part.
...............................................................................................................................................
Answer:
Option (2).
Step-by-step explanation:
From the figure attached,
Since there is a common difference in each successive term and previous term of y,
= -3
= -3
Therefore, this data represents a linear equation.
Now we choose two points from the table given.
Let the points are (0, -6) and (1, -9)
Slope of this line 'm' =
m = = -3
Y-intercept 'b' = -6
Equation of the line will be,
y = -3x - 6
Option (2) will be the answer.
pls help me with this question and reply answer
Answers
Step-by-step explanation:
From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.
if i traveled 35 miles on his bike in 3.5 hours what is his rate of speed? i rlly need help- m not sure how to do the steps or whatever
Answers
Answer:
hes going 10 miles an hour,
Step-by-step explanation:
if it took you 3.5 hrs and you went 35 miles, you can do 35/3.5=10, which is 10 miles an hour
Answer:
10 miles per hour
Step-by-step explanation:
We know that distance = rate * time
35 miles = rate * 3.5 hours
Divide each side by 3.5 hours
35 miles / 3.5 hours = rate
10 miles per hour = rate
(f^3-5f+25)-(4f^2-12f+9)
Answers
Answer:
3−42+7+16
Step-by-step explanation:
if its simplify
3. Grace has twice as much money as tad
Together they have $36. How much Money
des Tad have?
Answers
Answer:
Tad has 12 dollars and Grace has 24
Step-by-step explanation:
Grace has twice as much, 24 is double 12. So Tad has 12 dollars.
what is value of y if 2x+3y=4
Answers
Answer:
y=(4-2x)/3
Step-by-step explanation:
3y= 4-2x
y= (4-2x)/3
Ms. Dawson’s call did a science experiment. The class started out with 650 bacteria cells. The growth rate predicted was 4.5%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 30 h from the start of the experiment. Round to the nearest whole number.
Answers
Answer:
your slope would be 4.5.... so go up 4 and to the right 5. the y-intercept is 650 so that is where your line would start instead of at 0... hope this helped :)
Step-by-step explanation:
The exponential function gotten from the table is given by y = 650(1.045)ˣ
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multipliers.
Let y represent the bacteria population after x hours.
The class started out with 650 bacteria cells.
a = 650Growth rate = 4.5%
b = 100% + 4.5% = 104.5% = 1.045The exponential function gotten from the table is given by y = 650(1.045)ˣ
After 30 hours:
y = 650(1.045)³⁰ = 2434Find out more on exponential function at: https://brainly.com/question/12940982
[tex](a+b)^{2}[/tex]
Answers
Answer:
[tex] ({a + b})^{2} [/tex]
[tex](a + b)(a + b)[/tex]
[tex] {a}^{2} + 2ab + {b}^{2} [/tex]
hope this help you
Jo bought a used car for $6000 and paid a 15% deposit. How much did he still have to pay?
Answers
Answer:
900 is the correct awnser
