Answer:
D. Function
Step-by-step explanation:
Function:a relationship or expression involving one or more variables.
"the function (bx + c)"
Prove that the equation x^2+px-1=0 for every p has two different solutions
Answer:
To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.
Consider x2+px−1=0
Discriminant D=p2−4(1)(−1)=p2+4
We know p2≥0 for all values of p
⇒p2+4≥0 (since 4>0)
Therefore D≥0
Hence the equation x2+px−1=0 has real and distinct roots for all real values of p
Sophia drew a scale drawing of the elementary school. The scale of the drawing was 1 centimeter : 4 meters. The schoolyard is 52 meters wide in real life. How wide is the schoolyard in the drawing
Answer:
13 cm
Step-by-step explanation:
The scale of the drawing was 1 centimeter : 4 meters.
x cm : 52 m Divide by 4
13 cm : 52 m
Please help I don't know how to do this
Answer:
(a) (2x +7), (x -4)
(b) (-7/2, 0), (4, 0)
Step-by-step explanation:
(a)When looking for integer factors of a quadratic of the for ax² +bx +c = 0, it is useful to start by looking for factor pairs whose product is a·c and whose sum is b.
Here, that means you're examining the factors of 2·(-28) = -56, and looking for a pair that have a sum of -1. We can start by examining the ways that -56 can be factored:
-56 = -56(1) = -28(2) = -14(4) = -8(7)
Sums of these factor pairs are -55, -26, -10, -1, so it is the last pair we're interested in.
At this point, you can rewrite the x-term using these factors and then factor the quadratic by pairs.
2x² -8x +7x -28 = 0 . . . . . . . use -x = -8x+7x
(2x² -8x) +(7x -28) = 0 . . . . group into pairs of terms
2x(x -4) +7(x -4) = 0 . . . . . . factor each pair of terms
(2x +7)(x -4) = 0 . . . . . . . . . the factored equation
The factors of this equation are (2x +7) and (x -4).
__
(b)The x-intercepts are the values of x that make the factors zero.
2x +7 = 0 . . . looking for x that makes the first factor zero
2x = -7 . . . . . subtract 7
x = -7/2 . . . . divide by the coefficient of x
__
x -4 = 0 . . . . looking for x that makes the second factor zero
x = 4 . . . . . . add 4
The x-intercepts are x = -7/2 and x = 4.
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{QUESTIONS:}[/tex]
3. Given this quadratic equation, 2x²-x-28= 0.
(a) List the factors of this equation.
(b) Determine the x-intercepts
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{ANSWER:}[/tex]
(a) (x-4) and (2x+7)
(b) x=4 and x=-7/2
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{SOLUTION:}[/tex]
2x²-x-28=02x²+7x-8x-28=02x²-8x+7-28=02x(x-4)+7(x-4)=0(x-4)(2x+7)=0x-4= 0 or 2x+7=0x=4 or 2x=-7x=4 or x= -7/2[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnlearning
Answer the following questions. Make sure to show all your work.
1. In each case below, show if the point given is a solution to the system of
equations.
a.)
Point (-0.8,-0.6)
Equation 1 - y = 2x + 1
Equation 2 - y = -3x - 3
b.)
Equation 1 - x + y = 3
Equation 2 - y + 2 / 2 = x
POINT - (1/3, 2)
PLZ HELP ME
a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
b) since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equation
In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value
For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:
f(x) = 2x + 1
f(-0.8) = 2(-0.8) + 1
f(-0.8) = -1.6 + 1
f(-0.8) = -0.6
Simiarly;
y = -3(-0.8)- 3
y = 2.4 - 3
y = -0.6
Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
For the point (1/3, 2), substitute x = 1/3 into both functions as shown:
x = (y+2)/2
x = (2+2)/2
x = 4/2
x = 2
Simiarly;
x + 2 = 3
x = 3-2
x = 1
Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equations
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HELP ME PLEASE
(NO LINKS PLEASE FOR REAL NO LINKS PLEASE)
1. A student and a teacher work together to make toy cars. The student made 2/7 of the total toy cars, 21 less than the teacher. How many toy cars are there?
The total number of cars both the student and the teacher made is 49
let
total cars = x
cars made by student = s
cars made by teacher = t
Total = student + teacher
x = s + t
s = 2/7x
So,
x = 2/7x + t
x - 2/7x = t
t = (7x - 2x) / 7
t = 5/7x
Similarly,
s = t - 21
s = 5/7x - 21
equate both s equation
2/7x = 5/7x - 21
2/7x - 5/7x = -21
(2x - 5x) / 7 = -21
- 3/7x = -21
x = -21 ÷ -3/7
= -21 × - 7/3
= (-21 × -7) / 3
= 147/3
x = 49
Therefore, the total number of cars both the student and the teacher made is 49
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0.36 as a standard form
Answer:
0.36 x 10⁰Step-by-step explanation:
how many solutions are there for 2x−5=8x+7−6x
Answer:62
Step-by-step explanation:
2 times 5=10-5=5
8 times 7=56+7= 63-6=57+5=62!
No solution. hope this helps
there were 8000 people at a festival. people bought their tickets online, by phone, or in person.based on a random sample of people at the festival, 60% bought their tickets online, 15% bought their tickets by phone, and the rest bought their tickets in person
Answer:
People who bought tickets = 100%
= 8000
People who bought their tickets in person = (100%-60%-15%) × 8000
= 2000
The number of tickets sold online is 4800, by phone is 1200, and in person is 2000.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that there were 8000 people at the festival. people bought their tickets online, by phone, or in person. based on a random sample of people at the festival, 60% bought their tickets online, and 15% bought their tickets by phone.
The number of the tickets will be calculated as below:-
Total tickets = 8000
Online tickets = 60% of 8000 = 8000 x 0.6 = 4800
By phone = 15% of 8000 = 8000 x 0.15 = 1200
In-person = 25% x 8000 = 0.25 x 89000 = 2000
Therefore, the number of tickets sold online is 4800, by phone is 1200, and in person is 2000.
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#SPJ2
8 less than the sum of 6 and a number
Answer:
(6 + n) - 8
Hope this helps.
Pls mark brainliest. :D
Answer:x < 2
Step-by-step explanation: 6+x < 8
x < (8-6)
x < 2
PLEASE HELP!
Determine the value of X.
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Step-by-step explanation:
using the letters from the word equation, how many 5-letter patterns can be formed in which q isfollowed immediately by u?
Using the arrangements formula, it is found that there are 720 words that can be formed.
The number of possible arrangements of n elements is the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem:
The non-qu letters of the word equation will be arranged in 5 positions.The "qu" can be positioned in 6 ways(letters 1-2 to letters 6-7), hence:[tex]T = 6 \times 5! = 6! = 720[/tex]
There are 720 words that can be formed.
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Write an equation of the line that passes through (0,5.2) and (-1.5,1).
y=
Answer:
Step-by-step explanation:
Given:
y1 = 5.2
y2 = 1
x1 = 0
x2 = -1.5
Solution:
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( 1 - 5.2 ) / ( -1.5 - 0 )
m = -4.2 / -1.5
m = 2.8
then
y - y1 = m ( x - x1 )
y - 5.2 = 2.8 ( x - 0 )
y - 5.2 = 2.8x - 0
y = 2.8x + 5.2
A set of 6 art books costs $241.25. A copy of one of the books, bought separately, costs $38.25. About how much less is the cost of the 6 books if you buy the set?
The cost of the 6 books if you buy the set is $11.75 less.
The given parameters:
Total number of books, n = 6Cost of the books, c = $241.25Cost of one book, = $38.25The total cost of the 6 books when bought separately is calculated as follows;
Cost = 6 x $38.25
Cost = $229.5
The difference in price is calculated as follows;
= $241.25 - $229.5
= $11.75
Thus, the cost of the 6 books if you buy the set is $11.75 less.
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What is the area of the parallelogram?
Answer:
24cm
Step-by-step explanation:
because 6 x 4 = 24 centimeters
Compare the values.
9 x 10^2 is
?
times as much as 3 x 10^-2.
Answer:
Hopefully this explains o_O, also Merry Christmas!
Step-by-step explanation:
9 x 10^2 = 9 x 100 = 900
3 x 10^-2 = 3 x 1/100 = 0.03
Ratio of 900:0.03
The first one is 30000 bigger than the second
will mark brainleist
Answer:
Figure a) 2
figure b) 4
figure c) 5
Step-by-step explanation:
Twelve is sixteen less than four times a number. Write it as a mathematical statement.
Answer:
12=4x-16
x would represent the unknown number.
a store pays $60 for the shoes and sells them for $90. What is the percent markup
Twice the difference of a number and 2 is at least 16 use the variable y for the unknown number
Answer:
2(y-2) is greater then or equal to 16
Step-by-step explanation:
can someone help me with this
Answer: i think you should label it with numbers first
maybe??
Step-by-step explanation:
Which equation best fits the graphed data?
6+
4+
2+
+X
-6
-4
- 2
2
6
N
-2+
.
.
-4
-6+
Answer:
D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
HELP HURRY PLS
What is the equation of this line?
A. y= 3/2x -2
B. y=2x+2/3
C. y=2/3x-2
D. y= -2x+3/2
Answer:
The answer is C, y = 2/3x -2
Step-by-step explanation:
Use the rise over run strategy on linear functions such as this one
please help meeee, thank youuuu
Answer:
45
Step-by-step explanation:
I think so i dont know
Answer:
45
Step-by-step explanation:
Just do the regular number sequence (1-44) but add 1 since this specific sequence starts with 2.
Hope this helped! ^^A boat heading out to sea starts out at Point AA, at a horizontal distance of 968 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 7^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 3^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
As the distance from the lighthouse, LH, increases, the angle of elevation,
reduces.
The distance from point A to point B is approximately 1,269.9 feet.Reasons:
The distance of point A from the light house = 968 feet
Angle of elevation from point A to the lighthouse = 7°
Angle of elevation from point B to the lighthouse = 3°
Required:
The distance from point A to point B.
Solution:
[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{Horizontal \ from \ boat \ to \ the\ LH}}[/tex]
Which gives;
[tex]\displaystyle tan(7^{\circ}) = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{968 \ feet}}[/tex]
Height to the lighthouse = tan(7°) × 968 feet ≈ 118.86 feet
From point B, we have;
[tex]\displaystyle tan(3^{\circ}) = \mathbf{ \frac{118.86 \ feet }{Horizontal \ distance \ from \ point \ B\ to \ LH}}[/tex]
Therefore;
[tex]\displaystyle Horizontal \ distance \ from \ boat \ to \ LH = \frac{118.86 \ feet }{tan(3^{\circ})} \approx \mathbf{2237.9 \, feet}[/tex]
Therefore;
Distance from A to B = D
D = Horizontal distance from B to LH - Horizontal distance from A to LH
Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet
The distance from point A to point B, D ≈ 1,269.9 feet
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PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
Answer:
Hypotenuse: 20√2
Acute Angle measurements: 45
Step-by-step explanation:
Note that the two leg sides are both 20 measurements, suggesting that it is an isosceles triangle.
By definition of a isosceles triangle, the angles will be 45-45-90, and the sides will follow the 1-1-√2 rule, in which the 1 stands for the legs, and the √2 stands for the hypotenuse.
Note that the leg side measures 20. Multiply:
20 * √2 = 20√2.
Hypotenuse: 20√2
Acute Angle measurements: 45
If no denominator equals zero, which expression is equivalent to ? A. B. C. D.
The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] and it can be determined by using LCM and fraction.
Given that,Expression;[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
We have to determine,Which expression is equivalent to the given expression?
According to the question,Expression;
[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]
If no denominator equals zero,
To determine the equivalent relation of the given equation following all the steps given below.
Step1; First take the LCM,[tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]
Step2; Multiply the terms and simplify the equation,[tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]
Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .
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Which ordered pair is a solution of the equation?
y + x = 3(x – 4)
f(x) is graphed below. If g(x)=f(x+2)-4, what are the roots of g(x)?
Answer:
fortnit 90s
Step-by-step explanation:
crank and c until u get too 90 height
7.098/09.977x979.97878
Answer:
697.19248074 is the answer
y + 4= -6
Find the slope and the Y-intercept of the graph of this equation