Considering the discriminant of zero for a quadratic equation, the correct option is given by:
C. It has one real solutions.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it is a perfect square, it has 2 rational solutions.If [tex]\mathbf{\Delta > 0}[/tex], and it is not a perfect square, it has 2 irrational solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 rational solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.Discriminant of zero is [tex]\Delta = 0[/tex], hence option C is correct.
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what is the ratio 3:1
Answer:
3:1
Step-by-step explanation:
3 and 1 is not divisible by any number
Find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2).
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y= - \cfrac{x}{ 3} + 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Equation of line (two point form) :
[tex]\qquad \tt \rightarrow \: (y - y_1) = \cfrac{y _1- y_2}{ x_1 - x_2} (x - x_1)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = \cfrac{2 - ( - 1)}{ - 3 - 6} (x - ( - 3))[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = \cfrac{2 + 1}{ - 9} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = - \cfrac{3}{ 9} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = - \cfrac{1}{ 3} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: y - 2= - \cfrac{x}{ 3} - \cfrac{3}{3} [/tex]
[tex]\qquad \tt \rightarrow \: y = - \cfrac{x}{ 3} - 1 \cfrac{}{} + 2[/tex]
[tex]\qquad \tt \rightarrow \: y = - \cfrac{x}{ 3} + 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Express 10cm as percentage of 50cm
Answer:
10 cm is 20% of 50 cm.
Step-by-step explanation:
1) Put the "question" into fraction form: 10/50
2) Divide the numerator by the denominator (essentially changing the fraction into the decimal form): 10 ÷ 50 = 0.2
3) Multiply the quotient by 100: 0.2 × 100 = 20
4) Slap a "%" on the end and you're good to go!! : 20%
the tabel show the time merrida spent driving and the number of miles she drove she drove the same number of miles each other
Answer:
35 miles per hour
Step-by-step explanation:
Speed of a car or any other object is given by distance divided by time taken.
therefore,
according to the given data in the table :
speed = miles covered/ time taken
= 140/4 = 35 miles per hour
= 175/5 = 35 miles per hour
= 210/6 = 35 miles per hour
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What is the slope of the line thatpasses through these two points?(2,3)(2,9)
Answer:
The slope is undefined
Step-by-step explanation:
[tex]m=\frac{9-3}{2-2}[/tex]
The denominator leads to 0 so it would not be possible to find the answer
Answer:
undefined
Step-by-step explanation:
anything divided by zero is undefined since you cant logically give (for example) 2 apples to 0 people.
For slopes not so obvious, the formula is (slope)m= (rise)y/(run)x
What is the volume of the cone shown below?
A. 1344 cu. units
B. 504 cu. units
C. 4032 cu. units
D. 2016 cu. units
Volume = PI x r*2 x h/3
r = radius which is shown as 8
h is the height which is shown as 63
Volume = 3.14 x 8^2 x 63/3
Volume = 3.14 x 64 x 21
Volume = 4,220.16 cubic units.
QUESTION 2
Evaluate x4 + 5x3-3x2 + 11x - 6 for x = 3
Answer:
The answer is (-84)
putting the value of X =(- 3)
2) X = 216
Hello!
We are going to evaluate the expression with our given x-value for question 2.
We know that our expression is: x^4 + 5x^3 - 3x^2 + 11x - 6
We also know that our x-value = 3
We will simply plug in "3" to "x" in our expression and solve.
Solve:
x^4 + 5x^3 - 3x^2 + 11x - 6
Plug in 3 to x:
(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6
Simplify:
(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6
81 + 5(3)^3 - 3(3)^2 + 11(3) - 6
81 + 135 - 3(3)^2 + 11(3) - 6
81 + 135 - 27 + 33 - 6
216 - 27 + 33 - 6
189 + 33 - 6
222 - 6 = 216
Therefore, our final answer would be 216.
Answer:
216
Which equation is equivalent to y−3=4(x−5)?
y=4x−2y is equal to 4 x minus 2
y=−4x−23y is equal to negative 4 x minus 23
y=4x−17y is equal to 4 x minus 17
y=−17x+4
Answer:
y = 4x - 17
Step-by-step explanation:
y - 3 = 4(x - 5) ← distribute parenthesis by 4
y - 3 = 4x - 20 ( add 3 to both sides )
y = 4x - 17
The length of the rectangle is 4 more than the width. The area of the rectangle is 45
square centimeters. Identify the length and width of this rectangle.
Answer:
You need 2 numbers whose product is 45 and whose difference is 4.
so the length is 9 and the width is 5.
Hope this helps.
3. Complete the square for the following equations:
a. y = 2x² 12x + 1
b. y = 4x² + 48x - 10
Answer:
a. y = 2(x + 3)² - 17
b. y = 4(x + 6)² - 154
Step-by-step explanation:
a. y = 2x² + 12x + 1
y = 2[(x² + 6x)] + 1
y = 2[(x + 3)² - 9] + 1
y = 2(x + 3)² - 18 + 1
y = 2(x + 3)² - 17
b. y = 4x² + 48x - 10
y = 4[(x² + 12x)] - 10
y = 4[(x + 6)² - 36)] - 10
y = 4(x + 6)² - 144 - 10
y = 4(x + 6)² - 154
Solve the discriminant
Answer:
a
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
then the discriminant
Δ = b² - 4ac
• if b² - 4ac > 0 then 2 real solutions
• if b² - 4ac = 0 then 2 real and equal solutions
• if b² - 4ac < 0 then no real solutions
given
[tex]\frac{3}{4}[/tex] x² - 3x = - 4 ( add 4 to both sides )
[tex]\frac{3}{4}[/tex] x² - 3x + 4 = 0 ← in standard form
with a = [tex]\frac{3}{4}[/tex] b = - 3 , c = 4
then
b² - 4ac = (- 3)² - ( 4 × [tex]\frac{3}{4}[/tex] × 4) = 9 - 12 = - 3
since b² - 4ac < 0 then equation has no real solutions
Answer:
a. -3; no real solutions.
Step-by-step explanation:
Discriminant
[tex]\boxed{b^2-4ac }\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{When }\:b^2-4ac > 0 \implies \textsf{two real solutions}.[/tex]
[tex]\textsf{When }\:b^2-4ac=0 \implies \textsf{one real solution}.[/tex]
[tex]\textsf{When }\:b^2-4ac < 0 \implies \textsf{no real solutions}.[/tex]
Given equation:
[tex]\dfrac{3}{4}x^2-3x=-4[/tex]
Add 4 to both sides of the equation so that it is in standard form:
[tex]\implies \dfrac{3}{4}x^2-3x+4=-4+4[/tex]
[tex]\implies \dfrac{3}{4}x^2-3x+4=0[/tex]
Therefore, the variables are:
[tex]a=\dfrac{3}{4}, \quad b=-3, \quad c=4[/tex]
Substitute these values into the discriminant formula to find the value of the discriminant:
[tex]\begin{aligned}\implies b^2-4ac&=(-3)^2-4\left(\dfrac{3}{4}\right)(4)\\&=9-(3)(4)\\&=9-12\\&=-3\\\end{aligned}[/tex]
Therefore, as -3 < 0, the discriminant is less than zero.
This means there are no real solutions.
1. At which point do Line CF and Line GF intersect? They intersect at point?
2. Look at Line AD and Like BE. Do these lines intersect?
(a) yes they will intersect at Point F?
(b) no they will never intersect?
(c) yes they will point at Point G
(d) yes they will intersect at Point F?
3. Look at Line BG and Line AC. Where do they intersect? They intersect at Point?
(Please hurry giving 50 points!)
Answer: i think no?
Step-by-step explanation:
AD and BE are both parallel lines (they are parallel to eachother), so they will never intersect
CF and GF intersect at point F (i think)
Bg and Ac intersect at point B (i think)
i dont want to give a definite answer in the event im wrong bc I just learned this like a few weeks ago-
Use properties to evaluate 3/4(1/5÷3/5)(-8).
A. 2
OB. 5
O C. -2
OD. -5
Answer:
C. -2
Step-by-step explanation:
Use A-P-E-X
How I solved it:
3/4(1/5÷3/5)(-8)
3/4(1/5×5/3)(-8)
3/4(1/3)(-8)
1/4(-8)=-2
Hope this helps!
If not, I am sorry.
Choose all of the following angles that cannot
be an interior angle in a regular polygon.
40° 45° 108° 132° 179°
Answer:
40 45 because the minimum internal angle is 60
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(1) = -1³ - 91² +41 +96
Based on these key features, which statement is true about the graph representing function h?
A.
The graph is negative on the intervals (- infinity, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, -4) and (3, infinity).
OC. The graph is negative on the intervals (-3, 4) and (8, ∞).
D. The graph is positive on the intervals (-infinity ,-8) and (-4, 3).
Based on the key features, the end behavior and the zeros of function h [h(x) = -x³ - 9x² +4x +96], the statement that is true of the above graph is: "The graph is positive on the intervals (-8, -4) and (3, infinity) (Option B)"
A function's "end behavior" refers to how the function's graph behaves at its "ends" on the x-axis.
In other words, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞ ), the end behavior of a function represents the trend of the graph.
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Which of the equations have only 1 solution -5x+12=5x-5
Answer:
in the pic...
Step-by-step explanation:
Hope it Helps!!!
Step 1: 4 x minus x + 2 + 6 = 6 x + 16
Step 2: 3 x + 8 = 6 x + 16
Step 3: 8 minus 16 = 6 x minus 3 x
Step 4: Negative 8 = 3 x
Step 5: Negative StartFraction 8 Over 3 EndFraction = x
Jorge verifies his solution by substituting Negative StartFraction 8 Over 3 EndFraction into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error?
Jorge distributed incorrectly.
Jorge incorrectly combined like terms.
Jorge incorrectly applied the addition and subtraction properties of equality.
Jorge incorrectly applied the multiplication and division properties of equality
The error from Jorge's arithmetic operation on the given algebraic expression is that he distributed it incorrectly.
What is an algebraic expression?An algebraic expression is a mathematical equation that is made up of variables together with arithmetic operations.
From the given expression, we have:
4x - x + 2 + 6 = 6x + 16
Add similar elements together;
3x + 8 = 6x + 16
Using distributive property, subtract 8 from both sides:
3x + 8 - 8 = 6x + 16 - 8
3x = 6x + 8
Simplify
3x-6x = 8
-3x = 8
Divide both sides by -3
-3/-3x = -8/3
x = -8/3
So from Jorge's calculation, because he distributed incorrectly, we can conclude that could be his error.
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In the above diagram, the demand for pepper is an example of price __________.
A.
elasticity
B.
shifting
C.
inelasticity
D.
controlling
Please select the best answer from the choices provided
A
B
C
D
Answer:
B. shifting
Step-by-step explanation:
When the price is rising or shifting higher, the demand curve moves to the left. But, t here is a corresponding change in the demand curve in that scenario while the cost stays unchanged. Since it relies on variables other than price, the simultaneous shift might go either left or right. However, the upward-pointing line depicts a rise in price and a fall in supply.
Help please giving Brianlest
Answer:
Maybe the answer will be C. P ( A and B )
explanation:
I think it is OPTION C , P(A and B)
as this is the only option which has the value of 80, which we got from the table...
PLEASE HELP ME WITH THIS ASAP
Answer:
4 rows
Step-by-step explanation:
First set:
unknown rows, 5 tiles each
meaning old total is divisible by 5
Second set:
3 additional rows, 3 tiles each
meaning that the new total is divisible by 3
so, our total number of tiles is divisible by 5, add 1 and it is divisible by 3 when added 1
{another way I solved it : [and when it is divided by 3, it has 8 that fit into the original pattern; which is another way of knowing that each of the rows of 5 [each have 2 removed when turned into rows of 3] add up to having a remainder of 8 tiles; 8 / 2 = 4; so there were four rows in the original pattern contributing to the change--there were four rows] }
x is divisible by 5, x + 1 is divisible by 3
essentially, we are looking for a number that ends in 5 or 0, and the next number [ending in 6 or 1] is divisible by 3
I know that 5 goes into 20, and that 21 is divisible by 3, so let's test it out:
4 (rows of 5) turns into 7 [4 + 3] rows of 3
because 21 can be split into 7 rows, this number of tiles is possible
so, in the original pattern, there must have been 4 rows
hope this helps!! {so sorry if this confuses you, please let me know if I should explain my reasoning further}
have a lovely day :)
L
N
(x-4) in. O
(x-3) in.
(x + 2) in.
x in.
K
Which value of x would make NO || KJ?
1
6
08
O 10
Answer:
x = 8
Step-by-step explanation:
[tex]\sf If\:\: \overline{NO} \parallel \overline{KJ}\:\:then\:\: \triangle LNO \sim\triangle LKJ[/tex]
Therefore:
[tex]\implies \sf \overline{LN} : \overline{LO} = \overline{LK} : \overline{LJ}[/tex]
[tex]\implies (x-3):(x-4)=(x-3)+(x+2):(x-4)+x[/tex]
[tex]\implies \dfrac{x-3}{x-4}=\dfrac{2x-1}{2x-4}[/tex]
[tex]\implies (x-3)(2x-4)=(2x-1)(x-4)[/tex]
[tex]\implies 2x^2-10x+12=2x^2-9x+4[/tex]
[tex]\implies -10x+12=-9x+4[/tex]
[tex]\implies 12=x+4[/tex]
[tex]\implies x=8[/tex]
find the measure of major arc RUT. shiw your work please.
Answer:
well not sure but I think it is 8° or 17.8°
Identify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is
units.
The center of the circle is at
Answer:
centre (5,0)
radius:9
I hope it will be helpfulness
What is the solution to -2|x − 1| = -4? A. x = 3 B. x = -1 or x = 3 C. x = 1 or x = 3 D. No solutions exist.
Answer:
B
Step-by-step explanation:
-2|x - 1| = -4
|x - 1| = 2
since we are dealing with a function that brings 2 values to the same result, the reverse function (needed to find the values of x that create the result y) has 2 branches :
(x - 1) = 2
and
(x - 1) = -2
x - 1 = 2
x = 3
x - 1 = -2
x = -1
therefore, B is the right answer.
What function represents this graph??
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
Piecewise functionsThe graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.
For the line crossing the negative x-axis
Using the coordinate points (-4, 2) and (-2, -4)
Slope = -6/2
Slope = -3
2 = -3(-4) + b
2 - 12 = b
b = -10
The equation of the line will be y = -3x-10
For the line crossing the negative y-axis
Using the coordinate points (-2, -4) and (2,-2)
Slope = 2/4
Slope = 1/2
-2 = 1/2(2) + b
-2 - 1 = b
b = -3
The equation of the line will be y = -1/2x-3
For the line crossing the positive x-axis
Using the coordinate points (2, -2) and (3, 0)
Slope = 2/1
Slope = 2
0 = 2(3) + b
0 - 6 = b
b = -6
The equation of the line will be y = 2x-6
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
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my father is 4 times old as me. after 5 years my father will be 3 times old how old is my father now
Answer:
Step-by-step explanation:
Which of the following sets of ordered pairs represents a function?
{(-6,-1), (13,8), (1,6), (1,-10)}
{(10,5), (10,-5), (5,10), (5,-10)}
{(3,5), (-17,-5), (3,-5), (-17,5)}
{(10,5), (-10,-5), (5,10), (-5,-10)}
Answer:
Step-by-step explanation:
A function can only have one output for an input. That is, for any value of x, there must be a unique value of y.
{(-6,-1), (13,8), (1,6), (1,-10)} Not a Function: (1,6) and (1,-10)
{(10,5), (10,-5), (5,10), (5,-10)} Not a Function: (10,5) and (10,-5)
{(3,5), (-17,-5), (3,-5), (-17,5)} Not a Function: (3,5) and (3,-5)
{(10,5), (-10,-5), (5,10), (-5,-10)} Function: No duplicate values of y for a value of x.
If function g has the factors (x - 7) and (x + 6), what are the zeros of function g?
When a given function is written with factors in the form of ( x - r ), then r is a zero of the function.
Solving the QuestionWe're given:
Function g has factors (x-7) and (x+6)Therefore, the zeros of the function are 7 and -6.
Answer-6, 7
The zeroes of the function will be equal to ( 7, -6 ).
What is a quadratic equation?
It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given function:-
( x- 7 ) ( x+ 6 )As we can see that the quadratic equation in the factorized form is ( x - 7 ) ( x+ 6 ) so we will equate each factor to zero.
( x- 7 ) = 0
x = 7
( x+ 6 ) = 0
x = -6
Therefore zeroes of the function will be equal to ( 7, -6 ).
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there are 3 red pens, 4 blue pens, 2 Blac pens, and 5 green pens in drawer, suppose you choose a pen at random
help :(:
Answer:
1. 3/14
2. 2/7
3. 1/7
4. 5/14
5. 11/14
6. 9/14
Step-by-step explanation:
first get the total number of pens
3 red pens + 4 blue pens + 2 black pens + 5 green pens =
14 total number of pens
1. What is the probability that the pen chosen red?
3 red pens out of a total of 14 pens = 3/14
2. What is the probability that the pen chosen is blue?
4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7
3. What is the probability that the pen chosen is black?
2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7
4. What is the probability that the pen chosen is green?
5 green pens out of a total of 14 pens = 5/14
5. What is the probability that the pen chosen is NOT red?
of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens
4 blue pens, 2 black pens and 5 green pens are NOT red
4 blue pens + 2 black pens + 5 green pens =
11 total number of pens that are NOT red
11 total number of pens that are NOT red out of a total of 14 pens = 11/14
6. What is the probability that the pen chosen is NOT green?
of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens
the 3 red pens, 4 blue pens, 2 black pens are NOT green
3 red pens + 4 blue pens + 2 black pens =
9 total number of pens that are NOT green
9 total number of pens that are NOT green out of a total of 14 pens = 9/14
gathmath.com
Given :-
Red pens = 3Blue pens = 4 Black pens = 2 Green pens = 5>> Total no. of outcomes = 3 + 4 + 2 + 5
>> Total no. of outcomes = 3 + 4 + 7
>> Total no. of outcomes = 10 + 4
>> Total no. of outcomes = 14
Solution 1 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are three red pens. Therefore,
P(E) = 3 / 14Solution 2 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are four blue pens. Therefore,
P(E) = 4 / 14Solution 3 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are two black pens. Therefore,
P(E) = 2 / 14Solution 4 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are five green pens. Therefore,
P(E) = 5 / 14Solution 5 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there 11 pens that are not red (Green + black + blue).
P (E) = 11 / 14Solution 6 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are 9 pens that are not green (Red + blue + black).
P (E) = 9 / 14please help me solve this LCM
Note that
[tex]x^2 - y^2 = (x - y) (x + y)[/tex]
and
[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]
Then their LCM is [tex]\boxed{x + y}[/tex].