Answer:
Let y=x
2
−5x+6, when we substitute different values of x in the equation y=x
2
−5x+6 then value of y changes accordingly.
When x=0 then
y=(0)
2
−(5×0)+6=0−0+6=6
The point is (0,6)
When x=2 then
y=(2)
2
−(5×2)+6=4−10+6=10−10=0
The point is (2,0)
When x=3 then
y=(3)
2
−(5×3)+6=9−15+6=15−15=0
The point is (3,0)
Therefore, the coordinates are (0,6), (2,0) and (3,0) and the graph of the quadratic equation y=x
2
−5x+6 is as shown above.
Hence, from above graph, we get that x=2 or x=3.
Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is
Answer:
f(x) = -3x^2 + 10x + 3
Step-by-step explanation:
(0,3) (2,11)(3,6)
Using the form ax^2 + bx + c = y
From the first set we know that c = 3
Write an equation for the last two sets
x=2; y=11
a(2^2) + b(2) + 3 = 11
4a + 2b = 11 - 3
4a + 2b = 8
simplify divide by 2
2a + b = 4
and
x=3, y=6
9a + 3b + 3 = 6
9a + 3b = 6 - 3
9a + 3b = 3
simplify divide by 3
3a + b = 1
:
Use elimination to find a
3a + b = 1
2a + b = 4
--------------subtracting eliminate b
a = -3
Find b using the equation 2a + b = 4
2(-3) + b = 4
b = 4 + 6
b = 10
:
The equation: f(x) = -3x^2 + 10x + 3
On the first day of December, 34,789 people went to the mall. On the second day 63,587 people went to the mall. How many people went to the mall over the two days
Answer:
98376
Step-by-step explanation:
Kristen is creating a rectangular garden in her back yard. The length of the garden is 13 feet. The perimeter of the garden must be at least 54 feet and no more than 82 feet.
Show that 5x^2 + 2x - 3 < 0 can be written in the form | x + 1/5 | < 4/5
if possible with the explanation as well
Step-by-step explanation:
First let solve the inequality
[tex]5 {x}^{2} + 2x - 3 < 0[/tex]
Factor by grouping
[tex]5 {x}^{2} + 5x - 3x - 3 < 0[/tex]
[tex]5x(x + 1) - 3(x + 1)[/tex]
So the factor are
[tex](5x - 3)(x + 1)[/tex]
So the factor are
[tex]x = \frac{3}{5} [/tex]
and
[tex]x = - 1[/tex]
Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics
creates 2 roots and/or double roots.
The inequality
[tex] |x - b| < c[/tex]
works as
b is the midpoint between 2 roots. And c is the
[tex] |x + b| = c[/tex]
We know that the midpoint between both roots is-1/5.
so
[tex] |x - ( - \frac{1}{5} )| < c[/tex]
[tex] |x + \frac{1}{5} | < c[/tex]
Let use roots 3/5
[tex] | \frac{3}{5} + \frac{1}{5} | = \frac{4}{5} [/tex]
-1 works as well.
[tex] | - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5} [/tex]
So the absolute value equation is
[tex] |x + \frac{1}{5} | < \frac{4}{5} [/tex]
I need help, NO LINKS
Answer this question.
Answer:
B) Both functions have a y-intercept of -2.
Step-by-step explanation:
Hi there!
A) Both functions are always increasing.
⇒ False
Let's first take a look at the given equation, [tex]y=3x-2[/tex]. This is a linear equation, and it is organized in slope-intercept form: [tex]y=mx+b[/tex]. m is the slope and b is the y-intercept. When m is positive, it is always increasing.
In [tex]y=3x-2[/tex], 3 is m, and because it's positive, this line is always increasing on a graph.
However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).
B) Both functions have a y-intercept of -2.
⇒ True
In the given equation [tex]y=3x-2[/tex], this is true. -2 is the y-intercept.
On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.
C) Both functions are symmetric about the y-axis.
⇒ False
The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form [tex]y=b[/tex], which isn't the case here with [tex]y=3x-2[/tex]. [tex]y=3x-2[/tex] has a slope.
D) Both functions are linear relationships.
⇒ False
Sure, [tex]y=3x-2[/tex] is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.
I hope this helps!
6. The unit circle with center at the origin is a relation but not a function.
Find the two functions which are semicircles of the unit circle, and determin
e
their domains and ranges?
b. Are these functions onto functions? Justify.
c. Find the two functions which are lie in one of the semicircle in part a, and
determine their domains and ranges?
d. Are these functions one to one correspondence functions? Justify.
Whi
Answer:
Step-by-step explanation:
Which of the following is NOT true about the hypotenuse of a triangle?
A. It is across from the right angle
B. It is always greater than 1
C. IT is always across from the largest angle in the triangle
D. It is the longest side
Depending on the length of the two sides of the triangle the length could be smaller than 1.
The answer that is not true is :
B. It is always greater than 1
If AB is parallel to DE, then CD is:
Answer:
4
Step-by-step explanation:
because BC=CD as it is parallel that means all the sides are equal
The value of CD is 20/3.
The correct option is (A).
What is Similarity in Triangles?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
In ACB and ECD,
angle CAB= angle DEC
angle CBA= angle EDC
angle DCE = angle ACB
By, AA similarity criteria,
ΔACB~ΔECD
Now,
AC/CE= BC/CD
3/5=4/CD
CD= 20/3
Learn more about similarity property here:
https://brainly.com/question/25882965
#SPJ2
Let A={1,2,3,4,5,6,7,8}A={1,2,3,4,5,6,7,8}. Define a relation ∼∼ on AA by a∼ba∼b if and only if 33 divides a−ba−b for all a,b∈Aa,b∈A. 1. Find all the pairs (a,b)∈A×A(a,b)∈A×A such that a∼ba∼b. 2. Show that ∼∼ is an equivalence relation on AA. 3. Find the equivalence classes [2][2] and [3][3].
Define relation.
Let A and B are only two non-empty set,then A*B is cartesian product of A*B.Then any subset of A*B is known as the relation fromA to B.
PLEASE HELP ASAP! FAST! Thank you xoxo
Answers and Step-by-step explanation:
Question 8:
Since angle BCD is opposite angle DAB, this means that they are similar angles as the shape is a parallelogram, and so BCD is 115 degrees, or answer D
Question 3:
We can use process of elimination on this question - The first choice is all squares are rhombuses, which is true. The second question is all rectangles are squares, which is not true, therefore the answer is B
Question 4:
m angle 2 is equal to 106, as it is similar to question 8, and angle 3 is equal to 360 (the total degrees of the shape) - 106 - 106, then divided by 2 and divided by 2 again.
This will equal to angle 3 being 37 degrees, and the answer will be C
Question 5:
We can draw a rectangle from this graph. We can also tell that, in theory, the diagonals are the same, that rules out answer B, and also 5x-5 = x+11
We can then find out x.
+5 on both sides
5x = x+16
-x on both sides
4x = 16
x = 4.
Therefore, each of the sides will be 4+11 = 15, and the answer being C
2. STEM A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm more than or less than 100 ohms. Resistors A and B are rejected. Resistor A's resistance differs from 100 ohms by 0.15 ohm. Resistor B's resistance differs from 100 ohms by -0.78 ohm. How do the resistances of these two resistors compare? Explain.
The comparison of both resistors is defined by an inequality. Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
Given that:
[tex]R = 100 \Omega[/tex] ---- the reference resistor
First, we calculate the resistance of both resistors
Resistor A differs by [tex]0.15\Omega[/tex] means that:
[tex]R_A = 100\Omega + 0.15\Omega[/tex]
[tex]R_A = 100.15\Omega[/tex]
Resistor A has a resistance of [tex]100.15\Omega[/tex]
Resistor B differs by [tex]-0.78\Omega[/tex] means that:
[tex]R_B = 100\Omega -0.78\Omega[/tex]
[tex]R_B = 99.22\Omega[/tex]
Resistor B has a resistance of [tex]99.22\Omega[/tex]
By comparing the calculated values, we can conclude that:
Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
Read more about inequality comparison at:
https://brainly.com/question/11772136
Rewrite as a product of the GCF and another sum 36 + 48
Answer:
72+12
Step-by-step explanation:
given the equation 4x + 3y = 18. find the value of y when x = −3
9514 1404 393
Answer:
y = 10
Step-by-step explanation:
Put -3 where x is and solve for y.
4(-3) +3y = 18
-4 +y = 6 . . . . . . . divide by 3
y = 10 . . . . . . . . . add 4
write a clear instructions explaining how to perform the following calculation (125+47-2.5)÷140+37×249
Answer:
It is 9214.2
Step-by-step explanation:
[tex](125 + 47 - 2.5) \div 140 + 37 \times 249[/tex]
first solve the bracket:
[tex] = (169.5) \div 140 + 37 \times 249[/tex]
form brackets of division and multiplication:
[tex] = (169.5 \div 140) + (37 \times 249)[/tex]
solve the brackets:
[tex] = 1.211 + 9213[/tex]
then add:
[tex] = 9214.211[/tex]
100 yojan=how much km?
Answer:
100 yojan=how much km
1287.48
please brainlist
A mountain is 15,062 feet above sea level, and a valley is 350 feet below sea level, what is the difference in elevation between the mountain and the valley?
Answer:
14,712 ft difference
Step-by-step explanation:
15,062 - 350 = 14,712
Answer:
Step-by-step explanation:
Difference in elevation is 15,062-(-350)=15,062+350=15,412
HELP!! TRUTH TABLE
I would really appreciate it, if someone could walk me through how they did it! Thanks.
p ∧ q (i.e. "p and q") is true only if both p and q are true. This is the case for the first two rows, but not the third.
Similarly, (p ∧ q) ∧ r is true only if both p ∧ q and r are true. We know when p ∧ q is true, so (p ∧ q) ∧ r is true only when all three of p, q, and r are true. This happens only in the first row.
All other cases are false.
The table should look like this:
[tex]\begin{array}{c|c|c|c|c}p&q&r&p\land q&(p\land q)\land r) \\---&---&---&---&--- \\T&T&T&\boxed T&\boxed T\\&&&&\\T&T&F&\boxed T&\boxed F\\&&&&\\T&F&T&\boxed F&\boxed F\end{array}[/tex]
A wall is 1200 sq ft.
A gallon of paint covers 200 sq ft.
Complete the conversion factor: 1 gallon / ? sq ft
8 thousands + 4 thousands
What is the answer in standard form?
Answer:
12000
Step-by-step explanation:
8000+4000=12000
please help!!! what is the interquartile range?
4 2/3 - (1 4/5). PLEASE HELP MEEEEE
Answer: 2 13/ 15
Step-by-step explanation:
what is the distance between the points (7, 8) and (9, 10).
Help please! thank you xoxo!
2 math problems
3. x = 45
4. 73°
Step-by-step explanation:
3. The sum of the interior angles of a pentagon is 540° so
90° + 112° + 2x + (2x + 10) + 148° = 540°
Simplifying this, we get
4x + 360 = 540 => 4x = 180 or x = 45
4. The sum of the interior angles of a pentagon is 540° which means that the unknown interior angle is 107°. This angle is a supplementary angle to [tex]\angle{A}[/tex] so [tex]\angle{A}[/tex] is
180° - 107° = 73°.
please help will bark brainliest
Answer:
A.
Step-by-step explanation:
What is the value of the digit 6 in 873,261?
What is the value of the digit 6 in 137,2617?
Answer:
Step-by-step explanation:
60
600
write as an expression :the quantity 10 less than x, divided by 4
Answer:
(x-10)/4
Step-by-step explanation:
10 less than x means,
x - 10
and the divide by 4.
=> (x-10)/4
Answer:
x-10/4
10 less than x
x-10
divided by 4
/4
Anton joined a golf club. He pays an annual membership fee of $895 and greens fee of $30 each time he plays golf. Last year he paid $2,065 as a total golfing fee. How many games did he play? Write and solve the equation.
Use the order of operations to evaluate the expression below.
3 + 5 x 5 - 50 ÷ 2 + 3 - 4
Answer here
Answer:
2
Step-by-step explanation:
=3+5×5-25+3-4
=3+25-25+3-4
=28-22-4
=28-26
=2
Answer:
2
Step-by-step explanation:
3 + 5 * 5 - 50 / 2 + 3 - 4
3 + (5 * 5) - 50 / 2 + 3 - 4 => Multiplication what ever comes first
3 + 25 (-50 / 2) + 3 - 4 => Division left to right
(3 + 25) - 25 +( 3 - 4) => Addition what ever comes first
28 - 25 - 1 => Substraction left to right
2
Leave comment if you're curious.
what is the zero turn for the arithmetic sequence 128,96,64,32
You are falling by [tex]32[/tex],
[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]
In general your sequence is defined as,
[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].
The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].
If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].
If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].
The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].
Hope this helps :)