14.
Solve x2 + 2 = 6 by graphing the related function.
A. There are no real number solutions.
B. There are two solutions: ±[tex]\sqrt{8}[/tex].
C. There are two solutions: 2 and –2.
D. There is one solution: 2
Answers
Answer:
C. There are two solutions: 2 and –2.
Step-by-step explanation:
Answer:
Step-by-step explanation:
we have
we know that
The solution of the function is equivalent to solve the following system of equations
------> equation A
------> equation B
The x-coordinate of the intersection point both graphs is the solution of the given function
Using a graphing tool
see the attached figure
The intersection points are and
therefore
The solution of the given function are
Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.
Answer: option C.
Step-by-step explanation:
Given a quadratic function of the form , if the coefficient a is less than zero, then the function is opened upward.
The options A is not opened upwards, then it is not the answer.
Then the given equation can be written as:
This function is equal to the parent function, shifted 4 units down.
Therefore, the graph that you are looking for must be a parabola that is opened upwards and has its vertex in the point (0,-4).
Then, the correct option is C. And the solution is:
Related Questions
What is the approximate distance between two points with coordinates (3,5) and (-4, -8)? Round your answer to the nearest hundredth.
Answers
Answer:
15 (rounded) 14.7 (not rounded)
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
use the distance formula
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((-4-3)^2 + (-8-5)^2)
d = √((-7)^2 + (-13)^2)
d = √(49 + 169)
d = √218
d = 14.76 ≅ 15
Which equation represents a proportional relationship that has a constant of proportionality equal to 2?
y = x + 2
y = x/2
y = 2 x
y = 2
pls hurry
Answers
A North American river otter wants to cross the North Saskatchewan river. It can swim at a speed of 2.75 m/s. In that location, the distance directly across the river is 45.0 m and the current velocity is 2.5 m/s.
a) How much time does the otter take to get to the other side, if it points directly across the river?
Answers
Answer:
time=16.3 sec
Step-by-step explanation:
let time taken be x
speed=distance/time taken
2.75=45/x
2.75x=45
x=45/2.75
x=16.36
x=16.3 seconds
The time taken is 16.3 seconds.
What is speed?Speed = Distance/Time
This informs us how slowly or quickly an object moves. It defines the distance traveled divided by the time brought to cover the distance. Speed stands directly proportional to distance and inversely proportional to Time.
Let x be the time taken
speed = distance/time taken
2.75 = 45/x
2.75x = 45
x = 45/2.75
x = 16.36
x = 16.3 seconds
Therefore, the time taken is 16.3 seconds.
To learn more about speed
https://brainly.com/question/21904438
#SPJ2
Find measure of angles B, E, D and C and the length of BC.
Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.
Answers
Answer:
< B = 180-30-65=85°
< E = 85°
< D = 30°
< C = 65°
BC = 20/35 × 28 = 16
Answer:
<D = 30
< C = 65
<B = <E = 85
16 = BC
Step-by-step explanation:
ABC ~ Triangle DEF
<A = <D = 30
< C = <F = 65
Since they are similar triangles
A+ C + B = 180 since the angles of a triangle = 180
30+65+B =180
95+ B = 180
<B = 180 -95 = 85
<B = <E = 85
The triangles are similar so the sides are proportional
AB BC
---- = ---------
DE EF
20 BC
---- = ---------
35 28
Using cross products
20*28 = 35 BC
Divide each side by 35
20*28/35 = 35/35 BC
16 = BC
The question's attached in the file; I tried solving it in 4 different ways and ended up confusing myself more and more each time.
Answers
(x+3)² = (16+x-3) (x-3)
x²+6x+9=(x+13)(x-3)
x²+6x+9=x²+10x-39
6x-10x=-39-9
-4x=-48
x = 12
=> NM = 12+3 = 15
Which equation represents a relationship where y is a nonlinear function
of x?
O x = -6y
O y = IxI- 3
O 3x + 4y = 8
O 4x - 3y + 2 = 8x-5y+12929
Answers
Step-by-step explanation:
if you use the online graphing calculator it will help you
Add the following complex numbers:
(4-2i) + (12 + 7i)
O A. -8 + 9i
O B. 16 + 9i
O C. 16 + 5i
O D. -8 + 5i
Answers
Answer:
option c
Step-by-step explanation:
(4 - 2i) + (12 + 7i)
multiply the brackets first
4 - 2i + 12 + 7i
combine like terms
16 + 5i
Answer:
O C. 16+5i
Step-by-step explanation:
=(4+12) + (7i-2i)
=16+5i
[tex](5^{3})^{-3}[/tex] pls
Answers
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]( { {5}^{3} })^{ - 3} \\ \\ which\:means \:that \: {5}^{3}\: is \:multiplied \:thrice\: with\: itself\\ \\ = {5}^{3 \times - 3} \\ \\ = {5}^{ - 9} \\ \\= \frac{1}{ {5}^{9} } \\ \\ = \frac{1}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5} \\ \\ = \frac{1}{1953125} [/tex]
Note:-
[tex]( { {a}^{m} })^{n} = {a}^{m \times n} [/tex]
[tex]{a}^{ - m} = \frac{1}{ {a}^{m} }[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
these two questions plzz help mee
Answers
2^5×8^4/16=2^5×(2^a)4/2^4=2^5×2^b/2^4=2^c
A=
B=
C=
Please I'm gonna fail math
Answers
9514 1404 393
Answer:
a = 3, b = 12, c = 13
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
(a^b)^c = a^(bc)
___
You seem to have ...
[tex]\dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)[/tex]
_____
Additional comment
I find it easy to remember the rules of exponents by remembering that an exponent signifies repeated multiplication. It tells you how many times the base is a factor in the product.
[tex]2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}[/tex]
Multiplication increases the number of times the base is a factor.
[tex](2\cdot2\cdot2)\times(2\cdot2)=(2\cdot2\cdot2\cdot2\cdot2)\\\\2^3\times2^2=2^{3+2}=2^5[/tex]
Similarly, division cancels factors from numerator and denominator, so decreases the number of times the base is a factor.
[tex]\dfrac{(2\cdot2\cdot2)}{(2\cdot2)}=2\\\\\dfrac{2^3}{2^2}=2^{3-2}=2^1[/tex]
I need help with first question ??
Answers
Answer:
Slope = 3
Step-by-step explanation:
Slope formula
(y2 - y1) / ( x2 - x1)
Where the x and y values are derived from the coordinates
Choose any two given ordered pairs and plug them into the formula
The points chosen may vary but the points I chose were (1,3) and (2,6)
( Note that ordered pairs are written as (x,y))
Next we want to define the variables
x1 = 1
x2 = 2
y1 = 3
y2 = 6
Finally we plug in the values into the slope formula
(6-3) / (2-1)
Subtract top values
3/(2-1)
Subtract bottom values
3/1
Simplify
slope = 3
please help !!! 5 minutes !!!
Answers
Answer:
Step-by-step explanation:
2 is the correct answer
Answer:
4
Step-by-step explanation:
The answer is the LCM of all the denominators (Least Common Multiple)
All the denominators: 4, 2, 4
The LCM of this set of denominators is 4.
The answer is 4.
Check: [tex]-\frac{3}{4} m-\frac{1}{2} =2+\frac{1}{4} m[/tex]
[tex]-\frac{3}{4} m(4)-\frac{1}{2}(4) =2(4)+\frac{1}{4} m(4)==-3m-2=8+m[/tex]
How many kittens weigh at least 3/8 of a pound please help fast
Answers
The clock has a diameter of 22 inches. What is the circumference of the clock?
Answers
Answer:
The circumference is 44
Answer:
34.56
Step-by-step explanation:
C = 2πr = 2 · π · 5.5 ≈ 34.55752
which of the following functions best describes this graph
Answers
Answer:
D
Step-by-step explanation:
when x=2,6 then y=0
when y=12 then x=0
only applies for D
justin surveyed his freibds about how mant pets they have use the data in the table to find the median mode and range
Answers
Answer:
where is the data from the table?
My grades depend on this question! Please help! Brainliest will be given out for this!
Answers
Answer:
2006
Step-by-step explanation:
1 + 2(1027) + 6 + 7 - 8 • 9 + 10
1 + 2054 + 6 + 7 - 72 + 10
2006
help please! the question is in the picture below for reference when answering! thank you so much!
Answers
Answer:
(a, 0) I give 50% credit to the answer in the comments
Step-by-step explanation:
Because it is isosceles, we must have the same y distance, (a) as an x distance
So we must have (a) in the x coordinate
The correct option is number 2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
pls help me ill give brainliest and no links ty!<3:)
Answers
T is the midpoint of PQ
PT=TQ
5x+7 = 7x-7
2x= 14
x= 14/2
x= 7
PT = 5(7)+7 = 42
what is the slope of the line that passes through (2,0) and (1,0)??
Answers
Answer:
The slope would be 0
Step-by-step explanation:
used a graphing calculator
hope this helps
please help!!
find x
Answers
X = 90 - 32
X = 58 degrees
Answer:
since the square indicates the angle is a right angle ( 90 ° )
then x = 90 - 32
x = 58 °
The measures of the angles of a triangle are shown in the figure below. Solve X.
Answers
Answer:
x = 106º
Step-by-step explanation:
There are 180º in every triangle
x = 180 - 32 - 42
x = 106º
Answer:
x= 106 degree
Step-by-step explanation:
x + 42 + 32=180 degree (sum of interior angles of a triagle is 180 degree)
x + 74 = 180
x = 180 - 74
x = 106 degree
Find the are of the segment
Answers
Answer:
[tex](9\pi - 18)cm^2[/tex]
Step-by-step explanation:
To find the area of this section of the triangle, we will have to find the area of the sector, and then subtract the area of the triangle. To first find the area of the sector of the circle. Remember that the sector of a circle can be found using a proportion of angles. Since there is an angle of 90 degrees in the center. We will take that and divide it by 360 degrees, which is an entire circle. [tex]\frac{90}{360} = \frac{1}{4}[/tex], so the sector is one-quarter of the entire circle. Now find the area of the entire circle which will be [tex]\pi r^{2}[/tex]× [tex]\frac{1}{4}[/tex], where r is 6 since it is the radius of the circle. So therefore the area of the sectore will be a quarter of 36[tex]\pi[/tex], which is 9[tex]\pi[/tex].
Now you must find the area of the triangle with side length 6. Remember, this is an isosceles triangle with sides length of 6 because two of the sides are radii. Also, remember that this is a 90 degree triangle, so the area of the triangle is simply [tex]\frac{6*6}{2}[/tex], which is 18 cm^2.
Now to find the area of just the yellow segment, just take the area of the sector we found, and subtract the area of the triangle. Therefore, the answer is [tex](9\pi - 18)cm^2[/tex]
Hope this helped.
write the set builder form of
{1, 1/4, 1/9, 1/16, 1/25}
Answers
can someone help with this ASAPP <3, giving brainlist to anyone who answers
Answers
Answer:
1.60x + 1.75y is less than or equal to 10
Step-by-step explanation:
the strawberries cost 1.60
x pounds times 1.60 for the total cost of strawberries
for the raspberries it would be 1.75 times y
total cost or 1.60x + 1.75y must be less than ten or equal to because she can not spend more than that
there are 3 liters of orange juice at a school party. 10 students want to drinkable of the orange juice, and they all want to get exactly the same amount. how much orange juice can each get? help noooowwww
Answers
Answer:
Each student gets 0.3 liters or 300 milliliters of orange juice.
Step-by-step explanation:
3 liters = 3000 milliliters
3L/10 or 3000ml/10 = 0.3 L or 300 ml
(18)Calculate the volume of this shape
Answers
Answer:
108 cm cubed
Step-by-step explanation:
(1/2 of length•height)•width
(1/2 of 6•4)•9
(1/2 of 24) •9
12•9
108
In Hackensack High School, the ratio of students to teachers is 9 to 2. If there
are 90 teachers at the High School, how many students are there?
Answers
I guess the answer is 405.
Because the value of 1 is 45 and 2×45 =90
9×45=405.
Hope it helps you:)
Step-by-step explanation:
students : Teachers
9 : 2
? : 90
students = 9 x 90 ÷ 2
students = 405
Which letter in the word HAPPY has an order 2 rotational symmetry?
H
A
P
Y
Answers
Answer:Option 1) H
Step-by-step explanation:
Answer:
its H
Step-by-step explanation:
EDG 2021
If an relationship is proportional what is the missing value from the table?
Answers
Explanation :
In the first row of the table, we find that the -2 is the change, and in the third row -6 is the change.
Using this, we can find that the second row should have -4 subtracted from 16.
We know this because from looking at the changes from the first and second row, the differences multiply by two, as the rows increase. So -2 multiplied by 2 is -4, and 16 subtract 4 is 12.