Answer:
The quadratic equations and their solutions are;
9 ± √33 /4 = 2x² - 9x + 6.
4 ± √6 /2 = 2x² - 8x + 5.
9 ± √89 /4 = 2x² - 9x - 1.
4 ± √22 /2 = 2x² - 8x - 3.
Explanation:
Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.
We have to solve all of the five equations to be able to match the equations with their solutions.
2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.
2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.
2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.
2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .
Step-by-step explanation:
Answer with Explanation:
To qualify as a function, each x value may not have more than 1 Y value.
This rules out A, B, and D.
The answer is C.
Why is A incorrect? -5 (the x value) has more than one y value so it is wrong.
Why is B incorrect? 9 (the x value) has more than one y value so it is wrong.
Why is D incorrect? -7 (the x value) has more than one y value so it is wrong.
You can also use the vertical line test to graph these pairs. Then, test by drawing a vertical line through the graph. If the vertical line goes through more than 1 pair, it is not a function.
The diagram shows the position
of three towns represented by
letters A, B and C.
NA
B is 7 km from A on a bearing of 037°
C is 8 km from B on a bearing of 140°
Find the bearing of C from A.
Give your answer correct to 1 decimal place.
Answer:
Step-by-step explanation:
143º I’m not sure
The bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
If we extend the line NA and NB
As we can see, line NA and NB are parallel and cut by transversal AB
The angle NBA and BAN' will be equal.
Angle BAN' = 180 - 37 = 143 degree = angle NBA
Angle CBA = 360 - 140 - 143
Angle CBA = 77 degree
Now, applying cos law:
b² = a² + c² - 2ac[cos B]
b² = (8)² + (7)² - 2(8 x 7 x cos77)
b = 9.37 km
To find the measure of the angle A applying sin law:
(sinA)/a = (sinB)/b
sinA = (axsinB)/b
sinA = (8xsin77)/9.37
A = 56.3⁰
Bearing of town C from town A:
α = A + 37⁰
α = 56.3⁰ + 37⁰
α = 93.3⁰
Thus, the bearing of town C from town A is 93.3 degree if the B is 7 km from A on a bearing of 037° C is 8 km from B on a bearing of 140°
Learn more about the angle here:
brainly.com/question/7116550
#SPJ2
8(__+__)=8m+8n Please help,
Answer: m and n
8(m+n)= 8m + 8n
A runner runs at an average speed of 9 m/s for 20 seconds
How far did the runner run in metres?
Answer:
The answer would be 180 meters.
Step-by-step explanation:
We are told the runner runs at 9 m/s for 20 seconds.
Since they run 9 meters per second, all we have to do is multiply 9 by 20, which will give us 180 meters.
9 x 20 = 180
If , then what is mto the nearest degree?
Answer:
70 degrees
Step-by-step explanation:
If cosm<A = 342/1000, we are to find the value of a
Take arccos of both sides
cosm<A = 342/1000
cosm<A = .342
arccos(cosm<A) = arccos(0.342)
m<A = arccos(0.342)
m<A = 70 degrees
Hence the measure of m<A is 70 degrees
x + y = -6 The slope is and the y-intercept is
The circumference of a circle is 9.31cm. Find the length of the diameter. Give your answer rounded to 2 DP.
Answer:
2.96cm
Step-by-step explanation:
C= 2x Pi x Radius
9.31 = 2 x Pi x Radius
9.31/2 = Pi x Radius
4.655 = Pi x Radius
4.655/3.14 = Radius
1.4824840764331210191082802547771 = Radius
Now, that you have worked out the radius which is half the diameter
Radius + Radius = Diameter
1.4824840764331210191082802547771 + 1.4824840764331210191082802547771 = 2.964968153
= 2.96cm to 2 d.p
You can double check because C= 2 x Pi x Radius
9.31 = 2 x 3.14 x 1.482
Gloria rides a bike 8 miles in 40 minutes. Nanette rides a bike 5 miles in 30 minutes. Who bikes faster? Explain.
Answer:
Nanette
Step-by-step explanation:
Nanette.
Gloria's rate = 40/8 = 5mph
Nanette's rate = 30/5 = 6mph
Hope that helps!
Answer:
gloria
Step-by-step explanation:
40 divided by 8 = 5
30 divided by 5 =6
Remove all perfect squares from inside the square root.
\sqrt{30b^5}=
Answer:
The answer is b=0 or b=9.085603
Answer:
[tex]b^{2} \sqrt{30b}[/tex]
Step-by-step explanation:
The graph shows the number of cycles of a crosswalk signal during the day and during the night.
Answer:
Step-by-step explanation:
a). Since, both the lines are passing through origin (0, 0) y-intercept of the lines are zero.
For day periods,
Let the equation is, y = mx
Since, this line passes through (2, 80),
80 = 2m
m = 40
Therefore, equation for the day periods will be,
y = 40x
For night periods,
Let the equation is, y = mx
Since, this lines passes through (3, 90),
90 = 3m
m = 30
Therefore, equation of the line is,
y = 30x
b). For x = 6 hours,
Number of cycles in the day (y) = 40 × 6 = 240
Number of cycles in the night (y) = 30 × 6 = 180
Therefore, difference in the cycles in day and night = 240 - 180 = 60
4(y – 3) = y – pls help me on this question
Answer:
y=4
Step-by-step explanation:
can someone help me with this real quick?
Answer:
11. A) 6x = 13
Step-by-step explanation:
11. Subtract 10 from both sides to make it equal 6x=13
12. For #12... None of the answers seem right? If you distribute and subtract, it should be
-4x + 44 = 66 then
-4x = 22...
Sorry if this didn’t help much, I know that 11 is right though ;)
is it a, b, c, or d?
Answer:
The answer is B. 4,7.5,8
Step-by-step explanation:
Becouse A and C Both of them is Right-angled triangle and D is Obtuse triangle
MULTIPLE CHOICE
What is your output when x is -5?
A. 1
B. -9
C. -1
D. 9
Identify the scale factor if the length of a model train engine is 3 feet and the length of the engine itself is 24 feet
Answer:
jHshshshhzysjshhddbhxsbsshshsgshyskinsdisbandedsAnswer:
it should be 1 over 8
Step-by-step explanation:
Are the two triangles similar? How do you know?
Answer:
Yes the triangles are similar.
if you look at Angle C it's 60° and F is also 60°
60 + 67 is 127
127 + 53 is 180° which is the amount a triangle is. (assuming that E is 67°)
Similar triangles may or may not be congruent triangles.
The two triangles are similar.
From the figure, we have:
[tex]\mathbf{\angle F \cong \angle C = 60}[/tex] ----- Angles F and C are corresponding
[tex]\mathbf{\angle D \cong \angle G = 53}[/tex] ----- Angles D and G are corresponding
[tex]\mathbf{\angle H \cong \angle E = 67}[/tex] ----- Angles H and E are corresponding
Add the above angles.
[tex]\mathbf{Sum = 60 + 53 + 67}[/tex]
[tex]\mathbf{Sum = 180}[/tex]
The sum of the angles equal 180 degrees,
Hence. the triangles are similar triangles.
Read more about similar triangles at:
https://brainly.com/question/14926756
uHhhhhHHHhHhHhHh heLp?
Answer and Step-by-step explanation:
Use the Pythagorean theorem to solve.
Plug in the value 5 for a, and 6 for b. c will stay as c.
[tex]a^{2}+ b^{2}= c^{2} \\\\\\5^{2}+6^{2}= c^{2} \\\\\\25 + 36= c^{2} \\\\\\61 = c^{2} \\\\\\\sqrt{61} = c[/tex]
5 squared is equal to 25, and 6 squared is equal to 36.We add those together to get 61.
We then square root both sides of the equation to get c by itself, resulting in the square root of 61.
The square root of 61 becomes 7.810249676
c = 7.8102
To check, you would multiply that number by itself, then you will get 61. With the rounded version, you would get close to 61.
If you got 7.08 as an answer, then multiplying it by itself results in 50.1264, which isn't close to 61.
#teamtrees #PAW (Plant And Water)
which one is right, i need to knowwwwwwwwwwwwwwwww!!!!!!!!!!!!!!!!!!!1
Answer:
what is the question?
Step-by-step explanation:
lol
I'll give brainliest
Answer:
its 2/3
my bad
what is first three common multiples of 4,9,and 12
Answer:
36 is the answer of this question
Answer:
Methods to Find LCM of 4, 9 and 12
Least Common Multiple of 4, 9 and 12 is the smallest number, which is exactly divisible by all of them without any remainder.
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36.
Multiples of 9 = 9, 18, 27, 36.
Multiples of 12 = 12, 24, 36.
PLEASE HELP.. A LOT OF POINTS GIVEN!! JUST PLEASE GIVE ME THE RIGHT ANSWER.
Question 1 :
The graph of f(x)=x2 was transformed to create the graph of g(x)=(x−4)2.
Which statement describes this transformation?
A) a horizontal shift to the right 4 units
B) a horizontal shift to the left 4 units
C) a vertical shift up 16 units
D) a vertical shift down 16 units
Question 2 :
The graph f(x)=x2 was transformed to create the graph g(x)=−(x2)2.
Which statement describes this transformation?
A) a reflection over the y-axis and a vertical stretch
B) a reflection over the x-axis and a horizontal stretch
C) a reflection over the x-axis and a vertical stretch
D) a reflection over the y-axis and a horizontal stretch
Answer:
A) a horizontal shift to the right 4 units
Step-by-step explanation:
As you can see in the image we simply went 4 unites to the right.
someone help pls?!? ill give brainliest
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Similar Triangles.
Since here we can see that, similar triangles different by size of the side by 0.5 ration,
hence,the value of x = 0.5 times of MN
hence, x = 5/2
so the mixed fraction representation is given as,
[tex]2 \times \frac{1}{2} [/tex]
mixed fraction ration is 2(1/2)
===> hence option is B.)
5 donuts and 2 cups of hot Chocolate costs 24$. 2 donuts and 3 cups of hot chocolate costs 14$.How much does each donut and each cup of hot chocolate cost
Answer:cost of each donut =$4
and cost of each cup of hot chocolate =$2
Step-by-step explanation:
Step 1
Let donuts be represented as d
and cups of hot chocolate be rep as c so that
5 donuts and 2 cups of hot Chocolate costing 24$ will be expressed as
5 d+ 2 c= 24
And 2 donuts and 3 cups of hot chocolate costing 14$ will be expressed as
2d +3 c= 14
Step 2
Using elimination method,Multiply equation 1 by 3 and equation 2 by 2
15d+ 6c= 72----equation 3
4d+ 6c= 28-----equation 4
Subtracting equation 4 from equation 3 gives us
11 d=44
d= 44/11
d= 4
To find c, using equation 1
5 d+ 2 c= 24
5 x 4+ 2c=24
20+2c=24
2c=24-20
2c=4
c=4/2 =2
cost of each donut =$4
and cost of each cup of hot chocolate =$2
Find the measure of one of the interior angles of a
regular polygon with 12 sides.
A 30°
B 165°
C 150°
D 2160°
please help me!!
basic Radicals
Answer:
C)
Step-by-step explanation:
[tex]x = \frac{\sqrt{a}}{ \sqrt{b}} = \sqrt{\frac{a}{b}}\\\\[/tex]
Both sides take square
[tex]x^{2}= ( \sqrt{\frac{a}{b}})^{2}=\frac{a}{b}[/tex]
If Amy has two apples and drops one, how many does she have then?
Answer:
one
Step-by-step explanation:
Answer:
one
Step-by-step explanation:
one
1. Two students went to McDonald's. They each bought the same snack, which included a shake
and a burger. The shakes cost $2 each. In total, they spent $12.
Part A: Enter an equation to represent this equation. Let x represent the cost of one burger.
Part B: Enter the cost of one burger.
Answer:
12-2=10 b=10
Step-by-step explanation:
Could someone possibly help me with this question? Thanks
Answer:
[tex]12\sqrt{2}[/tex]
good luck, hope this helps :)
What graph represents the inequality? Whoever answers first gets brainliest!
Answer:
B
We know the circle is closed
How can you write the expressiHow can you write the expression 7(b – 2) in words?
A.
two subtracted from the quotient of seven divided by b
B.
seven added to difference of b minus two
C.
the quotient of seven divided by b minus two
D.
two subtracted from seven times b
E.
the product of seven and the difference of b minus two
on 7(b – 2) in words?
Answer:
E.
the product of seven and the difference of b minus two
Answer:
The correct answer would be E
Step-by-step explanation:
the product of seven and the difference of b minus two
I did the test and got it right.
Becca joins a gym that charges a $150 starting fee, plus $50 per month she will quit before she’s payed the total of $1000, How many months can she work out at the gym?
Answer:
I believe it 13
Step-by-step explanation:
150+50= 200 then 100= two months so i added up till i got 13 weeks