Answers
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Explanation:
If we plugged (x,y) = (0,8) into the first inequality, then we get
y < x^2+6
8 < 0^2+6
8 < 0+6
8 < 6
which is false. So we can rule out choice A.
----------------
Trying choice B leads us to
y < x^2+6
2 < 4^2+6
2 < 16+6
2 < 22
That last statement is true, so the first inequality is true for (x,y) = (4,2)
Let's try the other inequality
y > x^2-4
2 > 4^2-4
2 > 16-4
2 > 12
That's false. Since one of the inequalities is false (it doesn't matter which one), this means the entire system is false. We cross choice B off the list.
----------------
Now onto choice C
You should find that y < x^2+6 becomes -4 < 10 after plugging in (x,y) = (-2,-4). Since -4 < 10 is true, we move onto the next inequality.
The inequality y > x^2-4 becomes -4 > 0 after plugging in those mentioned x,y values. The inequality -4 > 0 is false.
We cross choice C off the list.
----------------
The only thing left is choice D. It has to be the answer.
Let's find out if we get true inequalities when plugging in (x,y) = (2,6)
y < x^2+6
6 < 2^2+6
6 < 10 ... true
and
y > x^2-4
6 > 2^2-4
6 > 4-4
6 > 0 .... also true
Both inequalities are true, so the entire system is true. Therefore, (x,y) = (2,6) is one of the infinitely many solutions to this system.
Choice D is confirmed as the answer
----------------
Refer to the diagram below. I've graphed the two dashed boundary curves and the shaded region between. This region is above the y = x^2-4 curve, and below the y = x^2+6 curve. So we're ignoring the stuff above the y = x^2+6 curve.
Points A through D represent the four answer choices in the order given. We see that point D is the only point in the shaded region, so that visually confirms we have the correct answer.
Note: points on the dashed boundaries do not count as solutions.
Related Questions
If sin θ +cosec θ = 2 then sin2θ+ cosec2θ is equal to
a) 1 b) 4
c) 2 c) 9
Answers
Answer:
C
Step-by-step explanation:
We are given that:
[tex]\sin \theta +\csc \theta = 2[/tex]
And we want to find the value of:
[tex]\sin^2\theta + \csc^2\theta[/tex]
From the first equation, we can square both sides:
[tex](\sin \theta + \csc \theta)^2=(2)^2[/tex]
Square:
[tex]\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4[/tex]
Let csc(θ) = 1 / sin(θ):
[tex]\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4[/tex]
Simplify:
[tex]\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4[/tex]
Therefore:
[tex]\sin ^2\theta + \csc^2\theta =2[/tex]
Our answer is C.
A triangle has a angle of x, 40 and 30 what is the angle of x
Answers
Sum of interior angles of a triangle = 180°
x+40+30= 180°
x+ 70=180
x= 180-70
x= 110°
Answer:
x = 110
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
x + 40° + 30° = 180°
x + 70° = 180° ( subtract 70° from both sides )
x = 110°
v = u + at
solve for a
Answers
Step-by-step explanation:
v = u + at
u+at=v
at = v-u
a = v-u
t
Hope this helps you :)
I need help finding the function.
Answers
Answer:
-2
Step-by-step explanation:
I hope it helps
To find the slope of the trend line below Reilly chose the points (1,80) and (2,30). explain whether the points she chose will help her write the correct equation of the line and find the equation of a trend line
Answers
Answer:
We can't see the graph
Step-by-step explanation:
I kinda need help with this
Find the mean:40,13,49,53,35
Find the Range:40,13,49,53,35
Find the median:40,13,49,53,35
Answers
Answer:
mean: 38
range: 27
median: 40
Step-by-step explanation:
mean: 40+13+49+52+35 / 5
range: 40 - 13
median : 40
Answer:
Mean = 38
Range = 40
Median = 40
Step-by-step explanation:
Arrange the terms in ascending order :
13, 35 , 40 , 49 , 53
[tex]Mean = \frac{40 + 13 + 49 + 53 + 35}{5} = 38[/tex]
[tex]Range = {53 - 13} = 40[/tex]
[tex]Median = \ the \ middle \ term = 40[/tex]
determine the volume of a cube with a side length of 7.5m
Answers
Answer:
V≈421.88
Step-by-step explanation:
11. In the diagram which of the following statements is true?
Angles 6 and 8 are supplementary
Angles 1 and 5 are corresponding
Angles 3 and 7 are vertically opposite
Angles 2 and 4 are alternate
Answers
Answer:
Angles 1 and 5 are corresponding
Math help please and thank you :)
Answers
Answer:
173
Step-by-step explanation:
Area of dirt in the flower bed = area of flowerbed - area of 3 trapezoids
Area of flowerbed:
The flowerbed is in the shape of a parallelogram
The area of a parallelogram can be calculated by multiplying the base length times the height
Base length = 20ft
Height = 10ft
Area of flowerbed = 10 * 20 = 200ft^2
Area of rockbeds
The rockbeds are in the shape of trapezoids
The area of a trapezoid can be calculated using this formula
A = (a + b)/2 * h
Where a and b = bases and h = height
The rockbeds of base lengths of 2 and 4 and have heights of 3
So area of rockbeds = (4 + 2)/2 * 3
4 + 2 = 6
6 / 2 = 3
3 * 3 = 9
We then multiply that by 3 ( because there are three rockbeds )
9 * 3 = 27
Finally we subtract the areas
200 - 27 = 173
The area of a square is 81 cm squared find its perimeter
Answers
Answer:
the answer is 36
Step-by-step explanation:
Helppppppp please ASAP
Answers
And your length for GH is 58.9
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Answers
Answer:
5050 = 225f + 125p
If p = 17 this month, then, f = 13
Step-by-step explanation:
Kiri owns a coworking space that has two primary types of memberships, full time and part-time. In order to pay her bills each month (rent on the building, electricity, internet, and so on) she needs to make $5050. Full-time memberships (f) cost $225 per month, and part-time memberships (p) cost $125 per month.
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Total cost = $5050
cost of full-time memberships = $225
number of full time members = f
cost of part-time memberships = $125
number of part-time members = p
Total cost = cost of full-time memberships * number of full time members + cost of part-time memberships * number of part-time members
5050 = 225f + 125p
If p = 17 this month,
5050 = 225f + 125p
5050 = 225f + 125(17)
5050 = 225f + 2,125
5050 - 2,125 = 225f
2,925 = 225f
f = 2,925/225
f = 13
number of full time members = f = 13
If p = 17 this month, then, f = 13
Two towns, A and B, are 198 kilometres apart.
a) Kenan travelled by car from A to B at an average speed of 66km/h.
How long did his journey take?
11
hours?
Answers
Answer:
t = 3 hours
Step-by-step explanation:
The distance between A and B is 198 km
Kenan traveled by car from A to B at an average speed of 66km/h
We need to find the time taken to complete the journey. It can be solved as follows :
[tex]v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{198}{66}\\\\t=3\ h[/tex]
So, the required time is equal to 3 hours.
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution set of this problem?
O (,-21)
O (--,-21]
O [-21,700)
O (21,+0)
Answers
In the system of equations , x represents .... ( please answer 12a and 12b )
Answers
Answer:
x = cost of each t-shirt
y = cost of each sweatshirt
Step-by-step explanation:
Given equation:
2x + 2y = 26 (1)
x + 3y = 33 (2)
From (2)
x = 33 - 3y
Substitute x = 33 - 3y into (1)
2x + 2y = 26 (1)
2(33 - 3y) + 2y = 26
66 - 6y + 2y = 26
- 6y + 2y = 26 - 66
-4y = -40
y = -40/-4
y = 10
Substitute y = 10 into (2)
x + 3y = 33 (2)
x + 3(10) = 33
x + 30 = 33
x = 33 - 30
x = 3
Where,
x = cost of each t-shirt = $3
y = cost of each sweatshirt = $10
A line's y-intercept is 1, and its slope is -5. What is its equation in
slope-intercept form?
help please
Answers
Slope intercept form is y=mx+b
m is slope and b is the y-intercept
As general equation of y-intercept is y=mx +b
Hope it helps!
Find the mean of the data.
The number of trophies won by
each team in the district.
1, 3, 1, 5, 7, 8, 10
Mean: [? ] trophies
Answers
Answer:
5
Step-by-step explanation:
explanation:
1 + 1 + 3 + 5 + 7 + 8 + 10= 35
35 divided by 7 (how many number you added up to get 35)
and then 35 divided by 7 is 5
hope this helped :))
(HELP) A glass jar contains 5 red, 7 green, 9 blue and 11 yellow marbles. If a single marble is picked at random from the jar, what is the probability of it being a blue marble? *
1/11
5/18
9/32
5/12
Answers
Answer:
Find the volume of this prism.
?
Answers
Answer:
Step-by-step explanation:
She made the -2(6) as a positive 12. it should've been a negative 12 because a negative multiplied by a positive is a negative.
A box shown below is to paint blue except the bottom. What is the area of the surface, and square inches, that will be covered with the paint?
Answers
Answer:
186
Step-by-step explanation:
Your entire surface area is
216
the area of the rectangle on the bottom is 30
substract 30 from 216
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP
Answers
Tony sold t-shirts and hats at the festival. He made a $4 profit for each t-shirt he sold. He also made a profit of $34 from selling hats. If he made a total profit of $106, how many t-shirts did he sell?
Answers
Answer:
18 T-shirts
Step-by-step explanation:
$4×18= $72 $72+$34=$106
106 - 34 = 72
72 / 4 = 18
Two similar triangles, the perimeter of the first is 74cm and the side lengths of the other one are 4.5cm 6cm and 8 cm. Find the length of the longest side of the first triangle.
Answers
Answer:
the longest side of the first triangle is 32 cm
Step-by-step explanation:
Given;
dimension of the smaller triangle = 4.5cm 6cm and 8 cm.
the longest side of this smaller triangle = 8 cm
Perimeter of the first triangle = 74 cm
let the increase in dimension of the similar first triangle = x
the longest side of the first triangle = 8x
4.5x + 6x + 8x = 74
18.5x = 74
x = 74/18.5
x = 4
the longest side of the first triangle = 8 x 4 = 32 cm
I need help please PLEASE PLEASEEEEEEEE
Answers
Answer:
Step-by-step explanation:
At a show, there are 19 adults, 45 teenagers, and 36 children.
What is the probability that a person chosen at random from the audience is not a teenager?
Answers
Answer:
55% or 0.55 or 11/20
Step-by-step explanation:
probability the person chosen is an adult or child out of all
so 19+36/19+36+45
55/100
The probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
What is probability?
Probability is a measure of happening or non happening of the outcomes of the random experiment.
Probability formulaP(E) = Total number favorable of outcomes/ Total number of outcomes
Where,
P(E) is the probability of an event.
According to the given question.
Total number of adults in the audience = 19
Total number of teenagers in the audience = 45
Total number of children in the audience = 36
Total audience = 19 + 45 + 36 = 100
Now, the probability that the selected person is teenager = [tex]\frac{45}{100} = \frac{9}{20}[/tex]
Therefore,
The probability that a selected person is not a teenager
= [tex]1 -\frac{9}{20}[/tex]
= [tex]\frac{11}{20}[/tex]
Hence, the probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].
Find out more information about probability here:
https://brainly.com/question/11234923
#SPJ2
2) Three people shared some money in a
ratio of 4:3:5. The second person got
£21 as a result. How much money did
they share?
Answers
Answer:
£ 84
Step-by-step explanation:
Let :-
Total amount be x .Given ratio :-
4 : 3 : 5 .→ Sum of ratios = 4 + 3 + 5 = 12 .
According to Question :-
→ 3/12 × x = £21
→ x = £21 × 12/3
→ x = £ 84 .
Answer:
£84.
Step-by-step explanation:
There are 4 + 3 + 5 = 12 parts.
The second person got 3 parts so we can write:
3/12 x = 21 where x is the required amount of money
x = 21 * 12/3
= 21 * 4
= £84.
Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown.
Answers
Answer:
16.6 inches
Step-by-step explanation:
using the pythagorean theorem which is a^2 + b^2 = c^2 you can add 9^2 + 14^ together to get 277 and when you find the square root of 277 you get 16.6
1. For each relation, state
i) the domain and the range
ii) whether or not it is a function, and justify your answer
Answers
Answer:
A and C are functions.
The domain is x and the range is y
Step-by-step explanation:
Each x - value can have only one y -value
Function= unique x-values
Y can be the same answer but the X has to be different
Which expression is equivalent to (x^4/3 x^2/3)^1/3
?
x^2/9
x^2/3
x^8/27
x^7/3
Answers
Answer:
X^2/3
Step-by-step explanation:
the union of 2 sets is all the elements of both set's, excluding the common elements true or false
Answers
Answer:
true
Step-by-step explanation:
AUB=A+B-(A∩B)