Answers
=================================================
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
A sector with an area of \goldE{48\pi,\text{cm}^2}48πcm 2 start color #a75a05, 48, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{16,\text{cm}}16cmstart color #ca337c, 16, start text, c, m, end text, end color #ca337c. What is the central angle measure of the sector in radians? Choose 1 answer: Choose 1 answer:
Answers
Answer:
3/8 π radians
Step-by-step explanation:
The Area of a sector when then central angle is in radians = 1/2r² θ
Where
θ = central angle = ?
r = 16 cm
Area of the sector = 48πcm²
Hence
Central angle = Area of a sector ÷ (1/2r²)
= 48πcm² ÷ (1/2 × 16²)
= 48πcm² ÷ 128
Central angle = 3/8π radians
Therefore, Central angle = 3/8π radians
A woman is trying to remove holiday decorations from the roof of her house by climbing a ladder. The height of her house is 24 feet, and the distance she has to travel on the ladder is 30 ft. How far away is the ladder from the house?
Answers
Answer:
18 ft
Step-by-step explanation:
We are to determine the base given the hypotenuse and length.
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
30² = 24² + b²
900 = 576 + b²
b² = 900 - 576
b² = 324
square root = 18
Find the surface area
Answers
Step-by-step explanation:
so for this one u do
[tex]15 \times 9 + 9 \times 4 + 15 \times 4[/tex]
231 the times it by 2 for the both sides
231×2=462 cm2
hope this make sense :)
Karl is purchasing a $205,000 home with a 30-year mortgage at 5.5%. Because he is not making a down payment, PMI in the amount of $97.50/month is required for the first 2 years of the loan. Based on this information, what is the total cost of this loan? A. $421,369.20 B. $444,923.03 C. $423,042.96 D.$452,092.10
Answers
The total loan payment is $1,024,050.
What is Mortgage Loan?Another name for mortgage loans is "loans against property." A mortgage loan can be used to refinance real estate or to buy, build, or remodel a home. Getting a new loan for a piece of property while the old one is still being paid off is referred to as refinancing. Typically, it is done to obtain a loan with better terms.
We have,
The 30-year mortgage loan of $205,000 at 5.5% interest rate
We know, the total cost of this loan can be calculated as
L=LM+PMI
So, LM=$205,000 x (1+0.055[tex])^{30[/tex]
LM=$205,000 x 4.984
LM = $1,021,710
Now, the PMI over 24 months
= $97.5 x 24
= $2,340
So, the total loan payment is:
= $1,021,710 + $2,340
= $1,024,050
Learn more about mortgage loan here:
https://brainly.com/question/29538161
#SPJ5
Use the replacement set {3, 4, 9} to find the solution of the equation below.
3n−18=9
Answers
Answer:
[tex]n=9[/tex]
Step-by-step explanation:
[tex]3n-18=9[/tex]
[tex]3n+18=[/tex] +18
[tex]3n=27[/tex]
[tex]3(9)=27[/tex]
[tex]n=9[/tex]
Solve 3n – 5p + 2n = 10p for n.
Answers
Answer:
n = 3p
Step-by-step explanation:
3n−5p+2n=10p
5n−5p+5p=10p+5p
5n=15p
5n/5 = 15p/5
n = 3p
Answer:
3n+2n=10p+5p
5n=15p
Divide both sides by 5
n=3p
At a pet store, Rhonda paid $55 for 8 dog bowls and 6 bones. Kelly paid $32.50 for 2 dog bowls and 9 bones. Determine the cost of one dog bowl (x) and one bone (y). Write a system of linear equations that models this situation.
Answers
Answer:
8d + 6b = 55
2d + 9b = 32.50
Step-by-step explanation:
let 'd' = # dog bowls
let 'b' + # bones
Rhonda: 8d + 6b = 55
Kelly: 2d + 9b = 32.50
we can multiply Kelly's equation by -4 to eliminate the 'd' terms:
Kelly: -4(2d + 9b) = 32.5(-4)
-8d - 36b = -130
now add the above equation to Rhonda's equation:
-8d - 36b = -130
+ 8d + 6b = 55
-30b = -75
b = 2.50
now we can use either equation and substitute 2.5 for 'b' to find 'd'
2d + 9(2.5) = 32.5
2d + 22.5 = 32.5
2d = 10
d = 5
Answer the question pleaseeeee
Answers
NECESITO AYUDA URGENTE...
1- Ordena en forma descendente el siguiente polinomio con respecto a la
variable n. Luego identifica el término independiente:
6n 3 + 7n 4 -2n 2 -5 + 9n 5
2- Completa el polinomio para que cada término tenga el mismo grado
absoluto:
5x 4 y 3 – 3x 6 ___ + 5x 2 4__ + 7___ y 2 + 8y 7 - 6
3- Observa el siguiente polinomio e identifica cuáles son los términos
semejantes:
-8 + 3m 3 n – 4m 2 n + 7mn 2 -11nm 3 + 5 + 6m 2 n
4- Evalúa la veracidad de cada afirmación de la siguiente afirmación:
El grado absoluto de un polinomio no puede ser 1: ___________
5- El grado absoluto de un polinomio se obtiene sumando los grados relativos
de las variables: _________
_
6- El grado absoluto de un binomio puede ser cero: _________
_
7- Si el grado relativo de una variable es tres, entonces, el grado absoluto es
un número mayor que tres: __________
8- Si el grado absoluto de un término es uno. Entonces, el polinomio tiene una
sola variable: ___________
9- Completa el polinomio, luego ordénalo en forma descendente:
15x 4 + 5x 6 + 3x 3 + 2x 2 + 8 + +
10- Cuál es el valor numérico del siguiente polinomio cuando la x = -2 ; y= -3
: 3x 2 y – 5xy 2 + x -3y + 2
Answers
Answer:
Step-by-step explanation:
1- Order in descending order the following polynomial with respect to the
variable n. Then identify the independent term:
[tex]6n^3 + 7n^4 - 2n^2 - 5 + 9n^5[/tex]
The independent term is - 5.
3- Look at the following polynomial and identify what the terms are
similar:
[tex]- 8 + 3m^3 n - 4m^2n + 7mn^2 - 11nm^3 + 6 m^2 n[/tex]
The similar terms are + 3m^3 n and - 11 nm^3 and
- 4 m^2 n and 6 m^2 n
a rectangle has the height of n^3 + 4n^2 and the width of n^3 + 5n^2
Answers
Answer:
2^3
Step-by-step explanation:
which of the following is an experiment,? A. Rolling a pair die. B.Rolling two pair dice twice. C.Tossing a coin. D.None of these
Answers
Step-by-step explanation:
Hint : we will check for each option whether it is an experiment or not by using the concepts of probability first we will check then if a coin is tossed then it is an experiment or not ? then we will check that if a dice is rolled is it an experiment or not and then we will repeat the same process for choosing a marble from a jar
complete step by step answer and event is a set of outcomes of an experiment to which probability is assigned as take an example when we and I the possibility of 5 appearing on the die is an event if for tossing a coin we do not know the result when a coin is tossed in can give any result whether it will be a head or tails so this is an example for a random experiment if a six-sided dice will be rolled then we do not know what is about to come there result can be anything from 126 so it is also an example for random experiment choosing a marble from a jar is also an experiment because we are choosing one marble from the jar and experiment is a work in which a result can be anything hence option d is the correct option not probability is how likely something is about to happen when a coin is tossed there are two possibility outcomes heads or tails show the probability of an outcome 1
( number of ways it can happen )÷
( total number of outcomes)
so when a coin is tossed the total number of outcomes are to solve the probability of a current head is 1/2
2 m − 3 ≤ 5 m + 15 solve this equation
Answers
Answer:
m≥ -6Step-by-step explanation:
Answer:
m ≥-6
Step-by-step explanation:
that is the procedure
A line segment joins points P(-1, -7) and Q (7, 3) Determine the length of PQ to 1 decimal place?
This unit is square roots and Pythagorean Therorum.
Answers
Answer:
12.8 units
Step-by-step explanation:
PQ=(X2-X1)²+(Y2-Y1)²
=(7-(-1))²+(3-(-7)
=164
then find square root of 164 that gives you 12.8units
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary): 261. 256, 251.... Find the 50th term.
Answers
Answer:
50th term = 16
Step-by-step explanation:
the expression (x^2-1)^-2/3 is equivalent to
Answers
Answer:it’s x
Step-by-step explanation:
Sry if I’m wrong
13 14 14 17 18 20 20 what's the mode?
Answers
Answer:
mode is 14,20
if you dont know mode is the frequency of the numbers
Step-by-step explanation:
Answer:
14 & 20
Step-by-step explanation:
the number that appears the most
a bucket contains 3 1/2 gallon of water. If Marie adds 5 gallons more, how many gallons of water will there be in all?
Answers
Answer:
8 1/2
because 3 + 5= 8+ 1/2= 8 1/2
Which is the graph of g(x) = 2x – 1 + 3?
Answers
Answer:
Your question is not very clear, hope I get what you want
Step-by-step explanation:
2x-1+3
=2x+2
=2(x+1)
Answer:The graph in the attached figureStep-by-step explanation:we have[tex]g(x)=2^{x-1}+3[/ tex
factoring polynominaly
Answers
Answer:
Most of the question is missing. If you could type out the rest, we might be able to help you.
Please answer properly.
Answers
Answer:
Step-by-step explanation:
$15 is a constant value while $5 change depending by the hours.
We can write this expression to find the total cost:
5r + 15
part b
1) substitute r with 3
5 * 3 + 15
2) solve the expression
15 + 15 = $30
(7^2*5^6)^4 equivalent expression
Answers
This is what you get when you simplify the problem.
Which one of the following is a correct equation?
Answers
Answer:
B. cos 41° = [tex]\frac{x}{19}[/tex]
Step-by-step explanation:
cos of an angle is the adjacent side of the angle over the hypotenuse.
Answer:
Answer is a
[tex]{ \boxed{ \bf{ \cos( \theta) = \frac{adjacent}{hypotenuse} }}} \\ { \tt{ \cos(41 \degree) = \frac{x}{19} }} \\ \\ { \boxed{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}} \\ { \tt{ \sin(41 \degree) = \frac{ - }{19} }}[/tex]
f(x) = x +1 g(x) = x^2 - 3
find f 3
find gf3
Answers
1. Solve for f(3)
Let f(x) = f(3).
Substitute 3 for x
f(3) = 3 + 1
= 4
Therefore f(3) = 4
Solve for gf(3)
Substitute f(3) into g(x).
f(3) = 4
gf(3) = 4² − 3
= 13
Therefore gf(3) = 13
Type in the value of y.
If x = 7, then y =
Answers
Explanation:
The rule says "whatever x is, add 1 to it to get y"
So for instance, if x = 3, then y = x+1 = 3+1 = 4
Now if x = 7, then y = x+1 = 7+1 = 8
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Given that,
[tex]1 + 1 = 2 \\ 2 + 1 = 3 \\ 3 + 1 = 4 \\ 4 + 1 = 5...[/tex]
So from this we can infer that, [tex]\large\bold{ x + 1 = y}[/tex]
Now,
[tex]x = 7 \\ y= \: ?[/tex]
Use the rule ⎆ [tex]\large\bold{ x + 1 = y}[/tex]
[tex]x + 1 = y \\ 7 + 1 = y \\ 8 = y[/tex]
✐ The value of y is 8.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Please help test tomorrow everything you need is in the photo below
Answers
Answer:
yes
Step-by-step explanation:
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.
Which are equivalent equations? Select two correct answers.
Answers
Step-by-step explanation:
The formula for the lateral area of a right cone is :
LA = rs
Where
r is the radius of the base and s is the slant height of the cone
Equivalent expression,
[tex]r=\dfrac{LA}{s}[/tex]
or
[tex]s=\dfrac{LA}{r}[/tex]
Hence, this is the required solution.
In this exercise we have to use the formula for volume of the cone and we find that:
[tex]s=\frac{LA}{r}[/tex]
The formula for the lateral area of a right cone is :
LA = rs
Where:
r is the radius of the base s is the slant height of the coneEquivalent expression is:
[tex]s=\frac{LA}{r}[/tex]
See more about volume at brainly.com/question/1578538
Does anyone know the answer to this?
Answers
Answer:
3
Step-by-step explanation:
Answer:
The answer is number 2
Step-by-step explanation:
Since the price of a quarter is 25 cents we put the .25 it next to the Q and since dimes are worth 10 cents we put the .10 next to the D. D + Q should equal 30 since that is the total number of coins and the other should equal 4.80
roatate triangle p 90* clockwise about the point (2,-1)
Answers
Answer:
hope this helps
Step-by-step explanation:
What is 1/6
as a decimal?
Give your answer rounded to 3 decimal places.
Answers
0.167 I believe!
<3
I'm sure you'll do great!
Answer:
0.167(rounded 3dp)
Step-by-step explanation:
100/6=16.6666...
[tex]\frac{16.666}{100}[/tex]= [tex]\frac{1}{6}[/tex]
[tex]\frac{16.666}{100}=(into decimal)0.167[/tex]
Triangle PQR is similar to triangle XYZ. The length of PQ is one-half the length of XY. THe length of RP is 2 cm. Which proportion can be used to find the length of ZX?
Answers
Answer:
[tex]ZX = 4cm[/tex]
Step-by-step explanation:
Given
[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex]
[tex]PQ = \frac{1}{2}XY[/tex]
[tex]RP = 2cm[/tex]
Required
Find ZX
[tex]\triangle PQR[/tex] similar to [tex]\triangle XYZ[/tex] implies that, the following sides are similar
[tex]PQ \to XY[/tex]
[tex]QR \to YZ[/tex]
[tex]RP \to ZX[/tex]
To find ZX, we make use of the following equivalent ratio
[tex]PQ : XY = RP : ZX[/tex]
Where
[tex]PQ = \frac{1}{2}XY[/tex]
[tex]RP = 2cm[/tex]
So, we have:
[tex]\frac{1}{2}XY : XY = 2cm : ZX[/tex]
Express as fraction
[tex]\frac{\frac{1}{2}XY }{ XY }= \frac{2cm }{ ZX}[/tex]
[tex]\frac{1}{2}= \frac{2cm }{ ZX}[/tex]
Make ZX the subject
[tex]ZX = 2 * 2cm[/tex]
[tex]ZX = 4cm[/tex]
