y+2>9
-2 on both sides
y>7
-y+3<8
-3 on both sides
-y<5
y is still negative so simply divide both sides by -1
y>-5
The inequality y > 7 represents the solution set of the given compound inequality.
What is inequality?
Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given is the following compound inequality.
- y + 3 < 8 and y + 2 > 9
We have -
- y + 3 < 8 and y + 2 > 9
Now, first we will solve inequality (1)
- y + 3 < 8
- y + 3 < 8
- y + 3 - 3 < 8 - 3
- y < 5
y > 5
Solving inequality (2)
y + 2 > 9
y + 2 - 2 > 9 - 2
y > 7
We have two possible solution sets -
y > 5 and y > 7
To satisfy both the solution sets, the inequality y > 7 will be the final solution of the given compound inequality.
Therefore, the inequality y > 7 represents the solution of the given compound inequality.
To solve more questions on inequality, visit the link below-
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What is the prime factorization for 180?
A. 4 · 5 · 9
B. 2 2 · 5 · 9
C. 2 · 9 · 10
D. 2 2 · 3 2 · 5
Answer:
2^2 x 5 x 9.
Step-by-step explanation:
This will give you the answer because when multiplying all of this you will get 180. Answer B.
Jen bought 5 CDs for $57.50 What was the unit price ?
Answer:
$11.50
Step-by-step explanation:
Use simple division
[tex]57.5/5=11.5[/tex]
Answer:
$130.00
Step-by-step explanation:
ASAP
please help me with this
The opening of a tunnel that travels through a mountainside can be modeled by [tex]y = - \frac {2}{15} (x - 15)(x + 15)[/tex], where x and y are measured in feet. The x-axis represents the ground.
a. Find the width of the tunnel at ground level.
b. How tall is the tunnel?
Answer:
(a) 30 feet
(b) 30 feet.
Step-by-step explanation:
Given that the opening of a tunnel that travels through a mountainside can be modeled by
[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.
[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]
[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]
(a) At the ground level, [tex]y=0[/tex]
So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.
For, [tex]y=0[/tex], the extreme points of the tunnel.
[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]
[tex]\Rightarrow (x-15)(x+15) =0[/tex]
[tex]\Rightarrow x= 15, -15[/tex]
So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].
Hence, the width of the tunnel at the ground level
[tex]= | x_1 - x_2 |[/tex]
[tex]=|15-(-15)|[/tex]
[tex]=30[/tex] feet.
(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.
First determining the value of x for which the slope of the graph is zero.
[tex]\frac{dy}{dx}=0[/tex]
From equation (i),
-2x=0
[tex]\Rightarrow x=0[/tex]
And [tex]\frac{d^2y}{dx^2}= -2[/tex]
which is always negative, so at x=0 the value of y is maximum.
Again, put x=0 in equation (i), we have
[tex]y=\frac{-2}{15}{0^2-225}[/tex]
[tex]\Rightarrow y=30[/tex] feet.
Hence, the tunnel is 30 feet tall.
PLZ HELP ME I NEED THIS ASAP PLZZZ
Your parents have been advised to save 5% of their income for your college education, which would include money for housing, tuition, books, and fees. How much would your parents have saved in one year, following the recommended 5%, if they had an average household income of $48,948? Show your work
Answer:
2447.40
Step-by-step explanation:
48,948 * .05 = 2447.40
Answer:
2447.40 that the answer
Identify the factored form of each polynomial. 4r + 11x + 6 4x + 10x + 6 11. 4r + 14x +6 (4x+3)(x+2) :: (x+3)(4x + 2) :: (2x+3)(2x + 2)
Answer:
1) 4x^(2)+11x+6 Factored--> (4x+3) (x+2)
2) 4x^(2)+10x+6 Factored--> (2x+3)(2x+2)
3) 4x^(2)+14x+6 Factored--> (x+3)(4x+2)
Step-by-step explanation:
Factor: 4x^(2)+11x+6 (step by step)
1) Split the second term (11x) into two terms
4x^2 + 8x + 3x + 6
2)Factor out common terms in the first two terms, then in the last two terms.
4x(x + 2) + 3(x + 2)
3) Factor out the common term x + 2
(x + 2) (4x + 3)
Repeat the above steps for similar questions!
100 points if you do this correctly. Just simply tell me where the words need to be in struggling ;ccc (i can't give brainliest so reward is a bumblebee).
Answer:
one: perpendicular
2 : hypotenuse
Step-by-step explanation:
what is 4%5*7-2= to?
what is the answer for -9=-x-5
Answer:
x=4
Step-by-step explanation:
-9=-x-5
-9+5=-x
-4=-x
x=4
Gabriela asistió al buen fin y compró a crédito un refrigerador de $8,500.50, un televisor de $3,500.50, una computadora de $6,999.00 y una lavadora de $4,999.00. ¿A cuánto asciende la deuda de Gabriela?
Answer:
23,999
Step-by-step explanation:
Un refrigerador de $8,500.50
Un televisor de $3,500.50
Una computadora de $6,900.00
Una lavadora de $4,999.00
8,500.50 + 3,500.50 + 6,999.00 + 4,999.00 = 23,999.00
What is the change in elevation from -87.2 Feet to 33.6 Feet?
Answer:
120.8 feet
Step-by-step explanation:
pls help meh
i will give brainlyest
Answer:
75
Step-by-step explanation:
Use order of operations to solve this.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction.
First, do 20 x 4.
[tex]80 - 100 / 20[/tex]
Then, divide 100/20.
[tex]80 - 5[/tex]
= 75
Russ and Vickie are trying to solve this problem: There are 139 students taking buses to the museum. If each bus holds 24 students, how many buses will they need?
Vickie says the students need 5 buses. Russ says they need 6 buses. Who is correct?
They will need
_______buses.
So,
_____ is right.
Answer:
5 busses and vicke is right
Step-by-step explanation:
Jessica completed 20 haircuts in 8 hours. On average how many haircuts per hour did Jessica do?
Answer:
two and a half
Step-by-step explanation:
Factor completely 4x^2-81
Answer:
(2x - 9)(2x + 9)
Step-by-step explanation:
4x^2 - 81 = (2x - 9)(2x + 9)
Answer:
(2x+9)(2x-9)
Step-by-step explanation:
kind of simple actually
4x^2-81=(2x+9)(2x-9)
Simplify the expression
Answer:
14
Step-by-step explanation:
5+(3*3)
5+9
14
A child needs to take 1/2 tablespoons of medicine per day in 4 equal doses. How much medicine is in each dose?
PLEASE HELP
Answer:
1/8 tablespoons
Step-by-step explanation:
Since the child needs to take 1/2 tablespoons off medicine per day in 4 equal doses, you will divide the 1/2 tablespoons into 4 equal doses, so you need to divide by 4.
You can do this by multiplying 1/2 by 1/4.
[tex]\frac{1}{2} * \frac{1}{4} = \frac{1}{8}[/tex]
Answer:
it would be 1/8
Step-by-step explantion:
simply divide
1/2÷4
=1/8
(that should be right)
being a rectangle is a necessary condition for being a square
Answer:
false
Step-by-step explanation:
all rectangles are squares not all squares are rectangles
Help me ASAP major grade
Answer:
$5.58
Step-by-step explanation:
Because divide 12 by 67:
67 ÷ 12 = 5.58
5.58 is the answer
Hope this helped! Pls Brainliest!
Answer:
$5.58
Step-by-step explanation:
$67.00÷12=$5.58
Hope this helps!
Given the equivalent expressions below, which property is being applied?
(2+n)+7 and 2+(n+7)
Get off my Property
Commutative Property
Distributive Property
Associative Property
Answer:
Distributive property
Find the total earnings based on the given information.
Base: $22,000, Total Sales: $99,000, Commission: 3%
Enter the correct answer in the box.
Answer:
$24,970
Step-by-step explanation:
22,000+(99,000•0.03)=22,000+2,970=24,970
Please select the best answer from the choices provided
A
B
C
D
Answer:
1. Is -3, or answer choice C
The snooze buttonon your alarm clock activates the alarm every 5 minutes. The snooze button on your cell phone activates the alarm every 7 minutes. Both alarms activate at 7:00 A.M. You hit each snooze button as each alarm activates. At what time are both alarms activated again?
Answer: 7:35 a. M
Step-by-step explanation:
Given that:
Snooze on alarm = 5 minutes
Snooze on cellphone = 7 minutes
If both activates at 7:00 a. M
Time at which both will activate again ;
Obtain the Lowest Common Multiple of 5 and 7
_5 __|5 ___|7
_7__ |1 ___|7
____ |1 ___| 1
Lowest common multiple = (5 * 7) = 35
Hence, both alarms will sound together again after 35 minutes = 7:00a.m + 35 minutes = 7:35 A. M
The sum of 3 consecutive even numbers is 72 what is the smallest of the three numbers
Answer:
23
Step-by-step explanation:
x + (x + 1) + (x + 2) = 72
3x + 3 = 72
3x = 69
x = 23
check answer:
23 + 24 + 25 = 72
HELP ME TAKING TEST!
A line passes through the points (−6,−8) and (−3,−7) . What is the equation of the line in Slope-Intercept Form?
Answer:
Try out this app called Conects. it is really helpful
A line passes through the points (–3, –4) and
(6, 2).
what is the x intercept of this line
Answer:
3,0
Step-by-step explanation:
use the slope formula and slope-intercept form to find
x and y intercepts
Answer:3
Step-by-step explanation:Use your brain
Create a polynomial with two terms and a degree of 4
hey mate☺️☺️ here's your answer......
4x'4 + 1
What is the slope of the line through (-1,8) and (3,-4) ?
Answer:
m = −3
Step-by-step explanation:
Use the slope formula to find the slope m .
What is the answer to this 3x-15= ax+7
Answer:
x=11
Step-by-step explanation:
Han wants to build a dog house. He makes a list of the materials needed:
At least 60 square feet of plywood for the surfaces
At least 36 feet of wood planks for the frame of the dog house
Between 1 and 2 quarts of paint
Han's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, and paint costs $8 per quart.
write inequalities to represent the material constraints and cost constraints in this situation.
Answer:
a) [tex]p \geq 60\,ft^{2}[/tex], b) [tex]w \geq 36\,ft[/tex], c) [tex]1\,qt \leq q \leq 2\,qt[/tex], d) [tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex]
Step-by-step explanation:
In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:
a) At least 60 square feet of plywood for the surface
Let [tex]p[/tex] the surface area of plywood, measured in square feet, and the inequation is:
[tex]p \geq 60\,ft^{2}[/tex] (Eq. 1)
b) At least 36 feet of wood planks for the frame of the dog house
Let [tex]w[/tex] the total length of wood planks, measured in feet, and the inequation is:
[tex]w \geq 36\,ft[/tex] (Eq. 2)
c) Between 1 and 2 quarts of paint
Let [tex]q[/tex] the total capacity of paint, measured in quarts, and the inequation is:
[tex]1\,qt \leq q \leq 2\,qt[/tex] (Eq. 3)
d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.
Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let [tex]p[/tex], [tex]w[/tex] and [tex]q[/tex] the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:
[tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex] (Eq. 4)
Write an inequality to represent each constraint(material and cost)
Inequality to represent cost constraints is 0.70p + 0.10pw + 8pa ≤ 65Plywood:
plywood ≥ 60 square feet
Planks:
planks ≥ 36 feet
Paints
1 quarts ≤ paints ≤ 2 quarts
Inequality to represent cost constraint
Plywood = $0.70
planks of wood = $0.10
paint costs $8
Total cost = $65
0.70 × p + 0.10 × pw + 8 × Pa ≤ 65
0.70p + 0.10pw + 8pa ≤ 65
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