Answers
You want x alone, so subtract 4 from each of the 3 parts.
[tex] -3 \le x + 4 \le 13 [/tex]
[tex] -3 - 4 \le x + 4 - 4 \le 13 - 4 [/tex]
[tex] -7 \le x \le 9 [/tex]
[tex] x \ge -7 [/tex] and [tex] x \le 9 [/tex]
Related Questions
What is the distance between the points (9, 32) and (9, 17) in the coordinate plane?
Answers
In Veronica’s art class 5 out of 9 people speak Spanish. What decimal number shows what part of the class speaks Spanish?
Answers
Hope that helps
_________________________________________________
Note:
_________________________________________________
" 5 out of 9" = 5/9 = (5*10) / (9*10) = 50/90;
Divide side by "9" :
(50÷9) / (90÷9) ;
(5.555555555555555... ) / (10) =
___________________________________________________
" 0.55555555555555...... "
___________________________________________________
Note: To check our answer; consider the "reverse order" of the problem:
"Write the decimal number, "0.5 (with a repeating bar over the "5")" ; as a fraction:
Let x = 0.555555555555555....... ;
10x = 5.555555555555555555......" ;
Note: We consider "10x" ; since, the number of "decimals being repeated" ends in the "tenths" place.
_______________________________________________________
So:
_______________________________________________________
10x = 5.55555555555555555555555555555555.......................
– x = 0.55555555555555555555555555555555.......................
_______________________________________________________
9x = 5.0000000000000000000000000000000...................... ;
_______________________________________________________
→ 9x = 5 ;
Divide EACH SIDE of the equation by "9" ;
to isolate "x" on one side of the equation; & to solve for "x" :
→ 9x / 9 = 5 / 9 ;
to get:
x = 5/9 ; which is "5 out of 9" .
_____________________________________________
The answer makes sense!
_____________________________________________
Which of the following are monomials?
Check all that apply.
A. x - y
B. 9x
C. 24 + 2x2
D. 2x + 12
E. x20
F. 13
Answers
A monomial has only one term
What is the correct answer for number 9
Answers
You have to simplify the equation. So combine like terms. 10n-4n=6n. 81-9=72. The simplified equation is 6n+72. That’s answer C.
I hope this helps!
Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the second map is 5 cm.
(a) 1 cm on the first map represents 3.5 km on the actual trail. What is the scale factor from the map to the actual trail? What is the length of the actual trail according to the first map?
(b) A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 6 mm. What is the scale factor from the first map to the second map? What are the side lengths of the landmark on the second map?
please show your work.
Answers
Map : Actual
1cm : 3.5km
1cm : 3500m
1cm : 350 000 cm
Scale Factor:
1 : 350 000
--------------------------------------------------------------------------------------------
Answer: Scale factor for map 1 to actual is 1: 350 000
--------------------------------------------------------------------------------------------
1 cm : 3.5 km
8cm : 3.5 x 8 km
8cm : 28 km
--------------------------------------------------------------------------------------------
Answer: The actual trail according to the first map is 28km
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(b)
First Map : Second Map
8cm : 5 cm
1cm : 0.625 cm
Scale Factor
1 : 0.625
--------------------------------------------------------------------------------------------
Answer: The scale factor from map 1 to map 2 is 1: 0.625
--------------------------------------------------------------------------------------------
Map 1 : Map 2
1mm : 0.625mm
3mm : 3 x 0.625mm
3mm : 1.875mm
Map 1: Map 2
1mm : 0.625mm
4mm : 0.625 x 4 mm
4mm: 2.5mm
Map 1:Map 2
1mm : 0.625mm
6mm : 0.625 x 6 mm
6mm : 3.75mm
--------------------------------------------------------------------------------------------
Answer: The side length on the second are 1.875mm, 2.5mm and 3.75mm
--------------------------------------------------------------------------------------------
Selena is buying an audio system for her car. She can choose among 3 types of stereos, 4 kinds of speakers, and 2 kinds of amplifiers. Which describes how Selena can show her options?
Answers
Answer:
Step-by-step explanation:
d
Complete the rectangle above. What are the coordinates of the missing vertex?
Select one:
A. (7, 3)
B. (7, 4)
C. (6, 3)
D. (3, 7)
Answers
Go over 7 (first), and then go up 3 (second) to plot the last point.
Pythagorean Theorem
Is this a right triangle?
a = 15 b = √207 c = 12√3
*Please Explain!!*
Answers
Plug in values.
15^2+sqrt(207)^2=(12sqrt(3))^2
225+207=432
432=432
Yes, this is a right triangle.
---
Hope this helps!
NEED HELP!!!!!!
For the following geometric sequence find the recursive formula and the 6th term in the sequence.
{36, 12, 4, ...}
Answers
2nd term = 12
3rd term = 4
recursive formula
q = 12/36 = 1/3
If you use this formula and continue going down, you'll eventually find that the 6th term will be 4/27.
Hope that helps!
The 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series.
The 6th term of the series is calculated as:-
1st term = 36
2nd term = 12
3rd term = 4
The recursive formula is,
q = 12/36 = 1/3
The 6th term is,
[tex]a_n = a_1( r )^{n-1}[/tex]
[tex]a_6=36 ( \dfrac{1}{3})^5=\dfrac{4}{27}[/tex]
Therefore, the 6th term is ( 4 / 27 ) and the recursive formula is q = 1/3.
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For the level 3 course, exam hours cost twice as much as workshop hours, workshop hours cost twice as much as lecture hours. How much are lectures per hour?
Answers
Cost of lectures = $7.33 per hour
ExplanationLet [tex]e[/tex] the cost of the exam hours
Let [tex]w[/tex] be the cost of the workshop hours
Let [tex]l[/tex] be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
[tex]e=2w[/tex] equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
[tex]w=2l[/tex] equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
[tex]3e+24w+12l=528[/tex] equation (1)
Now, lets find the value of [tex]l[/tex]:
Step 1. Solve for [tex]l[/tex] in equation (3)
[tex]3e+24w+12l=528[/tex]
[tex]12l=528-3e-24w[/tex] equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
[tex]12l=528-3e-24w[/tex]
[tex]12l=528-3(2w)-24w[/tex]
[tex]12l=528-6w-24w[/tex]
[tex]12l=528-30w[/tex] equation (5)
Step 3. Replace equation (2) in equation (5) and solve for [tex]l[/tex]
[tex]12l=528-30w[/tex]
[tex]12l=528-30(2l)[/tex]
[tex]12l=528-60l[/tex]
[tex]72l=528[/tex]
[tex]l=\frac{528}{72}[/tex]
[tex]l=\frac{22}{3}[/tex]
[tex]l=7.33[/tex]
Cost of lectures = $7.33 per hour
c. Which volume-to-surface-area ratio would be better for an ice cube¡X the lowest possible or the highest possible?
Answers
When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slow melt and cool the drink for as long as you can.
If your ice cube is mostly surface area with less volume, it will melts to quickly and water down your drink. If your ice cube has a higher ratio of volume to surface area, it will stay solid longer and chill your drink longer.
Solve for x.
6/59=3/x
Answers
[tex]\dfrac{6}{59}=\dfrac{3}{x}\qquad\text{cross multiply}\\\\(6)(x)=(3)(59)\\\\6x=177\qquad\text{divide both sides by 6}\\\\\boxed{x=29.5}[/tex]
The sum of four consecutive integers is -22
Answers
The four integers you're looking for are
-4
-5
-6
-7
This is because they add up to -4 + -5 + -6 + -7 = - 4 - 5 - 6 - 7 = - 22
x+1= 2nd integer
x+2= 3rd integer
x+3= 4th integer
Add the above integers and set equal to -22.
x + (x+1) + (x+2) + (x+3)= -22
combine like terms
4x + 6= -22
subtract 6 from both sides
4x= -28
divide both sides by 4
x= -7
ANSWER:
x= -7
x+1= -6
x+2= -5
x+3= -4
Hope this helps! :)
How many ways are there to choose a card from a deck of cards (52 cards in a deck) and roll a regular 6-sided number cube? 58 52 156 312
Answers
so the answer is 312
line XY is perpendicular to line CD at D. Which conclusion can be drawn?
Answers
Answer:
measure angle XDC = 90 degrees
Explanation:
The term "perpendicular" implies that the angle formed between the two lines is 90 degrees.
These two lines do not have to be equal in length, they just intersect forming a 90-degree angle.
Comparing the explanation with the given choices, we would find that the only correct choice is:
measure angle XDC = 90 degrees
Hope this helps :)
given the geometric sequence with the first three terms shown as (2,10,50..) answer the following questions:
Write a recursive definition for the sequence
What is the 10th term of the sequence?
Answers
[tex]\bf a_n = 2(5)^{n-1}[/tex]
The 10th term is:
[tex]a_{10} = 2(5)^{10-1}[/tex]
[tex]a_{10} = 2(5)^9[/tex]
[tex]\bf a_{10} = 3906250[/tex]
Final answer:
The recursive definition for the given geometric sequence is an = 5an-1, with a1 = 2. Using the geometric formula to find the 10th term, we calculate the 10th term to be 3906250.
Explanation:
The given sequence is a geometric sequence, in which each term after the first is found by multiplying the previous term by a constant ratio. In this case, the ratio is obtained by dividing the second term by the first term. Therefore, the recursive formula for the given geometric sequence is an = 5 × an-1, with the first term a1 = 2.
To find the 10th term of the sequence, we use the formula: an = a1 × r(n-1), where r is the common ratio and n is the term number. Substituting the given values we get a10 = 2 × 5(10-1) = 2 × 59.
Calculating this we find that the 10th term of the sequence is 2 × 1953125 = 3906250.
Fill in the blanks to solve the Pollution Problem.
• What do you want to know?
When the pollution level in the lake will reach 50 tons
• What do you know?
The exponential growth function that models the
problem is P(t) = 3 • e^0.0866t, where P(t) = the number
of tons of ________ in the lake t ________ after 1970.
Answers
If the "Pollution problem" has to do with tons of pollution and the way that amount increases over the years, then the descriptive words might be
.. (pollution, years)
_____
If you actually want to know when the pollution level will be 50 tons, this can be solved a couple of ways.
1) graph the function
.. f(x) = 3*e^(0.0866x) -50
and find the value of x that makes f(x) = 0.
That value is x = 32.487, so the pollution level will reach 50 tons in 2002.
2) Find t that satisfies P(t) = 50.
.. 50 = 3*e^(0.0866t)
.. 50/3 = e^(0.0866t) . . . . .divide by 3 to isolate the exponential term
.. ln(50/3) = 0.0866t . . . . . take the natural log
.. ln(50/3)/0.0866 = t ≈ 32.487
Write the answer in terms of a year number.
.. The pollution level will reach 50 tons in 1970+32 years, 2002.
Mr. Macady has an old cylindrical grain silo on his farm that stands 25 feet high with a diameter of 10 feet. Mr. Macady is planning to tear down the old silo and replace it with a new and bigger one. The new cylindrical silo will stand 30 feet high and have a diameter of 15 feet.
A. What is the volume of the old silo
B. What is the volume of the new silo
C. How much greater is the volume of the new silo than the old silo
Answers
The volume is the space the silos hold.
Here are the answers:
A. 1962.5 square feet
B. 5298.74 square feet
C. 3335.25 square feet
The volume of the old silo is 1962.5 cubic feet, the volume of the new silo is 5298.75 cubic feet and about 3336.25 greater is the volume of the new silo than the old silo.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Mr. Macady has an old cylindrical grain silo on his farm that stands 25 feet high with a diameter of 10 feet.
h=25 feet and r =5 feet
Volume of cylinder = πr²h
=3.14×5²×25
=3.14×25×25
Volume =1962.5 cubic feet.
Now let us find the volume of new cylinder which has height 30 feet and diameter is 15 feet
Radius =15/2
r=7.5
Volume = 3.14× (7.5)² × 30
=3.14×56.25× 30
V=5298.75 cubic feet
Now let us find how much the new volume of silo is greater than old silo.
Difference = 5298.75 - 1962.5
=3336.25
Hence, the volume of the old silo is 1962.5 cubic feet, the volume of the new silo is 5298.75 cubic feet and about 3336.25 greater is the volume of the new silo than the old silo.
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If it takes one hour to fill a pool with 50 ft^3 of water, how many hours will it take to fill a pool that measures 10 ft by 8 ft with a depth of 5 ft?
Answers
Answer:
8 hours
Step-by-step explanation:
10 x 8 x 5 = 400. 400 / 50 = 8. So it will take 8 hours to fill a pool with 400ft3
One positive number is 5 times another number . The difference between the two numbers is 80, Find the numbers.
The two numbers in increasing order are ________ and ______
Answers
Define the numbers:
---------------------------------------------------------------------------------------------------
Let x be one number.
One number = x
Other number = 5x
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Construct the equation:
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5x - x = 80
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Combine like terms:
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4x = 80
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Divide by 4 on both sides:
---------------------------------------------------------------------------------------------------
x = 20
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Find the 2 numbers:
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One number = x = 20
Other number = 5x = 5(20) = 100
---------------------------------------------------------------------------------------------------
Answer: The two numbers in increasing order are 20 and 100.
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Find the surface area of the sphere to the nearest square unit. Use a calculator.
the inside is 2in
A.13 in.2
B.50 in.2
C.6 in.2
D.3 in.2
Answers
.. A = 4πr^2
For a radius of 1 in, the area is
.. A = 4π(1 in)^2 = 4π in^2 ≈ 13 in^2 . . . . . selection A
20x+13=53
solve for x, right?? Help??
Answers
20x=40
20x/20=40/20
x=2
Which modified box plot represents the data set?
10,12,2,4,24,2,7,7,9
Answers
Answer with explanation:
The Data Set is→ 10,12,2,4,24,2,7,7,9
Arranging the data in ascending order
2,2,4, 7,7,9,10, 12, 24
Number of observation is odd,
So, Median
[tex]\frac{9+1}{2}=5^{th} Observation[/tex]
5th Observation = 7
[tex]Q_{1}[/tex]
=First Quartile of data set that is from first variate to Median value
={2,2,4,7,7}
So, [tex]Q_{1}=4[/tex]
[tex]Q_{3}[/tex]
=Third Quartile of data set that is from last variate to Median value
={7,9,10,12,24}
So, [tex]Q_{3}=10[/tex]
Minimum value in data set = 2
Maximum value in data set = 24
Plotting the Box plot
Option C , is correct Box plot.
Answer: The answer is C
Step-by-step explanation:
Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.
Answers
The correct answer is 58 viable solutions.
To model the given situation, we need to define variables, create inequalities, and then solve the system of inequalities.
Let x = the number of pens, and y = the number of pencils.
Given information:
- The total number of writing utensils must be less than or equal to 25.
- The number of pencils must be greater than or equal to the square of (3 less than the number of pens).
Step 1: Create the first inequality for the total number of writing utensils.
x + y ≤ 25
Step 2: Create the second inequality for the condition on the number of pencils.
y ≥ (x - 3)^2
Step 3: Solve the system of inequalities.
We can substitute different values of x into the second inequality to find the corresponding values of y.
For x = 1, y ≥ (-2)^2 = 4
For x = 2, y ≥ (-1)^2 = 1
For x = 3, y ≥ 0^2 = 0
For x = 4, y ≥ 1^2 = 1
For x = 5, y ≥ 2^2 = 4
...
Substituting these values into the first inequality, we get:
1 + y ≤ 25 (y ≥ 4)
2 + y ≤ 25 (y ≥ 1)
3 + y ≤ 25 (y ≥ 0)
4 + y ≤ 25 (y ≥ 1)
5 + y ≤ 25 (y ≥ 4)
...
Therefore, the viable solutions are:
(x, y) = (3, 0), (3, 1), (3, 2), ..., (3, 22)
(x, y) = (4, 1), (4, 2), ..., (4, 21)
(x, y) = (5, 4), (5, 5), ..., (5, 20)
There are a total of 22 + 20 + 16 = 58 viable solutions.
30% of the employees at a company picnic ate a hot dog for lunch. If 18 employees ate a hotdog, how many people were at the picnic?
A) 20
B) 30
C) 60
D) 90
Answers
60•30%=18
3%=0.3
0.3*60=18.
Hope this helped☺☺
which sets of side lengths could form a triangle? Choose all that apply A. 3 centimeters,4 centimeters,9 centimeters B. 3 centimeters, 6 centimeters,9 centimeters C. 4 centimeters, 5 centimeters, 9 centimeters D. 4 centimeters, 6 centimeters, 9 centimeters E. 5 Centimeters, 5 centimeters, 9 centimeters
Answers
To solve this question we will have to make use of the triangle inequality which states that "the sum of the lengths of any two sides of a triangle must be greater than the length of the third side".
Let us now use this inequality to check Part A to Part E.
Part A: [tex] 3+4\ngtr9 [/tex] therefore, triangle is not possible
Part B: [tex] 3+6\ngtr9 [/tex] therefore, triangle is not possible
Part C: [tex] 4+5\ngtr9 [/tex] therefore, triangle is not possible
Part D: [tex] 4+6>9, 4+9>6, 6+9>4 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.
Part E: [tex] 5+5>9, 5+9>5, 9+5>5 [/tex] As all the three sides adhere to the triangle inequality, a triangle is possible with these dimensions.
Thus, only Options D and E apply
The area of a rectangle or a 48 square inches the length is 8 inches what is the measure of its width
Answers
Answer: 48
By using double inequality describe all the numbers that are:
a) greater than (−8) but less than (−2)
b) less than 0, but greater than (−5)
c) greater than (−3), but less than 3
First one to answer correctly gets brainliest answer
Answers
a) Numbers greater than -8 but less than -2 are represented by the double inequality [tex]\(-8 < x < -2\).[/tex]
b) Numbers less than 0 but greater than -5 are represented by the double inequality [tex]\(-5 < x < 0\).[/tex]
c) Numbers greater than -3 but less than 3 are represented by the double inequality [tex]\(-3 < x < 3\).[/tex]
To describe each set of numbers using double inequalities, we'll define the range of numbers that satisfy each condition.
a) For numbers greater than -8 but less than -2:
[tex]\[ -8 < x < -2 \][/tex]
This double inequality represents all numbers that are greater than -8 on the number line and less than -2, but not including -2 itself.
b) For numbers less than 0 but greater than -5:
[tex]\[ -5 < x < 0 \][/tex]
This double inequality represents all numbers that are less than 0 on the number line and greater than -5, but not including 0 itself.
c) For numbers greater than -3 but less than 3:
[tex]\[ -3 < x < 3 \][/tex]
This double inequality represents all numbers that are greater than -3 on the number line and less than 3, but not including 3 itself.
In summary:
a) Numbers greater than -8 but less than -2 are represented by the double inequality [tex]\(-8 < x < -2\).[/tex]
b) Numbers less than 0 but greater than -5 are represented by the double inequality [tex]\(-5 < x < 0\).[/tex]
c) Numbers greater than -3 but less than 3 are represented by the double inequality [tex]\(-3 < x < 3\).[/tex]
PLEASE HELPP
What is the solution of the system of equations?
{13x−6y=23x−4y=−10
Enter your answer in the boxes..
Answers
Answer:
the solution is the point [tex](2,4)[/tex]
Step-by-step explanation:
we have
[tex]13x-6y=2[/tex] ------> equation A
[tex]3x-4y=-10[/tex] ------> equation B
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection point is the point [tex](2,4)[/tex]
see the attached figure
therefore
the solution is the point [tex](2,4)[/tex]
the answer is (2,4) the expert is right i put it and got it right
Ms.Gartland bought x number of shirts for the new members of her chorus.The cost for x number of shirts,including $3.99 shipping,was $ 77.49.Each shirt cost $12.25.There was no sales tax on this purchase.Which equation could be used to find x?
A 3.99(x+12.25)=77.49
B 3.99x+12.25=77.49
C 12.25(x+3.99)=77.49
D12.25x+3.99=77.49
Answers
She bought 'x' number of shirts.
The price of one shirt = 12.25 dollars.
Then total price of all shirts would be '12.25x' dollars.
Given is the shipping charge = 3.99 dollars.
Given is the total bill = 77.49 dollars.
It says no other tax would be charged on this order, so total bill would be sum of total price of all shirts and shipping charges.
Total Bill = Total price of all shirts + Shipping charges.
77.49 = 12.25x + 3.99
Hence, option D is correct i.e. 12.25x + 3.99 = 77.49