Answers
Answer:
See explanation below
Step-by-step explanation:
In all cases you need to isolate x on one side of the inequality symbol using inverse operations.
1.-
[tex]15+x\leq -45\\15-15+x\leq -45-15\\x\leq -60[/tex]
where we subtracted from both side 15 in order to leave x by itself on the left.
2.-
[tex]x-14>12\\x-14+14>12+14\\x>26[/tex]
where we added 14 in order to isolate x on the left
3.-
In this case we need to divide both sides by -5 in order to isolate the x which is being multiplied by the factor -5, but he have to recall that multiplying or dividing by a negative number changes the direction of the inequality symbol (in our case from < into > )
[tex]-5x<35\\\frac{-5\,x}{-5} >\frac{35}{-5} \\x>-7[/tex]
4.-
[tex]2x>-42\\\frac{2\,x}{2} >\frac{-42}{2} \\x>-21[/tex]
In this case we simply divide both sides by two, and there is no change in the direction of the inequality because the number we are using to divide is a positive number (2)
Related Questions
5-2(2x - 3) = 12
Cual es el resultado de x?
Answers
Answer:
[tex]x = - \frac{1}{4} [/tex]Step-by-step explanation:
5-2(2x - 3) = 12
Expanda los términos en el corchete
Eso es
5 - 4x + 6 = 12
Agrupar términos similares
Envíe las constantes al lado derecho de la ecuación y aquellas con variables al lado izquierdo
Tenemos
- 4x = 12 - 5 - 6
- 4x = 1
Divide ambos lados entre - 4
[tex] - \frac{4x}{ - 4} = - \frac{1 }{4} [/tex]Tenemos la respuesta final como
[tex]x = - \frac{1}{4} [/tex]Espero que esto te ayude
A manufacturer drills a hole through the center of a metal sphere of radius R = 8. The hole has a radius r. What value of r will produce a ring whose volume is exactly half the volume of the sphere? (Round your answer to two decimal places.)
Answers
Answer:
New radius(r) = 3.65 (Approx)
Step-by-step explanation:
Given:
Radius of sphere(R) = 8
Find:
New radius(r)
Computation:
Volume of sphere = (4/3)πR³
Volume of sphere = (4/3)π(6)³
Volume of sphere = 288π
Volume of ring = (4/3)π(R²-r²)³/²
Half volume of sphere = Volume of ring
288π / 2 = (4/3)π(R²-r²)³/²
144 = (4/3)(6²-r²)³/²
108 = (6²-r²)³/²
New radius(r) = 3.65 (Approx)
URGENT!!! What is the real part of 4−5i?
Answers
Answer:
4
Step-by-step explanation:
The real part of a complex number is the part that does not have "i" as a factor.
Here, the real part is 4.
You spend $30 20 on 4 CDs Each CD costs the same amount and is on sale for 80% of the original price
2 Write and solve an equation to find how much you spend on each CD. Let p represent the price you pay for each CD
Equation QS-2240
You spent $ 5.5 on each CD
The next day, the CDs are no longer one sale You have $25. Will you be able to buy 3 more CDS?
Yes you will
be able to buy 3 more CDs
Explain your reasoning for part b).
Each CD COSTS
at the regular price, so 3 CDs would cost $
Answers
Answer:
You will only be able to buy two at the original price the following day.
Step-by-step explanation:
You spend $30.40 on 4 CDs. Each CD costs the same amount and is on sale for 80% of the original price.
If x = original cost of one CD
80% of one CD = 0.8x
0.8x = the price you pay for one discounted CD
You buy 4 of the discounted CDs for $30.40
4(0.8x) = 30.40
solve for x, the original cost of one CD
3.2x = 30.40
x = 9.50
The next day, the CDs are no longer one sale. You have $25. Will you be able to buy 3 more CDs?
25$ / $9.50 = 2.63 CDs
Help please!!!! Thank you
Answers
Answer:
Option (C) : 3
Step-by-step explanation:
Circumference of front tire = Circumference of back tire
[tex]3(2\pi\: r) = 2\pi \R[/tex]
[tex] \R = 3r[/tex]
25b +15b combine like terms
Answers
Answer:
40b
Step-by-step explanation:
25 + 15 = 40
Answer:
40b
Step-by-step explanation:
We are given the expression:
25b+15b
and asked to simplify.
To simplify, we must combine like terms. Let's analyze the terms.
25b ⇒ has a variable "b"
15b ⇒ also has a variable "b"
The like terms in this expression are the terms with a variable, b.
To combine like terms, add the coefficients and leave a b on the end.
(25+15)*b
(40)*b
40b
The expression 25b+15b simplified is 40b.
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran 1/6 the loop in an hour. What is Selma’s unit rate in miles per hour for Monday’s run? In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow to calculate Selma’s unit rate in miles per hour. In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow to calculate Selma’s unit rate in miles per hour. According to the question, the unit rate is to be expressed in which units?
Answers
Hello There!!~
The units of per hours is = 4.5
Explanation:
Unit rate in miles per hour is the ratio of total distance covered in miles to total time taken in hour to cover that distance.
L = 3/4
Time taken to cover the loop on monday:-
T = 1/6 hours.
Unit rate in miles per hour :-
V = L/T
=> 3/4 ,1/6 =18/4
18/4 = 4 5
Hope This Helps!! :)
By °~Itsbrazts°~
What property allows us to multiply or
divide by one whole to make an equivalent
fraction?
Answers
Answer:
Identity Property of Multiplication
Step-by-step explanation:
Required
State with property that describes the question
I'll answer this question using the following instances;
[tex]1.\ \frac{x}{3} = 1[/tex]
[tex]2.\ 3x = 1[/tex]
For the first expression, we multiply both sides by 3
[tex]3 * \frac{x}{3} = 1 * 3[/tex]
[tex]x = 1 * 3[/tex]
[tex]x = 3[/tex]
For the second; divide both sides by 2
[tex]\frac{3x}{3} = \frac{1}{3}[/tex]
[tex]x = \frac{1}{3}[/tex]
The property applied in both expressions is the identity property of multiplication
what is the length of a rectangle with width 16 in. and area 120 in^2
Answers
Answer:
It will have to be 7.5 inches.
Step-by-step explanation:
120 divided by 16 is 7.5 inches.
Answer:
Hey there!
A=LW
120=L16
L=7.5 in
Let me know if this helps :)
you move 2 units and down 9 units. you end at (5, -5). where did you start
Answers
the area of a triangle is 54 cm. if the height is 3 cm more than the base, find the length of base
Answers
A van can travel 18 miles on each gallon of gasoline. At that rate, how many miles can the van travel on 15 gallons of gasoline? -33 miles -83 miles -120 miles -270 miles
Answers
Answer:
Hey there!
1 gallon of gas is equal to 18 miles of road.
15 gallons of gas is equal to 18(15) miles, or 270 miles of road.
Let me know if this helps :)
Answer:
D) because if you take 18 times 15 you would get 270
Step-by-step explanation:
Stay safe, positive, and healthy C:
Have a wonderful morning c:
You are told a professional cyclist eats around 5120 calories everyday for the Tour de Abroad. Estimate how many calories a cyclist would eat during a 21 day race
Answers
Answer:
Total calories eat = 107,520 calories
Step-by-step explanation:
Given:
Number of calories everyday = 5120 calories
Number of days = 21
Find:
Total calories eat
Computation:
Total calories eat = Number of calories everyday × Number of days
Total calories eat = 5120 × 21
Total calories eat = 107,520 calories
1а - За =
o4a
O
-2а
О2а
О-4а
Answers
Answer:
-2aStep-by-step explanation:
[tex]1a - 3a \\ = - 2a[/tex]
Hari borrowed Rs. 126000 from a money-lender at 15% per annum simple interest,
After 3 years, he paid Rs. 70700 and gave a buffalo to clear off the debt. What is the
cost of the buffalo?
Answers
Answer:
Rs. 112000
Step-by-step explanation:
Borrowed money = Rs. 126000Interest rate = 15% PA simpleTime = 3 yearsHari is due to pay after 3 years:
126000* (1+ 3*15/100) = 182700He pays Rs. 70700, remaining money is cleared by giving buffalo.
Cost of buffalo:
182700 - 70700= Rs. 112000Answer is: Rs. 112000
Answer:
Solution,
principal(P)= Rs. 126000
Rate(R)=15%
Time(T)=3 years
Money paid=Rs.70700
Cost of buffalo=?
We know that,
Interest=P*T*R
100
= Rs. 126000*3*15
100
= Rs. 56700
Now,
Amount(A)=P+I
=Rs. ( 56700+126000)
= Rs.182700
Again,
by the question,
Cost of buffalo= Amount- Money paid
= Rs.(182700- 70700)
= Rs. 112000
Therefore, the cost of buffalo is Rs. 112000.
A 50 ft pole has a support wire that runs from its top to the ground with an angle of depression of 75°. To the nearest tenth of a foot, how much wire is used? Enter a number answer only.
Answers
Answer:
Step-by-step explanation:
Given:
height of pole = 50 ft
angle of depression = 75°
to find:
how much wire is used
Solution:
Let x be the wire used
sin 75° = 50/x
x = 50/sin 75°
= 50 / 0.9659
= 51.765
x = 51.8 ft
Use the number line below, where RS = 7y +5, ST = 2y + 7, and RT = 14y - 28.
a. What is the value of y?
b. Find RS, ST, and RT.
Answers
Answer:
a. 8
b. 61, 23, 84
Step-by-step explanation:
As we can see, point S is between points R and T, therefore:
RS + ST = RT7y + 5 + 2y + 7 = 14y - 289y + 12 = 14y - 2814y - 9y = 12 + 285y = 40y = 40/5y = 8------------
RS = 7y+5 = 61ST = 2y + 7= 23RT = 14y - 28 = 84Subtract 12h+1 from 34h+4 . what is the answer? a.−1/4h+5 b.1/4h+5 c.−1/4h d.1/4h+3
Answers
Answer:
D
Step-by-step explanation:
We would like to solve:
(3/4h + 4) - (1/2h + 1)
This is equivalent to:
3/4h + 4 - 1/2h - 1
First, combine like terms; that is, combine the terms with h in them and combine the terms without h in them:
3/4h - 1/2h + 4 - 1
The common denominator for 3/4 and 1/2 is 4, so:
3/4h - 1/2h = 3/4h - 2/4h = 1/4h
Put this back in:
1/4h + 4 - 1
1/4h + 3
The answer is thus D.
~ an aesthetics love
What’s the measure of X in this short answers are fine
Answers
Answer:
28 = x
Step-by-step explanation:
62 = angle BAC since they are vertical angles
angle ABC is a right angle since KL is perpendicular to FG
Adding the angles in triangle ABC
BAC + ABC + BCA = 180
62 + 90 + BCA = 180
152 + BCA = 180
BCA = 180-152
BCA = 28
BCA = x since they are vertical angles
28 = x
Keith has 39 books in his library he brought several books at a yard sale over the weekend he now has 84 in his library how many? Keith has 45 boooks
Answers
Subtract original amount from new amount:
84 - 39 = 45
He bought 45 books.
What is the term, coefficient, constant, and factor of 1/2(base1 + base2)h? (Formula used to find area of trapezoid)
Answers
Answer:
i. Term = [tex]\frac{b_{1}h }{2}[/tex] + [tex]\frac{b_{2}h }{2}[/tex]
ii. Coefficient = [tex]\frac{1}{2}[/tex]
iii. Constant = [tex]\frac{1}{2}[/tex]
iv. Factor = [tex]\frac{h}{2}[/tex]
Step-by-step explanation:
A trapezoid is a quadrilateral which has its base parallel to the opposite side. It's area can be determined by;
Area of trapezium = [tex]\frac{1}{2}[/tex] ([tex]b_{1}[/tex] + [tex]b_{2}[/tex])h
Where [tex]b_{1}[/tex] is the measure of length of its fist base, [tex]b_{2}[/tex] is the measure of its second base and h is its height.
Considering the given question,
Term = [tex]\frac{b_{1}h }{2}[/tex] + [tex]\frac{b_{2}h }{2}[/tex]
Coefficient = [tex]\frac{1}{2}[/tex]
Constant = [tex]\frac{1}{2}[/tex]
Factor = [tex]\frac{h}{2}[/tex]
How do I solve for y in this equation? 3xy-28=15x
Answers
Answer:
x = 28/(3y -15)
Step-by-step explanation:
Put the x-terms on the same side of the equal sign and everything else on the other side. Divide by the coefficient of x.
3xy -28 = 15x . . . . . . given
-28 = 15x -3xy . . . . . subtract 3xy
-28 = x(15 -3y) . . . . . factor out x
-28/(15 -3y) = x . . . . . . divide by the coefficient of x
We prefer to have a positive sign where possible, so we can multiply this by -1/-1 to get ...
x = 28/(3y -15)
is y=-2+5x a function
Answers
Answer:
No
Step-by-step explanation:
Because of the y^2, each value of x will be represented twice on the y-axis. Henceforth, the vertical line will pass through this line twice. THIS IS NOT A FUNCTION. ... It passes the vertical test for function.
Which of the following is a statement? What talent! He is talented. Is he talented?
Answers
Answer:
he is talented
Step-by-step explanation:
Identify the number that does not belong with the other three. Explain your reasoning (24 points)
Answers
Answer:
See explanation
Step-by-step explanation:
The number that would not belong is [tex]\sqrt{48}[/tex] since it is irrational
Answer:
[tex]\sqrt{48}[/tex]
Step-by-step explanation:
Looking at the numbers, we can see that the first number, third, and fourth number are all rational numbers since they either repeat or terminate.
On the other hand, let's try and simplify the square root of 48:
[tex]\sqrt{48}=\sqrt{16\cdot3}=\sqrt{16}\cdot\sqrt3=4\sqrt3[/tex]
The square root of 3 is irrational. Therefore, 4 times the square root of 3 is also irrational. All of the given numbers are rational instead of the second one. So, the second number does not belong .
describe a situation with an output of area in square feet that can be modeled using the function f(x) = (x)(2x + 5)
Answers
Answer: The length of a rectangle is 5 more than two times the width. If the width of the rectangle is represent by x then what is the area of the rectangle?
Step-by-step explanation:
Answer: 3 feet
Step-by-step explanation: The area of a rectangular garden can be represented by the function
f(x) = x(2x + 5)
Find the area if the length, x, is 3 feet.
Need help giving 13 points
Answers
Answer:
Read Exp:
Step-by-step explanation:
9.) (-6)^2
10.) 10^3
11.) (2/3)^6
Answer:
see below
Step-by-step explanation:
( -6) * (-6)
The base is -6. It is multiplied 2 times so the exponent is 2
(-6)^2
10*10*10
The base is 10 It is multiplied 3 times so the exponent is 3
10 ^3
2/3 * 2/3 * 2/3 * 2/3 *2/3 *2/3
The base is 2/3. It is multiplied 6 times so the exponent is 6
(2/3) ^6
don’t understand why I have to type a question each time when I have a picture but anyone know this?!
Answers
Answer:
3/8
Step-by-step explanation:
There are 8 boxes and 3 shaded columns
[tex]\frac{3}{4}\times \frac{1}{2} \\\\=\frac{3\times \:1}{4\times \:2}\\\\=\frac{3}{4\times \:2}\\\\=\frac{3}{8}[/tex]
Answer:
Hey there!
The correct answer is 1/2(3/4)=3/8
Hope this helps :)
The football team lost three yardsOn the first play game 5 yards on the second play in lost to yards on the third play represent the total yards after three plays as an integer
Answers
Answer:
Total lost yards = 10 yards
Step-by-step explanation:
Given:
First match = lost 3 yards
Second match = lost 5 yards
Third match = lost 2 yards
Find:
Total lost yards
Computation:
Total lost yards = First match + Second match + Third match
Total lost yards = 3 yards + 5 yards + 2 yards
Total lost yards = 10 yards
A family travels, by plane, five hundred miles from their city to a beach town. Then they take a taxi from the airport to the hotel at the beach. When they ask the driver how far the airport is from the hotel, he tells them twenty kilometers. What is the approximate total distance, in miles, the family traveled
Answers
Answer:
512.4274 miles
Step-by-step explanation:
500m + 20k = distance
1 kilometer = 0.621371 miles
20k = 12.4274
500 + 12.4274 = 512.4274 miles