[tex]\dfrac{2x -3}{5} - \dfrac x3 \leq 2\\\\\implies \dfrac{6x-9-5x}{15} \leq 2\\\\\implies x-9 \leq 15 \times 2\\\\\implies x -9 \leq 30\\\\\implies x \leq 30 +9 \\\\\implies x \leq 39\\\\\text{Interval,}~ (-\infty, 39 ][/tex]
Answer:
x
Step-by-step explanation:
Refer to '<' as ' less than or equal to '
Whenever you are deal with these types of inequalities / equations, nake sure to equate the denominators of both entities involved in the operation be it ( -, × , ÷ ,+ )
with that in mind
* 2x - 3/5 - x/3 < 2 has 2 different denominators i.e - 5 & 3
so to equate both sides, let's multiply each by the denominator they are lacking.
* 2x - 3/5 lacks 3 compared to -x/3.
* similarly, -x/3 lacks 5 compared to 2x - 3/5
multiply both by what they lack (2)
thus, (2x - 3 )×3 /(5) × 3 - (x × 5) × 5/ (3) × 5 < 2
* 6x - 9/ 15 - 5x/15 < 2
we can now combine the numerators since we now have a common denominator which is 15.
* 6x - 9 - 5x/ 15 < 2 (6x-9-5x) is equal to -9 + x = x - 9.
criss cross
* x - 9 < 30
* x < 39
Don’t answer just for points please !! I really need help~
This is going to take a while: get ready...
I like two-columns, so...
Statements_______________|_____Reasons___
l||m Given
angle 1 congruent angle 7 Given
angle 3 congruent angle 5 corresponding alternate angles
a||b CPCTC
I usually do proofs for triangles, not parallel lines, but I hope this helped!
A person bought a water tank of circular base having the radius 1.05 meter and height 3.5 m for the use of own house from the shop. If the upper part of the tank is semi spherical , how many liters of water will be contained in the tank. Find it!
Help!! :)
11000 litre of water is needed to fill the tank.
Answer:
solution given:
radius [r]=1.05m
Total height[H]=3.5m
height of cylinder[h]=2.45m
Now
The volume of the cylindrical part of tank=[tex]\pi r^2h=3.14*1.05^2 *2.45=8.4815m^3[/tex]
again
the volume of semi-spherical part of tank=[tex]\frac{2}{3} \pi r^{3} =\frac{2}{3}*3.14*1.05^3=2.4233m^3[/tex]
now
total volume=volume of the cylindrical part of tank + volume of semi-spherical part of tank
=8.4815+2.4233=10.9048 [tex]m^{3}[/tex]
we have
[tex]1m^3=1000litre[/tex]
[tex]10.9048m^3=1000*10.9048=10904.8\:litre[/tex]
Step-by-step explanation:
Two cars leave an intersection at the same time. One drives east while the other travels south at 25 miles per hour faster than the other. After 2 hours, the cars are 250 miles apart. How fast is the southbound car driving?
Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (side opposite of the right angle), which is in our case the distance of the 2 cars.
after 2 hours the east car was driving x miles. and the south car was driving x + 2×25 = x + 50 miles.
x² + (x + 50)² = 250²
x² + x² + 100x + 2,500 = 62,500
2x² + 100x = 60,000
x² + 50x = 30,000
x² + 50x - 30,000 = 0
the solution for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 50
c = -30,000
x = (-50 ± sqrt(2500 - 4×1×-30000))/(2×1) =
= (-50 ± sqrt(2500 + 120000)/2 =
= (-50 ± sqrt(122500))/2 = (-50 ± 350)/2 =
= -25 ± 175
x1 = -25 + 175 = 150 miles
x2 = -25 - 175 = -200 miles.
negative distances don't make any sense here in our scenario, so the solution is x = 150 miles.
therefore, the east car was going 75 mph (traveled in 2 hours 150 miles).
and the south car was going 75 + 25 = 100 mph (traveled in 2 hours 200 miles).
Subtract: x2 + 2x + 1 – (x – 3)
Therefore, the answer is 3x - 2.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
1 Name the shapes that are being described. a I have three sides that are all the same length. I have three equal angles. Thave three lines of symmetry and rotational symmetry of order 5. b I have four sides. Thave one line of symmetry and rotational symmetry of order 1. Two of my angles are equal. I have two pairs of equal length sides' C I have six sides. All my sides are the same length. I have six lines of symmetry and rotational symmetry of order
Answer:
a. Equilateral triangle
b. Quadrilaterals
c. Hexagon
Step-by-step explanation:
What is the slope of the line that passes through the points shown in the table?
X Y
-1 -5
0 -3
1 -1
2 1
Jenna has 38 coins. She uses 19 coins to buy a notebook. How many coins does she have left?
Explain how you can solve and check this problem.
Answer: 19 coins
Step-by-step explanation:
38-19=19
To check, take any one of the nubers and replace it with x, and when you solve for x. you'll get that number back. For example:
Let x represent the amount used to buy a notebook
19+x=38
x=38-19
x=19
Write an expression that is equivalent to 4(x + 1) - 7 (x + 3)
Answer:
-3x-17
Step-by-step explanation:
We need to expand this term by multiplying a term and an expression.
The following product distributive property will be used:
.
In our example, the resulting expression will consist of 2 terms:
the first term is a product of and .
the second term is a product of and .
Therefore, one expression that is equivalent to 4(x + 1) - 7(x + 3) is -3x - 17.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
X=-2y,x-y=6 solve by substitution show all work
Answer:
y=-3
x=3
Step-by-step explanation:
x=-2y
x-y=9
substitute -2y for x in the second equation
you get:
-2y-y=9
combine like terms
-3y=9
divide by -3 on both sides
y=-3
Consider a parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5).
2) Suppose the parallelogram is reflected over the x-axis, which vertex of the parallelogram will have the same coordinate before and after the reflection?
A) (0, 3)
B) (2, 0)
C) (2, 5)
D) (4, 2)
Answer:
B
Step-by-step explanation:
So a reflection over the x is a change in the y value.
Only point (2,0) is on the x-axis, so it will not move.
Gatorade comes in two different sizes A 16 ounce costs $2.10 and a 20nounce bottle costs $3.15 which is a better deal to explain your thinking.
How much do you save per ounce by buying the better one?
Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03
The first step is to find the cost per ounce of each bottle.
For the 16 ounce bottle:
= 2.10 / 16
= $0.13 per ounce
For the 20 ounce bottle:
= 3.15 / 20
= $0.16
The 16 ounce size is therefore better and the amount saved per ounce is:
= 0.16 - 0.13
= $0.03
In conclusion, the 16 ounce is better as it saves $0.03 per ounce.
Find out more at https://brainly.com/question/16805756.
There are 36 boys for every 54 girls
Answer:
2 : 3 is ur ratio
Step-by-step explanation:
Answer:
2 : 3 is ur ratio
Step-by-step explanation:
Which one of Aiko's steps makes a false assumption? Why is it false?
Aiko's Proof:
1. Draw 2 rectangles. Label one ABCD and the other PQRS
2. Translate rectangle ABCD by the directed line segment from A to P.A' and P now coincide. The points coincide because that's how we defined
our translation
3. Rotate rectangle A'B'C'D' by angle D'A'S. Segment A"D" now lies on ray PS. The rays coincide because that's how we defined our rotation.
4. Dilate rectangle A"B"C"D" using center A" and scale factor AD. Segments A"D" and PS now coincide. The segments coincide because A" was
the center of the rotation, so A" and P don't move, and since D" and S are on the same ray from A", when we dilate D" by the right scale factor, it
will stay on ray PS but be the same distance from A" as S is, so S and D' will coincide.
5. Because all angles of a rectangle are right angles, segment A'B' now lies on ray PQ. This is because the rays are on the same side of PS and
make the same angle with it (If A'B' and PQ don't coincide, reflect across PS so that the rays are on the same side of PS.)
6. Dilate rectangle A"B"C"D" using center A" and scale factor AB Segments A'"'**" and PQ not coincide by the same reasoning as in step 4.
7. Due to the symmetry of a rectangle, if 2 rectangles coincide on 2 sides, they must coincide on all sides.
Answer:
6th step is wrong
Step-by-step explanation:
We have the dilation transformations we only needed one, and that is the 6th step. It would make more sense to do the dilation transformation early in the steps and we already did these steps at the beginning.
DOM
The weight of a car is modeled with the polynomial 3x2 – 25x + 204. The weight of a truck is modeled with the polynomial x² + 17x + 40
What polynomial represents the total weight of the car and truck?
Answer:
4x^2-8x+244
Step-by-step explanation:
What is the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4?
Answer:
[tex]f(x)\longrightarrow\infty[/tex] as [tex]x\longrightarrow\infty[/tex]
Step-by-step explanation:
We can see that all parts of the polynomial are positive, so as x gets larger, y will also get larger.
I need help on this question
3n + 2 = 17
Answer:
The value of n is 5.
Step-by-step explanation:
Concept :
Here, we will use the below following steps to find a solution using the transposition method:
Step 1 :- we will Identify the variables and constants in the given simple equation.Step 2 :- then we Simplify the equation in LHS and RHS.Step 3 :- Transpose or shift the term on the other side to solve the equation further simplest.Step 4 :- Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.Step 5 :- Then the result will be the solution for the given linear equation.Solution :
By using the transposition method. we get,
[tex]{\dashrightarrow{\tt{3n + 2 = 17}}}[/tex]
[tex]{\dashrightarrow{\tt{3n= 17 - 2}}}[/tex]
[tex]{\dashrightarrow{\tt{3n= 15}}}[/tex]
[tex]{\dashrightarrow{\tt{n= 15 \div 3}}}[/tex]
[tex]{\dashrightarrow{\tt{n= \dfrac{15}{3}}}}[/tex]
[tex]{\dashrightarrow{\tt{n= \cancel{\dfrac{15}{3}}}}}[/tex]
[tex]{\dashrightarrow{\underline{\boxed{\tt{\red{n= 5}}}}}}[/tex]
Hence, the value of n is 5.
[tex]\rule{300}{1.5}[/tex]
Solve : 3n + 2 = 17
Answer:-n = 5
Explanation:-=> 3n + 2 = 17
=> 3n = 17-2
=> 3n = 15
=> n = 15/3
=> n = 5
write an equation
(X-P) (x-q)=0
Answer:
[tex]x^{2} -pqx+pq[/tex]
Step-by-step explanation:
Find 85 - 72 x 4 ÷ 2 (13 - 11)
Answer:
13
Step-by-step explanation:
using BODMAS
13-11=2
SO 2*2=4
4/4=1
1*72=72
THEREFORE it is 85-72 =13
Anna saved $20 in a jar each month for 2 1/2
years. She spent 75% of her savings on a computer. How much money did Anna have left in the jar?
Answer:
20*2.5=50
50*0.75=37.5
Hope This Helps!!!
Answer:270
Step-by-step explanation:
Please help it depends on my grade i have a 50 i need to pass this test.do the ordered pairs represent y as a function of x?
(9, 0), (8, 0), (-8, 3), (-3, -3), (-4, 2)
A. No, because there is more than one y-value for the same x-value.
B. Yes, because for every x-value there is only one y-value.
C. No, because there is more than one x-value for the same y-value.
D. Yes, because for every y-value there is only one x-value.
Answer:
a
Step-by-step explanation:
An astronomical unit (AU) is the average distance between Earth and the sun. One AU is equal to approximately 150,000,000 km. Astronomers also use light years to measure distance. A light year is approximately 9.5×10^12
km.
Use scientific notation to rewrite the measure of one astronomical unit (1 AU) in kilometers
Using scientific notation, it is found that the measure of one astronomical unit in kilometers is [tex]1.5 \times 10^8[/tex]
A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
In which [tex]a \in [1, 10)[/tex]To realize the conversion from decimal to scientific notation, b is the number of decimal places the comma moves, being positive if to the left, negative if to the right.In this problem, 1 AU = 150,000,000 km.
The comma has to move 8 places to the right, hence [tex]b = 8[/tex]Then, the measure is: [tex]1.5 \times 10^8[/tex]
For more on scientific notation, you can check https://brainly.com/question/16394306
can someone help me pls
Answer:
i think you add them not sure...
Step-by-step explanation:
40+44+44+??
ok?
Answer:
x=88°
x-44°=88°-44°=44°
Step-by-step explanation:
angle A+ angle B+angle C=180°
48°+x-44°+x°=180°
=48°-44°+x°+x°=180°
=4°+2x°=180°
=4°-4°+2x°=180°-4°
=2x°=176°
=2x°/2=176°/2
=x°=88°
x°-44°=88°-44°
=x°-44°=44°
Plz help with this question.If can't do it don't answer.
Answer:
the total surface area of this triangular prism is 976cm2
Answer:
i think TSA = 976 cm²
Step-by-step explanation:
TSA = 2(1/2×14×24) + (14+25+25)×10
TSA = 2(7×24)+(64×10)
TSA = 336+640
TSA = 976 cm²
explain please i dont get it
Answer:
.........................
......
An 18-foot ladder is leaning against a wall. The bottom of the ladder is 4.5 feet from the base of the wall.
How high up the wall does the ladder reach? Round your answer to the nearest tenth, if necessary.
A
13.5 feet
B
18.6 feet
o
С
22.5 feet
D
17.4 feet
Answer:
d
Step-by-step explanation:
use Pythagoras theorem
that is a²+b²=c²
so 4.5²+b²= 18²
rearrange to b²=18²-4.5²
so you get b=
[tex] \sqrt{303.75} [/tex]
that is equal to 17.42842506
how much is 3 liters in 50 bottles
Answer : 0.06 liters per bottle
Step - by - step explanation :
3 liters divided by 50 bottles = 0.06 liters per bottle
[ Sorry if this wasn't what you meant when you asked the question ]
Happy holidays ! :3
what is 21-3+18 divided by 6=6 equal
ehhehehehe u will never find out
Answer:
I really :3? i’m up for a challenge
Step-by-step explanation:
21 - 3 = 18
18 + 18= 36
36/6= 6
hope this helped!
write one in factor form with solutions 3,-1,-3i?
Answer:
Factored form: [tex](x-3)(x+1)(x^2+9)[/tex]
Expanded form: [tex]x^4-2x^3+6x^2-18x-27[/tex]
Step-by-step explanation:
[tex](x-3)(x+1)(x^2+9)[/tex]
[tex](x^2-2x-3)(x^2+9)[/tex]
[tex]x^4+9x^2-2x^3-18x-3x^2-27[/tex]
[tex]x^4-2x^3+6x^2-18x-27[/tex]
[tex]x-3=0[/tex] has a solution of [tex]x=3[/tex]
[tex]x+1=0[/tex] has a solution of [tex]x=-1[/tex]
[tex]x^2+9=0[/tex] has a solution of [tex]x=\pm 3i[/tex]
Here is a photo of the question it self. I hope it makes it easier to understand
Thank you for anyone who helps with the question
Answer:
a. R>S
b. It means that R is to the right of S
c. City R is warmer
Step-by-step explanation:
a *blank* *blank* trinomial has only one element in the solution set
Answer:
a solution set trinomial has only one element in the solution set
Step-by-step explanation: