Answers
9514 1404 393
Answer:
3 < x < 6
Step-by-step explanation:
Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.
P = 2(L +W)
P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify
The perimeter wants to be between 38 and 74 cm, so we have ...
38 < 12x +2 < 74
36 < 12x < 72 . . . . . subtract 2
3 < x < 6 . . . . . . . . . divide by 6
_____
Additional comment
Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.
Here, our first step was to subtract 2 from all parts of the inequality:
38 -2 < 12x +2 -2 < 74 -2 ⇒ 36 < 12x < 72
The division by 12 worked the same way: all parts are divided by 12.
36/12 < (12x)/12 < 72/12 ⇒ 3 < x < 6
__
If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.
Related Questions
Y-(-3y) create an equivalent equation
Answers
9514 1404 393
Answer:
4y
Step-by-step explanation:
There are an infinite number of equivalent expressions. One of them can be obtained by combining the terms
y -(-3y) = y +3y = y(1 +3) = 4y
__
All of the expressions shown as equal are equivalent.
Write an equation of the line that passes through the point (3,3) and is Parallel to the line y=-1/2x+3
Answers
Answer:
[tex]y = - \frac{1}{2} x + \frac{9}{2} [/tex]
Step-by-step explanation:
find the y-intercept
[tex]3 = - \frac{1}{2} (3) + b \\ 3 = - \frac{3}{2} + b \\ \frac{6}{2} + \frac{3}{2} = b \\ b = \frac{9}{2} [/tex]
HELP PLEASE !!!!!!!!
Answers
Answer:
4 3 4 4 4 2 3 4 5 5 3.5 5
Just divide the number by 4
Sry if the list is kinda confusing
Solve the inequality 2x + 5 2 27
Answers
Answer:
[tex]2x + 5 \geqslant 27 \\ = 2x \geqslant 27 - 5 \\ = 2x \geqslant 22 \\ = x \geqslant 22 \div 2 \\ x \geqslant 11 \\ x[11 \: \infty ) \\ thank \: you[/tex]
Step-by-step explanation:
Hope this help you
If this help you then mark me as a brainliest
Explain step by step please!
Thirty copies of a textbook weigh a total of 75lb. What is the weight of each book?
Answers
Answer:
Each book weighs 2.5 pounds.
Step-by-step explanation:
75/2.5 is 30. Or you could also get the answer by 30* 2.5 which it would be 75. So, therefor, the answer is 2.5.
Answer:
2.5lb
Explanation:
In equation form the question is asking for x in
[tex]30(x) = 75[/tex]
Since multiplication is reversible (to be division), we can switch the equation up.
[tex]75[/tex] ÷ [tex]30 = x[/tex]
So the answer is
[tex]75[/tex] ÷ [tex]30 = 2.5[/tex]
find equation of line a line that is parellel to the graph of 2x+3y=5 and contains the point (3,-1)
Answers
Answer:
[tex]y = - \frac{2}{3} x + 1[/tex]
Step-by-step explanation:
2x +3y= 5
3y= -2x +5
Divide both sides by 3:
[tex]y = - \frac{2}{3} x + \frac{5}{3} [/tex]
[tex]y = - \frac{2}{3} x + 1 \frac{2}{3} [/tex]
Now that the equation is in the slope-intercept form (y= mx +c), the slope of the given line is the coefficient of x.
[tex]slope = - \frac{2}{3} [/tex]
Parallel lines have the same slope.
Slope of unknown line= -⅔
y= -⅔ +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 3, y= -1,
[tex] - 1 = - \frac{2}{3} (3) + c[/tex]
-1= -2 +c
c= -1 +2
c= 1
Thus, the equation of the line is y= -⅔x +1.
How can distributive property be used to solve 7 x 391
Answers
Answer:
7x ³⁹¹
Step-by-step explanation:
1: "x3" was replaced by "x^3".
BRAINLIEST!! What’s 36.3 square root ?
Answers
Answer:
6.02
Step-by-step explanation:
Base BC of an equilateral triangle ABC is root2 x+y+2=0. If vertex A is the origin, then the area of triangle ABC is (in sq. units) A) 3 root3 B) 2/3 root3 C) 4/3 root3 D) 6 root3
Answers
Answer: Choice C
4/(3*sqrt(3))
which is the same as writing [tex]\frac{4}{3\sqrt{3}}[/tex]
==============================================================
Explanation:
We have the line [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] in which points B and C are on this line. In other words, all of segment BC is on that line.
Point A is somewhere off that line as the diagram below indicates. We need to find the line through A that is perpendicular to the given line.
Recall that for any line of the standard form [tex]Px+Qy+R = 0\\\\[/tex], any perpendicular line will look like this: [tex]Qx-Py+S = 0\\\\[/tex]. Note the swap and sign change for the P,Q coefficients.
So anything perpendicular to [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] will be of the form [tex]x-\left(\sqrt{2}\right)y+S = 0[/tex]. The sub-goal here is to find what S is equal to.
If you plugged in the origin point (x,y) = (0,0), then you should find that S = 0.
Therefore, the equation [tex]x-\left(\sqrt{2}\right)y = 0[/tex] is perpendicular to the given line and it passes through point A(0,0).
---------------------------
The reason why we computed that perpendicular line is to help determine the point D as shown in the diagram below. This point is at the intersection of the green perpendicular lines. This is at the base of the triangle such that BC is the base.
To find the location of point D, you need to solve this system of equations
[tex]\begin{cases}\left(\sqrt{2}\right)x+y +2 = 0\\\\x-\left(\sqrt{2}\right)y = 0\end{cases}[/tex]
Let's isolate x in the second equation
[tex]x-\left(\sqrt{2}\right)y = 0\\\\x=\left(\sqrt{2}\right)y\\\\[/tex]
Then substitute that into the other equation. Solve for y.
[tex]\left(\sqrt{2}\right)x+y +2 = 0\\\\\left(\sqrt{2}\right)*\left(\sqrt{2}\right)y+y +2 = 0\\\\2y+y +2 = 0\\\\3y +2 = 0\\\\3y = -2\\\\y = -2/3\\\\[/tex]
Now we can find x like so
[tex]x=\left(\sqrt{2}\right)y\\\\x=\left(\sqrt{2}\right)*(-2/3)\\\\x=\frac{-2\sqrt{2}}{3}\\\\[/tex]
The point D is located at the exact coordinates of
[tex]D=(x,y) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\[/tex]
---------------------------
Next, we use the distance formula to compute the distance between point A and point D.
I'll use lowercase d to represent distance.
[tex]A = (x_1,y_1) = (0,0)\\\\D = (x_2,y_2) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{\left(0-\left(\frac{-2\sqrt{2}}{3}\right)\right)^2 + \left(0-\left(\frac{-2}{3}\right)\right)^2}\\\\d = \sqrt{\left(\frac{2\sqrt{2}}{3}\right)^2 + \left(\frac{2}{3}\right)^2}\\\\d = \sqrt{\frac{8}{9} + \frac{4}{9}}\\\\d = \sqrt{\frac{12}{9}}\\\\d = \sqrt{\frac{4}{3}}\\\\d = \frac{\sqrt{4}}{\sqrt{3}}\\\\d = \frac{2}{\sqrt{3}}\\\\[/tex]
This represents the exact length of segment AD.
---------------------------
Since triangle ABC is equilateral, this means triangles ADB and ADC are identical mirrored copies of each other. Those two smaller triangles are equal in area and combine to form triangle ABC back again. Furthermore, they are right triangles. This last fact mentioned will allow us to use the pythagorean theorem like so
[tex]a^2+b^2 = c^2\\\\\left(\text{AD}\right)^2+\left(\text{DC}\right)^2=\left(\text{AC}\right)^2\\\\\left(\frac{2}{\sqrt{3}}\right)^2+\left(\frac{x}{2}\right)^2=\left(x\right)^2\\\\[/tex]
where x represents the lengths of AB, BC and AC.
After skipping a bit of steps, solving that said equation should lead to these two solutions
[tex]x = -\frac{4}{3}, \ x = \frac{4}{3}[/tex]
Because x is a side length, we ignore the negative solution.
---------------------------
We can now compute the area of triangle ABC
[tex]\text{area of triangle} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area of triangle ABC} = \frac{1}{2}*\text{BC}*\text{AD}\\\\\text{area of triangle ABC} = \frac{1}{2}*\frac{4}{3}*\frac{2}{\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{1*4*2}{2*3*\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{8}{6\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{4}{3\sqrt{3}}\\\\[/tex]
which points us to choice C as the final answer.
When writing this on a keyboard, we would write "4/(3*sqrt(3))" without quotes. The use of parenthesis is needed to ensure we divide by all of 3*sqrt(3). Otherwise, the computer might mistake it for [tex]\frac{4}{3}\sqrt{3}[/tex] which is entirely different.
write the ratio in three ways 10 home runs for every 15 games
Answers
Answer:
................................
Answer:
10 to 15 (simplified: 2 to 3)
10/15 (simplified: 2/3)
10 : 15 (simplified: 2 to 3)
Write the equation of a line that goes through the point (2, 4) that is parallel to the
line y = 3x - 6.
Answers
Answer:
y = 3x - 2
Step-by-step explanation:
Parallel lines have the same gradient in this case 3 is the gradient.
We will use the point (2,4) to form our own equation.
4 will be y, 3 will be m, 2 will be x
All we need is to find the C in the equation y=mx + c
4 = 3(2) + c
4 = 6 + c
C = -2
Therefore;
y = 3x - 2
when erin got her puppy cuddles he weighed 788.52 grams. He now weighs 2,313.6 grams more than he did when Erin first brought him in. How much does cuddles weigh now?
Answers
Answer:
3102.12
Step-by-step explanation:
add the starting weight 788.52 plus the weight he gained 2.313.6
788.52 + 2.313.6 = 3102.12
3.HELP plz No LINKS AND NO HACKERS i will give brainlyiest NO COPIE D ANSWERSFROM OTHER USERS OR WEBSITE I WILL REPORT!!!! A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.
(a) Write an equation to model the situation. Use the formula d = rt.
(b) Explain why it is reasonable to write the distance, d, as a positive number.
(c) How long did it take the diver to reach the surface?
Answers
Answer:
A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.
a. using the formula d = rt, so 32.12 m = 8.8m/min (t)
b. it is reasonable to write the distance as positive because the diver is accending/ going up the surface
c. t = 32.12/ 8.8 = 3.65 min
Step-by-step explanation:
hope this helps
Kim bought a $2,310.25 snow thrower on an installment plan. The installment agreement
included a 15% down payment and 24 monthly payments of $125 each. What is the total
finance charge?
O d) $1,036.29
O c) $346.54
O a) $3,346.54
Ob) $3,000
Answers
why is this an impossible sequence to solve?
3x + 1 ?
thanks
Answers
Answer:
[tex]T(x)=\begin{cases}\frac{3x+1}{2} & x\text{ is odd} \\ \frac{x}{2} & x\text{ is even}\end{cases} \\ for \: instance \: start \: with \: 7 \: \\ which \: is \: an \: odd \: number \\ \frac{21 + 1}{2} = \frac{22}{2} = 11 \\ 11 \: is \: odd \\ \frac{11 + 1}{2} = 6\\ 6 \: is \: even \\ \frac{6}{2} = 3 \\ 3\: is \: odd \\ \frac{9 + 1}{2} = 5 \: \\ 5 \: is \: odd\\ \frac{15 + 1}{2} = 8 \\ 8 \: is \: even \\ \frac{8}{2} = 4 \\ 4 \: is \: even \\ \frac{4}{2} = 2 \: then \: 1 \\ [/tex]
Step-by-step explanation:
Can we connect to 1 for all numbers?
A general proof for a simple pattern seems almost impossible, probably a new branch of mathematics maybe needed to tackle this conjecture...
A volunteer at the zoo is responsible for feeding the animals in 15 exhibits in the reptile house. This represents 20% of the total exhibits in the reptile house. How many exhibits are in the reptile house?
Answers
Answer:
75
Step-by-step explanation:
15 is 20% of the total.
The total is x since it is unknown.
20% of the total = 15
20% of x = 15
0.2x = 15
Multiply both sides by 5.
x = 75
There are 6 triangles and 8 squares. What is the simplest ratio of triangles to total shapes?
Answers
Answer:
3:7
Step-by-step explanation:
The number of triangles is 6.
The number of squares is 8.
The total number of shapes is 14.
The unsimplified ratio of triangles to total shapes is 6:14.
The bigger number that both 6 and 14 can be divided by is 3.
That makes the ratio 3:7, and it cannot be simplified further.
Given f(x) = -x – 1, find f(5).
Please help! marking brainliest
Answers
Answer:
f(5) = -6
Step-by-step explanation:
[tex]f(5) = -x - 1[/tex] [tex]f(5) = -5-1[/tex] [tex]f(5) = -6[/tex]Solve 48-5i=-4x+10yi
Answers
Answer:
Step-by-step explanation:
Suppose we decide to solve for y first. y will then be in terms of x AND a real and an imaginary term:
48-5i=-4x+10yi
The goal here is to solve for y. Adding 4x to both sides yields
48 - 5i + 4x = 10yi
and then we divide both sides by 10i to isolate the variable y:
48 - 5i + 4x
----------------- = y This result is "y in terms of the constant 48, the
10i imaginary terms 5i and 10i, and the expression 4x.
We solve the original equation for x in a similar manner:
48-5i=-4x+10yi becomes 48 - 5i - 10yi = -4x, so that:
-(48 - 5i - 10yi)
x = ------------------------
4
Next time, please specify which variable (x or y) you're solving for. Thank you.
It was recently estimated that homes without children outnumber homes with children by about nine to seven. If there are 4912 homes in a county, how many of them
are homes without children
Answers
Answer:
Answer:929
Step-by-step explanation:
Step-by-step explanation:For every 11 children, 7 will have homes
Identify the situation that involves opposite quantities adding up to zero Climbing up 6 feet and climbing down 4 feet Hiking 10 feet due north, then hiking 10 feet due south Ascending 2 feet and descending 3 feet Earning $5 and spending $3
Answers
9514 1404 393
Answer:
(b) Hiking 10 feet due north, then hiking 10 feet due south
Step-by-step explanation:
Any pair of numbers that totals zero will be a pair of opposites. The offered choices are ...
+6 -4 = 2 . . . not zero
+10 -10 = 0
+2 -3 = -1 . . . not zero
+5 -3 = 2 . . . not zero
Hiking 10 feet due north, then hiking 10 feet due south is a situation involving opposite numbers adding up to zero.
The elevation of a submarine with respect to sea level is displayed as - 125 feet. Which statement is correct?
A. The submarine is 125 feet above sea level.
B. The submarine is 125 feet below sea level.
C. The submarine is -125 feet above sea level.
D. The submarine is -125 feet below sea level.
Answers
B. The submarine is 125 feet below sea level.
Step-by-step explanation:
-124 feet because - (negative) means the submarine is 124 meters below sea level (masl).
Answer:
The elevation of a submarine with respect to sea level is displayed as - 125 feet. Which statement is correct?
A. The submarine is 125 feet above sea level.
B. The submarine is 125 feet below sea level.
C. The submarine is -125 feet above sea level.
D. The submarine is -125 feet below sea level.
Step-by-step explanation:
The keyword is below so it means it is a negative integer. Therefore the answer is letter D.PLEASE HELP ME! Only answer if correct. :)
Answers
Answer:
i don't know
im kinda silly lol lol lol lol lol lol lol lol lol
Solve for z
Please help me, thank u!!!
Answers
-3.6
Step-by-step explanation:
z/(-2) + -5 = -3.2 → times -2
z + 10 = 6.4
z = 6.4 - 10
z = -3.6
Robert types 152 words per minute. How long will it take Robert to type 2,508
words?
Answers
Answer:
16.5 minutes
Step-by-step explanation:
2508/152 = 16.5
Check: 152 x 16.5 = 2508
CAN SOMEONE PLEASE DO THESE 4 QUESTIONS
3.2x-1.7x+5.5=10
3/4x-1/4x+14=3
3(2x+1)+x=-39
m+4(2m-3)+-3
I WILL GIVE BRAINLIEST AND YOU ARE A LIFESAVER
ALSO PLEASE SHOW STEPS!!
THANKS!!!!!
Answers
Problem
3.2x-1.7x+5.5=10
Steps:
1.5x + 5.5 = 10
1.5x X 10 + 5.5 X 10 = 10 X 10
15x + 55 - 55 = 100 - 55
15x = 45
15x/15 = 45/15
x = 3
Therefore questions ones answer is x = 3
Problem
3/4x-1/4x+14=3
Steps:
3/4x - 1/4x + 14 = 3
3/4x - 1/4x + 14 - 14 = 3 - 14
3/4x - 1/4x = -11
3/4x X 4 - 1/4x X 4 = -11 X 4
2x = -44
2x/2 = -44/2
x = -22
Therefore question two's answer is x = -22
Problem
3(2x+1)+x=-39
Steps:
7x + 3 = -39
7x + 3 - 3 = -39 - 3
7x = -42
7x/7 = -42/7
x = -6
Therefore question three's answer is x = -6
Problem
m+4(2m-3)+-3
Steps:
= m + 4 (2m - 3) - 3
= m + 8m - 12 - 3
= 9m - 15
Therefore question four's answer is 9m - 15
3r+(7+8)/(t-3)when r=4, s=3 and t=5
Answers
Answer:
19.5
Step-by-step explanation:
3r+(7+8)/(t-3)
3(4)+(15)/(5-3)
12+(15/2)
12+7.5
19.5
what new realization do you have about finding the nth term of the arithmetic sequence and finding the arithmetic means how would you use this in making decision
Answers
Step-by-step explanation:
Arithmetic Sequnce in our daily life
The knowledge of calculating the nth term of a sequence can be very helpful. Calculating loans, discounts, salary, savings are some of the use of arithmetic method. If I save P5 per day for 5 years, I can simply use arithmetic sequence to find how much I saved from day 1 to last. Salary increase can also be solved using arithmetic sequence. Below is an example.
Sample real life problem:
1. I earn P300 on the first day. After each succeeding day, I earn P2 more than the previous day. How much should I be able to earn after 30 days?
In this situation, I would use the arithmetic sequence formula which is:
an = a1 + (n - 1)d
an is the nth term
a1 is the first term
n is the term position
d is the common difference
Lets subsitute:
an = P300 + (30 - 1)P2
an = P358
I should earn P348 at the end of 30 days
Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased
Answers
Answer:$8.25 ÷ 3= x or 3·x =8.25
Step-by-step explanation:
3*x=8.25
help help help help thankyou
Answers
Answer:
3.4×10⁴
Step-by-step explanation:
1.6×10⁴=1.6×10000=16000
5×10⁴=5×10000=50000
5000-16000=34000
=3.4×10⁴