Answers
Answer: Check out the diagram below
[tex]1.5 \le x \le 5.5[/tex]
The lengths can be between 4 and 12 units
=======================================================
Explanation:
Let's find an expression that represents the area.
The length is 2x+1 and the width is 3. Multiply those two and we get
3(2x+1) = 6x+3
The area is 6x+3 square units.
In other words, A = 6x+3 represents the area.
------------------
We're then told that [tex]12 \le A \le 36[/tex] saying that the area is between 12 and 36 square units (including both endpoints).
We'll replace the A with 6x+3 and solve for x like so:
[tex]12 \le A \le 36\\\\12 \le 6x+3 \le 36\\\\12-3 \le 6x+3-3 \le 36-3 \ \text{ .... see note1}\\\\9 \le 6x \le 33\\\\\frac{9}{6} \le \frac{6x}{6} \le \frac{33}{6} \ \text{ .... see note2}\\\\\frac{3}{2} \le x \le \frac{11}{2}\\\\1.5 \le x \le 5.5\\\\[/tex]
note1: I subtracted 3 from all sides to undo the "plus 3"
note2: I divided all sides by 6 to undo the multiplication
------------------
We just found that [tex]1.5 \le x \le 5.5\\\\[/tex] so it says that x is between 1.5 and 5.5 including both endpoints.
Plug in the smallest possible x value to find the smallest possible length
length = 2x+1
L = 2(1.5)+1
L = 3+1
L = 4
The smallest possible length is 4 units. Multiply this with the height 3 and we get L*W = 4*3 = 12 which is the smallest possible area.
------------------
Now use x = 5.5 to find the largest value of L possible
L = 2x+1
L = 2(5.5)+1
L = 11+1
L = 12
Then note how L*W = 12*3 = 36 is the max area possible, which matches with that your teacher wrote. So this confirms we have the correct value.
If you're not sure which values go where, check out the diagram below.
Related Questions
Wesley makes spherical fish tanks with a diameter of 30 cm. A customer requests a smaller tank with half the volume of the tank that Wesley usually makes. What is the approximate diameter of the smaller tank?
Answers
Answer:
23.8
Step-by-step explanation:
v = 4/3 pi r cube
v =4/3 pi r (15) cube
v=4500 pi
v= 45000 pi /2=4/3pi r cube
1687.5=r cube
r =11.9
d =23.8
(please tell me if its wrong, if it is i will fix it!) :).
The perimeter of a rectangular field is 344m . If the length of the field is 93m , what is its width?
Answers
Answer:
width is 79 m
Step-by-step explanation:
P = 2l + 2w
344 = 2(93) + 2w
344 = 186 + 2w
158 = 2w
w = 158/2
w = 79
The radius of a circle is 11 meters. What is the circle's area?
Answers
Answer:
379.94 m²
Step-by-step explanation:
3.14×11²= 379.94 m²
Step-by-step explanation:
The area of a circle is
π[tex]r^{2}[/tex]
The r is 11 so we get 11^2 * π
121π is our exact area,
380.13 m^2 is our approximate area
What is the mesure of angle AXB?
Answers
A snow cone cup is 12cm tall and has a diameter or 8cm find the volume of the flavored ice that can be held inside the snow cone cup
Answers
Answer:
200.96 cm³
Step-by-step explanation:
Volume of a cone = πr²h/3
Pi, π = 3.14
Radius, r = diameter/2
= 8 cm/2
= 4 cm
Height, h = 12 cm
Volume of a cone = πr²h/3
= 3.14 * (4 cm)² * 12 cm / 3
= 3.14 * 16 cm² * 12 cm / 3
= 602.88 cm³/3
= 200.96 cm³
Volume of a cone = 200.96 cm³
Find the distance between the two points in simplest radical form.
(-9,3) and (-3,-5)
Answers
Answer:
10
Step-by-step explanation:
Distance Formula: sqrt_/(x1-x2)^2 + (y1-y2)^2
sqrt_/(-9-(-3))^2 + (3-(-5))^2
sqrt_/(-6)^2 + (8)^2
sqrt_/36+64
sqrt_/100
Simplify and you get the number 10.
LABEL THE TRIANGLE!! PLEASE HELP!!
Answers
Answer:
Determination of HYP,OPP,ADJ with respect to x.
Opposite side of right angle:Hypotenuse: AC
Opposite side of given angle: Opp:BC
remaining side of a triangle: Adjacent:AB.
PLEASE ANSWER THIS IS DUE TOMORROW!!!!!!!!!!!
Answers
Answer:
x-intercept: 15
y-intercept: -6
The slope is positive because 2/5 (the slope) is positive.
Step-by-step explanation:
The x-intercept is where the line crosses the x-axis.
The y-intercept is where the line crosses the y-axis.
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year’s value.
At this rate, what can Dan expect the approximate value of the computer to be after 12 years?
A $73
B. $90
C. $29
D. $85
Answers
Answer:
$29, that is the answer for this question
What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?
Answers
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts1) Determine the slope (m)
[tex]x-2y=6[/tex]
Rearrange this equation into slope-intercept form (this will help us find the slope)
Subtract x from both sides
[tex]x-2y-x=6-x\\-2y=-x+6[/tex]
Divide both sides by -2
[tex]y=\frac{1}{2} x-3[/tex]
Now, we can identify clearly that the slope of the given line is [tex]\frac{1}{2}[/tex] since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of [tex]\frac{1}{2}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (-6,-8)
[tex]-8=\frac{1}{2}(-6)+b\\-8=-3+b[/tex]
Add 3 to both sides to isolate b
[tex]-8+3=-3+b+3\\-5=b[/tex]
Therefore, the y-intercept is -5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x-5[/tex]
I hope this helps!
A bag contains 4 blue marbles, 6 red marbles, 3 yellow marbles, and 5 black marbles. What is the probability that you choose two marbles, without replacement, that are both black? Answer as a decimal to the nearest thousandths place (3 after the decimal).
Answers
Answer:
.065
Step-by-step explanation:
The total number of marbles is
4 blue marbles+ 6 red marbles+ 3 yellow marbles+5 black marbles=18
P(1st black) = Black/total = 5/18
You keep the marble
The total number of marbles is
4 blue marbles+ 6 red marbles+ 3 yellow marbles+4 black marbles=17
P(2st black) = Black/total = 4/17
Multiply the probabilities together
P(black,black)= 5/18 * 4/17 =10/153=.065359477 =.065
Find the range of the relation {(-8,1),(-3,-6),(-7,-5),(9,5),(-2,9)}
Answers
Explanation: the range is to subtract the maximum and the minimum. The maximum is 9,5 and the minimum is -2,9
(5. solve for x )
2/5 + x = 1
Answers
ALRIGHT 66% WE NEED AT LEAST AN 80, WHAT WONDERFUL PERSON IS GONNA HELP!?
Answers
Answer:
I got 45
Step-by-step explanation:
so I did the triangle first I did 5 times 6 divided by 2 and got 15 then I did 5 times 6 and got 30 then I added the 30 and 15 together.
Answer:
Formula of trapezoid:
B1(base 1) + B2(base 2) x Height(h) x 1/2
Area of Trapezoid:
10(base 1) + 6(base 2) = 16
16 x 5 = 80
80 x 1/2 = 40
In a 3-digit number, the hundreds is one more than the ones digit and tens digit is twice the hundred digit. If the the sum of the digits is 11, find the number.
Answers
Answer:
362
Step-by-step explanation:
Let u = the units digit
2(u + 1) = the tens digit
u + 1 = the hundreds digit
u + 2(u + 1) + u + 1 = 11
u + 2u + 2 + u + 1 = 11
4u + 3 = 11
4u = 8
u = 2 = ones digit
u + 1 = 3 = hundreds digit
2(u + 1) = 2(3) = 6
The number is 362
Please help. Thank you....
Answers
Hopefully this helps
Which of the following is not a triangle similarity theorem
Answers
Answer:
D. SSA
Step-by-step explanation:
The SSA postulate does not exist because an angle and two sides does not guarantee that the two triangles are congruent. This is because if two triangles have two congruent sides but a non-included congruent side, this does not indicate that it is necessarily congruent.
If you have 5 questions and get an 80% how many questions did you get wrong?
Answers
Answer:
4
Step-by-step explanation:
Multiple Rules (Condense)
You can also use multiple rules at a time to condense
multiple log expressions to one.
2 log(x) +3 log(y) – 4 log(z)
Would condense to which of the following?
2 3
log
4
log
23
log
1,3,4
log(x21324)
Answers
Answer:
A
Step-by-step explanation:
Log poperties
[tex] {x}^{2} + 16x + 10 = 0[/tex]Split the middle term.
Answers
Liz records her pet hamster's weight once every month for one year. How many observations does she make?
Answers
Answer: 12 observations
Step-by-step explanation:
1 year = 12 months
Number of observations = 1 per month
Therefore number of observations
for a year = 1 × 12
= 12 observations.
Please help 15 points!!!
Answers
Answer:
20 m²
Step-by-step explanation:
Figure 1: 4 x 4 = 16
Figure 2: 2 x 2 = 4
16 + 4 = 20
I need to find this angle please help i know it is adjacent but i need the angle.
Answers
Answer:
148 degrees!
Step-by-step explanation:
They are 180 degrees together so just subtract 32. 180- 32 = 148.
Answer:
148°
Step-by-step explanation:
A flat angle measures 180°
180° - 32° = 148°
can some one help me plzz!! No links!!
Answers
In the coordinate plane, what is the length of the line segment that connects points at (5,4) and (-3,-1)
Enter your answer in the box. Round to the nearest hundredth.
units
Answers
Answer:
9.434 units
Step-by-step explanation:
Given data
points (5,4) and (-3,-1)
x1= 5
y1= 4
x2= -3
y2= -1
The expression for the distance between two points is
d=√((x_2-x_1)²+(y_2-y_1)²)
substitute
d=√((-3-5)²+(-1-4)²)
d=√((-8)²+(-5)²)
d=√64+25
d=√89
d=9.4339
d= 9.434 units
Hence the distance between the points is 9.434 units
What is the perimeter of the garage if d=3
I’m marking branliest
Answers
Answer:
perimeter= 46
Step-by-step explanation:
(3(3)-2) + (3(3)-2) + (5(3)+1) + (5(3)+1)
7 + 7 + 16 + 16
= 46
Write the expressions for the following:
(i) 3 added with the product of x and y.
(ii) 4 subtracted from the product of -2 and m.
Answers
Answer:
i) (xy)+3 or 3+(xy)
ii) (-2×m)-4
Answer:
3+xy
-2m-4
Step-by-step explanation:
Two wires, a = 90 ft apart, tether a balloon to the ground, as shown. How high is the balloon above the ground? (Round your ans
Answers
Answer:
180
Step-by-step explanation:
A laptop is in the shape of a rectangular prism. The laptop has a length of 14
inches, a width of 10 inches, and a height of 1.5 inches.
What is the volume of the laptop?
Answers
Answer:
V=210 square inches
Step-by-step explanation:
Volume formula for a rectangular prism is V=lwh
So Volume=Length x Width x Height
V= 14 x 10 x 1.5
V=210 square inches
What is the slope for y = - 6x + 12 on a graph
Answers
Answer:
For question A) y = -6 , b = 12
For question B) x = 2
Step-by-step explanation: