Answer:
[tex]\huge\boxed{A=6x^2-11x+3;\ \text{for}\ x>1.5}[/tex]
Step-by-step explanation:
The formula of an area of a rectangle:
[tex]A=a\cdot b\\\\a,\ b-\text{sides of a rectangle}[/tex]
We have:
[tex]a=2x-3\\b=3x-1[/tex]
The domain:
[tex]2x-3>0\ \wedge\ 3x-1>0\\\\2x-3+3>0+3\ \wedge\ 3x-1+1>0+1\\\\2x>3\ \wedge\ 3x>1\\\\\dfrac{2x}{2}>\dfrac{3}{2}\ \wedge\ \dfrac{3x}{3}>\dfrac{1}{3}\\\\x>1.5\ \wedge\ x>\dfrac{1}{3}\Rightarrow\boxed{x>1.5}[/tex]
Substitute:
[tex]A=(2x-3)(3x-1)[/tex]
use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]A= (2x)(3x)+(2x)(-1)+(-3)(3x)+(-3)(-1)\\\\A=6x^2-2x-9x+3[/tex]
combine like terms
[tex]A= 6x^2+(-2x-9x)+3\\\\A=6x^2-11x+3[/tex]
Answer:
6x² - 11x + 3
Step-by-step explanation:
To find the area of a rectangle, we multiply the length by the width.
A = l • w
length: 2x-3
width: 3x-1
A = (2x-3) • (3x-1)
To multiply these two binomials, we must FOIL (first | outer | inner | last) them.
F: 2x • 3x = 6x²
O: 2x • -1 = -2x
I: -3 • 3x = -9x
L: -3 • -1 = 3
Combine the terms.
6x² - 2x - 9x + 3
Combine like terms.
6x² - 11x + 3
This is your area.
Hope this helps!
root 225 rational or irrational? plzz help urgent.
Find an equivalent ratio 24:9
F 6 to 2
H 36 to 13.5
G 5:12
J 6:5
Determine the area of the rectangle. Write your answer as a decimal.
Answer: all you have to do is times length times width
which is 1 1/2x4 1/2 and then make it a decimal
Which line is parallel to the line y= x + 7 ?
Answer: y=x+
Step-by-step explanation:
In order for two lines to be paralell, their slopes must be the same but their y intercepts must be different. Therefore, any line that looks like y=x+ (anything but 7) will be paralell.
What is (1/2+i √3/2)^5?
Answer:
Hello! I know I am late but here is the answer for anyone else who might need it.
D. 1/2-i√3/2
Step-by-step explanation:
I got it right on edge. Hope this helps!
The value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
What is binomial theorem?
The expression of the form (a+b)^n is expand by binomial theorem.
The expansion is [tex](a+b)^{n}=\sum_{r=0}^{n}{ }^{n} C_{r} a^{n-r} b^{r}[/tex].
What is the value of given expression?Use a=1/2 and b=[tex]b=\frac{i\sqrt{3} }{2}[/tex] into the expansion of binomial.
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\sum_{k=0}^{5}\left(\begin{array}{l}5 \\k\end{array}\right)\left(\frac{1}{2}\right)^{5-k}\left(\frac{\sqrt{3} i}{2}\right)^{k}[/tex]
When k=0 then, [tex]\left(\begin{array}{l}5 \\0\end{array}\right)\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{5 !}{(5-0) ! 0 !}\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{1}{32}[/tex]
When k=1 then, [tex]\left(\begin{array}{l}5 \\1\end{array}\right)\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 !}{(5-1) ! 1 !}\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 \sqrt{3} i}{32}[/tex]
When k=2 then, [tex]\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=\frac{5 !}{(5-2) ! 2 !}\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=-\frac{15}{16}[/tex]
When k=3 then, [tex]\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=\frac{5 !}{(5-3) ! 3 !}\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=-\frac{15 \sqrt{3} i}{16}[/tex]
When k=4 then, [tex]\left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{5 !}{(5-4) ! 4 !}\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{45}{32}[/tex]
When k=5 then, [tex]\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{5 !}{(5-5) ! 5 !}\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{9 \sqrt{3} i}{32}[/tex],
Now we will add all the results to get the expansion of given expression,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{32}+\frac{5 \sqrt{3} i}{32}-\frac{15}{16}-\frac{15 \sqrt{3} i}{16}+\frac{45}{32}+\frac{9 \sqrt{3} i}{32}[/tex]
On simplifying,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex]
Therefore, the value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
Learn more:https://brainly.com/question/13672615
#SPJ2
A. ________________ of these pairs of identical triangles can be composed into a rectangle. B. ________________ of these pairs of identical triangles can be composed into a parallelogram.
The question is incomplete. The complete question is :
Discuss your responses to the first question with your group. Then, complete each of the following statements with all, some, or none. Sketch 1–2 examples to illustrate each completed statement.
A. ________________ of these pairs of identical triangles can be composed into a rectangle.
B. ________________ of these pairs of identical triangles can be composed into a parallelogram.
Solution :
A. None
None of the identical triangles provided in the sketch can be composed into a rectangle, it can be formed into a square. A rectangle is a quadrilateral with four sides having opposite side equal in length. The two adjacent sides of a rectangle are different in size. Thus a rectangle cannot be a square.
B. All
All of the figures provided in the sketch can formed a parallelogram. Two identical triangles can always be composed into a parallelogram by the segments that connects the opposite vertices.
Help please?
.........................
Determine whether the triangle with the given side lengths is acute,
right, obtuse or not a triangle 14,16,27
Answer:
this triangle is "obtuse
Step-by-step explanation:
Since sides 14 and 16 add up to 30, which is more than the third side, 27, we DO have a triangle here. The sides of lengths 14 and 16 form an angle greater than 90 degrees, and so this triangle is "obtuse." It's not a right triangle either, because the Pythagorean Theorem is not satisfied: 14^2 + 16^2 = 452, which is NOT 27^2.
PLEASE HELP, I'll GIVE BRAINLIEST FOR BEST ANSWER.
A drawer contains black socks and white socks. 40% of the socks are black socks. A number generator simulates randomly selecting 10 socks from the drawer. The number generator is used 10 times and the number of black socks in each trial is shown in the dot plot.
Which description is correct about the number generator being fair or not?
A.)The number generator is fair. It picked black socks half of the time.
B.)The number generator is not fair. It picked black socks half of the time.
C.)The number generator is not fair. In three experiments, it picked black socks 50% of the time.
D.)The number generator is fair. It picked the approximate percentage of black socks most of the time.
Answer:
the number generated is fair . it picked the approximate percentage of black socks most of the time
A two-word Phrase that indicates a ratio or fraction
Answer:
For every
Step-by-step explanation:
Hope this helps!
Answer:
Ratio-Proportion is the answer
Solve- 5x - 2(2x - 7) = 2(3x - 1) + [tex]\frac{7}{2}[/tex]
Pls help mehhh
Which equation describes this graph?
Answer: C ([tex]y = x - 3[/tex]).
"doNT Youu wiSH your GRaNDMa was hoT like Mee"
Answer: XD that was great
Andre is preparing for the school play. He needs to paint a cardboard box to look like a dresser. The box is a rectangular prism that measures 5 feet tall, 4 feet long, and 2.5 feet wide. Andre does not need to paint the bottom of the box. 1. How much cardboard does Andre need to paint?
Answer:
Step-by-step explanation:
75 is right
I have 47 missing assignments .
Answer:
60 ft cubed
Step-by-step explanation:
3 x 4 x 1
= 12
6 x 8 x 1
=48
The 6 comes from dividing the shape into smaller rectangles, one rectangle is a 3 x 4 and the other is a 6 x 8
For a unit circle determine the ordered pairs that are associated with any angle that has a reference to 30 degrees?
Ordered pairs on an unit circle..
Exact values of the ordered pairs of the unit circle is represented in pictorial form above in degrees and radians.
Hope this helps.
Find the volume of the solid. Round your answer to the nearest tenth.
Answer:
31.71 mm
Step-by-step explanation:
#1: Find V of cube
(L)(W)(H) = V
(3)(3)(3) = V
27= V
#2: Find V of the half sphere.
3 (diameter) × π = 9.42 (rounded)
9.42/2 (since 9.42 is the volume for a whole sphere)
=4.71
#3: 4.71+27= 31.71
:)
Write an exponential function in the form y=ab^x that goes through points (0,17) and (2, 612).
Answer:
y = 17 * (± 6)ˣ
Step-by-step explanation:
y=abˣ
pass (0 , 17): 17 = a b⁰ = a a = 17
pass (2 , 612): 612 = 17 * b² b² = 36 b = ± 6
y = 17 * (± 6)ˣ
Derek put 10 crickets in his pet lizard’s cage. After one day, Derek’s lizard had eaten 20% of the crickets he had put in the cage. By the end of the next day, the lizard had eaten 25% of the remaining crickets. How many crickets were left in the cage at the end of the second day?
Answer:
6 crickets
Step-by-step explanation:
First day: 20% of 10 is (.20)(10) = 2, so there were 10 - 2 = 8 crickets left.
Second day: 25% of 8 is (.25)(8) = 2, so there were 8 - 2 = 6 crickets left.
How would you describe the difference between these to figures? J K J K
Answer:
the second one is separate points on a line while the first one is a line segment.
explanation:
this is what I got based of my understanding and knowledge of this question. I hope it helps I am sorry if it is not exactly what you wanted for an answer. have a great day.
Which expressions are equivalent to 5^{12}\cdot 5^85
12
⋅5
8
5, start superscript, 12, end superscript, dot, 5, start superscript, 8, end superscript
Answer:
start fraction, 5, dot, x, start superscript, 3, end superscript, divided by, x, start superscript, 2, end superscript, end fraction
for
x=2x=2
x=2
x, equals, 2
The given expression 5, start superscript, 12, end superscript, dot, 5, start superscript, 8, end superscript equivalent to the 5 start superscript 97 end superscript.
We have given that
[tex]5^{12}\cdot5^{85}[/tex]
We have to find the equivalent expression
Here we use the exponent rule:
Which exponent rule we use here?[tex]a^b\cdot a^c=a^{b+c}\\[/tex]
here base is the same of both the number
If base are same then we can add the exponent
Therefore,In a given expression base is 5 therefore the
[tex]5^{12}\cdot5^{85}=5^{12+25}\\5^{12}\cdot5^{85}=5^{97}[/tex]
Therefore the given expression [tex]5^{12}\cdot5^{85}[/tex]equivalent to the [tex]5^{97}[/tex].
To learn more about the exponent visit:
https://brainly.com/question/2456547
A car travels according to the table of value shown.what equation can be used to predict the distance (d) the car travels in the number of hours (h)
Answer:
Vajsjke
Step-by-step explanation:
ggzodxkdfdjhs
Two cemented walls are parallel to each other. A ladder is placed touching the top of the two walls and is inclined at an angle of 30 degrees. If the walls are 6 meters and 16 meters high, at least how long should the ladder be? (with solutions)
Answer:
20 meters
Step-by-step explanation:
the length of ladder = (16-6)/ sin30°
= 10/ ½ = 20 meters
The distance around a circle
Answer:
circumference
Step-by-step explanation:
Answer:
circumference
Step-by-step explanation:
center (3,-2), radius =5
Answer:
(x-3^2+y+2^2 =25
Step-by-step explanation:
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 14. What percentage of people has an IQ score greater than 114?
Answer:
15.87%
Step-by-step explanation:
We start with getting the z score
Mathematically , we have this as;
z-score = (x-mean)/SD
where x = 114
z-score = (114-100)/14 = 14/14 = 1
So we want to calculate the probability values that are greater than 1
We can use the standard normal distribution table
so we have P(z> 1) = 0.15866
in percentage, we multiply by 100 and that gives 15.866 which is 15.87 people
What shape has
4 equal sides and
No right angles
Answer:
Rhombus
Step-by-step explanation:
Answer:
The answer is a rhombus
Hope this helps!
Mark me brainliest?? :)
Oliver's family took a 4-hour-and-30-minute trip on a train. They left at 7:30 a.m.
What time did Oliver's family arrive?
Answer:
12pm
Step-by-step explanation:
7:30am + 4 hours and 30 minutes = 12 pm
Answer:
Well, assuming that they just drove for four and half hours straight, without the train stopping for any reason, they would arrive at 12:00pm
7 + 4 = 11
30 + 30 = 60, and since that 60 is an hour then...
11 + 1 = 12
Hope this helps(:
GIVING BRAINLIEST!!!PLS HELP :((
The first rule is subtract 5 starting from 30. The second rule is add 8 starting from 0. What is the fourth ordered pair using the terms in each sequence?
(16, 20)
(8, 25)
(15, 24)
(32, 10)
Answer:
D (32, 10)
Step-by-step explanation:
30 - 5 - 5 - 5 - 5 = 10
0 + 8 + 8 + 8 + 8 = 32
The scale factor of a model car is the actual car is 300. If the model car is 2 in tall, how all is the car
Answer:
600
Step-by-step explanation:
The length of the actual car is 600.
What is a scale factor?Scale factor is that it is a number that multiplies times a given quantity to produce a smaller or larger version of the original number. The ratio of any two corresponding lengths in two similar geometric figures.
For the given situation,
The scale factor of a model car = 2
The length of the model car = 300
The length of the actual car = [tex]300(2)[/tex]
⇒ [tex]600[/tex]
Hence we can conclude that the length of the actual car is 600.
Learn more about scale factor here
https://brainly.com/question/22644306
#SPJ2