Answer:
Step-by-step explanation:
The width of the rectangle is (x - 9)
(x + 4)(x - 9)
x^2 - 9x + 4x - 36
x^2 - 5x - 36
Answer:
W = ( x - 9 )
Step-by-step explanation:
The area of a rectangle is equal to the length times the width of the rectangle.
So we can say A = LW
A = (x^2 - 5x - 36)
L = (x + 4)
A = LW
W = A / L
W = (x^2 - 5x - 36) / (x + 4)
W = (x + 4) (x - 9) / (x + 4)
W = (x - 9)
Cheers.
Flying against the wind, a jet travels 2920 miles in 4 hours. Flying with the wind, the same jet travels 7140 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the wind
Answer:
Velocity in still air is = 960 miles per hour
Velocity of wind = 230 miles per hour.
Step-by-step explanation:
The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.
The velocity when flying with the wind = 7140 / 6 = 1190
Let the rate of jet in still Air = x
Let the rate of jet in wind = y
Therefore, velocity against wind = x-y and wind = x + y
x - y = 730
x + y = 1190
Add both equation, 2x = 1920
x = 960
Now find the value of “y” = 1190 – 960 = 230
Thus, velocity in still air is = 960 miles per hour
Velocity of wind = 230 miles per hour.
Answer:
Rate of jet in still air = 960 miles/ hr
Rate of the wind = 230 miles/ hr
Step-by-step explanation:
Let the speed of jet in still air = [tex]u[/tex] miles/hr
Let the speed of air = [tex]v[/tex] miles/hr
So, against the wind, the resultant speed = [tex](u-v)[/tex] miles/hr
And, with the wind, the resultant speed = [tex](u+v)[/tex] miles/hr
Distance traveled against the wind = 2920 miles
Time taken against the wind = 4 hrs
Formula for distance is:
[tex]\bold{Distance =Speed \times Time}[/tex]
[tex]2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)[/tex]
Distance traveled with the wind = 7140 miles
Time taken against the wind = 6 hrs
[tex]\bold{Distance =Speed \times Time}[/tex]
[tex]7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)[/tex]
Adding (1) and (2):
[tex]2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}[/tex]
Putting [tex]u[/tex] in (1):
[tex]960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}[/tex]
Therefore, the answer is:
Rate of jet in still air = 960 miles/ hr
Rate of the wind = 230 miles/ hr
I'm genuinely lost in any problems like this and my teachers are no help, I need help doing exponents in general, everything to do with them. I genuinely need help
Answer:
See below.
Step-by-step explanation:
4)
So we have the expression:
[tex](-6n^{-3})^2[/tex]
We can use the power of a product property, where:
[tex](ab)^n=a^n\cdot b^n[/tex]
So:
[tex]=(-6)^2\cdot(n^{-3})^2[/tex]
For the left, -6 squared is the same as -6 times -6. This equals positive 36.
For the right, we can use the power of a power property. The property says that:
[tex](a^n)^k=a^{nk}[/tex]
So:
[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]
So, all together, we have:
[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]
6)
We have the expression:
[tex]-\frac{3x^0}{x^4}[/tex]
First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:
[tex]=-\frac{3}{x^4}[/tex]
And that's the simplest we can do :)
Notes for 6)
We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:
[tex]x^n=\frac{1}{x^{-n}}[/tex]
And vice versa:
[tex]\frac{1}{x^{-n}}=x^n[/tex]
So, we can write the above as:
[tex]=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}[/tex]
However, traditionally, we want only positive exponents, so this wouldn't be correct.
Answer:
Step-by-step explanation:
x^m×x^n=x^{m+n}
x^m÷x^n=x^{m-n}
[tex]\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}[/tex]
[tex]x^0=1[/tex]
Find two numbers in-between 0.004 and 0.005
(4 + 2i) + (-3 – 5i) show your work
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ - 3i + 1}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(4 + 2i) + ( - 3 - 5i)}[/tex]
When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign.
That means the expression remains the same.
Just remove the parentheses
[tex] \sf{4 + 2i - 3 - 5i}[/tex]
Collect like terms
⇒[tex] \sf{ - 3i + 4 - 3}[/tex]
Calculate the difference
⇒[tex] \sf{ - 3i + 1}[/tex]
Hope I helped!
Best regards!!
9514 1404 393
Answer:
1 -3i
Step-by-step explanation:
For purposes of addition or subtraction, the i can be treated as though it were a variable. Terms can be collected in the usual way.
4 +2i +(-3 -5i) = 4 +2i -3 -5i
= (4 -3) +i(2 -5) = 1 -3i
Please help
Identify the slope, m, and y-intercept, b, of the equation.
y = 2x + 1
Enter the correct values in the boxes.
m=1); b =
Answer:
m = 2 (the slope is 2/1), b = 1 (the y-intercept is (0,1))
Step-by-step explanation:
First, plot a point on the y-intercept (0,1). Then go up twice and to the right once to find the next point (since the slope is 2/1). You can continue doing this to form a line. The graph is shown below
Answer:
m=2
b=1
Step-by-step explanation:
We are given the equation of a line. The equation is:
y=2x+1
This equation is in slope-intercept form, or
y=mx+b
where m is the slope and b is the y-intercept. Essentially, the coefficient of x is the slope and number that is added or subtracted from that is the y-intercept.
When we analyze the equation given, we see that x is being multiplied by 2. Therefore, the slope must be 2.
We can also see that 1 is added to 2x. Therefore, the y-intercept must be 1.
The slope of the line is 2 and the y-intercept is 1.
m=2 and b=1
The graph of the line is shown below.
can someone help me graph this.
Answer:
Use a graphing calc.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
For the third equation, m = 2
y = 2x + b
3 = 3(2) + b
3 = 6 + b
b = -3
y = 2x - 3
Marcie solved the following inequality, and her work is shown below:
−2(x − 5) ≤ 6x + 18
−2x + 10 ≤ 6x + 18
−8x +10 ≤ 18
−8x ≤ 8
x ≤ −1
What mistake did Marcie make in solving the inequality?
Answer:
She forgot to flip the sign in the last step.
Step-by-step explanation:
In inequality, if you multiply or divide by a negative number, you would have to reverse the inequality sign.
Marice forgot to do this in the final step. She had to divide '-8' to get x completely on one side. All other steps are correct.
The correct answer is x ≥ -1.
Hope this helps.
Find f(5) if f (x) = x2 – 3x?
Explanation:
Everywhere you see an x, replace it with 5. Then simplify using PEMDAS
f(x) = x^2 - 3x
f(5) = 5^2 - 3(5) ... plug in x = 5
f(5) = 25 - 15
f(5) = 10
2/3x+15=17 please and thank you
Answer:
x=3
Step-by-step explanation:
2/3x+15=17
first subtract 15 from both sides
2/3x=2
multiply by 3 to eliminate the fraction
2x=6
divide by 3
x=3
Answer:
x=3
Step-by-step explanation:
2/3x +15 = 17
2/3x = 17-15
2/3x = 2
x = 2 / 2/3
x = 2/1 * 3/2
x = 6/2
x = 3
Need help with this question. I tried simplifying the radical, but apparently it’s not the answer
Answer:
-1/5+(√3)/20i or -0.2+0.05√3i
Step-by-step explanation:
[tex]\dfrac{-8+\sqrt{-12}}{40}=-\dfrac{8}{40}+\dfrac{2\sqrt{3}i}{40}=\boxed{-\dfrac{1}{5}+\dfrac{1}{20}\sqrt{3}\,i=-0.2+0.05\sqrt{3}\,i}[/tex]
_____
Comment on answer form
Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.
There are 30 names in a hat. If two names are picked without replacement, which expression shows the probability that Jack and Jill will be picked?
Answer: Choice C)
(1/30)*(1/29)
Explanation:
Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.
an object is dropped from the top of a cliff 675 meters high. its height above the ground t seconds after it is dropped is 675-4.9t^2. determine its speed 7 seconds after it is dropped, the speed if the object 7 seconds after it's dropped in m/sec
Answer:
V= 68.6 m/s
Step-by-step explanation:
height above the ground t seconds after it is dropped is 675-4.9t^2
For seven seconds
Height above ground= 675-4.9(7)²
height above ground= 675-240.1
Height above ground= 434.9 m
But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff
Distance= 675-434.9.
Distance= 240.1
To determine it's speed
V²= U² +2gs
V= velocity we are looking for
U= initial velocity= 0
G= acceleration due to gravity= 9.8 m/s²
s= distance covered
V²= U² +2gs
V²= 0+2(9.8)(240.1)
V²= 4705.96
V= 68.6 m/s
Simplify. 1/2−3(12+1)2 Enter your answer, as a simplified fraction, in the box.
Answer: -506.5 or -253.25
Step-by-step explanation:
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{1}{2}-3\ \left(12\ +\ 1\right)^2[/tex]
[tex]= \frac{1}{2}-3 (13^2)[/tex]
[tex]= \frac{1}{2} - (3) (169)[/tex]
[tex]= \frac{1}{2} - 507[/tex]
[tex]= \frac{-1013}{2}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Evaluate 1/3m−1−1/2n when m=21 and n=12
Answer:
[tex]0[/tex]
Step-by-step explanation:
[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]
Answer:
0
Step-by-step explanation:
1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0
Simplify -3(2x - 5)
If someone could plz help. p÷5=3.
Answer:
p=2
Step-by-step explanation:
so how to find this u take the five and three and u subtract them both and whatever is left over that is your answer
To combine integers with different signs find their _ _ then _ the smaller absolute value from the larger one give the sum the sign of the number with the _ absolute
Answer:
absolute valuessubtractlargestStep-by-step explanation:
To combine integers with different signs find their absolute values then subtract the smaller absolute value from the larger one. Give the sum the sign of the number with the largest absolute value.
Your hotel sells four types of rooms: double queen beds for $140/night; king bed for $160/night; junior suite for $220, and full business suites for $285. If there are 200, 150, 100, and 50 of each, respectively, what is your average price per room?
Answer:
$176.50
Step-by-step explanation:
Take each room type and multiply the number of rooms by the price of the room. Add the total for prices and add the total for the number of rooms. Divide the total prices by the total number of rooms.
Type of room Number Cost Total
Double queen 140 $200.00 $28,000.00
King 160 $150.00 $24,000.00
Junior Suite 220 $100.00 $22,000.00
Full business 285 $50.00 $14,250.00
$500.00 $88,250.00
Average cos per room $176.50
Jay just bought a new 75" television for his apartment. The opening in the entertainment center (where the tv will be placed) is only 70 inches by 35 inches. If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center? Justify your answer by finding the width and height of the new television.
Answer:
Width of the new tv= 65.44 inches
Height of the new tv = 36.41 inches
If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?
Since the old entertainment set has a dimension of 70 inches by 35 inches
,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.
Step-by-step explanation:
The newer TV set has an aspect ratio of 16: 9 and it is 75 inches
We are going to make use of Pythagoras theorem
= Width² + Height ² = Size of TV²
Width = 16x
Height = 9x
75² = (16x)² + (9x)²
5625 = 256x² + 81x²
5625 = 337x²
x² = 5625/337
x² = 16.691394659
x = √16.691394659
x = 4.0855103303
Approximately = 4.09
Hence, we can find the width and height of the new TV
Width = 16x
Width = 16 × 4.09
Width = 65.44 inches
Height = 9x
Height = 9 × 4.09
Height = 36.81 inches
Hence, the dimensions of the new TV set = 65.44 inches by 36.81 inches
If the newer television has an aspect ratio of 16:9, will the new tv fit in the old entertainment center?
Since the old entertainment set has a dimension of 70 inches by 35 inches
,new TV set, has dimension of 65.44 inches by 36.81 inches, the new TV may not be able to fit into the old entertainment set properly because it is 1.81 inches higher than the entertainment set.
What is the speed of a vehicle when it covers a distance of 60m in 3
seconds? *
Answer:
Hey there!
Thus, the vehicle can cover 20 m per second and would have a speed of 20 meters per second.
Let me know if this helps :)
12d^2 + 3dx + x
- (-4d^2 + 2dx - 8x)
Answer:
dx+9x+16d^2 dont know it it helps any but i tried
Step-by-step explanation:
What are the factors of x2 – 100?
Answer:
[tex] {x }^{2} - 100[/tex]
[tex] {x}^{2} - {10}^{2} [/tex]
[tex](x - 10)(x + 10)[/tex]
this is the answer
hope this is helpful for you.
Find the length of arc RQ. Use 3.14
for ti. Round to the nearest tenth.
6.48 m
789
1500 650
(R
[ ? Jin
Answer:
7.4
Step-by-step explanation:
NOT 8.1 !!
The length of arc RQ is 7.35 inch.
What is Length of Arc?The distance between two places along a segment of a curve is known as the arc length.
Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°)
Given:
Angle = 65
radius = 6.48 inch
So, length of Arc
= 2πr( [tex]\theta[/tex]/ 360)
= 2 x 3.14 x 6.48 (65/360)
= 40.6944 x 0.1805
= 7.3453392
Hence, the length of arc is 7.35 inch.
Learn more about Arc Length here:
https://brainly.com/question/16403495
#SPJ2
6(n - 2) - 8 = 22 + 4(2-n)
Answer:
5
Step-by-step explanation:
6n -12 -8=22+8-4n
6n-20=30-4n
6n=50 -4n
10n = 50
5
Mrs. Taylor is making new football uniforms for Fridays nights homecoming game. The trim fro the sleeves of one uniform requires 26 inches of fabric. Mrs Taylor needs to make 63 uniforms total. How many yards of fabric should she buy?
Answer:
Mrs Taylor should buy 45.5 yards of fabric ( 45.5364 actually but rounded to the nearest tenth)
Step-by-step explanation:
Here in this question, we are interested in calculating the total yards of fabric that Mrs Taylor should buy.
From the question, we are made to know that one uniform requires 26 inch of fabrics and she wants to make a total of 63 uniforms
The total inches of fabric needed is thus; 26 * 63 = 1,638 inches of Fabrics
But we want our answer in yards.
Mathematically;
1 inch = 0.0278 yard
1638 inches = x yard
x = 1638 * 0.0278 = 45.5364 yards which is approximately 45.5yards
The 14 digits of a credit card are written in the boxes shown.If the sum of any three consecutive digits is 20, what is the
value of A?
Answer:
9
Step-by-step explanation:
Working backwards, the blank box between the 7 and 4 at the end must be 9 in order for the three digits to equal 20. Then we see the pattern of 947 repeated. The whole number would be 94794794794794. That way, any three consecutive numbers would be 20. The number in the box marked a would be 9.
Twelve decreased by twice a number is -8. Find the number
Let the number be "x" , then according to the question :
• 2x - 12 = -8
Further solving
→ 2x = -8 + 12
→ 2x = 4 .
→ x = 2
★ Solution :
Let number be n.
[tex]\rule{130}{1}[/tex]
☯ [tex]\underline{\boldsymbol{According\: to \:the\: Question\:now :}}[/tex]
[tex]:\implies\sf 2n - 12 = -8 \\\\\\:\implies\sf 2n = -8 + 12\\\\\\:\implies\sf 2n = 4\\\\\\:\implies\sf n = \dfrac{4}{2}\\\\\\:\implies\underline{\boxed{\sf n = 2}}\:\:\:\:\:\Bigg\lgroup\bf{Required\: number}\Bigg\rgroup[/tex]
[tex]\therefore\:\underline{\textsf{The required number is \textbf{2}}}.[/tex]
Prove the proposition p (0), where p (n) is the proposition "if n is a positive integer greater than 1, then n2 > n." what kind of proof did you use?
Answer:
Vacuous proof is used.
Step-by-step explanation:
Given:
Proposition p(n) :
"if n is a positive integer greater than 1, then n² > n"
To prove:
Prove the proposition p (0)
Solution:
Using the proposition p(n) the proposition p(0) becomes:
p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"
The proposition that "0 is a positive integer greater than 1" is false
Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.
Thus this is the vacuous proof which states that:
if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.
So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.
Compute $(1 + i)(2 + i)(3 + i).$
Answer:
10i
Step-by-step explanation:
Step 1: Expand first 2
(1 + i)(2 + i)
2 + i + 2i + i²
2 + 3i + (-1)
1 + 3i
Step 2: Expand again
(1 + 3i)(3 + i)
3 + i + 9i + 3i²
3 + 10i + 3(-1)
3 + 10i - 3
10i
Can someome please help me solve this my teacher hasn't done a good with teaching us this.
[tex](5.{10}^{2)} + (3 \times {10}^{4}) [/tex]
Answer:
30500 = 3.05·10^4
Step-by-step explanation:
Your calculator can do this for you. You may need to set the display to scientific notation, if that's the form of the answer you want.
__
This can be computed by converting both numbers to standard form:
(5·10^2) +(3·10^4)
= 500 +30000 = 30500 = 3.05·10^4
__
Addition of numbers in scientific notation in general requires that they have the same power of 10. It may be convenient to convert both numbers to the highest power of 10.
5·10^2 + 3·10^4
= 0.05·10^4 +3·10^4 . . . . now both have multipliers of 10^4
= (0.05 +3)·10^4
= 3.05·10^4