======================================================
Explanation:
Any vector of the form v = (a,b) will have a length of |v| = sqrt(a^2+b^2).
This is derived from the pythagorean theorem. It's the same as saying the distance from (0,0) to (a,b) is sqrt(a^2+b^2).
In this case, a = 3 and b = -4, which means...
|v| = sqrt(a^2+b^2)
|v| = sqrt(3^2+(-4)^2)
|v| = sqrt(9+16)
|v| = sqrt(25)
|v| = 5
The vector is 5 units long.
Note: we have a 3-4-5 right triangle
[tex]2 {a}^{2} - 3ab + {b}^{2} from3 {a}^{2} + 2ab - {b}^{2} [/tex]
Answer:
a (a - b)
Step-by-step explanation:
[tex]2a^{2}-3ab+b^{2} from 3a^{2} + 2ab - b^{2}[/tex]
Now, as [tex]2a^{2}-3ab+b^{2}[/tex] is from [tex]3a^{2} + 2ab - b^{2}[/tex]
so it will be subtracted :
[tex]3a^{2} + 2ab - b^{2}[/tex] [tex]-2a^{2}-3ab+b^{2}[/tex]
= [tex]a^{2} - ab[/tex]
= a (a - b)
hey can i get help here? im just a middle schooler and my school just jumped into this with no explanation. so far highschoolers helped me understand it more than any teacher could. so in those terms, thank you so much!
Answer:
the closest answer is the last option, so I would say that is the correct one.
Step-by-step explanation:
4.5 x 4.5 x π =
20.25 x π =
63.6172....
Subtract the sum of -6 and -2 from -18. *
Answer:
-26
Step-by-step explanation:
Because -6+ -2= -8
-18- 8= -26
Solve 2x^2
+ x - 4= 0.
x2 +
= 0
DONE
[tex]\\ \sf\longmapsto 2x^2+x-4=0[/tex]
[tex]\\ \sf\longmapsto 2x^2+x=4[/tex]
[tex]\\ \sf\longmapsto 8(2x^2+x=4)[/tex]
[tex]\\ \sf\longmapsto 16x^2+8x=32[/tex]
[tex]\\ \sf\longmapsto (4x)^2+2(4x)(1)=32[/tex]
[tex]\\ \sf\longmapsto 4x^2+2(4x)(1)+1^2=32+1^2[/tex]
[tex]\\ \sf\longmapsto (4x+1)^2=33[/tex]
[tex]\\ \sf\longmapsto 4x+1=\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto 4x=-1\pm\sqrt{33}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-1\pm\sqrt{33}}{4}[/tex]
does anyone know the answer to this i need help really bad!!!
Step-by-step explanation:
1/20.5 is yr ansstay safe healthy and happy...Teresa is loading her car with boxes that each weigh 4 pounds. If Teresa loads 9 of these boxes, find the combined weight of the boxes.
A.42 3/4
B.13 3/4
C.36 3/4
D.40 1/4
Determine the value of x.
Question 11 options:
A)
5
B)
5
C)
10
D)
Answer: [tex]\frac{10}{\sqrt{3}}[/tex]
This is equivalent to [tex]\frac{10\sqrt{3}}{3}[/tex]
======================================================
Explanation:
To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.
This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.
The expression [tex]\frac{10}{\sqrt{3}}[/tex] is the same as [tex]\frac{10\sqrt{3}}{3}[/tex] after we multiply top and bottom by sqrt(3) to rationalize the denominator.
Side notes:
This entire process only applies to 30-60-90 triangles.The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is [tex]2x = 2*\frac{10\sqrt{3}}{3} = \frac{20\sqrt{3}}{3}[/tex] units long. You could use the tangent ratio to help isolate x. You would either say tan(30) = x/10 or tan(60) = 10/x as the first equation to set up.Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers.
1. x2 - 6x + 8 = (ax + b)(cx + d)
2.3x3 - 6x2 - 24x = 3x(ax + b)(cx + d)
3. 2x2 - 2x - 24 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
9514 1404 393
Answer:
(a, b, c, d) = (1, -4, 1, -2)(a, b, c, d) = (1, -4, 1, 2)(a, b, c, d) = (1, -4, 2, 6)Step-by-step explanation:
Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.
__
1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)
(a, b, c, d) = (1, -4, 1, -2)
__
2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)
(a, b, c, d) = (1, -4, 1, 2)
__
3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)
(a, b, c, d) = (1, -4, 2, 6) or (2, -8, 1, 3)
Find the volume of the trapezoidal prism following.
Answer:
60 cm³
Step-by-step explanation:
Applying,
Volume (V) = Area of the base(A)×Height(h)
V = Ah................ Equation 1
From the diagram,
A = Area of Trapezium
A = 1/2(a+b)c............. Equation 2
Substitute equation 2 into equation 1
V = [1/2(a+b)c]h........... Equation 3
Given: a = 3 cm, b = 7 cm, c = 3 cm, h = 4 cm
Substitute these values into equation 3
V = [3(3+7)/2]4
V = (3×10/2)4
V = (3×5)4
V = 15×4
V = 60 cm³
in a study of 225 adults the average heart rate was 72 beats per minute assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute what does a margin of error of 1.1 for the 90% confidence interval of the average beats per minute mean
Answer:
There Is A 90% Chance That The Population Mean Is Between 70.9 And 73.1 Beats Per Minute. There Is A 90% Chance That The Population Mean Is Between 62 And 82 Beats Per Minute. There Is A 10% Chance That The Population Mean Is Less Than 72 Beats Per Minute
Hope it helps
Find the missing measure for a right circular cone given the following information.
Find h if r = 5 and V = 100 pi.
4
12
30
Answer:
[tex]Volume = \frac{1}{3} \pi r^2 h \\\\r= 5\\Volume = 100\pi\\\\Find \ h.\\\\h = 3\frac{V}{\pi r^2} = 3 \times \frac{100 \pi}{\pi \times 5^2} = 3\times \frac{100}{25} = 3 \times 4 = 12[/tex]
24% of what is 25? Round to the nearest tenth.
The diameter of a cone-shaped storage tank is 14 feet and it's height is 9 feet. Find the volume of liquid the tank can hold. Round your answer to the integer, if necessary. Use the approximate of value of /pi , that is 3.14.
Answer:
461.6 ft³
Step-by-step explanation:
V(cone) = 1/3πr²h
= 1/3π(7²)(9)
= 49·3π
= 147(3.14)
= 461.6 ft³
is 0.45 greater than 0.5
Answer:
0.5
hope this helps
have a good day :)
Step-by-step explanation:
Construct the indicated confidence interval for the difference in proportions. Assume that the samples are independent and that they have been randomly selected.A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference in the proportions of New Yorkers and Californians who knew the product.
Answer:
CI 99% = ( - 0.0009 ; 0.0541 )
Step-by-step explanation:
Sample 1 New Yorkers
sample size n₁ = 558
x₁ = 193
p₁ = x₁/n₁ = 193/ 558 p₁ = 0.3458 q₁ = 1 - p₁ q₁ = 1 - 0.3458
q₁ = 0.6542
Sample 2 Californians
sample size n₂ = 614
x₂ = 196
p₂ = x₂/n₂ = 196 / 614 p₂ = 0.3192 q₂ = 1 - p₂ q₂ = 1 - 0.3192
q₂ = 0.6808
CI 99 % means significance level α = 1 αα% α = 0.01
α/2 = 0.005
In z-table we look for z score for 0.005 z (c) = 2.57
CI 99 % = [ ( p₁ - p₂ ) ± z(c) * √( p₁*q₁)/n₁ + ( p₂*q₂)/n₂
p₁ - p₂ = ( 0.3458 - 0.3192 ) = 0.0266
√( p₁*q₁)/n₁ + ( p₂*q₂)/n₂ =√ 0.3458*0.6542)/558 + 0.3192*0.6808)/614
√( p₁*q₁)/n₁ + ( p₂*q₂)/n₂ = √ 4.05*10⁻⁴ + 3.54 * 10⁻⁴
√( p₁*q₁)/n₁ + ( p₂*q₂)/n₂ = 10⁻² * √7.59 = 10⁻² * 2.75
Then:
CI 99 % = 0.0266 ± 2.75 * 10⁻²
CI 99% = 0.0266 ± 0.0275
CI 99% = ( - 0.0009 ; 0.0541 )
This box is packed with cubes that measure one cubic foot.
enter the volume of the box in cubic feet.
Answer:
72ft^3
Step-by-step explanation:
I first took a single slice off the box and counted how many cubes there were. By looking at the blue side, I counted 12 cubes in that slice. I then counted how many slices were in the box, which were 6.
12* 6 = 72ft^3
Suppose that you have the option to buy an itern with either cash or credit?Under which condition would you use credit?
A if you don't want to pay interest
B if you want to build a good credit history
C if you like carrying a lot of cash on you
Answer:
Step-by-step explanation:
B. You build credit by using credit cards so b is the answer.
6. Yenni bought some apple pies for $13 and had some money left. If she
buys 1 more apple
pie, she would have $0.20 left. If she decided to buy 3
more apple pies, she would be short of $1.80.
(a) How many apple pies did she buy with $13?
(b) How much money did Yenni have at first?
Answer:
A) Since each apple pie costs $ 1, with $ 13 Yenni bought 13 apple pies.
B) Yenni had $ 14.20 at the beginning.
Step-by-step explanation:
Since Yenni bought some apple pies for $ 13 and had some money left, and if she buys 1 more apple pie, she would have $ 0.20 left, while if she decided to buy 3 more apple pies, she would be short of $ 1.80, for To determine how many apple pies did she buy with $ 13, and how much money did Yenni have at first, the following calculations must be performed:
0.20 - (-1.80) = X
0.20 + 1.80 = X
2 = X
2/2 = 1
Therefore, since each apple pie costs $ 1, with $ 13 Yenni bought 13 apple pies.
13 + 1 + 0.20 = 14.20
14.20 - 13 = 1.20
In turn, Yenni had $ 14.20 at the beginning.
Find the sum of -3x2 -4x+3 and 2x2-x+3
Answer:
Assuming the 2 at the ends are the exponents,
the answer is -x^2-5x+6 (x^2+5x-6)
from here, it cannot be simplified more
Explanation --
Just add everything by putting the terms in parentheses and adding them.
Keep simplifying by putting the like terms together and adding/subtracting them.
At the end, you come up with -x^2-5x+6, so multiply -1 on the whole thing (by putting parentheses on its sides. This makes x positive. But they are the same thing, but this step is just for simplifying the end product a little more.
Hope this helps!! Have a nice day!
Determine whether the statement is always, sometimes, or never true. Lines AB, CD, and EF determine plan P. If GH intersects AB, then GH lies on plan P.
=======================================================
Explanation:
The plane P can be thought of a perfectly flat ground. Now imagine a flag pole which represents line GH. If AB is drawn in chalk on the pavement, and this line AB intersects the base of the flagpole, then we've made AB and GH intersect. However, this example shows that GH is not on the plane P.
Is it possible to have GH be in the the plane? Yes. We could easily draw another chalk line on the ground to have it intersect AB somewhere. But as the previous paragraph says, it's also possible that GH is not in the plane.
Therefore, the statement is sometimes true
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18y – 3.x = -90
Answer:
Step-by-step explanation:
Rob has 6 quarts of apple cider for the fall fair. He pours the cider into glasses to set on picnic tables. He pours 6 ounces of cider into each glass. How many glasses of cider does Rob set on the tables? Show your work.
Answer:
6 x 32 = 192 divided by 6 = 34
Step-by-step explanation:
Choose the three rectangular prisms that have a volume of 24 cm3.
= 1 cm
A.
D.
E.
Answer: I think is A, D, E
Step-by-step explanation:
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden
The confidence interval is pretty wide and leaves a lot of uncertainty over the proportion of UCI students who live on campus. With the goal to estimate a narrower 95% confidence interval, what is a simple change to this study that you could suggest for the next time that a similar survey is conducted
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Researchers must increase the response rate to achieve a narrower confidence interval. Because we see that the trust gap is inverse to sample size. We must increase data in estimating a narrower 95-percent trust range. Since the sample has increased, its error margin has decreased, this reduces the width of the trust interval.
Twice a number is 14. What is the number
Answer:
7
Step-by-step explanation:
Divide 14 by 2
What is the miss angle in F?
Answer:
45
Step-by-step explanation:
The two angles add to 90 degrees since they are a right angle
F + 45 = 90
F = 90-45
F = 45
6 people share 12 muffins
What is the answer to this question?
Find the length of side b
B= _m
Answer:
b= 0.09475
Step-by-step explanation:
What percentage of $250 is $75?
To calculate the percentage,
75/250×100 = 30%
Answer:
30%
Step-by-step explanation:
75/250=0.3
0.3= 3/10
3/10=30%