Answer:
Step-by-step explanation:
please include a picture of the question! :)
what does 30b/6b equal? (30b divided by 6b)
Answer:
5
Step-by-step explanation:
Given
[tex]\frac{30b}{6b}[/tex]
Cancel the b on the numerator/ denominator.
Also the 30 and 6 can both be cancelled by 6 , thus
[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5
Answer:
[tex]\boxed{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{30b}{6b}[/tex]
[tex]\sf Simplify[/tex]
[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]
[tex]5 \times 1[/tex]
[tex]=5[/tex]
Find the slope of the line that passes through (6, 7) and (2, 16). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
m = -9/4
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug in the coordinates into the slope formula:
m = (16 - 7)/(2 - 6)
m = 9/-4
m = -9/4
HELP MAJOR ASSIGNMENT PLEASE HELP pls?
Answer:
1: V:56.52 SA:94.2 Ratio: 3:5
2: V:113.04 SA:62.8 Ratio: 9:5
3: V:113.04 SA:138.16 Ratio: 9:11
4: V:113.04 SA:131.88 Ratio: 6:7
Step-by-step explanation:
Hey there!
By using the following formula for volume of a cylinder I got,
[tex](3.14) r^2h[/tex]
1: 56.52
2: 113.04
3: 113.04
4: 113.04
Now to find SA we'll use the following formula,
1: 94.2
2: 62.8
3: 138.16
4: 131.88
Now for the ratio,
56.52:94.2 - 3:5
113.04:62.8 - 9:5
113.04:138.16 - 9:11
113.04:131.88 - 6:7
Hope this helps :)
suppose that consumer usage time of computers in the public library is uniformly distributed with a minimum of 20 minutes and a maximum of 80 minutes. what is the standard deviation of the distribution
Answer:
17.32 minutes
Step-by-step explanation:
The standard deviation for a uniform distribution is:
[tex]\sigma =\frac{b-a}{\sqrt12}[/tex]
If a = 20 minutes and b = 80 minutes, the standard deviation is:
[tex]\sigma =\frac{80-20}{\sqrt12} \\\sigma=17.32\ minutes[/tex]
The standard deviation of the distribution of consumer usage time of computers in the public library is 17.32 minutes.
NEEEED HELPPPPP PLEASEEEEEE Use long division to find the quotient below.
(8x^2 + 4x^2 + 100) - (2x + 5)
Answer:
[tex]4x^2 - 8x + 20[/tex]
Step-by-step explanation:
The correct equation is:
[tex]8x^3 + 4x^2 + 100[/tex]
We want to divide that by (2x + 5)
To do the long division, divide each term by 2x and then subtract the product of the result and (2x + 5) from the remaining part of the equation.
When you get to 0, you have reached the end of the division.
Whatever term you get from each step of division is part of the quotient.
Go over the steps above carefully while following them below:
Step 1:
Divide [tex]8x^3[/tex] by 2x. You get [tex]4x^2[/tex].
Step 2
Multiply [tex]4x^2[/tex] by (2x + 5) and subtract from [tex]8x^3 + 4x^2 + 100[/tex]:
[tex]8x^3 + 4x^2 + 100[/tex] - ([tex]8x^3 + 20x^2[/tex]) = [tex]-16x^2 + 100[/tex]
Step 3
Divide [tex]-16x^2[/tex] by 2x. You get [tex]-8x[/tex].
Step 4
Multiply -8x by (2x + 5) and subtract from [tex]-16x^2 + 100[/tex]:
[tex]-16x^2 + 100[/tex] - ([tex]-16x^2 - 40x[/tex]) = 40x + 100
Step 5
Divide 40x by 2x. You get 20.
Step 6
Multiply 20 by (2x + 5) and subtract from 40x + 100:
40x + 100 - (40x + 100) = 0
From the three steps of the division, we got [tex]4x^2[/tex], -8x and 20.
Therefore, the quotient is [tex]4x^2 - 8x + 20[/tex]
x and x+1 are the two continuous natural numbers, then (i) Write the next two natural numbers. (ii) Find the product of first and the fourth number. (iii) Find the product of second and the third number. (iv) Find the relation between these products.
Answer:
(i) X+2 and x+3;
(ii) x( x+4)= X^2 +4x;
(iii) x( x+4)=a
(x+1)(x+3)= a+3
Step-by-step explanation:
(i) X+2 and x+3;
(ii) x( x+4)= X^2 +4x;
(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;
x(x+4)=a
(x+1)(x+3)= a+3
Step-by-step explanation:
x is followed by x+1 so each time we add one
our sequence goes like this:
xx+1 x+1+1⇒ x+2 x+2+1⇒x+3the first number is x and the fourth one is x+3
x*(x+3) x²+3xthe second number is x+1 and the third one is x+2
(x+1)(x+2)x²+2x+x+2 x²+3x+2the first product is x²+3x and the second one is x²+3x+2
Let P be x²+3x and P' be x²+3x+2
P'-P = 2P' = P+2Consider a regular pyramid A with a square base and a right circular cone B.
It is given that the length of a side of the square base of pyramid A is the same as the base radius of cone B.
If the two solids have the same volume, which solid will have a greater height? Explain your answer.
Please help me solve this question with steps!orz
Answer:
Pyramid
Step-by-step explanation:
[tex]\text{Volume of a Square Pyramid }=\frac{1}{3} \times l^2 \times Height\\\\ \text{Volume of a Cone }=\frac{1}{3} \pi r^2 \times Height[/tex]
Given that the two solids have the same volume
[tex]\frac{1}{3} \times l^2 \times Height=\frac{1}{3} \pi r^2 \times Height[/tex]
If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r
[tex]\frac{1}{3} \times l^2 \times $Height of Pyramid=$\frac{1}{3} \pi l^2 \times $Height of cone$\\\\$Cancel out $ \frac{1}{3} \times l^2$ on both sides\\\\Height of Pyramid= \pi \times $ Height of cone$[/tex]
If the height of the cone is 1
[tex]H$eight of Pyramid= \pi \times 1 \approx 3.14$ units[/tex]
Therefore, the pyramid has a greater height.
Last week Betty practiced her guitar for 45 minutes on Monday, 25 minutes on Tuesday, 35 minutes on Wednesday, 20 minutes on Thursday, and 40 minutes on Friday. What was the mean number of minutes that she spent practicing each day?
Answer:
33 minutes
Step-by-step explanation:
To find the mean, you first must add up the values given.
45 + 25 + 35 + 20 + 40 = 165
Now, divide the sum by the number of values you have.
165/5 = 33
The mean number of minutes she spent practicing is 33.
Simplify
[tex]\ \textless \ br /\ \textgreater \ \sqrt[4]{16a^- 12}\ \textless \ br /\ \textgreater \ [/tex]
Answer:
[tex]\huge\boxed{\sqrt[4]{16a^{-12}}=2a^{-3}=\dfrac{2}{a^3}}[/tex]
Step-by-step explanation:
[tex]16=2^4\\\\a^{-12}=a^{(-3)(4)}=\left(a^{-3}\right)^4\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\sqrt[4]{16a^{-12}}=\bigg(16a^{-12}\bigg)^\frac{1}{4}\qquad\text{used}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\bigg(2^4(a^{-3})^4\bigg)^\frac{1}{4}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\bigg(2^4\bigg)^\frac{1}{4}\bigg[(a^{-3})^4\bigg]^\frac{1}{4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{(4)(\frac{1}{4})}(a^{-3})^{(4)(\frac{1}{4})}=2^1(a^{-3})^1=2a^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]=2\left(\dfrac{1}{a^3}\right)=\dfrac{2}{a^3}[/tex]
the square root of 5 is
Step-by-step explanation:
The square root of 5 can be approximately found by doing the square root of 4 to get 2, and the square root of 9 to get 3. Then, because 5 is closer to 4 than 9, the square root of 5 is about 2.2.
Otherwise, simply do sqrt(5) in a calculator to get 2.23606798
Hope it helps <3
0.719 to the nearest hundredth
Answer:
.72
Step-by-step explanation:
9 rounds up because 1-4 stay the same and 5-9 round up
Answer: 0.719 to the nearest hundredth is 0.72
Simplify $(1-3i)(1-i)(1+i)(1+3i)$
[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]
Answer:
[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]
Step-by-step explanation:
[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]
please solve it 100 POINTS please help- PLEASE HELP its Identify the following for the quadratic relations please slove it all please if you can save the picture and do it on the page
Answer:
[tex]\boxed{\mathrm{view \: attachments}}[/tex]
Step-by-step explanation:
Vertex is the highest or lowest point of a parabola.
Axis of symmetry is the line that cuts the parabola in half.
y-intercept is the point where the parabola touches the y-axis.
The maximum or minimum values are the highest or lowest values the parabola can reach.
x-intercepts are the points where the parabola touches the x-axis.
g(x)=5-2x what is domain
Answer:
all real numbers
Step-by-step explanation:
The domain of any polynomial function is "all real numbers."
The level of water in a dam was decreasing by 20% each day. If the level of water was 1500cm,what was the level after two days?
Answer:
[tex] L_o= 1500 cm[/tex]
And we know that the level is decreasing 20% each day so then we can use the following model for the problem
[tex] L_f = L_o (1-0.2)^t[/tex]
Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:
[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]
Step-by-step explanation:
For this case we know that the initial volume of water is:
[tex] L_o= 1500 cm[/tex]
And we know that the level is decreasing 20% each day so then we can use the following model for the problem
[tex] L_f = L_o (1-0.2)^t[/tex]
Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:
[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]
The area of the rectangle below is __sq. units.
5
16
Answer:
C.
Step-by-step explanation:
To find the area of a rectangle, times the length and the breadth together. So, it would be 16×5=80. option C is 80.
Answer:
80 sq.units
Step-by-step explanation:
A of rectangle = L×B
L= 16 units
B=5 units
A of rectangle = L×B
=16×5 units
=80 sq.units
Why the order of a succession is important
Answer:
Step-by-step explanation:
The order of a succession is a way that the terms (the first, the second, the third, etc.) can be distinguished according to a certain formation law or order criterion.
Example:
a¹/a²/a³/a⁴ And successively
In the order of a sequence you can assign any letter.
1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. (a) Write an equation for the volume V of the box in terms of x. (b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Step-by-step explanation:
The dimensions are (8-2x) and (10-2x) We will say the depth of the box is x. The equation we use for the volume of the box is V=x(8-2x)(10-2x)
Answer:
part b of the answer is x=1.5 inches
Step-by-step explanation:
Please answer it now in two minutes
Answer:
5.5
Step-by-step explanation:
We use right triangle XVW.
For <W, VX is the opposite leg.
WX is the hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine.
[tex] \sin W = \dfrac{opp}{hyp} [/tex]
[tex] \sin W = \dfrac{VX}{WX} [/tex]
[tex] \sin 43^\circ = \dfrac{VX}{8~mi} [/tex]
[tex] VX = 8~mi \times \sin 43^\circ [/tex]
[tex] VX = 5.5~mi [/tex]
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answer:
a) 18
b) 20
c) 12
d) 12
Step-by-step explanation:
a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18
b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20
c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12
d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12
Please answer this question now
Answer:
MN = 14 ft
Step-by-step explanation:
NP tangent => ∡PNM = 90°
Pythagoras
MN = √MP² - NP²
= √50² - 48²
= √(50 - 48)(50 + 48)
= √2×98
= √196
= √14²
= 14 ft
Hi how to solve this simultaneous equation
Answer:
[tex]\large \boxed{\sf \ \ x=\pm8 \ \ or \ \ x=\pm2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
First of all, we can assume that x and y are different from 0, as we cannot divide by 0.
And from the first equation we can write y as a function of x as below.
[tex]y=\dfrac{16}{x}[/tex]
And then, we replace it in the second equation to get.
[tex]\dfrac{x}{\frac{16}{x}}+\dfrac{\frac{16}{x}}{x}=\dfrac{17}{4}\\\\<=> \dfrac{x^2}{16}+\dfrac{16}{x^2}=\dfrac{17}{4}\\\\\text{*** We multiply by }16x^2 \text{ both sides ***}\\\\x^4+16*16=\dfrac{17*16}{4}x^2\\\\x^4-68x^2+3600=0\\\\\text{*** The product of the zeroes is 3600 = 64*4 and the sum is 64+4=68 ***}\\\\\text{*** So we can factorise *** }\\\\x^4-64x^2-4x^2+3600=x^2(x^2-64)-4(x^2-64)=(x^2-64)(x^2-4)=0\\\\x^2=64=8^2 \ \ or \ \ x^2=4\\\\x=\pm8 \ \ or \ \ x=\pm2\\[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the y-intercept of the function y=4-5x?
Answer:
4
Step-by-step explanation:
y=mx+b
b=y-intercept.
In this case...
mx=-5<-- this is the slope of the line.
b=4<-- y intercept.
Hope this helps, any further questions, please feel free to ask.
prove that : ( sin 4 theta + cos 4 theta )= 1-2 sin square theta cos square theta
Answer:
From sin²θ + cos²θ = 1, we have;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ
Step-by-step explanation:
The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ
We have;
(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;
(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1
Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ = 1
From which we can get;
(sin²θ + cos²θ)·(sin²θ + cos²θ) = 1
Given that sin²θ + cos²θ = 1
Therefore;
1 × 1 = 1
To get to the initial equation in the question, we have;
sin²θ + cos²θ = 1
(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1
(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1
∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ = 1 - 2·sin²θ·cos²θ
Therefore;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.
Please help, ty if you do
Answer:
C
Step-by-step explanation:
4,800 times 7% is 336, and 1200 times 14% is 168, and 168 is half as much as 336, so the correct answer is c
Answer:
C
Step-by-step explanation:
Multiply .7 to 6000 and solve
what the formula of speed
Answer:
The formula for speed is s=(distance traveled)/(time elapsed)
Answer:
[tex]\huge \boxed{S =\frac{d }{t} }[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The formula to find speed is as follows:
[tex]\Longrightarrow \ \ \displaystyle \sf speed =\frac{distance \ travelled }{time \ taken}[/tex]
[tex]\Longrightarrow \ \ \displaystyle S =\frac{d }{t}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Which of these is the absolute value parent function?
O A f(x) = 12x1
O B. f(x) = (x + 1
O c. f(x) = [xl - 2
O D. f(x) = [X]
Answer:
D. f(x) = |x|
Step-by-step explanation:
The absolute value parent function has nothing added or subtracted or multiplied. It is simply ...
f(x) = |x|
Lucy is a dress maker. She sew 4/7 of a dress in 3/4 hour. lucy sews at a constant rate At this rate, how many dresses does lucy sew in one hour
Answer:
(5 1/3)/7
Step-by-step explanation:
Divide 4 by 3, then times it by four and put it over the 7
À television ser costs $350 cash. When
bought on hire purchase, a deposit of $35 is
required, followed by 12 monthly payments
of $30. How much is saved by paying cash
Answer:
$45.
Step-by-step explanation:
When the TV is bought on hire purchase, you deposit $35 and pay $30 monthly. There are 12 payments. 12 * 30 = $360. 360 + 35 = $395.
Since cash would've cost $350, the amount of money saved by paying cash is 395 - 350 = $45.
Hope this helps!
Zero product property
x(2x+4)(x+5)=0
A) x=0, x=-2, X=-5
B) x=0, x=2, x=5
C) x greater than or equal to 0
D) x=-2, x=5
Answer:
A
Step-by-step explanation:
Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.