Answer: A) 1 B) [tex]\sqrt5[/tex]
Step-by-step explanation:
[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]
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.
A weight is attached to a spring, which moves up and down as a function of time. p(t) gives the position of the weight at time (t). Position is in centimeters, and time is in seconds. Complete the following sentences based on the graph of the function. · The graph is a linear, nonlinear, or constant function. · The initial position of the weight is _ centimeter(s). · The weight first reaches equilibrium when t = _ second(s). Note: We say that the weight is at equilibrium whenever p(t)=0 cm and we say that the initial position of the block is its position when t=0s PLZ help me look at the picture for the graph plz answer ASAP thank you
Answer:
This graph is nonlinear
The initial displacement of the weight is 40cm
The weight first returns to equilibrium when t=1/2
Step-by-step explanation:
thats the answer i only had time to give not to explain
Answer:
the answer is in the photo ^^
Step-by-step explanation:
the correct thing is there for confirmation ;)
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
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
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
PLEASE HELP I REALLY NEED HELP
Answer:
16
Step-by-step explanation:
perimeter of B = 21
divide by 3 to get each side: 21/3 = 7 = Y
perimeter of hexagon is 50. subtract 2Y: 50 - 14 = 36
divide 36 by 4 to find X = 9
add X + Y
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
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.
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]
A right triangle has a height of 18 inches and a base of 12 inches find the area of the triangle in square inches find the area of the triangle in square inches
Answer: 108 square inches
Step-by-step explanation:
The formula for any square is base*height/2. The formual to find the area of a square is base*height. If you draw out a square and cut it in half diagonaly, you get a right triangle. That is why you divide it by 2. (sorry if the explanation was clunky/ hard to understand)
1. You would multiply 18*12 which equals 216.
2. Divide 216 by 2. 216/2= 108.
The answer is 108. Hope this helped you:)
The area of the triangle is 108 square inches.
What is the area of the triangle?The area of the triangle is defined as the product of half the base and the height of the triangle.
The area of the triangle = 1/2 x b x h
If we draw out a square and cut it in half diagonaly, you get a right triangle. That is why we need to divide it by 2.
The area of the triangle = 1/2 x b x h
The area of the triangle = 1/2 x 12 x 18
= 216/2= 108.
The area of the triangle is 108 square inches.
Learn more about the area;
https://brainly.com/question/1658516
#SPJ2
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
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
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]
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]
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
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.
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.
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
if a translation of (x, y) → (x + 6, y – 10) is applied to figure ABCD, what are the coordinates of D'? (–5, –2) (1, –12) (4, –15) (–9, –6)
Answer: The coordinates of D are (1,-12) .
Step-by-step explanation:
Given : Translation rule : (x, y) → (x + 6, y – 10) is applied to figure ABCD.
From the figure below, we have figure ABCD in which
The coordinates of D = (-5,-2)
According to the given translation rule :
D(-5,-2) → D'(-5 + 6, -2 – 10) (coordinates of image point D')
i.e. D(-5,-2) → D'(1, -12) [-5+6 = 1, -2-10 = -12]
Hence, the coordinates of D are (1,-12) .
Answer:
B. (1, –12)
Step-by-step explanation:
edge2021
jasper owns a small retail store as a sole proprietor. the business records show that the cost of the stores inventory items has been steadily increasing. the cost of the end of the year inventory is 200,000 and the cost of the beginning of the year inventory was 250,000. jasper uses the fifo method of inventory valuation. Which of the following statements are true?
a. jasper purchases more inventory during the year than sold during the same one year period.
b. jasper would have a higher net income
if he used the lifo method of inventory valuation instead of the fifo method
c. jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory
d. since the cost of the stores inventory items is increasing, jasper will have a greater cost of goods sold figure under the fifo than the lifo.
e. none of the above
Answer:
c. jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory
Step-by-step explanation:
First In First Out FIFO is a type of inventory system in accounting, it literally implies that the oldest purchase goes out first when you made a sale. The oldest purchase are charged based on cost of good sold. If price are rising, :
FIFO will yield a lower cost of good sold
FIFO will yield a higher net income
FIFO will yield higher tax liability
FIFO will yield a higher inventory
From the information given:
the business records show that the cost of the stores inventory items has been steadily increasing. the cost of the end of the year inventory is 200,000 and the cost of the beginning of the year inventory was 250,000.
What the statement implies is that:
jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory
A box contains 5 yellow toys and 4 red toys. Two toys are selected with replacement.
- Draw a tree diagram showing all outcomes and probabilities
-Find the probability that:
A. Two toys of the same colour will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked
-if there was no replacement, find the probability that:
A. Two toys of the same colours will be picked
B. Toys of different colours will appear
C. A red toy will be picked first
D. At least one red toy will be picked
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Yellow (Y) toys = 5
Red (R) toys = 4
Total toys = yellow + red = (5 +4) = 9
WITH REPLACEMENT :
Probability that two toys of same color will be picked.
From the tree diagram.
Two toys of the same color
a.)P(Y, Y) + P(R, R) = (25/81) + (16 / 81) = 41/81
b) toys of different color :
P(Y, R) + P(R, Y) = (20/81) + (20/81) = 40/81
c.) A red toy will be picked first :
P(R, Y) = 20/81
d.) Atleast one red toy will be picked
P(Y, R) + P(R, Y) + P(R, R)
20 /81 + 20/81 + 16/81 = 56/81
2) WITHOUT REPLACEMENT :
a.)P(Y, Y)+P(R, R) = (20/72) + (12/72) = 32/72 = 4/9
b) P(Y, R)+P(R, Y) = (20/72)+(20/72)= 40/72 = 5/9
c) p(R, Y) = 12/72 = 1/6
d) P(Y, R) + P(R, Y) + P(R, R) = 20/72 + 20/72 + 12/72 = 52/72 = 13/ 18
25 percent of 510,000
Answer:
127 500
Step-by-step explanation:
Let x be the missing value.
● 510 000 => 100
● x => 25
x = (25*51000)÷100 = 127 500
Answer:
hope it helps
Step-by-step explanation:
25 percent of 510,000 = 127,500
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]
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]
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.
A bowl contains pecans, cashews, and almonds in a ratio of 6 : 10 : 15, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?
i. 1 : 2 : 3
ii. 2 : 3 : 4
iii. 4 : 7 : 10
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
Answer:
iii
Step-by-step explanation:
because of the amount taken from the cashews.and nuts and 1 of 3 were taken away
Suppose we have three urns, namely, A B and C. A has 3 black balls and 7 white balls. B has 7 black balls and 13 white balls. C has 12 black balls and 8 white balls. We first choose one urn from A, B and C. Then we randomly pick up two balls from that urn without replacement. Let Ai, i 1,2,3 denote the event that the urn we choose is A, B and C respectively. Suppose P(A1): P(A2): P(A3) =1:2:2. Compute :
(a) The probability that the first ball is black.
(b) The probability that the first ball is black given that the second ball is white.
Answer:
a. 11/25
b. 11/25
Step-by-step explanation:
We proceed as follows;
From the question, we have the following information;
Three urns A, B and C contains ( 3 black balls 7 white balls), (7 black balls and 13 white balls) and (12 black balls and 8 white balls) respectively.
Now,
Since events of choosing urn A, B and C are denoted by Ai , i=1, 2, 3
Then , P(A1 + P(A2) +P(A3) =1 ....(1)
And P(A1):P(A2):P(A3) = 1: 2: 2 (given) ....(2)
Let P(A1) = x, then using equation (2)
P(A2) = 2x and P(A3) = 2x
(from the ratio given in the question)
Substituting these values in equation (1), we get
x+ 2x + 2x =1
Or 5x =1
Or x =1/5
So, P(A1) =x =1/5 , ....(3)
P(A2) = 2x= 2/5 and ....(4)
P(A3) = 2x= 2/5 ...(5)
Also urns A, B and C has total balls = 10, 20 , 20 respectively.
Now, if we choose one urn and then pick up 2 balls randomly then;
(a) Probability that the first ball is black
=P(A1)×P(Back ball from urn A) +P(A2)×P(Black ball from urn B) + P(A3)×P(Black ball from urn C)
= (1/5)×(3/10) + (2/5)×(7/20) + (2/5)×(12/20)
= (3/50) + (7/50) + (12/50)
=22/50
=11/25
(b) The Probability that the first ball is black given that the second ball is white is same as the probability that first ball is black (11/25). This is because the event of picking of first ball is independent of the event of picking of second ball.
Although the event picking of the second ball is dependent on the event of picking the first ball.
Hence, probability that the first ball is black given that the second ball is white is 11/25
Which lists all of the y-intercepts of the graphed function? (0, –3) (–1, 0) and (3, 0) (0, –1) and (0, 3) (–1, 0), (3, 0), and (0, –3)
Answer:
The correct option is;
(0, -3), (-1, 0) and (3, 0)
Step-by-step explanation:
From the given graph of the function we have the following observations;
There are two x-intercepts which are;
1) To the left of the vertical y-axis having coordinates (-1, 0)
2) To the the right of the y-axis having coordinates (3, 0)
There is only one y-intercept having coordinates, (0, -3)
Therefore, all the intercepts of the function are, (0, -3), (-1, 0) and (3, 0).
Answer:
(0, -3), (-1, 0) and (3, 0)
Step-by-step explanation:
The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13 centimeters. What is the approximate surface area of the cone? Use 3.14 for π and round to the nearest whole number. 267 cm2 283 cm2 456 cm2 487 cm2
Answer:
283 cm^2
Step-by-step explanation:
Solution:-
We have a cone with a circular base of radius r = 5 cm
The height of the cone is h = 12 cm
The slant height of the cone is L = 13 cm
We are to determine the surface area of the cone. The surface area of the cone is comprised of two parts:
Base Area : Circle
[tex]A_1 = \pi r^2\\\\A_1 = \pi 5^2\\\\A_1 = 25\pi[/tex]
Curved Surface: conical
[tex]A_2 = \pi * r*L\\\\A_2 = \pi * 5*13\\\\A_2 = 65\pi[/tex]
The total surface area of the cone can be written as ( A ):
[tex]A = A_1 + A_2\\\\A = (25 + 65 )*\pi \\\\A = 90*(3.14) \\\\A = 282.7433 cm^2[/tex]
Answer: The surface area of the cone to nearest whole number would be 283 cm^2