[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 14 }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } [/tex]
[tex] \\= \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } [/tex]
[tex] \\= \frac{2 \: (2 + \sqrt{3} )+ \sqrt{3} \: (2 + \sqrt{3} )}{ ({2})^{2} - ({ \sqrt{3} })^{2} } + \frac{2 \: (2 - \sqrt{3} ) - \sqrt{3} \: (2 - \sqrt{3} ) }{ ({2})^{2} - ( { \sqrt{3} })^{2} } [/tex]
[tex]\\ = \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 - 3} + \frac{4 - 2 \sqrt{3} - 2 \sqrt{3} + 3}{4 - 3} [/tex]
[tex]\\ = \frac{7 + 4 \sqrt{3} }{1} + \frac{7 - 4 \sqrt{3} }{1} [/tex]
[tex] \\= 7 + 4 \sqrt{3} + (7 - 4 \sqrt{3} )[/tex]
[tex] \\= 7 + 4 \sqrt{3} + 7 -4 \sqrt{3} [/tex]
[tex] \\= 14[/tex]
Note:[tex] (a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
In the ordered pair below, which value represents the input to a function?
(2, 3)
Answer:
2
Step-by-step explanation:
In an order pair
(x,y)
The first number is the input and the second number is the output
(2,3) 2 is the input and 3 is the output
Eve's sequence decreases by 2 hundreths each time. she picks a number to start with. what is the difference betwen her 3rd and 6th number?
Answer: 0.06
Step-by-step explanation:
Given
Eve's number decreases by 2 hundredths each time i.e. [tex]0.02[/tex]
Difference between 3rd and 4 th number is [tex]0.02[/tex], while the difference between 3 rd and 5 th is double the previous i.e. [tex]2\times 0.02=0.04[/tex]
So, the the difference between the 3 rd and 6 th number is three time the difference
[tex]\Rightarrow 3\times 0.02\\\Rightarrow 0.06[/tex]
Lauren eats 1/8 of a chocolate cake before supper, and then eats another 1/8 after supper.
a) What fraction of the cake did she eat altogether? ______
b) What fraction of the cake was left? __________ 2 marks
Answer:
she ate 2/8ths and left 6/8ths
which of the following is true?
Answer:
the right ones are a c and d maybe
Step-by-step explanation:
these are probably wrong but I need my points so figure it out.
how do you find the area of a rectangle
Answer:
You multiply length by width.
Step-by-step explanation:
To find the area of a rectangle you multiply length and width together.
For example if a rectangle has length 2 and width 3 the area of the rectangle would be 6, since 2 * 3 is 6.
Answer:area =length x width
Step-by-step explanation:
x2+ y2 − 8x + 12y + 27 = 0
Using the standard form of the equation in question 1, what are the length of the radius and the coordinates of the center for this particular circle? Watch your signs for the variables h and k.
Central (4,–6)
Radius 5
Answer:
this was the answer from edmentum
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
(-8, -2) and (-6,2)
Answer: [tex]2\sqrt{5}\\\\[/tex]
To get that answer, we apply the distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-6))^2 + (-2-2)^2}\\\\d = \sqrt{(-8+6)^2 + (-2-2)^2}\\\\d = \sqrt{(-2)^2 + (-4)^2}\\\\d = \sqrt{4 + 16}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.472136\\\\[/tex]
As an alternative, you could plot the two points on the same xy grid, and then form a right triangle. Afterward, apply the pythagorean theorem and you should get the same result as shown above.
what is the definition of risk ?
Answer: DOING SOMETHING THAT HAS THE POSOBILITY OF IT BEING BAD
Step-by-step explanation: BECAUSE
Answer:
D
Step-by-step explanation:
just got it right on edge
A skateboard that is originally $107 is on sale for 90% off!! How much does the skateboard cost?
90% off means is is selling for 10% of the original price.
Multiply original price by 10%
107 x 0.01 = $10.70
It is selling for $10.70
I need help does the table represent a function
Answer:
b. no, because one x-value corrseponds to two different y-values
Step-by-step explanation:
for a set/table to be a function, the each x-value must correspond to exactly one value, not more, therefore the set of points in this table do not represent a function as the x-value 6 corresponds to more than one number.
Which inequality is true?
A) |−6| > −6
B) |12| < |−5|
C) |−8| < 8
D) 7 > |−10|
Answer:
A) |−6| > −6
Step-by-step explanation:
Absolute value means take the non negative number
A) |−6| > −6 = 6> -6 true
B) |12| < |−5| 12 < 5 false
C) |−8| < 8 8 < 8 false
D) 7 > |−10| 7 > 10 false
Confused on how to solve this problem, please help and offer a step by step explanation
Answer:
7x+5=180
7x=175
x=25
Hope This Helps!!!
I need help on this
A quarter circles fits exactly into a square of side 4 cm, as shown.
Determine the area of the shaded region, giving your answer correct to 3 significant figures.
Side of square = Radius of circle = 4cm
Area of full circle
= πr²
= (22/7) × 4cm × 4cm
= 352/7 cm²
Area of the quarter of circle
= Area of full circle/4
= (352/7)/4
= (352/7) × (1/4)
= 352/28
= 12.571 {approximately}
Pls help me with this!
Answer:
Your answer would be X ≥ -3
Step-by-step explanation:
Can someone help me plz
Step-by-step explanation:
the answer is in the image above
5(4)-4/2 ??
Some know how to respond
Answer:
19 1/2??? Read explanation
Step-by-step explanation:
I am not sure entirely by your formatting when you put it into Brainly but since 5x4=20 and 20-1/2 = 19 1/2, the answer would be 19 1/2 but I am not sure due to the format.
Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)
Answer:
18
20 -2 = 18
Step-by-step explanation:
Please answer number 13 only
Answer:
44%
Step-by-step explanation:
5 ½=5.5
12½=12.5
5.5/12.5=0.44
0.44×100=44%
Answer:
Answer:
44%
Step-by-step explanation:
5 ½=5.5
12½=12.5
5.5/12.5=0.44
0.44×100=44%
Step-by-step explanation:
How many eighths does it take to equal 1/4 model
Answer:
2 eighths.
Step-by-step explanation:
Answer:
2 eighths
Step-by-step explanation:
1/8 + 1/8 = 2/8 or 1/4
Consider the function shown in the table.
What are the inputs of the function?
-1, 0, 1, 2
-1,0,3
-1, 0, 1, 2, 3
Answer: a
Step-by-step explanation:
its the first one
Answer:
the first one is A and the second one is B
Step-by-step explanation:
im doing the assignment right now
Assume the following: 1) the scattergraph intersects the Y axis at $200; 2) the estimated line on the scattergraph increases by $10 for every 1 unit of volume increase. What is total cost if volume is 20 units
Answer:
The total cost is:$400
Step-by-step explanation:
Given
[tex]x \to units[/tex]
[tex]y \to cost[/tex]
[tex](x,y) = (0,200)[/tex] --- when the graph intersects the y-axis
[tex]m = 10[/tex] -- the rate
Required
y when x = 20
First, we determine the equation of the plot using:
[tex]y = mx + c[/tex]
Substitute 10 for m
[tex]y = 10x + c[/tex]
Next, solve for c.
Substitute [tex](x,y) = (0,200)[/tex]
[tex]200 = 10*0+c[/tex]
[tex]200 = 0+c[/tex]
[tex]c = 200[/tex]
So:
[tex]y = 10x + c[/tex]
[tex]y =10x + 200[/tex]
When x = 20
[tex]y =10*20 + 200[/tex]
[tex]y =200 + 200[/tex]
[tex]y = 400[/tex]
which step in the construction of coping a lin segment ensures that the new line segment has the same length as the original line segment
Step-by-step explanation:
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Here are the steps I think you probably will go through.
1. Draw a line that is longer than the segment but shorter than the width of the page.
1a. Make sure this line is at least 1/2 inch from the left hand side.
2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.
3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.
The key step either two or three.The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
select all explanation that prove triangle ABC is congruent to triangle A'B'C
Answer:
AB = A'B'
BC = B'C'
AC = A'C'
angle ABC = angle A'B'C'
angle CAB = angle C'A'B'
angle CBA = angle C'A'B'
Step-by-step explanation:
use different axomes to show relation,
Answer: Reflect ABC across the vertical line passing through C
Step-by-step explanation:
The cuboid and the triangular prism have the same volume. Find the value of x.
Answer:
x = 25
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular face and l is its length )
A = [tex]\frac{1}{2}[/tex] bh = 0.5 × 5 × 8 = 20 cm² , then
V = 20 × 20 = 400 cm³
The volume of the cuboid is calculated as
V = lbh = 3.2 × 5 × x = 16x
Given V = 400 cm³ , then
16x = 400 ( divide both sides by 16 )
x = 25
Jade has seven cards. Each card is labeled with a letter. A B C D E F G H J Jade picks one of her cards at random. Find the probability that the card she picks is a) labelled F, b) labelled with a letter in her name JADE c) labelled with a letter that has at least one line of symmetry
Answer:
(a) [tex]\frac{1}{7}[/tex]
(b) [tex]\frac{4}{7}[/tex]
(c) [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Probability (P) of an event is the likelihood that the event will occur. It is given by;
P = number of favourable outcomes ÷ total number of events in the sample space.
Given letters of cards:
A B C D E F G H J
∴ Total number of events in sample space is actually the number of cards which is 7
If a card is picked at random;
(a) the probability P(F), that it is labelled F is given by;
P(F) = number of favourable outcomes ÷ total number of events in the sample space.
The number of favourable outcomes for picking an F = 1 since there is only one card labelled with F.
∴ P(F) = 1 ÷ 7
=> P(F) = [tex]\frac{1}{7}[/tex]
(b) the probability P(N), that it is labelled with a letter in her name JADE is given by;
P(N) = P(J) + P(A) + P(D) + P(E)
Where;
P(J) = Probability that it is labelled J
P(A) = Probability that it is labelled A
P(D) = Probability that it is labelled D
P(E) = Probability that it is labelled E
P(J) = [tex]\frac{1}{7}[/tex]
P(A) = [tex]\frac{1}{7}[/tex]
P(D) = [tex]\frac{1}{7}[/tex]
P(E) = [tex]\frac{1}{7}[/tex]
∴ P(N) = [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex]
∴ P(N) = [tex]\frac{4}{7}[/tex]
(c) the probability P(S), that it is labelled with a letter that has at least one line of symmetry is;
P(S) = P(A) + P(B) + P(C) + P(D) + P(E) + P(H)
Where;
P(A) = Probability that it is labelled A
P(B) = Probability that it is labelled B
P(C) = Probability that it is labelled C
P(D) = Probability that it is labelled D
P(E) = Probability that it is labelled E
P(H) = Probability that it is labelled H
Cards with letters A, B, C, D, E and H are selected because these letters have at least one line of symmetry. A line of symmetry is a line that cuts an object into two identical halves. Letters A, B, C, D, E and H can each be cut into two identical halves.
P(A) = [tex]\frac{1}{7}[/tex]
P(B) = [tex]\frac{1}{7}[/tex]
P(C) = [tex]\frac{1}{7}[/tex]
P(D) = [tex]\frac{1}{7}[/tex]
P(E) = [tex]\frac{1}{7}[/tex]
P(H) = [tex]\frac{1}{7}[/tex]
∴ P(S) = [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex]
∴ P(S) = [tex]\frac{5}{7}[/tex]
Which statement is true regarding the graphed functions?
Answer:
f(2) = 0 and g(2) = 0
f(2) = g(2) TRUE
b) f(0) = 2 and g(0) = -2
f(0) = g(0) FALSE
c) f(2) = 0 and g(0) = -2
f(2) = g(0) FALSE
d) f(0) = 2 and g(2) = 0
f(0) = g(2) FALSE
pls help I'll mark brainliest
Answer:
305°
Step-by-step explanation:
The angle between the north line at L and the line connecting PL is
125° (75° + 50° ) ← alternate angle between parallel lines
Then
bearing of P from L is 180° + 125° = 305°
What is the period of the graph of…
PLEASE THIS PICTURES ANSWER PLEASE 10 POINTS ............................
NO WRONG ANSWER REPORT......
Hey buddy I am here to help!
1. 8*5*2 = 40*2= 80cm2
3. 10*25*60 = 250*60 = 15000m2
2. 12*12*12 = 36cm2
4. 3*5*18 = 90*4 = 360m2
Hope my answer helps!
Plz mark me brainliest!
● Question 3. answer is wrong in last multiply so their answer is 1728m^3...
In this image their in question (1,2,3,4) answer...
I hope you understand...
Mark me as brainliest....
Thanks
Anyone knows how to do "Using Congruence Postulates," I need help with an equation, can someone show me step by step.
what is the cofficient in the expression 8x^2+1?
Answer:
8
Step-by-step explanation:
Answer is 8