Step-by-step explanation:
[tex] \tt \longrightarrow \dfrac{8}{2 \sqrt{6} + 3 } - \dfrac{4}{2 \sqrt{6} - 3 } \\ \\ \tt \longrightarrow \dfrac{8(2 \sqrt{6} - 3) - 4(2 \sqrt{6} + 3)}{(2 \sqrt{6} + 3)(2 \sqrt{6} - 3 ) } \\ \\ \tt \longrightarrow \dfrac{16\sqrt{6} - 24 - 8 \sqrt{6} - 12}{(2 \sqrt{6} ) {}^{2} - (3) {}^{2} } \\ \\ \tt \longrightarrow \dfrac{8\sqrt{6} - 36}{24 - 9 } \\ \\ \tt \green{\longrightarrow \dfrac{8\sqrt{6} - 36}{15 }} [/tex]
Laura made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces was $21.30. If the beads cost $3.90 for each necklace, how much did each pendant cost?
How to solve it and explain it
Answer:
2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
let the third side ( hypotenuse ) be x , then
x² = 1² + ([tex]\sqrt{3}[/tex] )² = 1 + 3 = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
The equation |x-3| = 4 has what solutions?
Answer:
x-3=4
x=4+3
X=7
or
x-3=-4
x=-4+3
x=-1
-1 and 7
Step-by-step explanation:
Any equation within the | | notation is an absolute value, where the the value of the equation can only be positive.
So within the notation, we have two possibilities to the solution, a positive and negative value.
In other words, |4| = 4 and |-4| = 4
Hence, we only need to substitute x with an appropriate integer to satisfy the answer.
|x - 3| = 4
substitute x = 7
|7 - 3| = 4
|4| = 4
substitute x = -1
|-1 - 3| = 4
|-4| = 4
Therefore the solutions to x is x = 7 and x = -1.
Hello! I wanted answer with explanation
If you didn't understand what question in the screen I can't tell you...
Question: In an election, there are a total of 80,000 voters and there are two candidates A and B. 80% of the voters go for the polls and out of which 60% vote for A. How many voters does B get?
I hope you answer...
Thank you!
Divide 4000 into two parts such that 15% of the first part equals 25% of the second part.
4. What is the unit rate for a pound of seed? Circle the correct answer choice.
Pounds of Seed
10
20
Total Cost
$17.50
$35.00
$52.50
$70.00
30
40
$3.50
$1.75
$17.50
$7.25
===================================================
Explanation:
To get the unit cost, we divide the total cost over the number of pounds.
We can do this for any row
row one: ($17.50)/(10) = $1.75row two: ($35.00)/(20) = $1.75row three: ($52.50)/(30) = $1.75row four: ($70.00)/(40) = $1.75You don't need to show all four row calculations. You can simply pick one row.
This tells us that each pound costs $1.75
Put another way: the price is $1.75 per pound
John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?
Answer:
61.6 dollars
Step-by-step explanation:
So, lets go over what we know:
The shows orginally cost 88 dollars.
They are 30% less than that.
This basically means that the shoes will cost 70 percent of their orginal price.
We can basically find the new cost by multiplying the 88 dollars by the 70 percent.
Or, multiplying 88 by 0.7, which is the decimal form of 70%.
88*0.7=61.6
How did I get this?
Multiply 80 by 0.7:
7*8=56
We have 0.7 so it = 5.6
However, it's tens place is 80, not 8, so it will be = 56
It is the same thing in the ones place, however it is 8 not 80, so it will be 0.7*8
= 5.6
56+5.6=61.6
So 61.6 is our answer.
Hope this helps!
Answer:
$61.60
Step-by-step explanation:
the other answer is correct.
just to add some explanation about the % considerations.
we know $88 is 100%
in order to get any other % value, we need to divide the original value by 100 (that gives us 1%), and then multiply with the number of % we want to have - in our example 70, as the discount is 30% (so the remaining part is 70% of the original price).
so, in order to get 70% we actually have to do the above things and divide by 100 and multiply by 70.
70% = (100% / 100) × 70 = 100% × 70 / 100
70 / 100 = 0.7 (that is how answer 1 actually got that multiplication factor)
70% = 100% × 0.7
70% = $88 × 0.7 = $61.60
For a car to qualify as a High Occupancy Vehicle (HOV), it must have at least _____ people.
A.
4
B.
2
C.
varies
D.
3
Answer: i would like to sad it varies
Step-by-step explanation: the number of people required for a Vehicle to be an HOV i would say exactly 2 and greater. The state Laws also applies, so i'll add that onto it varies
Plz help meee <3 kitty’s
Answer:
linear means a line (that eliminates c and d)
as "X" increases the "Y" value "DECREASES" so the answer is "B"
Step-by-step explanation:
Answer:
B. Linear decreasing
Step-by-step explanation:
The graph appears to have a negative slope, and it is a straight line. This means the graph will be linear. An exponential growth/decay would have a curved line, so those are automatically out. Since the farther the points go the more downwards the line is, this means it is decreasing.
hope this helped. :)
can someone help please
Answer:
3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic
(ii). Sequence [tex]W_{n}[/tex] is in Geometric
3b. 2520 Sum of First 20 Arithmetic Sequence
3c. 98292 Sum of First 13 Geometric Sequence
Step-by-step explanation:
According to the Question,
3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....
it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12
(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....
A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2
3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]
(Where, a=first term of sequence , n= number of term & d=common difference)
[tex]S_{n}[/tex]=10[2×12 + 19×12]
[tex]S_{n}[/tex] =10×252 ⇔ 2520
3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]
(Where, a=first term of sequence , n= number of term & r= common ratio)
[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1
[tex]S_{n}[/tex]=12×8191 ⇔ 98292
What 2 numbers add to get -9 and multiply to get -30?
Answer:
[tex]y_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]y_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
[tex]x_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]x_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
Step-by-step explanation:
Let be x the first number and y the second number.
So we have:
[tex]x+y=-9[/tex] (1)
[tex]x*y=-30[/tex] (2)
Solve x from equation 1 and put it into equation 2
[tex]x=-9-y[/tex]
[tex](-9-y)*y=-30[/tex]
[tex]-9y-y^{2}=-30[/tex]
[tex]y^{2}+9y-30=0[/tex]
Solving this quadratic equation and put it on the equation (1) the solutions will be:
[tex]y_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]y_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
[tex]x_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]x_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
I hope it helps you!
Determine the value of x.
A right triangle has 2 sides with a length of 6 centimeters. The length of the hypotenuse is x centimeters.
Answer:
6^2 + 6^2 = 72 sqrt(72) = 8.49
Step-by-step explanation:
use pythagorean therom a^2 + b^2 = c^2
where c is the hyp.
Answer: 6 sqrt 2
Step-by-step explanation:
Please help me out I don't remember how to do this
Answer:
D)
Step-by-step explanation:
0.04, 0.40, 4.04, 40.04
Need help with this question
Answer:
B.
Step-by-step explanation:
you know that (a+b+c)/d is the same as a/d + b/d + c/d.
and (a×b)/(c×d) is the same as (a/c)×(b/d).
and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.
14a⁸y³ / 7a⁴y
14/7 = 2
a⁸/a⁴ = a⁴
y³/y = y²
=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.
but let's practice and look at the second part :
-7a⁴y⁵ / 7a⁴y
-7/7 = -1
a⁴/a⁴ = 1
y⁵/y = y⁴
=> -y⁴ is the second part. B is still confirmed.
the third part :
28a¹²y² / 7a⁴y
28/7 = 4
a¹²/a⁴ = a⁸
y²/y = y
=> + 4a⁸y is the third part. B confirmed.
Hello help me with these ones pls
Answer:
(-1,3)
Step-by-step explanation:
Solve for x in the first equation
3x = 6 - 3y
9x - 5y= -24
Replace all occurrences of x with 2 - y in each equation
9(2 - y) - 5y = -24
x = 2 - y
Simplify the left side
18 - 4y = -24
x = 2 - y
Solve for y in the first equation
-14y = -42
x = 2 - y
y=3
x = 2- y
Replace all occurrences of y with 3 in each equation
x=-1
y=3
(-1,3)
Hope this helps!
Please give brainliest :)
If you need more help with these types of equations reach out to me!
Simplifying
3x + 6 = 9x + -24
Reorder the terms:
6 + 3x = 9x + -24
Reorder the terms:
6 + 3x = -24 + 9x
Solving
6 + 3x = -24 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
6 + 3x + -9x = -24 + 9x + -9x
Combine like terms: 3x + -9x = -6x
6 + -6x = -24 + 9x + -9x
Combine like terms: 9x + -9x = 0
6 + -6x = -24 + 0
6 + -6x = -24
Add '-6' to each side of the equation.
6 + -6 + -6x = -24 + -6
Combine like terms: 6 + -6 = 0
0 + -6x = -24 + -6
-6x = -24 + -6
Combine like terms: -24 + -6 = -30
-6x = -30
Divide each side by '-6'.
x = 5
Simplifying
x = 5
Find the squares of a+3b
Answer:
3ab
Step-by-step explanation:
because it is answer
DEF is a dilation image of ABC. What is the scale factor?
2
1/2
1/4
2/3
Answer:
Option (2)
Step-by-step explanation:
ΔDEF is a dilation image of ΔABC.
Rule for the dilation,
Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the original triangle}}[/tex]
= [tex]\frac{DE}{AB}[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, scale factor by which ΔABC is dilated is [tex]\frac{1}{2}[/tex].
Option (2) will be the correct option.
Volume How many fluid ounces are in each size?
1 cup = 8 oz. 1pint = 2 cups. 1 quart = 2 pints. 1 gallon = 4 quart
1 Quart = _________fl oz
Answer:
32
Step-by-step explanation:
a quart is four cups 8,16,24,32 so 32
Answer: 1 Quart is equal to 32 fluid ounces (oz).
Step-by-step explanation:
a classrom contains 25 children ,out of which 6 are girls.What percent are boys?
Answer:
76%
Step-by-step explanation:
Number of students=25
Number of girls=6
Number of boys=25-6=19
% of boys=number of boys/number of students x 100
=19/25x100
=19x4=76%
Solve 12x + 5 = 4x + 37
Step-by-step explanation:
12x-4x=37-5
8x=32
x=32/8
x=4
A number line is shown below. The
numbers 0 and 1 are marked on the line, as are two
other numbers a and b.
Which of the following numbers is negative? Choose
all that apply.
a-b
ab
-b
ab + 1
Answer:
-b
Step-by-step explanation:
1 is b and a negative sign shows that the number is a negative in -b there is a negative sign and b = 1 so this -b shows the number -1
Triangle ABC is similar to triangle DEF. Find the measure of side EF. Round your
answer to the nearest tenth.
B
50
F
D
41
HELP PLEASEEEE
Answer:
83.5units
Step-by-step explanation:
Find the diagram attached
Since both triangles are similar, then;
AB/DB = BC/EF
11/54 = 17/EF
Cross multiply
11EF = 17 * 54
11EF = 918
EF = 918/11
EF = 83.5
Hence the length of EF to the nearest tenth is 83.5units
Which statements are true about the graph of
y< 2x + 1? Check all that apply.
y < 2
The slope of the line is 1.
O The line is solid.
The area below the line is shaded.
A solution to the inequality is (2, 3).
The x-intercept of the boundary line is (-3,0).
Answer:
I think the answer is The x-intercept of the boundary line is (-3/2,0).
Step-by-step explanation:
the x-intercept of boundary line is (-3,0)
Step-by-step explanation:
hope it helps thanks❤
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.
Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees.
What is the value of x?
5
10
20
25
Given:
In parallelogram PQRS, [tex]m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ[/tex].
To find:
The value of x.
Solution:
In a parallelogram, the consecutive interior angles are supplementary angles.
In parallelogram PQRS,
[tex]m\angle Q+m\angle R=180^\circ[/tex] (Supplementary angles)
[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]
[tex](20+8x)^\circ=180^\circ[/tex]
[tex]20+8x=180[/tex]
Subtracting 20 from both sides, we get
[tex]8x=180-20[/tex]
[tex]8x=160[/tex]
Divide both sides by 8.
[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]
[tex]x=20[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
what is the simplist form of 240/1000
Divide by 100 to reduce it to 24/100
Now divide by 4 to get 6/25
The simplest form is 6/25
A used automobile dealership recently reduced the price of a used compact car by %. If the price of the car before discount was $, find the discount and the new price.
Answer:
$1674
$16926
Step-by-step explanation:
A used automobile dealership recently reduced the price of a used compact car by 9%. If the price of the car before the discount was $18,600, find the discount and the new price?
Discount = percentage discount x original price
0.09 x $18,600 = $1674
New price = original price - discount
$18,600 - $1674 = $16926
The radius of the circle is 7 cm. What is the area of the shaded part? Use π = 227
Answer:
227 * 7^2
Put into calculator
Step-by-step explanation:
Area of a circle is pi * r^2 (pi times radius squared)
Just put the numbers in
227 * 7^2
Put into calculator and there you go
m∠RST =______because they are __________ (Fill in the blanks)
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
Aere are two squares. A and B.
A
B
The length of each side of square B is 4 cm greater than the length of each side of square A.
The area of square B is 70 cm² greater than the area of square A.
Find the area of square B.
Give your answer correct to 3 significant figures.
You must show all your working.
Answer:
116 cm²
Step-by-step explanation:
a = side length of A
b = side length of B
b = a + 4
b² = a² + 70
(a+4)² = a² + 70
a² + 8a + 16 = a² + 70
8a + 16 = 70
8a = 54
a = 54/8 = 27/4 = 6.75
b² = a² + 70 = 6.75² + 70 = 45.5625 + 70 =
= 115.5625 ≈ 116 cm²
our does your teacher mean 3 significant figures after the decimal point ? then it would be
115.563 cm²
7.80/hour=________ cents/minute?
Answer: 0.13 cents per minute.
Step-by-step explanation:
7.80 divided by 60(min per hour.)= .13 cents.