Answer:
1/2, 4/8, 5/10, 6/12 (examples of equivalent fractions)
Step-by-step explanation:
all you have to do is keep the ratio the same, so whatever change you make to one side of the fraction, you do the same to the other
here's an example: 2/4 divided by 2/2 = 1/2
- you would divide 2 by 2 AND 4 by 2
Using the equation
[tex] \sqrt{x + 7} + 5 = x[/tex]
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.
Given:
The equation is:
[tex]\sqrt{x+7}+5=x[/tex]
To find:
Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.
Solution:
We have,
[tex]\sqrt{x+7}+5=x[/tex]
Subtract 5 from both sides.
[tex]\sqrt{x+7}=x-5[/tex]
Taking square on both sides, we get
[tex]x+7=(x-5)^2[/tex]
[tex]x+7=x^2-10x+25[/tex]
[tex]0=x^2-10x+25-x-7[/tex]
[tex]0=x^2-11x+18[/tex]
Splitting the middle term, we get
[tex]x^2-2x-9x+18=0[/tex]
[tex]x(x-2)-9(x-2)=0[/tex]
[tex](x-2)(x-9)=0[/tex]
[tex]x=2,9[/tex]
Now, substitute [tex]x=2[/tex] in the given equation.
[tex]\sqrt{2+7}+5=2[/tex]
[tex]\sqrt{9}+5=2[/tex]
[tex]3+5=2[/tex]
[tex]8=2[/tex]
This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.
Substitute [tex]x=9[/tex] in the given equation.
[tex]\sqrt{9+7}+5=9[/tex]
[tex]\sqrt{16}+5=9[/tex]
[tex]4+5=9[/tex]
[tex]9=9[/tex]
This statement is true. So, 9 is a solution of given equation.
Therefore, 2 is an extraneous solution and 9 is a solution of given equation.
Factorise fully 2a^2b + 6ab^2
Answer:
Step-by-step explanation:
2a^2b + 6ab^2
take common
2 can be taken common because there is 2in first term and there is 6 in second term and 2 can exactly divide 6 .there is a*a in first term and only a in second term so u can take a as common.There is only b in first term and b*b in second term so take u can take b as common.
total we can take
2ab as common.So,
2ab(a+3b)
therefore 2ab(a+3b) is the required answer.
The required factorization is 2ab(a+3b).
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Expanding brackets in reverse is a procedure known as factorizing.
Fully factorizing an equation entails putting it in brackets by eliminating the components with the highest common denominator.
Finding the highest common factor between all the terms in the phrase is the easiest technique to factorize.
We have, 2a²b + 6ab²
Here,
we have the highest common factor 2ab,
So, 2ab (a + 3b)
Therefore, 2ab(a+3b) is the required factorization.
To learn more about the factorization;
https://brainly.com/question/28187946
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find out the arc length of DG and the measure of angle DHG
Answer:
is it timed, because i need like 20 mins to answer this question.
Step-by-step explanation:
Which side lengths form a right triangle?
Answer:
[tex]\text{B. }1.5, 2, 2.5,\\\text{C. }4, 4, \sqrt{32}[/tex]
Step-by-step explanation:
All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.
Verify:
[tex]1.5^2+2^2=2.5^2\checkmark,\\4^2+4^2=\sqrt{32}^2\checkmark[/tex]
Find the value of x in the isosceles triangle shown below
Answer:
x²+4² =8²
x²+16 =64
x² =64-16.
x² =48
x. =√48
answer is option D
Answer:
D
Step-by-step explanation:
The segment x is a perpendicular bisector and divides the triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles, then
x² + 4² = 8²
x² + 16 = 64 ( subtract 16 from both sides )
x² = 48 ( take the square root of both sides )
x = [tex]\sqrt{48}[/tex] → D
This is my hw. heelp
Answer:
1/14
Step-by-step explanation:
PLEASE HELP ME WITH THIS
What is the volume of the cylinder shown below?
15
10
Answer:
option B
Step-by-step explanation:
Given r = 10 , h = 15
[tex]Volume = \pi r^2 h = \pi \times 10^2 \times 15 = \pi \times 100 \times 15 = 1500 \pi \ cubic \ units[/tex]
(a)Find the commission on Rs65 000 if 4% commission is paid.
(b)On selling an article for Rs2700,a shopkeeper made a profit of 8%.find cost price of the article.
Answer:
Step-by-step explanation:
commission amount = 4 % of Rs 65000
=4/100 * 65000
=260000/100
=2600
therefore commision amount is Rs 2600
SP od an article = Rs 2700
profit %=8%
let CP be x
SP=CP + profit% of CP
2700=x + 8/100 *x
2700=100x + 8x/100
2700*100 = 108x
270000=108x
270000/108=x
2500=x
therefore cost price (CP) of an article is Rs 2500.
Which graph shows the solution to the system of linear inequalities?
x+5y>5
Y<2x+4
PLEASE HELP!!!
Answer:
x+5y >5 => red
y< 2x+4 => blue
Step-by-step explanation:
you can substitute x and y in each inequality to determine
if im writing 200 post cards , and stamps are 0.36 cents a piece, how much money would 200 stamps be?
Answer:
72
Step-by-step explanation:
1 stamp costs 0.36 cents
Then, 200 post cards will cost 0.36 × 200 = 72
Answer:
$72 dollars
Step-by-step explanation:
200 x 0.36 = 72
s
is inversely proportional to
t
.
When
s
=
0.5
,
t
=
7
Work out
s
when
t
=
0.8
Answer:
4.375
Step-by-step explanation:
s=1/t
s=k/t
0.5=k/7
k=7x0.5=3.5
s=3.5/0.8
s=4.375
These two lines represent a system of equations.
What is the solution to that system?
Help ?
Answer: (-1,1)
Step-by-step explanation: Look at the intersection point of the lines
Two cables are attached to a 30-foot wall and a 22-foot wall. If the tie down for the cables is located in the center of a 40-foot wide alley between the two walls, what is the angle \thetaθ that is formed between the cables? Round your answer to the nearest whole number.
Answer:
76°
Step-by-step explanation:
Applying trigonometry :
Angle x ;
Tan x = opposite / adjacent
Tan x = (30/20)
x = tan^-1(30/20)
x = 56.31°
Angle y;
Tan y = opposite / adjacent
Tan y = (22/20)
x = tan^-1(22/20)
x = 47.73°
The angle θ ;
Sum of angles in a straight line = 180
56.31 + 47.73 + θ = 180°
θ = 75.96°
Hey!! Can you guys help me !!
No links!!
No spams!!
Ahmed paid $34 000 for a car. His car decreased in value by 40% at the end of the first year. The value at the end of the second year was 10% less than the value at the end of the first year. . Calculate the value of Ahmed's car after 2 years .
40% of 34 000
40/100 * 34 000 = 13 600
subtract : 34000 - 13 600 = 20 400
Second step:10% of 20 400
10/100 * 20 400 = 2040
subtract : 20 400 - 2040 = $ 18 360
Final Answer = $ 18 360factorise:
k² - 2k - 8
with explaining the steps
Answer:
( k-4)(k+2)
Step-by-step explanation:
k² - 2k - 8
What 2 numbers multiply to -8 and add tp -2
-4*2 = -8
-4+2 = -2
( k-4)(k+2)
Refer to the attachment for steb-by-step explanation.
Pls help I need this
Answer:
what you need help in we see nothing
can someone help please...
Answer:
the answer is median (b)
cho số phức z thỏa mãn 2iz-5+i=i-(z-2i) tính modun của số phức w=z-1+i
Solve the given equation for z :
2iz - 5 + i = i - (z - 2i )
2iz - 5 = 2i - z
(2i + 1) z = 2i + 5
z = (2i + 5)/(2i + 1)
z = (2i + 5)/(2i + 1) × (2i - 1)/(2i - 1)
z = (4i ² + 10i - 2i - 5) / (4i ² - 1)
z = (8i - 9)/(-5)
z = 9/5 - 8/5 i
Then
w = z - 1 + i = 4/5 - 3/5 i
HELP ASAP PLS I NEED HELP
Answer:
B
Step-by-step explanation:
r^2 is 0.9997, and after 10 years it'll be 95660
the sum of the squares of two consecutive integers is 481. Find the integers
Answer:
{15, 16} or {-15, -16}
Step-by-step explanation:
Quick solution:
take half of the sum (approx. 240), sqrt(240)=15.5
So the numbers are 15 and 16. and also the negative equivalents since squares are always positive.
Exact method:
Let
x=smaller integer,
x+1 = next integer.
sum:
x²⁺(x+1)^2 = 481
2x^2 + 2x + 1 = 481
2x^2 + 2x - 480 = 0
x^2 + x -240 = 0
x = 15 or x = -16
so the integers are
either
{15, 16} or {-15, -16}
The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.
Assume 'x' is the number and the successive number is (x + 1).
The sum of the square of the consecutive number is 481. Then the equation of the number is given as,
x² + (x + 1)² = 481
Simplify the equation, then we have
x² + (x + 1)² = 481
x² + x² + 2x + 1 = 481
2x² + 2x - 480 = 0
x² + x - 240 = 0
x² + 16x - 15x - 240 = 0
x(x + 16) - 15(x + 16) = 0
(x + 16)(x - 15) = 0
x = 15, -16
Then the successive numbers are given as,
x + 1 = 15 + 1
x + 1 = 16
x + 1 = - 16 + 1
x + 1 = - 15
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Encuentra el volumen de un prisma rectangular que mide 14m de largo y 10 m de ancho 34m de altura.
Please help
Honestly cant understand
can someone help please...
Answer:
C. 8
Step-by-step explanation:
You double the distance of the x coordinate (ignore the sign in front of it) because you reflect it across the y-axis. So your math should look like this:
4*2= 8
How many quarters are there in 5 and 3/4
Answer:
23
Each 1 has 4 quarters
5*4=20
20+3
23
Step-by-step explanation:
the ratio of blue to yellow paint when mixed to make green paint is 3:2 what percentage of the green paint is made from yellow paint
Answer:
40%
Step-by-step explanation:
3 + 2 = 5
Since 2 is the ratio of yellow paint, 2/5 x 100 = 40%
Hope this helped!
I. NEED. HELP! PLEASE!
Answer:
x = 2.5
Step-by-step explanation:
We know the adjacent and the opposite sides to the angle in a right triangle
tan theta = opp / adj
tan 26 = 1.2 /x
x tan 26 = 1.2
x = 1.2 / tan 26
x =2.46036461
Rounding to the nearest tenth
x = 2.5
tan tita = opp/adj
tan 26°=1.2/x
x=1.2/tan 26
x=2.46
x=2.5
a circle shown below, m AC = 89° and m BC = 153°. Determine m∠ACB.
Answer:
m<ACB = 59degrees
Step-by-step explanation:
To get <ACB, first we need arcAB
arcAB + arcAC + arcBC = 360
arcAB + 89 + 153 = 360
arcAB+242 = 360
arcAB = 360 - 242
arcAB = 118
Also, m<ACB = 1/2arcAB
m<ACB = 1/2*118
m<ACB = 59degrees
pls help me i need help asap 30!! points pls help on all 4 questions
Answer:
b
d
a
d
Step-by-step explanation:
A teacher recorded the number of days her students went on vacation. Which statements describe the data? Select all that apply. Please help
Answer:
The students went on vacation for average 40 days.
The high school students went for more days than college students.
Step-by-step explanation:
The data shows number of students who went for vacation. The data class frequency shows that students who are in high school went for more days in vacation than college students. The students went for average of 40 days on vacation.
