Prove that with any natural number n (5n-4)^2-(2n+11)^2 divides by 21
Answer:
let natural no be 1
(5.1-4)^2-(2.1+11)^2/21
25-16-4-121/21
-5.52
Step-by-step explanation:
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3. What is the greatest common factor of 6 and 16? *
Answer:
2
Step-by-step explanation:
2 is the only factor that goes into 6 and 16. (6th's Factors) 1, 2, 3 and 6
(16th Factors) 1, 2, 4, 8 and 16.
The greatest common factor of 6 and 16 is 2.
To find the greatest common factor (GCF) of 6 and 16, we need to determine the largest number that can divide both 6 and 16 without leaving a remainder.
First, we find the factors of each number:
Factors of 6: 1, 2, 3, 6
Factors of 16: 1, 2, 4, 8, 16
By comparing the factors, we can identify that both 6 and 16 have a common factor of 2. However, 6 also has a factor of 3, which is not a factor of 16.
To determine the GCF, we select the highest common factor, which is 2.
Therefore, the greatest common factor of 6 and 16 is 2.
The GCF is an essential concept in mathematics as it helps simplify fractions, factorize expressions, and solve various mathematical problems. It allows us to identify the largest number that can evenly divide two or more given numbers.
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ted wants to buy a skateboard that is 59 dollars but is 30 percent off how much will he save
Answer:
Step-by-step explanation:
Ted will save $15.
Answer:
He will save $17.7.
Step-by-step explanation:
30% of 59= 41.3
59-41.3= 17.7
Determine the area of the triangle when tana=1 the image is in the picture above
Answer:
The area will be:
[tex]A=18(1+\sqrt{3}) \: u^{2}[/tex] or [tex]A=49.18 \: u^{2}[/tex].
Step-by-step explanation:
Using the definition of tangent, we have:
[tex]tan(\alpha)=\frac{6}{\vec{AB}}[/tex]
We know that tan(α) = 1, then we can find AB
[tex]1=\frac{6}{\vec{AB}}[/tex]
[tex]\bar{AB}=6\: u[/tex]
u means any unit.
Now, we need to find the distance BC. If the angle ∠D is 60°, then ∠C must be 30°. Using the tangent definition in the triangle BCD we have:
[tex]tan(30)=\frac{6}{\bar{BC}}[/tex]
[tex]\bar{BC}=\frac{6}{tan(30)}[/tex]
[tex]\bar{BC}=\frac{6}{1/\sqrt{3}}[/tex]
[tex]\bar{BC}=6\sqrt{3} \: u[/tex]
So, the base of the triangle will be:
[tex]b=\bar{AB}+\bar{BC}=6+6\sqrt{3}=6(1+\sqrt{3}) \: u[/tex]
The area of a triangle is given by the following equation:
[tex]A=\frac{b*h}{2}[/tex]
b is the base ([tex]b=6(1+\sqrt{3})\: u[/tex])h is the height (h=6 u)[tex]A=\frac{6(1+\sqrt{3})*6}{2}[/tex]
[tex]A=18(1+\sqrt{3})[/tex]
Therefore, the area will be [tex]A=49.18 \: u^{2}[/tex].
I hope it helps you!
Two sides of a triangle have sides 11 and 16. The length of the third side must be greater than
__and less
than
A) 10, 17
B) 4,28
C) 5,27
D) 11,16
Answer:
c
Step-by-step explanation:
Erika is working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Answer:
Step-by-step explanation:
The Lakewood Wildcats won 5 of their first 8 games this year. There are 32 games in the season. How many games would you expect the Wildcats to win this season?
Answer:
x=20
Step-by-step explanation:
Rewrite the equation as
x /32 = 5/ 8
Multiply both sides of the equation by 32
32 ⋅ x /32 = 32 ⋅ 5/8
Simplify both sides of the equation.
Cancel the common factor of
32
Cancel the common factor.
32· x/32 · 5/8Rewrite the expression.
x = 32 ⋅ 5/8
Simplify
32⋅5/8
Cancel the common factor of
8
Factor 8 out of 32
x = 8 ( 4 ) ⋅ 5/8
Cancel the common factor.
Rewrite the expression.
x = 4 ⋅ 5
Multiply 4 by 5
what is the quadrilateral ?
Answer:
its either a rectangle or a square
Step-by-step explanation:
for it to be a rectangle there must be 4 right angles, but for it to be a square, there must be both 4 right angles and each side must be the same
2. Determine the value of each variable for parallelogram INDY has diagonals that intersec at P.1P=3x DP = 6x - 2 NP = 3y and YP=7x-2,
Answer:
x = 2/3 and y = 8/9
Step-by-step explanation:
If a parallelogram INDY has diagonals that intersects at P, then O bisects ID and YN
Hence IP = PD and NP = YP
Given
IP=3x
DP = 6x - 2
NP = 3y and
YP=7x-2,
Substitute
3x = 6x-2
3x-6x = -2
-3x = -2
x = 2/3
x = 0.67
Also NP = YP
3y = 7x-2
3y = 7(2/3) - 2
3y = 14/3 - 2
3y = 14-6/3
3y = 8/3
9y = 8
y = 8/9
Hence x = 2/3 and y = 8/9
A bag contains 9 red tiles, 10 blue files, and 6 green tiles. A tile is randomly drawn from the bag. Which statement is true?
A. The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%.
B.
The probability of drawing a blue tile is 30% and the probability of NOT drawing a blue tile is 70%.
C. The probability of drawing a green tile is 25% and the probability of NOT drawing a green tile is 75%.
D. The probability of drawing a red tile is greater than the probability of NOT drawing a green tile. David hiked 24 miles in Ahon-
Answer: A. The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%
Step-by-step explanation:
Number of red tiles = 9
Number of blue files = 10
Number of green tiles = 6
Total number of tiles = 9 + 10 + 6 = 25
Probability of drawing red tile = 9/25 = 0.36 = 36%
Probability of drawing blue tile= 10/25 = 0.40 = 40%
Probability of drawing green tile = 6/25 = 0.24 = 24%
Based on the explanation above, the correct answe is option A "The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%".
8 = 6 + a/4 a=___help
Answer:
[tex]8 = 6 + \frac{a}{4} \\ \frac{a}{4 } = 8 - 6 \\ \frac{a}{4} = 2 \\ a = 2 \times 4 \\ a = 8[/tex]
Simplify the expression:
-5 – 3 (4x – 9)
Answer:
Step-by-step explanation:
lets remove the paranthesis and multiply
-5-3(4x-9)=
=-5-12x+27=
=-12x+22
step bro... im stuck, need help with this question
Answer:
i GOT C
Step-by-step explanation:
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HELP ME ASAP PLS PLS
Answer:
linear
Step-by-step explanation:
Not sure but it would be helpful if you can show me the options. Thank y!!
HELPPP PLEASEE!!!
Roger goes shopping and saves $48 with a 30% off coupon. What was his total bill before tax?
Answer:
160$
Step-by-step explanation:
✨Magic✨ jkjk 160*.30=48
If it costs $0.15 per square inch for the cardboard label, then what is the cost for plan B?
Answer:
a box of plan B cost roughly $50.00
it is pretty expensive but you don't need an I.D.
Step-by-step explanation:
Write the equation of the line passing
through: (-4,-2) and (-3, 5)
Answer:
formula = y2-y1/x2-x1
Step-by-step explanation:
(-4,-2) (-3,5)
x1=-4 x2=-3
y1=-2 y2=5
5+2/-3+4=7
so M=7
y-y1=m(x-x1)
y+2=7(x+4)
2y=7x+28
rearrange
-7x+2y-28=0
Solve for x. Leave your answer in simplest radical form.
SOMEONE HELP ME PLEASE I NEED IT, it needs to be in radical form
Step-by-step explanation:
step 1. let's call the line in the middle y.
step 2. y = sqrt(5^2 + 7^2) = sqrt(74). pythagorean theorem.
step 3. x^2 + y^2 =100 (pythagorean theorem))
step 4. x^2 + (sqrt(74))^2 = 100.
step 5. x^2 = 100 - 74
step 6. x^2 = 26
step 7. x = sqrt(26). note: sqrt is the square root.
The value of the x is [tex]\sqrt{26}[/tex].
To understand more, check below explanation.
Pythagoras theorem :Apply Pythagoras theorem in right side triangle,
Hypotenuse[tex]=\sqrt{5^{2}+7^{2} } =\sqrt{25+49}=\sqrt{74}[/tex]
Now apply Pythagoras theorem in the left side triangle,
[tex]Hypotenus^{2} +x^{2} =10^{2} \\\\(\sqrt{74} )^{2} +x^{2} =100\\\\x^{2} =100-74=26\\\\x=\sqrt{26}[/tex]
Hence, the value of the x is [tex]\sqrt{26}[/tex].
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Find the slope (rate of change) from the table. Simplify if necessary.
X
1
2
3
4
у
-3
-9
-21
-15
Answer:
i think it would be 2 because its in the middle of the slope and it would make scence
Step-by-step explanation:
PLS Helpppp
(4y – 3x – 2) – (7y + 4x +3).
you have to simplify, linear equations
Answer:
-3y - 7x - 5
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
(4y - 3x - 2) - (7y + 4x + 3)
Step 2: Simplify
Distribute negative: 4y - 3x - 2 - 7y - 4x - 3Combine like terms (y): -3y - 3x - 2 - 4x - 3Combine like terms (x): -3y - 7x - 2 - 3Combine like terms (Z): -3y - 7x - 5The area of a circle is 16π ft². What is the circumference, in feet? Express your answer in terms of \piπ.
The circumference when the area of a circle is 16π ft² is 8π feet.
How to calculate the area?The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.
From the information given the area of a circle is 16π ft² be we want to calculate the circumference, in feet. This will be Illustrated this:
Circumference of a circle = 2πr
Area of a circle = πr²
r = radius.
Therefore, based on the information regarding the area given, the radius will have to be calculated first.
Area = 16π
πr² = 16π
r² = 16π / π
r² = 16
r =✓16
r = 4
Radius = 4ft.
Therefore, the circumference will be:
= 2πr
= 2 × π × 4
= 8π
Circumference is 8π feet.
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Help ASAP. Give you answer as a fraction.
Answer:
1/12
Step-by-step explanation:
I need help answering this question for trig equations.
Sec^2x+4secx=-4
Answer:
x = 120°
Step-by-step explanation:
We are given;
sec²x + 4secx = -4
Rearranging gives;
sec²x + 4secx + 4 = 0
Factorizing the left hand side gives;
(sec x + 2)(sec x + 2) = 0
This means that;
(sec x + 2) = 0
From trigonometry, we know that sec x = 1/cos x
Thus;
(1/cos x) + 2 = 0
1/cos x = -2
cos x = -1/2
cos x = -0.5
x = cos^(-1) -0.5
x = 120°
What inverse operation should be used to isolate the variable in the equation
k - 9 = 10?
Answer:
k-9=10
k=10+9
k=19
take care of yourself
have a nice day
what is 3x(2-4x)
pls i need help
Answer:
6x−12x^2
Step-by-step explanation:
Answer:
Evaluated it is 6x-12x^2
Step-by-step explanation:
3x*2=6x
add minus sign
3x*4x=12x
Since 2 x add 2 as an exponent!
7. Choose an appropriate variable for each situation. Then write and solve an
equation.
a. If I doubled the money in my savings account, I would have $150.62.
b. three times the hourly wage plus $7.65 in tips equals $27.90
Answer: See explanation
Step-by-step explanation:
a. Let the money in m savings account be represented by x.
If I doubled the money in my savings account, I would have $150.62. This means that:
(2 × x) = $150.62
2x = $150.62
Divide both side by x
2x/2 = $150.62/2
x = $75.31
The amount in the savings account is $75.31
b. Let the hourly wage be represented by x.
Three times the hourly wage plus $7.65 in tips equals $27.90. This will be:
(3 × x) + 7.65 = 27.90
3x + 7.65 = 27.90
3x = 27.90 - 7.65
3x = 20.25
x = 20.25/3
x = 6.75
The hourly wage is $6.75
Bryan earns $5.00 per lawn mowed and $5.00 per car washed. Let m be the number of lawns mowed and let c be the number of cars washed. Select all the expressions that could represent the total earned, E in dollars, by Bryan.
Answer:
where.... are the expressions?
Step-by-step explanation:
Answer:
The most logical choice for the expression would be 5m + 5c = E
But it could also be 5(m + c) = E
Please help!!! Slope beginners
Answer:
-1/2
Step-by-step explanation:
Gradient=Change in value of Y coordinates/Change in value of X coordinates.
Take two points on the line.( -2,2) and (-4,3)
Find Delta or change in the values
let assume X is the gradient.
X=3-2/-4-(-2)
X= 1/-4+2
X=1/-2 which is written as -1/2
A driver descends -15 after 1 minute, -30 feet after 2 minutes and -45 after 3 minutes? If the driver keeps descending at this rate, what is their position after 12 minutes
Answer:
I think it's -180
Step-by-step explanation:
He keeps descending -15 feet every 1 minute
1 x -15 = -15
2 x -15 = -30
12 x -15 = -180
FIRST PERSON TO ANSWER CORRECTLY GETS BRAINLIEST!! YOU HAVE TO TELL/SHOW ME HOW TO SHOW MY WORK TOO BE ABLE TO GET BRAINLIEST AS WELL. THE QUESTION IS IN THE SCREENSHOT. DUE IN 8 MINUTES!!
Answer:
Here is 16 divided by 1/4 displayed mathematically in colors:
16
÷
1
4
The numbers in 16 divided by 1/4 are labeled below:
16 = whole number
1 = numerator
4 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
16 x 4
1
=
64
1
Thus, the answer to 16 divided by 1/4 in fraction form is:
64
1
To make the answer to 16 divided by 1/4 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
64 / 1 = 64
The answer is rounded to the nearest two decimal points if necessary.
64/1 is an improper fraction and should be written as 64.
Step-by-step explanation: