Answer:
option A
Step-by-step explanation:
The given Series:
10,14,18,22,26... is an Arithmetic Progression.
Concept:
The difference between consecutive numbers always remains the same.
For instance:
14 - 10 = 18 - 14 = 22 - 18 = 4
This difference is known as the common difference.
In an A.P., the nth (an) term of a series can be found out by:
[tex] \boxed{ \sf{a _{n} = a + (n - 1)d}}[/tex]
Here,
an is the nth terma is the first term of the series = 10n is the number of termsd is the common difference = 4[Don't get confused by (n- 1), it's simply the number of terms - 1. If the number of terms, somehow, is (n - 1) itself, your formula will be an = a + ((n - 1) -1)d]
Soltution:
The first term of the given Series is 10.
==> a1 = 10
Finding an:
the nth term will be:
an = 10 + (n - 1)4
==> 10 + 4n - 4
==> 6 + 4n
Strategy:
All the given options have an and a(n-1). So we have to deduce a relation between an and a(n- 1).
Finding a(n-1):
==> a(n-1) = 10 + ((n - 1) -1)4
= 10 + (n- 2)4
= 10 + 4n - 8
= 4n + 2
Subtracting a(n-1) from an:
==> an - a(n-1) = 6 + 4n - (4n + 2)
==> an - a(n-1) = 6 + 4n - 4n - 2
==> an - a(n-1) = 4
==> an = 4 + a(n-1)
Hence, option A is the answer.
What is the most simplified expression that is equivalent to (5y)^2. (16y^4)^1/2
The most simplified expression for [tex](5y)^2(16y^4)^{\frac{1}{2}[/tex] is [tex]100y^4[/tex]
The given expression is:
[tex](5y)^2(16y^4)^{\frac{1}{2}[/tex]
Expand the expression using the laws of indices
[tex]5^2y^2 \times 16^{\frac{1}{2}}y^{\frac{4}{2}\\\\[/tex]
[tex]25y^2 \times 4y^2[/tex]
Multiply like terms
[tex](25 \times 4)y^{2+2}[/tex]
The resulting expression is:
[tex]100y^4[/tex]
Therefore, the most simplified expression for [tex](5y)^2(16y^4)^{\frac{1}{2}[/tex] is [tex]100y^4[/tex]
Learn more on indices here: https://brainly.com/question/10339517
What is 100X190
I give brainliest to the one who answers correctly.
Answer:
it is 19000 hope this helps!
Answer:
19,000
Step-by-step explanation:
Basically add 2 zeros to 190
Hope this helps!
please help
thank you!
The equation y=1/8xrelates proportional quantities x and y. What is the value of x when y is 6?
Answer:
48
Step-by-step explanation:
6 = 1/8x
x = 48
What is the slope and and y-int of y≤3
Answer:
0
I hope this is the correct answer
Answer: Slope = 0, y-intercept = 3
Step-by-step explanation:
The inequality is a horizontal line, where everything below 3 is agrees with the inequality
The slope of any flat line is 0, and the y-intercept is always the constant (y=mx+b) in slope-intercept form, in this case it is 3
Consider the equation.
8x - 16y = - 14
The equation representing a line that is parallel to the line given and passing through the point (3, 0) is y= ___ x + ___
Answer:
[tex]y= \frac{1}{2}x+3[/tex]
Step-by-step explanation:
Rearrange equation to isolate y variable.
[tex]16y=8x+14[/tex]
Divide by 16 on both sides.
[tex]y=\frac{1}{2} x+7[/tex].
To make the line parallel to the given equation and pass through (3,0),
we will move the y intercept to 3.
[tex]y= \frac{1}{2}x+3[/tex]
1. Reduce the ratio to the simplest form:
a)5:10=_____.
b)60:54=____.
Answer:
1:2 by division of 5
10:9 by division of 6
If 5 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline 5, what is the value of x? â€"3 â€"2 2 3.
The value of x is 3.
Given that,
If [tex]5 + 20 \times 2^{2-3x}[/tex],
And Baseline = [tex]10 \times 2^{-2x}+5[/tex]
We have to find,
The value of x?
According to the question,
To determine the value of x in the equation following all the steps given below.
Equation; [tex]\rm 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5[/tex]
Step1; Subtract 5 from both sides,[tex]\rm5- 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5-5\\\\\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}[/tex]
Step2; Divided by 10 on both sides,[tex]\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\\\\\dfrac{ 20 \times 2^{2-3x} }{10}= \dfrac{10 \times 2^{-2x}}{10}\\\\\rm 2 \times 2^{2-3x} = 2^{-2x}[/tex]
Step3; Rewrite the term into their power form and add the powers,[tex]\rm 2 \times 2^{2-3x} = 2^{-2x}\\\\2^1 \times 2^{2-3x} = 2^{-2x}\\\\2^{2-3x+1} = 2^{-2x}\\\\[/tex]
Step4; The base is the same on both sides, we equate exponents,[tex]\rm 2-3x+1 = -2x\\\\-3x+2x = -1-2\\\\-x = -3\\\\x=3[/tex]
Hence, The required value of x is 3.
For more details about the Exponent refer to the link given below.
https://brainly.com/question/25959524
Five swimmers are entered into the competition. Four of the swimmers have had their turns. Their scores are 9.8s, 9.75s, 9.79s, and 9.81s. What score must the last swimmer get in order to win the competition?
Answer:
We must order these decimals from least to greatest. Then we must determine how the least compares with the winning score.
9.80 -> 3
9.75 -> 1
9.79 -> 2
9.81 -> 4
The least decimal is 9.75. Now we must determine how 9.75 compare with the winning score.
The last swimmer must get a score less than 9.75 s in order to win.
Step-by-step explanation:
Hopes this helps
Answer:
less than or equal to 9.74.
what does 1/4 divided by 1/10 equal
Answer: 2/5
Step-by-step explanation: hope it helps
f(x) = -x^3+8x^2-15x
Domain:
Range: R
Rel. Maximum: X=3
Rel. Minimum(s): X2
End Behavior:
As x, f(x)
As x, f(x)
Incr. Intervals:
Zeros
Decr. Intervals
That's all I got hope it helps
Help. Here's the question, could you please put the letter answer, please.
Answer:
A
Step-by-step explanation:
the difference of a number and 7
Answer:
x-7
Step-by-step explanation:
thank you in advance to whoever answers this question !!!!
ILL MARK BRAINLIEST PLEASE HELP! Solve and graph its solution:
In 2005, the average cost of a 32" flat-screen TV was $1,700. In 2015, the average cost of a 32" flat-screen TV was $550. Assuming those were the least and greatest costs during that period, write a compound inequality that describes the cost c of a 32" flat-screen TV between 2005 and 2015.
Answer:x < 1,700. ×> 550
Step-by-step explanation:
Answer:AHHHH
Step-by-step explanation:
If x=a sintheta and y=bcostheta, show that (b^2)(x^2)+(a^2)(y^2)=(a^2)(b^2)a
solve 7e^(2x)-5>58. Round to the nearest hundredth.
Answer:
[tex]x\gtrapprox1.1[/tex]
Step-by-step explanation:
[tex]7e^{2x}-5>58[/tex]
[tex]7e^{2x}>63[/tex]
[tex]e^{2x}>9[/tex]
[tex]2x>ln(9)[/tex]
[tex]x>\frac{ln(9)}{2}[/tex]
[tex]x\gtrapprox1.1[/tex]
Plz help me with this
Answer:
C = 11.18
Step-by-step explanation:
You're trying to find c's value, right?
For triangles, a^2 + b^2 = c^2
What you want to do is replace the values into the formula.
A = 5
B = 10
5^2 + 10^2 = c^2
(^2 means squared by the way if you don't know)
Square the values.
25 + 100 = c^2
125 = c^2
You then have to find the root value of 125. What number squared equals 125?
Using a calculator, you would find the number is 11.18.
So, the value of c is 11.18
Please let me know if that wasn't what the question was asking and I'll try to help :)
If the two legs of one right triangle are congruent to the two legs of another right triangle, then the two triangles are congruent.
a) True
b) False
Answer:
Step-by-step explanation:
This only happens with right triangles. You need only 2 legs. The reason is that the two legs given are the arms of the right angle so secretly you are using SAS. The right angle is enclosed by the two legs, and that must be stated among your givens.
So the answer to the question is true.
The sum of twice a number and 5 is 25
Answer:
If the directions say write an equation: 2n + 5 =25
If the directions say also to solve the equation and find the number: 10
Step-by-step explanation:
"The sum" means we're using adding. So what things are we adding together? The question says "twice a number" and 5. Well we've got the 5. And "twice" means two times. And "a number" means we don't know the number yet, so we choose a variable, like n.
"Twice a number" can be written 2n.
So far we have:
2n + 5 is 25
We use = for the "is" in this sentence.
2n + 5 = 25
Now we can solve it.
Subtract 5 from both sides.
2n = 20
Divide by 2 on both sides.
2n/2 = 20/2
n = 10
The number is 10.
Please help me solve this problem ASAP
Answer:
∠ = 130°
Step-by-step explanation:
They are vertical angles: a pair of opposite angles formed by intersecting lines. These two angles are considered congruent, which means they have exactly the same measure. So, you simply solve for x when they equal each other. Remember, both angles share the same measurement.
15x -5 = 13x + 13
5 + 15x - 5 = 13x + 13 + 5
13x - 15x = 13x + 18 - 13x
2 ÷ 2x = 18 ÷ 2
x = 9
Now you must put 9 in for x to solve the measurement of the angles.
15 (9) - 5 = 130°
13(9) + 13 = 130°
Both angles equal 130°, so you know you've done the math correctly.
A cable is 40 decimeters long how long is the cable in meters and be sure to include the correct unit
Answer:
4 m
Step-by-step explanation:
1 m = 10 dm
1 dm = 0.1m
(pls brainliest)
What is the equation of the oblique asymptote?
h(x) = x² – 3x - 4/x + 2
Simplifying h(x) gives
h(x) = (x² - 3x - 4) / (x + 2)
h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)
h(x) = ((x + 2)² - 7x - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)
h(x) = (x + 2) - 7 - 22/(x + 2)
h(x) = x - 5 - 22/(x + 2)
An oblique asymptote of h(x) is a linear function p(x) = ax + b such that
[tex]\displaystyle \lim_{x\to\pm\infty} h(x) - p(x) = 0[/tex]
In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.
Simplify x⁷y⁹ ÷ x³y⁶
Please help (Math)......
[tex]|x|^2 -2|x|-3=0\\\\\implies |x|^2 - 3|x| + |x| - 3 =0\\\\\implies |x|(|x| -3) + (|x| -3) = 0\\\\\implies (|x| - 3)(|x| +1) =0\\\\\implies |x| -3 = 0~~ \text{Or} ~~ |x| +1 =0\\\\\implies |x| = 3 ~~ \text{Or}~~ |x| = -1;\\\\\text{For}~ |x|= -1 ,~\text{ there are no solution for } x \in \mathbb{R}\\\\\text{So,}\\\\|x| = 3 \implies x = \pm 3[/tex]
Help me pls right now I give brainliest
Answer:
4 + (2 x 3)^2
Step-by-step explanation:
4 + 6^2
4 + 36
40
What is k(-8) when given the function
k(x) = x +5 – 2x2?
Subtract. Use models if needed. (9x - 12) - (5x - 7)
[tex](9x - 12) - (5x - 7)\\\\=9x-12-5x+7\\\\=4x-5[/tex]
Which one is not a function??
Answer:
The first one. All the x values are 2. So it wouldn't pass the vertical line test.
Step-by-step explanation:
Examine Kaitlyn’s steps for solving the system of equations. â€"3x 2y = 8 3x 2y = â€"6 Step 1: 4y = 2 Step 2: y = 2 Step 3: â€"3x 2(2) = 8 Step 4: â€"3x = 4 Step 5: x = â€"1. 333 Kaitlyn found the solution to be (1. 3, 2). Is her solution correct? Explain. Yes, she correctly solved the system of equations. No, she made an error in step 1. The y variable should have been eliminated when adding the system of equations. No, she made an error in step 2. She should have found y = 0. 5. No, she substituted y into the wrong equation to solve for x in step 3.
The error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
Given the system of linear equations:
-3x + 2y = 8 ---> eqn. 1
3x + 2y = -6 ---> eqn. 1
First add both equations together:
Step 1: 4y = 2
Next, divide both sides by 4:
Step 2: y = 2/4
y = 0.5
Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect since an error has occurred here.Therefore, the error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.
The right option will be: No, she made an error in step 2. She should have found y = 0. 5.
Learn more about system of equations on:
https://brainly.com/question/11767839