Answer:
x = 4, -4, 7i, -7i
Step-by-step explanation:
(x^2 – 16)(x^2 + 49) = 0
x^2 – 16 = 0 or x^2 + 49 = 0
x^2 = 16 or x^2 = -49
x = ± 4 or x^2 = ±7√-1 =±7i
SOMEONE PLEASE HELP ME OUT ON THIS. PLEASE!
n= 1. then a1= 7+3(1)
How to solve it.
Answer:
I think this is right for the 2nd problem
Step-by-step explanation:
a1=7+(3)(1)
Step 1: Simplify both sides of the equation.
a1=7+(3)(1)
a=7+3
a=(7+3)(Combine Like Terms)
a=10
a=10
Answer:
a=10
* if my savings of $x grows 10% each year how much money would i have in 1 year
I WILL MARK BRAINLIEST
Answer:
10/100*$x
Step-by-step explanation:
You will multiply the $x by 10%
what is the solution?
Answer: x = 36
Step-by-step explanation:
[tex]\frac{2}{3} x-4=20\\\\\frac{2}{3} x=20+4\\\\\frac{2x}{3} =24\\\\2x=24*3\\\\x=\frac{72}{2} =36[/tex]
what is the answer to this
3x-y=7
2x-2y=2
Answer:
x = 3
y = 2
Step-by-step explanation:
3x - y = 7 ------------(i)
2x - 2y = 2 ---------(ii)
Multiply equation (i) by (-2)
(i)*(-2) - 6x + 2y = -14
(ii) 2x - 2y =2 {Add both equation. now y will be eliminated}
-4x = -12 {Divide both sides by -4}
x = -12/-4
x = 3
Plug in x = 3 in equation (i)
2*3 - 2y = 2
6 - 2y = 2
Subtract 6 from both sides
-2y = 2 - 6
-2y = -4
Divide both sides by 2
y = -4/-2
y = 2
Answer:
x = 3, y = 2
Step-by-step explanation:
Given the 2 equations
3x - y = 7 → (1)
2x - 2y = 2 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 6x + 2y = - 14 → (3)
Add (2) and (3) term by term to eliminate y
- 4x + 0 = - 12
- 4x = - 12 ( divide both sides by - 4 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
3(3) - y = 7
9 - y = 7 ( subtract 9 from both sides )
- y = - 2 ( multiply both sides by - 1 )
y = 2
solution is (3, 2 )
What is the distance between (-5, 3) and (7, 3)? Explain using absolute values.
Use pythagoras theorem
d = √((x₁ - x₂)² + (y₁ - y₂)²)
d = √((-5 - 7)² + (3 - 3)²)
d = √((-12)² + 0)
d = √144
d = 12
Answer:
Step-by-step explanation:
distance is √((x2-x1)^2+(y2-y1)^2)
so it will be √((12)^2+(0)^2)
or simply 12. since we are calculating distance, it is always going to be positive so technecally the formula is |√((x2-x1)^2+(y2-y1)^2)|
An image of a right triangle is shown with an angle labeled x.
If tan x° = e divided by 8 and sin x° = e divided by f, what is the value of cos x°?
A) cos x° = 8 divided by f
B) cos x° = f divided by 8
C) cos x° = 8f
D) cos x° = 8e
Step-by-step explanation:
here's the answer to your question
By using given trigonometric functions, Value of [tex]cosx^{0}[/tex] is [tex]\frac{8}{f}[/tex].
What are trigonometric functions?"Trigonometric functions are the basic six functions that have a domain input value as an angle of a right triangle, and a numeric answer as the range. There are six basic trigonometric functions used in Trigonometry. These functions are trigonometric ratios. The six basic trigonometric functions are sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function."
Given
[tex]sinx^{0}[/tex] = [tex]\frac{e}{f}[/tex] = [tex]\frac{Opposite Side}{Hypotenuse}[/tex]
[tex]tanx^{0}[/tex] = [tex]\frac{e}{8}[/tex] = [tex]\frac{Opposite side }{Adjacent}[/tex]
[tex]cosx^{0}[/tex] = ?
Formula to find the [tex]cosx^{0}[/tex]
[tex]cosx^{0}[/tex] = [tex]\frac{Adjacent }{Hypotenuse}[/tex]
⇒ [tex]cosx^{0}[/tex] = [tex]\frac{8}{f}[/tex]
By using given trigonometric functions, Value of [tex]cosx^{0}[/tex] is [tex]\frac{8}{f}[/tex].
Learn more about trigonometric functions here
https://brainly.com/question/14746686
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the unknown side of a trapezium.
Answer:
11 mm
Step-by-step explanation:
121=area of a rectangle and area of triangle
121=x*8+(0.5)*x*(14-8), 11x=121, x=11
Answer:
[tex]11mm[/tex]
Step-by-step explanation:
Let the unknown side be x
[tex]Area \: \: \: of \: \: the \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: \: the \: \: parallel \: sides) \times height \\ 121= \frac{1}{2} \times (8 + 14) \times x \\ 121 \times 2 = 22x \\ 242 = 22x \\ \frac{242}{22} = \frac{22x}{22} \\ 11 = x[/tex]
Seena’s mother is 7 times as old as Seena. After 4 years
her mother will be 4 times as old as she will be then .Find
their present ages.
Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.
Solution :✧ Let us assume :
Seena's age be x
Her mother's age be 4x
✧ After 5 years :
Seena's age = x + 5
Her mother's age = 4x + 5
✧ Ratio of age after 5 years :
Seena's mother = 3
Seena's ratio = 1
Hence, the equation is :
[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]
By cross multiplying we get
[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]
[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]
[tex] \looparrowright \frak{x = 10}[/tex]
Hence, the ages are
Seena's age = x = 10 yrs
Her mother's age = 4x = 4 × 10 = 40 years
∴ Seena's age is 10 and her mother's is 40 respectively
8abx−10a2b+12ax2−15a2x plz regroup and factories this expression
Answer:
2x (4a-5b)2+ 3x (3a-4b)
I hope this answer was helpfull for you
The length of the pencil is 8x + 2 and length of pen is 4x + 1. Find the difference between their lengths.
Answer:
4x + 1
Step-by-step explanation:
(8x + 2) - (4x + 1)
subtract the terms that are common,,
8x-4x=4x
2-1=1
therefore, it would be 4x + 1
if you need more help with these, feel free to sub to gauthmath on subreddit
Urgent ! Help me please
Answer:
B
Step-by-step explanation:
x -> x and y -> y+5
-1 -> - 1 and - 3 -> 2, so b is the correct answer.
Can someone please help me with this I don't understand take your time if you can explain it
ABCDEFGHIJ is a regular decagon and the measure of <D is 144º. What is the measure of <A?
A) 90°
B) 100°
C) 144°
D 220°
ABC is an equilateral triangle and the measure of <A is 60°. What is the measure of <C?
A) 45°
B) 60°
C) 90°
D) 180°
Answer:
1. 144⁰
2. 60⁰
Step-by-step explanation:
The formula to find the measure of the interior angles of a regular polygon is:
m< = (n - 2) • 180/n where n = the number of sides
For a decagon, there are 10 sides.
m< = (10-2) • 180/10 = 144°
A regular polygon/equilateral triangle is defined as having equal sides and angles.
Answer:
given ABCDEFGHIJ is a decagon
As we know the sum of all ten interior angles of a decagon = 1440°
so measure of each angle of decagon = (1440/10)° = 144°
so the measure of ∠A would be 144° (C)
given Δ ABC is a equilateral triangle
As we know the sum of all three interior angles of a equialter traingle = 180°
so if one angle of an equilateral triangle is 60°
then the remaining of the angles would have the measure of 60° each
So answer = 60°(B)
Hope it helps
pls halp ////////////////
Answer:
9x^2 + 2x - 5
Step-by-step explanation:
7x^2 - 5x + 3
2x^2 + 7x - 8
__________
9x^2 + 2x - 5
Option B is the correct answer.
The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
Answer:
The sample size needed is of 10,484.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars.
This means that [tex]\sigma = 88[/tex]
Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 2.327\frac{88}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 2.327*88[/tex]
[tex]\sqrt{n} = \frac{2.327*88}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*88}{2})^2[/tex]
[tex]n = 10483.3[/tex]
Rounding up:
The sample size needed is of 10,484.
In trying to determine whether air pollution causes reduction in children's lung health a researcher proposes to see if the lung volume of 10-year-old boys who live in high ozone pollution is significantly less than the lung volume of all 10-year-old boys. The mean volume for all 10-year-old boys is 2.05 liters. A random sample of 26 10-year-old boys who live in a community with high levels of ozone pollution is found to have a mean volume of 1.98 liters, with a sample standard deviation of 0.3 liters. Test the researcher's claim that the mean lung volume of 10 -year-old boys who live in a community with high levels of ozone pollution is less than 2.05 at the 5% significance level.
Answer:
The test statistic will be "-2.33". A further explanation is provided below.
Step-by-step explanation:
According to the question,
[tex]H_0: \mu = 2.05[/tex]
[tex]H_0: \mu < 2.05[/tex]
Given:
[tex]\bar x = 1.98[/tex]
[tex]s = 0.3[/tex]
[tex]n = 100[/tex]
The test statistics will be:
⇒ [tex]t_0 = \frac{\bar x - \mu_0}{\frac{s}{\sqrt{n} } }[/tex]
[tex]=\frac{1.98-2.05}{\frac{0.3}{\sqrt{100} } }[/tex]
[tex]=-2.33[/tex]
and the P-value will be:
= [tex]0.011< \alpha[/tex]
Find a recursive rule for the nth term of the sequence.
-7, -42, -252, -1512, ...
Answer:
-7*6^n
Step-by-step explanation:
The sequence is -7*6^n.
A few examples of this are the following,
ex.)
-7*6^0 = -7
-7*6^1 = -42
-7*6^2 = -252
The zeros of a function are the values of x for which the function is equal to zero. Enter a number in each blank to make true statements about the function h(x)=(2x−2)(x−5).
Answer:
i) h(x) = 0 when x = 1, and when x = 5
ii) The graph of h intercepts the x-axis at x = 1 and x = 5
iii) The zeros of h are 1 and 5
Step-by-step explanation:
Question;
From a similar question on the website, we have;
i) h(x) = 0 when x = _, and when x = _
ii) The graph of h intercepts the x-axis at x = _ and x = _
iii) The zeros of h are _ and _
Explanation;
The given function is h(x) = (2·x - 2)·(x - 5)
When h(x) = 0, we have;
h(x) = (2·x - 2)·(x - 5) = 0
Therefore, we have;
(2·x - 2) = 0/(x - 5) = 0
(2·x - 2) = 0
x = 2/2 = 1
x = 1
Where we proceed with (x - 5) = 0/(2·x - 2) = 0, we get;
(x - 5) = 0/(2·x - 2) = 0
(x - 5) = 0
x = 5
Therefore, when h(x) = 0, x = 1, and x = 5
ii) The graph of h intercepts the x-axis at h(x) = 0, at x = 1, and x = 5
Therefore, the graph of h intercepts the x-axis at (1, 0), and (5, 0)
iii) The zeros of h are the values of x for which h(x) = 0, which are x = 1, and x = 5
On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?
Answer:
Step-by-step explanation:
The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:
by finding the slope. Remember, that slope is the same thing as rate of change.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:
[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]
Which situations can be presented by an exponential function?
Select EACH correct answer
A.In a structure made of soup cans, each row has 6 more cans that the previous row
B.a doctor’s office accepts 20 new patients each month
C.The value of a motorcycle decrease by 12% each year
D.Every year, the number of online subscribers to a service is 4 times what it was the previous year
Answer:
C.The value of a motorcycle decrease by 12% each year
D.Every year, the number of online subscribers to a service is 4 times what it was the previous year
Step-by-step explanation:
A function is said to be exponential if it changes (increases or decreases) by a fixed percentage or proportion over a certain period of time.
From the options given, only options C and D is defined as changing based on a certain percentage. And option D cgbages by a clfixed proportion from the initial value.
The option that represents the exponential function are situation C) and D) and this can be determined by making the mathematical expression of each situation.
Try to make a mathematical expression of the situation given below in order to check which option shows an exponential function.
A) According to the given data, in the first row there are 6 cans, in the second row there are 12 cans, in the third row there are 18 cans, and so on. Now, let 'a' be the total number of rows then, the mathematical expression of this situation is given by:
= 6a
This situation is not representing the exponential function.
B) According to the given data, in the first month there are 20 patients, in the second month there are 40 patients, and so on. Let the total number of months be 'b' then the mathematical expression is given by:
= 20b
This situation is not representing the exponential function.
C) According to the given data, in the first year the value of the motorcycle decrease 12%, in the second month the value decreased by 24% of the initial value, and so on. So, the price of motorcycle decreases exponentially. Therefore, this option is correct.
D) According to the given data, every year, the number of online subscribers to service is 4 times what it was the previous year. The mathematical expression of this situation is:
= [tex]4^x[/tex]
where 'x' is the number of years. Therefore, this option is correct.
For more information, refer to the link given below:
https://brainly.com/question/2263981
If a sequence of 8 consecutive odd integers with increasing values has 9 as its seventh term. What is the sum of the terms of the sequence?
Answer:
[tex]Sum = 32[/tex]
Step-by-step explanation:
Given
Sequence = Consecutive Odds
[tex]T_7 = 9[/tex]
Required
The sum of the terms
A sequence of odd number has a difference of 2. So, the sequence is represented as:
[tex]S = \{-3,-1,1,3,5,7,9,11\}[/tex]
Add up all terms in the sequence
[tex]Sum = -3-1+1+3+5+7+9+11[/tex]
[tex]Sum = 32[/tex]
Luna flew from Boston to Orlando with a stop in Atlanta to switch planes. The flight from Boston to Atlanta was 3 hours and 30 minutes long. Luna was in Atlanta for 1 hour and 30 minutes, and her flight from Atlanta to Orlando was 1 hour and 15 minutes long. Luna landed in Orlando at 1:45 P.M. What time did Luna's first flight leave Boston?
Answer:
1:15 minuites
Step-by-step explanation:
30 minuites
Answer:
8:30 A.M.
Step-by-step explanation:
Start by adding up the total time spent traveling.
3h 30min + 1h 30min + 1h 15 min = 5h 15 min
If she arrived in Orlando at 1:45 P.M., count back 5 h 15 min.
1:45 - 15 min = 1:30 - 5h = 8:30 A.M.
The sum of two rational numbers is 9 and one of them is − 3, then the other is_.( ) 10
Answer:
12
Step-by-step explanation:
let the rational number be x
x+(-3) = 9
x = 9+3 = 12
Answer:
12
Step-by-step explanation:
x + y = 9
x = -3
=>
-3 + y = 9
y = 12
TIME REMAINING
43:02
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Mark this an
the answer of this question is (-2,2)
please please jhelp me....
Answer:
2·v - (u + w) = (5, 0, -10)
Step-by-step explanation:
The given values of the vectors are;
u = (2, -1, 3), v = (4, 0, -2), and w = (1, 1, 3)
The required vector is 2·v - (u + w)
2 × v = 2 × (4, 0, -2) = (8, 0, -4)
(u + w) = (2, -1, 3) + (1, 1, 3) = (3, 0, 6)
Therefore;
2·v - (u + w) = (8, 0, -4) - (3, 0, 6) = (5, 0, -10)
2·v - (u + w) = (5, 0, -10)
HELPPP HELP PLS PRONTO ASAP
Ahmed is working at a restaurant. His boss pays him $16.00 per hour and
promises a raise of $1.25 per hour every 6 months. Which sequence
describes Ahmed's expected hourly wages, in dollars, starting with his current
wage?
Answer:
B
Step-by-step explanation:
each of the numbers is just adding 1.25 on to it
Answer: Choice B
16.00, 17.25, 18.50, 19.75, ...
==========================================================
Explanation:
We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.
Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.
We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25
The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.
need help with this refer to picture
Answer:
Step-by-step explanation:
which of the following one is true
Find the volume of this cylinder.
As soon as possible please
Answer:
36
Step-by-step explanation:
pi (3) x 1^2 x 12 = 3 x 12 = 36
Function g can be thought of as a scaled version of f(x)=|x|
Answer:
g(x) = 1/2 |x|
Step-by-step explanation:
Scaling f(x) means it's of the form g(x) = a|x|
From the graph, it appears to pass through the point (2, 1). By subbing in the values for this point, the equation can be found to be:
1 = a|2|
a = 1/2
Therefore, g(x) = 1/2 |x|
