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Answer:
105 ft
Step-by-step explanation:
Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.
The Pythagorean theorem gives us the relation ...
(x +14)² = x² +(x -49)²
x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses
x² -126x +2205 = 0 . . . . . . . . put in standard form
x² -126x +3969 -1764 = 0 . . . . "complete the square)
(x -63) = ±√1764 . . . . . . add 1764, take the square root
x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet
The height of the pole is 105 feet.
A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of a new function compare to the domain and range of the original function?
Answer:
The domain and range remain the same.
Step-by-step explanation:
Hi there!
First, we must determine what increasing a by 2 really does to the exponential function.
In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).
Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).
The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.
The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.
I hope this helps!
I am authoring you to offer free insurance for a year the regular price is 6.99 this will save the customer almost_ a year
I RLLY NEED HELP!!!!!!
Answer:
Angle ADB = 60 degrees
Step-by-step explanation:
This is a 60 60 60 triangle, which means all of its angles equal 60 degrees. Therefore angle ADB is 60 degrees.
Yogi is 6 years older than Michelle. The sum of their ages is 26. Write a system of linear equations to represent this information. What are their ages?
Answer:
10 and 16, x+(x+6)=26
Step-by-step explanation:
Michelle has an age we don't know, so we put her age as x.
Yogi is 6 years older than her, so her age is x+6
Michelle=x
Yogi=x+6
we know both their ages equal 26. so we set it up as
x+(x+6)=26
combining like terms we get
2x+6=26
subtract 6 from both sides
2x=20
divide both sides by 2
x=10
now that we have the value for x, we plug it into their original ages
Michelle is 10, because her age is just x.
Yogi is 16, because her age is x+6
Simplify the trigonometric expression cos(2x)+1 using Double-Angle identities
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Answer:
C. 2cos²(x)
Step-by-step explanation:
The relevant identities are ...
cos(2x) = cos²(x) -sin²(x)
cos²(x) = 1 -sin²(x)
__
Then the expression can be simplified to ...
cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)
= 2cos²(x)
There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour).
What does the slope of the line represent?
A. the change in wind speed for every 1 kPa increase in air pressure
B. the wind speed of a hurricane with an air pressure of 1000 kPa
C. the wind speed of a hurricane with an air pressure of 0 kPa
D. the change in wind speed for every hour
Answer:
A. the change in wind speed for every 1 kPa increase in air pressure
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b;
where y, x are variables, m is the slope (rate of change) of the line and b is the y intercept (value of y when x = 0)
Given the line y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots.
The slope of the line is -1.22. The slope means that there is a decrease in wind speed by 1.22 miles per hour for every increase of 1 kPa in air pressure.
The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are listed below. Find the mean and median number of home runs. Round the mean to the nearest whole number. Which measure of central tendency- the mean or the median- best represents the data? Explain your reasoning.
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Answer:
Mean = 35.56
Median = 35.5
Step-by-step explanation:
Given the data:
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Reordered data :
16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 45, 46, 46, 49, 73
The mean = ΣX / n
n = sample size ; ΣX = sum of values
The mean = 658 / 18
The mean = 36.56
The Median = 1/2(n+1)th term
1/2(18+1)th term = 1/2(19)th term = 9.5 term
Median = (9th + 10th) / 2 = (34 + 37) / 2 = 35.5
A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?
Answer:
The time required is 60.3 days.
Step-by-step explanation:
initial amount, No = 0.3 g
rate, r = 1.15 % per day = 0.0115 per day
final amount, N = 0.15 g
Let the time is t.
[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]
Question 1 of 10
If f(x)= 2 -3 and g(x) = 4x2 + x - 4, find (f+ g)(x).
O A. 4x+x-7
O B. 4x2 +5x-1
O c. 6x2 - 7
OD 6+x-1
A
SUBMIT
Answer:
I believe it's A
Step-by-step explanation:
I'm not sure sorry if its wrong
What is 5x4 please help
Answer:
5 x 4 = 20.
Step-by-step explanation:
5 + 5 = 10
5 + 10 = 15
5 + 15 = 20!
Please mark brainliest!
- KanaKittyKat
Answer:
5 x 4 = 20
5 + 5 + 5 + 5 = 20
A machining center is in charge of producing 225 parts per day. The parts width. Any parts produced between 250mm and 260mm are considered gless than 250mm must be reworked at an additional cost of $8 per part. 260mm must be reworked at an additional cost of $2.50 per part. The varquantified as a standard deviation of 5.0mm. Measurements on these parhave the ability to set up the machine to achieve whatever mean width value you wish.
Required:
Setup a data table to determine the mean width setting that will minimize expected rework cost ($8 per small part and $2.50 per large part).
Donald has x twenty dollar bills and 1 yen dollar bill. How much money does Donald have?
Write your answer as an expression
A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14
Required:
a. Compute the value of the test statistic.
b. What is the p-value?
Answer:
1.944 ;
0.026
Step-by-step explanation:
Given :
Sample size, n = 34
Sample mean, xbar = 15
Population standard deviation, σ = 3
The hypothesis :
H0: μ ≤ 14
H1: μ > 14
The test statistic :
Test statistic = (xbar - μ) ÷ (σ/√(n))
Test statistic = (15 - 14) ÷ (3/√(34))
Test statistic = 1 / 0.5144957
Test statistic, Z = 1.944
The Pvalue :
Using the Pvalue from test statistic value :
Pvalue(1.944) = 0.026
Pvalue < α ; Reject H0
Find the scale factor where the pre-image is the large triangle and the image is the small triangle.
A. 4/5
B. 3/2.4
C. 2.4/3
D. 5/4
Answer:
Option B
Step-by-step explanation:
If the larger triangle (Preimage) is dilated by a scale factor 'k' to form the image triangle (small triangle),
Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the preimage}}[/tex]
k = [tex]\frac{3}{2.4}[/tex]
Therefore, Option B will be the correct option.
If a number is divisible by 6 and 8 then is it also divisible by 48?
Answer:
No
Step-by-step explanation:
Let's look at an example
24
24 is divisible by 6 24/6 = 4
24 is divisible by 8 24/8 = 3
24 is not divisible by 48 24/48 = 1/2 which is not an integer
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.)
(s + 1)3
Expand the expression as
(s + 1)³/s ⁵ = (s ³ + 3s ² + 3s + 1)/s ⁵
… = 1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵
Then taking the inverse transform, you get
LT⁻¹ [1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵]
… = LT⁻¹ [1/s ²] + LT⁻¹ [3/s ³] + LT⁻¹ [3/s ⁴] + LT⁻¹ [1/s ⁵]
… = LT⁻¹ [1!/s ²] + 3/2 LT⁻¹ [2!/s ³] + 1/2 LT⁻¹ [3!/s ⁴] + 1/24 LT⁻¹ [4!/s ⁵]
… = t + 3/2 t ² + 1/2 t ³ + 1/24 t ⁴
Please help due tomorrow
Answer: x= 2.5, y = 10
Step-by-step explanation:
I'm going to assume that these photocopies are proportional in relations to each other.
If they're proportional, you can set up two proportions:
[tex]1) \frac{x}{5} =\frac{3}{6} \\\\2) \frac{5}{y} =\frac{3}{6}[/tex]
And cross-multiply:
[tex]1) 6x = 5*3 \\\\2) 3y = 5*6[/tex]
Then solved for x and y:
[tex]1) 6x = 15\\x=\frac{15}{6} =\frac{5}{2} =2.5 \\\\2) 3y = 30\\y=\frac{30}{3} =10[/tex]
Need help ASAP
In the figure, if the measure of ∠8 = 72o, what's the measure of ∠14?
Four Bisecting Lines
Question 3 options:
108°
72°
98°
62°
Answer:
72°
Step-by-step explanation:
[tex] m\angle \: 6 = m \angle \: 8 \\ (corresponding \: \angle s) \\ m\angle \: 8 = 72 \degree \\ \therefore \: m\angle \: 6 = 72 \degree \\ \\ m\angle \: 14 = m \angle \: 6 \\ (corresponding \: \angle s) \\\therefore \: m\angle \: 14 = 72 \degree [/tex]
Which number can be distributed across two terms
inside parentheses? 3/5 V
X-6
18-4x-1
5
tep 2 Combine like terms that are on the same side of
the equation. Which terms can be combined?
18 and -1
3/5x and 4x
6 and 1
Check
Intro
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Answer:
3/5 can be distributed (correct answer is shown)18 and -1 can be combinedStep-by-step explanation:
The only factor outside parentheses that contain 2 terms is the factor 3/5. It can be distributed. (The correct response is shown.)
3/5 can be distributed
__
The only like terms that reside on the same side of the equal sign are ...
18 and -1
Translate the following sentence into an algebraic inequality:
The difference of twice a number, x, and eleven is, at most, the sum of twenty and a number, x.
Question 4 options:
A)
2x∕11 ≥ 20 – x
B)
9x ≥ 20 + x
C)
2x + 11 ≥ 20x
D)
2x – 11 ≤ 20 + x
Answer:
it have to be letter c
Step-by-step explanation:
this the only problem matches with the question
The inequality represent the given phrase is 2x-11≤20+x. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, the difference of twice a number, x, and eleven is, at most, the sum of twenty and a number, x.
The difference of twice a number, x, and eleven is
2x-11
The sum of twenty and a number, x
20+x
So, inequality is 2x-11≤20+x
The inequality represent the given phrase is 2x-11≤20+x. Therefore, option D is the correct answer.
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Solve equation by using the quadratic formula
Answer:
x = -2
Step-by-step explanation:
x^2 + 4x + 4 = 0
quadratic formula:
-b +or- sqrt(b^2-4ac)/2a
-4 +/- sqrt ((-4)^2-4*1*4)/2*1
-4+/- sqrt(16-16) / 2
-4 +/- 0 / 2
-4/2
-2
Hari earns Rs 4300 per month. He spends 80% from his income. How much does he save in a year? please give answer in step by step explaination
Answer:
4300 x 12= 51600
20/100 x 51600
10,320 Rs (also pay bohat kam hai :D )
Solve the system using substitution. x+y=-2 and x-y=-8
Answer:
1) x+y=-2
x=-2-y
2) x-y=-8
substitude value of x
(-2-y)-y=-8
-2-2y=-8
-2y=-6
y=3
Substitute value of y in 1
x=-2-3
x=-5
Brainliest please~
Rewrite the fraction in the sentence below as a percentage. From 125 yards away, a marksman hit 11/20 of the targets last year.
Answer:
Step-by-step explanation:
11/20 = 55/100 = 55%
When a closed curve is parameterized by {x[t], y[t]}, then as you advance along the curve in the direction of the parameterization, which way do the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point; in the direction you are going, or in the direction opposite to the direction you are going?
Answer:
In the direction you are going,
Explanation:
We know that the tangent to {x[t], y[t]} are {x'[t], y'[t]}. Since {x'[t], y'[t]} are tangents at {x[t], y[t]}, we know that the tangent at a point is always parallel to the direction of the function at that point and in the direction of the function. So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in my direction of motion as I move along the curve.
So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in the direction you are going.
if (a + b) = 73 and a b =65 find value of a²+ b²
Step-by-step explanation:
Here,
by formula a^2+b^2=(a+b)^2-2ab
so,
or,(a+b)^2-2ab
or,(73)^2-2×65
or,5329-126
=5203 is the answer
obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the progression.
If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which
x - 5 = r (x + 1)
==> r = (x - 5) / (x + 1)
and
x - 2 = r (x - 5)
==> r = (x - 2) / (x - 5)
Then
(x - 5) / (x + 1) = (x - 2) / (x - 5)
Solve for x :
(x - 5)² = (x - 2) (x + 1)
x ² - 10x + 25 = x ² - x - 2
-9x = -27
x = 3
It follows that the ratio between terms is
r = (3 - 5) / (3 + 1) = -2/4 = -1/2
Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by
a(n) = 4 (-1/2)ⁿ⁻¹
The sum of the first 12 terms - denoted here by S - is then
S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹
Solve for S :
S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]
(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]
==> S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]
==> 3/2 S = 4 (1 - 1/4096)
==> S = 8/3 (1 - 1/4096)
==> S = 1365/512
Couldn’t figure this out help please
(B)
Step-by-step explanation:
Rewrite the equations into their standard forms. The first one can be rewritten as
[tex]10x - 12y = -5[/tex]
and the 2nd can be rewritten as
[tex]3x + 5y = -1[/tex]
Solving this system either by substitution or elimination, we get
[tex]x = -\dfrac{37}{86}\:\:\text{and}\:\:y= \dfrac{25}{86}[/tex]
If you add x + y, you'll get a negative number.
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Answer:
B. x + y < 0
Step-by-step explanation:
The two equations can be cleared of fractions by multiplying by 15.
15(2/3(x +1) -4/5y) = 15(1/3)
10(x +1) -12y = 5
10x -12y = -5
and
15(2/5x +1/3(2y +1)) = 15(1/5)
6x +5(2y +1) = 3
6x +10y = -2
3x +5y = -1 . . . . . eliminate common factor of 2
__
You can find the solutions any way you like, but you can answer the question without doing that. The lines are not parallel, nor coincident, so there is exactly one solution. (choices C and D are incorrect)
If we can locate the solution relative to the line x + y = 0, we can tell if choice A or choice B is correct. A quick look at the intercepts of the equations tells us the solution cannot lie in quadrants 1 or 4. The negative y-intercept and shallow slope (-3/5) of the second equation tells us the solution must lie below the line x + y = 0. That means x+y < 0, choice B.
_____
In the attached graph, the line x+y=0 is dashed orange. Above that line, x+y>0; below that line, x+y<0. We see the intersection point of the red and blue lines is in the region where x+y < 0.
For standard form equation ax+by = c, the x- and y-intercepts are c/a and c/b, respectively, so are easy to find from that form. Knowing these makes it easy to make a sketch of the graph, locating the solution point relative to the line x+y = 0.
12,963 rounded to the nearest hundredth
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Answer:
12,963.00 (in the US)12,96 (some other places)Step-by-step explanation:
In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:
12,963.00
__
Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.
12,96
If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz. Her third quiz score is what percent higher than her first quiz score?
Answer:
30%
Step-by-step explanation:
you just add 10% and 20%
Hope it helps c:
Zelina scored 32% higher on the third quiz than on her first quiz.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
Given that:-
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz.From the given data we will see that:-
1 ) Zelina scored 10% higher on her second quiz than on her first quiz.
SQ = 1.10 FQ
2 ) On her third quiz, Zelina scored 20% higher than on her second quiz
TQ = 1.20SQ
From the above to expression solve for the first quiz:-
TQ = 1.20 x 1.10 FQ
TQ = 1.32FQ
Therefore Zelina scored 32% higher on the third quiz than on her first quiz.
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