Answer:
-15
Step-by-step explanation:
Let a = 2 and c = -7.
[tex]c-4a\\(-7)-4(2)\\-7-8\\-15[/tex]
we know that the value of a is 2 and c is -7
Expression-
c-4a
= (-7)-4×2
= (-7)-8
= -15
~If ∠G measures 45°, ∠F measures 82°, and f is 7 feet, then find g using the Law of Sines. Round your answer to the nearest foot. triangle EFG with side e across from angle E, side f across from angle F, and side g across from angle g 4 feet 5 feet 6 feet 7 feet
The value of g across from angle G is 5feet
According to sine rule
[tex]\frac{e}{sinE}=\frac{f}{sinF}=\frac{g}{sinG}[/tex]
Given the following
∠G = 45°
∠F = 82°
f = 7feet
Required
side g
Substitute the given values into the formula
[tex]\frac{f}{sinF}=\frac{g}{sinG}\\ \frac{7}{sin82}=\frac{g}{sin45}\\\frac{7}{0.9903}=\frac{g}{0.7071}\\7.0686=\frac{g}{0.7071}\\g=7.0686*0.7071\\g=4.998\\g\approx5ft[/tex]
Hence the value of g across from angle G is 5feet
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The length of the line segment EF ([tex]g[/tex]) is approximately 5 feet.
Let be [tex]EFG[/tex] a Triangle, whose expression derived from the Law of Sines is described below:
[tex]\frac{e}{\sin E} = \frac{f}{\sin F} = \frac{g}{\sin G}[/tex] (1)
Where:
[tex]e[/tex] - Measure of the line segment FG, in feet.
[tex]f[/tex] - Measure of the line segment EG, in feet.
[tex]g[/tex] - Measure of the line segment EF, in feet.
[tex]E[/tex] - Angle at vertex E, in sexagesimal degrees.
[tex]F[/tex] - Angle at vertex F, in sexagesimal degrees.
[tex]G[/tex] - Angle at vertex G, in sexagesimal degrees.
We can determine a missing length, by knowing the length of a neighboring side and two consecutive angles. If we know that [tex]f = 7\,ft[/tex], [tex]G = 45^{\circ}[/tex] and [tex]F = 82^{\circ}[/tex], then the measure of the line segment EF is:
[tex]g = f\cdot \left(\frac{\sin G}{\sin F} \right)[/tex] (2)
[tex]g = (7\,ft)\cdot \left(\frac{\sin 45^{\circ}}{\sin 82^{\circ}} \right)[/tex]
[tex]g\approx 4.998\,ft[/tex]
[tex]g \approx 5\,ft[/tex]
The length of the line segment EF ([tex]g[/tex]) is approximately 5 feet.
Which is the equation of the line with slope o passing through the point (-3,-1)?
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Answer:
y = -1
Step-by-step explanation:
We assume you want the line with a slope of zero. That is a horizontal line, so y is a constant. In order to make the line go through the point with y=-1, the equation of the line is ...
y = -1
The distance a race car travels is given by the equation, [tex]d=v_{0} t+\frac{1}{2} at^{2}[/tex], where [tex]v_{0}[/tex] is the initial speed of the race car, a is the acceleration and t is the time traveled. Near the beginning of a race, the driver accelerates for 9 seconds at a rate of [tex]4m/s^{2}[/tex]. The driver's initial speed was 75 m/s.
Find the driver's average speed during the acceleration.
Step-by-step explanation:
here's the answer to your question
Find the exact value by using a half-angle identity.
tan seven pi divided by eight
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Answer:
1 -√2
Step-by-step explanation:
[tex]\tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}[/tex]
tan(7π/8) = 1 -√2
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
SOMEONE PLS HELP!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
Step-by-step explanation:
Is the function f(x) = 3x+1, f(x) = 3ˣ⁺¹, or f(x) = 3ˣ+1 ?
f(x) = 3x+1 is not an exponential function. It is a straight line.
f(x) = 3ˣ⁺¹ Is an exponential function. The base is 3.
f(x) = 3ˣ+1 is an exponential function. The base is 3.
(PLEASE ITS ACTUALLY MY LAST ONE HELP)
Which two figures represent circles of the same size?
A) D and G
B) C and G
C) none of them.
D) C and D
Answer:
B) C and G
Step-by-step explanation:
The radius is equal to 1/2 the diameter
r = 1/2 d
G has a diameter of 45
1/2 (45) = 22.5
C and G are the same
Answer:
c and g!
Step-by-step explanation:
The rate of change for yyy as a function of xxx is
, therefore the function is
.
For all values of xxx, the function value y\:yy
\:000.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
When x=1x=1x, equals, 1, the function value y=\:y=y, equals
.
everything seems to be correctly filled.
if you wanted confidence by confirmation: here, take some
It is an exponentially decaying function.
What is an exponential function ?An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.
Exponential functions are of two types one is exponentially growing function and exponentially decaying function.
when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.
In the given question f(x) = 8e⁻ˣ
when, x = 0 f(x) = 8
f(x) = 8e⁻ˣ
f(0) = 8e⁰
f(0) = 8
Learn more about Exponential functions here :
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inverse of f(x)=e^(3x-1)
Answer:
f(x) = 3ex - e
Step-by-step explanation:
In this equation we have basically the times e by 3x and -1
so first let's do e times 3x
here...
e X 3x = 3ex
so let's rewrite the equation
3ex - 1
now we times e by 1. (Note - Negative sign stays)
3ex - 1e
we don't have to write 1e cause 1e = e, they are the same.
Therefore the answer is 3ex - 1e
Following are the calculation of inverse:
Given:
[tex]\to f(x)=e^{3x-1}[/tex]
To find:
inverse function=?
Solution:
A function g is the inverse of function F if for [tex]y=f(x), x=g(y)[/tex]
[tex]\to y=e^{3x-1}[/tex]
Replacing the value of x with y
[tex]\to x=e^{3y-1}[/tex]
Solve for [tex]y, x=e^{3y-1}[/tex]
Therefore, the answer is [tex]\frac{\log(x)+1}{3}[/tex].
Learn more about the inverse function:
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A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed
Answer:
It will be 31.4 cm rounded off for circumference
It will be 78.53 cm2 rounded off for area
Step-by-step explanation:
Diameter = 10 cm
Radius = 10/2 cm = 5 cm
Circumference = 2×pi×radius
= 2pi×5
= 31.4 cm
Area = pi × r square
= 25 pi
= 78.53cm2
The decimal for an irrational number never terminates or repeats. The
rational and irrational numbers together form the set of real numbers.
If false, explair:
Answer:
Step-by-step explanation:
No that is true. I can't make anything more out of it.
PLEASE HELP! 50 POINTS
Identify the intervals on which the function is increasing, decreasing or constant. Write your answers in interval notation. Write the end behavior for each function in limit notation.
f(x)=-4x^4+3x^3-2x^2+x-9
(Type a 0 before the decimal to hold the ones place for answers that don't have a value in the ones place. Ex. 0.24)
Use inf for infinity
For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
Round your answer to the nearest whole number (percent).
Answer:
95%
Step-by-step explanation:
Mean , xbar = 64.3; standard deviation, s= 2.4
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
percent of heights that lie between 59.5 inches and 69.1 inches.
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4
-2 < Z < 2
Thia is within 2 standard deviations of the means :
2 standard deviation form the mean = 95% according to the empirical rule.
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?
Answer:
a.
[tex] \frac{36}{40} [/tex]
-p/3-8=3 what is the variable
Answer:
-33
Step-by-step explanation:
-p/3-8=3
or,(-p-24)/3=3
or,(-p-24)=9
or,-p=33
Therefore, p=-33
The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.
Answer:
Step-by-step explanation:
x+y = 67
2x-y = 38
Add the equations together
3x = 108
x = 36
y = 67-x = 31
Identify the domain of the graph given below.
Answer:
(-∞,∞) is the domain.
2 is the range
Step-by-step explanation:
What is the purpose for post tests?
Answer:
The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.
HaLP a beggar in need
Answer:
C) 2
Step-by-step explanation:
From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.
An investment of $8,120 is earning interest at the rate of 5.8% compounded quarterly over 11 years. How much
interest is earned on the investment? Show your work.
Answer:
5180.56 Dollars...........
3. (02.01)
Solve for x:
wim
(x – 4) = 2x. (1 point)
2
-2
-8
-4
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
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Solve 2x2 – 3x = 12 using the quadratic formula.
Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a
2x^2 - 3x = 12
2x^2 - 3x - 12 = 0
a = 2
b = -3
c = -12
(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)
3 +/- sqrt( 9 + 96 ) / 4
3 +/- sqrt(105) / 4
Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]
Hope this helps!
Help. The graph shows the system of equations below.
2x -3y = -6
y = - 1/3x -4
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Answer:
(a) The blue line ... solution ... (-6, -2)..
Step-by-step explanation:
The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.
The blue line represents the equation 2x -3y = -6.
The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.
1/10
9/10
Q
Find the perimeter of the rectangle pictured above. Give your answer as a reduced mixed number.
Answer:2
Step-by-step explanation:
6( n - 2) in word form please c:
Answer:
six in parenthesis n minus two
Step-by-step explanation:
2 ways could be:
A. N minus two then multiply by six
B. Six times parentheses n minus two end parentheses
I need help please thank you
Answer:
A
Step-by-step explanation:
in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.
recall this formula :
(a-b)(a+b) = a^2 - b^2
in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of 3 -
after multiplying the denominator by its conjugate, we get:
(3 - [tex]\sqrt{6x}[/tex]) (3 +
at this point there is no need to solve the numerator as there is only one answer with this denominator.
hope this helps :)
Answer:
Step-by-step explanation:
What should be subtracted from 13/(-56) to get 11/28
Answer:
-5/8
Step-by-step explanation:
13/ -56 -x = 11/28
Add 13/56 to each side
13/ -56 + 13/56 -x = 11/28+ 13/56
-x = 11/28 + 13/56
Get a common denominator
-x = 11/28 *2/2 +13/56
-x = 22/56 + 13/56
-x = 35/56
Divide top and bottom by 7
-x = 5/8
Multiply both side by -1
x = -5/8
What effect will replacing x with (x - 4) have on the graph of the equation y = (x - 3) ^ 2
A. Slides the graph 4 units up
B. Slides the graph 7 units down
C. Slides the graph 4 units right
D. Slides the graph 1 units
Answer:
C)slides graph 4 units to the right
What is the inverse of the function ? f(x)=x+1 over x?
plato
Answer:
[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]
Step-by-step explanation:
bxhrrrhi5u44ftj7gttjoy
Answer:
x = (y+1)/y
xy = (y+1)
xy -y = 1
y(x-1)=1
y = 1/(x-1)
Step-by-step explanation:
