Answer:
You can use your graphing calculator to find the answer.
Go to STAT, then TESTS, and hit "1: Z-Test..."
Make sure it is set to Stats, then for mu0, do 70; for standard deviation, do 9; for mean, you do 62; for sample size, you do 19. For mu, you do not equal to mu0. Then you hit "Calculate".
You then get a z-value (critical value) of -3.874576839, and a p-value of 0.00010685098.
This means that...
We reject the null hypothesis that the average height of lodgepole pines in Yellowstone is 70 feet because p = 0.0001 is less than the significance level of alpha = 0.01. There is sufficient evidence to suggest that the mean height of lodgepole pines in Yellowstone is NOT equal to 70 feet.
Hope this helps!
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
Draw the straight line y = x + 2
Answer:
Graph is attached below
Step-by-step explanation:
You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.
The plotted straight line is as shown in below graph.
Given straight line equation is y = x + 2
To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.
After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.
Example, take x = 1 and x = 2 for straight line y = x + 2
Then we get:
For x = 1, y = 1 + 2 = 3
For x = 2, y = 2 + 2 = 4
The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.
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A six sided number cube is rolled twice. What is the probability that the first roll is an even number and the second roll is a number grater than 4?
Answer:
1/6
Step-by-step explanation:
The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.
Multiply these two values
1/2*1/3= 1/6
what's the thickness of a rectangle prism with a height of 12 inches, a width of 8 inches and surface area 992 square inches?
Answer:
Thickness of rectangle prism is 20 inches.
Step-by-step explanation:
Given:
Surface area of rectangular prism, A = 992 sq inches.
Height, h = 12 inches
Width, w = 8 inches
To find:
Thickness / length of prism, [tex]l[/tex] = ?
Solution:
First of all, let us learn the formula for surface area of a rectangular prism.
Formula for surface area of a prism is given as:
[tex]A=2(wl+hl+hw)[/tex]
As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.
Putting all the given values in the formula to find the value of [tex]l[/tex]:
[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]
So, the answer is Thickness of rectangle prism is 20 inches.
You're at a clothing store that dyes your clothes while you wait. You get to pick from 444 pieces of clothing (shirt, pants, socks, or hat) and 333 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?
Answer:
Probability of orange hat = 0.0833
Step-by-step explanation:
We have to find the probability of getting an orange hat while we randomly choose from 444 pieces of clothing and 333 colors.
So we have to get hat from the clothing and we have to get orange color from the colors. All shirts , pants , socks and hats are in equal numbers and are 111 each. Also purple, blue and orange are 111 each in number.
The probability of getting hats =
= 0.25
The probability of getting orange = = 0.333
Final probability = 0.25 0.333
= 0.0833
Answer: 1/12
Step-by-step explanation:
I just had khan academy
Two functions can be linked together by using the output of the first function
as the input of the second function. Which term describes this process?
A. Input/output
B. Relation
C. Domain
D. Composition
Answer: Option D, composition.
Step-by-step explanation:
In a function f(x) = y
x is the input, and the set of the possible values of x is called the domain.
y is the output, and the possible values of y is called the range.
Now, if we have two functions:
f(x) = y
g(x) = y.
we can define the composition of functions as: using the output of one function as the input of the other function, we can write this as:
f( g(x)) or fog(x)
In words, first we evaluate the function g in the point x, and the output of that is used as the input for the function f.
Then, the correct option here is D, composition.
Area of right triangle with legs of 9 and 12 units
Answer:
54 units^2
Step-by-step explanation:
The formula to find the area of a right triangle is bh/2.
Plug the values in.
9*12/2
Multiply.
108/2
Divide.
52
The area is 54 units squared.
Answer: 54u²
Step-by-step explanation:
The area of a triangle is 1/2bh
1/2bh
1/2(12)(9)
(6)(9)
54
Hope it helps <3
(8x - 5)(7x-8)
Find the product
Answer:
x=−3
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 7*x-8-(8*x-5)=0
Pull out like factors : -x - 3 = -1 • (x + 3)
Solve : -x-3 = 0
Add 3 to both sides of the equation : -x = 3
Multiply both sides of the equation by (-1) : x = -3
Answer:
56x^2−99x+40
Step-by-step explanation:
Evaluate (8x−5)(7x−8)
Apply the distributive property by multiplying each term of 8x−5 by each term of 7x−8.
56x^2−64x−35x+40
Combine −64x and −35x to get −99x.
56x^2−99x+40
the sum of two numbers is -26. One number is 148 less than the other. Find the numbers
Answer:
61 and -87
Step-by-step explanation:
If the numbers are x and x - 148, we can write the following equation:
x + x - 148 = -26
2x - 148 = -26
2x = 122
x = 61 so x - 148 = 61 - 148 = -87
Which equation satisfies all three pairs of a and b values listed in the table ?
A) a-3b=10
B) 3a+ b=10
C) 3a-b=10
D) a+ 3b=10
Answer:
The answer is option C.
3a - b = 10
Hope this helps you
Find the graph of the inequality y>-(1/6)x+1.
Answer:
y > -x/6 + 1
Step-by-step explanation:
Hope this can help
The graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex] is option "A" .
What is graph of inequality?The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
According to the question
The inequality : [tex]y > -(\frac{1}{6} )x+1.[/tex]
now first we take out points to plot graph for that we will assume inequality to equation
i.e
[tex]y = -(\frac{1}{6} )x+1[/tex]
x y
0 1
6 0
Now , as inequality have > sign
i.e according to the graph of inequality rules:
The boundary line is dashed for > and < and If the symbol ≥ or > is used, shade above the line.
Therefore,
Graph will be option "A" only .
Hence, the graph of the inequality [tex]y > -(\frac{1}{6} )x+1[/tex] is option "A" .
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Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)
z = x8y9, x = s cos(t), y = s sin(t)
∂z/∂s =
∂z/∂t =
Answer:
Step-by-step explanation:
Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;
∂z/∂s = ∂z/∂x*∂x/∂s + ∂z/∂y*∂y/∂s
Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)
∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)
On substitution;
∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)
∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)
∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t
∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t
∂z/∂s = 17s¹⁶cos⁸tsin⁹t
∂z/∂t = ∂z/∂x*∂x/∂t + ∂z/∂y*∂y/∂t
∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)
∂z/∂t = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))
∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))
∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t
∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)
Solve triangle ABC given:
(a) angle A = 40°, angle B = 60°, b = 8 cm.
(b) a = 4, b = 5, c = 6.
(c) angle B = 104°, a = 17 cm, c = 11 cm.
Answer:
(a) C = 80 a = 5.938cm c = 9.097cm
(b) unsure
(c) b= 22.147cm
A = 48.16 degrees
C = 22.82 degrees
Note angle sum higher than 180 due to rounding inaccuracies
Step-by-step explanation:
(a) <C == 180 - (40 + 60) == 80 (Interior angles on triangle have sum of 180 degrees)
side a = (8*sin(40))/sin(60) == 5.938cm by law of sines
side c = (8*sin(80))/sin(
60) == 9.097cm by law of sines
(b) unsure
(c) b^2 = 17^2 + 11^2 - 2(17)(11)cos(104) --> Law of cosines
b^2 = 289 + 121 - 2(187)cos(104)
b^2 = 400 - -90.479
b^2 = 490.479
b = 22.147 cm
sin(A)/17cm = sin(104)/22.147cm
A = arcsin((17/22.147)*sin(104))
A = 48.16 degrees
sin(C)/11cm = sin(104)/22.147cm
C = arcsin((11/22.147)*sin(104))
C = 28.82 degrees
A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n. A one-way analysis of variance showed that job satisfaction did not vary by marital status, F(2, 24) = 1.93, p > 0.05.
a. k = _____
b. N = _____
c. n = _____
Answer:
a. k = 3
b. N = 27
c. n = 9
Step-by-step explanation:
Given that,
Source : sS dF mS F
Between: k -1 sSB/k-1 mSB
within N-K sSw/N-K mSw
total N-1
Therefore F ( 2, 24 ) = F ( K - 1, N - K )
so K - 1 = 2
K = 2 + 1
K = 3
N - K = 24
N - 3 = 24
N = 24 + 3
N = 27
married, single and divorced are equal sizes
so n = N/3
n = 27 / 3
n = 9
a. k = 3
b. N = 27
c. n = 9
The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. The manufacturer wants to be certain that the mean battery life exceeds 25 hours in accelerated lifetime testing.
Construct a 90%, two sided confidence interval on mean life in the accelerated test.
Answer:
The confidence interval is [tex]25.16 < \mu < 26.85[/tex]
Step-by-step explanation:
From the question we are given a data set
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.
The mean of the this sample data is
[tex]\= x = \frac{\sum x_i}{n}[/tex]
where is the sample size with values n = 10
[tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]
[tex]\= x = 26[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]
substituting values
[tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]
[tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]
[tex]\sigma = 1.625[/tex]
The confidence level is given as 90% hence the level of significance is calculated as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha =10[/tex]%
[tex]\alpha = 0.10[/tex]
Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining the critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering two tails of the area under the normal curve
The margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]
[tex]MOE = 0.845[/tex]
The 90%, two sided confidence interval is mathematically evaluated as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
[tex]26 - 0.845 < \mu < 26 + 0.845[/tex]
[tex]25.16 < \mu < 26.85[/tex]
Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours
Which ordered pair is a solution of this equation 6x-y=-4 . -2,0 -1,-2 -2,-1 0, -2
Answer:
(-1,-2)
Step-by-step explanation:
[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]
so the only one is (-1,-2)
The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population in 2010 was 12 million. a. Find an exponential model n(t)= no e^rt for the population t years after 2010. b. Estimate the fish population in the year 2015. c. After how many years will the fish population reach 14 million? d. Sketch a graph of the fish population.
Answer:
(a) n(t) = P(0)*e^(0.010939940t)
(b) 12,674,681 (nearest unit)
(c) 14 years (nearest year)
Step-by-step explanation:
rate = 1.1% / year = 1.011
(a)
P(0) = 12,000,000 = population in 2010
In compound interest format, after t years
P(t) = P(0)* (1.011)^t
Given format = P(0)* e^(rt)
therefore
e^(rt) = 1.011^t use law of exponents
(e^r)^t = 1.011^t
e^r = 1.011
r = log_e(1.011) = 0.010939940 (to 9 decimal places)
required formula is
n(t) = P(0)*e^(0.010939940t)
(b)
in 2015,
P(0)=12000000, n = 5 (years after 2010)
n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)
(c)
to reach 14 million, we equate
n(t) = 14,000,000
12,000,000 *e^(0.010939940*t) = 14,000,000
e^(0.010939940*t) = 14000000/12000000 = 7/6
take log on both sides
0.010939940*t = log(7/6)
t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.
See graph attached. Y-axis is in millions, x-axis is in years.
a) [tex]n(t) = 12e^{0.011t}[/tex]
b) The estimate for the population in 2015 is of 12.7 million.
c) The fish population will reach 14 million after 14 years.
d) The sketch is given at the end of this answer.
------------------------------------
Item a:
The exponential model is:
[tex]n(t) = n(0)e^{rt}[/tex]
In which:
n(0) is the population is 2010.r is the growth rate, as a decimal.Population of 12 million, thus [tex]n(0) = 12[/tex]Growth rate of 1.1%, thus [tex]r = 0.011[/tex].
Thus, the model is:
[tex]n(t) = 12e^{0.011t}[/tex]
Item b:
2015 is 2015 - 2010 = 5 years after 2010, thus this is n(5).
[tex]n(5) = 12e^{0.011(5)} = 12.7[/tex]
The estimate for the population in 2015 is of 12.7 million.
Item c:
This is t for which n(t) = 14, thus:
[tex]n(t) = 12e^{0.011t}[/tex]
[tex]14 = 12e^{0.011t}[/tex]
[tex]e^{0.011t} = \frac{14}{12}[/tex]
[tex]\ln{e^{0.011t}} = \ln{\frac{14}{12}}[/tex]
[tex]0.011t = \ln{\frac{14}{12}}[/tex]
[tex]t = \frac{\ln{\frac{14}{12}}}{0.011}[/tex]
[tex]t = 14[/tex]
The fish population will reach 14 million after 14 years.
Item d:
At the end of this answer, the sketch is given.
A similar problem is given at https://brainly.com/question/23416643
I bought a tv for 532.50 including the 6%sales tax. What was the original price of the tv without the sales tax?
Step-by-step explanation:
Hey, there !!!
According to your question,
total c.p = 532.50
tax rate =6%
let original price be x.
now,
total c.p = x + tax rate of x.
or, 532.50= x+ (6/100) × x
or, 532.50 = 106x/100
or, 53200 = 106x
or, x= 53200/106
Therefore, the original price was 501.88.
Hope it helps...
Please can anyone tell me how too solve this question, thank you.
Suppose that you have just been hired at an annual salary of $85,000 and expect to receive an annual raise of 6% per year. What
will be the total amount of money you will have earned after 8 years?
Answer:
$125,800
Step-by-step explanation:
Amount (A) = ?
Principal (P) = $85,000
Rate (r) = 6%
Time (t) = 8 years
Simple interest formula;
A = P(1 + rt)
A = $85,000(1 + 0.48)
A = $125,800
the angle between two plane is 3x+2y-z=7 and x-4y+2z=0 is
Answer: 114°
Step-by-step explanation:
[tex]\overrightarrow{u}=\bigg<3, 2, -1\bigg>\\\\\overrightarrow{v}=\bigg<1,-4,2\bigg>\\\\\\u\cdot v=3(1)+2(-4)+\ -1(2)\quad =-7\\\\|u|=\sqrt{3^2+2^2+(-1)^2}\quad =\sqrt{14}\\\\|v|=\sqrt{1^2+(-4)^2+2^2}\quad =\sqrt{21}\\\\\\\cos\theta=\dfrac{u\cdot v}{|u|\ |v|}\\\\\\\cos\theta=\dfrac{-7}{\sqrt{14}\cdot \sqrt{21}}\\\\\\\cos\theta=\dfrac{-1}{\sqrt6}\\\\\\\large\boxed{\theta=114^o}[/tex]
if f(x)=3x+7 what is f(2)
Answer:
13
Step-by-step explanation:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rob is an engineer. The mean salary for engineers with less than 5 years’ experience is $60,000 with a standard deviation of $5,000. Rachel works in the retail industry, where the mean salary for executives with less than 5 years’ experience is $35,000 with a standard deviation of $8,000.
Compute the z values for both Rob and Rachel and comment on your findings.
Answer:
z-value of rachel = 1.875
z-value of rob = -2
z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.
Step-by-step explanation:
Let's denote the salary of Rob and Rachel per year by X. So, X = $50,000
We are told that;
For Rachel's industry;
Mean salary;μ1 = $35,000
Standard deviation;σ1 = $8,000
For Rob's industry;
Mean salary;μ2 = $60,000
Standard deviation;σ2 = $5,000
Formula for z - value is;
z = (X - μ)/σ
Thus;
z-value for rob is;
z2 = (X - μ2)/σ2
z2 = (50000 - 60000)/5000
z2 = -2
z-value for rachel is;
z1 = (X - μ1)/σ1
z1 = (50000 - 35000)/8000
z1 = 1.875
z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.
Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $10$ steps, how many different points could Franklin end up at?
Answer: Franklin could end at 4 different points.
Step-by-step explanation:
Given: Franklin the fly starts at the point (0,0) in the coordinate plane.
At each point, Franklin takes a step to the right, left, up, or down.
i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]
If he moves 10 steps, then the number of different points Franklin could end up at = choices of directions
= 4
Hence, Franklin could end at 4 different points.
Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters. H0: μ=174; Ha: μ>174 α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
Answer:
3.87
Step-by-step explanation:
The computation is shown below:
Data provided in the question
mean distance = [tex]\bar x[/tex] = 188 meters
Standard deviaton = [tex]\sigma = 14[/tex]
Hits drivers = 15
The distance = 174 meters
H_0: μ≤174;
H_a: μ>174
Based on the above information, the test statistic z-score is
[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]
= 3.87
Hence, the test statistic is 3.87
Note:
We take the μ≤174 instead of μ=174;
Is the given triangle scalene, isosceles, or equilateral? The Vertices are T(1,1), V(4,0), S(3,5)
Answer: It is a scalene triangle.
Step-by-step explanation:
It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.
Solve for w in terms of t
3w-8=t
Please explain steps
Answer:
[tex]w=\frac{t+8}{3}[/tex]
Step-by-step explanation:
[tex]3w - 8 = t[/tex]
Add 8 on both sides.
[tex]3w - 8 + 8 = t + 8[/tex]
[tex]3w = t + 8[/tex]
Divide both sides by 3.
[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]
[tex]w=\frac{t+8}{3}[/tex]
The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an equation:
3w - 8 = t
To solve for w in terms of t
Make the subject as w
In the equation:
3w - 8 = t
Add 8 on both sides:
3w - 8 + 8 = t + 8
3w = t + 8
Divide by 3 on both sides:
3w/3 = (t + 8)/3
w = (t + 8)/3
The equation represents a function of w in terms of t
As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below. -2(bx-5) = 16 the value of x in terms of b is. The value of x when b is 3 is.
The value of x in terms of b is x = [tex]\frac{-3}{b}[/tex]. Therefore the value of x when b = 3 is x = [tex]\frac{-3}{3}[/tex] = -1.
We can find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
- 10
-2bx = 6
÷ -2
bx = -3
÷ b
x = -3/b, which is the answer to the first part.
To get the second answer, we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
I hope this helps!
The value of x in terms of b is x = -3/b. Therefore, the value of x when b = 3 is x = -1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We need to find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
-2bx = 6
bx = -3
x = -3/b,
Now we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
The value of x in terms of b is x = -3/b.
Therefore, the value of x when b = 3 is x = -1.
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How many solutions does the system have? You can use the interactive graph below to find the answer. 4x-2y=8 2x+y=2 4x−2y=8 2x+y=2 A.One solution B.two solutions. C.Many solutions
Answer:
one solution
Step-by-step explanation:
The given system of equations has one solution.
Hence option A is correct.
The given system is
4x-2y=8
2x+y=2
Since we know that,
For system
a₁x + b₁ y = c₁
a₂x + b₂y = c₂
If
a₁/a₂ = b₁/b₂ = c₁/c₂ then it has an infinite solution
a₁/a₂ ≠ b₁/b₂ then unique solution
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then no solution
Here we have
a₁ = 4, b₁ = -2 and c₁ = 8
a₂ = 2, b₂ = 1 and c₂ = 2
Now since
a₁/a₂ ≠ b₁/b₂ ⇒ 4/2 ≠ -2/1
⇒ 2 ≠ -2
Hence, the given system has a unique solution.
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Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x