for the first one the answer are
add 5 to both sides
subtract 5 from both sides
add 1/2x to both sides
subtract 1/2 from both sides
the second one is
multiply both sides by 1/5
dived both sides by 1/5
multiply both sides by 6/7
dived both sides by 6/7
Answers
Answer:
1. add 1/2x to both sides
a. you want to combine the like terms. in this case, it is the x variable.
you are left with 7/6x = 5
2. multiply by 6/7
a. the reciprocal of 7/6 will cancel out the values
Related Questions
Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.
Answers
Answer:
Solution : Third Option
Step-by-step explanation:
The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.
[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]
Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.
Therefore, the third option is a solution to the system.
32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:
A. x = 0, −5, 1.7i, −1.7i
B. x = 0,−5, 1.7i
C. x = −5, 1.7i, −1.7i
D. x = 0,−3, −5
Answers
Answer:
x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Step-by-step explanation:
Solve for x:
x^3 + 5 x^2 + 3 x + 15 = 0
The left hand side factors into a product with two terms:
(x + 5) (x^2 + 3) = 0
Split into two equations:
x + 5 = 0 or x^2 + 3 = 0
Subtract 5 from both sides:
x = -5 or x^2 + 3 = 0
x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:
x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2
sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):
x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2
sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):
x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2
(2 i sqrt(3))/2 = i sqrt(3):
x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2
(2 (-i sqrt(3)))/2 = -i sqrt(3):
Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Answer:
C. x = −5, 1.7i, −1.7i
Step-by-step explanation:
Quick answer:
C. x = −5, 1.7i, −1.7i
explanation:
C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.
Complete answer:
All odd degree polynomials have at least one real root.
By the real roots theorem, we know that
if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).
Values of [tex]\pm[/tex]p/q are
On trial and error, using the factor theorem, we see that
f(-5) = 0, therefore -5 is a real root. By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i
The answer is {-5, +/- sqrt(5) i}, or again,
C. x = −5, 1.7i, −1.7i
Make Q the subject of the formula A = Q2 - 2a.
Answers
Answer:
[tex]\huge\boxed{Q = \sqrt{A+2a}}[/tex]
Step-by-step explanation:
[tex]A = Q^2 -2a[/tex]
Adding 2a to both sides
[tex]Q^2 = A+2a[/tex]
Taking sqrt on both sides
[tex]Q = \sqrt{A+2a}[/tex]
What is the x-intercept?
Answers
∠3 and ∠6 can be classified as:
Answers
Answer:
Alternate Interior Angles
Step-by-step explanation:
Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.
Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.
Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.
Therefore, we are left with Alternate Interior Angles.
Answer:
angle 3 and angle 6 are
1) Alternate Angles
2) Interior Angles
Step-by-step explanation:
(see attached for reference)
Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0
Answers
Answer:
x=0 or x=2 or x=−4 or x= (7)(2)
Step-by-step explanation:
Use the gradient to find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye^z, P(2, 4, 0), Q(0, 0, 0)
Answers
Answer: Find answer in the attached files
Step-by-step explanation:
Complete each ordered pair so that it is a solution of the given linear equation.
x - 4y = 4; (_,3), (4,_)
Answers
Answer: (16,3) and (4,0)
Step-by-step explanation:
Using the equation x-4y=4 is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.
x-4(3)=4 multiply the left side
x - 12 = 4 add 12 to both sides
x= 16
You will now have the coordinates (16,3)
In the second pair it gives the x coordinate which is 4 but we need to solve for y.
4 - 4y=4 subtract 4 from both sides
-4 -4
-4y = 0 Divide both sides by 4
y = 0
The ordered pair will be (4,0)
what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answers
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, start text, space, c, m, end text. How far did Chubby run? Round your answer to the nearest \text{cm}cmstart text, c, m, end text.
Answers
Answer:
63 cm
Step-by-step explanation:
If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.
The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.
We can know substitute inside the formula:
[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]
62.8 rounded to the nearest cm is 63.
Hope this helped!
Answer:
6280
Step-by-step explanation:
You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.
Answers
Answer:
20 by 20 by 20
Step-by-step explanation:
Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz ... 1
Given the volume V = xyz = 8000 ... 2
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.
The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.
The calculation for total surface area:Let the total surface of the rectangular box be expressed as:
S = 2xy + 2yz + 2xz
where,
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz .................(1)
Given:
Volume V = xyz = 8000 .............(2)
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since, Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20*20*20.
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wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answers
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Which expression is equivaleny to 0.7 + p + 0.86p?
A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p
Answers
Answer:
None of the above.
1.86p + 0.7
Step-by-step explanation:
Step 1: Write expression
0.7 + p + 0.86p
Step 2: Combine like terms
0.7 + 1.86p
None of those answer choices are correct unless you wrote the problem incorrectly.
Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.
Answers
Jay is copying an angle. His work so far is shown below. Explain the importance of his next step, which is placing the point of the compass on L, opening the compass to N, and drawing an arc.
A. This ensures that when he draws another arc for angle Y, that it will be the right distance from point Z. <-- MY ANSWER
B. This arc is to make sure that both L and N are equidistant from M.
C. This arc makes sure that the distance from L to N is the same as the distance from Y to Z.
D. This way there will be two arcs drawn on both angles when he is done.
Answers
Answer:
your answer is correct.
Step-by-step explanation:
For the purpose here, we'll call the missing point on the arc through Z point X.
Essentially, you want to make ΔXYZ ≅ ΔLMN by SSS. The construction so far ensures LM ≅ MN ≅ XY ≅ YZ. By copying the length LN to XZ, you ensure the congruence of the remaining sides of the triangles.
Then ∠XYZ ≅ ∠LMN because corresponding parts of congruent triangles are congruent.
In short, XZ needs to be the same distance as LN.
Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05
Answers
Answer:
Calculated χ² = 13.425
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
Step-by-step explanation:
Color Blue Orange Green Red Yellow Brown
Frequency 30 48 55 66 70 131
Expected 40 40 40 80 80 120
H0: The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown
Ha: The color distribution is not equal to the distribution stated in the null hypothesis.
Calculate chi square
χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120
χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425
The critical region for χ² for 5 degrees of freedom with ∝= 0.05 is
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
|5x|=3 please help me
Answers
Explanation:
|5x| = 3
5x = 3
x = 3/5
5x = -3
x = -3/5
a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero
Answers
Answer:
-11/13
Step-by-step explanation:
The equation of the line through these points can be written using the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-3))/(-9-4)/(x -4) -3
y = (-7/13)x +28/13 -3
For x=0, the value of y is ...
y = 28/13 -39/13 = -11/13
The output for an input of 0 is -11/13.
The equation of a circle centered at the origin with a radius of unit length is x2 + y2 = 1. This equation changes if the center of the circle is not located at the origin or the radius is not of unit length.
Answers
Answer:
The equation for a unit radius circle, centered at the origin is:
x^2 + y^2 = 1
Now, if we want to move it horizontally, you can recall to the horizontal translations:
f(x) -----> f(x - a)
Moves the graph to the right by "a" units.
A vertical translation is similar.
Then, if we want a circle centered in the point (a, b) we have:
(x - a)^2 + (y - b)^2 = 1.
Now, if you want to change the radius, we can actually write the unit circle as:
x^2 + y^2 = 1^2
Where if we set x = 0, 1 = y, this is our radius
So if we have:
x^2 + y^2 = R^2
And we set the value of x = 0, then R = y.
So our radius is R.
Then:
"A circle of radius R, centered in the point (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.
Answers
Answer:
x ≈ 4.5
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
Here k = 76 and y = 17 , thus
17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )
17x = 76 ( divide both sides by 17 )
x ≈ 4.5 ( to the nearest tenth )
Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
Answers
Answer:
Margin of Error = z∝/2 * Standard Error
Step-by-step explanation:
The formula for standard error is given by
SE = [tex]\sqrt{\frac{pq}{n} }[/tex]
Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.
Now Margin of Error is given by
ME = z∝/2 * Standard Error
The confidence level is used to estimate the value of alpha.
For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96
What fraction of a ton is a pound?
Answers
Answer:
There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.
Answer:
5/100000 tons
Step-by-step explanation:
Find the sum of the first 12 terms of the sequence 512, 256, 128, …
Answers
Answer: 1023.75 (a)
Step-by-step explanation:
The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.
a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.
Now to calculate the sum, we consider two formula here and select the one that is most appropriate,
(1) a( rⁿ - 1 )/r - 1, when r is greater than 1
(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.
In this question, formula 2 shall be appropriate because r is less than 1.
so,
S₁₂ = 512( 1 - 0.5¹² )/1 - 0.5
512( 1 - 2.44 ₓ 10⁻⁴ )/0.5
= 512( 0,9998 )/0.5
= 511.875/0.5
= 1023.75
The answer is a
A leaf blower was marked up 100% from an original cost of $152. If Eva bought the leaf blower and paid 7% sales tax, how much in total did she pay?
Answers
Answer:
$325.28
Step-by-step explanation:
152+152=304
304x1.07=325.28
Answer:
325.28
Step-by-step explanation:
increase the price by 100 %
152* 100%
152
Add this to the original price
152+152 = 304
Now find the sales tax
304 * 7%
304 * .07
21.28
Add this to the amount of the purchase price
304+21.28
325.28
please answer! I need these points for grade!
Answers
∡NMO = 59°
Step-by-step explanation:if MO bisect =>
=> ∡LMN = 2∡LMO =>
=> 5x - 22 = 2(x + 31)
5x - 22 = 2x + 62
5x - 2x = 62 + 22
3x = 84
x = 28°
∡LMO = ∡NMO => ∡NMO = x + 31
=> ∡NMO = 28 + 31 = 59°
A teacher shares sweets among 8 students so they get 6 each. How many sweets would they each have got if there had been 12 students?
Answers
Answer:
4 sweets
Step-by-step explanation:
we know that there is a total of 48 sweets being handed out, and we can tell that this is an example of inverse proportion:
when one increases the other decreases
So, we multiply 8 * 6 to get 48, and then divide that by 12 to get 4 which is how many each student gets
for some constant k -> xy/z=k
x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please
Answers
Answer:
x = s, y = t, z = -6 -s -t
Step-by-step explanation:
These are dependent equations. For some values s and t, the solution is ...
x = s, y = t, z = -6 -s -t
A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.
Answers
Answer:
[tex]\large \boxed{\$10000.00}[/tex]
Step-by-step explanation:
We can use the formula for continuously compounded interest.
[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]
A random sample of 1003 adult Americans was asked, "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without.
Requried:
a. Obtain a point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
b. Verify that the requirements for constructing a confidence interval about p are satisfied.
c. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
d. Is it possible that a supermajority (more than 60%) of adult Americans believe that television is a luxury they could do without ? Is it likely?
e. Use the results of part (c) to construct a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.
Answers
Answer:
a)0.519
b)requirements for constructing a confidence interval about p are satisfied.
c)0.488, and 0.550
d)yes this is because there is no possibility
that the true proportion is not captured in the confidence interval.
e)
0.450, 0.512
Step-by-step explanation:
a)The point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without can be calculated as
521 of that adult that indicated that televisions are a luxury they could do without/1003 adults surveyed,
p = 521/1003
= 0.519.
b)
np(1-p)=1003×(0.519)×(1-0.519)
=250.39≥10 and the sample size is less than 5% of the population
therefore, requirements for constructing a confidence interval about p are satisfied.
c) we were given 95% confidence,
Then α=(1-0.95)
= 0.05
From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96
confidence interval can the be calculated using the formula below
- p ± Z*√ p (1 – p)/n
=0.519 ± 1.96√0.519×(1 – 0.519)/(1003)
= 0.519 ± 1.96×0.0158
0.519 ± 0.031
= 0.488, and 0.550
d) yes this is because there is no possibility
that the true proportion is not captured in the confidence interval.
e)the sample size can be calculated as
P=x/n
=(1003-521)/1003
=0.481
But we're given 95% confidence interval
Then
α=(1-0.95)=
0.05
From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96
Then convidence interval=
- p ± Z*√ p (1 – p)/n
=0.481 ± 1.96√0.481×(1 – 0.481)/(1003)
0.450, 0.512
Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.
Answers
Answer:
A. The point that splits a line segment into two equal parts.
Step-by-step explanation:
A. The point that splits a line segment into two equal parts.
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.
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