Answer: (0,1/3)
Step-by-step explanation:
Answer:
The y-intercept of the function f(x) = -2/9x + 1/3 is 1/3.
Step-by-step explanation:
Given, function is
f(x) = -2/9x + 1/3.
The y-intercept is the point where the graph intersects the y-axis.
The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.
We know that the x-coordinate of any point on the y-axis is 0.
So the x-coordinate of a y-intercept is 0.
To find the y - intercept set x = 0.
f(0) = (2/9 . 0) + 1/3
f(0) = 0 + 1/3
f(0) = 1/3.
Find the sum of the arithmetic series given a1=45, an=85, and n=. 5
The sum of the arithmetic series is 325
How to determine the sum?The given parameters are
a1 = 45
an = 85
n = 5
The formula for the sum of arithmetic series is:
[tex]S_n = \frac n2 * (a_1 + a_n)[/tex]
Substitute the values of a1, an and n in the above equation
[tex]S_5 = \frac 52 * (45 + 85)[/tex]
Add 45 and 85
[tex]S_5 = \frac 52 * 130[/tex]
Divide 130 by 2
[tex]S_5 = 5 * 65[/tex]
Multiply
[tex]S_5 = 325[/tex]
Hence, the sum of the arithmetic series is 325
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The equations of four lines are given. Identify which lines are parallel.
Line 1: y=−5x−5
Line 2: x+12y=−4
Line 3: y=−2x+4
Line 4: y+8=−15(x−9)
None of the equation of the line is parallel because there slope are not equal.
How to find lines that are parallel?Parallel line have the same slope.
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence,
y = −5x − 5 , slope = -5
x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12
y = −2x + 4: slope = -2
y + 8 = -15x + 135; y = -15x + 127, slope = -15
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What is the equation,in point-slope from ,of the line that is perpendicular to given line and passes through the point (-4,-3)?
The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
How to determine the equation of the line?The complete question is added as an attachment
The points on the line are given as:
(-1, 1) and (0, -3)
Start by calculating the slope of the line using
m = (y2 - y1)/(x2 - x1)
The slope of the perpendicular line is
m2 = -(x2 - x1)/(y2 - y1)
So, we have:
m2 = -(0 + 1)/(-3 - 1)
This gives:
m2 = 1/4
The equation of the line is then calculated as
y - y1 = m(x - x1)
This gives
y + 3 = 1/4(x + 4)
Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
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help me please
What is the midpoint of the horizontal line segment graphed below?
A. (4,3)
B. (8,6)
C. (8,3)
D. (4, 6)
-10
10
(-2,3)
$10
(10, 3)
10
Answer: A
Step-by-step explanation:
Find the difference: -2-6
Let sets A and B be defined as follows.
A is the set of integers greater than -14 and less than -5.
B={h,i,s,x,z}
a) find the cardinalities of A and B
n(A)=
n(B)=
b) select true or false
-12 ∈ A
-21 ∈ A
s ∈ B
m ∉ B
A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.
-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.
Cardinalities of A and B
It is given that,
A = {n : -14 < n < -5, n ∈ Z} ............ (1)
B = {h, i, s, x, z} ......... (2)
Thus, from (1),
A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)
Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,
n(A) = 8
n(B) =5
Reason Behind True or False
As seen from (3), set A contains the element -12. Thus, -12 ∈ A is True.Again from (3), we can see that -12 does not belong to the set A. Thus, -21 ∈ A is FalseFrom (2), s is present in set B. Hence, s ∈ B is TrueSimilarly, m is not present in set B. Therefore, m ∉ B is TrueLearn more about cardinalities here:
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Ivanhoe Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $11.85 million. This investment will consist of $2.15 million for land and $9.70 million for trucks and other equipment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5.25 million, which is $2.00 million above book value. The farm is expected to produce revenue of $2.10 million each year, and annual cash flow from operations equals $1.90 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment. (Do not round factor values. Round final answer to 2 decimal places, e.g. 15.25.)
The NPV of this investment if the discount rate is 10 percent is: 1.58%.
Net present value (NPV)Year Cash flow PVIF 10% Present value
0 ($11.86) 1.000 ($11.86)
1 1.90 0.909 $1.73
2 1.90 0.826 $1.57
3 1.90 0.751 $1.43
4 1.90 0.683 $1.30
5 1.90 0.621 $1.18
6 1.90 0.564 $1.07
7 1.90 0.513 $0.98
8 1.90 0.467 $0.89
9 1.90 0.424 $0.81
10 6.45 0.386 $2.49
NPV $1.58
1.9+5.25-2×35%=6.45
Hence, the NPV is $1.58.
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Jed wants to prove that his test scores are greatly improving. He makes the graph shown here.
Explain why someone may think this graph is misleading.
Someone may think this graph is misleading because it does not start from the origin
How to determine the reason?As a general rule, graphs are to begin from the origin
The origin of a graph is
(x, y) = (0, 0)
From the given graph, the origin is
(x, y) = (0, 60)
This means that someone may think this graph is misleading because it does not start from the origin
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the set of all months that contain less than 31 years
The set of all months that contains less than 31 days is; {February, April, June, September, November}.
What is the set of all months that contain less than 31 days?It follows from the task content that the set whose elements are to be determined is characterized by containing less than 31 days.
On this note, it follows that the elements of the set are; February (28/29 days), April (30 days), September (30 days), June (30 days) and November (30 days).
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Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
3x4
Name? [?]
Degree? [ ]
Answer:
monopoly, order 1
Step-by-step explanation:
because the x has just power of one that is why is monopoly and in order 1
Solve for x, 3x+21=8x*54
Answer:
Exact form: 7/143
Decimal form: /0.048951
Answer:
[tex]x=\frac{7}{143}[/tex]
Step-by-step explanation:
Simplify the right side of the equation. [tex]3x+21=432x[/tex]. Subtract 21 from both sides of the equation. [tex]3x=432x-21[/tex]. Subtract 432x from both sides of the equation, [tex]-429x=-21[/tex]. The negative signs cancel out to get [tex]429x=21[/tex]. Divide both sides but 429 to get [tex]x=\frac{21}{429}[/tex]. Reduce to get [tex]x=\frac{7}{143}[/tex].
Simplify the expression completely if possible.
x^{3}-8x^{2}}{x^2-64}
The simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex]
Factor the numerator
[tex]\frac{x^{2}(x-8)}{x^2-64}[/tex]
Express the denominator as a difference of two squares
[tex]\frac{x^{2}(x-8)}{(x-8)(x + 8)}[/tex]
Cancel out the common factor
[tex]\frac{x^2}{x + 8}[/tex]
Hence, the simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]
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factor 18x^(2)+39x-15
Answer:
[tex]3(2x + 5)(3x - 1)[/tex]
Step-by-step explanation:
Hello!
We can first factor out the greatest common factor between the coefficients: 3.
[tex]f(x) = 18x^2 + 39x - 15[/tex][tex]f(x) = 3(6x^2 + 13x - 5)[/tex]Now, let's work with what we have inside the brackets.
Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]
Given our equation: [tex]6x^2 + 13x - 5[/tex]
a = 6b = 13c = -5We need to find two numbers that add up to b (13) and multiply to ac (-30).
The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.
Factor by Grouping[tex]6x^2 + 13x - 5[/tex][tex]6x^2 -2x + 15x - 5[/tex][tex]2x(3x- 1) +5(3x - 1)[/tex][tex](2x +5)(3x - 1)[/tex]
Now, we simply add the other factor, 3, to the final factored form.
Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]
8 to the second power to the -4 power is equivalent to
Answer:
1.138789 is equivalent to 8 to the second power to the -4 power.
Hope this helps :)
Pls help me i'm stuck
Answer: [tex]m\angle BAM=30^{\circ}[/tex]
Step-by-step explanation:
[tex]AD=x\sqrt{3}[/tex] (Pythagorean theorem)
[tex]m\angle ACD=60^{\circ}[/tex] (30-60-90 triangle)
[tex]m\angle MCA=30^{\circ}[/tex] (angle subtraction)
[tex]m\angle MAC=30^{\circ}[/tex] (base angles theorem)
[tex]m\angle CAD=30^{\circ}[/tex] (30-60-90 triangle)
[tex]m\angle BAM=30^{\circ}[/tex] (angle subtraction)
Measure the length of this segment in inches.
Answer:
3 [tex]\frac{3}{4}[/tex] inches
Answer: I'm pretty sure it's 3 5/8, it's the S that's blocking the view but it gotta be 3 5/8.
Step-by-step explanation: PLS MAKE ME BRAINLIST
Find the x and y intercepts on the graph of the line, if they exist.
3x + 4y = 24
The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.
What are the intercepts of a line?The standard equation of a line is ax + by + c = 0.
Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.
In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.
Calculation:It is given that,
The equation of the given line is 3x + 4y = 24
Rewriting the given equation into the general form,
3x + 4y - 24 =0
On comparing with ax + by + c = 0,
a = 3, b = 4 and c = -24
So,
The x-intercept of the line (-c/a) = -(-24)/3 = 8 and
The y-intercept of the line (-c/b) = -(-24)/4 = 6
Therefore, the required x and y intercepts are 8 and 6 respectively.
(The graph showing the intercepts of the given line is shown below)
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25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure
based on the number of mice that took part in the experiment, the total number of mice that had at least one effect is 20 mice.
how many mice had a health effect?15 mice had at least 1 tumor while 4 mice had both a tumor and respiratory failure.
the number of mice with just a tumor is:
= 15 - 4
= 11 mice
the number of mice with respiratory failure alone is:
= 9 - 4
= 5 mice
the mice that had at least one symptom is:
= 11 + 5 + 4 mice with both
= 20 mice
question is:
what are the number of mice with at least one effect?
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Let f(x) = √3x and g(x) = x + 3. What's the smallest number that is in the domain of
fºg?
Answer:
-3
Step-by-step explanation:
[tex]f\left( x\right) =\sqrt{3x} \ \ \text{and} \ \ g\left( x\right) =x+3[/tex]
it’s clear that :
f is defined if and only if x ≥ 0
Therefore ,
fºg is defined if and only if x + 3 ≥ 0
x + 3 ≥ 0
⇔ x ≥ -3
Then ,the smallest number that is in the domain of fºg is -3
29) Selecting a blue marble, a white marble, and then a red marble.
O a.) 4/19
Ob.) 4/91
Oc.) 3/19
Od.) 7/91
Answer:
4/91
Step-by-step explanation:
There are a total of 15 marbles. In the first selection there are 15 marbles and 6 are blue. That would be 6/15.
Since we are not replacing marbles, we now have 14 marbles and we want to select one of the 5 white marbles. That would be 5/14.
Lastly we now only have 13 marbles and of those we want to select one of the 4 red ones. That would be 4/13.
Now we take these 3 fractions and multiply them together.
6/15(5/14)(4/13). I am going to try to make this a little easier and see if I can find any factors that any top number shares with any bottom number.
I see 5 on the top shares a common factor with 15 on the bottom. I will divide these numbers by 3, so now I have
6/3(1/14)(4/14). I think that I can do better than that. I see that 6 on the top and 3 on the bottom share a common factor of 3. I will divide both of these numbers by 3. Which will give me:
2/1(1/14)(4/13) I see a 4 on top and a 14 on the bottom. Those are both divisible by 2 so, I will divided them both by 2 and that leaves me with
2/1(1/7)(2/13) That is a lot easier, now I will just multiple the top numbers and multiply the bottom numbers to get
4/91
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Proving a uadrilateral is a Parallelogram
Assignment Active
Determining Side Lengths in a Parallelogram
In quadrilateral ABCD, AD 1, BC.
3x+7
D
A
B
5x-9
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
O 8 units
O 16 units
O 31 units
O 62 units
Answer:
31 units
Step-by-step explanation:
If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.
Sides AD and BC are given as parallel.
If they are also congruent, then quadrilateral ABCD is a parallelogram.
3x + 7 = 5x - 9
-2x = -16
x = 8
AD = 3x + 7
AD = 3(8) + 7
AD = 31
Answer: 31 units
If a person rows to his favorite fishing spot 21 miles downstream in the same amount of time that he rows 7 miles
upstream and if the current is 7 mph, find how long it takes him to cover 28 miles.
28 miles upstream requires 28/7 = 4 hours.
28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.
How long does it take him to cover 28 miles?Apply the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
21 = t*(r+7) = rt+ 7t
7 = t *(r-7) = rt - 7t
28 = 2rt
14 = rt
21 = rt + 7t
21 = 14 + 7t
7 = 7t
t=1
21 = (r+7)*1 = r+7
r = 14
The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.
28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.
28 miles upstream requires 28/7 = 4 hours.
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Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 35
The diameter of the circle is 11.8 units
How to determine the diameter of the circle?The circle equation is given as:
(x - 2)^2 + (y + 6)^2 = 35
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Diameter = 2r
By comparing both equations, we have
r^2 = 35
Take the square root of both sides
r = 5.9
Multiply by 2
2r = 11.8
Hence, the diameter of the circle is 11.8 units
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Calculate a and b if
[tex] \sqrt{ \frac{ {7}^{2014} - {7}^{2012} }{12} } = a( {7}^{b} )[/tex]
and a is not a multiple of 7.
Notice that
[tex]7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}[/tex]
[tex]12=2^2\times3[/tex], so
[tex]\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}[/tex]
Then taking the positive square root gives
[tex]\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}[/tex]
so [tex]\boxed{a=2}[/tex] and [tex]\boxed{b=1006}[/tex].
binary add:
(e) 10110₂ +1010₂ = (?)
Answer:
278,861,394
Step-by-step explanation:
put in the calculator e but then just square the numbers add it and there is your answer
Census Bureau data shows that the mean household income in the area served by a shopping mall is $64,500 per year with the standard deviation of $8,000. A market research gathers a random sample of 100 shoppers at the mall to find out whether the mean household income of mall shoppers of $61,000 is different than the general population.
Q: What is the null hypothesis ?
Considering the situation described, the null hypothesis is given as follows:
[tex]H_0: \mu = 64,000[/tex].
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is the same as in the Census, of $64,000, hence:
[tex]H_0: \mu = 64,000[/tex].
At the alternative hypothesis, it is tested if the mean is different from the Census, hence:
[tex]H_1: \mu \neq 64,000[/tex].
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Graph the function f(x) = 2√x +3.
The graph is shown in the attached image.
Sets J and F are defined as follows.
J= {c,e,f}
F={g,k,j}
Answer each part below. Write your answer in roster form or as 0.
Find the intersection of J and F.
FInd the union of J and F.
The value of J ∩ F = ∅
The value of J ∪ F = {c, e, f, g, k, j}
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sets J and F are defined as follows;
J = {c, e, f}
F = {g, k, j}
Now,
Since, Sets J and F are defined as follows;
J = {c, e, f}
F = {g, k, j}
Hence, The value of J ∩ F = {c, e, f} ∩ {g, k, j}
= ∅
The value of J ∪ F = {c, e, f} ∪ {g, k, j}
= {c, e, f, g, k, j}
Thus, The value of J ∩ F = ∅
The value of J ∪ F = {c, e, f, g, k, j}
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I cant figure this one out pls help
The value of x from the given expression is -2
Slope of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the following parameters
m = 1
(x1, y1) = (0, 2)
(x2, y2) = (x, 0)
Substitute
1 = x-0/0-2
1 = x/-2
x = -2
Hence the value of x from the given expression is -2
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solve for unknown in 2x^3+6x^2-20x=0
The solution of x is x = 0, x =2 and x = -5
How to solve for the unknown?The equation is given as:
2x^3+6x^2-20x=0
Factor out x
x(2x^2+6x-20)=0
Split the equation
x = 0 or 2x^2+6x - 20=0
Solve for x in 2x^2+6x - 20=0
Expand the equation
2x^2 + 10x - 4x - 20 = 0
Factorize the equation
(2x - 4)(x +5) = 0
Split the equation
2x - 4 = 0 and x + 5 = 0
Solve for x
x =2 and x = -5
Hence, the solution of x is x = 0, x =2 and x = -5
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