enter an equation in slope-intercept form that describes a line that contains the points (4,1) and (4,2)
Simplify 5 − (−1).
a. 6
b. −6
c. 4
d. −4
Answer: it is a
Step-by-step explanation: :) :v :B
Two less than twice a number is the same as four times the number
Final answer:
The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.
Explanation:
The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.
Subtract 2n from both sides: -2 = 2n.
Divide both sides by 2 to find the value of n: n = -1.
In conclusion, the number that satisfies the condition given is -1.
A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
Find the missing length.
The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common ratio is one over five find the sum of the infinite series that will be the upper limit of this population. 87,105,425, or this series is divergent
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 6
A =
37.68 sq. units
113.04 sq. units
226.08 sq. units
Answer: 113.04 sq. units
Divide 35b^5 +20ab^3 +20a^2b^2 by 5b^2
The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
Redo, Answers please?
HELP if f(x)=-14x-2, then f^-1(x)=?
HOW DO YOU MOVE A VARIABLE FROM ONE SIDE OF AN EQUATION TO ANOTHER? I need to know as I'm reviewing module 7 algebra and i want to know please
When 332 college students are randomly selected and surveyed, it is found that 113 own a car. find a 99% confidence interval for the true proportion of all college students who own a car?
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2
Final answer:
Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.
Explanation:
The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.
By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work
4n-3<12 solve and please don't give me the answer just the equation
Match the perfect square trinomials with their factors 4a2 + 4a + 1 (2 + a)(2 + a) 4a2 − 4a + 1 (2a + 1)(2a + 1) 4 − 4a + a2 (2a − 1)(2a − 1) 4 − 4a − a2 (2 − a)(2 − a) 4 + 4a + a2
The circle given by x^2+y^2-4x-10=0 can be written in standard form like this: (x-h)^2+y^2=14. What is the value of h in this equation??
Answer: H=2
Step-by-step explanation:
we just need to complete the square for the x terms
gropu x terms
x^2-4x
take 1/2 of linear coefient and square it
-4/2=-2, (-2)^2=4
x^2-4x+4
factor
(x-2)^2
h=2
The value of h is 2.
Completing the square for the x terms by grouping x terms
x^2-4x
Taking 1/2 of linear coefficient and squaring it.
-4/2=-2, (-2)^2=4
x^2-4x+4
Factorizing the equation.
(x-2)^2
h=2.
What is an equation?An equation is a mathematical statement this is made of two expressions related with the aid of an identical sign. As instance, 3x – 5 = 16 is an equation. To fix this equation, we get the value of the variable x as x = 7.
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Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3
What is the circumference of this circle, in millimeters? use 22/7 for pi
r = 49
Answer: circumference = 308mm
Step-by-step explanation: the formula for the circumference of a circle is given by
C=2πr
Given that r=49mm
Pi=22/4
C=2*22/7*49
C=44*7=308mm
In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.
Smallville’s town council has records of the town’s budget over a 10-year period. Create a best fit and model for the data. What does the model predict the town’s budget will be in the year 2011?
A)$391,000
B)$417,000
C)$404,000
D)$411,000
My answer is D) $411,000 in 2011.
There is an average increase of 4% from the previous budget to arrive at the amount of the current year.
2009 budget $381,700
381,700 * (1.04)² = 381,700 * 1.0816 = 412,846.72 only Choice D. is nearest to the amount
2000 budget $265,100
265,100 * (1.04)¹¹ = 265,100 * 1.540 = 408,254 only Choice D. is nearest to the amount.
A given line has the equation 10x + 2y = −2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
Subtract [tex]10x[/tex] both sides
[tex]2y=-10x-2[/tex]
Divide by [tex]2[/tex] both sides
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
Step 2
Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]
we know that
If two lines are parallel. then their slope are equal
In this problem we have
[tex]m=-5[/tex]
[tex](0, 12)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]12=-5*0+b[/tex]
[tex]b=12[/tex]
the equation of the line is
[tex]y=-5x+12[/tex]
therefore
the answer is
[tex]y=-5x+12[/tex]
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -(x-4)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
How many cans of paint are needed to cover an area of 2,200 square units if one can of paint covers an area of 400 square units? 4 5 6 8?
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is
a-36
b-18
c-288
d-5
A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.
For this case, we use
the cylindrical coordinates:
x² + y² = r²
dV = r dz dr dθ
The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞
θ = 0 to 2π
Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ
V = ∫ [0 to 2π] 1/18 dθ
V = θ/18 |[0 to 2π]
V = π/9
The volume of the volcano is an illustration of definite integral
The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
The graphs are given as:
[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]
The cylinder is:
[tex]\mathbf{x + y =1}[/tex]
For cylindrical coordinates, we have:
[tex]\mathbf{r^2 =x^2 + y^2}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]
[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]
Where:
[tex]\mathbf{r = 1 \to \infty}[/tex]
[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]
So, the integral is:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]
Cancel out r
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]
Integrate
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]
Expand
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]
Integrate
[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]
Expand
[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]
[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]
Cancel out 2
[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]
Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
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What percent of 210 is 70?
Constantine picks two letters at random from the word constantinople with replacement. what is the probability that both letters picked are consonants?
please help on b (left of c) and c !!!
rewrite each of the following expressions so that your answer has no negative or fractional exponents