Answer:
1) y = 2/3x - 2
2) y = -1/2x + 3
Step-by-step explanation:
1) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.
y = 2/3x + c
0 = 2/3(3) + c
0 = 2 + c
0 - 2 = c
- 2 = c
Therefore, the slope-intercept form for the first part is y = 2/3x - 2.
2) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.
y = -1/2x + c
1 = -1/2(4) + c
1 = -2 + c
1 + 2 = c
3 = c
Therefore, the slope-intercept form for the second part is y = -1/2x + 3.
Flo has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Flo expect to be her outcome for the solutions of these two graphs?
The point of intersection is (-2,1) and this is the solution of the two graphs and the correct option is A.
What is a System of Equations?The system of equations is the set of equations that have a common solution.
The solution to the graph given is the answer to the Flo's model
The intersection point of the line of the two-equation is the solution to the two equations.
The point of intersection is (-2,1) and so the correct option is A.
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A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 47 hours. How long with it take for the drug to decay to 82% of the original dose?
This is a two-step problem.
The drug will decay to 82% of the initial dosage after 7.18 hours.
Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 47 hours
λ = 0.693 / (47)
λ = 0.01925 /hour
Time is taken for 82% decay:
How do find the decay?Since decay is first-order, we will use the formula:
[tex]t = \frac{2.303}{0.0192} log\frac{100}{82}[/tex]
Final amount = 100*82/100 = 82 mg
Replacing the values in the equation:
t = 2.303/ 0.0192 x 0.06
t = 7.18 hours
Therefore, the drug will decay to 82% of the initial dosage after 7.18 hours.
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Is the function y = –9x^8+3 linear or nonlinear?
Answer:
It is nonlinear
Step-by-step explanation:
Solve 4(5)^x= 500.
help please
Answer:
x=3
Step-by-step explanation:
Isolate x.
[tex]4(5)^x=500[/tex] Divide both sides by four
[tex]5^x=125[/tex] Take [tex]log_{5}[/tex] of both sides. In other words, what power must you raise 5 to in order to get 125? ([tex]5^3=125[/tex])
x=3
Simplify, state all restrictions.
The simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1[/tex]
Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Rewrite the expression as products
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1[/tex]
Express 4x^2 - y^2 as (2x - y)(2x + y)
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{x + y} -1[/tex]
Take the LCM
[tex]\frac{1 - x - y}{x + y}[/tex]
Hence, the simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
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Find the LCM of 10 and 25?
Pleaseeee helppppppp
Answer:
The second choice (-6, -5 2/5, -4 1/5)
Step-by-step explanation:
1) Find the nth term by using the rule given. Foil them out.
A(n) = -6 + 1/5n - 1/5
A(n) = 1/5n - 31/5
2) Find the first term by substituting 1 into n.
a1 = 1/5(1) - 31/5
a1 = -6
3) Find the fourth term by substituting 4 into n.
a4 = 1/5(4) - 31/5
a4 = -27/5 or -5 2/5
4) Find the tenth term by substituting 10 into n.
a10 = 1/5(10) - 31/5
a10 = -21/5 or -4 1/5
Therefore, the second choice (-6, -5 2/5, -4 1/5) is correct.
What is the equation of the line that passes through the point (-5,4)(−5,4) and has a slope of 3/5?
Answer: y = 3/5x + 7
Explanation:What we know:
The final equation will be in the form y=mx+bThe slope (m) is 3/5The slope must go through the point (-5,4)How to solve:
By substituting the point the slope passes through into slope-intercept form, we can calculate the y-intercept (b.) From here, we can use our slope and y-intercept values to set up the final equation.
Process:
Finding the y-intercept
Set up equation y = mx + b
Substitute 4 = 3/5(-5) + b
Simplify 4 = -3 + b
Simplify +3 +3
Solve 7 = b
Creating final equation
Set up equation y = mx + b
Substitute y = (3/5)x + 7
Answer: y = 3/5x + 7Check:
If you graph this equation (a good tool to use is desmos graphing calculator,) then this equation creates a line that has a slope of 3/5 and passes through the point (-5,4)
By what percent will the fraction increase if its numerator decreased by 30% and the denominator decreased by 50%
Answer:
140%
Step-by-step explanation:
So a fraction can be expressed as: [tex]\frac{a}{b}[/tex] and if a number decreases by x%, the new number is (100-x)% the original value. So since the numerator decreases by 30%, it's not 70% the original value, and it's very similar with the denominator, with it only retaining 50% of it's original value. This gives you the formula: [tex]\frac{0.70a}{0.50b}[/tex]. You can rewrite the fraction as: [tex]\frac{1.4 * 0.5 * a}{0.5 * b}[/tex] in doing so it's easy to see that you can cancel out the 0.5 and get: [tex]1.4\frac{a}{b}[/tex]. This means the value is increasing by 1.4 or 140%
Answer:
140%
Step-by-step explanation:
since the numerator decreases by 30%, it isnt 70% the original value, This gives a formula: . You can rewrite the fraction as so, in doing so it's easy to see that you can cancel out the 0.5 and get: . This means the value is increasing by 1.4 or 140%.
Factorise the following:
a) x² + 10x + 16 answer
Factoring polynomials is breaking them down to the products of other smaller polynomials. Identifying the greatest common divisor (GCF) is an important first step because it will reduce the number of factors in each term and thus make factoring easier. In addition to polynomials, it can be factored by decomposition of the intermediate term or by difference of squares. Then, the Zero Product Property can be applied to solve the equation.
x² + 10x + 16Use the sum-product pattern.
x² + 8x + 2x + 16Extract the common factors.
x (x + 8) + 2(x + 8)Rewrite factored
( x + 2 ) ( x + 8 ) ===> Answer{ Pisces04 }Answer:
(x+2)(x+8)
Step-by-step explanation:
two numbers that multiply to 16 and add up to 10 is 2 and 8. You just plug both numbers in this factored form (x+ n1)(x+n2). if you chech the answer by multiplying the binomials, you will find out that the answer is the original question (x^3 +10x+16).
The variables A, B, and C represent polynomials where A = x², B = 3x + 2, and C = x - 3. What is AB - C² in
simplest form?
3x³ + 2x²-x+ 3
O 3x³ + 2x²-x-3.
O 3x³ + x² - 6x +9
O 3x³ + x² + 6x-9
The polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.
What are Polynomials ?The algebraic expression that consists of variables and coefficients are called Polynomials.
It is given that
The variables A, B, and C represent polynomials
where
A = x²
B = 3x + 2
C = x - 3
The Polynomial AB -C² = ?
From the value given
AB -C² = x² (3x + 2) - (x - 3)²
= 3x³ + 2x² - x² - 9 + 6x
= 3x³ + x² + 6x-9
Therefore the polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.
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There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
The probability that the person uses exactly one of the facilities is 0.64
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Find analysis in the attached file.
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Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
Answer:
B = 1.875
Step-by-step explanation:
given that A varies directly as B and inversely as C then the equation relating them is
A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation
to find k use the condition A = 12 when B = 3 and C = 2 , then
12 = [tex]\frac{3k}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
24 = 3k ( divide both sides by 3 )
8 = k
A = [tex]\frac{8B}{C}[/tex] ← equation of variation
when A = 10 and C = 1.5 , then
10 = [tex]\frac{8B}{1.5}[/tex] ( multiply both sides by 1.5 )
15 = 8B ( divide both sides by 8 )
1.875 = B
How many positive three-digit numbers are evenly
divisible by 33?
Answer:
27
Step-by-step explanation:
smallest multiple of 33 that is 3 digits is 132 (33*4), and largest is 990 (33*30)
then all the numbers between 4 and 30 would also be 3 digits
including 4 and 30, that makes 27 number in total
Verbal
2. How can you tell whether an absolute value function
has two x-intercepts without graphing the function?
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Without graphing an absolute value function, you can tell whether it has two x-intercepts by isolating the absolute value term to have an equation of the form |A| = B and then form two different equations.
Lastly, solve each equation for the two x-intercepts.
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Which best explains if quadrilateral WXYZ can be a parallelogram?
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,
1.) For the first pair.
(x+8) = 15
x = 7
2.) For the second pair
(x+2)=(2x-5)
x + 2 = 2x - 5
2 + 5 = 2x - x
x = 7
(x+2) = (7+2) = 9
Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.
Hence, the correct option is A.
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Martha climbs 40 steps to reach the first floor of a building. If the vertical and horizontal distance of each step is 1.5 ft and 1 ft, find the distance between the start and end points of each step
The distance between the initial position and the final position is 72.1ft
How to get the distance?
The initial position is (0ft, 0ft). Where the notation used is:
(horizontal position, vertical position).
Martha climbs 40 steps, then the final position is:
(40*1ft, 40*1.5ft) = (40ft, 60ft)
The distance between the initial position and the final position is:
[tex]d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft[/tex]
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Discuss the implications of an infinite-dimensional space in generalization ability of the hard-margin SVM. What are the strategies we can use to improve generalization
The SVM classifier's generalization performance is improved by decreasing the VC dimension.
What is SVM ?SVM stands for Support Vector Machine .
A potent machine learning technique for classification and regression is called a Support vector machine. The selection of a margin type is crucial if we want to use it to solve an issue.
A soft margin or a hard margin can be chosen on the basis of the data , If the data is linearly separable , hard margin is used , If the data is not separable linearly and misclassifications can be allowed then soft margin is used.
The hard margin SVM's capacity for generalization is significantly influenced by VC.
the SVM classifier's generalization performance is improved by decreasing the VC dimension.
We contend that by using dimensionality reduction and bootstrapping techniques, the VC dimension of an SVM classifier can be decreased.
The SVM classifier's performance was now enhanced by bootstrapping both the original data and the projected data that is dimensionally reduced .
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\sqrt{27} - \sqrt{ 12} + \sqrt{48 }
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
I'm assuming you're asking for most simplified form?
Original Equation:
[tex]\sqrt{27} - \sqrt{12} + \sqrt{48}[/tex]
Rewrite sqrt(27) using the exponent property: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]\sqrt{9} * \sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Simplify sqrt(9)
[tex]3\sqrt{3} -\sqrt{12} + \sqrt{48}[/tex]
Rewrite the radical sqrt(12)
[tex]3\sqrt{3} -\sqrt{4}\sqrt{3} + \sqrt{48}[/tex]
Simplify sqrt(2)
[tex]3 \sqrt{3} -2\sqrt{3} + \sqrt{48}[/tex]
Rewrite the radical sqrt(48)
[tex]3\sqrt{3} -2\sqrt{3} + \sqrt{16}\sqrt{3}[/tex]
Simplify the sqrt(16)
[tex]3\sqrt{3} -2\sqrt{3} + 4\sqrt{3}[/tex]
You can think of sqrt(3) as x, in which case you have 3x - 2x + 4x, so you just add the coefficients and leave the sqrt(3) alone.
Subtract 2 from 3
[tex]1\sqrt{3} + 4\sqrt{3}[/tex]
Add 1 and 4
[tex]5\sqrt{3}[/tex]
Find m/CDU if m/CDE-154° and m/UDE = 108°.
U
E
D
C
Answer: [tex]46^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle CDE=m\angle UDE+m\angle CDU\\\\154^{\circ}=108^{\circ}+m\anlge CDU\\\\m\angle CDU=46^{\circ}[/tex]
There are 4 circles and 6 triangles. What is the simplest ratio of circles to triangles?
Answer:
2/3
Step-by-step explanation:
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6
4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6
The simplest ratio of circles to triangles would be; 2/3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that there are 4 circles and 6 triangles.
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be as given;
4/6
when divided by two we get;
2/3
This is the simplest form of the fraction 4/6
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Distance (feet)
2
14
12
10
20
5
4
2
2
4
6
garden
Distance (feet)
12 14 15
The diagram shows a garden plot. The area of the garden is
garden is … square feet.
square feet. The length of fencing required to completely enclose the garden is … feet.
The area of a 2D form is the amount of space within its perimeter. The area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The diagram for the given garden is given below.
1.) The area of the garden is,
The area of the garden = Area of rectangle + Area of triangle
= (6 x 8) + (0.5 x 6 x 8)
= 48 + 24
= 72 feet²
2.) The perimeter of the garden is,
The perimeter of the triangle = 12 + 8 + 6 + 10 = 36 feet
Hence, the area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
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Two similar triangles have areas 16 and 4. if a side of the smaller triangle measures 2, find the length of the corresponding side in the larger triangle.
Answer: 4
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the side length.
Since the ratio of the areas is 16:4 = 4:1, the ratio of the side lengths is 2:1.
So, the length of the corresponding side is 2(2) = 4.
4. (07.06)
Write a simplified polynomial expression in standard form to represent the area of the rectangle below. (2 points)
2x - 4
O 2x² + 6x-20
2x² - 4x-20
D
2x² + 6x + 20
2x² + 10x + 20
X+5
The expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.
The area of the rectangle is the product of its length and its width. Therefore, the area of the given rectangle is,
Area = (2x-4)(x+5)
= 2x² + 10x - 4x - 20
= 2x² +6x - 20
Hence, the expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
The complete question is:
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
2x² + 10x + 202x² + 6x + 202x² + 6x − 202x² − 4x − 20The image of the rectangle is given below.
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in which quadrant will you find the point (-2,-2)
⊱________________________________________________________⊰
Answer:
Quadrant 3Step-by-step explanation:
Points with both negative co-ordinates are found in the third quadrant.
[tex]\boxed{\begin{tabular}{c | 1} \sf{~~Quadrant 2 (-x,y)~~& Quadrant 1~ (x,y)~~} \\ \\\\\\\\\\\\ \cline{1-2} \sf{Quadrant \ 3 (-x,-y) \ & Quadrant \ 4 (x,-y)} \\\\\\\ \\\\\\\\\\\end{tabular}}[/tex]
done !!
⊱_____________________________________________________⊰
First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces Then find the area of the divisions.
The figure will have a triangle and a rectangle. The area of a triangle is 10 in² and the rectangle is 80 in². Therefore, the total area is 90 in².
Area of Compound ShapesThis question requires your knowledge about the area of compound shapes. For solving this, you should:
Identify the basic shapes; Calculate your individual areas; Sum each area found. STEP 1 - Identify the basic shapes.The figure is composed of a triangle and a rectangle.
Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.
STEP 2 - Find the area of the trinagle.Area of the triangle= [tex]\frac{b*h}{2}[/tex]. The figure shows that: the base = 10 in and the height =2 in
Thus, A_triangle=[tex]\frac{b*h}{2}=\frac{10*2}{2} =10 in^{2}[/tex]
STEP 3 - Find the area of the rectangle.Area of the rectangle = bh . The figure shows that: the base = 10 in and the height =8 in
Thus, A_rectangle=bh= 10*8=80 in²
STEP 4 - Find an expression for the total area of the figure.
A_total= A_triangle + A_rectangle
A_total= 10+80=90 in²
A_total= 90 in²
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Random assignment to treatments helps control for lurking variables ? true ? false.
It is true that Random assignment to treatments helps control for lurking variables
The main purpose for using randomization in an experiment is to create sure that the results are accurate. you wish to avoid biasis and lurking variables. Having a randomized experiment will facilitate your to create sure that your information is correct
The main purpose for using randomization in an experiment is to manage the lurking variable and establish a cause and effect relationship. Also, by randomizing an experiment the evidence is more supported
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The graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
―
F(x)=x3
-6
O A. G(x) = (x+1)³
OB. G(x) = x³-1
OC. G(x) = (x-1)³
OD. G(x)= x³ +1
GX) = ?
Using translation concepts, it is found that the equation of the blue graph is given by:
C. G(x) = (x - 1)³.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function G(x) is a shift of one unit right of F(x) = x³, hence it's equation is:
G(x) = F(x - 1) = (x - 1)³.
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Which ordered pair below is a solution to the following system of equations?
-x + 2y = 5
x + y = 1
Answer:
The correct option is OPTION (A) .
Does this graph represent a function? Why or why not?
C A. Yes, because it passes the vertical line
test.
B. No, because it is not a
straight line.
No, because it fails the vertical line test.
O D. Yes, because it passes the horizontal line test.
Answer:
A. Because it passed the y axis