The interpretation of the likelihood of randomly selecting a terrier from the dog shelter where terriers are 85% is A. Likely.
What is probability?Probability refers to the chance or likelihood of an expected event occurring when there are many possible chances.
Probability is depicted as a fractional value lying between zero and one when it is not 100% uncertain or certain.
Thus, since the percentage of terriers in the dog shelter is 85%, it is 85% likely that one selects a terrier.
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Answer: A: Likely.
Step-by-step explanation:
PLEASE HELP SERIOUSLY NEED IT
Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.
Describe the circle.Every point in the plane of a circle is equally separated from the center and is a closed, two-dimensional object. Each line tracing the circle contributes to the formation of the line of reflection symmetry. Additionally, each angle has rotational symmetry around the center.
Here,
calculation
The formula for arc length is (/2) 2r.
because of length of an arc equals r.
16 = 4θ
=> θ = 4
4r is the length of an arc.
Four times the radius, the subtended arc is longer.
Angle A is subtended by an arc if its length and radius are equal.
=> θ = 16 /4
=>4 rad
Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.
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Use the distributive property to write an equivalent expression. Then
evaluate the expression.
(9+3)
Equivalent Expression
=
The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression 2/5(s + 20)
Using distributive property
2/5s+2/5*20
2/5s+2*4
2/5s+8
and (9+3)=12
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Right question:-
Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).
Which ordered pairs lie on graph of the exponential function f(x) = 5(4)^x
Answer:
(0,5) and (3,320)
Step-by-step explanation:
Plug in the ordered pair into the function and see if it makes sense.
Plug in 5 for y and 0 for x:
5= 5(4)^0
4^0 = 1 (anything to the power of 0 except 0 is one)
5x1 = 5
5=5
(0,5) works
320 = 5(4)^3
4^3 = 64
64x5 = 320
320=320
320=320 (3,320) works
(0,5) and (3,320) both work.
Determine the graph that represents a function. On a coordinate plane, a circle is shown that crosses the x-axis at (negative 5, 0), the y-axis at (0, 5), the x-axis at (5, 0), and the y-axis at (0, negative 5). On a coordinate plane, a parabola opens to the left. It crosses the y-axis at (0, 3) and (0, negative 3), and the x-axis at (9, 0). On a coordinate plane, a straight line with a positive slope crosses the y-axis at (0, negative 2) and the x-axis at (1.2, 0).
Answer: The graph that represents a function is the parabola that opens to the left.
This can be determined by the following characteristics of the graph:
It is a parabola because it opens to the left and has a vertex on the y-axis.
It crosses the y-axis at (0, 3) and (0, negative 3), which means that it is symmetric about the y-axis, and also it crosses the x-axis at (9, 0) which means that it is a function.
A circle is not a function because, for any value of x, there are two different values of y that can be plotted on the graph (i.e. the point (5,0) and (-5,0) produce two different y values)
A straight line with a positive slope is not a function because, for any value of x, there is only one value of y that can be plotted on the graph.
So the parabola is the graph that represents a function.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
ANYONE GOOD AT MATH COME ON OVER AND HELP A FELLOW SLOW PERSON PLEASE WILL GIVE 30 POINTS!!!
The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x)) included is presented as follows;
[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]
f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different
What are composite functions?Composite functions are functions in which the input or argument are also functions.
The values of the composite functions based on the defined functions are found as follows;
f(x) = x² + 1, g(x) = -2·x + 5
Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;
f(x) = x² + 1
f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1
-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1
4·x² - 10·x - 10·x + 25 + 1 = 4·x² - 20·x + 26
When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = -2·x + 5
f(x) = x² + 1
g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5
g(f(x)) = -2·x² + 3
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;
f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4
2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16
f(g(x)) = 2·x² + 10·x + 16
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = x + 3
f(x) = 2·x² - 2·x + 4
g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7
g(f(x)) = 2·x² - 2·x + 7
When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;
f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]
g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4
g(f(x)) = 2·x - 4
The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.
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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?
In a linear graph line diagram, A line passes through (minus 4, minus 6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at minus 3 units.
A.
y
=
−
4
3
x
−
47
3
B.
y
=
3
4
x
−
11
C.
y
=
3
4
x
+
1
D.
Answer:
Step-by-step explanation: The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.
What is Algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
Variables and constants can both be used in an algebraic expression.
A coefficient is any quantity that is added before a variable and then multiplied by it.
The Algebraic expression in this case is:
x + y = 8
which traverses points (8,-5)
Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.
y = mx + c →(1)
x + y = 8
y = -x + 8
Comparing the aforementioned Algebraic expression to equation (1), we obtain
m = -1
The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.
Let's use the point-slope equations of line to determine the linear equation now:
(y-y₁) = m(x-x₁)
Changing every value in the equation above to obtain the Algebraic expression for a line
(y-(-5)) = -1(x-8) (x-8)
(y+5) = -x+8
y + 5 = -x +8
y = -x +3
The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3
Pleaseeeee help me i need the full answer for everything single one please I WILL GIVE MORE POINTS
Answer:
Step-by-step explanation:
it depends on where each point is on each chart because they can't be blank
what is 2 over x to the power of 2 equivilent to
The equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
How to obtain the equivalent exponential expression?The expression for this problem is defined as follows:
(2/x)².
We have a fraction that is squared, meaning that both the numerator and the denominator are squared, hence:
2² = 4.x².This means that the equivalent exponential expression for this problem is given as follows:
(2/x)² = 4/x².
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Felipe, Jill, and Cindy are neighbors. Jill is 7 years older than Cindy and Felipe is two-
thirds the age of Jill. The sum of their three ages is 137.
a. If a represents Jill's age, write an equation in terms of that can be used to
determine each person's age.
b. How old is Felipe?
On solving the provided question, we can say that vertex form of the equation is in the form of y = a(x-h)^2 + k.
In mathematics, what is the vertex?A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedral, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.
Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.
a = -1/4 * (4 - 12) = -1
h = -b/(2a) = 12/(2(-1)) = -6
k = f(h) = -(-6)^2 + 12(-6) - 4 = 36
Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.
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Calculate the degrees of freedom associated with a small-sample test of hypothesis for (H H2 assuming o12 o22 and n n2 16. O A. 15 O B. 31 O C. 32 O D. 30
Option A, The degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex], and [tex]n_1[/tex], [tex]n_2[/tex] is 15.
To calculate the degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex] and [tex]n_1[/tex], [tex]n_2[/tex], you would use the following formula:
df = ([tex]o_{12}^2[/tex]/n_1) + ([tex]o_{22}^2[/tex]/n_2)
In this case, the degrees of freedom would be:
df = ([tex]o_{12}^2[/tex]/16) + ([tex]o_{22}^2[/tex]/16) = 15 and represents the number of values that are free to vary in the sample.
So, the answer would be A. 15
It's important to note that this formula is only used for small sample sizes. For large sample sizes, the degrees of freedom are approximated using the Welch-Satterthwaite approximation.
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Write an expression to represent emaily number
On solving the provided question we can say that the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
here,
the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]
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In a triploid of genotype B/b/b, what proportion of gametes will be B? A) 1/2 B. 1/3 C.1/8
D. 1/4
E. 1/6
Answer:
I think it’s D
Step-by-step explanation:
trust
12. Suppose U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} is the universal set and G = \{1, 2, 3, 4, 5, 6, 7\} . What (1 point)
O \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
O cannot be determined
O \{1, 2, 3, 4, 5, 6, 7\}
O \{8, 9, 10\}
is G'?
The complement of A∪B is A′∩B ′.
In sets, what does complement mean?A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.
Given, universal set, U={1,2,3,4,5,6,7}
A={1,2,5,7}
B={3,4,5,6}
(A∪B) ′=U−(A∪B)
={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ
A′∩B′=(U−A)n(U−B)
={3,4,6}n{1,2,7}=ϕ
Hence ( A∪B)′=A′∩B ′.
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Examine the triangle below, solve for x, rounded to two decimal places.
45°
Please help me with this...
Answer:
[tex]\boxed{x = 8 \;m}[/tex]
Step-by-step explanation:
Nice drawing! :)
From the figure we see that the rectangle has a length of 30 m and a width of 20 m
The total area of the rectangle PQRS = 20 x 30 = 600 m²
The square footage of the planted area = area of figure MNSR = 388 m²
Therefore the rest of the area (the unshaded portion) is:
600 - 388 = 212 m²
This is the combined area of the two triangles ΔPNM and ΔMRG
Let's find the area of each of these triangles. Each of them is a right triangle which makes calculations easier
Area of a right triangle = (1/2) x base x height
ΔPNM has base = 30 - x and height = 20 -x
Area of ΔPNM
= (1/2) (30-x)(2-x)
We can use the FOIL method to evaluate (30-x)(2-x)
(30-x)(20-x)
= 30·20 + (30)(-x) + x(20) + (-x)(-x)
= 600 - 30x + 20x + x²
= 600 -50x + x³
We usually rewrite with coefficients in decreasing magnitude of x degree
Area of ΔPNM
[tex]=\dfrac{x^2 - 50x + 600}{2}[/tex]
Let's now find the area of ΔMRQ with a base of x and a height of 20
Area of ΔMRQ
[tex]=\dfrac{1}{2}\cdot 20 = \dfrac{20x}{2}[/tex]
Adding both terms together we get
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} \\[/tex]
We have computed the area of the unshaded region as 212
So the above sum must be equal to 212
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} = 212[/tex]
Multiply throughout by 2 to get rid of the denominator:
[tex]\rightarrow \;\;x^2 - 50x + 600 + 20x = 212\times 2 = 424\\\\\rightarrow \;\;x^2 -30x + 600 =424\\[/tex]
Move 424 to the left:
[tex]x^2-30x+600-424=424-424\\\\x^2-30x+176=0[/tex][tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]
This is a quadratic equation which can be solved using the quadratic formula or by factoring
[tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]
So
[tex]x^2-30x+176=0 \rightarrow (x -8)(x-22) = 0\\\\[/tex]
So x = 8 or x = 22 are two possible solutions to this quadratic
If x = 22, it will be greater than the width of 20 and also 20-x = -2 so it is not a valid solution for this situation
Therefore we get the final answer as [tex]\boxed{x = 8 \;m}[/tex]
Help me solve please y-9 terms,variables, coefficient s,constants
The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression,
⇒ y-9
In given expression, y is term which is variable
And coefficient of y is 1
constant term is -9
Therefore, we can write our terms are, y, 1, -9
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i need help please i don’t get thus
According to the solving the lengths of right angle triangle using Pythagorean theorem x = 6, y = 3
How does the Pythagorean theorem work?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
According to the given information:The following is one way to perform the calculation. It may not be the best way.
c = b/cos(α)
= 6
a = √c2 - b2
= √62 - 5.192
= √9.0639
= 3.01063
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Amelia used 6 liters of gasoline to drive 48 kilometers. How many kilometers did Amelia drive per liter?
A house on the market was valued at $289,00 . After several years, the value increased by 17% . By how much did the house's value increase in dollars? What is the current value of the house?
Answer:
the answer is 338.13
Step-by-step explanation:
289,00×.17=49.23
49.13+289.00
hope this helps:)
john wants to buy a bicycle worth R750 . how many hours should he work to earn R750
Answer: To determine how many hours John needs to work to earn R750, you would need to know his hourly wage. If John earns R50 per hour, he would need to work 15 hours to earn R750 (R750 / R50/hour = 15 hours). If his hourly wage is different, the number of hours he needs to work will be different.
Step-by-step explanation:
A manager of a clothing store always orders 2 small T-shirt and 3 small T-shirts for every 4 medium T-shirt. The manager plans to order 24 medium T-shirts. How many small T-shirts should the manager order
The manager of the clothing store always orders 2 small T-shirts and 3 small T-shirts for every 4 medium T-shirts.
What in mathematics is a linear equation?
According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The manager plans to order 24 medium T-shirts and we want to find out how many small T-shirts the manager should order.
We can use the information given to set up an equation to represent the relationship between the number of small T-shirts and medium T-shirts. Let S be the number of small T-shirts and M be the number of medium T-shirts.
We know that:
S = 2 + (3/4)M
We are given that the manager plans to order 24 medium T-shirts, so we can substitute this value into the equation:
S = 2 + (3/4) * 24
We can simplify and solve for S:
S = 2 + (3/4) * 24
S = 2 + 18
S = 20
Therefore, the manager should order 20 small T-shirts.
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(x'2-3x+5) dived (x-1)
The quotient of the division (x^2-3x+5) divided (x-1) is x - 2 with a remainder of 3
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
(x^2-3x+5) divided (x-1)
Using the long division method of quotient, we have
x - 1 | x^2 - 3x + 5
The division steps are as follows
x - 2
x - 1 | x^2 - 3x + 5
x^2 - x
------------------------------------------------
-2x + 5
-2x + 2
------------------------------------------------
3
Hence, the quotient is x - 2
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calculate the molar solubility of cui (ksp= 1.27×10−12).
CuI's molar solubility is determined to be 1.27 x 10⁻¹².
The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.
Think about the equation.
Cu+(aq) CuI.(s) + I- (aq)
Let's assume that CuI (s) has a molar solubility of "S" mol/L.
Thus,
Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp
[ I-(aq)] ———(1)
We are aware of
For CuI, the solubility product Ksp is 1.27 x 10⁻¹².
Consequently, from equation (1)
1.27 × 10⁻¹² = S.S
S² =1.27 × 10⁻¹²
= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M
Therefore, CuI has a molar solubility of 1.127 x 10-6 M.
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QS bisects PQR and m/PQR = 119°.
Find m/PQS and m/RQS.
Q
m/PQS = ?
m/RQS =
Therefore , the solution to the given problem of angles comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Define angles.
An angled structure in geometry is composed of two rays that converge at the vertex, or core, of the angle. These rays are referred to as the angle's faces. Depending upon where they are situated, two beams may be able to form any angle within a plane. The intersection of two planes also produces an angle. Diahedral angles are the name for them. Light beams or lines that share the same endpoint in plane geometry can have a wide variety of shapes or angles. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of the two rays is known as the vertex, or vertex of the angle.
Here,
QS cuts an angle. PQR, followed by ∠SQR = ∠ PQS and
∠PQS + ∠RQS = ∠PQR.
The equation then changes to
∠PQR = ∠PQS + ∠PQS
∠PQR = 2∠PQS
∠PQS equals ∠PQR/2
assuming∠ PQR = 119°
Replace in the resulting expression from the above;
∠PQS equals ∠PQR/2
∠PQS = 119/2
∠PQS = 59.5°
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Therefore , the solution to the given problem of angle comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
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write the equation of the line given the following information in
point-slope form then re-write in slope-intercept form.
20. through the points (1, 3) and (-4, 5)
21. Through the point (4, -7) and is parallel to y = -2x-5
22. Through the point (3, 5) and is perpendicular to y = -3/2x + 1
We can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
Describe a slope.In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
The point-slope form of the line is then:
[tex]y - 3 = (2/5)(x - 1)[/tex]
To convert this to slope-intercept form (y = mx + b), we can solve for y:
[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]
21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:
[tex]y - (-7) = -2(x - 4)[/tex]
or
[tex]y + 7 = -2x + 8[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = -2x + 1[/tex]
22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:
[tex]y - 5 = (2/3)(x - 3)[/tex]
or
[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = (2/3)x + 3[/tex]
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The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
What is the value of y when x = 28?
The value of y when x = 28 in the proportional relationship is 112.
How to find the value of y in the proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.
Therefore, let's find the constant of proportionality.
y = kx
14 = 3.5k
divide both sides by 3.5
k = 14 / 3.5
k = 4
Let's find the value of y when x = 28.
Hence,
y = 4x
y = 4 × 28
Therefore,
y = 112
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For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
36,13
Answer:
9 and 4
Step-by-step explanation:
xy = 36
x+y = 13 or 13 - x = y <====sub this into the first equation
x ( 13-x) = 36
-x^2 + 13x - 36 = 0 multiply the entire equation by -1 to make it easier solve
x^2 -13x+36 = 0 this factors to
(x -9)(x-4) = 0 showing x = 9 or 4 with y being 4 or 9
can someone please solve this
The <HDI of the circle is 70 degree. A circle is divides into 360 equal degrees.
How to find <HDI?A circle is divides into 360 equal degrees.
In relation to a circle, angles are measured in degrees or radians, with one full rotation being equal to 360 degrees or 2 Pi radians.
so, <EDI = 140 degree.
so
A circle is 360 equal degrees.
360 - 140 = 220
< IDH = <EDF = 2x
<FDG = <GDH = 2y
so
2x + 2y = 220
2 * 70 + 2 * 40 = 220 degree
so,
<HDI = 70 degree.
so
The <HDI of the circle is 70 degree.A circle is divided into 360 equal degrees.
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A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by
y = 659,000 − 1800x dollars.
After how many months will the value of the building be $450,200?
Answer:
116 months
Step-by-step explanation:
A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by:
y = 659,000 − 1800x
After how many months will the value of the building be $450,200?
y = 659,000 − 1800x
450,200 = 659,000 − 1800x
subtract 659,000 from both sides:
450,200 - 659,000 = 659,000 − 1800x - 659,000
-208,800 = − 1800x
divide both sides by -1800:
-208,800/1800 = − 1800x/1800
116= x
so:
x = 116
sometimes a change of variable can be used to convert a differential equation into a separable equation. one common change of variable technique is as follows. consider a differential equation of the form , where , and are constants. use the change of variable to rewrite the differential equation as a separable equation of the form . solve the initial value problem (a) help (formulas) (b) help (formulas)
The differential equation is [tex]y=\frac{-7t^2+22t-7}{7t-22}[/tex]
We are given the Initial value problem:
y'=(t=y)²-1, y(3)=4
Substitute the value z=t+y
When t=3 and y=4 then z=3+4=7
y'=z²+1
Differentiate z w.r.t t
[tex]\frac{dz}{dt} =1+y'[/tex]
Then, we get [tex]z'=1+z'-1=z^2[/tex]
z⁻²dz=dt
Integrate on both sides:
-1/zdz=t+c
z=-1/t=c
Substitute t=3 and z=7
Then, we get
7=-1/3+c
21+7c=-1
7c=-1-21=-22
c=-22/7
Substitute the value of C then we get:
z=-1/t-22/7
z=-7/7t-22
y=z-t
y=-7/7t-22-t
y=-7-7t²+22t/7t-22
y=-7t²+22t-7/7t-22.
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