Using the slope formula, the required equation is y = -4x + 1.
What is the slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
The slope of a line can be used to gauge how steep it is.
The slope is theoretically determined as "rise over run" (change in y divided by change in x).
So, slope formula: m = y2 - y1/x2 - x2
Now we have: y = - 1/4 x + 6 and points (2, 9)
Now, substitute as follows:
(y-9) = -4(x+2)
In order to convert this equation into the slope-internet form, we can additionally solve it for y:
(y-9) = (-4*x+(4*2)
(y-9) = -4x - 8
y - 9 + 9 = -4x - 8 + 9
y - 0 = -4x + 1
y = -4x + 1
Therefore, using the slope formula, the required equation is y = -4x + 1.
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Evaluate the function graphically.
By evaluating the function graphically , f (4) = -4
What is a function ?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
How to represent Function Graphically ?The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).
According to the Given information
f( x ) = y
where x is an input and y is an output
We need to find the value for f(4)
f( 4 ) = y
For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant
f (4) = -4
By evaluating the function graphically , f (4) = -4
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A parabola has a y intercept of 5 and contains the points (2,-3)
and (-1,12). What are the coordinates of the vertex?
Answer:
Here
Step-by-step explanation:
The vertex of the parabola is at (0.5, 8.5).
1st question ,easy answer
Answer:
a
Step-by-step explanation:
Answer:
The answer is: A. Hope it helps.
Reese's monthly bank statement says she has a balance of $228.32, but Reese's check register says that her balance is $248.32. Which of the following are still outstanding?
I. A $48.16 deposit from Reece's mom
II. A $116.16 deposit from Reece's work
III. $28.16 check to the nail salon
IV. A $126.16 check to the hair salon
I and II
I and III
II and III
Answer:
l and lll
Step-by-step explanation:
228.32 + 48.16 - 28.16 = 248.32
Is triangle ABC a dilation of triangle def?
The triangle ABC is a Dilation of triangle DEF.
A dilation is a transformation that produces an image that is the same shape as the original one but in a different size. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. So, the shape of triangles ABC and DEF are the same.
Since they have similar shapes, their angles will be the same. The largest angle measured in triangle DEF = The largest angle measured in triangle ABC.
Dilation can reduce the shape of an object. The dilation can also enlarge a shape proportionally resulting in a giant monster version of itself.
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Joe is on a sidewalk 100ft away from the tree ,jim is on a perpendicular sidewalk 70ft from the tree how far away are they from earth other
Answer:
30 ft
Step-by-step explanation:
Answer:
122 ft
Step-by-step explanation:
The 100 ft and the 70 ft are two legs of a right triangle....their distance apart is the hypotenuse of this triangle ....use Pythagorean theorem
d^2 = 100^2 + 70 ^2
d = 122 ft
true or false: a confidence interval is the rejection region of a two-sided test. group of answer choices true false
This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).
Given that,
The statement is a confidence interval is the rejection region of a two-sided test.
We have to say if the statement is true or false.
We know that,
In statistics, a confidence interval describes the probability that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.
Therefore, This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).
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55% prefer oda over port drink. Of thoe who prefer port drink, 61% alo prefer coffee over tea, while 51% who enjoy oda prefer tea over coffee. What percentage of all cutomer prefer port drink and tea
The percentage of all customers prefer port drink and tea is 17.55%. The result is obtained by multiplying the two percentages of the data.
How to calculate the percentage?We have a number of customers.
55% prefer soda over port drink.61 % who prefer port drink also prefer coffee over tea.51% who prefer soda also prefer tea over coffee.Of all customers, find the percentage that they prefer port drink and tea!
If 55% prefer soda over port drink, then the ones who prefer port drink is
100% - 55% = 45%
Of the customers who prefer port drink, 61% prefer coffee over tea. So, the ones who prefer tea is
100% - 61% = 39%
From that information, we can get the ones who prefer port drink and tea. Let's say pt = port drink and tea.
pt = 39% × 45%
pt = 0.39 × 0.45
pt = 0.1755
pt = 17.55%
Hence, of all customers, the percentage who prefer port drink and tea is 17.55%.
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(4+6)x5x5-2 (four plus six)times 5 times 5 subtracted by 2
Answer: 248
Step-by-step explanation: First, you add 4 + 6 to get 10, then you multiply that by 5 to get 50. Then you multiply 50 by 5 to get 250, so 250-2 = 248. I hoped this solved your problem.
Answer:
248
Step-by-step explanation:
(4+6)x5x5-2
10x5x5-2
50x5-2
250-2
248
(if wrong sorry)
A function has a degree of 8. It has two x-intercepts, one of multiplicity 1 and one of multiplicity 3. How many imaginary zeros does the function have?
Answer:
two or four
Step-by-step explanation:
Any degree-X polynomial can have up to 8 zeros (some of them can have multiciplity higher than 1).
The polynomial can be written as:
f(x) = (x-a)(x-b)(x-c)(x-d)(x-e)(x-f)(x-g)(x-h)
and we're already told that there are 2 x-intercepts, one with multiplicity 1. Let's assign those x-intercepts a and b=c=d (multiplicity 3).
We're left with (x-e)(x-f)(x-g)(x-h), where e, f, g and h need to be non-real complex numbers (otherwise they'd provide x-intercepts).
The complex zeros (more accurate term than imaginary) must come in pairs - if a number c is a zero of the function, its conjugate is a zero too. That means that we need to have an even number of complex zeros.
We can either have 4 distinct complex zeros, or 2 complex zeros, each with multiplicity of 2.
Write a reflection rule for each triangle and
its image.
a. J(1, 0), K(-5, 2), L(4, -4) and
J'(-9, 0), K'(-3, 2), L'(-12, -4)
The rule of reflection for the triangle △JKL to △J'K'L' is x = -4.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Given that the vertices of △JKL are J(1, 0), K(-5, 2), L(4, -4).
The vertices of △J'K'L' are J'(-9, 0), K'(-3, 2), L'(-12, -4).
The formula of midpoint of (x₁, y₁) and (x₂, y₂) is
((x₁+x₂)/2, (y₁+y₂)/2)
The midpoint of J(1, 0) and J'(-9, 0) is ((1+(-9)/2,(0+0)/2) = (-8/2,0) = (-4,0)
The midpoint of K(-5, 2) and K'(-3, 2) is ((-5+(-3)/2,(2+2)/2) = (-8/2,4/2) = (-4,2)
The midpoint of L(4, -4) and L'(-12, -4) is ((4+(-12)/2,(-4+(-4))/2) = (-8/2,-8/2) = (-4,-4)
Thus the x-coordinate of the midpoint is the same.
Thus the line of reflection is x = -4.
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find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative.) f(x)
The given function is x² - 7x + 5 and the most general antiderivative of the function is F(x) = x³/3 - 7x²/2 + 5x + c.
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = ∫f(x)dx
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = ∫x² - 7x + 5
F(x) = x³/3 - 7x²/2 + 5x + c
Where c is the constant of the integration (antiderivative).
The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
Therefore, F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.
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The graph of y=f(x) is graphed below. What is the end behavior of f(x)?
The graph of y = f(x) has end behavior as x ⇒ ∞, y ⇒ - ∞ and
as x ⇒ - ∞, y ⇒ ∞.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
The given function f(x) has end behavior as x approaches infinity y approaches negative infinity and as x approaches negative infinity y approaches infinity.
As when x value is positive y value is negative and when y value is negative x value is positive.
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To indirectly measure the distance across a river, Carson stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Carson draws the diagram below to show the lengths and angles that he measured. Find P R PR, the distance across the river. Round your answer to the nearest foot.
Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
ABC refers to a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
So, the triangles PRE and POC appear to be comparable triangles in the diagram.
Utilizing the similarity theorem:
PR/RE = PR+RO/OC
x/135 = (x+140)/230
By cross-multiply:
230x = 135(x+ 140)
230x = 135x + 18,900
230x - 135x = 18,900
95x = 18900
x =18900/95
x = 198.94
Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
what is the vaule expression of m4 - 11 when m = 3
Answer:
m4 - 11 = 1
Step-by-step explanation:
Given information,
→ m4 - 11
→ m = 3
Now the value of expression is,
→ m4 - 11
→ (3)4 - 11
→ 12 - 11 = 1
Hence, value of expression is 1.
2x + y = 5
x - 2y = -15
Answer: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `
Step-by-step explanation: Straight lines `2x + y = 5` and `x-2y = 3` intersect at point `A`. Points `B` and `C` are chosen on these two lines such that `AB = AC`. Then the equation of a line `BC` passing through the point `(2.3)` is: (`A) 3x-y-3=0 55. (B) x+3y-11=0 (C) 3x + y-9=0 (D) x-3y +7=0 `
I hope this helps :)
The point (5,4) is not a solution to the inequality. Why? Explain your reasoning using the graph and using algebra
By using algebra (5, 4) is not a solution of the inequality.
Boundary does not contain in the given graph this is the error was made when graphed.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
x + 2y ≤ 12
Here the inequality contain ≤ .
Since, if there is ≤ sign then graph must contain boundary line.
The boundary line is solid line need to use in the graph.
But in the given graph the boundary line is dotted.
Boundary does not contain in the graph.
Hence, this is the error was made when graphed.
Also from graph we can see that the point (5, 4) is not contain in the graph.
Hence, (5, 4) is not a solution of the inequality.
Now prove by using algebra.
Plug x = 5, y = 4 in the given inequality
⇒ 5 + 2(4) ≤ 12
5 + 8 ≤ 12
13 ≤ 12
It is not possible that 13 ≤ 12.
Hence, (5, 4) is not a solution of the inequality.
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Are the whole numbers closed under subtraction justify with example?
The whole numbers are closed under subtraction only by distributive property else they are not closed under subtraction.
Whole numbers constitute natural numbers including zero. The subset is given by {0, 1, 2, 3, 4, 5, …}, the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}
To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.
Let us consider each property one by one -
1. The closure property-
let's take two whole numbers say 5 and 2.
now 5-2=3, but 2-5= -3 which is not a whole number.
Thus, whole numbers are not closed under subtraction by closure property.
2. The commutative property-
let's take two whole numbers say 5 and 2.
now 5-2=3 and 2-5=-3
hence, we get 2-5 ≠ 5-2.
Thus, whole numbers are not closed under subtraction by commutative property.
3. The associative property-
let's take three whole numbers say 5, 3, and 2.
now (5-3)-2 = 0 and 5-(3-2)= 4
hence, we get (5-3)-2 ≠ 5-(3-2).
Thus, whole numbers are not closed under subtraction by associative property.
4. The distributive property-
let's take three whole numbers say 20, 6, and 5.
now, 20 × ( 6 – 5 ) = 20 × 6 – 20 × 5 = 20
and 20 × ( 6 – 5 ) = 20 × 1 = 20
Hence, 20=20.
Thus, whole numbers are closed under subtraction only by distributive property.
Hence, we can conclude that whole numbers are closed under subtraction only by distributive property.
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Help me on this please and thank you
Answer:
The probability for the green one is 6/10
and for the next one, it is 4/10
Step-by-step explanation:
What is the absolute value of 3/2?
what is the value of 32^4?
what is the value of 32 to the fourth power?
what is the value of 42?
The value of all the given expression are as follow:
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
As given in the question,
Simplification of the given expressions are :
a. The absolute value of ( -3 / 2 )is
| - 3 / 2 | = ( 3/2 )
b. The value of the expression 32^4 is:
32^4
= 32 × 32 × 32 × 32
= 1048576
c. The value of the given expression ( 32 ) ^ 1/4 :
( 32 ) ^ 1/4
= ( 2⁵) ^ 1/4
= 2^(5/4)
d. Value of 4^2 is
4^2
= 4 × 4
= 16
Therefore, the value of the given expression is given by :
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
The complete question is:
What is the absolute value of -3/2 ?
what is the value of 32^4?
what is the value of 32 to the one - fourth power?
what is the value of 4^2?
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which graph best represents the equation y=1.5x-2?
The graph is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 1.5x - 2
We can have the following coordinates on the graph.
x = 1, y = 1.5 - 2 = -0.5
(1, -0.5)
x = 2, y = 3 - 2 = 1
(2, 1)
x = 3, y = 4.5 - 2 = 2.5
(3, 2.5)
x = 4, y = 6 - 2 = 4
(4, 4)
And so on.
The graph of y = 1.5x - 2 is given below.
Thus,
Some of the coordinates on the graph are:
(1, -0.5), (2, 1), (3, 25), (4, 4), and so on.
The graph is given below.
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please help, answers only!!
Answer:
Step-by-step explanation:
slope=-5/4
b=5
y=-5/4x+5
Ty get spends 25 mins studying mathematics 35 minutes study science and 20 mins studying history
Answer:
1 hour and 20 minutes I think
Step-by-step explanation:
add all of them up then divide by 60
a student believes that the average grade on the final examination in statistics is at least 85. she plans on taking a sample to test her belief. the correct set of hypotheses is
By using testing of hypothesis, it can be concluded that-
The correct set of hypotheses is
[tex]H_0 : \mu \geq 85[/tex]
[tex]H_a : \mu < 85[/tex]
What is testing of hypothesis?
Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.
A student believes that the average grade on the final examination in statistics is at least 85.
The null hypothesis is [tex]\mu \geq 85[/tex]
The alternative hypothesis is [tex]\mu < 85[/tex]
So, the correct set of hypotheses is
[tex]H_0 : \mu \geq 85[/tex]
[tex]H_a : \mu < 85[/tex]
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What is the solution to the equation 5 (x minus 6) = 2 (x 3)? x =
the solution to the equation is x=12
The distributive property is defined as
Let us now solve the equation.
5(x - 6) = 2(x + 3)
Using the distributive property, simplify the parentheses on both sides.
5(x - 6) = 2(x + 3)
5x - 30 = 2x + 6
The parenthesis was simplified. However, we have one x term on one side and another x term on the other.
5x - 30 - 2x = 2x + 6 - 2x
3x - 30 = 6
We only have an x term on one side of the equation now.
To begin, reverse the subtraction by adding 30 to either side of the equation.
To keep an equation balanced or true, we do the identical operation on both sides.
3x - 30 + 30 = 6 + 30
3x = 36
We're getting close to an answer. Only one more step.
The x term is multiplied by 3.
We can undo the multiplication operation by dividing both sides by 3.
3x / 3 = 36 / 3
x = 12
So, x is equal to 12.
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Triangles a b c and d b c share common side b c. sides a c and c d are congruent. in order to prove △abc ≅ △dbc by sas, what additional information must be given? ∠abc ≅ ∠dbc ab ≅ db ∠acb ≅ ∠dcb bc ≅ bc
Answer:
(c) ∠acb ≅ ∠dcb
Step-by-step explanation:
You want to know what additional information is required to show ∆abc ≅ ∆dbc by SAS, given ac ≅ dc.
SASThis postulate tells you triangles are congruent if two corresponding sides are congruent, and the angles between them are congruent.
In the given geometry, the corresponding sides are given as congruent, so the additional information required is that the angles between them are congruent.
The angle between sides ac and bc is ∠acb.
The angle between sides dc and bc is ∠dbc.
The additional information required is ...
∠acb ≅ ∠dcb . . . . . matches choice C
<95141404393>
The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards. Enter the function f(x) that describes the area, in square yards, as a function of the width, x.
f(x) = _____
f(x) = Area = (length)(width)
width = x
The length is 16 yards greater than 3 times x
length = 3x+16
f(x) = (3x+16)(x) = 3x^2 + 16x
Answer:
f(x) = 3x² + 16xStep-by-step explanation:
We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards
Length of parking lot is 16 + 3x
Width of parking lot is x
We have to write the function f(x) that describes the area, in square yards, as a function of the width, x
Area of rectangle is Length × width
[tex] \sf Area = f(x) [/tex]
put value of length and width here,
[tex] \sf f(x) = (16 + 3x)(x )[/tex]
[tex] \sf f(x) = 3x^2 + 16x [/tex]
Therefore, f(x) = 3x² + 16x
Which numbers are less than –8/3? Select all that apply.
The number which is less than that of -2.67 are -2.8, -2.9, -3.0.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
Which numbers are less than –8/3 = -2.67
So given in the option which is less than -2.67
Numberless -2.7 are
-2.8, -2.9, -3.0.
Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.
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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2
Use completing the square to rewrite the given function in vertex form. Determine whether the vertex is a maximum or minimum value. Select the TWO correct answers.
y = x2 + 10x + 15
A The vertex is a maximum value at point (5, 10)The vertex is a maximum value at point (5, 10)
B The vertex form is y = (x+5)2 − 10.The vertex form is y = ( x + 5 ) 2 − 10.
C The vertex form is y = (x−5)2 + 10.The vertex form is y = ( x − 5 ) 2 + 10.
D The vertex form is y = (x+5)2 + 10The vertex form is y = ( x + 5 ) 2 + 10
E The vertex is a minimum value at point (−5, −10)
The function x^2 +10x +15 in vertex form is (x+5)^2 - 10 and the vertex is a minimum at (-5, -10)
What is the vertex of a curve?The vertex of a parabola is a point at which the parabola makes its sharpest turn. A parabolic function has either a maximum value (if it is of the shape '∩') or a minimum value (if it is of the shape 'U"). The vertex of a parabola is also the point of intersection of the parabola and its axis of symmetry.
y = x^2 + 10x +15
making x^2 + 10x +15 a perfect square expression we square the half of the coefficient of x on both sides which is (5)^2
y + (5)^2 = x^2 + 10x + (5)^2 + 15
y + 25 = x^2 + 10x + (5)^2 + 15
x^2 + 10x + (5)^2 can be written as (x+5)^2 since iti is now a perfect square expression
y + 25 = (x+5)^2 + 15
y = (x+5)^2 + 15 - 25
y = (x+5)^2 -10
Equation of parabola in vertex form is y = a (x - h)2 + k
where k is the minimum or maximum point of vertex and h is the x coordinate of vertex.
comparing both equations, the coordinate of vertex (h, k) is (-5, -10) which is a minimum point.
In conclusion the vertex is a minimum at (-5, -10) and the equation in vertex form is (x+5)^2 -10
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The equation for line q is 3x + 5y 10, Line r is parallel to line q and passes through the
point (5,-4).
Write the equation for line r in slope-intercept form.
The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.
What is the equation for line r in slope-intercept form?The slope-intercept form is expressed as;
y = mx + b
The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line q : 3x + 5y = 10Point: (5,-4)Equation line r = ?First, determine the slope of the line q using the slope intercept-form.
y = mx + b
3x + 5y = 10
5y = -3x + 10
y = (-3/5)x + 10/5
y = (-3/5)x + 2
Hence;
Slope of line q m = -3/5
Since, line r is parallel to line q, they both have the same slope.
Therefore, slope of line r will be m = -3/5
Now, plug the point (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - (-4) = (-3/5)( x - 5 )
y + 4 = (-3/5)x + 3
y = (-3/5)x + 3 - 4
y = (-3/5)x - 1
Therefore, the equation of line r is y = (-3/5)x - 1.
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