The values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)
In the above question, a horizontal line is given whose equation is Ax + By = C which passes through a point (-4, 2)
We can make two observations from the given information of horizontal line passes through point (-4,2) which are as follows:
1. The slope of a horizontal line will be parallel to the x-axis whose slope will be, m=0.
2. The given point and the line meet at (-4,2).
Now as the point (-4,2) lie on the line it will satisfy the equation of the horizontal line
We get,
A(-4) + B(2) = C
-4A + 2B = C ..... eqn 1
Also, we can write the given equation in the slope-intercept form which is
y = mx + c
By = -Ax + C
y = [tex]\frac{-A}{C}[/tex]x + [tex]\frac{C}{B}[/tex]
So, we can imply that m = [tex]\frac{-A}{C}[/tex] = 0
A = 0
Putting this in eqn 1 we get,
-4A + 2B = C
0 + 2B = C
C = 2B
Hence, we conclude that values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2) are ( 0, B, 2B)
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Evaluate the expression. – 2 5 ÷ – 1 3 – 3 5 × – 2 3 Write your answer as a fraction or as a whole or mixed number.
The solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
– 25 ÷ – 13 – 35 × – 23
Evaluate the quotient
So, we have
– 25 ÷ – 13 – 35 × – 23 = 25/13 – 35 × – 23
Evaluate the product
So, we have
– 25 ÷ – 13 – 35 × – 23 = 25/13 + 805
Evaluate the sum
So, we have
– 25 ÷ – 13 – 35 × – 23 = 805 25/13
Divide the fraction
So, we have
– 25 ÷ – 13 – 35 × – 23 = 805 + 1 12/13
Evaluate the sum
So, we have
– 25 ÷ – 13 – 35 × – 23 = 806 12/13
Hence, the solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13
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pleasem help i dont remember
The line of the graph is a solid line and the region to be shaded depends on the type of the inequality
How to use the graph to determine whether the line will be dashed or solid?The graph represents the given parameter
On the graph, we have a straight continuous line
A straight continuous line is an illustration of a solid line
This means that the line of the graph is a solid line
Hence, the line of the graph is a solid line
How to use the graph to determine whether the graph would be shaded above or below?
The graph represents the given parameter
On the graph, we can see that no region of the graph is shaded
This means that the shaded region would be determined by the type of the inequality
≥ means that the region would be shaded above
≤ means that the region would be shaded below
Hence, the region to be shaded depends on the type of the inequality
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the quotient of a number x and five is half the difference of the number and four. write an equation that represents the statement.
The equation that represent the statement "quotient of a number x and five is half the difference of the number and four" is x / 5 = 4 - 1/2x
EquationQuotient means divisionThe unknown number = xx / 5 = 4 - 1/2x
collect like termsx/5 + 1/2x = 4
(2x+5x) / 10 = 4
7/10x = 4
divide both sides by 7/10x = 4 ÷ 7/10
= 4 × 10/7
= 40/7
= 5.714285714285714
Approximately,
x = 5.7
Therefore, the value of x in the equation is approximately 5.7
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Solve 23 - 7x
=
3x + 8
Give your answer as a decimal.
Step-by-step explanation:
[tex]23 - 7x = 3x + 8 \\ - 7x - 3x = 8 - 23 \\ - 10x = - 15 \\ - 10x = - 15 \\ - 10 \: \: \: \: \: \: \: \: \: \: \: \: - 10 \\ x = \frac{15}{10 \\ } \\ x = 1.5[/tex]
The value of the Equation 23 - 7x = 3x + 8 is x = 3.1
What is an Equation?A mathematical statement that shows that two mathematical expressions are equal.
Given an equation, 23 - 7x = 3x + 8
7x + 3x = 23 + 8
10x = 31
x = 3.1
Hence, The value of the Equation 23 - 7x = 3x + 8 is x = 3.1
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9/53
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
The proof of DE is parallel to BC in the given triangle is shown.
What is defined as the parallel line?Parallel lines are defined as two lines that remain the same distance away and never intersect. To be parallel, two lines must be driven in the same plane, which is a perfectly flat surface such as a wall or sheet of paper.As per the given data in the question;
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)B has coordinates (2,-2)C has coordinates (-2,-4)Whereas,
D lies at the midpoint of AB.
E lies at the midpoint of AC.
The mid piont formula is;
Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
The coordinates of D is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and B (2,-2).
D = (4 + 2 / 2, 6 - 2 / 2)
D = (3, 2)
The coordinates of E is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and C (-2,-4)
E = (4 - 2 / 2, 6 - 4 / 2)
E = (1, 1)
Now, the slope is calculated by;
m of DE = (y₂ - y₁)/(x₂ - x₁)
The slope of E is
m of DE = (1 - 2)/(1 - 3) = 1/3
Slope of BC
M of BC = (-4 + 2)/(-4 - 2)
M of BC = 1/2
As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.
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A stop sign is a regular octagon, formed by cutting triangles off the corners of a square. If a stop sign measures 36 in. from top to bottom, what is the length of each side?
The length of each side will be 14.8 inches approx.
It's given that an Octagon sign is drawn out of a square by cutting out triangles from its corners and the total length of the stop sign is 36 inches. We know that squares are Right Angled at each side so in the picture mentioned below, we apply Pythagoras' theorem to find an equation for the side of the sign.
=> [tex]s^{2} = x^{2} + x^{2}[/tex]
=> [tex]s^{2} = 2x^{2}[/tex] ----> Eq. 1
Also, it is a square. So, the measurement of length from side to side
=> 2x + s = 36 inch ----> Eq. 2
By solving Eq.1 we get s = (√2)(x), Putting this value in Eq.2
=> s = 36 - 2x => (√2)(x) = 36 - 2x
=> x(2 + √2 ) = 36 => x = 36/(2+√2)
Putting this value of x in Eq.1 , s^2 = 2(x^2)
=> s = √2.(x) => s = √2 (36/(2 + √2)
=> s = 14.8
Hence, the length of each side of the sign will be 14.81-inch approx.
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what shape do i draw?
Answer:
You draw the exact same shape but at a different scale
Step-by-step explanation:
You just draw it bigger.
Find the least integer greater than each number. Do not use a calculator.
log√₇ √50
It follows that the least integer greater than log√₇ √50 is 3.
We have a logarithm function that is given to us.
Let x = log√₇ √50
We get that:√ 7 ˣ = √ 50
So, we must find an integer x, such that √ 7 ˣ > √ 50.
We know that √ 49 = 7
√ 7 ˣ > 7
7 ⁰°⁵ˣ > √ 7
x / 2 > 1
x > 2
In this case, x = 3 will be the least integer to satisfy this inequality.
Therefore, it follows that the least integer greater than log√₇ √50 is 3.
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Write each expression in simplest form. (√y-√3)(√y+2√3)
We write the expression in its simplest form and we are left with.
y²√3 + y - 6
Before proceeding let's define an algebraic expression.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The first thing we will do is to write the expression:
(√y-√3)(√y+2√3)
Then we perform the multiplication, with the distributive property, which gives as a result
(y + 2√3y - √3y - 6)
y²√3 + y - 6
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What is each expression in simplest form?
b. (9x ⁴√y)³/²
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squaresExpand the following:
(9×4 x sqrt(y)) ^(3/2)
9×4 = 36:
(36 x sqrt(y))^(3/2)
(36 x sqrt(y))^(3/2) = 36^(3/2) (x sqrt(y))^(3/2):
36^(3/2) (x sqrt(y))^(3/2)
36^(3/2) = 36^(2/2 + 1/2) = 36^(2/2)×sqrt(36):
36^(2/2) sqrt(36) (x sqrt(y))^(3/2)
2/2 = 1
Answer:
36 sqrt(36) (x sqrt(y))^(3/2).
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6. Jordan rounds a number, X, to one decimal place.
The result is 6.3.
Write down the error interval for X
If the approximated number is given as 6.3 Then the error interval of x is 6.24≤x≤6.35
What is Approximation?A value or quantity that is nearly but not exactly correct.
The number is given as x.
So, we have:
x = 6.3
The smallest number that can be approximated to 6.3 is 6.25 (to 1 decimal place), while the largest number is 6.34
Given that there are possibilities of error, the lower and upper bound of the error interval would be:
6.25-0.01≤x≤6.34+0.01
6.24≤x≤6.35
Hence, the error interval of x is 6.24≤x≤6.35
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Oumou has to multiply 67x5 what’s her answer
We can multiply 67 x 5 using distributive property and answer will be 335.
What is the distributive property of multiplication ?
The distributive property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
It is given that we have to multiply 67 x 5.
We can multiply the two numbers using the distributive property.
We know that , the distributive property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
Distributive property is written in form : A × (B + C) = AB + AC
So , 67 x 5 can be written as : 5 × (60 + 7)
or
5 × (60 + 7)
= (5 × 60) + (5 × 7)
= 300 + 35
= 335
Therefore , we can multiply 67 x 5 using distributive property and answer will be 335.
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can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ig
can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ?
Here, in the figure we can see a diagram with 3 lines and few points.
1.Name a line that contains point A is A point is an intersection point of 2 lines that are line "l" and line "n".
2.Name a line that contains point D is D point is an intersection point of 2 lines that are "n" and line "m".
3.What is the another name of line m is line BD, B and D point are on the line "m" so we can say as line BD.
4.what is the another name of line n is line AD, A and D points are on the line "n" so we can say as line AD.
5.Name a point not on line AC is there are two points that are not on line AC is D and E points.
6. Name a point not on line BD is there are three points that are not on line BD is A,C and E points.
7.Name the intersection of AC and DB, B is the intersection of AC and DB.
8. Name the intersection of AD and AC, A is the intersection of AD and AC.
9. Name a point not on line l or line m is point E.
10.Name a point not on line n or line m is point E.
Intersection is nothing but a point where lines intersect is the intersection.
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This is a question from line segments part of geometry.
1. A line that contains point A is line l.
2. A line that contains point D is line n.
3. Another name for line m is line BD.
4. Another name for line n is line AD.
5. A point not on the line AC is the point D.
6. A point not on the line BD is the point A.
7. The intersection point of line AC and line DB is the point B.
8. The intersection point of line AC and line AD is the point A.
9. A point not on the line l or line n is the point E.
10. A point not on the line m or line n is the point D.
Geometry is a branch of mathematics that broadly deals with the measurement, characteristics, and connections of points, lines, angles, surfaces, and solids: the study of the characteristics of given elements that hold true even after being transformed in a certain way.
It is from line segments part of geometry.
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A hexagon has three sides of length (2x+5) in and three sides of length (x-6) in. What is the length of the longest side of the hexagon if the perimeter is 60 in?
Help I'm Being Timed!!
Answer:
varies inversely as √t
Step-by-step explanation:
Answer:
a hexagon has three sides of length (2)+ in and other three side is equal to
the length of longest side
Step-by-step explanation:
Solve. Check for extraneous solutions. x¹/₂-(x-5)¹/₂=2
No extraneous solution to the equation:
The equation is:
[tex]x^{1/2}[/tex] - [tex](x- 5)^{1/2}[/tex] = 2
To know whether the equation has an extraneous solution first we need to find the value of x.
[tex]x^{1/2}[/tex] - 2 = [tex](x - 5)^{1/2}[/tex]
[tex]x^{1/2} - 2[/tex] = [tex](x - 5)^{1/2}[/tex]
Now squaring both sides of the equation we have:
[tex](x^{1/2} - 2)^{2}[/tex] = x - 5
x - 4[tex]x^{1/2}[/tex] + 4 = x -5
[tex]x^{1/2}[/tex] = -9/4
x = 81/16
Now we have to put the value of x in the equation.
[tex](81/16)^{1/2}[/tex] - [tex](81/16 - 5)^{1/2}[/tex] =2
9/4 - 1/4 =2
8/4 = 2
2 =2
Therefore we get to know that there is no extraneous solution to the equation.
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Thomas withdrew $55 from his account and later added $30. What was the overall change in his account balance?
It should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance is -$25.
How to illustrate the information?It should be noted that regarding a bank account, it should be noted that the withdrawal has to do with the amount of money that the person removes from the account.
It should be noted that deposit is an addition to the amount in the account while the withdrawal is the subtraction.
Therefore, should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance will be:
= -$55 + $30
= -$25.
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Which of the following is not viable in order to solve the following systems of equations using Substitution?
The only option that is not viable to solve the systems of equations is:
D. Substitute y = 6/5x - 12 into the first equation
How to Solve Equations?Given the systems of equations,
2x + y = 20 ----> equation 1
6x - 5y = 12 ----> equation 2
In order to solve the system of equations using the substitution method, rewrite 2x + y = 20:
2x + y - 2x = 20 - 2x
y = 20 - 2x
Or
2x = 20 - y
x = 10 - 1/2y
Or
6x - 5y = 12
-5y = -6x + 12
y = -6/5x - 12/5
or
6x = 12 + 5y
x = 2 + 5/6y
Therefore, the only option that is not viable to solve the systems of equations is:
D. Substitute y = 6/5x - 12 into the first equation
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Does the function below represent a linear function, an exponential function, a quadratic function, or none of these?
function----> f(x)=5*2^x
Question 1 options:
linear
exponential
quadratic
none of these
The equation of the function given as (x)= 5 * 2^x is an exponential function
How to determine the function type?The equation of the function is given as
f(x)= 5 * 2^x
An exponential function is represented as
f(x) = a * b^x
Where
Initial value = a
Rate = b
This means that
a = 5
b = 2
Hence, the equation of the function given as (x)= 5 * 2^x is an exponential function
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Solve for t.
4t + 2 + =18
Please help
Answer:
4
Step-by-step explanation:
18 - 2= 16
16/4=4
Use the dropdown menus to complete the definition of a midpoint. please help
image below
given that x is (near, between, or before) a and b, x is the midpoint of segment ab (if or if and only if) ax= (xa, ax,ab,xb)
select the right answers for each
X is between A and B, X is the midpoint of segment AB if and only if
AX = XB.
What is a midpoint?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
We have,
A_____X_____B
Given that X is ___________A and B, X is the midpoint of segment AB____________ AX= ______
We need to fill in the blanks.
X would be in between A and B.
X is a midpoint of segment AB if and only if AX = XB.
Thus,
X is between A and B, X is the midpoint of segment AB if and only if
AX= XB.
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a sequence is defined by f (n) =-4+2n for n is greater than or equal to 1. which of the following statements is the recursive definition of f?
a. f(1)=-2, f(n)=f(n-1) +2
b. f(1)=-4, f(n)=f(n-1) +2n
c. f(1)=-2, f(n)=f(n-1) + (-4)
d.f(1)=-4, f(n)=f(n-1) +2
EXPLAIN WHY
The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
How to determine which of the following statements is the recursive definition of f?The function definition is given as
f(n) = -4 +2n for n > 1
Start by calculating f(2), f(3) and f(4)
So, we have
f(2) = -4 +2(2)
f(2) = 0
f(3) = -4 +2(3)
f(3) = 2
f(4) = -4 +2(4)
f(4) = 4
In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2
So, we have
f(n) = f(n - 1) + 2
Also, we have
f(1) = -4 +2(1)
f(1) = -2
Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2 for n > 2
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Simplify a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
Given,
a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The expression : ( a⁻⁴ / 2 × b² )³
Simplify the expression :
( a⁻⁴ / 2 × b² )³
= a⁻⁴⁽³⁾ / 2³ ˣ b²⁽³⁾
= a⁻¹² / 2³ ˣ b⁶
= a⁻¹² / 8b⁶
Therefore, the simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
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fraction in simplest form. 48 over 64
(5x^2+8x-4)+(7x^2-11x+3) simplify
Describe how the variables in the given equation are related.
p= k q r t / s
k, q, r, t are directly proportional to p and s is inversely proportional to p.
What is inversely proportional ?The inversely proportional property state that two values are opposite to each other. If there will increase in one value or quantity then the another quantity will automatically decrease with the same ratio and if one quantity will decrease then another will increase with that ratio.
Say if x and y are inversely proportional, then mathematically
x ∝ 1 / y
What is Directly proportional ?The directly proportional property state that two values are same to each other. If there will increase in one value or quantity then the another quantity will automatically increase with the same ratio and if one quantity will decrease then another will also decrease with that ratio.
Say if x and y are directly proportional, then mathematically
x ∝ y
In the given equation,
k, q, r, t are directly proportional to p and s is inversely proportional to p.
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What is the product of (p3)(2p2 - 4p)(3p2 - 1)? 6p7 4p4 6p7- 2p5 - 12p5 4p3 6p7 - 12p6 - 2p5 4p4 6p12 - 14p6 4p3
The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.
For multiplication, the rule of exponents to be used is -
aᵇ×aⁿ = aᵇ⁺ⁿ
Rewriting the expression
Product = (p³)(2p² - 4p) (3p² - 1)
Performing multiplication of first two brackets -
Product = (p³ × 2p² - p³ × 4p) (3p² - 1)
Product = (2p⁵ - 4p⁴) (3p² - 1)
Further performing multiplication of product with third bracket -
Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)
Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴
Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
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Answer:
C: 6p7 - 12p6 - 2p5 + 4p4
Step-by-step explanation:
Source: Trust me bro
PLEASE ANSWER!
Simplify the following expression. 7^-5/6 x 7^-7/6
A. 1/14
B. 14
C. 1/49
D. 49
What are the vertex and x-intercepts of the graph of the function below?
y=(x+4)(x+2)
ООС
A. Vertex: (1,-5); Intercepts: x= -4,2
B. Vertex: (1, -9); Intercepts: x= 4,-2
C. Vertex: (-4, 2); Intercepts: x= 3, -3
OD. Vertex: (-3,-1); Intercepts: x = -4,-2
Help very much needed 30 points.
Answer:
1. 32/80 2. 9/3 3. 1/3 4. 12/4 5. 4/1 6. 3/6 or 1/2 7. 21/18 8. 24/15 9. 25/5 10. 7/21
Step-by-step explanation:
good fraction brain
Nick estimates that 50% of his income goes toward living expenses. Of the rest 50% goes to paying for his car and 25% of what is left goes to. his other expenses. IF nick has $300 remaining at the end of the month how much does he earn?
Based on the amount that Nick is left with at the end of the month, the amount he earns is $2,400
What does Nick earn?The amount of $300 that is left is 25% of 50% of Nick's income as the other 75% of the 50% went to paying for the car and other expenses.
25% of 50% is:
= 25% x 50%
= 12.5%
The amount Nick makes per month is:
= Amount remaining / Amount remaining in percentage terms
= 300 / 12.5%
= $2,400
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