Find a point-slope form for the line with slope 1/2 and passing through the point (-1,-4)
The linear equation with the given slope in the slope-point form is:
y = (1/2)*(x + 1) + 4
How to find the equation for the slope?
We know that for a line with a slope m and a point (a, b), the point-slope form of the line is written as:
y = m*(x - a) + b
In this case, we know that our line has a slope of 1/2 and it passes through the point (-1, 4), so we can replace this on the above formula to get:
y = (1/2)*(x + 1) + 4
This is the linear equation in the point-slope form.
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What is the slope of the line that passes through the points (8, 2) and (10, 2)? Write
your answer in simplest form.
Answer:
0
Step-by-step explanation:
The y-coordinates are the same, so the line is horizontal. Therefore, the slope is zero.
Please help I was sick and missed out on class.Thank you
What was the question? or was this only meant for your classmates?
Are M, N, and O collinear? If so, name the line on which they lie.
Answer: MO
Step-by-step explanation:
A system contains two or more linear equations that can be solved or graphed together at once.
True
False
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
A system contains two or more linear equations that can be solved or graphed together at once.
This statement is true.
For example,
The two linear equations can be:
ax + by = c ____(1)
dx + ey = F _____(2)
We can solve this equation using the substitution method or elimination method.
We can find the point of intersection.
And we can solve and graph together at once.
Thus,
The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
How to determine true statements about the circle?Given: the equation is x²+y²–2x–8 = 0
In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
using the completing square method on the given equation:
x²+y²–2x–8 = 0
x²-2x + (-1)² + y² + (0)²= 8 + (-1)²
(x-1)² + (y-0)² = 9
(x-1)² + (y-0)² = 3²
Thus, the center is (0, 1) and the radius is 3
Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
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(((20 POINTS)))
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box
Answer:
4.7 cm
Step-by-step explanation:
what is the slope of the line that passes thru (7,-6) and (6,-6)
The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.
Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.
Let the slope of the line joining A (7,-6) and B(6,-6) be m.
We know that the slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line
= (6-7) / (-6+6)
= -1 / 0
= undefined
Since the slope is undefined we can say that the straight line is parallel to the y axis.
we know that tan 90° = ∞
So any line parallel to this line will have the same slope as the y axis.
Hence the slope of the given line is undefined or infinity.
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Which graph shows the solution to this system of linear inequalities?
y> -2x+2
y<2x-1
The portion of the graph which does not contain (0, 0) is shaded.
What are Linear Inequalities?
When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Given the inequalities :
y ≥>2x + 1
y ≤<2x - 2
From y > 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y > 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 > 2(0) + 1
0 >0 + 1
0 >1
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
From : y < 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y < 2x - 2
Graph the line y < 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y < 2x - 2:
0 < 2(0) - 2
0 < 0 - 2
0 < - 2
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
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Solve the following linear equation and simplify your answer.
8z−6=−2(−4z+3)
Answer:
Step-by-step explanation:
8z-6=-2(-4+3)
8z-6=8z-6
on transposing,
8z-8z-6+6=0
Has slope of 2 and passes through (-2, 1) write equation in point slope form of the line that passes through the given point and has the given slope. write the equation in slope intercept form.
Slope = m = 2
y = mx + b
y = 2x + b
Plug in (-2, 1) to find b
1 = 2(-2) + b
b = 5
y = 2x + 5
The telephone company offers two types of service. With plan A, you can make an unlimited number of local calls for $50 per month plus a $25 plan activation fee. With plan B you pay $25 monthly plus $50 activation fee
Y=mx+b form please
Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:
Plan A: Y = 50x + 25Plan B: Y = 25x + 50.What is the slope intercept equation?The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.
Generally, the formula y = mx + b depicts the slope intercept equation with the following values:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Plan A Plan B
Fixed cost (b) $25 $50
Variable cost (m) 50 25
x = monthly 12 12
y = the total cost for the period
Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.
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Write an equivalent expression for 11(9a + 3b)
The equivalent expression for 11(9a+3b) is 33(3a+b)
How should an equivalent be written?
The numerator and denominator must be multiplied or divided by the same number when writing equivalent fractions. This explains why these fractions have the same value when they are simplified.
How does math equivalent work?
We need to multiply the denominator of 7 by a number that will give us 21 in order to obtain equivalent fractions, which requires multiplying both the numerator and the denominator by the same number. We may find an equal fraction by multiplying the numerator and denominator by 3, so 3 times 7 gives us 21.
Given expression: 11(9a+3b)
Take 3 outside from the expression, we get,
= 33(3a+b), which is called the equivalent expression
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To solve we must expand the terms and then simplify and finally multiply.
¿What are equivalent expressions?The expressions are two algebraic expressions which are equivalent when they both take the same numerical value, for any value of the domain of each of the variables.
Solving the problem:11 (9a + 3b)11 × 9a + 11 × 3b99a + 11 × 3b99a + 33bSo the Result of the Expression is 99a + 33b
¡Hope this helped!
Brainliest if correct 5 points
math
The sum of two numbers is 36. Their difference is 4. Determine the two unknown numbers.
(NOTE: Show answer in the following format # and #. If not entered in this format, will be scor
incorrect.)
Enter answer:
Answer:
One number is 16 and the other number is 20
Step-by-step explanation:
Let x = one number
Let y = the other number
x + y = 36
x - y = 4 Or x = 4 + y
Substitue in 4 + y for x in the first equaion
4 + y + y = 36 Combine like terms
4 + 2y = 36 Subtract 4 from both sides
2y = 32 Divide both sides by 2
y = 16
Substitute 16 for y in either of the orginal equaions
x + y = 36
x + 16 = 36 Subtract 16 from both sides
x = 20
Studies show that the minimum half-life of
Diazepam is 20 hours.
Use the following to construct a function
that will model the minimum amount of
Diazepam left in the body after an initial
dose of 35 mg.
Q(t) = Pert
Where Q(t) describes the amount of
Diazepam left in the body after t hours
following an initial dose of P mg.
1. Q(t) =
2. How long (in hours) will it take for the
amount of Diazepam left in the body to
reach 7 mg?
1. After constructing the function according to the question, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex].
2. It will take 50 hours for the amount of Diazepam left in the body to reach 7 mg.
What is a function?
Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function of the domain and codomain, respectively. Examples include f(x) = x/2 ("f of x equals x split by 2") ("f of x equals x divided by 2") Every input "x" has a single output "x/2," which makes it a function: • f(2) = 1.
Solution explained:
According to the question,
Q(t) = [tex]Pe^{rt}[/tex]
The half-life of Diazepam is 20 hours = t
Q(0) = p = 35 { the initial value}
Q(20) = [tex]35e^{20r} = \frac{1}{2} X 35[/tex]
= [tex]e^{20r} = \frac{1}{2}[/tex]
= [tex]20r = -ln2[/tex]
= [tex]r = \frac{-ln2}{20}[/tex]
Therefore, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex]
Now, Let
Q(t) = 7
[tex]35e^{\frac{-ln2}{20}t}[/tex] = 7
[tex]e^{\frac{-ln2}{20}t} = \frac{1}{5}[/tex]
[tex]{\frac{-ln2}{20}t} = -ln5[/tex]
After calculating,
t = 50 (hours)
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Which point is the midpoint of AB
If 125 kg of food is sufficient for 30 soldiers for 6 days, how long will the food last for 45 soldiers?
Answer:
30 = 6
45 = x
cross multiply
30x = 45*6
30x = 270
divide both sides by
30x/30 = 270/30
X = 9
9-6 = 3 days
Question 3
Rearrange the formula 5√x + y = z to make x the subject
Answer:
x = [tex](\frac{z-y}{5}) ^{2}[/tex]
Step-by-step explanation:
5[tex]\sqrt{x}[/tex] + y = z ( subtract y from both sides )
5[tex]\sqrt{x}[/tex] = z - y ( divide both sides by 5 )
[tex]\sqrt{x}[/tex] = [tex]\frac{z-y}{5}[/tex] ( square both sides to clear the radical )
([tex]\sqrt{x}[/tex] )² = [tex](\frac{z-y}{5}) ^{2}[/tex]
x = [tex](\frac{z-y}{5}) ^{2}[/tex]
(a²-8a26) ÷ (a + 2) synthetic division
Value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.
As given in the question,
Given expression is equal to,
(a²- 8a - 26) ÷ (a + 2)
Simplify the given expression using synthetic division is shown in the attached file,
Another way of division,
(a²- 8a - 26)
= a² -10a + 2a -20 -6
= a (a -10) + 2( a - 10) -6
= ( a + 2 )( a - 10 ) - 6
Quotient of the given division is equal to ( a - 10 )
Remainder of the given division is equal to -6
Therefore, value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.
The complete question is :
Evaluate the given expression using synthetic division :
(a²- 8a - 26) ÷ (a + 2)
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Factor -4 out of -8+20 factored expression
Factoring -4 out of -8+20 factored expression is -4(2 + 5).
What is a factor?Factor expressions, also known as factoring, refer to the process of rewriting an expression as the product of factors. 3x + 12y, for example, can be factored into a simple expression of 3 (x + 4y). Calculations become easier in this manner. The terms 3 and (x + 4y) are referred to as factors.
To factor a given expression goes thus:
Each term should be written as the prime factorization.
Determine the factors that all of the terms share.
Multiply those common variables.
In this case, factoring 4 out of -8+20 factored expression is -4(2 + 5).
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what - (-7/12) = a negitive number
Answer:
nu tg hi yum
Step-by-step explanation:
help pls, i’ll mark brainliest!!
Answer: x = 9.; B=4
Step-by-step explanation:
AABC = AKLM
AB=LK
8=28 — b= 4
LC=LM
27=3x — x=9
Congruent triangles correspond to equal angles and sides
Answer:
x=11
t=6
Step-by-step explanation:
angle M=angle C
3x=33
/3. /3
x=11
Side AB= Side KL
18=3t
/3. /3
6=t
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Write the phrase as an expression. Then evaluate when y=20.
3 less than the quotient of a number y and 4
write the Expression:
The value of 3 less than the quotient of a number y and 4 when y is 20 is 2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
The expression less than the quotient of a number y and 4 will be:
y/4 - 3
When y is 20, the value will be:
y/4 - 3
20/4 - 3
5 - 3
= 2
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students were asked which night they planned on attending the book fair. the results of the survey are shown in the table.
monday= 55 students
tuesday= 80 students
wednesday= 70 students
thursday= 112 students
friday= 65 students
20% of the students who planned to attend on Wednesday attended on Thursday instead. 25% of the students who planned to attend on Thursday attended on Wednesday instead. which day, Wednesday or Thursday, had a greater actual attendance? by how many students?
The day with greater actual attendance is Thursday with 98 students
How to determine the day that had a greater actual attendance?
A percentage is defined as the ratio that can be expressed as a fraction of 100
Given:
Expected numbers: Wednesday= 70 students andThursday= 112 students
20% of Wednesday = 20/100 x 70 = 14 students. That is 14 students are absent on Wednesday but attended on Thursday instead. This means 56 (70 -14) students scheduled for Wednesday attended.
25% of the students who planned to attend on Thursday attended on Wednesday instead:
25% of Thursday = 25/100 x 112 = 28 students. This means 84 students scheduled for Thursday attended
Actual Wednesday attendance = 56 + 28 = 84 students
Actual Thursday attendance = 14 + 84 = 98 students
Therefore, Thursday had a greater actual attendance with 98 students
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PLEASE HELP I WILL GIVE BRAINLIEST IF ANSWERED QUICKLY
The compound expression (a⁵ · a ÷ a⁻³)⁻¹ is equivalent to the power a⁻⁹.
How to simplify a power expression by algebraic properties
In this problem we find a compound expression formed by several powers of equal base that must be simplified in a single power with the same base. This can be done by using algebra properties related to powers. First, write the given expression:
(a⁵ · a ÷ a⁻³)⁻¹
Second, multiply the powers of equal base:
(a⁵⁺¹ ÷ a⁻³)⁻¹
(a⁶ ÷ a⁻³)⁻¹
Third, by definition of division and the power of a power:
[a⁶ · (a⁻³)⁻¹]⁻¹
(a⁶ · a³)⁻¹
Fourth, use the multiplication of power of same base:
(a⁶⁺³)⁻¹
(a⁹)⁻¹
Fifth, use the property of a power of a power once again:
a⁻⁹
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please help me solve this question !
The solution of the function is x = 12
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.
Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB
6cos(5x) = 3
divide both sides by 6, we have
cos(5x) = 3/6
cos(5x) = 0.5
taking the anti cosine of both sides
5x = Arc cos 0.5
5x = 60
x = 60/5
x = 12°
In conclusion, the value of x = 12°
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The population of a pigeons in a city is
7000 and is growing exponentially at 19%
per year. Write a function to represent the
population of pigeons after t years, where
the quarterly rate of change can be found
from a constant in the function. Round all
coefficients in the function to four
decimal places. Also, determine the
percentage rate of change per quarter, to
the nearest hundredth of a percent.
Answer: p(t) = 100×1.0153^(12t)
1.53% per month
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Step-by-step explanation:
Estimate the difference of 25.92 - 5 4/10
Answer: 20 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
First of all, 5 [tex]\frac{4}{10}[/tex] = 5.4
Remember, 1/10 = 0.1, 2/10 = 0.2, and so on.
This means we can change the equation to 25.92 - 5.4, which gives us 20.52.
This is close to 20.50, which is equivalent to 20 [tex]\frac{5}{10}[/tex], which is equivalent to 20 [tex]\frac{1}{2}[/tex].
Find a polynomiat of degree n that has only the given zero(s). (There are many correct answers.)
x = -1, 3, 2, 4; n = 5
The polynomial function for the given zeros is x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72
Polynomial function:
An expressions that may contain variables of varying degrees, non-zero leading coefficients, positive exponents, and constants is known as polynomial function.
Given,
Here we have the value of zeros as x = -1, 3, 2, 4 and n = 5.
Now, we have to find the polynomial function from it.
Let us consider if a polynomial function f(x) has zeros x = -1, x = 3, x = 2, and x = 4, then it has factors
=> (x - 1)³ (x + 3)² (x +2) (x + 4)
Here there are four factor, in these polynomial so it can be Quintic Function.
Now, we have to expand this one to get the resulting polynomial,
=> x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72
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