The equation of the line that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10 is y = - 2 / 5 x - 11 / 5
How to find the equation of a line?The equation of a line can be represented in various form such as point slope form, slope intercept form and standard form.
Therefore, let's find the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.
Hence, parallel lines have the same slope.
5y = -2x + 10
y = - 2 / 5 x + 2
Therefore, the slope of the line is - 2 / 5.
Let's find the y-intercept using the slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptHence, (2, -3)
-3 = - 2 / 5(2) + b
-3 = - 4 / 5 + b
b = - 3 + 4 /5
b = - 11 / 5
Therefore, the equation of the line is y = - 2 / 5 x - 11 / 5
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The required equation of the line y = - (2/5)x - 11/5 passes through the point (2,-3) and is parallel to the line 2x + 5y = 10.
We have to determine the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10
Parallel lines are known to have the same slope.
Firstly, we have to find its slope by the given line
⇒ 5y = -2x + 10
⇒ y = - (2/5)x + 2
Thus, the slope of the line is - 2/5.
Let the required equation of the line is y - y₁ = m(x -x₁ )
Here x₁ = 3, y₁ = 1 and m = -2/5
y - 1 = (-2/5)(x - 3)
y - 1 = (-2/5)x + 3(-2/5)
y = - (2/5)x - 6/5 +1
y = - (2/5)x - 11/5
Therefore, the required equation of the line is y = - (2/5)x - 11/5.
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Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per
gigabyte. She wants to keep her bill under $70 per month. Write and solve an
inequality which can be used to determine x, the number of gigabytes Mayerlin can
use while staying within her budget.
The inequality can be represented as 55 + 5x < 70
what is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Mayerlin pays a flat cost of $55 per month and $5 per gigabyte.
She wants to keep her bill under $70 per month.
let x be the number of gigabytes Mayerlin can use.
So, the inequality can be represented as
55 + 5x < 70
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Find the value of each variable and the measure of each labeled angle
The 'x' and 'y' variables and the 4 angles are highlighted in the boxes
amber wants to have $300,000
Answer:
i hope i can answer your question
Step-by-step explanation:
Amber wants to have $300,000 so i don't see another number that you can solve on maybe type that first so i can answer please
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
The given expression is equivalent to the third option -19.5b - 6.9. We get this on solving the algebraic expression.
The given expression in the question is
3(-4.5b-2.1) - (6b +0.6)
= -13.5b - 6.3 - 6b - 0.6 (multiplying 3 and -1 respectively with the elements in the bracket)
= -19.5b - 6.9
Therefore we can see that on solving the given algebraic expression we get that it is equivalent to -19.5b - 6.9
Hence the third option which is -19.5b -6.9 is the correct answer.
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Your six year and three month investment of $40,000 at 14% compound interest is worth how much now?
Answer:
price ×time×rate/100 40000×6×14/100
33600
Pls, help me with MATH!!!
The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years is $3,075.00. With a principal of £1,500.00 and an interest rate of 3.5% over a 30-year period, Sarah-Jane will save UK £1,575.00. It is undoubtedly a wise investment because the original UK £1,500 doubled.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
What is the formula for Simple interest?A = P(1 + RT)
A=Final Amount
P = Principal
R = Rate of Interest
T = Time period
Here,
A = $3,075.00
I = A - P = $1,575.00
A = P(1 + rt)
First, converting R percent to r a decimal
r = R/100 = 3.5%/100 = 0.035 per year.
Solving our equation:
A = 1500(1 + (0.035 × 30)) = 3075
A = $3,075.00
$3,075.00 is the total amount accrued from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years (principal plus interest). In a 30-year loan with a £1,500.00 principal and a 3.5% interest rate, Sarah-Jane will save UK £1,575.00. The original UK £1,500 doubled, so it is unquestionably a smart investment.
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What is the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 ?
Enter your answer in the box.
The equation of the line passes through (2, -10) and to parallel to 14x +2y = 6 is 7x + y = 4
In the above question,
The equation of the line = 14x + 2y = 6
2y = 6 - 14x
y = [tex]- \frac{14x - 6}{2}[/tex]
y = -(7x - 3)
y = -7x + 3
The inclination of a line with respect to the horizontal is measured numerically is called as Slope
Slope of the given line = -7
The slope of a line parallel to the given line would be the same as they both are parallel to each other, hence the needed line's slope is also -7
The point through which is passes = (2, -10)
We need to find the equation of the line which passes through (2, -10) and to parallel to 14x +2y = 6
The equation of a line parallel to the given 14 x + 2 y = 6, and passing through the point (2, -10) is
[y - (-10)] = (-7)[x - 2]
y + 10 = -7x + 14
7x + y = 14 - 10
7x + y = 4
Hence, the equation of the line passes through (2, -10) and to parallel to 14x +2y = 6 is 7x + y = 4
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If sin - cos = 0 , then the value of sin^4 + cos^4 is
Answer:
sinθ-cosθ = 0
sinθ= cosθ
sinθ/cosθ = 1
tanθ = 1
Bu tan45 = 1
So,
tanθ=tan45
θ = 45°
sin45 = 1/√2 cos45 = 1/√2
sin⁴θ+cos⁴θ = (1/√2)⁴+(1/√2)⁴
= 1/4+1/4 = 2/4 = 1/2 = 0.5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope this helped you..................
If the first two terms of an arithmetic sequence are 3 and 9, what would be the explicit equation for this sequence?
The explicit equation of the sequence is an = 3 + (n-1)*6
First term = 3
Second term = 9
A series of numbers in mathematics whose each term is always expressed as a, a+d, a+2d, or a+3d. An arithmetic progression is defined as a + (n-1)d, where a is the first term,d is the common difference of the series and n is the number of terms in the sequence
Any two continuous terms in the arithmetic sequence differ by the same number.
Arithmetic sequence is given by an = a + (n-1)d
So, the common difference = 9-3 = 6
a = 3
Substituting the values in the formula we get:
For nth term: an = 3 + (n-1)*6
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In the diagram, M is the midpoint of AB.
Support the following argument for AM = MB by
writing the reason that validates each statement.
A. Definition of midpoint
B. Definition of congruent segments
C. Given information
We know that M is the midpoint of AB.
This means that AM = MB.
Therefore, AM=~MB.
Answer:
It goes
1.) C
2.) A
3.) B
Sandra saves 9% of her salary for retirement. this year her salary was $3,000 more than in the previous year, and she saved $4,050. what was her salary in the previous year?
Answer:
She earned $42,000 in the previous year
Step-by-step explanation:
9% can be rewritten as 0.09
0.09x is 4050
divide both sides by 0.09
0.09x becomes x
4050 becomes 45,000
then we subtract 3,000 from 45,000 to find the previous years salary
I need help finding the value of x for these problem?
ANSWER
No 3. x = 41 degrees
No 4. x = 6.5 degrees
EXPLANATION
Question 3
Note: One of the angles in a right triangle is 90 degrees. As a result, the sum of the other two angles is 90.
That is:
[tex]\begin{gathered} 45+(x+4)=90 \\ x+4=90-45 \\ x=45-4 \\ x=41^0 \end{gathered}[/tex]Question 4
Note: The sum of angles in a triangle is 180
That is:
[tex]\begin{gathered} 31+97+8x=180 \\ 128+8x=180 \\ 8x=180-128 \\ 8x=52 \\ x=\frac{52}{8} \\ x=6.5^0 \end{gathered}[/tex]100 POINTS + BRAINLEIST
Answer:The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases. If MN is the midsegment of trapezoid ABCD, then MN || AB, MN || DC, and MN = (AB + CD).
Step-by-step explanation:
Answer:
MN is 1/2 of DC
Step-by-step explanation:
DC= 44
MN= 22
please solve this with solution thankyou.
The value of the function operation of each one is represented below.
Function OperationTo solve this problem, we have to perform the operation on each one.
f(x) = 2x + 4g(x) = x^2 + 4x + 4h(x) = x^2 - 41) (fg)(x)
[tex](fg)(x) = 2x^3 + 12x^2 + 24x + 16[/tex]
2) (hg)(x)
[tex](hg)(x) = x^4 + 4x3 -16x -16[/tex]
3)
(fh)(2)
[tex](fh)(2) = 0[/tex]
4) (gh)(x)
[tex](gh)(x) = x^4 + 4x^3 - 16x -16[/tex]
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does anyone know how to solve this questions im confused. Thank you so much is you help!
[tex]g(f(\text{x})) = -3\text{x}^2+3[/tex]
[tex]g(f(2)) = -9[/tex]
=======================================================
Explanation:
Let's compute g(f(x))
We do this by starting with the outer function g(x). Then replace every x with f(x). Then plug in the definition of f(x) as shown below.
[tex]g(\text{x}) = \text{x}-1\\\\g(f(\text{x})) = f(\text{x})-1\\\\g(f(\text{x})) = 4-3\text{x}^2-1\\\\g(f(\text{x})) = -3\text{x}^2+3\\\\[/tex]
At this point, we then plug in x = 2 so we can find that...
[tex]g(f(\text{x})) = -3\text{x}^2+3\\\\g(f(2)) = -3(2)^2+3\\\\g(f(2)) = -3(4)+3\\\\g(f(2)) = -12+3\\\\g(f(2)) = -9\\\\[/tex]
Shape T is reflected in the line x = -1 to give shape R.
Shape R is reflected in the line y = -2 to give shape S.
Describe the single transformation that will map shape T to shape S.
Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. The sum of the transformations can be referred to as a single transformation.
How would you describe a single transformation reflection?Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. Every point of a shape will be separated from the line of reflection by the same amount as the reflected point is separated from the line.
There are occasions when a shape is altered in more than one step, such as when a rotation is followed by a reflection. Typically, the sum of the transformations can be referred to as a single transformation.
Enlargements are a particular kind of transformation where the original shape's size is altered by multiplying it by a scale factor to make it bigger or smaller. To employ a center of enlargement, lines must be drawn from the center via the original shape's vertices. They are known as ray lines.
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There's a roughly linear relationship between the number of times a species of
cricket will chirp in one minute and the temperature outside. For a certain
type of cricket, this relationship can be expressed using the formula
T= 0.27c+ 31, where T represents the temperature in degrees Fahrenheit
and c represents the number of times the cricket chirps in one minute. What
is the meaning of the c-value when T = 77?
Answer:
B
Step-by-step explanation:
i had the thing 2 days ago lol
Answer:
Step-by-step explanation:
T = 0.27·c + 31
0.27·c = T - 31
c = (T - 31) / 0.27 = (77 - 31) / 0.27 ≈ 170
Answer:
170 times a minute a cricket chirps at 77° F
What is the constant of proportionality in the equation y=3x, equals, 3, x?
constant of proportionality =equals
, The constant proportionality is 3
What is Proportionality Constant ?
The proportionality constant is the ratio between two variables that varies directly . For directly proportional variables, their ratio is always a constant and this constant is the proportionality constant.
Now, We have the equation is:
y = 3x
To get the constant of proportionality,
we will derive both sides of the equation by x.
y/x = 3x/x
y/x = 3
Hence, The constant proportionality is 3
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Any help can’t get the answer right
Answer:
-2
Step-by-step explanation:
f(x) = 2x, g(x) = x - 4
f(g(3)) = f(-1) = 2(-1) = -2
As the sample size becomes larger, the sampling distribution of the sample mean approaches a.
The sampling distributions reach a normal distribution as sample sizes increase.
What is termed as the normal distribution?The proper term for just a probability bell - shaped curve is the normal distribution.The mean of a normal distribution is zero, and the standard deviation is one. It has a skew of 0 and a kurtosis of 3.Even though all symmetrical distributions are normal, not all normal distributions are symmetrical.Many naturally occurring phenomena resemble the normal distribution.For the given statement in the question-
As sample sizes grow larger, sampling distributions reach a normal distribution.
The mean of the sampling distribution equals the population mean (µ) (with "infinite" numbers of the successive random samples).
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NEED HELP ERGENT!!!
Round
your answer to the nearest tenth of a mile.
Three boats are at sea: Jenny one (J1), Jenny two (J2), and Jenny three (J3). The crew of
J1 can see both J2 and J3. The angle between the line of sight to J2 and the line of sight to
J3 is 45 degrees. If the distance between J1 and J2 is 2 miles and the distance between J1
and J3 is 4 miles, what is the distance between J2 and J3?
The distance between J1 and J2 is 2.94 miles using cosine rule.
What is cosine rule?
Cosine rule relates to the lengths of the sides of a triangle with any of its angles being a cosine angle. With the help of this rule, we can calculate the length of the side of a triangle or can find the measure of the angle between the sides.
cos x = ([tex]b^{2} +c^{2} -a^{2}[/tex])/2bc
x = 45
b = 4
c = 2
to find a
cos 45 = 4(4) +2(2) - [tex]a^{2}[/tex]/2(4)(2)
1/[tex]\sqrt{2}[/tex] = 16 +4 - [tex]a^{2}[/tex]/16
16/[tex]\sqrt{2}[/tex] = 20 - [tex]a^{2}[/tex]
a = 2.94
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2
4x + 1
4
3
6
5
2x + 41
7
What is the value of x?
V
Answer:
x = 20
Step-by-step explanation:
4x + 1 and 2x + 41 are alternate exterior angles and are congruent , then
4x + 1 = 2x + 41 ( subtract 2x from both sides )
2x + 1 = 41 ( subtract 1 from both sides )
2x = 40 ( divide both sides by 2 )
x = 20
10% of the 70 students in the school orchestra are performing a solo at the spring concert. How many students are performing a solo?
Answer:
7 soloists
Step-by-step explanation:
10% is .1 in decimal form
70 x 0.1 = 7 soloists
Answer:
Step-by-step explanation:
The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the totalcost for m months of membership.State the meaning of the slope and y-intercept of this function with respect to the costs associatedwith the gym membership.Show all steps
Given:
The cost of belonging to a gym can be modelled by,
[tex]C\left(m\right)=50m+79.50[/tex]To find:
The slope and the y-intercept
Explanation:
The equation is of the slope-intercept form of the linear equation,
[tex]y=mx+c[/tex]Where m is the slope and c is the y-intercept.
Comparing we get,
[tex]\begin{gathered} m=50 \\ c=79.50 \end{gathered}[/tex]Here, the slope represents the cost per month of membership and the y-intercept represents the fixed initial fee to be given to the gym for joining.
Final answer:
• The slope is 50.
,• The y-intercept is 79.50.
8. For the following function, state the range.
Answer: [tex]y \geq 1[/tex]
Step-by-step explanation:
The range of a function is the set of y-values.
Which of the following numbers are perfect squares?
Select all that apply.
A 27
B 36
C 108
D 121
Answer:
B 36
Step-by-step explanation:
36 = 6×6 = 6^2
6^2 is a perfect square
Solve the formula Aa + By = C for B.
A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas.
What is literal equation?A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v=Dt) and the area of a circle (A=r2). In this part, we resolve straightforward one-variable equations.
Alternatively,
Ax +By = C
Any sign that crosses over equal(=) signs always change
In this case, Ax crosses over to C
By = C - Ax
To eliminate y from By, then
By/y = (C - Ax) /y
y cancel out y on the left side
B = (C - Ax) /y
The complete question is,
Solve for B in the literal equation Ax+By=C
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If you received $175.84 on $314 invested at a rate of 7%, for how long did you invest the principal?
The principal amount was invested for 8 Years.
In the given question, it is stated that when $314 was invested as the Principal amount, it got an Interest of $175.84 at an interest rate of 7%. We have to find out the total period of time the principal amount was kept and got interested in in order to complete the interest amount of $175.84.
To calculate the Interest, we know that the formula for Simple Interest is:
=> S.I. = (P*R*T)/100, where P = Principal amount, R = Rate of Interest, and T is the Time period. Now, putting values in the formula we get:
=> S.I. = (P*R*T)/100
=> 175.84 = (314*7*T)/100
=> T = 17584/2198
=> T = 8
Hence, we get Invested Time for 8 years.
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(root 10 - root 2 )^2
not that bad
goodluck tho :)
1+1+1-1-5-5r-3-3--2-6--4
Step-by-step explanation:
1 + 1 + 1 - 1 - 5 - 5r - 3 - 3 --2 - 6 --4
3 - 1 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4
2 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4
-3 - 5r - 3 - 3 -- 2 - 6 -- 4
-5r - 6 - 3 + 2 - 6 + 4
-5r - 9 + 2 - 6 + 4
-5r - 7 - 6 + 4
-5r -13 + 4
-5r - 9
This is the furthest it can be reduced to if you're not trying to find the value of r.
Hope this helps! :)