The equation of the line is y=x+12.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The points are
(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
We have to Write the equation of the line.
According to given question we have,
Equation of line passing through the point (-3,9) and (-9,3).
Slope of the line=
[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]
⇒y−9=1(x+3)
⇒y-9=x+3
Add 9 on both sides we get,
y=x+12
∴ y=x+12 which is in the form y=mx +c is the required equation.
Therefore, the equation of the line is y=x+12.
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y = x + 12
What is equation of a line?
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.
y-y₁=m(x-x₁)
mm₁=-1
Points (-3,9) and (−9,3).
Slope of the line m = (y₂ - y₁)/(x₂ - x₁)
m = (3-9)/(-9+3)
m = 1
Now equation of line passing through two points
(y - y₁)/(y₂ - y₁) = m*(x - x₁)/(x₂ - x₁)
(y - 9)/(3-9) = 1*(x - 3)/(-9+3)
y - 9 = x + 3
y = x + 12
Therefore, the equation of line is y = x + 12
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A county has 225 acres of vacant land.
Residents voted to turn some of the vacant land
into parks. Now, there are 36% less acres of
vacant land. How many acres of vacant land
does the county have now?
The acres of vacant land that the county have now will be 144 acres.
How to calculate the value?Since 36% has been used, the remaining percentage will be:
= 1 - 36%
= 64%
Therefore, the acres of vacant land that the county has now will be:
= 64% × 225
= 64/100 × 225
= 0.64 × 225
= 144
Therefore, the acres of vacant land that the county have now will be 144 acres.
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The cost of bananas varies directly with the number of pounds bought. If 6 pounds
cost $5.22, find the cost of 3 pounds.
Answer:
$2.61
Step-by-step explanation:
So, We have $5.22 for 6 pounds of Bananas.
If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3
In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100
5.22*100=522
Now we divide
522/2 = 261
Now we divide 261 by 100, since we multiplied by 100 earlier.
261/100 =2.61
So our answer is $2.61 for 3 pounds of bananas .
Hope this helps! ^^
Answer:$2.61 for 3 pounds
Thank for the brainliest
Step-by-step explanation:first you divided $5.22/6 because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61
A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - xo), where x and f(x) are measured in miles. find the rate of change of elevation when x = 2.
The rate of change of elevation is 0.32.
What is the rate of change of elevation?An easy-to-remember equation for finding change in elevation as a decimal is “rise over run,” meaning the rise (the change in vertical distance) divided by the run (the change in horizontal distance).
So the problem wants to ask to calculate the rate of change of the elevation if x=2 in the function f(x) = 0.32x. So base on that, the rate of change of elevations can be get through the formula of slope intercept form and the answer would would 0.32 is the rate of change in disregard of the value of x.
Hence, The rate of change of elevation is 0.32.
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FIND THE TERMS AND SUM OF TERMS:
Answer:
The terms are 2, 6 and 12
The sum is 20
Step-by-step explanation:
n n + 1 n(n+1)
-- ------- ---------
1 2 1 x 2 = 2
2 3 2 x 3 = 6
3 4 3 x 4 = 12
The terms are 2, 6 and 12
The sum is 2 + 6 + 12 = 20
Two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. the equation 2(x 1) = 2x 2 models the paths of the boats. solve for x.
Answer: Hi The Answer is 3 (the third one)
Step-by-step explanation: Am not sure if this is correct am taking the test right now
Answer:
all real numbers
Step-by-step explanation:
Florida
Esearchers followed 803 patients, of whom 398 ended up getting surgery. after two years, of those who had surgery, 63% percent said they had a major improvement in their condition, compared with 29% among those who received nonsurgical treatment. a. what is the probability that a patient had surgery and experienced a major improvement in his or her condition? b. what is the probability that a patient received nonsurgical treatment and experience a major improvement in his or her condition?
The required probability that a patient had surgery and experienced a major improvement 31% and that a patient received nonsurgical treatment 14.5%.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Number of patients who got surgery = 398,
63% of percent said they had a major improvement in their condition,
= 0.63 * 398 ≈ 250
29% among those who received nonsurgical treatment,
= 0.29 * (803 - 398)
= 0.29 * 405
≈ 117
Now,
The probability that a patient had surgery and experienced a major improvement in his or her condition.
= 250 / 803
= 31%
The probability that a patient received nonsurgical treatment and experienced an improvement in his or her condition.
= 117 / 803
= 14.5%
Thus, the required probability is 31% and 14.5%.
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The temperature at noon is 75 degrees. The temperature drops 3 degrees every half hour. What is the temperature at 4 p.m.
Answer:51 degrees
Step-by-step explanation:
At noon the temperature is 75 degrees
the temperature drops 3 degrees every half hour.
First solve for time elapsed between noon and 4, which is 4 hours.
Next, we can change our rate to be in terms of full hours instead of half hours using the fact that 1 hr = 2 half hours, so the temperature drops 6 degrees every hour.
Four hours have elapsed so multiply 6*4 = 24 degrees and then subtract it from the starting 75
75 - 24 = 51.
a G.P has 6 terms .if the 3rd term and the 4th terms are 28 and -56 respectively.find the common ratio,the first term ,and the sum of the G.P
Answer:
Hello,
Step-by-step explanation:
[tex]u_2=u_1*r\\u_3=u_1*r^2\\u_4=u_1*r^3\\\\\dfrac{u_4}{u_3} =r=\dfrac{-56}{28} =\boxed{-2}\\\\u_1=\dfrac{u_3}{r^2} =\dfrac{28}{(-2)^2} =\dfrac{28}{4}=\boxed {7}\\\\\\\displaystyle\ s=\sum_{i=1}^6\ u_i\\\\=u_1*\sum_{i=1}^6\ r^{i-1}\\\\=7*\dfrac{(-2)^6-1}{-2-1} \\\\=-7*\dfrac{65}{3} \\\\\\\boxed{s=-\dfrac{455}{3} }\\[/tex]
WILL MARK BRAINLIEST HURRY PLSSSS
Answer:
2.667
Step-by-step explanation:
the thousandths place is the third place after the decimal point, going
0.123
1 is the tenths
2 is the hundredths
3 is the thousands
all you have to do is divide 4 by 15 to get 2.66666667
rounded to the thousands the answer is about 2.667
Two printing presses, working together, can complete a job in 2 hours. If one press
requires 6 hours to do the job alone, how many hours would the second press need to
complete the job alone?
The number of hours needed for the second press to complete the job is 3 hours.
What is an equation?An equation represents the relationship of two expressions on either side of the sign
Given that together they can complete a job in 2 hours and one takes 6 hours to complete the work alone.
If we let x = amount of time required for the second press to complete the job alone
We can write as:
Second press work = 1/x of the job per hour.
First press work = 1/6 of the job per hour.
Together work = 1/2 of the job per hour.
We can write the equation as:
1/6 + 1/x = 1/2
1/x = 1/2 - 1/6
1/x = (3 - 1)/6
1/x = 2/6
1/x = 1/3
x = 3
Thus number of hours needed for the second press to complete the job is 3 hours.
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A sample of n = 100 scores has a mean of 5. a second sample has n = 25 scores and m = 7. if the two samples are combined, the sample mean for the combined sample will be __________.
A sample of n = 100 scores has a mean of 5. A second sample has n = 25 scores and m = 7. if the two samples are combined, the sample mean for the combined sample will be 5.4.
We are given the sample mean of n = 100, is 5. Therefore, the sum of 100 observations is 100 x 5 = 500
The sample mean of n = 25, is 7. Therefore, the sum of 25 observations is
25 x 7 = 175
The sum of two samples is 500 + 175 = 675.
And the sum of two sample size is 100 + 25 = 125
Now, the combined mean is:
675125=5.4
What is mean?
A dataset's mean(also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.
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Which equation correctly represents how the total mechanical energy (ME) of
a system relates to its kinetic energy (KE) and gravitational potential energy
(GPE)?
The accurately captures a system's gravitational potential energy:
ME = KE + GPE.
What is gravitational potential energy?Gravitational potential energy is the energy that an object possesses or acquires as a result of a change in its position when it is in a gravitational field. In layman's terms, gravitational potential energy is energy that is tied to gravitational force or gravity.
What is the difference between gravitational kinetic energy and potential energy?The energy held in an object due to its height above the ground is known as gravitational potential energy. It is determined by the object's mass, the gravitational acceleration caused by the Earth, and the object's height. Kinetic energy is the energy that an object possesses as a result of its motion.
According to the given data:An object's mechanical energy is equal to the sum of its kinetic energy and potential energy. If ME is mechanical energy and KE is kinetic energy, then PE is its potential energy.
ME = PE + KE
KE = (1/2) mv^2
PE = ME - KE
PE = ME - 1/2(mv²)
PE = ME - 1/2(mv²)
PE = ME - KE
ME = KE + GPE
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Answer:
B
Step-by-step explanation:
ME equals the sum of KE and GPE
rewrite (156 + 243) using factoring
Answer:
399
Step-by-step explanation:
Factor the polynomial, and that will give you 399.
Using factor (156 + 243), can be rewritten as 3.(52+81).
What is factor?Factor is a number that devides any other number and does not leave any remainder.
The given term is,
(156 + 243)
The factor of 156 = 2×2×3×13
The factor of 243 = 3×3×3×3×3
The common factor is 3,
So (156 + 243) can be rewritten as,
3(2×2×13+3×3×3×3)= 3.(52+81).
So, the required term is 3.(52+81).
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5. Analyze and Persevere A recipe calls for 0.5 cup of milk. Express the number of cups of milk as a fraction.
The number of cups of milk when represented as fraction is expressed as 1/2 cup.
Given a recipe indicates 0.5 cup of milk.
A numerical value that designates a portion of a whole is used to represent fractions.A fraction is a part or portion that is taken from the total, which might be any number, a specific sum, or an item.
To convert it into fraction, we first need to remove the decimal.
5/10
when 5 is divided by 10 we get 0.5, hence we have removed the decimal and converted it into its orignal form.
Now multiply and divide by 5.
= 5 × 5/10 × 5
= 1/2
we get the fraction part as 1/2
Hence 0.5 cup of milk represent 1/2 cup of milk as a fraction.
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Find the unknown angle measure
5 ➗ 1/7
Draw a model that represents the division expression
We have to draw the model for 5 divide 1/7 . In order to draw the model we use below steps.
Draw 1/7 boxes to represent 1/7 groups.
Assume 5 as the number which represents the total of these 1/7 groups.
Put a question mark at the first box.
Attached is the model to represents 5 divide 1/ 7 .
5/(1/7)
5*7
35
In the question mark we should put 35.
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Using heron's formula the sides of the tringleare 70cm,80cm and 90cm.find its area(use root 5=2.23)
The area of the triangle is 1200√5 cm².
Given that, the sides of the triangle are 70cm,80cm and 90cm.
We need to find the area of a triangle using Heron's formula.
What is Heron's formula?As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as 's' is determined using the below-given formula:
Area of triangle = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2
Now, semi perimeter = (70+80+90)/2=120
Area of triangle=√120(120-70)(120-80)(120-90)
=√120×50×40×30
=√40×3×2×25×40×30
=40×5√3×2×3×2×5
=40×5×3×2√5
=1200√5 cm²
Therefore, the area of the triangle is 1200√5 cm².
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Help asap I need to get this done asap and I’m struggling with it and I’d appreciate help and I’ll give you brainliest
Answer:
x = 10
Step-by-step explanation:
the angle is equally bisected from the middle so
3x - 3 = 4x - 13
13 - 3 = 4x - 3x
x = 10
<FGH = 3(10) - 3 = 27
< HGI = 4(10) - 13 = 27
<FGI = <FGH + <HGI = 27 + 27 = 54
Order 3/8, 3/7, and 3/9 from least to greatest withour writing equivalent fractions with a common denomanator. explain your strategy.
Answer:
3/9 3/8 3/7
Step-by-step explanation:
The higher the denominator, the higher number of times a number will be divided which means, the number will become smaller.
ANSWER PLS PLS PLS PLS PS I NEED HELP WITH THE TEST REACH OU TO ME
Part(A) Leslie's initial investment was $500 and
Part(B) The quarterly interest rate is 10.4 %
What is compound interest?
Compound interest is the interest calculated on the principal amount , which also considers all the accumulated interest of previous periods of deposit or loan.
If P is the principal amount and rate of compound interest is r then after t years of time , the present amount (if the interest is compounded annually) will be = P(1+(r/100))^n
If the interest is compounded quarterly, then the present amount be A
Where A = [tex]P (1+\frac{r/4}{100} )^{4t}[/tex]
Given that Leslie invests in a bank that earns interest quarterly , and account balance after t years is given as 500(1.026)^(4t)
A= [tex]P (1+\frac{r/4}{100} )^{4t} = 500(1.026)^{4t\\[/tex]
Comparing both sides we get P = 500
And 1+(r/400)=1.026
(r/400)=1.026-1
(r/400)=.026
r=400(0.26) = 10.4 %
Therefore , Leslie's initial investment was $500 and the quarterly interest rate is 10.4 %
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which statements are true regarding the sequence below? check all that apply. 10/3,4,24/5,144/25,...
Answer:
A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.
C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1
What is sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given:
10/3, 4, 24/5, 144/25, ...
From the above sequence we can generate the formula,
f (x) = 10/3
Also, for f(x+1) we can have
x=1,
f(1)= 10/3
f(2)= 4
So, f(x + 1) = 6/5(f(x))
Step-by-step explanation:
Express the interval using inequality notation.
(-∞, -11] U l-8, ∞)
The inequality notation for the given interval is -∞ < x ≤ -11 and -8 ≤ x < ∞
Disclaimer:
Considering the given interval as (-∞, -11] ∪ [-8, ∞).
Given interval is a union of two intervals.
The first interval denotes the set of all real numbers which are less than or equal to -11.
And the second interval denotes the set of all real numbers which are greater than or equal to -8.
The inequalities can be written as below:
(-∞, -11] ⇒ x ≤ -11 (or) -∞ < x ≤ -11
[-8, ∞) ⇒ x ≥ -8 (or) -8 ≤ x < ∞
And there is a union symbol between these two intervals.
So, x should satisfy both inequalities.
x ≤ -11 and x ≥ -8
or the above can be written as
-∞ < x ≤ -11 and -8 ≤ x < ∞
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Tres canastas tienen 575 manzanas. La primera canasta contiene 10 manzanas más que el segundo y 15 más que el tercero. ¿Cuántas manzanas hay en cada canasta? Jpancho
Step-by-step explanation:
what??? I don't understand what are you saying?????? please speak english :(
i wish you could help you but i don't know what you're saying
23
Which answer choice represents 4 as a mixed number?
5-/1/2
51-1
CT
3/4
61/1
Answer:
Its C: 5 3/4
Step-by-step explanation:
1: First we figure out how many times 4 goes into 23
4 goes into 23 5 times. So our whole number will be 5
2: Now, we put our remainder on the top and keep the denominator the same
Making the fraction - 3/4
5¾
28x-2=100 solve for x
Answer:
3.64
Step-by-step explanation:
collect like terms
divide both sides by x coefficient
Answer:
x=51/14
Step-by-step explanation:
28x-2=100
+2. +2
28x=98
28x/28=102/28
×=51/14
i am a 5-digit numaeral for five raised to the sixth power.what number am i?
Answer: 99,999
Step-by-step explanation:
what is equivalent to -28x2 + 35x?
(35x) + (-56) this is an equivalent equation.
Answer:
7x(-4x+5)
Multiplying: -56+35x
Step-by-step explanation:
[tex]\mathrm{Factor\:assuming\:x\ge-\\\infty}\\\:a^{b+c}=a^ba^c\\x^2 = xx\\-28xx+35x\\-7 \times 4xx + 7 \times 5x\\=7x\left(-4x+5\right)[/tex]
The only reason I had to assume x was any negative number was so that the absolute value did not matter in this instance, therefore making x become a negative number.
The other result, however, came from this:
[tex]-28\cdot \:2=-56\\=-56+35x[/tex]
Inform me of any concerns. Hope this helps.
Solve the systems of equation 4x + y = 10 3x - 2y = 13
The solution to the system of equation is (7/5, 22/5)
System of equationGiven the system of equation as shown below;
4x + y = 10 * 2
3x - 2y = 13 * 1
_____________
8x + 2y = 20
3x - 2y = 13
Subtract
8x - 3x = 20 - 13
5x = 7
x = 7/5
Substitute the value of x into any of the equation
4x + y = 10
4(7/5) + y = 10
28/5 + y = 10
y = 10 - 28/5
y = 22/5
Hence the solution to the system of equation is (7/5, 22/5)
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Find the lowest common denominator for the following set of fractions: 4/21, 3/7, 4/9
The lowest common denominator for 4/21, 3/7, 4/9 is 63.
Lowest common denominator is the lowest number that is divisible by the denominators of the set of fractions.
Step 1: we will write down the prime factors of all the denominators.
[tex]21=7^{1} *3^{1}[/tex]
[tex]7=7^{1}[/tex]
[tex]9=3*3=3^{2}[/tex]
Step 2 : write down highest power of each prime number.
[tex]7^{1} ,3^{2}[/tex]
Step 3 : Multiply the values
7x9=63
Therefore , The lowest common denominator for 4/21, 3/7, 4/9 is 63.
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Find a and b so that f(x) is continuous for all values of x f(x)={x^2-4/x-2 if x<2 ax^2-bx+3 if 2<=x<3 2x-a+b if x>=3
The values a = 1/3 and b = 1/6.
Given function is, f(x) =
[tex]\frac{x^2-4}{x-2}\ \ \ if\ x < 2 \\ax^2-bx+3 \ \ \ if\ 2\leq x < 3\\2x-a+b\ \ \ if\ x\geq 3[/tex]
The interval in which the function is defined is broke down into three. They are: x<2, 2≤x<3 and x≥3.
Now the function [tex]\frac{x^2-4}{x-2}[/tex] is continuous except at x = 2. But this function is defined in the interval x>2. The other two function are defined as polynomial, so are continuous any way.
So for the whole function f(x) to be continuous, we need to check the continuity at x = 2, x = 3.
When x = 2, [tex]\frac{x^2-4}{x-2}[/tex] =[tex]\frac{(x+2)(x-2)}{x-2}=x+2 = 4[/tex] and [tex]ax^2-bx+3[/tex] = 4a-2b+3
⇒ 4a-2b+3 = 4
⇒4a- 2b-1 = 0, for the function to be continuous at x = 2.
When x = 3, [tex]ax^2-bx+3[/tex] = 9a-3b+3 and 2x-a+b = 6-a+b
⇒ 9a-3b+3 = 6-a+b
⇒ 10a -2b-3 = 0, for the function to be continuous at x = 3.
On solving 4a-2b-1 = 0 and 10a -2b-3 = 0 by subtracting the two,
we get, -6a+2 = 0
⇒ a = 1/3 and therefore, b = 1/6
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