Answer:
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]2x-3y = 9[/tex]
We have to convert the equation in slope-intercept form. The slope-intercept form is given by:
[tex]y= mx+b[/tex]
Adding 3y on both sides and subtracting 9 from both sides
[tex]2x-3y+3y-9 = 9+3y-9\\2x-9 = 3y\\3y = 2x-9[/tex]
Dividing whole equation by 3
[tex]\frac{3y}{3} = \frac{2x-9}{3}\\y = \frac{2}{3}x - \frac{9}{3}\\y = \frac{2}{3}x-3[/tex]
Let m be the slope of given line then
m = 2/3
Let m1 be the slope of line parallel to given line. Slopes of two parallel lines is equal that means:
m = m1 = 2/3
The equation of line will be:
[tex]y = m_1x +b\\y = \frac{2}{3}x+b[/tex]
Putting the point (6,7) in equation
[tex]7 = \frac{2}{3}(6) +b\\7 = 2(2) +b\\7 = 4+b\\b = 7-4\\b = 3[/tex]
Putting the value of b
[tex]y = \frac{2}{3}x+3[/tex]
Hence,
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
If you have 3.15 pieces of chocolate and you give 1.6 pieces to your friend how many pieces of chocolate do you have left?
Answer:
1.55
Step-by-step explanation:
A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(t)=−0.3t2+30t+0.2 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t)=90000t+100, plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?a. Between 130 and 140 days b. Between 120 and 130 days
Answer:
The correct option is;
Between 40 and 50 days
Step-by-step explanation:
The number of seeds that are produced by a plant maturing at age t, S(t), is given as follows;
S(t) = -0.3·t² + 30·t + 0.2
The proportion of plants maturing at age (t) in the plants to be engineered by the geneticist P(t) = 90000/(t + 100)
The number of seeds produced by the plants = S(t) × P(t) = (-0.3·t² + 30·t + 0.2)×(90000/(t + 100))
To find the maximum number of seeds, we differentiate using an online tool, and equate to zero to get;
d((-0.3·t² + 30·t + 0.2)×(90000/(t + 100)))/dt = (-27000·t² - 5400000·t + 269982000)/(t + 100)² = 0
(-27000·t² - 5400000·t + 269982000)/(t + 100)² = 27000(t - 41.419)(t + 241.419)/(t + 100)² = 0
t = 41.419 or t = -241.419
Therefore, in order to maximize the production of seed of the crops of the farmer, the geneticist should select between 40 and 50 days.
Multiple Choice
What are the equivalent fraction and decimal for 25%?
A. one over twenty-fiveand 0.25
B. twenty-five over twenty-fiveand 4
C. one-fourthand 0.25
D. three-fourthsand 0.4
If a=1, b = 2 and c=-3, find the value of 4a3b2
Answer:
48
Step-by-step explanation:
(4*1)(3*2)*2
4*6*2
48
Wildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in a 16-square-mile area of the forest. In another part of the forest, conservationists counted 117 deer in a 13-square-mile area. Yet a third conservationist counted 216 deer in a 24-square-mile plot of the forest. Do conservationists need to be worried? a. Why does it matter if the deer population is not constant in a certain area of the National Forest? b. What is the population density of deer per square mile? The unit rate of deer per 1 square mile is _______. Constant of Proportionality: Explain the meaning of the constant of proportionality in this problem: c. Use the unit rate of deer per square mile (or 푦 푥 ) to determine how many deer there are for every 207 square miles. d. Use the unit rate to determine the number of square miles in which you would find 486 deer.
Answer
9 deer per square- mile
Step-by-step explanation:.
Whats the slope ?.please help me
Answer:
The slope is -3.
Answer me plzzzz fast ASAP
Answer:
this is payback for what you did here
Step-by-step explanation:
a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an inital speed of 120 feet per second. which equation correctly models the balls height as a function of time
Answer:
An equation that correctly models the ball's height as a function of time is:
h (t) = - 16t ^ 2 + 130t + 2
Step-by-step explanation:
i hope this helps !
Answer:
h(t) = -16t^2 + 120t + 2
Step-by-step explanation:
The perimeter of rhombus EFGH is 48 cm and the measure of FEJ=60°. (Please help)
Answer:
Hmmmmmmmmm I donno please help
What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches?
Use 3.14 for π. Round your answer to the nearest hundredth.
Answer:
V≈56.55in³
Step-by-step explanation:
Answer:
56.55
Step-by-step explanation:
just took the test dattebayo.
Polygon R and polygon S are similar. The perimeter of polygon R is 72 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 6 cm, what is the length of the corresponding side in polygon R?
Answer:
the answere is 10
Step-by-step explanation:
help what goes where? correct answer only pls :)
Answer:
2(3 + w) = 6 + 2w
2(1 + w) = 2 + 2w
3(2 + w) = 6 + 3w
6(1 + w) = 6 + 6w
Step-by-step explanation:
2 x 3 = 6 and 2 x w = 2w: Therefore your answer is 6 + 2w
2 x 1 = 2 and 2 x w = 2w: Therefore your answer is 2 + 2w
3 x 2 = 6 and 3 x w = 3w: Therefore your answer is 6 + 3w
6 x 1 = 6 and 6 x w = 6w: Therefore your answer is 6 + 6w
Select all lines with a slope of 2/5
Answer:
C and D
Step-by-step explanation:
Answer:
Pull a mil' in a day, ain't even have the bill
On your pill, everyday I just be sippin' Chamomile
Mass appeal, everybody show up 'cause they know I'm here
Every week, I be on the face, she think it's Cetaphil
Up in my business, pull up in my crib
I got people locked and loaded like they trained for ISIS
Askin' for forgiveness, I never said you have it
Pullin' all these dimes like, do you really want attention?
Step-by-step explanation:
What is the width plz help needed quickly brainiest will be given to whoever answers correctly
Answer:
2/3
Step-by-step explanation
The length of the park has been cut off in the question but if it is one mile, like I think it is, then this is the answer.
A = 2/3
A = L x W
2/3 = 1 X ?
? = 2/3
Answer:
width = 2/3 mile
Step-by-step explanation:
area = L * W
where area = 2/3 mile²
length = 1 mile
width = ?
2/3 = 1 (W)
2 = 3W
W = 2/3 mile
therefore the width = 2/3 mile
length = 1 mile
Which correctly describes how the graph of the inequality 4x − 2y > 20 is shaded?
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answer:D Below the Dashed line
Step-by-step explanation:
Just took the test
Answer:
Below the dashed line so the answer is D
Step-by-step explanation:
just finished taking the quiz with this same answer!!
A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.
a. create a system of equations or inequalities that models the situation. define the variables you use.
b. the graph shows one of the relevant equations in this situation. Draw the graph of the other relevant equation.
c. show all the points that represent the number of hours the student can work at each job and meet his goal.
Answer:
:)
Step-by-step explanation:
15x=300
x will equal 20
20x=300
x will equal 15
Inequalities are used to represent unequal expressions
System of equationsRepresent the number of lawns mown by x, and the number of gardens with y.
So, the system of inequalities are:
[tex]x + y \le 20[/tex] --- the number of hours worked, weekly[tex]15x + 20y \le 300[/tex] --- the earnings weeklyGraphSee attachment for the system of inequalities, and all the points that represent the hours worked
Read more about system of inequalities at:
https://brainly.com/question/14323743
A person is 6 feet tall and casts a shadow of 3.2 ft at the same time a tree casts a shadow of 36.8 ft how tall is the tree?
Answer:
18.5
Step-by-step explanation:
what’s the slope of (9,3) and (2,11)
Answer:
slope = - [tex]\frac{8}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 3) and (x₂, y₂ ) = (2, 11)
m = [tex]\frac{11-3}{2-9}[/tex] = [tex]\frac{8}{-7}[/tex] = - [tex]\frac{8}{7}[/tex]
Answer:
[tex]\boxed {m = -\frac{8}{7}}[/tex]
Step-by-step explanation:
Use the Slope Formula to help you determine the slope of two given points:
[tex]m =\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
First point: [tex](x_{1}, y_{1})[/tex]
Second point: [tex](x_{2}, y_{2})[/tex]
-Apply the two given points onto the formula:
First point: [tex](9, 3)[/tex]
Second point: [tex](2, 11)[/tex]
[tex]m =\frac{11 - 3}{2 - 9}[/tex]
-Solve for the slope:
[tex]m =\frac{11 - 3}{2 - 9}[/tex]
[tex]m =\frac{8}{-7}[/tex]
[tex]\boxed {m = -\frac{8}{7}}[/tex]
Therefore, the slope is [tex]-\frac{8}{7}[/tex].
The formula for the area of a triangle is A =12bh, in which b represents the length of the base and h represents the height. If a triangle has an area of 232 mm 2 and the height is 16 mm, what is the measure of the base? The measure of the base is mm.
Answer:
Step-by-step explanation:
Write it out: A = 1/2(bh)
substitute values: 232 = 1/2(16b)
Simplify: 232 = 8b
Divide each side by 8: b = 29
The base is 29 millimeters
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet Jane at the end of her run. How much farther does Jane travel than her trainer? Answer the questions to find out. 1. What is the total distance Jane travels biking and running? Include units with your answer. Write your answer in the space below. 2. Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes. Write your answer in the space below. 3. Solve your equation to find the distance Jane's trainer bikes. Show your work. Write your answer in the space below. 4. How much farther does Jane travel than her trainer? Write your answer in the space below.
Answer:
can you Please put screen shot in there
Step-by-step explanation:
22.34 miles much farther does Jane travel than her trainer.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here, given that,
she leaves the health club and bikes 16 miles south.
Then, She then runs 12 miles west.
so, we have,
It must be, hypotenuse = 16 miles
base= 12 miles
We have to find, the height.
by Pythagorean theorem, we get,
the distance Jane's trainer bikes=√16²-12² miles
=√32 miles
=5.66 miles
So. she travels in total = 28 miles
22.34 miles much farther does Jane travel than her trainer.
To learn more on Pythagorean theorem click:
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Pls wat is 2.66 in fraction
Answer:
2 33/50
Step-by-step explanation:
Look at the decimal place. It is in hundreths. So, the decimal itself is 2 66/100. However, once you simplify it, the answer becomes 2 33/50.
Hope this helps =-) have a good day!
If ABC ≌ DEF, and m∠A = (x + 30)°, m∠C = 45°, and m∠D = 80°, what is the m∠A? A. 15° B. 45° C. 50° D. 80°
Answer:
I think its 80 not sure
Step-by-step explanation:
The measure of ∠A will be 50°.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Δ ABC ≅ Δ DEF
And, m ∠A = (x + 30)°, m ∠C = 45°, and m ∠D = 80°
Now,
Since, Δ ABC ≅ Δ DEF
Hence, m ∠A = m ∠D
Substitute all the values, we get;
m ∠A = m ∠D
x + 30 = 80
Subtract 30 both side, we get;
x = 80 - 30
x = 50°
Thus, The measure of ∠A will be 50°.
Learn more about the triangle visit:
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Which expression has the same sum as the one below - 15 + 16
Answer:
6+(-15)
Step-by-step explanation:
Need more help!
I have to have 20 characters or more to be able to ask the question....
Answer:
m<QRS=48°
m<RSQ=69°
m<RQS=63°
Step-by-step explanation:
Since we know that the measures of the angles of any triangle is 180°, we can form this equation: 7a-1+10a-1+9a=180°
Then, we can use simple algebra to solve for a and plug in that value into the equations that the degrees represent to get our angle measures.
7a-1+10a-1+9a=180°
26a-2=180°
26a=182°
a=7
Now, plug in that value of a and you have your anlage measures!! Hope this helps!! :)
The Verrazano Narrows Bridge has a main span of 4,260 feet. The Akashi Kaikyo Bridge has a main span that is 53% longer. What is the length of the main span of the Akashi Kaikyo Bridge to the nearest foot?
Which of the following options is an equivalent function to f(x) = 4(3)2x? (2 points) f(x) = 36x f(x) = 4(9)x f(x) = 144x f(x) = 4(6x)
Answer:
f(x) = 4(9)x
Step-by-step explanation:
I took the test!!!
Answer:
Answer Down BelowStep-by-step explanation:
Q's Asked: Which of the following options is an equivalent function to f(x) = 4(3)2x?
Possible answers:
f(x) = 36^x
f(x) = 4(9)^x
f(x) = 144^x
f(x) = 4(6x)
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My answer: I Think the correct answer is (B) .The reason why I think the answer is (b) is bc:
[tex]f(x) = 4(3)^{2x}[/tex] =36
Calculations on How I got 36.
Frist we calculate the exponents [tex]\left(3\right)^2[/tex] --> [tex]\left(3\right)^2=9[/tex]---> =9
then we Multiply 4*9 which gives us : 36.
The reason why Its (B) is bc:
f(x) = 4(9)^x
which means 4 times nine is...... 36. thats the answer (B) f(x) = 4(9)^xHope this helps :3
~~Wdfads~~Solve the right triangle with the given information (round to the nearest tenth):
angle B =
b =
a =
Answer:
Step-by-step explanation:
m∠B = 90°
m∠C = 90° - 27° = 63°
cos27° = [tex]\frac{200}{b}[/tex] ⇒ b ≈ 224.5
sin27° = [tex]\frac{a}{b}[/tex] ⇒ a ≈ 101.9
A Rental Car Agency charges a flat fee of $25 per day plus $0.15 for each mile driven. The total charge for one day's rental was $75.30. Which equation below can be used to solve this problem?
Answer:
Step-by-step explanation:
75.30-25 for a day leaves 50.30 for mileage.
50.30/.15 per mile= 335.3 miles driven.
75.30>=25+0.15m. m=335.3
Sandra bought 3/4 pound of carrots. she used 2/3 of them for soup. How many pounds of carrots did she use for the soup
Answer:
She used 14 pounds of carrots for soup.
Step-by-step explanation:
Translate the sentence into an inequality..
The quotient of y and 7 is at least 18.
Answer: [tex]\frac{y}{7} \geq 18[/tex]
Step-by-step explanation:
Key things to remember:
- quotient signals dividing
- at least means greater than or equal to, so we use the greater than or equal to sign
Applying this to the problem, we can translate into a simpler sentence:
y divided by 7 is greater than or equal to 18 --> which leads us to the inequality above