Answers
Area of the triangle = 1/2 x 4 x 6 = 12 square units
Answer: 12 square units
Answer:
A. 12 square units.
Step-by-step explanation:
We have been given graph of a triangle and we are asked to find the area of our given triangle.
Since we know that area of a triangle is half the product of height of triangle and base of the triangle.
[tex]\text{Area of triangle}=\frac{1}{2}*\text{Base*Height}[/tex]
We can see that MN is base of our triangle and LM is height of triangle, so let us find lengths of MN and LM using distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(3--1)^2+(-4--4)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(3+1)^2+(-4+4)^2}[/tex]
[tex]\text{Distance between point M and N}=\sqrt{(4)^2+(0)^2}[/tex]
[tex]\text{Distance between point M and N}=4[/tex]
[tex]\text{Distance between point L and M}=\sqrt{(-1--1)^2+(-4-2)^2}[/tex]
[tex]\text{Distance between point L and M}=\sqrt{(-1+1)^2+(-6)^2}[/tex]
[tex]\text{Distance between point L and M}=\sqrt{0+36}[/tex]
[tex]\text{Distance between point L and M}=6[/tex]
Now let us substitute our side lengths is area formula.
[tex]\text{Area of triangle LMN}=\frac{1}{2}*4*6[/tex]
[tex]\text{Area of triangle LMN}=2*6[/tex]
[tex]\text{Area of triangle LMN}=12[/tex]
Therefore, area of triangle LMN is 12 square units and option A is the correct choice.
Related Questions
The average value of y=v(x) equals 4 for 1≤x≤6, and equals 5 for 6≤x≤8. what is the average value of v(x) for 1≤x≤8 ?
Answers
Area = 4*(6 -1) +5(8 -6) = 30
Width = 8 - 1 = 7
Average value = 30/7 = 4 2/7
The average value of v(x) for the interval 1≤x≤8 is calculated by summing up the products of the average values each times their respective lengths of interval, and dividing by the total length of the interval, which results in 4.2857 approximately.
Explanation:The average value of v(x) for 1≤x≤8 can be calculated using the formula for the average of a function over an interval, which is the sum of the function values times their respective lengths of interval, divided by the total length of the interval. For the first interval, 1≤x≤6, the average value of y is 4, and the length of the interval is 6-1=5. Hence, the sum of the product of the average value times the length of the interval is 4*5=20.
For the second interval, 6≤x≤8, the average value of y is 5, and the length of the interval is 8-6=2. Hence, the sum of the product of the average value times the length of the interval is 5*2=10.
Summing up these two products, we get 20+10=30. The total length of the overall interval 1≤x≤8 is 8-1=7. Hence, the average value of v(x) for 1≤x≤8 is 30/7=4.2857, approximately.
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A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 3 gal/min. determine a(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.
Answers
[tex]\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}[/tex]
[tex]A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4[/tex]
We're given that [tex]A(0)=30[/tex]. Multiply both sides by the integrating factor [tex]e^{t/100}[/tex], then
[tex]e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4[/tex]
[tex]\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4[/tex]
[tex]e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C[/tex]
[tex]A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}[/tex]
Given that [tex]A(0)=30[/tex], we have
[tex]30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02[/tex]
so the amount of salt in the tank at time [tex]t[/tex] is
[tex]A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}[/tex]
To determine the amount of salt in the tank at time t, we need to consider the inflow and outflow of the brine solution over time. The inflow rate is given as 3 gal/min, and the concentration of salt in the inflow varies with time according to the equation cin(t) = 2 + sin(t/4) lb/gal. The outflow rate is also 3 gal/min.
Explanation:To determine the amount of salt in the tank at time t, we need to consider the inflow and outflow of the brine solution over time. The inflow rate is given as 3 gal/min, and the concentration of salt in the inflow varies with time according to the equation cin(t) = 2 + sin(t/4) lb/gal. The outflow rate is also 3 gal/min.
To find the amount of salt in the tank at time t, we need to integrate the product of the inflow rate and the concentration of salt over the interval [0, t]. This will give us the total amount of salt that has entered the tank up to time t. We can then subtract the amount of salt that has been pumped out of the tank over the same interval to get the amount of salt remaining in the tank at time t.
a(t) = ∫[0,t] (3 gal/min * cin(t)) dt - 3 gal/min * t.
Hey can you please help me posted picture of question
Answers
3 x 6 x 4 = 72
answer A. 72
Explanation:
There is 3 flavors
6 cookie add ins
4 flavors of syrup
We multiply these answers using multiplication and we get 72!
:D
Good Day!
Answer:72
Which expression represents "6 more than x"?
x - 6
6x
x + 6
6 - x
Answers
this is because + means more, so 6 more
Fresh raspberries contain 80% water. Dried raspberries contain only 20% water. How many pounds of dried raspberries do you get from 36 lb of fresh berries?
Answers
36*0.2(20%)=7.2, this is how much water the berries obtain.
Now you do 7.2 divided by 0.8 which equals 9. You do this step to find out how much water and the rest of the stuff in the berries.
Happy to help! :)
The answer is 9
The answer is 9
The answer is 9
The answer is 9
Is 78990 divisible by 9
Answers
At a school, 129 students play at least one sport. This is 60% of the students at the school. How many students are at the school?
Answers
129 = (1.00-.60) x (whole school)
129 = .4 x (whole school)
129/.4 = Whole school
School size = about 323 students
An isosceles trapezoid has a perimeter of 40.9 feet. Its shorter base measures 3.5 feet and its longer base measures 4.4 feet. The two remaining sides have the same length; what is that length?
Answers
P= a + b + c + d
40.9 = 3.5 + 4.4
40.9 = 7.9
-7.9 -7.9
---------------
40.9-7.9=33 and since its calculating two equal sides, 33/2 = 16.5
Answer:
16.5 feet is the amount of the length
The diameter of a circle is 18 cm. What is its area in terms of π.
Answers
Answer:
Area, [tex]A=(81\pi )\ cm^2[/tex]
Step-by-step explanation:
Given that,
The diameter of the circle, d = 18 cm
The radius of a circle is half of its diameter, r = 9 cm
The formula to find the area of a circle is given by :
[tex]A=\pi r^2[/tex]
When r = 9 cm
[tex]A=\pi (9\ cm)^2[/tex]
[tex]A=(81\pi )\ cm^2[/tex]
So, the area of the circle is [tex](81\pi )\ cm^2[/tex]. Hence, this is the required solution.
A circle has a radius of 6x^9y^5 cm, what is the area of this circle in square centimeters
Answers
[tex]\text {Area of circle }= \pi (6x^9y^5)^2 \text{ cm}^2[/tex]
[tex]\text {Area of circle }= 12\pi x^{18}y^{10} \text{ cm}^2[/tex]
The area of the circle in square centimeters is [tex]\( 36\pi x^{18}y^{10} \)[/tex] cm².
The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.
Given that the radius [tex]\( r \)[/tex] of the circle is [tex]\( 6x^9y^5 \)[/tex] cm, we can substitute this value into the formula to find the area.
[tex]\( A = \pi (6x^9y^5)^2 \)[/tex]
Now, we square the radius:
[tex]\( (6x^9y^5)^2 = (6x^9y^5)(6x^9y^5) \)[/tex]
[tex]\( = 36x^{18}y^{10} \)[/tex]
Substituting this back into the area formula:
[tex]\( A = \pi \cdot 36x^{18}y^{10} \)[/tex]
[tex]\( A = 36\pi x^{18}y^{10} \)[/tex]
Therefore, the area of the circle in square centimeters is [tex]\( 36\pi x^{18}y^{10} \)[/tex] cm².
Find the shaded area of the basketball court to the nearest foot.
Answers
Rectangle - 12*19 = 228
Half a circle - [tex]\pi r^2 = \pi 6^2 = 36 \pi/2 = 18 \pi [/tex]
In the end there are 2 rectangles (2*228 = 456) and 1 full circle (18*2 = 36), which makes the shaded area 456 ft and 36[tex] \pi [/tex]
Then find the area of the semi-circle above it, which is pi times the radius squared. The diameter is 12ft, and we know the radius is half of the diameter, so the radius is 6ft. Our equation is pi times 6^2, or pi times 36.
We’ll just make pi 3.14, so 36•3.14=113.04 feet.
Add the area of the semi-circle and the rectangle together to get one of the shaded areas. 228+113.04= 341.04.
Now that we know the full area of one shaded region, we multiply it by two because there’s two of them. 341.04•2= 682.02.
Since we round it to the nearest foot, our final answer is that the shaded area of the basketball court is 682 square feet.
square root 2x -5 =11
Answers
How do you determine if two probabilities are conditional to each other?
Please help
Answers
Final answer:
You can determine if two probabilities are conditional by checking if the occurrence of one affects the probability of the other. If it does, the probability is conditional, represented by P(A|B), otherwise, the events are independent.
Explanation:
Determining Conditional Probabilities
To determine if two probabilities are conditional to each other, you consider if the occurrence of one event affects the probability of the other event happening. The conditional probability of event A given event B is denoted by P(A|B). This is calculated by dividing the probability of both events A and B occurring together (P(A AND B)) by the probability of event B:
P(A|B) = P(A AND B) / P(B)
This formula is applicable only when P(B) is greater than zero, meaning event B must have a chance of occurring. If the probability of A happening does NOT change whether B occurs or not, then A and B are independent events. Conversely, if the probability of A does depend on the occurrence of B, then A and B are dependent, and the probability P(A|B) is a conditional probability.
Independence is defined as the situation where the probability of A and B occurring together is the product of their individual probabilities (P(A) * P(B)). If this is true, P(A|B) would simply be P(A), as B's occurrence doesn't affect A's probability.
Daniel is using match sticks to do a square an a triangle. he uses 41 match sticks to do 12 figuring altogether .how many square did he made
Answers
Daniel made 5 squares.
Can the figure below tessellate a plane? Explain your answer.
Answers
Answer:
Step-by-step explanation:
A tessellation is created when a shape is repeated over and over again covering a plane without leaving any gaps or overlaps. Tessellation is also known as tiling. Triangles, squares and hexagon are perfect examples of figures that can create tessellation.
The figure below cannot, because there will be gaps.
I hope it helps, Regards.
Solve x^2 +14x = -24 by completing the square. Which is the solution set of the equation?
Answers
Find HALF the value of 14: 7
Square this: 49
Add 49, and then subtract 49: x^2 + 14x + 49 - 49 = -24 We have a
perfect square
Rewrite the quadratic as the sq. of a binomial: trinomial on
the left
(x+7)^2 = 25
Take the sqrt of both sides: x+7 = plus or minus 5
Then x = -2 and x = -12
Answer:
{−12, −2}
Step-by-step explanation:
The number of acres of wetland infested by an invasive plant species after t Years is given by u(t)=12•2^t/3. Solve the equation u(t)=50. What does your answer tell you about the wetland?
Answers
u (t) = 12 • 2 ^ t / 3
We equate the equation for u (t) = 50.
We have then:
12 • 2 ^ t / 3 = 50
We clear the value of t:
2 ^ t / 3 = 50/12
log2 (2 ^ t / 3) = log2 (50/12)
t / 3 = log2 (50/12)
t = 3 * log2 (50/12)
t = 6.2 years
Answer:
After 6.2 years 50 acres of wetland are infested by an invasive plant species
hey can you please help me posted picture of question
Answers
Shift towards right can be obtained by subtracting 4 from the x in the function and the upward shift can be obtained by adding 1 to the function.
So,
G(x) = F(x-4) + 1
Thus,
G(x) = (x-4)² + 1
So, the correct answer to this question is option B
When two births are randomly selected, the sample space for genders is bb, bg, gb and gg. assume that those four outcomes are equally likely. does the mean of the sample proportions equal the population proportion of girls in two births?
Answers
Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper (y) that Ben collected in a certain amount of time (x), in weeks:
(photo below)
What would most likely be the total amount of paper, in pounds, Ben would collect in 10 weeks?
230 pounds
270 pounds
300 pounds
330 pounds
Answers
30*11=330
A rectangular picture has dimensions 2 1/2 by 1 1/2. It is to be enlarged so that it is still similar to the original rectangle. If the longer dimension is now 10 , how much longer than the original is the perimeter now
Answers
p = 2 (w) +2 (l)
First we look for the scale factor of the longest dimension, which is given by:
k = (10) / (2 1/2)
k = 4
Then, the perimeter is given by:
p '= 2 (4w) +2 (4l)
Rewriting:
p '= 4 (2 (w) +2 (l))
p '= 4p
Answer:
the perimeter now is 4 times longer than the original
A jar holds 2 3/4 cups of water. How much is this in fluid ounces
Answers
Jay stores hay in cubic stacks on his farm. If the length of each stack is 2/3 yards, what is the volume of hay in each stack? 1/3 cubic yards, 4/9 cubic yards, 1/9 cubic yards, 8/27 cubic yards
Answers
The 4th selection is appropriate.
Answer: The volume of hay in each stack is 8/27 yards
Step-by-step explanation:
Since, the volume of a cube = (side)³
Here, the side of the a cubic stack = [tex]\frac{2}{3}[/tex] yards,
Hence, the volume of a cubic stack,
[tex]V=(\frac{2}{3})^3[/tex]
[tex]=\frac{8}{27}[/tex] cube yard.
⇒ The volume of hay in each stack is 8/27 yards
steph has 5 1/4 pounds of rice.she wants to place 1/4 pound of rice in each plastic bag.how many bags will she need?
Answers
total amount of rice in one bag = 1/4
Number of bags needed = 5 1/4 ÷ 1/4 = 21/4 ÷ 1/4 = 21/4 x 4 = 21 bags
Answer: 21 bags.
Suppose angle A is complementary to angle B, and angle B is supplementary to angle C. If measure of angle A is 21 degree, find measure of angle C.
Answers
Since A and B are complementary they add to 90. So we know that B must be 69 degrees.
Since B and C are supplementary they add to 180. So we know that C must be 111.
In solving this problem, we first identify that angle B is 69 degrees as it is complementary to 21-degree angle A (adding to 90 degrees). Then, we find angle C to be 111 degrees as it is supplementary to angle B (adding to 180 degrees).
Explanation:In this problem, we are told that angle A (measuring 21 degrees) is complementary to angle B. Complementary angles are angles that add up to 90 degrees. So, we can find the measurement of angle B by subtracting the measurement of angle A from 90 degrees, which gives us 90 - 21 = 69 degrees for angle B.
Next, we are told angle B is supplementary to angle C. Supplementary angles are angles that add up to 180 degrees. So, we can find the measurement of angle C by subtracting the measurement of angle B from 180 degrees, which results in 180 - 69 = 111 degrees for angle C.
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Hey can you please help me posted picture of question
Answers
Explanation:
Since, rolling a die and tossing a coin are independent events, the sample space of both events is the product of the outcomes for each event, i.e 6 × 2 = 12.
You can check that here:
roll a die toss a coin
1 head
1 tail
2 head
2 tail
3 head
3 tail
4 head
4 tail
5 head
5 tail
6 head
6 tail
So, as you see for each outcome of the event roll a die there are two different possible different outcomes for the event toss a coin; since there are 6 different outcomes for the die, the total number of possibilities is 6 × 2 = 12
what is the next number in this pattern 0.54,0.6,0.66,0.72
Answers
So, add 0.06 to 0.72.
0.06+0.72=0.78.
So, your answer is 0.78.
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Ivanova has a healthcare plan with $25 co-pays to see doctors, $10 co-pays for prescription drugs, and an annual deductible of $1,500. In February she has a broken ankle which costs $2,300 in hospital treatment. As a follow-up in March she sees three doctors who bill $657, $134, and $232 and buys two prescriptions which cost $12 and $27. What is Ivanova's share of the costs for March?
Answers
$800+$75+$20=$895.
The area of a triangle is 30 square feet. If the height of the triangle is 5 feet, what is the base of the triangle? 12 ft 6 ft 3 ft 24 ft
Answers
30=(1/2)*base*5
6=(1/2)*base
base=12 ft
To find the base of the triangle with a known area and height, apply the formula for the area of a triangle and solve for the base, resulting in 12 ft.
The base of the triangle can be found using the formula for the area of a triangle:
Area = 1/2 × base × heightGiven the area is 30 sq ft and height is 5 ftSubstitute the values: 30 = 1/2 × base × 5Solve for base: base = 30 / (1/2 × 5) = 30 / 2.5 = 12 ftThe base is 34 ya and it’s height is 20.5. What is the area