Answer:
B
Step-by-step explanation:
We know that AB has endpoints at A(4, -3) and B(3, 7).
To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.
So, let's find the slope of AB using the slope formula:
Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:
So, the slope of AB is -10.
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.
So, Line D has a slope of 1/10.
Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.
To find the midpoint, we can use the midpoint formula:
We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:
Evaluate. So, the midpoint is:
Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:
Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:
This is the same as choice C. So, choice C is indeed an equation of Line D.
We can distribute the right to obtain:
Add 2 to both sides to acquire:
This is the same as choice D. So, choice D is indeed an equation of Line D.
Moreover, we can put this into standard form by multiply everything by 10, which gives:
Subtracting x from both sides yields:
This is the same as A. So, choice A is also an equation of Line D.
There is no way to acquire choice B. So, B is not an equation of Line D.
Therefore, our answer is B.
And we're done!
jordan is cutting a 2 m by 1 1/4 m piece of rectangular paper into two pieces along its diagonal. find the area of each of the pieces
Answer:
The area of a rectangle is 5/4
Step-by-step explanation:
A cup of coffee contains 140 mg of caffeine. If caffeine leaves the body at 10% an hour, how long will it take for half of the caffeine to be eliminated from the body?
Answer: 5 hours
Step-by-step explanation:
If 10% of 140 is 14. And if 14 mg of caffeine is leaving per hour then it would take 10 hours to completely leave from ones body, but for half of it to leave it would take 5.
what is the value of x in the equation x= 2arcsin1/2
Step-by-step explanation:
it depends if you use degrees or radians as angle measure.
let's assume degrees.
arcsine is the inverse function of sine.
so, when sin(x) = 1/2, arcsin(1/2) = x
when now x = 2×arcsin(1/2), we get
x = 2×30 = 60°
A- 52/3
B- 52/7
C- 17
D- 3/4
The Answer is: A. 52/3
Show that the points A(-1,2), B (5,2) and C (2,5) are the vertices of an isosceles triangle. Find the area of ∆ABC
Answer:
the area of ∆ABC = 9
Step-by-step explanation:
[tex]CA=\sqrt{\left( -1-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}[/tex]
[tex]CB=\sqrt{\left( 5-2\right)^{2} +\left( 2-5\right)^{2} } = \sqrt{18} =3\sqrt{2}[/tex]
Since CA = CB then A(-1,2), B (5,2) and C (2,5) are the vertices of an isosceles triangle.
Area calculation:
Let The point H be the midpoint of side AB
[tex]x_{H}=\frac{-1+5}{2} =2\\y_{H}=\frac{2+2}{2} =2[/tex]
Then
H(2 , 2)
therefore,
[tex]CH=\sqrt{\left( 2-2{}\right)^{2} +\left( 2-5\right)^{2} } =3[/tex]
Finally,
[tex]\text{the area of triangle ABC} =\frac{\text{CH} \times \text{AB} }{2} =\frac{3\times 6}{2} =9[/tex]
What type of slope is demonstrated by the line below?
(-1,3)
A. Positive slope
B. Negative slope
C. Undefined slope
D. Zero slope
(0,-2)
Please help!!! Anything is helpful!
Step-by-step explanation:
Equation to find the sum of the first n terms :
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] x (2[tex]a_{1}[/tex] + (n - 1)d)
- where n is the first n terms
- where [tex]a_{1}[/tex] is the first term in the sequence
- where d is the difference (To find the difference: [tex]a_{1}[/tex] - [tex]a_{2}[/tex])
How to find n for the given sum :
1. Using the previous equation, plug in all the numbers that you know
2. PEMDAS then combine all like terms
3. Distribute what's on the outside to the inside of the parenthesis
4. Move [tex]S_{n}[/tex] to the other side to make a quadratic equation
5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)
Question 1:
Sum of first 10 terms : [tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] ( 2 x 2 + (10 - 1)6)
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] (4 + (9)6) = (4 + 54) = 58
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] x 58
Answer : 290
Find n for the given sum : 1704 = [tex]\frac{n}{2}[/tex] x (2 x 2 + (n - 1)6)
distribute 6 into (n-1)
1704 = [tex]\frac{n}{2}[/tex] x ( 4 + 6n - 6)
combine like terms
1704 = [tex]\frac{n}{2}[/tex] x ( -2 + 6n )
Distribute [tex]\frac{n}{2}[/tex] to ( -2 + 6n )
1704 = [tex]\frac{-2n}{2}[/tex] - [tex]\frac{6n^{2} }{2}[/tex]
Simplify fractions and move 1704 to the other side
-3[tex]n^{2}[/tex] - n + 1704 = 0
Use a quadratic calculator to find the answer and use the answer with the whole number
Answer : -24
Question 2:
(i'm just gonna show you the answers for the rest of them-)
Sum of the first 14 terms: 490
Find n for the given sum: 33.65 (I'm gonna round it to 34)
Question 3:
Sum of the first 21 terms: 483
Find n for the given sum: 11.48 (rounded: 11)
Question 4:
Sum of the first 32 terms: -1328
Find n for the given sum: -9.34 (rounded -9)
really hope this helps in any way :D
What is the volume?
Answer:
volume = l×b×h = 1.6 × 1.6 × 1.6 = 4.096cm³
A person standing at the top of Mountain Rainier would be approximately 2.7 mi high. The radius of earth is 3959 mi.What is the distance to the horizon from this point?
Answer:
103.4 mi to nearest hundredth.
Step-by-step explanation:
This is an application of the Tangent/secant of a Circle theorem.
If h is the distance to the horizon:
h^2 = 2.7 * (3959 + 2.7)
h^2 = 10696.59
h = 103.424 miles.
Using the equation, y=5x²−17x −12, determine the y-intercept.
A) (0, -12)
B) (4, 0)
C) (1.7, -26.4)
D ) (0, 12)
Answer:
A
Step-by-step explanation:
to find the y- intercept let x = 0 in the equation and solve for y
y = 5(0)² - 17(0) - 12 = 5(0) - 0 - 12 = 0 - 12 = - 12
then the y- intercept is (0, - 12 )
Answer:
[tex]\huge\boxed{\sf (0,-12)}[/tex]
Step-by-step explanation:
Given equation:[tex]y=5x^2-17x-12[/tex]
y-intercept is the point where x = 0
Put x = 0 in the above equation.
[tex]y=5(0)^2-17(0)-12\\\\y = 0-0-12\\\\y=-12[/tex]
So, y = -12, when x = 0.
Ordered pair = (x,y) = (0,-12)
[tex]\rule[225]{225}{2}[/tex]
_30. Solve the following logarithmic equation: log8(x + 9) + 3 = 3
A) x = -8
B) x = 87
C) x = 12.5
D) x = 0
=
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
[tex]log_{8}[/tex] (x + 9) + 3 = 3 ( subtract 3 from both sides )
[tex]log_{8}[/tex] (x + 9) = 0 , then
x + 9 = [tex]8^{0}[/tex] = 1 ( subtract 9 from both sides )
x = - 8
I need help I don’t know the answer
Answer: The date tree is 3 times as tall as the lemon tree
Step-by-step explanation:
There are two trees.
Date tree = unknown height
Lemon tree = 8 feet
Equation
? = 3 x 8
We can assume that the 8 in the equation is the height of the lemon tree since it was already given. The equation's purpose is to find the height of the date tree resulting in 3 times 8 which is 24.
If we compare their heights, we can say that the date tree is 3 times taller than the lemon tree since 24 is 3 times greater than 8.
Which equation matches the graph?
y=-2x
Step-by-step explanation:
it can't be y=2x and y=-½ because it passes by the opposite side of the given graph
Luis is flying a kite, holding his hands a distance of 3.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 35^{\circ} ∘ . If the string from the kite to his hand is 140 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
The height of the kite above the ground to the nearest tenth of a foot is 84.1 ft
Using the angle of elevation to find height?The situation forms a right angle triangle.
Therefore, the length of the string is the hypotenuse of the triangle formed.
Hence, using trigonometric ratios,
sin 35 = opposite / hypotenuse
sin 35 = h / 140
cross multiply
h = 140 sin 35
h = 140 × 0.57357643635
h = 80.3007010891
Height of the kite above the ground = 80.3007010891 + 3.75 = 84.0507010891
Height of the kite above the ground = 84.1 ft
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the area of a triangle is 49.28 square centimetres. if the base of the triangle is 8.8 centimeters, what is the height
Answer:
11.2
Step-by-step explanation:
Which are differences of perfect cubes? select two options. 9a3- 27 125a12 - 72 216a6 - 27y3 8a15 - 27 225a3 - 216
The expressions that are differences of perfect cubes from the options given are:
c. 216a⁶ - 27y³
d. 8a¹⁵ - 27
What is a Perfect Cube?A perfect cube can be described as a number that is gotten when an integer is multiplied by itself three times.
216a⁶ - 27y³ is a difference of perfect cubes because: (6a²)³ - (3y)³.
So also is the expression, 8a¹⁵ - 27.
The difference of perfect cubes are:
c. 216a⁶ - 27y³
d. 8a¹⁵ - 27
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Answer:
C 216a6 - 27y3
D 216a6 - 27y3
Step-by-step explanation:
I took the test on edge. :)
25) Ted spent $25 on a shirt and $89 on a pair of shoes. Ted had $40 left in his wallet. How much money did Ted have before he spent money
on a shirt and shoes?
A) $114
B) $144
C) $154
D) $164
PLS HELP ME I ONLY HAVE # HOURS TO COMPLETE I WILL MARK THE BRAINLIEST!!!
triangle on right is the same as the triangle on the left
use pythagorean theorem
hypotenuse will give to the sides of the rectangle
a^2 + b^2 = hypotenuse squared
10.4^2 = 108.16
15.3^2 = 234.09
342.25 = hypotenuse squared
take the square root in both sides
hypotenuse = the square root of 342.25 =
18.5
add up the areas of the 2 triangles and rectangle
triangle area is 1/2 times 10.4 times 15.3 =
79.56
2 triangles areas are 159.12
rectangle area is 18.5 × 7 = 129.5
159.12 + 129.5 = 288.62
answer 1 = 288.62
second question:
to get 1 side take the
square root of 702.25 which is
26.5
to get the perimeter
multiply 26.5 by 4 which is
106
answer 2 is choice B 106
A researcher determined that the heights of male students in a particular town are normally distributed
with a mean of 65 inches and a standard deviation of 1.7. Use the graph above to answer the following
questions:
a. What percentage of these students is taller than 66.7 inches?
b. If the data are based on 300 students, how many students are between 61.6 and 68.4 inches tall?
Explain.
The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
Mean of 65 inches and a standard deviation of 1.7.
From the graph:
P(X> 66.7) = (13.5 + 2.35 + 0.15)%
P(X> 66.7) = 16%
P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)% = 95%
= (300×95)/100
= 285 students
Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.
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Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour. a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home? b On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her? c On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta off and walks the rest of the way, while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike? d On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home. Meanwhile he returns to pick up Reeta and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off and pick-up points?
The distance between Reeta and the school when the cyclists arrive the home for this case is found to be 2 km
How to form mathematical expressions from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example, if it is asked to increase some items by 4, then you can add 4 in that item to increase it by 4. If something is, for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert descriptions to mathematical expressions.
How to find the speed of an object?
If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it travelled to the time it took to travel that distance.
If the object travelled D distance in T units of time, then that object's speed is
[tex]Speed = \dfrac{D}{T}[/tex]
Given that:
Distance from school to home = 5 kmWalking speed = 4 km / hoursCycling speed = 5 times walking speed = 20 km / hourThey all go and come together to and from school/home.On Monday: Nikita and Peter are coming by cycle, and Reeta walks.Cycle punctures at four-fifth of the way home = [tex]\dfrac{4}{5}\times 5[/tex] from school (as they're coming towards home, so went from school)After a puncture, cyclists walk to homeTo find the Distance of Reeta from school when the cyclist reaches home.Suppose at time 0 hours, all three people departed from school (on that Monday).
After 't' hours, suppose the cycle gets punctured.
Then, as the cycle was going by 20 km/hour speed, so in 't' hours, it must have covered d kilometres (suppose),
then we get:
[tex]S =\dfrac{D}{T}[/tex]
[tex]20=\dfrac{d}{t}[/tex]
d = 20t
This distance is measured from school. But we know that this distance is 4 km, so we get:
20t = 4
t = 1 / 4
The remaining 1 km (as the home is 5 km away from school and 4 km is already travelled) is walked by Cyclists. And walking speed is 5 km/hour, so let they take T hours to travel that 1 km walking, then we get:
5 = 1 / T
t = 0.2 hours
So, the total time cyclists took to reach home from school is: 0.2+0.2=0.4 hours
Reeta is walking that whole 5 km.
The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.
Thus, we have:
Time is taken 0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:
D = S x T
D = 5 x 0.4 = 2 km
So Reeta was 2 km away from school when cyclists reached home on that Monday.
Thus, the distance between Reeta and the school when the cyclists arrive at the home for this case is found to be 2 km
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Can a triangle be made with the sides 15, 15, 30?
Answer:
No
Step-by-step explanation:
15^2+15^2=450 not 900=3^2
Hope this helps! ;-)
An arc subtends a central angle measuring \dfrac{3\pi}{5}
5
3π
start fraction, 3, pi, divided by, 5, end fraction radians.
What fraction of the circumference is this arc?
Answer:
3/10 of the circumference
Step-by-step explanation:
Take the fraction between the central angle and the total degree measure of the circle, which is 2π.
(3π/5)/2π3π/10π3/10 of the circumference10% of 2100 is 210
Work out 43% of 2100
Answer:
43÷100*2100=903
Step-by-step explanation:
43 devide by 100 because it is a percentage, we always devide percentages by 100. It gives an answer of 0,43.
0,43 multiply by 2100 because we need a cost.
Calculate the price of melons if melons cost $2.38 a pound and the melon on the scale weighs 2.2 pounds, making sure to round your answer to the nearest cent.
Answer:
$5.24 to nearest cent.
Step-by-step explanation:
Price of 2.2 pounds
= 2.38 * 2.2
= $5.236
2700 bricks are needed to build 300 square feet of a wall. How many bricks will be needed to build 1800 square feet of wall
If 5 cars are selected from 8 and arranged side-by-side in a parking lot, how many permutations are
possible?
==========================================================
Explanation:
We have five slots which we can label A,B,C,D,E
There are 8 choices for slot AThen 7 choices for B6 for C5 for D4 for EWe start at 8 and count down by 1 each time until all slots are accounted for. Then multiply out those items: 8*7*6*5*4 = 6720
--------------
Another approach is to use the nPr permutation formula.
Plug in n = 8 and r = 5.
[tex]n P r = \frac{n!}{ (n-r)! }\\\\8 P 5 = \frac{8!}{ (8-5)! }\\\\8 P 5 = \frac{8!}{ 3! }\\\\8 P 5 = \frac{8*7*6*5*4*3!}{ 3! }\\\\8 P 5 = 8*7*6*5*4\\\\8 P 5 = 6720\\\\[/tex]
In the second to last line, the "3!" factorial terms cancel out.
We have the string 8*7*6*5*4 show up again to help reinforce the previous section.
What is the answer to 0.6-0.17
Help me with this question please
Answer:
A) D) F)
Step-by-step explanation:
A) Since the graph is 10x10, and there are 10 seasons, it makes sense for A) to be an option
D) There is a total of 50 values that will be on the verticle axis, which seems like a fair number when the highest value is 37
F) (Season 8, 30 average points per game)
Hey guys! Stuck on this problem. Can you please explain? Will give brainliest!
Answer:
60
Step-by-step explanation:
1. Calculate area of front surface:
Area of rectangle + Area of smaller rectangle
6*3 + 2*1 = 20
2. then multiply the area by the depth (3)
20 * 3 = 60 cm^3
Find the volume and surface area of the figure. Round to the nearest hundredth.
V = ________m^3
S.A. = _______m^2
Answer:
Step-by-step explanation: