Answer:
I) coordinate of P is (11, 5.5)
II) Points are not collinear
Step-by-step explanation:
I) Let the coordinates of P be (a, b)
We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b
Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;
PR = PS
Using the formula for distance between two coordinates, we have;
√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)
This gives;
(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²
Since a = 2b,then we have;
(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²
4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16
Simplifying this gives;
20 = 42 - 4b
42 - 20 = 4b
4b = 22
b = 22/4
b = 11/2
b = 5.5
Since a = 2b
Then a = 2 × 5.5
a = 11
Thus, coordinate of P is (11, 5.5)
II) Formula for area of triangle formed by three points is given as;
A = ½|(x1 - x2) (x2 - x3)|
|(y1 - y2) (y2 - y3)|
x1 - x2 = 11 - (-2) = 13
x2 - x3 = -2 - 6 = -8
y1 - y2 = 5.5 - 4 = 1.5
y2 - y3 = 4 - (-4) = 8
Thus;
A = ½|13 -8|
|1.5 8|
A = ½((13 × 8) - (1.5 × - 8))
A = ½(104 + 12)
A = 58
Since the area is not zero, then it means the points are not collinear.
Consider a city whose streets are laid out as a grid. Streets run north-south or east-west. A visitor is dropped off by a cab at a certain intersection and would like to visit a museum that is 6 blocks to the east and 3 blocks to the north of his current location. The visitor always takes a direct path and never travels west or south in the course of his walk. How many distinct paths are there for the visitor to walk to the museum
Answer:
84 possible paths
Step-by-step explanation:
Given
[tex]N =3[/tex] --- 3 blocks north
[tex]E = 6[/tex] --- 6 blocks east
Required
Number of distinct path
To solve this question, we make use of the following formula
[tex]^{m+n}C_n \ =\ ^{m+n}C_m[/tex]
The above formula implies that;
On a single path, there is a total of m + n steps to get to a particular position, where each path is either in m direction or n direction.
In this case:
[tex]m = 3[/tex]
[tex]n = 6[/tex]
So, we have:
[tex]^{m + n}C_n = ^{3+6}C_6[/tex]
[tex]^{m + n}C_n = ^9C_6[/tex]
Apply combination formula
[tex]^{m + n}C_n = \frac{9!}{(9-6)!6!}[/tex]
[tex]^{m + n}C_n = \frac{9!}{3!*6!}[/tex]
Expand the numerator
[tex]^{m + n}C_n = \frac{9*8*7*6!}{3!*6!}[/tex]
[tex]^{m + n}C_n = \frac{9*8*7}{3!}[/tex]
Expand the denominator
[tex]^{m + n}C_n = \frac{9*8*7}{3*2*1}[/tex]
[tex]^{m + n}C_n = \frac{504}{6}[/tex]
[tex]^{m + n}C_n = 84[/tex]
Hence, there are 84 possible paths
[tex]^{m + n}C_m[/tex] will also give the same result
WHATS THE ANSWER?? answer ASAP NO FILE
Answer:
a
Step-by-step explanation:
it is a because the shape is moving to the side
Answer:
The answer is B!
HELP PLEASE I BEG
Juan had $19000 and chose to split the money into two different mutual funds. During the first year, Fund A earned 7% interest and Fund B earned 3% interest. If he received a total of $1042 in interest, how much had he invested into each account?
Juan invested $_____ into Fund A.
Juan invested $_____ into Fund B.
Answer:
Juan invested $ 11,800 in Fund A and $ 7,200 in Fund B.
Step-by-step explanation:
Given that Juan invested $ 19000 in two mutual funds, and Fund A earned 7% profit during the first year, while Fund B earned 3% interest, if he received a total of $ 1042 profit, to determine how much she had invested in each mutual fund the following calculation must be performed:
19000 x 0.07 + 0 x 0.03 = 1330
15000 x 0.07 + 4000 x 0.03 = 1170
11000 x 0.07 + 8000 x 0.03 = 1010
11500 x 0.07 + 7500 x 0.03 = 1030
11800 x 0.07 + 7200 x 0.03 = 1042
Therefore, Juan invested $ 11,800 in Fund A and $ 7,200 in Fund B.
(8 2/3 - 3 1/2) x (4 1/6+2 1/3)
Which mixed number is equivalent to 38 divided by 7
The mixed number equivalent to 38 divided by 7 is 5 3/7.
To find the mixed number equivalent to 38 divided by 7,
we need to divide 38 by 7 and express the result as a mixed number.
=38 ÷ 7
= 5 remainder 3
Or 7 | 38 | 5
35
______
3
So, the quotient is 5 and the remainder is 3.
So, the mixed number equivalent to 38 divided by 7 is 5 3/7.
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How many feet are in 5 yards
Answer:
15 feet
Step-by-step explanation:
Forumula: Multiply the length value by 3.
5*3= 15 feet
Hope this helped! :)
Answer:
15 feet
Step-by-step explanation:
okay so in 1 yard is 3 feet
is it is 5 yards so there is 15 feet
HELP
WILL GIVE BRAINLIST
ANSWER
....
.
Given:
The numbers are [tex]-5,0,6,-3.5,-1\dfrac{2}{3}[/tex].
To find:
The number line one which each of the given number is plotted correctly.
Solution:
The given numbers are [tex]-5,0,6,-3.5,-1\dfrac{2}{3}[/tex].
To plot [tex]-5,0,6[/tex], we need to make dots at [tex]-5,0,6[/tex] respectively.
To plot [tex]-3.5[/tex], we need to make a dot in the mid of -4 and -3.
To plot [tex]-1\dfrac{2}{3}[/tex], we need to make a dot between -2 and -1. That point divides the segment between -2 and -1 in 1:2
In option A, -5 is not plotted correctly. So, option A is incorrect.
In option B, -3.5 is not plotted correctly and [tex]-1\dfrac{2}{3}[/tex] is not plotted. So, option B is incorrect.
In option C, all the points are plotted correctly. So, option C is correct.
In option D, [tex]-1\dfrac{2}{3}[/tex] is not plotted correclty. So, option D is incorrect.
Therefore, the correct option is C.
69 to the power of 2
Answer:
4761
Step-by-step explanation:
69 times 69 since it is to the power of 2.
Answer:
4761
Step-by-step explanation:
[tex]69 *69=4761[/tex]
please give brainliest I need to feed my children
Each girl on a cheerleading squad bought a bear. The leader paid for their cheerleading outfits for each of them. She spent $175. Write and solve an equation to find how many cheerleading outfits, c, the leader bought. Cheerleading outfit cost- $12.50
Answer:
175 ÷ 12.50 = 14
Step-by-step explanation:
Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. They randomly assigned 20 participants to either a control group or a relaxation training group and recorded the change in number of headaches each group reported the week before training to the week after training (the control group received no training). Which statistical analysis would we perform to see whether the training helped the participants in that group as compared to the control group
Question 5 of 10
The chord BC is a diameter of OO.
A. True
B. False
Answer: it’s true i just did the quiz
Step-by-step explanation:
Chord BC is a diameter of the circle as passes from the center O of the circle and its end points B,C lies on the circle so the statement is true.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
O is the center of the Circle
Chord BC is the line segment passing from the center of circle
Chord is a line segment whose end points lies on the circle.
Diameter is defined as a line segment passing from the center of the circle whose end point lies on the circle.
A chord that passes through the centre of a circle is called a diameter, and it is the longest chord.
Hence, chord BC is a diameter of the circle as passes from the center O of the circle and its end points B,C lies on the circle so the statement is true.
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Two candidates run for class president. After all the ballots are counted, one candidate has 50% of the votes. What decimal names the portion of the votes the second candidate has? Explain
Answer:
This link should help
Step-by-step explanation:
http://www.uvm.edu/~eclark/Math017LectureNotes.pdf
Answer:
0.50
Step-by-step explanation:
Because decimals are correlated with fractions, and fractions are correlated with percentage.
Essentially, everything is out of a hundred. For example, 100% is max capacity(aka the votes in this question).
In decimals, 0.50 is half of 1.00 which is essentially also max capacity. Following this logic, if you convert 50% into decimal form, it will be 0.50, and 0.50 is one half of 1.00. The other half must be 0.50 then, because if you subtract it, that's what you get, and you can check by adding it together.
Hope this helps.
jaslyyyyyyyyyyyyyyyy is good girl :3
Answer:
7/9
Step-by-step explanation:
this equation is true:
21/27 = 7/9
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
7/9 = Proper Fraction
A cross section is made parallel to the bases of a right triangular prism. Which of the following statements is true regarding the area of the cross section and the area of the base?
The area of the cross section is less than the area of the base.
The area of the cross section is greater than the area of the base.
There is insufficient data to determine these area relationships.
The area of the cross section is equal to the area of the base.
Answer:
The area of the cross section is equal to the area of the base.
Step-by-step explanation:
Find the area of the composite figure.
A. 122.5 sq ft
B. 171.5 sq ft
C. 196 sq ft
D. 296. 5 sq ft
Answer:
I think B is your answer if so then comment me and you can mark me as brainliest and please follow me
6th grade,PLSSSS HELP ME PLSSS, it’s on the imagee
Answer:
1, 2.5 at the top and 50 at the bottom
A figure was created using a tangle and a semicide. Use the ruler provided to measure the
dimensions of the triangle and the semidecle to the nearest centimeter. Which measurement is the closest to the area of the figure in square centimeters
a car gets 30 miles per gallon of gas. at this rate, how many gallons would it take for the car to go 360 miles
Answer:
The car would need 12 gallons of gas to go 360 miles
Step-by-step explanation:
360÷30=12
Answer:
it would take 12 gallons of gas
Step-by-step explanation:
[tex]360 \div 30 = 12[/tex]
How many times larger than
Answer:
i believe its D
Step-by-step explanation:
Find the values of x and y in the special right triangle below.
Answer:
x=6 y=12
Step-by-step explanation:
30-60-90 triangle
shorter leg is x
longer leg is [tex]x\sqrt{3}[/tex]
hypotenuse is 2x
since the longer leg is [tex]6\sqrt{3}[/tex] than makes x=6
and y=2(6)=12
When rotated about its center, a regular nonagon has__
rotational symmetries. In addition to rotational symmetry, a regular nonagon has __
lines of reflectional symmetry.
Answer:
Symmetry in a regular nonagon
A regular nonagon has 9 lines of symmetry and a rotational symmetry of order 9, meaning that it can be rotated in such a way that it will look the same as the original shape 9 times in 360°. Nine 40° of rotation about the center.
Step-by-step explanation:
Find the area of the composite figure.
A. 65.1 sq in
B. 90.3 sq in
C. 106.3 sq in
D. 241.1 sq in
Answer:
I think B but not so sure
Hoping you have a good dayAnswer:
Step-by-step explanation:
radius of semi circle=8/2=4 in
height of triangle=14-4=10 in.
area of composite figure=1/2×8×10+π×4²=40+16 π≈90.3 sq. in
What is 56 1/2% written as a fraction in the simplest form?
Answer:
7 / 28
Step-by-step explanation:
7 / 28 = 0 . 28
Need help no links please ASAP
A recipe for pancakes requires 3/4 cup of oil. If Mr. Darcy wants to triple the recipe, how much oil will he need?
Answer:
the answer is 2 1/4 cups of oil
Step-by-step explanation:
if he wants to triple the ingredient then you would triple the numerator and than simplify your new fraction
3 times 3 is 9 = 9/4
9 divided by 4 is 2.25 = 0.25 is equal to 1/4 so it would be 2 1/4 cups of oil
Anna has 32 red beads, 16 blue beads, and 8 green beads. She wants to put an equal number of each kind of bead on necklaces she is making. How many of each kind of bead can Anna put on each necklace?
8
2.4 or 8
2 or 4
1 .2.4, or 8
Answer:
8 of them would probably fit on there
A circle has a diameter of 10cm. Find the Area of this circle. Use 3.14 for Pi.
Step-by-step explanation:
to find area
A = Pi x r^2
r = d/2 = 10/2 = 5
I need help with this one .
Answer:
32/9
Step-by-step explanation:
2 to the fifth power is 32. 3 to the second power is 9.
Problem:
Prove the following:
(a) Suppose that a; b > 0. If a < b; then a2 < b2: (b) Suppose that a; b > 0. If a2 < b2; then a < b:
Answer:
a)
We know that:
a, b > 0
a < b
With this, we want to prove that a^2 < b^2
Well, we start with:
a < b
If we multiply both sides by a, we get:
a*a < b*a
a^2 < b*a
now let's go back to the initial inequality.
a < b
if we now multiply both sides by b, we get:
a*b < b*b
a*b < b^2
Then we have the two inequalities:
a^2 < b*a
a*b < b^2
a*b = b*a
Then we can rewrite this as:
a^2 < b*a < b^2
This means that:
a^2 < b^2
b) Now we know that a.b > 0, and a^2 < b^2
With this, we want to prove that a < b
So let's start with:
a^2 < b^2
only with this, we can know that a*b will be between these two numbers.
Then:
a^2 < a*b < b^2
Now just divide all the sides by a or b.
if we divide all of them by a, we get:
a^2/a < a*b/a < b^2/a
a < b < b^2/a
In the first part, we have a < b, this is what we wanted to get.
Another way can be:
a^2 < b^2
divide both sides by a^2
1 < b^2/a^2
Let's apply the square root in both sides:
√1 < √( b^2/a^2)
1 < b/a
Now we multiply both sides by a:
a < b
The ratio of green houses to white houses on Winthrop Street is equal to
2 to 3. There are 60 white houses on Winthrop Street. How many green houses are there?
A 20 C 40
B 30 D 60
please show step by step
Answer:
C
Step-by-step explanation:
2:3 = x:60
3 → 60 (*20)
2*20=40
Answer:
40 green houses
Step-by-step explanation:
Because the ratio is given, you can use the criss-cross method.
2:3
?:60
All you do is multiply 60 by 2 then divide by 3
(60×2)/3=40