Victor draws one side of equilateral ∆PQR on the coordinate plane at points P (–9, –2) and Q (–2, –2). What are the two possible coordinates of vertex R? Round to the nearest tenth.
Answer: [tex](-5.5,4.062)\ \text{and}\ (-5.5,-8.062)[/tex]
Step-by-step explanation:
Given
The two vertices of a equilateral triangle are [tex](-9,-2)\ \text{and}\ (-2,-2)[/tex]
Suppose the third vertex is [tex](x,y)[/tex]
Side length in equilateral triangle are equal.
[tex]\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+9\right)^2+\left( y+2\right)^2}\\\text{squaring both sides}\\\\\Rightarrow 7^2=\left( x+9\right)^2+\left( y+2\right)^2\quad \ldots(i)\\\\[/tex]
Similarly,
[tex]\Rightarrow \sqrt{\left( -2+9\right)^2+\left( -2+2\right)^2}=\sqrt{\left( x+2\right)^2+\left( y+2\right)^2}\\\\\Rightarrow 7^2=\left( x+2\right)^2+\left( y+2\right)^2\quad \ldots(ii)[/tex]
Subtract (i) and (ii)
[tex]\Rightarrow \left( x+9\right)^2-\left(x+2\right)^2=7^2-7^2\\\\\Rightarrow (x+9+x+2)(x+9-x-2)=0\\\Rightarrow (2x+11)7=0\\\\\Rightarrow x=-\dfrac{11}{2}[/tex]
Insert the value of [tex]x[/tex] in equation (ii)
[tex]\Rightarrow \left(-5.5+2\right)^2+\left(y+2\right)^2=7^2\\\\\Rightarrow \left(-5.5+2\right)^2+\left(y+2\right)^2-\left(-5.5+2\right)^2=7^2-\left(-5.5+2\right)^2\\\\\Rightarrow \left(y+2\right)^2=36.75\\\\\Rightarrow y=4.06217\dots ,\:y=-8.06217[/tex]
So, two possible vertex are [tex](-5.5,4.062)\ \text{and}\ (-5.5,-8.062)[/tex]
Work out
m
and
c
for the line:
y
=
3
x
+
1
Answer: m=3
Step-by-step explanation:
Solve the right triangle. Round decimal answers to the nearest tenth.
Answer:
Step-by-step explanation:
take angle A as reference angle
using cos rule
cos A = adjacent/hypotenuse
cos A =10/15
cos A =0.66
[tex]A=cos^{-1} (0.6666)[/tex]
A=48.194
A=48.2
angle A + angle B + angle C =180 degree (being sum of interior angles of a triangle)
48.2 + angle B + 90 =180
138.2 + angle B =180
angle B =180-138.7
angle B =41.8
for BC
using pythagoras theorem
a^2 + b^2 = c^2
AC^2 + BC^2 = AB^2
10^2 + BC^2 = 15^2
100 + BC^2 = 225
BC^2 = 225-100
BC^2 = 125
[tex]BC=\sqrt{125}[/tex]
BC=5[tex]\sqrt{5}[/tex]
BC=11.2
ANSWE PLEASEEEEEEEEEEEEEEE
Answer:
your answer is gonna be A!! <3
Step-by-step explanation:
1 Subtract 33 from both sides.
y-3=-2x
y−3=−2x
2 Divide both sides by -2−2.
-\frac{y-3}{2}=x
−
2
y−3
=x
3 Switch sides.
x=-\frac{y-3}{2}
x=−
2
y−3
Answer:
A
Step-by-step explanation:
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
(-infinity, 9]
Step-by-step explanation:
The range of the function is 'all real numbers less than or equal to 9.' We are told that the vertex is at (-2, 9) and that the curve opens downward, which indicates that 9 is the maximum function value, and that the function can take on any value less than or equal to 9.
The domain is 'the set of all real numbers,' which is true for any polynomial.
AIR TRAVEL - an airplane traveling at an altitude of 5,900m changes its altitude by - 2,900m. What does this change in altitude mean ?
Answer:
Step-by-step explanation:
altitude -2900 m means its height decreases by 2900 m or it comes down by 2900 m
100 POINTS HELP! THIS IS A PROJECT. NOT IN A RUSH.
Describe how to find the terms mean, median, mode, and range of a group of numbers.
Pretend you are a teacher trying to describe these terms to a student. Make sure you write as if you are the teacher and explain each term as if the student is learning this for the first time. Be descriptive and give examples. Make sure you include the data set (the group of numbers) you will be working with. Be sure to use complete sentences. Be creative!
Answer
Hello class!
Step-by-step explanation:
1. The mean is the average of a data set.
2. The mode is the most common number in a data set.
3. The median is the middle of the set of numbers.
Of the three, the mean is the only one that requires a formula. I like to think of it in the other dictionary sense of the word (as in, it’s mean as opposed to nice!). That’s because, compared to the other two, it’s not as easy to work with.
Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds? Henry's design would result in a larger flower bed because its area would be 2,500 square feet. Liani's design would result in a larger flower bed because its area would be 2,500 square feet. Henry's and Liani's designs would result in flower beds with the same area. Henry's and Liani's designs are not possible with the given amount of wood.
Answer:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Step-by-step explanation:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
B. Liani's design would result in a larger flower bed because its area would be 2,500 square feet.
C. Henry's and Liani's designs would result in flower beds with the same area.
D. Henry's and Liani's designs are not possible with the given amount of wood.
Length of wood = 200 feet
Henry's square bed design = 200 feet / 4
= 50 feet
Note: A square has 4 equal sides, hence, the division by 4
Each side of the square bed = 50 feet
Area of the square bed = length ²
= (50 feet)²
= 2,500 square feet
Liani rectangular bed design
Length = 55 feet
Width = 45 feet
Note: adding of 2 length and 2 width = 200 feet
That is,
2(55) + 2(45)
= 110 + 90
= 200 feet of wood
Area of Liani rectangular bed design = length × width
= 55 feet × 45 feet
= 2,475 square feet
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Answer:
A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.
Step-by-step explanation: magic
Describe the difference between a relation and a function
Answer:
A relation can have 2 output to 1 output bt not a function
Fill in the blank: 12(8x - 4) = __X - 48
Answer:
96x
Step-by-step explanation:
12(8x - 4)
=12*8x - 12*4
=96x - 48
Answer:
96
Step-by-step explanation:
You distribute the 12 to each term, the 8x term turns into 96x after distribution.
pleaseee help me with this questionnn
Answer:
itss8tsz85sz85s,85s,8td,8td,85dz85dzd85e,7554334567
Step-by-step explanation:
otdxd8td 8td 85sx8ts,ts8,8ts,8td,88ts8ts,8ts,8ts,8ts,8ts,8ts,8ts,8ts,8ts,,8ts8ts,8t,s8ts,8tz8txdxtitixtxtidittdxdctiti dttxdididez6z84gfiwz84wz85wzy0dcydcydc6dctr456887654
Solve 16x + 8 ≥ 12x + 20
Answer:
x ≥ 4
Step-by-step explanation:
16x + 8 ≥ 12x + 20
Subtract 12 from both sides
4x + 8 ≥ 20
Subtract 8 from both sides
4x ≥ 16
Divide both sides by 4
x ≥ 4
Help I have to submit it
What is the perimeter of a trapezoid?Units
Please help me! It is very important that I get this done but I am beyond confused!
Brandt invests an initial amount P of $180 into an account that pays interest at 2.5% compounded continuously. Carter invests $120 into an account that pays 4.8% compounded continuously. The balance of each investment, A, is calculated using the equation A=Peⁿ. The graph shows their investments over time.
When will their investments reach the same balance?
a. Their investments will never reach the
same balance.
b. Their investments will reach the same
value between years 15 and 16.
c. Their investments will reach the same
value between years 16 and 17.
d. Their investments will reach the same
value between years 17 and 18.
e. Their investments will reach the same
value between years 18 and 19.
Answer:
Step-by-step explanation:
i think it should be d 16 and 17
Based on the information marked in the diagram, ∆XYZ and ∆RST must be congruent.
A) True
B) False
Answer:
Can confirm the answer is true
Step-by-step explanation:
Just took the test
I need to find the area
Answer:
90 cm^2
Step-by-step explanation:
The area of a triangle is half of the base times height, so it is 1/2*15*12 = 7.5*12 = 90
Can anyone help me please I really need help.
Answer:
what do u need help with
Step-by-step explanation:
Shape ABC has the following coordinate
A (3,9) B (27,-15) C (-12,-6)
The Image A'B'C' of a dilation has the coordinate
A' (1,3) B' (9,-5) C' (-4,-2)
What is the Scale Factor of the Dilation
Megan bought beads for $9.95. She received a 10% discount. She then paid, a sales tax of 6%. How much did she pay for the beads?
Please help me ASAP tysm
Answer:
?
Step-by-step explanation:
please help!!!
what is the following sum?
Answer:
I think the answer is A
8x³y⁴ ³squareroot xy
Step-by-step explanation:
Mark as brainllest if it helps!!!
what is slop of the line that passes through the ponitss (5, -4) and (7, -4)
Answer:
The slope is 0
Step-by-step explanation:
Points on the graph:
(5, -4) and (7, -4)
Slope:
m=(y2 - y1)/(x2 - x1)
m=(-4 + 4)/(7 - 5)
m= 0/2
m=0
In stage 2 of a rocket's takeoff, the speed of the rocket increases at a rate of 4.3% per minute. The speed of the rocket at the beginning of stage 2 was 5,000 kilometers per hour. Its speed at the end of Stage 2 will be 25,000 kilometers per hour.
If t is the time, in minutes, from the beginning of stage 2, which equation could be used to determine how long it will take for the speed of the rocket to reach 25,000 kilometers per hour, assuming it increases at the same rate for all of stage 2?
A.
5,000 = 25,000(0.043)t
B.
5,000 = 25,000(0.957)t
C.
25,000 = 5,000(1.043)t
D.
25,000 = 5,000(1.43)t
altogether i have 10 bags of sweets. the mean number of sweets in the bag is 40
Answer the question : I don't get what the question is suppose to be
Step-by-step explanation:
Please help me with this
Answer: [tex]a_{n}=4n+-3[/tex]
Step-by-step explanation:
The way arithmetic sequences are usually written is:
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n}[/tex] is the the term you are looking for. It has an n because we aren't looking for a specific one.
[tex]a_{1}[/tex] is the first term of the sequence. In this case that is 1.
n is the term position. Meaning if you wanted to find the fifth term you'd sub 5 in for n.
d is the common difference. In this case it is 4.
Now we can sub these values in.
[tex]a_{n} =1 +(n-1)4[/tex]
We can simplify the right part of the equation.
[tex]a_{n} =1 +(n-1)4\\a_{n} =1 +(4)(n)-(4)(1)\\a_{n}=1+4n-4\\a_{n}=4n+1-4\\a_{n}=4n+-3[/tex]
Thank you to the person that is helping me. I don’t understand this one at all..
cuanto es 8por8por5por3
Answer:
yes
Step-by-step explanation:
Answer:192
Step-by-step explanation:
What are the slope and the y-intercept of the linear function that is represented by the equation 8x-2y = 5?
Answer:
The slope is 4 and the y intercept is -5/2
Step-by-step explanation:
8x-2y = 5
Solve for y to get the equation in slope intercept form
Subtract 8x from each side
8x-8x-2y =-8x+ 5
-2y = -8x+5
Divide by -2
-2y/-2 = -8x/-2 + 5/-2
y = 4x -5/2
This is in slope intercept form y= mx+b where m is the slope and b is the y intercept
The slope is 4 and the y intercept is -5/2
How many quarters does Annie have
A.35
B.49
C.3
D.7
Answer:
n = 7
Step-by-step explanation:
sarah = m
annie = n
sarah has 21 more than annie
m = 21+n
given sarah has 28 quareters
m = 21 + n
28 = 21 + n
28 - 21 = n
7 = n
annie has 7 quarters.
