Answer:
see below
Step-by-step explanation:
We need to write it on vertex form (f(x) = a(x - c)² + d where (c, d) is the vertex) and to do that we will complete the square.
f(x) = x² + 3x - 2
= (x² + 3x + 9/4) - 9/4 - 2
= (x + 1.5)² - 4.25
The vertex is (-1.5, -4.25).
(05.05)On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2). What is the length of Side RT of the polygon? 4 unit 6 units 7 units 11 units
Answer: 11 units
Step-by-step explanation:
Given: On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2).
To find : length of Side RT of the polygon.
Using distance formula to find distance between (a,b) and (c,d):
[tex]d=\sqrt{(d-b)^2+(c-a)^2}[/tex]
Length of RT = [tex]\sqrt{(2-2)^2+(5-(-6))^2}[/tex]
[tex]\\\\=\sqrt{0+(5+6)^2}\\\\= \sqrt{11^2}\\\\=11[/tex]
hence, the length of RT = 11 units.
Answer:
the answer is 11 units
Step-by-step explanation:
At a figure skating competition, the order of skaters is randomly selected. If
there are 20 skaters, what is the probability that Christie, Taylor, and Jona will
skate first, second, and third, respectively?
Answer: [tex]\dfrac{1}{6840}[/tex]
Step-by-step explanation:
According to the permutations:
The arrangement of n things in an order = n!
If we fix that the first, second, and third person for skating, then we to arrange only 17 of the skaters.
Number of ways to arrange rest of 17 skaters = 17!
Number of ways that Christie, Taylor, and Jona will skate first, second, and third, respectively = 1 x 17!=17!
Number of ways to arrange all 20 skaters = 20!
Now, the required probability = [tex]\dfrac{\text{favourable outcomes}}{\text{total ways}}[/tex]
[tex]=\dfrac{17!}{20!}\\\\=\dfrac{1}{20\times19\times18}\\\\=\dfrac{1}{6840}[/tex]
Hence, the required probability = [tex]\dfrac{1}{6840}[/tex]
In meters, find the value of x?
Answer:
75 meters
Step-by-step explanation:
30/50 = 45/x
x = 75
Answer:
x= 75m
Step-by-step explanation:
If we call the angle in the bottom left θ, then the sinθ=(opposite side)/(hypotenuse).
For the smaller triangle:
sinθ=30/50
And for the bigger triangle:
sinθ=45/x
So:
30/50=sinθ=45/x
30/50=45/x
x=(45•50)/30=2250/30=75
So x= 75 meters
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
A. $16.34
B. $16.13
C. $5.37
D. $16.63
Answer: B. $16.13
Step-by-step explanation:
Formula : Sum of n observations = Mean x n
Given, 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student.
Total students = 82+74+96+99 =351
Sum of earnings of 82 seniors = $26.75 x 82= $2193.5
Sum of earnings of 74 juniors = $12.25 x 74 = $906.5
Sum of earnings of 96 sophomores = $15.50 x 96 = $1488
Sum of earnings of 99 freshmen = $10.85 x 99 = $1074.15
Total earnings = $2193.5 + $906.5+ $1488 +$1074.15
= $5662.15
Average collection = (Total earnings) ÷ (Total students )
= $5662.15÷ 351
≈ $16.13
Hence, the average collection for a student in this school = 16.31
So, the correct option is B.
A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns. Write an equation that shows the relationship between n, the number of supervisors, and u, the number of baby unicorns.
Answer:
18x-2
Step-by-step explanation:
Answer:
u=9n
Step-by-step explanation:
Can I get some help?? Ty
================================================
Explanation:
Subtract straight down. The x terms subtract to 5x-2x = 3x. The y terms subtract to 3y-3y = 0y = 0, so the y terms go away and are eliminated. The terms on the right hand side subtract to 31-25 = 6.
After all that subtraction, we end up with the equation 3x = 6 which solves to x = 2 after dividing both sides by 3.
Use x = 2 to find the value of y
5x+3y = 31
5(2)+3y = 31
10+3y = 31
3y = 31-10
3y = 21
y = 21/3
y = 7
or
2x+3y = 25
2(2)+3y = 25
4+3y = 25
3y = 25-4
3y = 21
y = 21/3
y = 7
Using either equation has x = 2 lead to y = 7.
Therefore, the solution is (x,y) = (2,7)
If you were to graph the two original equations, then they would intersect at (2,7).
Adding Rational Numbers Using Properties of Operations we can
add integers in any order using the
and
properties of addition.
Consider the integers a, b, c, and -d. We can add this group of
integers in several different ways:
a + (-b) + C+ (-0)
a+c+ (-6) + (-d)
(a + c) + [(-b) + (-d)]
The sum of the integers remains the
regardless of
their arrangement. We can use the commutative and associative
properties to break up numbers by
to find the sum of two or more rational numbers.
Answer:
First blank: Commutative
Second blank: Associative
Third blank: Same
Fourth blank and fifth blank: Rearranging them? (Not entirely sure)
Hope this helps :)
Find the equation for a hyperbola centered at (0, 0), with foci at (0,-sqrt73)) and (0,-sqrt73)) and vertices at (0, -8) and (0, 8).
Answer:
[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .
Step-by-step explanation:
Since vertices lie on y-axis. So, it is a vertical parabola of the form
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]
where, (h,k) is center, [tex](h,k\pm c)[/tex] is focus and [tex](h,k\pm a)[/tex] is vertex.
Center is (0,0). So, h=0 and k=0.
Foci are [tex](0,\pm \sqrt{73})[/tex]. So [tex]c=\sqrt{73}[/tex].
Vertices are [tex](0,\pm 8)[/tex]. So [tex]a=8[/tex].
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex]8^2+b^2=(\sqrt{73})^2[/tex]
[tex]b^2=73-64[/tex]
[tex]b=3[/tex]
Put h=0,k=0, a=8 and b=3 in equation (1).
[tex]\dfrac{(y-0)^2}{8^2}-\dfrac{(x-0)^2}{3^2}=1[/tex]
[tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex]
Therefore, the required equation is [tex]\dfrac{y^2}{64}-\dfrac{x^2}{9}=1[/tex] .
find the value of x 4x+15=7x+2=
Answer:
4x+15=7x+2
15_2=7x_4x
13=3x
13/3=x
4.33=x
Answer:
[tex]\boxed{x=\frac{13}{3} }[/tex]
Step-by-step explanation:
Subtract both sides by 15 and 7x.
Then, divide both sides by -3.
[tex]4x+15=7x+2\\4x-7x=2-15\\-3x=-13\\\displaystyle x=\frac{13}{3}[/tex]
WILL MARK BRAINLIEST!!! :) My math teach gave this to us for fun and I keep trying but can't get it right lol. What is 1+3+5+1+9+8+4+3+5+6+12+24+11+3+9+8+1+4+5+6+2+32+1+1+2? Also we're not allowed to use a calculator so it's taken me a long time
Answer:
It equals 165
Step-by-step explanation:
I used a calculator to find my answer
Answer:
166
Step-by-step explanation:
So I'm not sure if you're supposed to solve this with a pattern or something but here's how I solved it,
1 + 3 = 4
4 + 5 = 9
9 + 1 = 10
10 + 9 = 19
19 + 8 = 27
27 + 4 = 31
31 + 3 = 34
34 + 5 = 39
39 + 6 = 45
45 + 12 = 57
57 + 24 = 81
81 + 11 = 92
92 + 3 = 95
95 + 9 = 104
104 + 8 = 112
112 + 1 = 113
113 + 4 = 117
117 + 5 = 122
122 + 6 = 128
128 + 2 = 130
130 + 32 = 162
162 + 1 = 163
163 + 1 = 164
164 + 2 = 166
Thus, our answer is 166
Hope this helps!
Please answer this question now
Answer:
This is simple! (Kind of)
Step-by-step explanation:
First, notice how HJ is tangent. HG is a radius intersecting HJ at H.
This means, (According to some theorem that I forgot the name of) that GHJ is a right angle.
Thus, we can use the 180* in a triangle theorem.
[tex]180=90+54+6x+6[/tex]
So, let's solve!
[tex]30=6x\\5=x[/tex]
So, there you go! Nice and simple!
Hope this helps!
Stay Safe!
Step-by-step explanation:
hope it helps yoy..........
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply. x = one-half y minus 3 2 x minus y = negative 6 2 x minus y = negative 3 x = one-half (y minus 3) y = 10 (x minus 1)
Answer: x=one-half y minus
Step-by-step explanation:
Answer:
x=1/2 y-3
Step-by-step explanation:
Look at the frequency table below. Of all the people surveyed, what is the probability of someone selecting dog?
Answer:
im guessing 58/100
Answer:
58/100 for sure
Step-by-step explanation:
i had nothing to explain
1 Calculator What is the area of this figure? Enter your answer in the box. units²
Answer:
44 units²
Step-by-step explanation:
For triangles: (bases and heights of both triangles are equal)
Base = 4 units, height = 3 units
For trapezoid:
Base 1 = 5 units, base 2 = 3 units, height = 8 units
Area of figure = Area of two triangles + Area of trapezoid
= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height
=4*3 + 1/2(5+3)*8
= 12 + 8*4
= 12 + 32
= 44 units²
The required area of the figure shown in the graph is given as 44 square units.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
The area of the given figure is given as,
Area = Area of 1 + Area of 2 + Area 3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]
Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.
Thus, the required area of the figure shown in the graph is given as 44 square units.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ6
Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 – species #2), and your interval is –3.6 to 61.6 ounces. What can you conclude?
Answer:
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Step-by-step explanation:
The following are what I will conclude about based on the information given in the question.
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Shrina is selling cookie dough for her soccer team. She sold 2 tubs of
Oatmeal Raisin and 2 tulbs of Peanut Butter.
How much money did she make?
Oatmeal Raisin
$6 a tub
$22
$24
Peanut Butter
$5 a tub
$20
$11
Answer: 22
Step-by-step explanation:
She sold two tubs of Oatmeal Raisins and it's 6 dollars a tub so we can do 6*2 or 6+6 (doesn't matter). We get $12. Then, she also sells 2 tubs of Peanut Butter, and since it's $5 a tub, then we do 5*2 or 5+5 to get 10. We add 12 and 10 (12+10) and get 22.
I'm not sure if this is right because you added $22, $24, $20, and $11 and I'm not sure what the purposes of those are.
In two or more complete sentences, describe how to find the interval(s) where the function is increasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is increasing
Answer:
(-5,0)
Step-by-step explanation:
In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number
For Decreasing:
(-8,-5)
(4,8)
For Increasing:
(-5,0)
Simplify: m(2+n-m)+3(3n+m^2-1)
Step-by-step explanation:
m(2+n-m)+3(3n+m^2-1)
= 2m + mn - m^2 + 9n + 3m^2 - 1
= 2m^2 + 2m + 9n + mn - 1
Answer:
mn+2m^2+9n+2m-3
Step-by-step explanation:
An automotive plant makes the Quartz and the Pacer. The plant has a maximum production capacity of 1200 cars per week, and they can make at most 600 Quartz cars and 800 Pacers each week. If the profit on a Quartz is $500 and the profit on a Pacer is $800, find how many of each type of car the plant should produce.
Answer:
x=400 and y=800
Step-by-step explanation:
let x be the Quartez and y is Pacer
x+y≤1200 ( maximum production capacity of 1200 cars per week)
0≤x≤600
0≤y≤800
profit : 500x+800y
at a point : x=0 y=800
profit=500x+800y ⇒ 500(0)+800(800)=640000
profit= 500(600)+0=300000 wen x=600(max), y=0
Profit=500(600)+800(600)= 780000
profit =500(400)+800(800)=840000 this is the max profit when
x=400 and y=800
HELP PLEASE Solve the equation for x. the square root of the quantity x plus 4 end quantity minus 7 equals 1 x = 4 x = 12 x = 60 x = 68
Answer:
679=49
Step-by-step explanation:
3838 is the one for 928 cause 666
Which of the following is a factor of x3+ 6x2 + 5x – 12?
A.X + 1
B. x - 3
C. x + 2
D. x + 4
1,3,4 that is the answer
Answer:
The answer is option D.Step-by-step explanation:
x³ + 6x² + 5x - 12
A factor of the polynomial is the value of x when substituted into the expression will make it zero
Choosing x + 4
x = - 4
We have
(- 4)³ + 6(- 4)² + 5(- 4) - 12
-64 + 96 - 20 - 12 = 0
Since the result is zero
x + 4 is a factor of the polynomial
Hope this helps you
Which number is the additive inverse of –5? A.– 1/5 B.0 C.1/5 D.5
Answer:
Hey there!
The additive inverse means the number opposite to five.
The additive inverse of negative five is positive five.
Hope this helps :)
Answer:
The additive inverse of negative five is positive five.
explanation:
IM BEING TIMED, WILL GIVE 25 POINTS (NEEDED WITHIN THE NEXT 20 MINUTES The graph g(x)=x^3-x is shown. (idk how to screenshot, so please pull it up on the desmos graphing website or something) What will the graph of 0.5g(x-2)+1 look like?
Answer:
The function is
[tex]f(x)=0.5x^3-3x^2+5.5x-2[/tex]
The graph is attached.
Step-by-step explanation:
We have a function g(x) and we need to graph a new function that is function of g(x).
The final function is
[tex]f(x)=0.5\cdot g(x-2)+1[/tex]
We start by calculating g(x-2):
[tex]g(x-2)=(x-2)^3-(x-2)\\\\g(x-2)=(x^3-6x^2+12x-8)-(x-2)\\\\g(x-2)=x^3-6x^2+11x-6[/tex]
Then, we can calculate f(x) as:
[tex]f(x)=0.5\cdot g(x-2)+1\\\\g(x-2)=x^3-6x^2+11x-6\\\\\\f(x)=0.5(x^3-6x^2+11x-6)+1\\\\f(x)=0.5x^3-3x^2+5.5x-3+1\\\\\\f(x)=0.5x^3-3x^2+5.5x-2[/tex]
A group of hikers buy 8 bags of trail mix. Each bag contains 3 1/2 cups of trail mix. The trail mix is shared between evenly between 12 hikers. How many cups of trail mix do each hiker receive?
Answer:
The hikers each receive 2 1/3 cups of trail mix.
1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which will come out as 28.
2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.
Find the amount and present value of 10 quarterly payments of $ 1500, if the interest rate is 25% compounded each month.
Given Information:
Monthly payment = MP = $1500/4 = $375
Monthly interest rate = r = 25/12 = 2.083%
Required Information:
Present Value = ?
Answer:
[tex]PV = \$10,110[/tex]
Explanation:
n = 10*4
n = 40 monthly payments
The present value is found by
[tex]$ PV = MP \times \frac{ (1 - \frac{1}{(1+r)^n} )}{r} $[/tex]
Where r is monthly interest rate.
MP is the monthly payment.
[tex]$ PV = 375 \times \frac{ (1 - \frac{1}{(1+0.02083)^{40}} )}{0.02083} $[/tex]
[tex]PV = 375 \times (26.96)[/tex]
[tex]PV = \$10,110[/tex]
Therefore, $10,110 is the present value of 10 quarterly payments of $1500 each at 25% interest rate compounded each month.
The quadrilateral shown is a (blank) x= (blank)
Answer:
The quadrilateral shown is a kite, because it has two non-congruent pairs of congruent sides
x = 3
Step-by-step explanation:
The vertex angles in a kite are bisected by the diagonals. Thus, 11x = 9x + 6.
11x=9x+6
2x=6
x=3
Hope it helps <3
A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what P-Value of 0.047 means in this context.
Answer:
A p-value if 0.047(same as 4.7%) means there is a 4.7% chance that there is no difference in how effective the new treatment is.
Step-by-step explanation:
When we talk of a p-value, we are referring to a conditional probability. What it tells us is the probability of getting results which are at least as unusual as the observed statistics in a case where we are given that the null hypothesis is not false.
A p-value if 0.047(same as 4.7%) means there is a 4.7% chance that there is no difference in how effective the new treatment is.
So what this means is that, in this case it is better that more data is collected to enable us know how effective the new treatment is
HELLLLLPPPPPPPPPPPPpppppppppppppp
Answer:
22.9 or round it up to 23
Step-by-step explanation:
SOHCAHTOA
C=A/H
acos (35/38)
=22.9
PLEASE HURRY I NEED HELP BAD
An equation is shown below:
5(2x – 3) = 5
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Answer:
One solution
2
Step-by-step explanation:
5(2x-3)=5
10x-15=5
10x=5+15
10x=20
x=2
Part A: 1
Part B: It has only one solution and it is 2.
Hope this helps ;) ❤❤❤
Answer:
I believe 1 solution
Step-by-step explanation:
divide both side of equation by 5= 2x-3)=1
add 3 to each side= 2x=1+3
2x=4
x=2
Which expression is equivalent to StartFraction (2 m n) Superscript 4 Baseline Over 6 m Superscript negative 3 Baseline n Superscript negative 2 Baseline EndFraction? Assume m not-equals 0, n not-equals 0. StartFraction 8 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction StartFraction 10 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction StartFraction 8 m Superscript 16 Baseline n Superscript 12 Baseline Over 3 EndFraction StartFraction m Superscript 4 Baseline n Superscript 6 Baseline Over 3 EndFraction
Answer:
[tex]\dfrac{8m^7n^6}{3}[/tex]
Step-by-step explanation:
[tex]\dfrac{(2mn)^4}{6m^{-3}n^{-2}}=\dfrac{2^4}{6}m^{4-(-3)}n^{4-(-2)}=\boxed{\dfrac{8m^7n^6}{3}}[/tex]
__
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
1/a^b = a^-b
(a^b)(a^c) = a^(b+c)
Answer:
A
Step-by-step explanation: