Given:
Two points are (6, 7) and I(-7,-6).
Point G lies [tex]\dfrac{1}{2}[/tex] of the way along Hl.
John says that point G is located at the origin.
To find:
Whether John is correct or not.
Solution:
Point G lies [tex]\dfrac{1}{2}[/tex] of the way along Hl. I means point G is the midpoint of HI.
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]G=\left(\dfrac{6-7}{2},\dfrac{7-6}{2}\right)[/tex]
[tex]G=\left(\dfrac{-1}{2},\dfrac{1}{2}\right)[/tex]
The location of point G is at [tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)[/tex], which is not equal to origin, i.e., (0,0).
Therefore, John is incorrect.
Will mark brainliest please help
Answer:
wuts the question?
Step-by-step explanation:
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23) It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels
at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of
the train? State what x represents, state the equation, and then state the answer.
Rate Time Distance
Bus x 6 бах
Train x-? 2(x+3)
Distance bus travels – Distance train travels
Answer:
x = 50 mph speed of the bus
y = 75 mph speed of the train
Step-by-step explanation:
Lt´s call "x" speed of bus and "y" speed of train.
According to the problem statement
6*x = 4*y (1)
y = x + 25 (2)
We solve for x and y the two equation system
y = ( 6/4)*x
( 6/4)*x = x + 25
6*x = 4*x + 100
2*x = 100
x = 50 mph
And
y = (6/4)*x
y = 300/4
y = 75 mh
PLS HELP SOMEBODY I NEED HELP
Answer: 36 + 4d
Step-by-step explanation:
so basically we just distribute to all the numbers in the parantheses. so 4 times 9 is 36 and 4 times d is 4d.
What form is the equation in?
y = 2x2-8x+7
Answer:
standard form
Step-by-step explanation:
f(x)=ax^2+bx+c
Which equation has the same solution as 4-2(x-5)=x-19
A. 2(x+5)=-8
B. 3(x-3)=9
C. x+2=2x-3
D. 3x-4=2x+7
Answer:
D
Step-by-step explanation:
Betsy, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
Answer:
$45,000 at 13% = B-rated bond
$5,000 at 3% = CD
Step-by-step explanation:
Let us assume the x amount at 13% be 0.13x
And, y amount at 3% be 0.03x
Total interest = $6,000
The equation is
0.13x + 0.03x = $6,000 ................(1)
Now the total amount is $50,000
So
x + y = $50,000
y = $50,000 - x ................(2)
Now put the y value in the equation 1
So,
0.13x + 0.03 ($50,000 - x) = $6,000
0.13x + $1,500 - 0.03x = $6,000
0.10x = $6,000 - $1,500
0.10x = $4,500
x = $4,500 ÷ 0.10
= $45,000 at 13%
now y value would be
= $50,000 - $45,000
= $5,000 at 3%
Use root test to determine the series is convergent/divergent or inconclusive
You can first condense the series to make it simpler to study. If n is odd, then n = 2k - 1, and if n is even, then n = 2k for some k ≥ 1. So for each k, you can pair up the k-th terms of the odd- and even-indexed series.
odd:
[tex]\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}[/tex]
even:
[tex]\dfrac1{3^{\frac n2}}=\dfrac1{3^k}[/tex]
So the series can be re-indexed as
[tex]\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}[/tex]
By the root test, the series converges, since
[tex]\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13<1[/tex]
answer choices
AAS
ASA
SSS
HL
SSA
AAA
SAS
A bookcase has 5 of these bookshelves that are 42 inches long. How many FEET of shelf space is there? Explain your reasoning.
Answer:
17.5
Step-by-step explanation:
The first step is to convert one bookshelf into feet, so 42 divided by 12=\
3.5
Now, we have 5 of these shelves, so we have to do 3.5 x 5=17.5.
15. Harold learned that 6 out of 10 students at his school live within two miles of the school. If 240 students attend Grade 6 at his school, about how many of these students should Harold expect to live within two miles of the school? A 24 ® 40 © 144, 180
Answer:
144
Step-by-step explanation:
Write a equation(or whatever it is called)
6/10=x/240Cross multiply, 1440=10xDivide, 144=xCheck your work:
6/10=144/240Cross multiply, 1440=1440Jen is sewing together fabric rectangles to make a bookmark
width 10 cm 9 cm
length 3 cm
What is the area of the bookmark?
A) 27 cm2
B) 30 cm2
C) 57 cm2
D) 60 cm2
Find the value of zα/2 to construct a confidence interval with level 95%. Round the answer to two decimal places.
Answer:
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Step-by-step explanation:
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
-8k + 6 = -10k + 10 SOMEONE HELP QUICKKKK
Answer:
k = 2
Step-by-step explanation:
-8k + 6 = -10k + 10
-8k = -10k +4
2k = +4
2k / 2 = 4 / 2
k = 2
Find the equation of a line that passes through the points (2,2) and (3,7).
Leave your answer in the form y = mx + c
Answer:
gradient = change in y/ change in X
= 7-2/3-2=5
the gradient = 5
use either one of the points to find the gradient
y-3/x-7 =5
y=5x-4
which statements are true select all that apply. Extra points!!!
A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places
Answer:
0.0475 or 4% professional language translators get paid less than $250 per hour
Step-by-step explanation:
Mean = 320
Standard Deviation = 41.75
We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)
First we will find value of z
Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]
We have x=250, finding z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]
Now we will find P(z<-1.67) by looking into the normal distribution table
[tex]P(z<-1.67)=0.0475\\[/tex]
So,0.0475 or 4% professional language translators get paid less than $250 per hour
In which of the following drawings are parallel to DE and AC?
Answer:
probably A
Step-by-step explanation:
Brainliest pls
Answer:
d
Step-by-step explanation:
ut is parrell in d because the bottom line is ac n the line parrell to that,is de
I’m stuck on this I would really appreciate if someone could answer this and explain so I could understand better :)
I need help please help me guys with the correct answer
Answer:the answer is D
Step-by-step explanation:
it is
Find the sum of 1
5
and 7
10
The expression written in equivalent form with common denominators is
.
The sum is
.
Answer:
1+5+7+10=23
hope that's what u meant?
Answer:
✔ 2/10 + 7/10
✔ 9/10
Step-by-step explanation:
Let L1 be the line through the origin and the point (6, 0, −1). Let L2 be the line through the points (1, −1, 1) and (7, 1, 7). Find the distance between L1 and L2.
Answer:
6
Step-by-step explanation:
find the measure of interior angle of a regular 15-gon
A. 158.8
B. 169
C. 156
D. 150
Answer:
c.155 the answer is C. 156
Rick is traveling at a rate of 9 miles every 12 minutes. Ann is traveling at a rate of 50 miles an hour. If both cars start at
the same place at the same time, and are going to the same place, who will reach their destination first? Show and
explain how you know. Be sure to include appropriate units.
Answer:
9
Step-by-step explanation:
George earns $8 1/4 an hours. He is paid 1 1/2 times the regular rate when he works over time. How much does he make per hours when he works overtime?
9. Alan invests £425 in a savings account paying 4.14% compound interest.
a. How much will his investment be worth after three years?
b. Express the amount paid as a percentage of the amount invested
Eight boys and fifteen girls are in a classroom. What is the probability of choosing a boy or a girl from the
class?
Answer:
it would be 8 to 15
Step-by-step explanation:
you would write it as a fraction 8/15. then, you would try and simplify it. because you cant simplify 8/15 anymore, your answer would be 8/15! hope this helps :)
A company manufactures fuel tanks for cars. The total weekly cost (in dollars) of producing x fuel tanks is given by ... C(x) = 10000 +90x - 0.08x2 Find the exact cost of producing the 501st item.
Answer:
cost of producing the 501st item = $9.92
Step-by-step explanation:
The function representing the cost is given by;
C(x) = 10000 + 90x - 0.08x²
To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.
Thus;
C(500) = 10000 + 90(500) - 0.08(500)²
C(500) = 10000 + 45000 - 20000
C(500) = $35000
Similarly;
C(501) = 10000 + 90(501) - 0.08(501)²
C(501) = 10000 + 45090 - 20080.08
C(501) = $35009.92
cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92
a) Show that x² - 8x + 20 can be written in the form (x - a)² + a where a is an integer.
b) Hence explain how you know that x² - 8x + 20 is always positive.
I have worked out the first bit of the question and the answer is:
x²-8x+20
x²-8x+16-16+20
(x-4)²+4
(x-a)²+a
a= 4
I just need help with part b and I'm struggling to do it. Please help.
Answer:
Step-by-step explanation:
b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.
You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive
Luke's pencil case measure 1.5 inches by 4 inches by 6 inches. How many pencils can he fit in his pencil case if each pencil has a volume of 3 square inches?
Answer:
b
Step-by-step explanation:
The Miller family wants to join a public swimming pool that charges a fee of $25.00 per year and then $3.00 for each visit.
A. Draw a graph to show the yearly cost to the Miller family.
B. Can the cost be represented by linear function? why or why not?
C. Write a function to model the yearly cost to the Miller family. Make sure to define variables.
D. If the pool decided to charge $3.50 per visit, how would you graph change?
Answer:
B) Yes
C) C = 3x + 25
Step-by-step explanation:
Given that:
Yearly charge = $25
Charge per visit = $3
The yearly cost will depend on the number of visits for the year :
B.) Cost can be represented by a linear function, as the graph it yields is a straight line graph having intercept and slope.
C.) C = mx + b
Where ;
b = intercept = yearly cost
m = slope or gradient = cost per visit
C = total cost
x = number of visits
Hence,
C = 3x + 25