Answers
Answer:
Step-by-step explanation:
a)
First I will calculate the equation of the line that goes trough the points
C (0, 0) and (-4, 3).
y= mx + b
y = [(3-0)/ (-4 -0) ] x + 0
y = (-3/4)x →the slope of tis line is (-3/4)
The slope of line l is the negative reciprocal of (-3/4) the slop of line that goes trough points C (0, 0) and (-4, 3) because the lines are ⊥.
Slope of line l is 4/3
b)
The equation of l is
y= (4/3)x + b
for point (x= -4, y = 3) that belongs to the line l, we have
3 = (4/3) (-4) + b
3 = (-16/3) + b
3 + (16/3) = b
(9+16)/3 = b
25/3 = b
The equation of the line l in slope intercept form is :
y = (4/3)x + (25/3)
c)
The radius of circle C is the distance between C (0, 0) and (-4, 3).
d² = (x2-x1)² +(y2-y2)²
d = √(-4-0)² +(3-0)²
d = √16+ 9
d = 5 → the radius of the circle C is 5
d)
Line l intersects the y-axis at (25/3) as we previously found out.
The radius is 5.
...therefore the distance between the line l's y-intercept and the circumference of the circle is
(25/3 ) - 5 = (25 - 5·3)/3 = 10/3
Related Questions
I know this is super random but I was never shown in class how to actually do this type of problem so if you could give an explanation it would be so so helpful :)
____________________________________
Winifred bought a bib necklace, which is just a big necklace in the shape of a dinner bib, at a 45% discount. If the discount saved her $63, what was the necklace's original price?
Answers
$140 was the original price.
discount : 45%
45% ⇒ $63
1% ⇒ $(63/45)
1% ⇒ $1.4
original price is always 100%
100% ⇒ $(1.4*100)
100% ⇒ $140
Let the original price of the necklace be ,'x',
then,
According to the question,
(45/100)x = 6345x = 6300x = 6300/45x =140Hence ,the necklace she bought worths $140 without the discount given to her.
[ Thanks to starrysoul100 ]
Write the equation of the line that passes through the points (2,-4) and (4,2) in slope-intercept form.
Answers
Answer:
y = 3x - 10
Step-by-step explanation:
Find the slope
(2 - (-4) ) / (4-2) = 3
Write in point-slope form using (4.2)
y - 2 = 3 ( x - 4)
y-2 = 3x-12
y=3x-10
Jace gathered the data in the table. he found the approximate line of best fit to be y = –0.7x 2.36. a 2-column table with 5 rows. the first column is labeled x with entries 0, 1, 4, 5, 7. the second column is labeled y with entries 3, 1, 0, negative 2, negative 2. what is the residual value when x = 5? –3.14 –0.86 0.86 3.14
Answers
The residual value is the difference in the value of the y coordinate between the real value and the expected value. The residual value will be equal to -0.86.
What is residual value?The residual value is the difference in the value of y coordinate between the real value and the expected value.
Residual Value = Real value of y - The predicted value of y
The value of y in the table is -2 when the value of x is 5. And as per the function, the value of y when the value of x is 5 can be written as,
[tex]y = -0.7x+2.36\\\\y = -0.7(5)+2.36\\\\y= -3.5+2.36\\\\y=-1.14[/tex]
Now, the residual value can be written as,
[tex]\text{Residual Value} = \text{(Value of y in the table)} - \text{(Value of y as per the function)}\\\\\text{Residual value} = -2 - (-1.14)\\\\\text{Residual value} = -2+1.14\\\\\text{Residual value} = -0.86[/tex]
Hence, the residual value will be equal to -0.86.
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Answer:
-0.86
Step-by-step explanation:
cuz im a slay queen boss
What is the volume??
Answers
Answer:
V=828.96cm²
Step-by-step explanation:
V=（4/3）∏r³*（1/2）+（1/3）∏r²h
r=6cm
h²=(2√34)²-6²=4*34-36=100
h=10cm
V=2/3*6³∏+1/3*36*10∏=144∏+120∏=264∏=264*3.14=828.96cm²
Expand the logs and show work
Answers
I’m not too sure what was meant by expanding?
What I’ve found is what power you need to get the number that’s being logged.
The last question uses a, because the question uses x.
The working I’ve done should be self-explanatory.
(3×10^6)+(3×10^6)
give your anwser in standard form.
Answers
Answer:
Solve in parenthesis first(exponents:
(3 x 10^6) + (3 x 10^6)
Will be:
(3 x 1,000,000) + (3 x 1,000,000)
Multiply in the parenthesis:
(3,000,000) + (3,000,000)
Add them:
= 6,000,000
Standard form:
6 x 6^10
Use the order of
PEMDAS:ParenthesisExponentsMultiplicationDivisionAdditionSubtraction!(45 x 54)/5
What is the answer?
Answers
Answer:
486
Step-by-step explanation:
Answer:
486
45x54=2430
2430/5 is 486
Step-by-step explanation:
I need help with this please
Answers
Answer:
The measure of the angle is exactly x.
I need help asap pls
Answers
Answer:
C = 8π
Area = 32π
Step-by-step explanation:
Radius = 4 cm
Circle Circumference Formula: 2πr
C = 2π*4 = 8π cm
Area Circle Formula: 2πr^2
Area = 2π*4^2 = 2π*4*4 = 2π*16 = 32π cm
What’s the center of a circle also called?
Answers
the focus of the circle
hope it helps...!!!
Standardized Test Practice
5. What is the least common denominator
A) x
C) (x + 2)(2x + 3)
B) x(x + 2)
D) x(x + 2)(2x + 3)
Answers
PLEASE HELP If a fair coin is tossed 9 times, what is the probability, to the nearest thousandth, of getting exactly 1 heads?
Answers
The probability of getting exactly 1 head when a fair coin is tossed 9 times is approximately 0.017, to the nearest thousandth.
To find the probability of getting exactly 1 head when a fair coin is tossed 9 times, we can use the concept of binomial probability. The probability of getting a head on a single coin toss is 1/2, and the probability of getting a tail is also 1/2.
In this case, we want to calculate the probability of getting exactly 1 head out of 9 tosses. This can be represented as a binomial probability with parameters n (number of trials) and p (probability of success).
Using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where n is the number of trials, k is the number of successful outcomes, and p is the probability of success.
In our case, n = 9, k = 1, and p = 1/2.
Plugging these values into the formula:
P(X = 1) = (9 choose 1) * (1/2)^1 * (1 - 1/2)^(9 - 1)
P(X = 1) = 9 * (1/2) * (1/2)^8
P(X = 1) = 9 * (1/2)^9
P(X = 1) = 9/2^9
P(X = 1) ≈ 0.017
Therefore, the probability of getting exactly 1 head when a fair coin is tossed 9 times is approximately 0.017, to the nearest thousandth.
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Which number has an absolute value greater than 5
A -6
B -5
C 0
D 5
Answers
Answer:
A -6
Step-by-step explanation:
The reason why this is your answer is because -6's absolute value is 6
As we know, 6 is higher than 5
so hence, your answer is A -6
EXTRAS:
Absolute values of other answer choices...
-5 = 5
0 = 0
5 = 5
Answer:
The number that has an absolute value greater than 5 is -6 so that answer will be A
The ratio of girls to boys in the school marching band is 3 to 2. If there are 24 boys in the marching, how many of the students in the marching band are girls.
A.42
B.28
C.32
D.36
Answers
Answer:
D. 36
Step-by-step explanation:
Ratios are a way to represent of how much there is one thing to another. It's a more simplistic representation.
For example, if there were 625 adults and 375 children, we don't say there are 625 adults to 375 children, we say there are 5 adults to 3 children.
All I did was divide both the number of children and adults by 125 and we have a ratio of 5:3 for adults to children respectively.
In this problem, we have a ratio of 3:2 for girls to boys. This 3:2 ratio is a simplistic representation of the number of girls to boys. We know that there are 24 boys.
Dividing 24/2 = 12
12 is the proportion which we multiply by the ratio to get the true numbers for boys and girls.
2 * 12 = 24 boys
3 * 12 = 36 girls
So there are 36 girls in the marching band.
cubic
The volume of the cylinder shown is about
2 m
meters.
12 m
Round to the nearest tenth.
Answers
Answer:
rephrase your question please
I need help to find the measures and lengths of these arcs
Answers
Answer:
Step-by-step explanation:
i)14π/9
ii)91π/18
iii)77π/9
iv)140⁰
A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 meter per second, while the cat can run at a speed of 24 meters per second. How soon will they meet if they simutaneously start running towards each other?
Answers
Answer:
They'll meet after 200 meters , if they simultaneously start running towards each other.
Step-by-step explanation:
Let x =distance travelled by dog and 200-x be the distance travelled by cat. Inorder to meet, the sum of their travelled distances shall be equal to 200 meters as they are far apart by 200 meters.
Dog: Distance =Speed x time: x=30t
Cat: Distance = 200-x
=24t
The sum of their distance travelled shall be 200 meters: 30t+ 24t= 200;54t=200;t=200/54=3.7secs
So they will meet after 3.7 seconds
To check:
Distance travelled by dog :x=30(3.7)
=111.11 meters
Distance travelled by cat: 24t=24(3.7)
=88.89 meters
Therefore since they are travelling towards each other and their distance apart is 200 meters, after 3.7 seconds they will meet because dog travelled 111.11 meters and cat travelled 88.89 meters and they covered already 200 meters as the sum of 111.11+ 88.89
=200 meters
Select the correct answer.
What is the equation of the parabola opening upward with a focus at and a directrix of ?
A. f(x) = 1/32(x - 9)^2 + 19 =
B. f(x) = 1/32(x + 9)^2 + 19 =
C. f(x) = 1/16(x - 9)^2 + 19 =
D. f(x) = 1/16(x + 9)^2 - 19 =
Answers
Answer:
b
Step-by-step explanation:
on plato
The equation of the parabola opening upward with a focus at and a directrix will be f(x) = 1/32(x + 9)^2 + 19. so option B is correct.
What is the equation of the parabola?The equation can be written as
f(x) = 1/(4p)(x -h)^2 +(k-p)
where (h, k) is the focus, and p is half the distance between focus and directrix.
Here, We have the upward parabola;
(h, k) = (-9, 7) and p = (7 - (-9))/ 2 = 8.
So the equation is
f(x) = 1/32(x + 9)^2 + 19
The equation of the parabola opening upward with a focus at and a directrix will be f(x) = 1/32(x + 9)^2 + 19. so option B is correct.
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Ally and Christian bought 4 pounds of butter and 2 pounds of chocolate chips for cookies. How many ounces of products did they purchase?
Answers
Answer: 96
Step-by-step explanation: Multiplying by 16 (6 × 16)
In math, do you still distribute even the number is behind the parentheses?
For example:
(2x+3)5+23
Would you still distribute the 5?
Answers
You’re gonna have 10x+15+23
Then 10x + 38
And then you are doing next (2x+3) •5 + 23
So you have 2(5x+19)
The graph of the function y = 2x^2 + bx + 8 is shown.
What is the value of b?
Answers
The value of b is 4 and the function becomes y = 2x²-12x+8 because (2, -8) lie on the function.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
[tex]\rm y = 2x^2+bx+8[/tex]
The above function shows the equation of the parabola.
From the graph, we can see the point(2, -8) lie on the graph of the function,
So point(2, -8) will satisfy the function.
Plug y = -8 and x = 2 in the function.
[tex]\rm -8 = 2(2)^2+b(2)+8\\\\-16 = 8+2b\\-24 = 2b \\b = -12[/tex]
Thus, the value of b is 4 and the function becomes y = 2x²-12x+8 because (2, -8) lie on the function.
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Write the absolute value equations in the form |X-B|=C (where B is a number and C can be either number or an expression) that have the following solution sets X=15
Answers
Answer:
|x - 15| = 0Step-by-step explanation:
|x - 15| = 0 ⇔ x - 15 = 0 ⇔ x = 15
solve using the square root method
Answers
x= 14
x=0
circles can be found along the Gambia
River in western Africa. The stones
are believed to be over 1000 years old.
In one of the circles at Ker Batch,
three stones have approximate
coordinates of A(3, 1), B(4, -2),
and C-6, -2).
a. What are the coordinates of the
center of the stone circle?
b. Each unit of the coordinate
plane represents 1 ft. What is the
diameter of the stone circle?
Answers
Answer:
-6 4
Step-by-step explanation:
hope it helps you have a great day
PLEASE ANSWER - BRAINLIEST IF 2 ANSWERS - 5 STAR RATING - THANKS (PROFILE TOO)
Gina is buying 24 oranges. Two stores offer the following deals:
Store A: 12 oranges for $6.48
Store B: 5 oranges for $2.65
Gina can buy oranges individually.
How much will Gina save if she buys 24 oranges at Store B?
Show your work
Answers
Answer:
12.72
2.65/5 = 0.53
0.53x24= 12.72
Step-by-step explanation:
The function f(x)is shown in the graph.
What is the equation for f(x)?
Answers
Answer:
(-5/6)x - 1
Step-by-step explanation:
the equation is given by: y = mx + b
m = slope
b = y intercept
m = -5/6
y intercept = -1
f(x) = (-5/6)x - 1
Is the graph increasing, decreasing, or constant where -3 < X < -1?
Answers
Answer:
{xI-3<x<-1}
Step-by-step explanation:
what is 252 in index form
Answers
Answer: The factors of 252 can either be prime or composite. Subsequently, 252 is an even composite number itself which comprises of factors that are either prime or composite.
Step-by-step explanation:
Factor pair Pair factorization
2 and 126 2 × 126 = 252
3 and 84 3 × 84 = 252
4 and 63 4 × 63 = 252
6 and 42 6 × 42 = 252
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Each year, a school sends 50 students to a
conference.
Last year, the cost was $12.50 per student.
This year, the cost per student has increased
by 16%.
What is the total cost to send 50 students to
the conference this year?
a $625
b $633
c $725
d $841
Answers
Answer:
c) $725
Explanation:
Last year price: $12.50
If increased by 16%, 100% + 16% = 116%
116% * $12.50
$14.5, each student
Total cost for all 50 students
$14.5 * 50
$725
5 Anita is using 36 cards to set up a card game. She wants to make
an array with the same number of cards in each row.
What are all the different ways Anita could arrange the cards?
Describe all the different ways.
Answers
Answer:
box is there so I'll put the money in the post