Answer: y = 0 and x = -1
Find an equation of the line that is the perpendicular bisector of the line segment joining the points (6,2) and (18,6)
Answer:
y= -3x +40
Step-by-step explanation:
Properties of perpendicular bisector:
• perpendicular to the given line
• cuts through the center of the given line
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.
Let's find the gradient of the given line first.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Gradient of given line
[tex] = \frac{6 - 2}{18 - 6} [/tex]
[tex] = \frac{4}{12} [/tex]
[tex] = \frac{1}{3} [/tex]
The product of the gradients of perpendicular lines is -1.
m(⅓)= -1
m= -1(3)
m= -3
Substitute m= -3 into the equation:
y= -3x +c
To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.
[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]
Midpoint
[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]
[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]
[tex] = (12,4)[/tex]
y= -3x +c
when x= 12, y= 4,
4= -3(12) +c
4= -36 +c
c= 4 +36
c= 40
Thus, the equation of the perpendicular bisector is y= -3x +40.
Find z such that 4.8% of the standard normal curve lies to the left of z. (Round your answer to two decimal places)
Answer:
The correct answer will be "-1.66".
Step-by-step explanation:
Let z₀ be,
[tex]P(z<z_0)=4.8 \ percent[/tex]
[tex]=0.048[/tex]
⇒ [tex]\Phi (z_0)=0.048[/tex]
Now,
⇒ [tex]\Phi (-1.6646)=0.048[/tex]
[tex]z_0=-1.6646[/tex]
[tex]\simeq -1.66[/tex]
Thus the above is the right answer.
Surds see attached 20 points
Answer:
[tex]5\sqrt{2} \\45[/tex]
Step-by-step explanation:
just multiply
Answer:
a) 5√2
b) 135
Step-by-step explanation:
√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.
√27·√75 can be simplified by factoring:
√3·√9·√3√25, or (because √3·√3 = 3):
(3)(9)(5) = 135
Answer by any chance?❤️
Step-by-step explanation:
Question 2.[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]
[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]
[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]
[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]
Question 3.[tex] \frac{18}{x} = \frac{6}{10} [/tex]
[By cross multiplication]
=> 18 × 10 = 6 × x
[tex] = > \frac{18 \times 10}{6} = x[/tex]
=> 3 × 10 = x
=> x = 30 (Ans)
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
7(x-9y) need an answer
Answer:
7x - 63y
Step-by-step explanation:
Given
7(x - 9y) ← multiply each term in the parenthesis by 7
= 7x - 63y
Denver's elevation is 5280 feet above sea level. Death Valley is -282 feet. Is Death Valley located above sea level or below sea level???
(plz answer, due date is semtemper)
9514 1404 393
Answer:
below
Step-by-step explanation:
When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.
What is y-3=3/4(x-5) in standard form?
Answer:
[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]
Is this standard form? :\
Answer:
3x-4y=3
Step-by-step explanation:
Hi there!
We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form
Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0
So let's expand the parentheses in the equation
Do the distributive property
y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]
Add 3 to both sides
y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]
We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
Remember that we want it in standard form, which is ax+by=c
Subtract [tex]\frac{3}{4}x[/tex] from both sides
[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]
Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative
So multiply both sides by -4
[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]
Distribute -4 to every number
[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]
Multiply
[tex]\frac{12}{4}x-4y=\frac{12}{4}[/tex]
Simplify
3x-4y=3
There's the equation in standard form
Hope this helps!
How many millitiers are in 4.55 liters?
Answer:
v nnv vb n
Step-by-step explanation:
b ng chfxhc.jx.gc,fhxfgfdkhgvn gghcjfuoctykfd mmyegfiuegfypgerukf khergfuoegrfyurgfirge jgreuyofrgiregvoifgr riygfepiygfreu;k frugfyrfbhrevf rrgfbreuobghfre rgeuherhbgerui freurehuregh ruogysfhurgiugwhlerghre rgiuyrge97grukbgr ker ruipuhrgeugregariyarga ;rskfglfsglgsfuifgryrgljs kjger;ugiergs hope this was helpful good luck!
Please help, I’m not sure about this question.
What is the average
number of 4th graders per
class from the table above?
Answer:
29
Step-by-step explanation:
You need to find the average number of students
Add up all the students
27+31+28+33+26
145
Divide by the number of classes
145/5
29
The average is 29
32
Step-by-step explanation:
answer of number 30 is 32
x=cos(2t), y=sin(2t) find a rectangular coordinate equation for the curve by eliminating the parameter
Answer:
x^2+y^2=1
Step-by-step explanation:
Since cos^2(x)+sin^2(x)=1, x^2+y^2=1
Paul baked 208 brown loaves. If the ratio of white loaves to brown loaves is 3:2, how many loaves did he bake in total?
Paul baked 520
loaves.
The owner of a restaurant is placing an order for bread.
On Friday there were 300 customers in the restaurant and 100 bread rolls were served.
On Saturday he is expecting 540 customers.
What would be a good estimate of how many bread rolls should he order? I
Os 2021
A Exit
Back
✓ Mark Question
172.000
13 :
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N
MacBook Air
Answer:
A. Total=520 loaves
B. Estimate= 180 rolls
Step-by-step explanation:
Given the functions below, find f(x) - g(x) f(x) = 3x^2 + 2x + 1 g(x) = x^2 - 6x + 3
Answer:
Here is your answer.....
Hope it helps....
The value of given function f(x) - g(x) is 2x² + 2x + 1.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.Given,
f(x) =3x² + 2x + 1
g(x) = x² - 6x + 3
f(x) - g(x) = ( 3x² + 2x + 1) - ( x²- 6x + 3)
= 3x² + 2x +1 - x² + 6x - 3
= 2x² +8x - 2
Therefore , the value of given function f(x) - g(x) is 2x² + 2x + 1.
Learn more about function brainly.com/question/11963913
#SPJ2
Write an equation of the line through each pair of points in slope-intercept form.
a(– 3,–2) and (–3,4)
b(3,2)and (–4,–5)
Answer and I will give you brainiliest
Answer:
see below
Step-by-step explanation:
a) (– 3, –2) and (–3, 4)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(4 - (-2) / (-3 - (-3))
Simplify the parentheses.
= (4 + 2) / (-3 + 3)
Simplify the fraction.
(6) / (0)
= undefined
If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.
In this case, the x-coordinate for both points is -3.
Therefore, your equation is x = -3.
b) (3, 2) and (–4, –5)
First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(-5 - 2) / (-4 - 3)
Simplify the parentheses.
= (-7) / (-7)
Simplify the fraction.
-7/-7
= 1
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = 1x + b or y = x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.
2 = 1(3) + b
To find b, multiply the slope and the input of x(3)
2 = 3 + b
Now, subtract 3 from both sides to isolate b.
-1 = b
Plug this into your standard equation.
y = x - 1
This is your equation.
Check this by plugging in the other point you have not checked yet (-4, -5).
y = 1x - 1
-5 = 1(-4) - 1
-5 = -4 - 1
-5 = -5
Your equation is correct.
Hope this helps!
Determine the volume of a sphere with a diameter of 5 inches.Use 3.14 for Pi, and round your answer to the nearest inch.
Answer:
[tex]{ \bf{formular : \: { \tt{volume = \frac{4}{3} \pi {r}^{3} }}}} \\ { \tt{volume = \frac{4}{3} \times 3.14 \times {( \frac{5}{2}) }^{3} }} \\ { \tt{volume = 65.4 \: cubic \: inches}}[/tex]
Answer:
65
Step-by-step explanation:
formula = 4/3 * 3.14* r^3
= 4/3 * 3.14 * 2.5^3 (radius is half of the diameter)
= 65.44985
rounded to 65
write the equation of a line of a line passing through the points (3,1) and (6,3).
Answer:
i think its 2 1
Step-by-step explanation:
Answer:
y =2/3x-1
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 3-1)/ (6-3)
= 2/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/3x +b
Using a point
3 = 2/3(6)+b
3 = 4+b
3-4 =b
-1=b
y =2/3x-1
Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
6/5 times 17/18 in lowest terms
Answer:
17/15
Step-by-step explanation:
6/5 * 17/18
1/5 * 17/3
17/15
Two long jumpers competed in a world-class track meet. The first athlete jumped a distance of 28.65 feet, and the second athlete reached a distance of 24.25 feet.
Answer:
Step-by-step explanation:
first athlete =28.65
second athlete=24.25
the first athlete jump - second athlete jump
28.65-24.25
= 4.40
the first athlete long jump then the second athlete
pleaseee i need help!
2 questions in one pleasee 90 points!
Answer:
A the answer is A if you look at it .
Answer:
The first one is B) point D
The second one is D) (0,0)
Hope this helps!
btw, coordinates are in (x,y) form, so the other answer above me is wrong.
Match each shape to the number of lines of reflection that will reflect the shape onto itself. Drag the items on the left to the correct location on the right.
Answer:
rectangle- 2 lines of reflection
trapezoid- 0 lines of reflection
regular pentagon- 5 lines of reflection
square- 4 lines of reflection
Step-by-step explanation:
Which of the following phrases should not be expressed using a negative number?
Answer:
its 1900 Bc. Because BC stand for before chirst
Step-by-step explanation:
the sum of five consecutive number is 45
Answer:
7, 8, 9, 10, 11
Step-by-step explanation:
7+8+9+10+11
7 + 8 = 15
15 + 9 = 24
24 + 10 = 34
34 + 11 = 45
a rectangle has an area of 186m2
one of the sides is 3m in length
work out the perimeter of the rectangle
seriously need help
Step-by-step explanation:
here is the ans
the perimeter= 130m
hope so this might help you
A university professor asked his class of 42 students when they had studied for his class the previous weekend. There responses were. please answer part a, b and c
ANSWERS:
a) 16 students
b) 25 students
c) 2 students
STEP BY STEP:
There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"
Question a)
The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:
the combos:
3, 10, 6, 2
Since the last combo included all of the other dates, we need to minus it:
1, 8, 4, 2
Now we can use the total of Sunday and minus the combos that includes Sunday:
30 - (4 + 2 + 8) = 16 students
Question b)
To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:
Friday: 9 - 4 - 1 -2 = 2 students
Saturday: 18 - 1 - 2- 8 = 7 students
and now add them all together: 2 + 7 + 16 = 25 students
That is the total number of students that studied on one day.
Question c)
Now for the numbers of students that didn't study... We can just use the total to minus everything else!
42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!
And thats all done! If you still don't get it, please ask!
If a concrete mix contains 1-1/2 cubic feet of gravel, 1/2 cubic foot of water,
1 cubic foot of cement, and 2 cubic feet of sand, what percentage of the mix is
sand?
Answer:
The correct answer is "50%".
Step-by-step explanation:
The given values are:
Gravel,
= [tex](1-\frac{1}{2} )[/tex]
Water,
= [tex]\frac{1}{2}[/tex]
Cement,
= 1
Sand,
= 2
Now,
The total mixture will be:
= [tex]Gravel+Water+Cement+Sand[/tex]
By substituting the values, we get
= [tex](1-\frac{1}{2} )+\frac{1}{2} +1+2[/tex]
= [tex]\frac{1}{2} +\frac{1}{2} +1+2[/tex]
= [tex]4 \ cubic \ feet[/tex]
hence,
The percentage of sand will be:
= [tex]\frac{Sand}{Total}\times 100[/tex]
= [tex]\frac{2}{4}\times 100[/tex]
= [tex]50[/tex]%
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P=0.006A2−0.02A+120. Find the age of a man whose normal blood pressure measures 126 mmHg.
Round your answer to the nearest year.
Answer:
33 years
Step-by-step explanation:
Given the quadratic model :
P=0.006A2−0.02A+120
P = blood pressure ; A = Age
Given a blood pressure value of 126 mmHg ; the age, A will be ;
The equation becomes :
126 = 0.006A2−0.02A+120
0.006A² - 0.02A + 120 - 126 = 0
0.006A² - 0.02A - 6 = 0
Using the quadratic formula :
-b ± (√b²-4ac) / 2a
a = 0.006 ; b = - 0.02 ; c = - 6
Using calculator :
The roots are :
a = 33.333 or a = - 30
Age cannot be negative, hence, the age, A will be 33.333
Total the nearest year ; Age = 33 years
Ms. Patel has 24 students in her class. When she collected yesterday's homework, Ms. Patel found that 16 students completed the homework in
pencil and 8 students used a pen.
What is the probability that the first two assignments Ms. Patel collected were completed in pencil?
Answer:
Maybe
1/8 is the probability that the first two assignments Ms.patel collected were completed in pencil
