Answer:
sqrt(150)
Step-by-step explanation:
We want to write the whole number inside the radical
5 = sqrt(5*5)
We know that sqrt(a) sqrt(b) = sqrt(ab)
5 * sqrt(6)
sqrt(5*5) * sqrt(6)
sqrt(5*5*6)
sqrt(150)
Answer:
[tex]\sqrt{150}[/tex]
Step-by-step explanation:
since the 5 is out of the sqrt root, you need to ^2 to put it back in again.
[tex]5^{2}[/tex]=25
and then in the sqrt you multiply the two variables
6* 25 = 150
so the answer is sqrt{150}
Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base .
Answer:
Given: An Isosceles Triangle ABC with a vertex at B.
Midpoint M of the base AC.
To Prove: BM is perpendicular to AC.
Proof:
Let the coordinates of the points of the isosceles triangle be given as:
A = (-k, 0)
Vertex, B = (0,a)
C = (k, 0)
Midpoint, M = (0,0)
Slope of the base segment, AC:
[tex]=\dfrac{dy}{dx} = \dfrac{0 - 0}{k - (-k)} = \dfrac{0}{2\cdot k}[/tex]
Slope of the base segment, AC= [tex]\dfrac{0}{2\cdot k}=0[/tex]
Slope of the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base, BM.
[tex]\text{Slope of BM =} \dfrac{0 - a}{0 - 0} = \dfrac{-a}{0}\\[/tex]
[tex]\text{Slope of BM = } \dfrac{-a}{0}[/tex] = Undefined
Two lines are perpendicular if the gradient of one is a negative reciprocal of the other.
Since [tex]-\dfrac{a}{0}[/tex] is a negative reciprocal of 0 for arbitrary values of a, BM and AC are perpendicular.
This concludes the proof.
On a particular day in July, there is a 20% probability of rain in Vancouver, a 65% probability of rain in Calgary, and a 75% probability of rain in Saskatoon. What is the probability that it will rain in all 3 cities on that day?
Answer:
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 0.93 = 93%
Step-by-step explanation:
Let 'V' be the event of rain in Vancouver
Given that the probability of rain in Vancouver
P( V) = 20% = 0.20
P( V⁻) = 1- P( V) = 1 - 0.20 =0.80
Let 'C' be the event of rain in Calgary
Given that the probability of rain in Calgary
P( C) = 65% = 0.65
P( C⁻) = 1- P( C) = 1 - 0.65 =0.35
Let 'S' be the event of rain in Saskatoon
Given that the probability of rain in Saskatoon
P( S) = 75% = 0.75
P( S⁻) = 1- P( S) = 1 - 0.75 =0.25
First we will prove that the probability that it will not rain in all 3 cities on that day
P( V⁻ ∩ C⁻ ∩ S⁻ ) = P( V⁻) P( C⁻) P(S⁻)
= 0.80 × 0.35 × 0.25
= 0.07
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 1-(P( V⁻ ∩ C⁻ ∩ S⁻ )
= 1 - 0.07
= 0.93
Two numbers add to 200. The first is 20 less than the second. What are the numbers?
Answer:
Step-by-step explanation:
Let's call the first number x.
We can write an equation representing the problem using x:
x+x+20=200 (because the second number is 20 more than the first, or x)
Combine like terms: 2x+20=200
Subtract 20 from each side of the equation: 2x=180
Divide by 2: x=90
The first number is 90, the second number is 110.
Hope this helps!
The slope of AB is -2/5. Segments CD has endpoints at C(-5,3) and D(10,-3). Are AB and CD parallel, perpendicular or neither? Justify.
Answer:
AB and CD are parallel
Step-by-step explanation:
AB has the slope of -2/5
lets see what slope the line CD has:
points are (-5, 3) and (10, -3)slope= m= (y2-y1)/(x2-x1)= (-3-3)/(10+5)= -6/15= -2/5as we see AB and CD have same slope, therefore they are parallel
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
To figure out if something is increasing or decreasing, you must read the graph from left to right. If it appears to be going down, then it is decreasing. When it appears to be to be going up, it is increasing. For both A & B, the graph is decreasing. When you look from when the x-values are between 2.5 and 3.5, you can see the line going down. That means it is decreasing.
I hope this helps!
Which pair of terms are not both true for the number 3? Mark Brainliest!
A. Integer and rational number
B. whole number and integer
C. Natural number and integer
D. whole number and irrational number
Answer:
D
Step-by-step explanation:
3 is not irrational, it can be converted into a fraction (ratio) 3/1 quite easily
Michael is an engineer and is drawing a scale model of a centrifuge for an oil company. If the centrifuge is 24 meters tall and he's using a scale of 1 centimeter=6 meters, then how many centimeters tall should the centrifuge be in the drawing?
What is the base of a triangle with a height of 14 cm and an area of 42 square cm?
Answer:
[tex]6cm[/tex]
Step-by-step explanation:
[tex]area = \frac{1}{2} \times base \times height \\ 42 = \frac{1}{2} \times b \times 14 \\ 42 = \frac{14b}{2} \\ 42 = 7b \\ \frac{42}{7} = \frac{7b}{7} \\ base = 6cm[/tex]
hope this helps
Answer:
6
Step-by-step explanation:
Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct? She is correct, because both solutions satisfy the equation. She is not correct, because she made a sign error. She is not correct, because there are no solutions. She is not correct, because there is only one solution: x = 3.5. help plz
Answer:
She is not correct, because there are no solutions
Step-by-step explanation:
–|2x – 10| – 1 = 2
Add 1 to each side
–|2x – 10| = 3
Divide by -1
|2x – 10| = -3
An absolute value is positive and it would have to equal -3
This cannot happen so there is no solution
Answer:
She is not correct, because there are no solutions
Step-by-step explanation: C
Jacob can run 9 miles in 1 hour and
15 minutes. What is his average running speed per minute?
Answer:
0.12 miles per minute
Step-by-step explanation:
9/75 is 0.12. 9 miles in 75 minutes
Average speed of Jacob is 0.12 miles per minute.
What is unitary method ?Unitary method is a method of finding value of a single unit.After finding value of a single unit we can determine values of any given unit.
According to the given question Jacob can run 9 miles in 1 hour and
15 minutes.
We know 1 hour is 60 minutes.
∴ 1 hour and 15 minutes is
= (60 + 15) minutes.
= 75 minutes.
So, Jacob can run 9 miles in 75 minutes.
∴ In one minute Jacob can run 9/75 miles shich is
= 0.12 miles per minute.
learn more about unitary method here :
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Given f(x) = -x – 4, solve for x when f(x) = 6.
Answer:
-10
Step-by-step explanation:
6=-x-4 plug in 6 for f(x)
10=-x add 4 to both sides in order to cancel out the -4
-10=x multiple each side by -1 to make the x positive
46+9a=-5a+74 solve for a
Answer: a=2
Step-by-step explanation:
-14a=-28
divide both sides by -14
a=2
Find the equation of the line that is perpendicular to y = -3/4x+1 and contains the point (9,12).
Answer:
[tex]y = \frac{4}{3} x[/tex]
Step-by-step explanation:
Perpendicular = m1*m2 = -1
[tex]-\frac{3}{4}*\frac{4}{3} = -1[/tex]
[tex]y = \frac{4}{3} x +b[/tex]
[tex]12 = \frac{4}{3}(9)+b\\12 = 12 + b\\b = 0\\y = \frac{4}{3} x+0\\y = \frac{4}{3} x[/tex]
The equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
Given that, the equation of a line [tex]y=\frac{-3}{4}x+1[/tex] and the coordinate point (9, 12).
What is the slope of perpendicular lines?Slope of a perpendicular line can be computed from the slope of a given line. The product of the slope of a given line and the slope of the perpendicular line is equal to -1. If the slope of a line is m1 and the slope of the perpendicular line is m2, then we have m1.m2 = -1.
From the given equation of a line slope m1=-3/4
The slope perpendicular to equation of line m2 = -1/m1 = 4/3
Now, substitute m=4/3 and (9, 12) in y=mx+c and solve for c.
That is, [tex]12=\frac{4}{3} \times 9 +c[/tex]
⇒ c=0
Put c=0 and m=4/3 in y=mx+c, we get
[tex]y=\frac{4}{3}x[/tex]
Therefore, the equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
To learn more about the slope intercept form visit:
https://brainly.com/question/24683642.
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What is an equation in point-slope form of the line that passes through (1, −6) and (4, 6)
Answer:
Step-by-step explanation:
6--6 = 12
4-1 = 3
12/3 = 4
y=4x
-6-4 = -10
y=4x-10
The formula of slope:
Slope = (d - b) / (c - a)
where (a, b) and (c, d) are the two points.
The equation of the line that passes through (1, -6) and (4, 6) is
y = 4x - 10
What is an equation of a line?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line passes through (1, -6) and (4, 6).
The formula of slope:
Slope = (d - b) / (c - a)
where (a, b) and (c, d) are the two points.
Now,
(1, -6) = (a, b) and (4, 6) = (c, d)
Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4
m = 4
The equation of a line is given as y = mx + c.
(1, -6) = (x, y)
-6 = 4 x 1 + c
-6 = 4 + c
-6 - 4 = c
c = -10
Now,
The equation of the line that passes through (1, -6) and (4, 6) is
y = 4x - 10
Learn more about equation of a line here:
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Can somebody help meeee witthhhh thisss plssss
Answer:
7.) (m+4)(m-16)
8.) Area= 3x^3-5x^2+7x+3
Step-by-step explanation:
7.) m^2-12m-64
=(m^2+4m)+(-16m-64)
=m(m+4)-16(m+4)
=(m+4)(m-16)
8.) Area = L(W)
x^2-2x+3(3x+1)
=x^2(3x)+x^2(1)+(-2x)(3x)+(-2x)(1)+3(3x)+3(1)
=3x^3+x^2-6x^2-2x+9x+3
=3x^3-5x^2-2x+9x+3
=3x^3-5x^2+7x+3
PLZ HLP MEEEEEEEEEEEEEEE
the table shows the distribution of students in Mrs boxer's sixth-grade class. what is the ratio of the number of boys to the number of girls? 10= boys 18= girls OPTIONS: A. 9/5 B. 5/4 C. 4/5 D. 14/9 E. 5/9 F. 9/14
Answer: 5/9
Step-by-step explanation:
Because you are looking for the ratio of BOYS to GIRLS you put those numbers in that order so it would be 10boys/18girls simplified that is 5/9
Answer:
Haaave youuu ever seen a troll
digging a hole
down by the bay?
Step-by-step explanation:
May I have brainliest please? :)
answer this plz quickly
Answer: THE ANSWER IS -1/36
Step by step: Find the LCD then combine
The answer is : -1/36
You forgot the 1 for 18 in the last question lol
Hope this helps, pls mark as brainliest :))))
Plssssssss........helppppppp meeeeeee
Answer:
The coefficient is 12
Step-by-step explanation:
The coefficient is the number next to the variable in the term
12p
The coefficient is 12 and the variable is p
Need help please ???
Answer:
i believe the answer is 0.75
Step-by-step explanation:
i used siri
Which expession is equivalent to 4-(-7)
Answer:
4 + 7 = 11
Step-by-step explanation:
Subtracting a negative means adding.
To subtract a number, add its opposite. The opposite of -7 is 7, so to subtract -7, add 7.
4 - (-7) = 4 + 7 = 11
Answer:
4+7
Step-by-step explanation:
A box of oranges weighs 4 kg. If one orange weighs 80 g, how many oranges are in the box?
Answer:
50 oranges
Step-by-step explanation:
Convert the measurements for them to be the same ie 4kg to g
1kg=1000g. 4kgx1000=4000g
4000g is the mass of all oranges
1 orange=80g
? =4000g that is 4000/80
=50 oranges
Answer:
50 oranges
Step-by-step explanation:
Since each orange is measured in grams, we convert the 4 kg to g to start.
4 kg is equal to 4000 g.
Each orange weighs 80 g, so we divide 80g into 4000g.
80 divided by 4000 equals 50.
50 oranges are in the box.
I Hope This Helps!
A bottle of iron supplement has 45g of iron in 330ml of solution. How many grams of iron are in
100ml of solution?
Answer:
45 * 100 / 330 = amount in 100 ml of solution
13.6363636364 grams
Step-by-step explanation:
Which number sentence below matches this word problem? Grandma's house is 12 miles away. Aunt Millie's house is only 9 miles away. How much farther is Grandma's house than Aunt Millie's?
Answer:12-9=3
Step-by-step explanation: I mean like the grandma house is 12 mile from your house and the Aunt is 9 mil from your house so th numbe sentence would be 12-9
Mrs Baker is preparing her students for their exams. The exams are two weeks away. Mrs Baker advises her students to spend 25% of each day revising.
A) How many hours does Mrs Baker expect her students to revise each day?
B)) How many hours in total will the students have revised if they follow Mrs Bakers advise for the next two weeks?
Answer:
A. 4 hours
Step-by-step explanation:
100 divided by 25
Sandra paid $85 for a dress that was on sale for 50% off. What was the original price of the dress?
Answer:
170$
Step-by-step explanation:
fully Factorise 7m^2 + 13m
Answer:
[tex]m(7m + 13)[/tex]
Step-by-step explanation:
[tex]7m {}^{2} + 13m \\ m(7m + 13)[/tex]
How much is $100 U.S. dollars in Canadian dollars?
Answer:
133.98
Step-by-step explanation:
You are drawing two cards, without replacement, from a standard deck of 52 cards. What is the
probability of drawing a 2. then a face card (King, Queen, or Jack)?
Leave your answer in decimal form to 4 decimal places.
Answer:
Dear student,
Answer to your query is provided below
Probability of drawing a 2 at first is (4/52) = (1/13)
Probability of drawing a face card in second try without replacement = 12/51
Step-by-step explanation:
Total no. Of cards = 52
Total no. Of cards of 2 = 4
Prob. Of drawing 2 = 4/52
Total no. Of face card = 12
Total no.of cards left in deck = 51
Prob. Of drawing face card = 12/51
what is the y intercept, function, domain and range, and horizontal asymptote of y=3^x
Answer: y−intercept is =(0,−2), the horizontal asymptote is y=4, Domain is − ∞ < x < −2 and −2 < x < ∞, Range is − ∞ < y < 4 and 4 < y < ∞
Step-by-step explanation: Vertical asymptote can be found by setting the denominator equal to 0 and solving for x : , Horizontal asymptote can be found by evaluating yas x→±∞,
two groups of students order cheeseburgers and chicken nuggets at mcdonald’s. one order of 9 cheeseburgers and 4 chicken nuggets cost $22.37. the other order of 3 cheeseburgers and 4 chicken nuggets cost $15.23. find the cost of a cheeseburger
Answer:
$1.19
Step-by-step explanation:
Let the cost of a cheeseburger be $b and that of a chicken nugget be $n.
From the given information, we can form 2 equations.
9b +4n= 22.37 -----(1)
3b +4n= 15.23 -----(2)
Notice that the 2 equations have '4n' in them. I'll be using elimination method to solve the equation by getting rid of the 4n.
(1) -(2):
9b +4n -(3b +4n)= 22.37 -15.23
9b +4n -3b -4n= 7.14
6b= 7.14 (simplify)
b= 7.14 ÷6 (÷6 on both sides)
b= 1.19
Thus, a cheeseburger cost $1.19.
Answer:
Step-by-step explanation
1.19
