Two numbers have these properties.
Both numbers are greater than 8.
Their highest common factor (HCF) is 8.
Their lowest common multiple (LCM) is 80.
Find the two numbers, writing your answers on one line in the form,
The two numbers are ... and ...
Answers
Answer:
16 and 40Step-by-step explanation:
Let the numbers be x and y
HCF is 8, so both numbers are multiples of 8 ⇒ x = 8n, y = 8m
As per property of numbers, the product of numbers is equal to product of their LCM and HCF:
xy = HCF(x,y) × LCM(x,y)Since LCM(x,y) = 80 we have:
8×80 = xy8×80 = 8n×8m10 = nmPossible option:
n = 2, m = 5Then the numbers are:
x = 2*8= 16y = 5*8 = 40Related Questions
The following diagram depicts a construction of copying a line segment.
If AB is 6.7 cm, what would the length of line segment CD be?
Answers
The diagram depicting the construction of copying a line segment indicates that AB = CD = 6.7 cm.
How can the length of the constructed line segment, AB be found?A line segment, which can be expressed as a segment of a line, has definite length. It is a line drawn that has two endpoints.
A line segment can be named by the capital letters placed at the endpoints.
Copying a line segment, therefore gives a segment of equal length as the original line segment.
Given that the length of AB = 6.7 cm, and the line segment, CD, is obtained by copying segment AB, we have;
Length of CD = Length of AB = 6.7 cm
Therefore;
CD is 6.7 cmLearn more about copying a line segment here:
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Is the given point interior,exterior, or on the circle (x+2^)2+(y-3^)2=81? Q(3,0)
Answers
i need help on this problem pls
Answers
Step-by-step explanation:
2 3 4 6...................
\frac{3}{8} times \frac{1}{9} in simplest form help me
Answers
Answer: 3/72 is your answer.
Simplify the following
Need the answer asap pls
Answers
1) 9y-1
2) x ³ - x ² + x
3)-3a²+ a + 2
4) -x ²
5) -4x ⁵ + 16x ³ - 20x ²
6) 8x ³ + 6x ² - 32x + 15
7) x - 6
8) 6x -3
9) x ² - 6x +5
10) 10x ⁵ +3x ³ - 2x ²
Pleaseee help me I need this done rn.
Area of a right triangle ABC is 120 sq feet. If AABC goes through a dilation transformation with a scale
factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?
Answers
Answer:
270
Step-by-step explanation:
The area is the same as the original area multiplied by the square of the scale factor.
What must be added to 3x + y to get 2x + 3y?
Answers
You have 3x+y and you need to make it 2x+3y
The difference between 3x and 2x is 1x(x)
And the difference between y and 3y is 2y
For the x you have to minus x from 3x to get 2x,(3x-x=2x)
For the y you have to add 2y to y to get 3y,(y+2y=3y)
Now add them
=3x+y+-x+2y=2x+3y
Therefore you add -x+2y
Answer:
-x+2yStep-by-step explanation:
What must be added to 3x + y to get 2x + 3y?
3x + y + z = 2x + 3y
3x + z = 2x + 3y - y
3x + z = 2x + 2y
z = 2x-3x+2y
z = -x+2y
-------------------
check
3x + y + (-x) +2y =
2x + 3y
the answer is good
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 61° and AB = 9.2.
Calculate the length of AC rounded to 3 SF.
Answers
Answer:
AC = 16.6
Step-by-step explanation:
Use sine rule
9.2 / sin(180-90-61) = AC/ sin(61)
Marco owed his father $210 and began paying him back $20 at the end of each week, beginning November 1. Joni owed her father $180 and began paying back $10 at the end of each week, beginning on the same day. What Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. What Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Find the value of n for which f(n) = g(n). What does that value mean in this situation?
After _____ weeks, Jonie and Marco each owed their fathers the same amount
Answers
In the given situation n gives us the number of weeks. after 3 weeks, Jonie and Marco each owed their fathers the same amount.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
We have been given that Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. and Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Also we get f(n) = g(n)
210 − 20n = 180 − 10n
Now n gives us the number of weeks thus solve for n
210 − 20n = 180 − 10n
210 - 180 = -10n + 20n
30 = 10n
n = 3
Now check your solution;
f(n) = 210 − 20n = 210 - 60 = 250
g(n) = 180 − 10n = 180 - 30 = 150
So our answer checks out after 3 weeks, Jonie and Marco each owed their fathers the same amount.
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- Lyle needs 200 g of chocolate that is 86% cocoa
for a cake recipe. He has one kind of chocolate
that is 99% cocoa and another kind that is 70%
cocoa. How much of each kind of chocolate
does he need to make the cake? Round your
answer to the nearest gram.
Answers
Answer: 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
===================================================
Work Shown:
x = amount of the 99% cocoa
200-x = amount of the 70% cocoa
0.99x = amount of pure coca from the first batch
0.70(200-x) = amount of pure cocoa from the second batch
0.99x+0.70(200-x) = total amount of pure cocoa
0.99x+0.70(200-x) = 200*0.86
0.99x+0.70*200-0.70x = 200*0.86
0.99x+140-0.70x = 172
0.29x+140 = 172
0.29x = 172-140
0.29x = 32
x = 32/0.29
x = 110.344827586207
x = 110
200-x = 200 - 110 = 90
Lyle needs 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
Both of these values are approximate.
Brianna picks tomatoes on a local farm. she receives 11 cents per crate. last week, her total piecework earnings was 500 dollars. express the number of crates she picked algebraically.
Answers
Answer:
4,545.45 crates
Step-by-step explanation:
.11x = 500
Divide both sides by .11
x = 4,545.45
The number of crates she picked algebraically is 4545.
Let us consider the variable "c" to represent the number of crates Brianna picked.
We know that she receives 11 cents per crate.
1 crate = $0.11 (11 cents)
Her total earnings from picking "c" crates can be expressed as:
Earnings = 0.11c
Now, we know her total piecework earnings for last week were $500. So, we can set up an equation:
Total Earnings = $500
0.11c = $500
To find the number of crates Brianna picked, we need to solve for "c":
c = $500 / 0.11
c = 4545.45...
c = 4545 crates
So, algebraically, Brianna picked approximately 4545 crates last week.
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Help please quite immediate am pro
Answers
construct potential hypotheses or research questions to relate the variables in each of the following examples. also, write a brief statement explaining why you believe there is a relationship between the variables as specified in your hypotheses.
Answers
Construct potential hypotheses or research questions to relate the variables in each of the following examples -
Political party and support of the affordable care act -
Given this, there can be a relationship between the ideological group and the support of the moderate consideration act.that various ideological groups may support various types of government disability conspiracies and might have various goals.A few gatherings might focus on a list of topics or problems and might provide serious thought at some random time.which might facilitate the implementation of the Affordable Care Act, while others would be gradually forgiving toward such arrangements.The implementation and success of the Affordable Care Act may depend on the rise of certain ideological movements.and their ability to express what they think about the Act's purpose.
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Please answer these for linear review
Answers
Answer: See explanation
Step-by-step explanation:
g(x)=2x-2
g(x+9)=2(x+9)-2 ==> x+9
(1,2), (4,5)
x=1, x=4: ==> pick the x-coordinates for domain
[1, 4] ==> segment is from 1 to 4 and includes x=1 and x=4
Six times a number w is at least -24
solve for the inequality
Answers
Answer:
w is -4
Step-by-step explanation:
W is -4 because a positive number times a negative number is always a negative that is why the answer is a negative and 6 times 4 is 24 but for the 24 to be a negative the 4 has to be a negative 4.
5
8. A tent in the shape of a right pyramid has 4 poles that are each 2.1 m long.
The side length of the base of the tent is 1.5 m.
a) Sketch a diagram of the tent.
b) What is the slant height of the tent to the nearest tenth of a metre?
My brodas and sisters please help me out for the love of god
Answers
Answer:
1.96 m or 2m when rounded to nearest tenth
Step-by-step explanation:
The question is referring to a square right pyramid. The base is square and the perpendicular axis is vertical to the base.
These are the different parts of a square right pyramid .
See figure for detailed description(taken from Wolfram website)
The ones of interest here are
a = base side length = = 2.1m (given).It is same on all 4 sides = 1.5m (given)e = edge length = 1.5m (given)
This corresponds to each of the poles of the tent.
Looking at the figure we can see the slant height
[tex]s^2 = r^2 + h^2[/tex] or [tex]\displaystyle s = \sqrt{r^2 + h^2[/tex]
This is the computation through the Pythagorean theorem where s forms the hypotenuse and r and h the two sides of a right triangler is nothing but half the side length = 1.5/2 = 0.75mh has to be computed first. Looking at the figure we can see that half the diagonal of the base, the edge and the height all form a right triangle. Therefore
[tex]e^2 = (\dfrac{d}{2})^2 + h^2[/tex]The diagonal of the square base is given by the formula
[tex]d = \sqrt{a^2 + a^2 }= \sqrt{2}a[/tex]
So d here = √2 a ;
d/2 = √2(a/2) = a/√2Substituting values for e=2.1, d = a/√2
==> 2.1² = (a/√2)² + h²
==> 2.1² = a²/2 + h²
==> (1.5²/2) + h²After moving h² to the left side and the constants to the right we get
h² = 2.1² - 2.25/2 = 3.285 (do not find square root yet, we have to square again)
Thus we get from substituting in formula for s²,
s² = r² + h²
s² = 0.75² + 3.285 = 0.5625 + 3.285 = 3.8475
s = √3.8475 = 1.96 m
Answer slant height s = 1.96 = 2 m when rounded to nearest tent
question 14(multiple choice worth 1 points) (01.05 lc) which calculation can be used to find the value of p in the equation p3
Answers
The response to this question is that p has a value of 8, or the cube root of 8. i.e. p=∛8.
Why do you use the term "Cube roots"?An integer y such that y³ = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. When we multiply a factor three times to obtain a number, we have obtained the cube root of that factor. Three cube root of, ending cubic root is the sign for the cube root. In contrast to cubing an integer, finding its cube root is a mathematical operation.
According to the equation, p³=8
We can clearly see that the power of p is 3.
Now by taking cube root on both the sides, we can see that the value of p is
∛p³=∛8
⇒p=∛8
The value of p in the equation cube root of 8.
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A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 7 times as long as the other. What is the length of the longer piece?
Answers
Answer: 39.5 cm long
Step-by-step explanation: The equation can also be written s 72=2x+7, (x= length of short piece) (x+7+length of long piece.):
72=2x+7
72-7=2x
65=2x
x=32.5
Then to find out the long piece:
x+7
32.5+7=39.5
at a gathering of50 people, there are 30 people who all know each other and 20 people who know no one. people who know each other hug, and people who do not know each other shake hands. how many handshakes occur within the group?
Answers
Total 790 number of handshakes occur within the group.
According to the given question.
Total number of people = 50
Number of people who know each other = 30
Number of people who know no one = 20
Since, 20 people doesn't knw each any one, so they will shake hands.
So, the total number of hand shakes by these 20 people
= 20(20 -1)/2
= 10(19)
= 190
Also, we have to consider that other 30 people will also shake hands with these 20 people.
So, the total number of hanshakes by these 30 and 20 people = 30 × 20 = 600
Therefore, the total number of handshakes occur within the group
= 600 + 190
= 790
Hence, total 790 number of handshakes occur within the group.
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There is a gas station exactly halfway between Stan and Drew’s houses. The map coordinates for Stan’s house are 5 miles East and 2 miles north. The map coordinates for Drew’s house are 3 miles East and 4 miles north. Find the map coordinates for the gas station
Answers
Answer:
4 miles east and 3 miles north (4, 3)
25% of the normal price of a watch is $15. What is the normal price?
Answers
15x4=60
Find the 11th term of the arithmetic seqence 2x+ 9, 7x+11 ,12x +13,...
Answers
Answer:
52x + 29.
Step-by-step explanation:
d = 7x + 11 - (2x + 9)
= 5x + 2.
11th term
= 2x + 9 + (11-1)(5x + 2)
= 2x + 9 + 50x + 20
= 52x + 29.
A line intersects the points
(3, 2) and (5, 12).
m = 5
Write an equation in point-slope form
using the point (3, 2).
y - [?] = [](x-[ ])
Answers
The point slope of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
Given that A line intersects the points (3, 2) and (5, 12) and asked to write an equation of line passing through (3,2) and having slope as 5.
Point slope form:
The point-slope form of a stright line is y-y1=m(x-x1)
Here (x1,y1) is the fixed point with which the line passes and m is the slope of the line
Here, (x1,y1) is given as (3,2) and m(slope)=5
The equation straight line in point-slope form is (y-2)=5(x-3).
Therefore,The point-slope form of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
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Mr. Cruz bought 3 roses for $30 each. How much is his change if he paid with a $100?
a
O b
P
$100-(3 x $30)= N
$3 x $30-$100 = N
100-$30 x 3=N
(3 x $30) - 100 = N
Answers
Answer:
10 is the answerplease i
Explain how to use compensation to find the difference of 30,000 and 6,985.
Answers
The difference of 30000 and 6985 using compensation is 23015
The method of compensation refers to calculating mentally without any paper work.
Here, we are asked to find the difference of 30000 and 6985 which are comparatively large numbers. Everyone would prefer using pen and paper to calculate this. But we can do this by compensation within a few steps.
Add 15 to 6985 [Addition is simpler than subtraction]. We get 7000.Now subtract 7000 from 30000 [ more zeros in the numbers make the mental calculation easy]. We just have to subtract 7 from 30 and adjoin 3 zeros in 7000. So we get 23000.Lastly add the 15 from the first step again to 23000.So the final answer is 23015.
i.e., 30000-6985 = 23015
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What is the area of a rectangle with a length of 9 feet and a width of 7 grade
Answers
9 x 7 = 63 feet
Answer:
63
Step-by-step explanation:
area=length×width so 9×7=63
points A(2, 3) B(-3,4).
area of triangle PAB = 8.5.
Answers
The equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
Let coordinate of P be (h, t)
We are given the coordinates of A and B as:
A = (2,3) and B = (−3,4)
Now, we also know that Area of triangle PAB is:
A = 1 / 2 (h ( 3 − 4 ) + 2 ( 4 − k ) − 3 ( k − 3 ) )
± 8.5 = 1 / 2 ( h ( - 1 ) + 2 ( 4 - k ) - 3 ( k - 3 ) )
± 17 = ( - h + 8 - 2 k - 3 k + 9 )
± 17 = ( 17 - 5 k - h )
When + 17 is there:
5 k + h = 0
When - 17 is there:
5 k + h = 34
So, locus of the point P will be 5 k + h = 34.
Therefore, the equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
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Your question was incomplete. Please refer the content below:
A(2,3) and B(−3,4) be two given points. Find the equation of the locus of P so that the area of triangle PAB is 8.5 square units.
Trey bakes 70 cupcakes for the school Bake Sale. Worried they might run out, he bakes some extra and now has 112 cupcakes.
What is the Percent Change in the number of cupcakes?
Answers
The Percent Change in the number of cupcakes is 60%
How to determine the Percent Change in the number of cupcakes?The given parameters are:
Initial number of cupcakes = 70
Final number of cupcakes = 112
The Percent Change in the number of cupcakes:
Percent = (Final number of cupcakes - Initial number of cupcakes)/Initial number of cupcakes * 100%
This gives
Percent = (112 - 70)/70 * 100%
Evaluate the quotient
So, we have
Percent = 0.6 * 100%
Evaluate the product
So, we have
Percent = 60%
Hence, the Percent Change in the number of cupcakes is 60%
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in a survey, 80 people were were questioned to find out how how many people read newspapers, S or D or both both. The survey revealed ya that 45 read D, 30 read read S and 10 read neither
Represents the information in a venn diagram.
Answers
Greetings from Brasil...
In this type of problem, we will use Set Theory
n(D ∪ S) = n(D) + n(S) - n(D ∩ S)
as n(U) - n(D ∪ S) = 10, then
n(D ∪ S) = 70, so
n(D ∩ S) = 5 (read both)
n(D) - n(D ∩ S) = 40 (read only D)
n(S) - n(D ∩ S) = 25 (read only S)
see attached figure
_________________________________
something similar
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What is the scale factor from polygon JKLM to polygon ABCD?
Answers
Answer:
for part c
JM=36
AD=12
36=3
JKLM is 3x bigger than polygon ABCD