Answer:
42
Step-by-step explanation:
When calculating the greatest common divisor, you must look for the smallest divisors that can divide the no. s given simultaneously.
So in this case the smallest divisor will be 2.
378 =189. 420 =210
2. 2
The next divisor that 189 and 210 can both be divided with is 3
189 =63. 210 =70
3. 3
The third smallest divisor that can 63 and 70 can be divided with is 7
63 =9. 70 =10
7. 7
9 and 10 have no common divisors that can divide them fully without leaving a remainder
So to get the greatest common divisor, multiply all the divisors you have used
In this case we've used 2,3,7
2x3x7= 42
The dimensions of a rectangle is 30cm x 20cm. When each dimension is
decreased by the same amount, the area of the new rectangle is
100cm^2. What are the new dimensions of the new rectangle (round to
one decimal place)? Hint: you will need to use the quadratic equation.
Answer:
The new dimensions are 6.18 cm by 16.18 cm.
Step-by-step explanation:
Original dimensions were 30 cm by 20 cm.
We decrease length and width by x and calculate the area:
Area = (length)(width)
= (30 - x)(20 - x) = 100
Performing the indicated multiplication, we get:
600 - 30x - 20x + x^2 = 100, or, after simplification,
x^2 - 50x + 500 = 0
Let's solve this by completing the square:
x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0
This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125
Taking the square root of both sides, we get:
x - 25 = ±√125, or
x = 25 ± 5√5
The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)
The dimensions of the new rectangle are
(30 - 13.82) cm by (20 - 13.82) cm, or
16.2 cm by 6.18 cm
Check: With these dimensions is the area 100 cm^2, as expected?
(6.18)(16.18) = 99.9979 YES
Bruno solved the following equation: 4x + one half(10x − 4) = 6 Step Work Justification 1 4x + 5x − 2 = 6 2 9x − 2 = 6 3 9x = 8 4 x = eight ninths Which of the following has all the correct justifications Bruno used to solve this equation? 1. Multiplication Property of Equality 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Subtraction Property of Equality 4. Division Property of Equality 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality 1. Multiplication Property of Equality 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality
Answer:
Statement Reason
1. [tex]4x+5x-2=6[/tex] 1. Distributive Property
2. [tex]9x-2=6[/tex] 2. Combine like terms
3. [tex]9x=8[/tex] 3. Addition Property of Equality
4. [tex]x=\dfrac{8}{9}[/tex] 4. Division Property of Equality
Step-by-step explanation:
The given equation is
[tex]4x+\dfrac{1}{2}(10x-4)=6[/tex]
Using distributive property, we get
[tex]4x+\dfrac{1}{2}(10x)+\dfrac{1}{2}(-4)=6[/tex]
[tex]4x+5x-2=6[/tex]
[tex]9x-2=6[/tex] (Combine like terms)
Using Addition Property of Equality, add 2 on both sides.
[tex]9x=6+2[/tex]
[tex]9x=8[/tex]
Using Division Property of Equality, divide both sides by 9.
[tex]x=\dfrac{8}{9}[/tex]
describe the solution to the system of equations graphed below.
Answer:
Step-by-step explanation:
The answer is B, the solution to your equation is at (2,1). Your solution is where the two lines meet.
Answer:
The second option.
Step-by-step explanation:
When two lines intersect, they usually intersect at just one point (unless they are parallel, where they never intersect; or no solutions when they infinitely intersect).
According to the graph provided, the lines are intersecting at one point: (2, 1).
So, your answer will be the second option!
Hope this helps!
Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is 1 50 and is independent from one topic to the next. If you discuss 17 topics, how surprising would it be to find that you match on at least one of them
Answer:
1/17 0r 6%
Step-by-step explanation:
the answer is rounded up for you
Bacteria in a petri dish doubles every 10 minutes.
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
(Show step by step)
Answer:
Step-by-step explanation:
Givens
Petri Dish A sees a double ever 10 minutes
Petri Dish B sees a double ever 6 minutes
Consequences
A doubles 60 / 10 = 6 times.
B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A
1,305 divided by 31,828 x100
Answer:
[tex]4 \frac{1}{10}[/tex]
Step-by-step explanation:
=> [tex]\frac{1305}{31828} * 100[/tex]
=> 0.041 * 100
=> 4.1
=> [tex]4 \frac{1}{10}[/tex]
Factor the expression 4x + 32. Explain each step you take in the process. 100 points goes to brainliest
Answer:
4(x+8)
Step-by-step explanation:
4x+32
x+8 in parentheses
and put the 4 on the outside of the parentheses
like this 4(x+8)
Answer:
4(x+8)
Step-by-step explanation:
4x + 32
Rewriting
4*x + 4*8
Factor out 4
4(x+8)
Which relation is not a function?
a) y = 1x + 7
by=- 4(x + 3)2 + 10
c) -2y = - 3x + 9
d) x2 + y2 = 25
Answer:
x^2+y^2=25
Step-by-step explanation:
x^2+y^2=25 graphs a circle. A relation is a function if every x only has one y value. This is not true in a circle.
Answer:
d) x^2 + y^2 = 25.
Step-by-step explanation:
D is the equation of a circle so it fails the vertical line test for a function. If a relation is a function then any vertical line passing through it's graph will only intersect it once. This is not true of a circle.
The mean per capita income is 19,292 dollars per annum with a variance of 540,225. What is the probability that the sample mean would be less than 19269 dollars if a sample of 499 persons is randomly selected? Round your answer to four decimal places.
Answer:
The probability is 0.2423.
Step-by-step explanation:
Given mean per capita = 19292 dollars
Given the variance = 540225
Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.
Below is the calculation:
[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]
Solve the equation x^2 – 16x + 25 = 0 to the nearest tenth.
Answer:
1.8 and 14.3
Step-by-step explanation:
Our equation is a quadratic equation so we will use the dicriminant method
Let Δ be our dicriminant a=1b= -16c= 25Δ= (-16)²-4*25*1=156≥0 so we have two solutions : x and y x= (16-[tex]\sqrt{156}[/tex])/2= 1.7555≈ 1.8y=(16+[tex]\sqrt{156}[/tex])/2=14.244≈ 14.3Select the correct answer.
Identify the expression equivalent to 4(x + x + 7) - 2x + 8 - 4 by substituting x = 1 and x = 2.
PLZ HELP
Answer:
Option (C)
Step-by-step explanation:
Given expression is 4(x + x + 7) - 2x + 8 - 4
When x = 1,
Value of the expression will be,
= 4(1 + 1 + 7) - 2(1) + 8 - 4
= 4(9) - 2 + 8 - 4
= 36 - 2 + 8 - 4
= 38
For x = 2,
= 4(2 + 2 + 7) -2(2) + 8 - 4
= 44 - 4 + 8 - 4
= 44
Now we will check the same for the given options.
Option (A). For x = 1,
6x + 11 = 6(1) + 11
= 17
For x = 2,
6x + 11 = 6(2) + 11
= 23
Option (B). For x = 1,
3(x + 7) = 3(1 + 7)
= 24
For x = 2,
3(x + 7) = 2(2 + 7)
= 18
Option (C), x = 1
2(3x + 16) = 2[3(1) + 16]
= 38
For x = 2,
2(3x + 16) = 2[3(2) + 16]
= 44
Option (D), For x = 1,
= 19
For x = 2,
2(3x + 16) = 2[3(2) + 16]
= 44
Since value of the expression for x = 1 and 2 matches with the value in option (C)
Therefore, Option (C) will be the answer.
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
The equation that describes the function is y = -6x-1
Step-by-step explanation:
Firstly we can see that the graph passes through the origin.
The general equation of a starlight line graph is;
y = mx + c
where m is the slope and c is the y-intercept
what’s left now is go find our slope
We need two points for this on the line.
Let’s identify these points;
The identifiable points are; (1,-7) and (-1,5)
So the formula for the slope is;
y2-y1/x2-x1 = (5-(-7))/(-1-1) = 12/-2 = -6
Thus, the equation of the line becomes
y = -6x + c
Looking at the graph again, we can see an obvious y-intercept at the point y = -1
So our intercept is -1
The equation of the line is thus;
y = -6x -1
Find all polar coordinates of point P = (2,14°)
Answer:
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex].
Step-by-step explanation:
If a point is [tex]P=(r,\theta)[/tex], the all polar coordinates are defined as
In radian : [tex](r,\theta +2n\pi)\text{ and }(-r,\theta +(2n+1)\pi)[/tex]
In degree : [tex](r,\theta +360^{\circ}n)\text{ and }(-r,\theta +(2n+1)180^{\circ})[/tex]
where, n is any integer.
The given point is
[tex]P=(2,14^{\circ})[/tex]
So, all polar coordinates are
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +(2n+1)180^{\circ})[/tex]
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +360^{\circ}n+180^{\circ})[/tex]
[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex]
Therefore, the required polar coordinates are [tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex], where n is any integer.
A: What are the solutions to the quadratic equation 9x2 + 64 = 0?
B: What is the factored form of the quadratic expression 9x2 +64?
Select one answer for question A, and select one answer for question B.
B: (3x + 81)(x - 1)
B: (x-8)(3x-8)
B:(3x8)(3x + 8)
B: (3x - 81)(3x + 81)
Ax = or x = -1
A:x =
A: x = i orx = -
O A x = 1
Answer:
B: (3x + 81)(x - 1)
Step-by-step explanation:
What monomial do you have to raise to the power of 2 to get the monomials below? (1000000m18)
Answer:
(1000m⁹)²Step-by-step explanation:
A monomial is an expression containing just one term. Given the monomial 1000000m¹⁸, to get the monomial we need to raise to the power of 2 to get this given monomials, the following steps must be taken using the laws of indices.
In indices, [tex](a^m)^n = a^m^n[/tex], applying this rule to the question we have;
1000000m¹⁸
= (10*10*10*10*10*10)m¹⁸
= 10⁶m¹⁸
= 10⁶*(m³)⁶
= (10*m³)⁶
= (10m³)⁶
= (10m³)²ˣ³
= (10³m⁹)²
= (1000m⁹)²
The last result gives the required expression
By first calculating the angle of LMN, calculate the area of triangle MNL. You must show all your working.
Answer:
16.66cm²
Step-by-step Explanation:
Given:
∆LMN with m<N = 38°
Length of side NL = 7.2cm
Length of side ML = 4.8cm
Required:
Area of ∆MNL
Solution:
Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b
Where sin(A) = Sin(M) = ?
a = NL = 7.2cm
sin(B) = sin(N) = 38°
b = ML = 4.8cm
Thus,
Sin(M)/7.2 = sin(38)/4.8
Cross multiply
4.8*sin(M) = 7.2*sin(38)
4.8*sin(M) = 7.2*0.6157
4.8*sin(M) = 4.43304
Divide both sides by 4.8
sin(M) = 4.43304/4.8
sin(M) = 0.92355
M = sin-¹(0.92355) ≈ 67.45°
Step 2: Find m<L
angle M + angle N + angle L = 180 (sum of angles in a triangle)
67.45 + 38 + angle L = 180
105.45 + angle L = 180
Subtract 105.45 from both sides
Angle L = 180 - 105.45
Angle L = 74.55°
Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)
Where,
a = NL = 7.2 cm
b = ML = 4.8 cm
sin(C) = sin(L) = sin(74.55)
Thus,
Area of ∆MNL = ½*7.2*4.8*0.9639
= ½*33.31
= 16.655
Area of ∆MNL ≈ 16.66cm²
Jim & Gavin share a lottery win of £4750 in the ratio 1 : 4. Jim then shares his part between himself, his wife & their son in the ratio 2 : 6 : 2. How much more does his wife get over their son?
Answer:
£380
Step-by-step explanation:
Consider the initial win of £4750
Sum the parts of the ratio, 1 + 4 = 5 parts
Divide the win by 5 to find the value of one part of the ratio.
£4750 ÷ 5 = £950 ← value of 1 part of the ratio
Thus Jim's share is £950
Sum the parts of the ratio shared in his family, 2 + 6 + 2 = 10 parts
Divide his share by 10 to find the value of one part
£950 ÷ 10 = £95 , thus
2 parts = 2 × £95 = £190 ← sons share
6 parts = 6 × £95 = £570 ← wife's share
£570 - £190 = £380
Wife gets £380 more than the son
Simplify the following expression. 3 – 2(–6x + 3)
Answer:
-3 + 12x
Step-by-step explanation:
3 - 2(-6x + 3)
3 + 12x - 6
-3 + 12 x
Hope this helped! :)
A truck is to be filled with packages that weigh 5.8kg. If the maximum capacity of the truck is 48000 grams and there is a 5500 gram package already on the truck how many 5.8kg packages can be loaded?
Answer: 7 packages
Step-by-step explanation:
From the question, we are told that a truck is to be filled with packages that weigh 5.8kg. The maximum capacity of the truck is 48000 grams(48kg) and there is a 5500 gram(5.5kg) package already in the truck.
First, we need to subtract 5.5kg from 48kg to know the amount of space left. This will be:
= 48kg - 5.5kg
= 42.5kg
To get the number of 5.8kg packages that can be loaded, we divide 42.5kg by 5.8kg. This will be:
= 42.5kg/5.8kg
= 7.3
= 7 approximately
Therefore, 7 packages will be loaded.
N.B: 1000 grams = 1 kilogram
(42) A school only provides bus service
to students who live a distance greater
than 2 miles away from the school. On a
coordinate plane, the school is located at
the origin, and Michael lives at the closest
point to the school on Maple Street,
which can be represented by the line
y = 2x – 4. If each unit on the coordinate
plane represents 1 mile, does Michael
live far enough from the school for bus
service?
Answer:
~1.8 mile
Step-by-step explanation:
Michael lives at the closest point to the school (the origin) on Maple Street, which can be represented by the line y = 2x – 4.
This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.
Denote equation of y2 is y = ax + b,
with a is equal to negative reciprocal of 2 => a = -1/2
y2 pass the origin (0, 0) => b = 0
=> Equation of y2:
y = (-1/2)x
To find location of Michael's house, we get y1 = y2 or:
2x - 4 = (-1/2)x
<=> 4x - 8 = -x
<=> 5x = 8
<=> x = 8/5
=> y = (-1/2)x = (-1/2)(8/5) = -4/5
=> Location of Michael' house: (x, y) = (8/5, -4/5)
Distance from Michael's house to school is:
D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) = ~1.8 (mile)
Find the coefficient of x^2 in the expression of (x - 7)^5. a. -3430 b. -3034 c. 3034 d. 3430
Answer:
let me know when you have the anwser
Step-by-step explanation:
A same side interior angle of two parallel lines is 20° less than the other same side interior angle. Find the measures of these two angles.
Answer:
The measures of the two angles are 80 and 100
Step-by-step explanation:
Let [tex]m_1[/tex] and [tex]m_2[/tex] represent the two angles such that
[tex]m_1 = m_2 - 20[/tex]
Required
Find [tex]m_1[/tex] and [tex]m_2[/tex]
The two angles of a same-side interior angle of parallel lines add up to 180;
This implies that
[tex]m_1 + m_2 = 180[/tex]
Substitute [tex]m_2 - 20[/tex] for [tex]m_1[/tex]
[tex]m_1 + m_2 = 180[/tex] becomes
[tex]m_2 - 20 + m_2 = 180[/tex]
Collect like terms
[tex]m_2 + m_2 = 180 + 20[/tex]
[tex]2m_2 = 180 + 20[/tex]
[tex]2m_2 = 200[/tex]
Divide both sides by 2
[tex]\frac{2m_2}{2} = \frac{200}{2}[/tex]
[tex]m_2 = \frac{200}{2}[/tex]
[tex]m_2 = 100[/tex]
Recall that [tex]m_1 = m_2 - 20[/tex]
[tex]m_1 = 100 - 20[/tex]
[tex]m_1 = 80[/tex]
Hence, the measures of the two angles are 80 and 100
Which expression can be simplified to find the slope of the line of best-fit in the scatterplot below? On a graph, a trend line goes through points (4, 35) and (16, 134). StartFraction 134 minus 35 Over 16 minus 4 EndFraction StartFraction 134 minus 16 Over 35 minus 4 EndFraction StartFraction 4 minus 16 Over 35 minus 134 EndFraction StartFraction 4 minus 16 Over 134 minus 35 EndFraction
Answer:
134-35/16-4 (A)
Step-by-step explanation:
I just know
Answer
A) 134-35/16-4
Step-by-step explanation:
i need the answer right now
3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use
the formula:
Vt) = P(1 + r) where V(t) is the value of the coin in t years, Please HELP! help on number three
Answer:
Coin A : [tex]V(t)=25(1.07)^t[/tex]
Coin B : [tex]V(t)=40(1.05)^t[/tex]
Step-by-step explanation:
Consider the given formula is
[tex]V(t)=P(1+r)^t[/tex]
where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.
For coin A, current value is 25 dollars and annual appreciation rate is 7%.
[tex]V(t)=25(1+0.07)^t[/tex]
[tex]V(t)=25(1.07)^t[/tex]
For coin B, current value is 40 dollars and annual appreciation rate is 5%.
[tex]V(t)=40(1+0.05)^t[/tex]
[tex]V(t)=40(1.05)^t[/tex]
Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.
A rectangular driveway has the dimensions shown below. Concrete costs $49.75 per square yard to pour. How much will it cost to pour concrete for the entire driveway?
[tex]\boxed{ \bf The~answer~is~$2,350.69.}[/tex]The answer is $2,350.69.
Explanation:First, we must find the area of the rectangular driveway.
A = l × w
A = 15.75 × 3
A = 47.25
So, the area of the driveway is 47.25 yd².
Next, we need to multiply the cost of each square yard by the area.
49.75 × 47.25 = 2350.6875
This can be rounded to 2,350.69.
Help
Use a calculator to find the
square root of 74 and round
to the nearest tenth.
d = 174.
d = [?]
Answer:
8.6
Step-by-step explanation:
The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6
The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The square root of the value 74 will be calculated as below:-
D = √74
D = 8.602325267
D = 8.6
Therefore, the square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.
To know more about expression follow
https://brainly.com/question/723406
#SPJ2
Which polynomial is factored completely?
g^5-g
4g^3+18g^2+20g
24g^2-6g^4
2g^2+5g+4
Answer:
Option (4)
Step-by-step explanation:
To solve this question we will try to factor the expressions given in each option.
Option (1)
g⁵ - g = g(g⁴ - 1)
= g(g² - 1)(g² + 1)
= g(g - 1)(g + 1)(g² + 1)
Option (2)
4g³ + 18g² + 20g = 2g(2g² + 9g + 10)
= 2g[2g + 5g + 4g + 10]
= 2g[g(2g + 5) + 2(g + 5)]
= 2g(2g + 5)(g + 2)
Option (3)
24g² - 6g⁴ = 6g²(4 - g²)
= 6g²(2 - g)(2 + g)
Option (4)
2g² + 5g + 4
This expression is the in the completely factored form.
Answer:
yes its D :)
Step-by-step explanation:
other guy has the math, i just know the answer, sorry lol
using Pythagoras theorem work out the length of AB
ABC is a triangle,
1 side is 22 cm 1 side is 8 cm
1 side is unknown the
1 unknown side is unknown
work out AB using Pythagoras theorem
Answer:
AB = 23.40 cmSolution,
Base ( BC ) = 22 cm
Perpendicular ( AC) = 8 cm
Hypotenuse (AB) = ?
Now,
Using the Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {h}^{2} = {(8)}^{2} + {(22)}^{2} [/tex]
[tex] {h}^{2} = 64 + 484[/tex]
[tex] {h}^{2} = 548[/tex]
[tex]h = \sqrt{548} [/tex]
[tex]h = 23.40 \: cm[/tex]
Hope this helps..
Good luck on your assignment...
Someone Help me please !
Answer:
[tex] \sqrt{9} \times \sqrt{16} [/tex]
Step-by-step explanation:
[tex] \sqrt{9} \times 16 = \sqrt{9} \times \sqrt{16} = 3 \times 4 = 12[/tex]
Hope this helps ;) ❤❤❤
Answer:
sqrt(9) * sqrt(16)
Step-by-step explanation:
sqrt( 9*16)
We know that sqrt(a*b) = sqrt(a) sqrt(b)
sqrt(9) * sqrt(16)
3*4
12