Answer:
5,33333.....
Step-by-step explanation:
A number is rational if it could be written as x/y with x and y are integer numbers
so 5,33333=5,(3)=5 3/9 =(5*9+3)/9=48/9 is a rational number
Answer:
If a number that can be expressed in the form of p/q is called rational numbers. Here p and q are integers, and q is not equal to 0. A rational number should have a numerator (p) and denominator (q). Examples: 10/2, 30/3, 100/5.
identify an equation in slope intercept form for the line parellel to y=-3x+7 that passes through (2,-4)
Answer:
y= -3x+2
Step-by-step explanation:
Parallel lines have the same slope. We can form an incomplete equation:
y= -3x+b
(make sure to see why the slope is -3)
We can plug in the coordinates of (2, -4):
-4= -3(2)+b
-4= -6+b
2=b
b is 2! We can form an equation: y= -3x+2
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
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]
1/5 of a chocolate chip cookie has 30 cal how many calories are in a whole cookie
Answer:
150 cal
Step-by-step explanation:
5x30=150
Answer:
150 calories.
Step-by-step explanation:
Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.
You know that 1/5 of a chocolate chip cookie has 30 calories.
Find one cookie, by multiply 5 to both numbers. Set the equation:
1/5x = 30
Isolate the variable. Multiply 5 to both sides:
(1/5x) * 5 = (30) * 5
x = 30 * 5
x = 150
150 calories is your answer.
Suppose it takes
12
hours for a certain strain of bacteria to reproduce by dividing in half. If
45
bacteria are present to begin with, the total number present after
x
days is
f
(
x
)
=
45
⋅
4
x
.
Find the total number present after
1
,
2
, and
3
days.
Answer:
Step-by-step explanation:
The formula is
[tex]y=45(4)^x[/tex]
which models the exponential function
[tex]y=a(b)^x[/tex] where a is the initial amount of whatever it is you have (in our case it's bacteria), b is the growth rate (ours is 4 which means that every day the number from the day before increases by a factor of 4), and x is the number of days. We plug into the formula the values we have, starting with x = 1:
[tex]y=45(4)^1[/tex]
Always raise what's inside the parenthesis first, then multiply in the 45. 4 to the first is 4, and 4 multiplied by 45 is 180. After the first day, there are 180 bacteria present in the culture.
Next, x = 2:
[tex]y=45(4)^2[/tex] which simplifies to
y = 45(16) so
y = 720.
Next, x = 3:
[tex]y=45(4)^3[/tex] which simplifies to
y = 45(64) so
y = 2880
Which triangles in the diagram are congruent?
70°
triangle 1
triangle 2
70°
70°
triangle 3
triangle 4
Answer: They all are congruent because there are no triangles
Step-by-step explanation:
Answer: the answer is 1 and 3
Step-by-step explanation:1 and 3
Can someone please help me I really need help please help me thank you
Answer:
This is modelling the exterior angle formula which states that the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles. Therefore, the answer is x = a + b.
Answer:
x = a+b
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
x = a+b
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:
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
Name the following polynomial:4x^(2)+8n+16
Answer:
a 2nd degree trinomial
Step-by-step explanation:
First, this polynomial has 3 terms which are 4x^2, 8n, and 16. This makes this polynomial a trinomial.
Second, the highest degree in this polynomial is a degree of 2 because of the term 4x^2. This makes this polynomial a 2nd degree polynomial.
Lastly, when you put all of this together you get a 2nd degree trinomial.
Answer:
Step-by-step explanation:
Cubic trinomial
What is the volume of a sphere with a radius of 18 units?
O A. 77767 units3
B. 12967 units3
O C. 58327 units3
D. 1944 units
Answer:
24,429.0245 square units
Step-by-step explanation:
The volume of a sphere can be found using the following formula.
[tex]V=\frac{4\pi r^3}{3}[/tex]
The radius is 18 units. Therefore, we can substitute 18 units in for r.
[tex]V=\frac{4\pi (18units)^3}{3}[/tex]
First, evaluate the exponents.
18 units^3= 18 units * 18 units * 18 units= 5832 units^3
[tex]V=\frac{4\pi (5832 units^3)}{3}[/tex]
Multiply 4 and pi.
[tex]V=\frac{12.5663706*5832 units^3}{3}[/tex]
Multiply in the numerator.
[tex]V=\frac{73287.0733 units^3}{3}[/tex]
Divide
[tex]V=24429.0245 units^3[/tex]
The volume of the sphere is 24,429.0245 units^3
HELP ASAP PLEASE ------ for the function f(x)=x^2 what effect will multiplying f(x) b y 1/4 have on the graph
Answer:
Vertical Shrink of a factor of 1/4
Step-by-step explanation:
Since we are manipulating a in f(x) = a(bx - h)² + k, we are dealing with vertical stretch (x > 1) and vertical shrink (x < 1). Since 1/4 < 1, we have a vertical shrink of 1/4.
Answer: if you multiply the f(x) by 1/4 the graph seems to narrow, which is interpreted as a positive vertical shift . The y value (output) is 4 times greater
If you multiply the x² by 1/4, the graph seems to widen, which is interpreted as a negative vertical shift. The y value is less by a factor of 1/4
Step-by-step explanation: I am reading the question literally: multiplying f(x) by 1/4. (This may be dangerous as mathematicians have their own lingo, and some words have specialized meanings that English majors haven't learned!)
I understand that f(x) or any other function is the y-output. So in order to graph a function, it is legitimate to substitute "y" for f(x).
I am attaching a graph with the f(x)=x² in red f(x) = (1/4)x² in green and (1/4)f(x) = x² in blue.
As you can see, very different results: Substituting 2 for x
in red original 4 = 2²
in green f(x) = (1/4)(2²) . 1 = (1/4)(4)
in blue (1/4)f(x) = x² (1/4) 16 = (2²) =. This is probably not the intended result, but it is literally what happens if you multiply the left side! 16 is the output on the graph.
So, despite my efforts to make sense of this, I realize that this answer is mistaken, and I hope someone can clear up my confusion, please!
2a^2 +7ab-15b^2
please solve the answer fast
Answer:
(2a - 3b) (a + 5b)
hope this helps!
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. what is the range of this function
Answer:
raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. (given)
thus, rate of draining of water gallons per minute = -1.5
amount of water remaining in the bathtub = y,
the function of the time in minutes that it has been draining = x, .
at 0 minutes the amount of water is 40 gallons.
thus,the volume of water is 40 is decreasing at the rate of 1.5 gallons per minute
the given function is a linear function
y = 0
however, the volume of water can be 0 but cannot ever be negative.
thus, the range of y will be all real numbers such that 0≤y≤40
Step-by-step explanation:
Answer:
y = 0
Step-by-step explanation:
i took test
WILL MARK BRAINLIEST!!!!!! The figure shows two triangles on the coordinate grid: What set of transformations is performed on triangle ABC to form triangle A′B′C′? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
Answer:
A 180°counterclockwise rotation about the origin,followed by a translation 5 units to the right
Answer:
The Answer is A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
Hope this helps :)
What is this expression in simplified form? 3√3 * 6√6
Answer:
The answer is 54√2Step-by-step explanation:
( 3 √ 3)(6√6) = ( 3 × 6) (√ 6 × 3)
= 18√18 = 18( √ 9 × 2)
= 18 ( √9 × √2)
= 18( 3√2)
= ( 18 × 3)√2
= 54√2Hope this helps you
3√3 x 6√6
multiply whats outside the radical and put it outside:
6 x 3 = 18 ------> 18√x
and multiply what's inside and place it inside:
3 x 6 = 18 --------> x√18
so now, you have 18√18, which can be simplified to:
18√(9 x 2)
18√9√2 = 18*3√2 = 54√2
What is the factored of the polynomial
x + 9x +20
(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)
2x-2/5=8 Please explain answer
Answer:
x=21
Step-by-step explanation:
1. 2x-2/5*5=8*5 Multiply the 5 on both sides to cancel out the denominator.
2. 2x-2+2=40+2 Add 2 on both sides to isolate the term with the variable.
3. 2x/2=42/2 Divide both sides by 2 in order to isolate the variable itself. Yay, you got the answer, 21!
Heyy I hope you have a great day, this took forever to type so it would be very appreciated if you marked this answer as brainliest... UwU
Select 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.
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
Find the equation of the line that passes through (3,-4) and is parallel to 3x+y+2=0 Leave your answer in the form y=mx+c
Answer:
2x+y
Step-by-step explanation:
Simply remove the +2
Answer:
y = - 3x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + y + 2 = 0 ( subtract 3x + 2 from both sides )
y = - 3x - 2 ← in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus
y = - 3x + c ← is the partial equation
To find c substitute (3, - 4) into the partial equation
- 4 = - 9 + c ⇒ c = - 4 + 9 = 5
y = - 3x + 5 ← equation of line in form y = mx + c
Written Response! Please help!
Evelyn believes that if she flips a coin 480 times, it will land tails up exactly 240 times. What would you tell Evelyn about her prediction?
Based on Evelyn's response, it can be said that she predicts that there is a 50% chance of the coin landing on tails and a 50% chance of the coin landing on heads.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the coin lands on tails is half of the number of times the coin is tossed. This means she belives that there is an equal chance that the coin would land on either heads or tails.
To learn more about probability, please check: https://brainly.com/question/13234031
Please answer this in two minutes
Answer:
VW = 1
Step-by-step explanation:
Tan 45 = 4/VW
VW = 4/Tan 45 = 1
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! :)
what is the factorization of the polynomial below 3x^2+36x+81
Answer:
(x+3) (x+9)
Step-by-step explanation:
using quadratic formular ...you will have
The above
Express £5 as a fraction of £4.
Answer:
£5/£4
Step-by-step explanation:
£5 over £4 can be expressed as a fraction.
⇒ £5/£4
convert 4 1/3 feet to inches
Answer:
52 inches
Step-by-step explanation:
Answer:
we have, 1 feet =12 inches
13/3 foot =12×13/3 inches
=52 inches.
thereforethe , the answer is 52 inches.
Based on a survey, assume that 32% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when six consumers are randomly selected, exactly three of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
Answer:
n = 6
x = 3
p = 0.32
q = 0.68
Step-by-step explanation:
Given:
32% are comfortable having drones deliver their purchases.
Suppose we are to find the probability that when 6 consumers are randomly selected, exactly 3 of them are comfortable with delivery by drones.
Required:
Find n, x, p, and q.
i) n represents the sample size. Here 6 consumers are selected randomly, therefore the sample size here is 6.
Thus, n = 6
ii) x represents the sample mean or number of successes. Since 3 consumers out of the selected 6 are comfortable with delivery by drones, the sample mean here is 3.
Thus, x = 3
iii) p represents population proportion or probability of success. Here population proportion(success probability) is 32% ≈ 0.32.
Thus, p = 0.32
iv) q represents probability of failure. To find probability of failure, use the formula:
1 - p
Thus,
1 - 0.32 = 0.68
q = 0.68
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