For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.
So, we have to:
We look for the factors of 18 and 36:
18: 1,2,3,6,9,18
36: 1, 2,3,4, 6,9,18 ...
It is observed that the GFC of both numbers is 18.
Then, the GFC of [tex]18x ^ 2[/tex] and [tex]36x[/tex] is:
18x
Answer:
18x
Please answer right away
Answer:
0.42
Step-by-step explanation:
There are total 7 end points, 3 of them lead to winning $10 and the other ones lead to nothing
so, [tex]\frac{3}{7}[/tex] = 0.42
Another Urgent one!! you know the drill. HEEEEEEEEEEELP
Answer:
Step-by-step explanation:
It is a right angle triangle with height and base = 3. The 4.24, for area, is not relevant.
Area = h * b / 2
Area = 3 * 3/2
Area = 9/2
Area = 4.5
Answer:
4.5 units
Step-by-step explanation:
A=1/2(b×h)
b=base
h=height
plug in what we know ...
A=1/2 (3×3)
A=1/2 (9)
A=4.5
lee walked a total of 4.48 miles. he walks 1.4 miles each hour. how long did lee walk?
Answer - 3.2 hours
because 4.48 miles divided by 1.4 mph equals 3.2
Answer:
3.2 hrs
Step-by-step explanation:
Recall that distance = rate times time, so:
4.48 mi = (1.4 mph)(time), and:
4.48 mi
the elapsed time was ------------------- = 3.2 hours
1.4 mph
8-102.
The graph at right represents this situation: Cara jogs every
morning, and after 30 minutes, she has run 3.5 miles.
a. How is Cara's speed represented on the graph?
b. Write a rule for Cara's distance if t represents
the number of hours.
Distance (miles)
c.
If Cara continues to run at this rate, predict
how far she will run in 4 hours.
a. The speed is represented by 7 miles an hour
b. f(t)=7t
c. 28 miles
10+13h-6-4h+9+12h simplified
Answer:
[tex]\boxed{\bold{21h+13}}[/tex]
Explanation:
Group Like Terms
= [tex]\bold{13h-4h+12h+10-6+9}[/tex]
Combine Similar Elements: [tex]\bold{13h-4h+12h=21h}[/tex]
= [tex]\bold{21h+10-6+9}[/tex]
Subtract: [tex]\bold{10-6+9=13}[/tex]
= [tex]\bold{21h+13}[/tex]
Mordancy.
A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election.
Which statement describes a method that will help him accurately estimate this percentage?
He could contact every resident in the town, ask whether the resident will vote for the particular candidate, and then calculate the percentage of residents who say they will vote for the particular candidate.
He could ask employees at the newspaper which candidate each will vote for, and then calculate the percentage who will vote for the particular candidate.
He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
He could ask his readers to respond to a survey that asks which candidate the reader will vote for and then calculate the percentage of people who say that they will vote for the particular candidate.
Answer:
i dont real know
Step-by-step explanation:
help!!!!!!!!!!!!!!!!!!!!
Answer:
π units^2.
Step-by-step explanation:
The area = π r^2 where r = the radius and the radius = 1/2 * the diameter.
So the radius of this circle = 1/2 * 2 = 1.
The required area = π * 1^2
= π units^2.
ANSWER
Exact form: π units square.
Or 3.14 square units.
EXPLANATION
The area of a circle is calculated using the formula:
[tex]Area = \pi \times {r}^{2} [/tex]
From the diagram, the diameter of the circle is d=2 units.
The radius is half of the diameter which is 1 unit.
We substitute r =1 into the formula to obtain;
[tex]Area = \pi \times {1}^{2} [/tex]
[tex]Area = \pi \: [/tex]
In decimal form, the area is
[tex]Area =3.14 \: square \: units[/tex]
Show that the maximum rate of change, with respect to radius, of the volume of a deflating balloon is four times the sphere's initial great circle circumference
Step-by-step explanation:
Let's say R is the initial radius of the sphere, and r is the radius at time t.
The volume of the sphere at time t is:
V = 4/3 π r³
Taking derivative with respect to radius:
dV/dr = 4π r²
This is a maximum when r is a maximum, which is when r = R.
(dV/dr)max = 4π R²
This is 4 times the sphere's initial great circle area, but not the great circle circumference. The problem statement contains an error.
factor the expression 36a^2 - 49b^2
The expression 36a^2 - 49b^2 can be factored into the product of two binomials by applying the difference of squares formula. The factored form of the expression is (6a - 7b)(6a + 7b).
Explanation:The expression 36a^2 - 49b^2 is a difference of squares. A difference of squares is a special type of binomial that can be factored into the product of two binomials.
In general, if you have an expression of the form x^2 - y^2, this is equal to (x - y)(x + y).
In the case of the expression 36a^2 - 49b^2, 36a^2 is the square of 6a, and 49b^2 is the square of 7b. Therefore, the expression 36a^2 - 49b^2 can be factored into (6a - 7b)(6a + 7b).
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Final answer:
The expression 36a² - 49b² is factored as (6a + 7b)(6a - 7b) using the difference of squares identity a² - b² = (a + b)(a - b).
Explanation:
The expression 36a² - 49b² is a difference of squares which can be factored using the identity a² - b² = (a + b)(a - b). In this case, the expression can be written as (6a)² - (7b)². This resembles the identity where a is 6a and b is 7b. Applying the identity, we get:
(6a + 7b)(6a - 7b)
This is the factored form of the given expression. To understand why this works, we recognize that squaring a number and then subtracting the square of another number creates two terms, one positive and one negative, whose products with themselves give us the original expression. The factored form thus represents two binomials that reflect the sum and the difference of the square roots of the original terms, respectively.
Please Help Quickly!! Will give Brainliest!!
Is the data set “types of fruit at the grocery store” qualitative or quantitative? If it is quantitative, is it discrete or continuous?
a.
quantitative, discrete
c.
quantitative, continuous
b.
qualitative
d.
neither
Answer:
The data set "types of fruit at the grocery store" is qualitative.
The correct answer is B.
The correct option is a. quantitative, discrete.
The data set "types of fruit at the grocery store" is quantitative because it involves counting the number of different types of fruit, which is a numerical value. Furthermore, it is discrete because the count of fruit types will result in whole numbers, with no fractional or continuous values between them. For example, one cannot have 3.5 types of fruit; it must be a whole number such as 3 or 4. Therefore, the data is not qualitative as it is not about the characteristics or attributes of the fruit but rather the count of different categories of fruit. It is also not continuous as the number of fruit types cannot vary smoothly and must be counted in whole units.
What are the solutions for x to the equation (x-3)(x+8)=0
For this case we have a factored expression, of a second degree equation:
([tex](x-3) (x + 8) = 0[/tex]
To find the solutions:
[tex]x-3 = 0[/tex]we add 3 to both sides of the equation:
[tex]x=3[/tex]
[tex]x+8=0[/tex]We subtract 8 on both sides of the equation:
[tex]x = -8[/tex]
Thus, the solutions of the equation are:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
Answer:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
A scientist enlarged a circular portion of a microscope slide to make it easier to count the number of bacteria present in the sample.He divided the circle into 5 sectors as shown below and plans to count bacteria only in the shaded sector. What is the area of the shaded sector to the nearest tenth of a square centimeter
A.141.4
B.212.1
C.377.0
D.424.1
Answer:
Option B. [tex]212.1\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the central angle of the shaded sector
Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)
so
Let
x -----> the measure of the central angle of the shaded sector
∠x+72°=180°
∠x=180°-72°=108°
step 2
Find the area of the circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ cm[/tex]
assume
[tex]\pi=3.1416[/tex]
substitute
[tex]A=(3.1416)(15)^{2}[/tex]
[tex]A=706.86\ cm^{2}[/tex]
step 3
Find the area of the shaded sector
Remember that the area of the complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 108 degrees
[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]
The choices for the first one is
1/4
1
5/4
Choice for the second one is
(3i square root 7)/4
(i square root 21)/2
(square root 112)/4
Answer:
[tex]\large\boxed{\dfrac{5\pm3\sqrt7}{4}}[/tex]
Step-by-step explanation:
[tex]m^2-\dfrac{5}{2}m=-\dfrac{11}{2}\qquad\text{add}\ \dfrac{11}{2}\ \text{to both sides}\\\\m^2-\dfrac{5}{2}m+\dfrac{11}{2}=0\qquad\text{multiply both sides by 2}\\\\2m^2-5m+11=0[/tex]
[tex]\text{Use the quadratic formula:}[/tex]
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have}[/tex]
[tex]a=2,\ b=-5,\ c=11[/tex]
[tex]\text{substitute:}[/tex]
[tex]\sqrt{b^2-4ac}=\sqrt{(-5)^2-4(2)(11)}=\sqrt{25-88}=\sqrt{63}=\sqrt{9\cdot7}=\sqrt9\cdot\sqrt7=3\sqrt7\\\\m=\dfrac{-(-5)\pm3\sqrt7}{2(2)}=\dfrac{5\pm3\sqrt7}{4}[/tex]
In last night’s baseball game, there were 4 walks and 15 hits. Express the ratio of walks to hits, written in three different ways.
Word form: 4 to 15
Fraction form: 4/15
Ratio form: 4:15
The ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.
What is a Ratio?When a number is divisible by another number then it can be written in the form of p:q, if two ratios are equal then they are said to be in proportion.
The number of walks in the baseball game is 4
The number of hits in the baseball game is 15
The ratio of walks to hits is 4 :15
The ratio of walks to hits is 0.2666 : 1
The ratio of walks to hits is 1 : 3.75
Therefore, the ratio has been written in three different forms as 4:15, 0.266:1 or 1:3.75.
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BgxjsjskznshshzdhhanakOaj
Answer:
12 mm : 5 meters
Step-by-step explanation:
We need to write the ratio of drawing: real life
48 mm: 20 meters
We can divide each term by 4
48mm/4 : 20 meters/4
12 mm : 5 meters
A basketball has a rebound ratio of 0.8. If you drop the basketball from a heigh of 10cm, what will the height of the 5th bounce be?
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} r=0.8\\ a_1=10\\ n=5 \end{cases} \\\\\\ a_5=10(0.8)^{5-1}\implies a_5=10(0.8)^4\implies a_5=4.096[/tex]
Which equation represents a circle with a center located at (-2,2) and a circumference of 16π
Answer:
(x + 2)² + (y - 2)² = 64
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 2, 2), thus
(x + 2)² + (y - 2)² = r²
Given C = 2πr = 16π ( divide both sides by 2π )
r = [tex]\frac{16\pi }{2\pi }[/tex] = 8
Hence
(x + 2)² + (y - 2)² = 64 ← equation of circle
To find the equation of the circle with center at (-2,2) and a circumference of 16π, first calculate the radius r=8 from the circumference, then use the formula (x+2² + (y-2)² = 64.
The question asks for the equation of a circle with a given center and circumference. The center of the circle is located at (-2,2), and the circumference is 16π. First, we calculate the radius of the circle using the formula for circumference, C = 2πr, where C is the circumference and r is the radius. Since C = 16π, we can solve for r to find that the radius r = 8 units.
Next, we use the standard equation of a circle, which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius. Therefore, substituting h = -2, k = 2, and r = 8 into the equation, we get (x + 2)² + (y - 2)² = 64, which is the equation that represents the circle with the given center and circumference.
a biology class has a total of 34 students the number of males is 14 more than the number of females how many males and how many females are in the class
x: females
x+14: males
so 34=x+x+14
To find the number of males and females in the biology class, we can create a system of equations based on the given information and then solve for the variables. After solving the equation, we find that there are 10 females and 24 males in the biology class.
Explanation:To find the number of males and females in the biology class, we can create a system of equations based on the given information:
Let's assume the number of females in the class is 'x'.
The number of males in the class is then 'x + 14'.
Since the total number of students in the class is 34, we can write the equation:
x + (x + 14) = 34
Simplifying the equation, we have 2x + 14 = 34.
Subtracting 14 from both sides, we get 2x = 20.
Dividing both sides by 2, we find x = 10.
Therefore, there are 10 females and 24 males in the biology class.
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if a coin is flipped 3 times what is the probability the first flip is heads then the second flip is tails and the third flip is heads
Answer:
25%
Step-by-step explanation:
The chance of flipping heads or tails is 50%.
We have to flip heads or tails 3 times.
To make this easier, I will convert 50% to 1/2 for the time being.
Since the chance of getting heads or tails is 1/2 and there are 3 flips, multiply 1/2 to the power of 3, which is 1/8
1/8 is the probability of getting this outcome.
How is the graph of y= 1/3x related to its parent function y=1/x
A)It is horizontally stretched by a factor of 3 and reflected over the x-axis.
B)It is horizontally stretched by a factor of 3 and reflected over the y-axis.
C)It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D)It is horizontally compressed by a factor of 3 and reflected over the y-axis.
B it is horizontally stretched by a factor of of 3 and reflected over the y
Answer:
itś C on edge :)
Step-by-step explanation:
what is the value of x?
Answer:
x ≈ 8.66
Step-by-step explanation:
Using the sine ratio in the right triangle
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]
Multiply both sides by 10
10 × sin60° = x, thus
x ≈ 8.66 ( to 2 dec. places )
Please help answer this geometry
Answer:
a. [tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. [tex]100x+225y=100x+225[/tex] Which means it is an identity
Step-by-step explanation:
The Pythagorean Theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.
If in a right triangle there are legs of length a, and b, and the measure of the hypotenuse is c, then The following relationship is fulfilled:
[tex]a^{2} +b^{2}=c^{2}[/tex]
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram
From the exercise shown in the image, we can get the values of a, b, and c.
a = 8x+12y, b = 6x+9y, and c = 10x+15y
Write an equation using the Pythagorean Theorem
We obtain:
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. Transform each side of the equation to determine if it is an identity.
In mathematics, an identity is the realization that two objects that are mathematically written differently, are in fact the same object. In particular, an identity is an equality between two expressions, which is true whatever the values of the different ones are.
So, we transform each side of the equation
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
[tex](8x)^{2} +(12y)^{2} +(6x)^{2} +(9y)^{2}= (10x)^{2}+(15y)^{2}\\64x+144y+36x+81y=100x+225y\\(64x+36x)+(144y+81y)=100x+225y\\100x+225y=100x+225[/tex] Which means it is an identity
.
Answer:
a). (10x + 15y)² = (8x + 12y)² + (6x + 9y)²
b). It's an identity
Step-by-step explanation:
a). Pythagoras theorem says
(Hypotenuse)² = Height² + Base²
Therefore, form the given picture
(10x + 15y)² = (8x + 12y)² + (6x + 9y)² will be the equation.
b). For an identity we have to prove Right hand side of the equation(R.H.S.) = Left hand side of the equation(L.H.S.)
Now we solve the L.H.S. of the equation
(10x + 15y)²
= 100x² + 225y² + 300xy [ (a + b)² = a²+ b² + 2ab
Now we solve R.H.S. of the equation
(8x + 12y)² + (6x + 9y)²
= 64x²+ 144y² + 36x² + 81y² + 108y + 192xy + 108xy
= 100x² + 225y²+ 300xy
Therefore, L.H.S. = R.H.S.
The given equation is an identity.
I need help please. Very plz correct answer plz.
Answer:
Step-by-step explanation:
The 9 is in the tens place in 75, 293 so rounding to the tens place means we need to round to the place the 9 is in, and we can sort of disregard the number after that, which is a 3. It will eventually round to a 0, but if that number is 5 or greater, it rounds the 9 up. It's a 3, so the 9 stays a 9: 75, 290.
The 2 is in the hundreds place, so just like above, we can change everything after the 2 to a 0, after we use the 9 for rounding. 9 is greater than 5, so the 2 rounds up to a 3: 75, 300.
The 5 is in the thousands place, so everything after that will become 0's, but use the 2 for rounding first. 2 is less than 5, so the 5 stays a 5: 75, 000.
What is the factorization of the polynomial below? x^3 + 8x^2 + 17x + 10
Answer:
This is your answer.
Step-by-step explanation:
Hope is helps!!
Answer: (x+1) (x+2) (x+5)
Step-by-step explanation:
Whitney needs to borrow $200 for school supplies. If she borrows the same amount from 5 friends, which equation will show now much she owes each friend? $200 ÷ 5 -$200 ÷ 5 $200 ÷ (-5) -$200 ÷ (-5)
Answer:
She'll owe each friend $40.
Step-by-step explanation:
That's a total of $200 borrowed from 5 friends, which comes to:
$200
------------- = $40/friend
5 friends
Answer: A. $200 ÷ 5
Step-by-step explanation:
Sorry about the answer above mine.. that's kinda embarrassing considering how easy this question is. Anyways, the correct answer is A because the outcome will be 40 which is what we want because if you did the math for any other answer, the outcome will be negative.
- |-9| x |7| =
whats the answer? help please!!
Answer:
Final answer is -63.
Step-by-step explanation:
Given expression is [tex]-|-9| \times |7|[/tex].
Now question says to simplify that expression [tex]-|-9| \times |7|[/tex]
| | indicates absolute function which results only in positive output so |-9| gives 9 only
and |7| gives 7.
then we can rewrite the expression as :
[tex]-|-9| \times |7|[/tex]
[tex]=-(9) \times (7)[/tex]
[tex]=-9 \times 7[/tex]
[tex]=-63[/tex]
Hence final answer is -63.
A 15 ft ladder is leaning against a house. The bottom of the ladder is 6 ft from the wall. How far up the wall is the ladder?
The square root of 189
the square root of 189
Unit 4 Lesson 10 MODIFIED Inequalities:
You are working a summer job as a retail salesperson at Macy’s. You earn $230 per week plus a commission of 8% of your sales. This week, you need to earn $510. You will write and solve an INEQUALITY to determine how to meet your goal.
1): Give the decimal form of 8%. __________________________
2): If you make $945 in sales, how much will you make from your 8% commission?
Show your work and circle your solution.
3): Create an expression representing how much you will make in one week if you sell
x amount of sales.
4): Create an inequality using the expression in problem 3 to find how much you need
to sell at a MINIMUM to make your goal.
Answer:
Part 1) 0.08
Part 2) $75.6
Part 3) y=230+0.08x
Part 4) The minimum amount to sell is $3,500
Step-by-step explanation:
Part 1) Give the decimal form of 8%
we know that
To convert percentage number to decimal number, divide by 100
8%=8/100=0.08 ----> decimal form
Part 2) If you make $945 in sales, how much will you make from your 8% commission?
Multiply the percentage of commission in decimal number by the total amount in sales
so
0.08*($945)=$75.6
Part 3) Create an expression representing how much you will make in one week if you sell
x amount of sales.
Let
x-----> amount of sales in a week
y ----> total earned in a week
we know that
The linear equation that represent this situation is
y=230+0.08x
Part 4) Create an inequality using the expression in problem 3 to find how much you need to sell at a MINIMUM to make your goal
we know that
The inequality that represent the situation is
[tex]230+0.08x \geq 510[/tex]
Solve for x
Remember that x is the amount of sales in a week
[tex]0.08x \geq 510-230[/tex]
[tex]0.08x \geq 280[/tex]
[tex]x \geq 280/0.08[/tex]
[tex]x \geq 3,500[/tex]
The minimum amount to sell is $3,500
A mathematical model is a simplified description of a system or a process. In your opinion, how are mathematical models helpful? What are the advantages and disadvantages of using a model?
Answer:
A model can show people how you did it so you don't have to explain it. It also helps people who learn visually
Step-by-step explanation:
Answer:
The advantages of using a model are familiar objects to represent unfamiliar things, can help you visualize, or picture in your mind, something that is difficult to see or understand, can help scientists communicate their ideas, etc while the disadvantages of using a model is the cost of running several different simulations may be high,time,people's reactions,etc.
Step-by-step explanation:
Please help :))) lol
Answer:
.6*.3=.18
Step-by-step explanation:
when two events must both happen, multiply their probabilities. (and=*, or=+)