Answer:
There will be 128 holes
Step-by-step explanation:
Simply think of each fold as doubling the number of holes. So since we have 6 folds, that will be 2^6 and then we have 2 holes in those folds, which makes 2*2^6 == 2^7 == 128 holes. Cheers.
Folding of the paper is an illustration of a geometric sequence
The number of holes in the rectangular paper is 128
The given parameters are:
[tex]\mathbf{h = 2}[/tex] --- holes
[tex]\mathbf{t = 6}[/tex] --- number of times
The sheet was folded in halves i.e. in 2's.
So, the amount of each time is:
[tex]\mathbf{f(t) = 2 \times h^t}[/tex]
Substitute values for h and t
[tex]\mathbf{f(6) = 2 \times 2^6}[/tex]
Evaluate the exponent
[tex]\mathbf{f(6) = 2 \times 64}[/tex]
Multiply
[tex]\mathbf{f(6) = 128}[/tex]
Hence, the number of holes in the rectangular paper is 128
Read more geometric sequence at:
https://brainly.com/question/10564422
Peter walked 10m from X to Y on bearing 020° and then he turned and walked 20m to Z with bearing 140° of Z from Y. Find the distance between X and Z. Find the bearing of Z from X.
Answer:
17.32m ; 110°
Step-by-step explanation:
Distance between X and Z
To calculate the distance between X and Z
y^2 = x^2 + z^2 - (2xz)*cosY
x = 20, Z = 10
y^2 = 20^2 + 10^2 - (2*20*10)* cos60°
y^2 = 400 + 100 - (400)* 0.5
y^2 = 500 - 200
y^2 = 300
y = sqrt(300)
y = 17.32m
Bearing of Z from X:
Using cosine rule :
Cos X = (y^2 + z^2 - x^2) / 2yz
Cos X = (300 + 100 - 400) / (2 * 20 '*10)
Cos X = 0 / 400
Cos X = 0
X = cos^-1 (0)
X = 90°
Bearing of Z from X
= 20° + X
= 20° + 90°
= 110°
Hey loves!!! Can any of you lovely people help me with this question?
Answer:
AAS
Step-by-step explanation:
As we can see, they tell us that both of the angles on the bottom are congruent. Since they share a side, that means that one side is congruent too. So it must be two angles and one side. It can't be ASA, because the congruent side is not in between the two congruent angles, so it must be AAS
Hey There!!
Your correct choice will be AAS Theorem.
Step-by-step explanation:
Because, two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent Thus, given a triangle ADB and CDB. ∠BAD = ∠BCD = 90°. (Angle), Then, BD = BD (The common side) As given AAS Theorem. Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.
Hope This Explaining was not confusing . . .
By ☆Itsbrazts☆
The polynomial function F(x)= 2x^2 +4 has a critical point at which of the
following x-values?
A. X=0
B. X=4
C. X=2
D. X=-2
the answer is A,when X=0
HELP ASAP The graph of a function h is shown below. Use the graph to find its average rate of change from x=-7 to x=-5. Simplify your answer as much as possible
Answer:
The average rate of change from x=-7 to x=-5 is -3
Step-by-step explanation:
In order to calculate average rate of change we would have to make the following calculation:
According to the given data we have the following:
x=-7 so, f(-7) is to be calculated in the graph y
x=-5 so, f(-5) is to be calculated in the graph y
Therefore, average rate of change=f(-5)-f(-7)/-5-(-7)
average rate of change=3-9/2
average rate of change=-6/2
average rate of change=-3
The average rate of change from x=-7 to x=-5 is -3
The average rate of change of a function is the unit change of the function.
The average rate of change from x = -7 to x = -5 is -3
The average rate of change is calculated as:
[tex]\mathbf{f'(x) = \frac{f(b) - f(a)}{b - a}}[/tex]
The interval is given as: x = -7 to x = -5.
This means that:
a = -5 and b = -7
So, we have:
[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-7 - -5}}[/tex]
This gives
[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-2}}[/tex]
From the graph
f(-7) = 9 and f(-5) = 3.
So, we have:
[tex]\mathbf{f'(x) = \frac{9 - 3}{-2}}[/tex]
Subtract
[tex]\mathbf{f'(x) = \frac{6}{-2}}[/tex]
Divide
[tex]\mathbf{f'(x) = -3}[/tex]
Hence, the average rate of change from x = -7 to x = -5 is -3
Read more about average rate of change at:
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A circle has a radius of 8cm use the value 3.1 for π to calculate the area of a sector of the circle if the angle at the center is 150°
Answer:
[tex]8\frac23\ cm^2[/tex]
Step-by-step explanation:
sector of the circle if the angle at the center is 150° means [tex]\frac{150^o}{360^o}[/tex] of full circle of given radius
area of a circle of given radius R is: πR²
so area of given sector:
[tex]A=\dfrac{150^o}{360^o}\cdot \pi\cdot8^2=\dfrac5{12}\cdot3.1\cdot64=82,(6)=8\frac23\ cm^2[/tex]
The area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
What is a circle?
A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -
x² + y² = r² (for circle centered at origin)
Given is a circle has a radius of 8 cm.
The area of the sector subtending the angle 150° at center is -
A = (150/360) x 3.1 x 8 x 8
A = 82.67 square centimeter.
Therefore, the area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
To solve more questions on circles, visit the link below-
https://brainly.com/question/17006280
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Enter the correct answer in the box. What is the standard form of function
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
Given
f(x) = 4(x + 6)² + 5 ← expand (x + 6)² using FOIL
= 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4
= 4x² + 48x + 144 + 5 ← collect like terms
= 4x² + 48x + 149 ← in standard form
Answer:
[tex]f(x)=4x^{2} +149[/tex]
Step-by-step explanation:
Start off by writing the equation out as it is given:
[tex]f(x)=4(x+6)^{2} +5[/tex]
Then, get handle to exponent and distribution of the 4 outside the parenthesis:
[tex]f(x)=4(x^{2} +36)+5\\f(x)=4x^{2} +144+5[/tex]
Finally, combine any like terms:
[tex]f(x)=4x^{2} +149[/tex]
Can someone help me with this
Answer:
D
Step-by-step explanation:
Apply rule : [tex]-(-a)=+a[/tex]
Negative times negative is positive.
The expression turns into a sum of fractions.
In △ABC, m∠A=45°, c=17, and m∠B=25°. Find a to the nearest tenth.
Answer:
12.8
Step-by-step explanation:
you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do
Sin(110)x=17sin(45)
and then it turns into 17sin(45)/sin(110)
then put it into desmos with it being in degrees mode
Consider the following equation. x^2 - 4 x - 1 = 0 To complete the square, first rewrite the equation as x^2 - 4 x = 1. What value would then be added to both sides of the equation to complete the square? (Enter an exact number.)
Answer:
[tex]\large \boxed{\sf \ \ \ 4 \ \ \ }[/tex]
Step-by-step explanation:
Hello, please find below my work.
[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1[/tex]
We know that for any a and x real numbers we can write
[tex](x-a)^2=x^2-2ax+a^2[/tex]
When we compare with the left part of the equation we can identify the term in x so that -4=-2a (multiply by -1) <=>4=2a (divide by 2) <=> a = 4/2 = 2
So we can write
[tex](x-2)^2=x^2-4x+2^2=x^2-4x+4[/tex]
So we have to add 4 to both sides of the equation to complete the square and it comes:
[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1 \ \boxed{\text{ add 4 to complete the square}} \\\\<=>x^2-4x\boxed{+4}=1+4=5\\\\<=>(x-2)^2=5 \ \text{ we take the root } \\ \\ <=>x-2=\pm \sqrt{5}\ \text{ we add 2 } \\ \\ <=> x = 2+\sqrt{5} \ \text{ or } \ x = 2-\sqrt{5}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
44. The length of a road is 380 m, correct to the nearest 10 m. Maria runs along this road at an average speed of 3.9 m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria.
Answer:
The greatest possible time taken by Maria is 97.4 seconds.
Step-by-step explanation:
The greatest possible time taken by Maria occurs when she moves at constant rate and is equal to the length of the road divided by the length of the road. That is to say:
[tex]t = \frac{\Delta s}{v}[/tex]
Where:
[tex]\Delta s[/tex] - Length of the road, measured in meters.
[tex]v[/tex] - Average speed, measured in meters per second.
Given that [tex]\Delta s = 380\,m[/tex] and [tex]v = 3.9\,\frac{m}{s}[/tex], the greatest possible time is:
[tex]t = \frac{380\,m}{3.9\,\frac{m}{s} }[/tex]
[tex]t = 97.4\,s[/tex]
The greatest possible time taken by Maria is 97.4 seconds.
Given that Arccos (√3/2)=β, what are all the angle measurements for right triangle ABC?
Answer:
30°, 60° and 90°
Step-by-step explanation:
Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.
Note that a right angled triangle is made up of two acute angles and a right angled (90°)
Let's get one of the acute angles first
If Arccos (√3/2)=β
β = cos^-1 √3/2
β = 30°
This shows that one of the acute angles is 30°
To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.
90+30+x = 180
120+x = 180
x = 180-120
x = 60°
All the angle measurement for the right angled triangle are 30°, 60° and 90°
I don’t have a graphing calculator, please help!
Answer: is your first option
Step-by-step explanation:
after going over all the available equations, your first option is the only one that had results that were much more reasonable than the others. hope it helps.
Solve for xxx. Your answer must be simplified. 7>x/4
Answer:
28>x
Step-by-step explanation:
7>x/4
remove the denominator by multiplying both sides by 4
4×7>x/4×4
28>x
Which glide reflection describes the mapping ABC DEF. This is practice for me plz, give answer with explanation. Non-sense answer will get reported
Answer:
c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Step-by-step explanation:
The strategy is to translate B to E then reflect about the x-axis (y=0)
From B to E, the process is
(x,y) -> (x-4, y-1)
Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0
4/6, 5/6, 2/6 how do you put it least to greatest?
Answer:
2/6 < 4/6 < 5/6
Step-by-step explanation:
2 < 4 => 2/6 < 4/6
4 < 5 => 4/6 < 5/6
=> 2/6 < 4/6 < 5/6
Answer:
2/6, 4/6 5/6
Step-by-step explanation:
If xy = 4, which is equivalent to y(x-4)(x+2)
Answer:
4x - 8 - 32/xStep-by-step explanation:
From the expression xy = 4, y = 4/x
Substituting y = 4/x into the expression y(x-4)(x+2) and expanding;
= y(x-4)(x+2)
= 4/x(x-4)(x+2)
On expansion;
= (4-16/x)(x+2)
= 4x+4(2)-(16/x)x-(16/x)2
= 4x+8-16-32/x
= 4x-8-32/x
The equivalent expression is 4x - 8 - 32/x
Natasha, Mark and Henry share some sweets in the ratio 7:3:2. Natasha gets 75 more sweets than Henry. How many sweets are there altogether?
Answer:
180
Step-by-step explanation:
Given the ratio = 7 : 3 : 2 = 7x : 3x : 2x ( x is a multiplier ), then
7x = 2x + 75 ( Natasha gets 75 more sweets than Henry )
Subtract 2x from both sides
5x = 75 ( divide both sides by 5 )
x = 15
Thus
total number of sweets = 7x + 3x + 2x = 12x = 12 × 15 = 180
Choose the answer based on the most efficient method as presented in the lesson. If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then what should the next step be? subtract 3 add 8 subtract 5x
Answer:
subtract 3, because that'll allow the variables to be on one side and the constants on the other
Step-by-step explanation:
(#1) Two thirds of Sandi's rose bushes bloomed this summer. One half of the roses that bloomed were pink. What part of Sandi's total rose bushes had pink blooms? If Sandi had 12 rose bushes, how many bore pink blooms? (#2) Mom has three quarters of a pound of chocolates. She divides the chocolates into portions that each weigh one eighth of a pound. If Mom eats one portion a day, for how many days will the chocolate last?
Answer:
The number of pink roses bloomed are 4.
Step-by-step explanation:
Write 5x^2 - 10x + 4 in vertex form.
Answer:
y=5(x-1)^2-1
Step-by-step explanation:
Answer:
5(x - 1)² - 1
Step-by-step explanation:
Given
5x² - 10x + 4
Using the method of completing the square
The coefficient of the x² term must be 1 , so factor out 5 from the first 2 terms
= 5(x² - 2x) + 4
add/ subtract ( half the coefficient of the x- term )² to x² - 2x
= 5(x² + 2(- 1)x + 1 - 1 ) + 4
= 5(x - 1)² - 5 + 4
= 5(x - 1)² - 1 ← in vertex form
This is Algebra 1 functions and I'm struggling with this one function-
-1•f(-9)+7•g(6)=_____
Answer:
38
Step-by-step explanation:
f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:
-1 * 4 + 7 * 6
= -4 + 42
= 38
I NEED HELP WITH THIS! I need to pass...
Answer: A) The log parent function has negative values in the range.
Step-by-step explanation:
The domain of y = ln (x) is D: x > 0
The domain of y = [tex]\sqrtx[/tex][tex]\sqrt x[/tex] is D: x ≥ 0
The range of y = ln (x) is: R: -∞ < y < ∞
So the only valid option is A because the range of a log function contains negative y-values when 0 < x < 1.
An exterior angle of a triangle is equal to the sum of________ opposite angle
Answer:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Answer:
Two remote interior angles.
Each CD at a music store is sold for $10. If n represents the number of CDs sold, which equation could be used to find the total number of dollars, d, the store receives from CD sales?
Answer:
10n = d
Step-by-step explanation:
We know that
Each CD is sold for 10 dollars
The music store has sold n amount of CD's
The total number of dollars 'd' depends on how many CD's were sold
The equation is: 10n = d
Hope this helps!
Answer:
D=10n
Step-by-step explanation:
Please help me with this question!!!
Answer:
tan (40°) = [tex]\frac{x}{100}[/tex]
Step-by-step explanation:
tan [tex]\theta[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
The opposite side to angle B is x. The adjacent side to angle B is 100 ft.
tan (40°) = [tex]\frac{x}{100}[/tex]
Answer:
tan 40° = x/100
Step-by-step explanation:
As, AC is perpendicular and BC is the with respect to angle ABC. So, tan 40° will be use to determine the distance in feet from point C to point A.
tan ABC = perpendicular/base
tan 40° = AC/BC
tan 40° = x/100 feet
You have a standard number cube. What is the probability of rolling a number less than 3, and then rolling a prime number? A. 1/3 B. 1/2 C. 1/36 D. 1/6
Hey Mate !
Your Answer is given in the snip below !!
Please do mark me as brainliest !!!
(ANSWER= (D) [tex]\frac{1}{6}[/tex] )
Explanation
Answer:
You have a standard number cube.
What is the probability of rolling a number less than 3, and then rolling a prime number?
D. 1/6
June is working on an addition problem and starts with 17,985. After she adds, she still has 17,985. Which property of addition did June use? How do you know?
Answer:
identity element property
Step-by-step explanation:
June's value did not change, so the value she added was the additive identity element: 0.
She made use of the identity element property of addition, which says that adding the identity element does not change the value.
What is the slope of the line that passes through the points (1, 1) and (9, 7)? 3/4 4/5 5/4 4/3
Answer:
3/4
Step-by-step explanation:
We can use the slope of the line by using the slope formula
m = (y2-y1)/(x2-x1)
= (7-1)/ ( 9-1)
= 6/8
= 3/4
Answer: 3/4
Step-by-step explanation: To find the slope of this line, I will be showing you the graphing method.
To find the slope of the line using the graphing method,
we first set up a coordinate system.
Next, we plot our two points, (1, 1), which we label point A, and (9, 7), which we label point B, and we graph our line, as shown below.
Now, remember that the slope, or m, is equal to
the rise over run from point A to point B.
To get from point A to point B, we rise
6 units and run 8 units to the left.
So our slope, or rise over run, is 6 over 8, which reduces to 3/4.
Eggs come in packets of 12 and English muffins come in packets of 10. What is the least number of packages of each that can be bought to be able to make egg sandwiches with no muffins left over?
Answer:
The LCM of 12 and 10 is 60 so you would need to buy 60 / 12 = 5 packs of eggs and 60 / 10 = 6 packs of muffins.
..........................
Answer:
[tex]\boxed{-10000}[/tex]
Step-by-step explanation:
[tex]F(x)=\frac{1}{x}[/tex]
Let x = -10000
[tex]F(-10000)=\frac{1}{-10000}[/tex]
[tex]F(-10000)= -0.0001[/tex]
-0.0001 is closest to 0 when x value is -10000.
No other value can work from the other options, options B and C increase the value from 0. Option D would make the function undefined.