Answer:
therefore the left over board is 0.216[tex]a^{2}[/tex] where 'a' is length of a side of the black poster board.
Step-by-step explanation:
i) Sasha cuts 4 identical circles from a square piece of black poster.
ii) let each side of the square piece be a.
iii) let us divide the square piece into four equal square parts from which the four identical circles will be cut
iv) therefore the side of each smaller square will be [tex]\frac{a}{2}[/tex].
v) therefore the diameter of each identical circle will be [tex]\frac{a}{2}[/tex]
vi) therefore the radius if each of the four identical circles will be [tex]\frac{1}{2} \times \frac{a}{2} = \frac{a}{4}[/tex]
vii) the area of each of the four identical circles will be = [tex]\pi \times (\frac{a}{4} )^{2} = 3.14 \times (\frac{a}{4}) ^{2} = \frac{3.14a^{2}}{16} = 0.196a^{2}[/tex]
vii) the area of each of the four smaller squares = [tex]\frac{a}{2} \times \frac{a}{2} = \frac{a^{2} }{4} = 0.25a^{2}[/tex]
viii) therefore the area left over from each of the four smaller squares
= 0.25[tex]a^{2}[/tex] - [tex]0.196a^{2}[/tex] = 0.054[tex]a^{2}[/tex]
ix) therefore the left over board is given by 4 [tex]\times[/tex] 0.054[tex]a^{2}[/tex] = 0.216[tex]a^{2}[/tex] where a is length of a side of the black poster board.
24 cupcakes for 168$ what is unit rate
Answer:
$7 per cupcake
Step-by-step explanation:
A unit rate is the cost of one item. So we would do $168 divided by twenty-four. That would be equivalent to seven.
What is the perimeter of 10 ft long and 9 feet wide?
Answer: Answer is 38ft.
Step-by-step explanation: The figure that measures 10ft by 9ft is a rectangle which means two sides measure 10ft each (length) and two sides measure 9ft each (width). A perimeter simply measures all sides of the entire shape, that is;
10ft + 9ft + 10ft + 9ft = 38ft.
Jason bought n candy bars. Write an expression to show the total cost of the candy bars if each candy bar cost $5.
HELP ME !
Answer:
5n
Step-by-step explanation:
Answer:
total cost of the candy bars = 5 x n
Step-by-step explanation:
What is 2/20 + 10/75
[tex]\text{Hey there!}[/tex]
[tex]\text{What is }\dfrac{2}{20}+\dfrac{10}{75}[/tex]
[tex]\text{For the LCD (Lowest Common Denominator) it should be equal to 300}[/tex]
[tex]\dfrac{2\times15}{20\times15}+\dfrac{10\times4}{75\times4}[/tex]
[tex]\bf{2\times15=30}\\\bf{20\times15=300}\\\\\bf{10\times4=40}\\\bf{75\times4=300}[/tex]
[tex]\text{Your new equation}\rightarrow\dfrac{30}{300}+\dfrac{40}{300}[/tex]
[tex]\text{With the denominators being alike we can leave the same}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{30+40}{300}[/tex]
[tex]\text{30 + 40 = 70}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{70}{100}[/tex]
[tex]\text{Since both of the terms have 10 in their like terms, let's divide both sides by it}[/tex]
[tex]\dfrac{70\div10}{300\div10}[/tex]
[tex]\bf{70\div10=7}[/tex] [tex]\leftarrow\text{Your numerator}[/tex]
[tex]\bf{300\div10=30}[/tex] [tex]\leftarrow\text{Your denominator}[/tex]
[tex]\boxed{\bf{Thus,\ your\ answer\ should\ be:\dfrac{7}{30}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
[tex]\frak{LoveYourselfFirst:)}[/tex]
Eduardo has 45 yards of rupe light.
Exactly how many more yards does he need to finish the car's ceiling?
Item
Length of Rope Light (yds)
Front spoiler
Rear spoiler
Ceiling
DONE
Naimmis
Dashboard
What is the fraction
Answer: 2 1/6
Step-by-step explanation:
Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.
4 1/2 -> 9/2
6 2/3 -> 20/3
Next, make the denominators the same by multiplying each fraction by the denominator of the other.
9/2 * 3 = 27/6
20/3 * 2 = 40/6
Then you can subtract the numerators because the denominators are the same:
40/6-27/6= 13/6
Then you can convert to a mixed fraction if need be.
Figure ABCD is a kite.
Kite A B C D is shown. Sides A B and B C are congruent. The length of A B is 3 x + 1 and the length of B C is 22. Sides A D and C D are congruent. The length of A D is 4 x.
What is the length of line segment CD?
7 units
8 units
28 units
35 units
Answer:
I think 28. Sorry if its wrong
Step-by-step explanation
The kite is a quadrilateral with 4 sides and angles. The length of line segment CD from the given kite is 28 units
Properties of a kiteThe kite is a quadrilateral with 4 sides and angles.
From the given diagram,
AB = 3x + 1
BC = 22
Since AB = BC, hence;
3x + 1 = 22
3x = 22 - 1
3x = 21
x = 7
Since AD = CD = 4x, hence;
CD = 4x
CD = 4(7)
CD = 28 units
Hence the length of line segment CD from the given kite is 28 units
Learn more on kite here: https://brainly.com/question/23279609https://brainly.com/question/23279609
#SPJ2
Jackie says that the fraction 7/8 is equivalent to 3/4. Is she right? Explain
Answer:
Jackie is incorrect.
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] [tex]\left {x2} \atop {x2}} \right.[/tex] = [tex]\frac{6}{8}[/tex]
[tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex] not [tex]\frac{7}{8}[/tex]
Jackie is mistaken when she claims that the fraction 7/8 is equal to 3/4. We compare the numerator (the top number) and denominator (the bottom number) of two fractions to see if they are equal.
In this instance, 3/4 has a denominator of 3 and a numerator of 4, whereas 7/8 has a numerator of 7 and a denominator of 8, respectively. The fractions cannot be equal since the numerators and denominators vary.
Two fractions must have the same numerator to denominator ratio in order for them to be equal. In this situation, 7/8 is a bigger fraction than 3/4. Jackie's assertion that 7/8 is comparable to 3/4 is therefore false.
To know more about Fraction :
https://brainly.com/question/10354322
#SPJ1.
Need help with question number 13. Can’t figure it out.
Answer:
least common multiple
Step-by-step explanation:
Find the lcm of the given numbers, do you know how to do that?
Alright, so you're looking for the GCF.
Greatest Common Factor
I don't wanna go into detail of what that is (if you don't already know what it is, please watch a video on what it is and how to find it.)
Our numbers are 18, 36, 54
What is the gcf of these numbers? They all are both divisble by 18 and that's the largest 18 can go, so 18 is the GCF.
18 is the answer.
Which pair of angles are corresponding angles? 1 and 4, 2 and 3, 3 and 6, 4 and 8 Please answer ASAP
Answer:
4 and 8
Step-by-step explanation:
corresponding angles are two angles that have the same angle degree and are on the same side of the graph if you were to take the bottom part and move it up to the top part
What is the simplest form of RootIndex 3 StartRoot 27 a cubed b Superscript 7 Baseline EndRoot?
Answer: [tex]3a\sqrt[3]{b^{7}}[/tex]
Step-by-step explanation:
We have the following expression:
[tex]\sqrt[3]{27 a^{3} b^{7}}[/tex]
This can be rearranged as:
[tex]\sqrt[3]{27} \sqrt[3]{a^{3}} \sqrt[3]{b^{7}}[/tex]
Since [tex]\sqrt[3]{27}=3[/tex] and [tex]\sqrt[3]{a^{3}}=a[/tex] we have:
[tex]3a\sqrt[3]{b^{7}}[/tex] This is the simplest form
Answer:
3ab^2 (^3sqrt{ b}) or A on Edg. 2020
Step-by-step explanation:
Which absolute value expression represents the distance between 3 and
9
2
on a number line?
A) |3 −
9
2
|
B) |3 − (−
9
2
)|
C) |−3 + (−
9
2
)|
D) |−3 −
9
2
)|
From other source on the internet this question is:
Which absolute value expression represents the distance between 3 and - 2 on a number line?
Answer:
|3 - (-2) |, or|-2 - 3|Both are equivalent.
Explanation:
The distance between two numbers in a number line is the absolute value of the difference between the two numbers.
Thus, the distance between a number x and a number y is |x - y|, which is also equivalent to |y - x|.
In this case the distance between 3 and - 2 can be represented by either of the expressions:
|3 - (-2) |, or|-2 - 3|Note that when you simplify them you get the same value:
|3 - (-2) | = |3 + 2| = |5| = 5|-2 - 3| = | -5| = 5Answer:
The distance between 3 and
9
2
on a number line is |3 −
9
2
|. The distance between two numbers is equal to the absolute value of their difference.
|3 −
9
2
| = |−
3
2
| =
3
2
Step-by-step explanation:
so the answer is A
what is 0.793 rounded to the nearest hundredths
Answer:
0.800
Step-by-step explanation:
its almost 0.800
Answer:
.800
If the second digit after the decimal is 50 or is over 50 you change the first digit after the decimal point to the next digit up, and make the rest of the digits after the decimal point zero. If it is lower than 50 then you do the same but keep the same first number after the decimal point.
If a function uses variables other than xand y for its input and output
variables, you take the original equation and solve for the input variable to
find the inverse.
A. True
B. False
Answer:
True
Step-by-step explanation:
Sorry if it's wrong lol
Twice a number x plus 8 is greater than 12
Answer:
2x+8>12
Step-by-step explanation:
A rectangle has an area of 18 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A
1 cm and 18 cm
®
4 cm and 5 cm
2 cm and 9 cm
0
3 cm and 6 cm
Write a minor function for the line with the slope of -5 that passes through points (7,3)
The equation of the line is [tex]5x+y-38=0[/tex]
Step-by-step explanation:
The slope is [tex]m=-5[/tex]
Also, the line passes through the points [tex](7,3)[/tex]
To find a line with slope [tex]m=-5[/tex] that passes through the points [tex](7,3)[/tex], let us use the equation of a line with slope that passes through the point is given by [tex](y-y_{1} )=m(x-x_{1} )[/tex] where m is the slope and [tex](x_{1} ,y_{1} )[/tex] are the points [tex](7,3)[/tex].
Thus, substituting the values in the equation of a line, we get,
[tex](y-3)=-5(x-7)[/tex]
Multiplying the term [tex](x-7)[/tex] by -5, we get,
[tex]y-3=-5 x+35[/tex]
Adding both sides by 5x,
[tex]5x+y-3=35[/tex]
Subtracting 35 from both sides of the equation,
[tex]5x+y-38=0[/tex]
Thus, the equation of the line is [tex]5x+y-38=0[/tex]
please help me with #4
The chances of it being less than 5 is 4/6
So if he spins it 150 times the chances of it landing on 5 or less than it will be: 4/6 * 150 = 100 (c)
Answer:
i think its c 100
Step-by-step explanation:
sorry if it makes no sense
Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy?
Answer:
Step-by-step explanation:
a + c = 24......a = 24 - c
5.5a + 2c = 83
5.5(24 - c) + 2c = 83
132 - 5.5c + 2c = 83
-5.5c + 2c = 83 - 132
-3.5c = - 49
c = -49 / -3.5
c = 14 <==== 14 child tickets
a + c = 24
a + 14 = 24
a = 24 - 14
a = 10 ........and 10 adult tickets
write and solve the differential equation that models the following statment. "the rate if change of W with respect to x is proportional to x+18."
Answer:
[tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
Step-by-step explanation:
i)it is given that the rate of change of W with respect to x is proportional to
x + 18. Therefore [tex]\frac{dW}{dx}[/tex] = k(x + 18) where k is a constant.
ii) Therefore [tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
iii) the complete solution can only be found if we know the constant of proportion and also the constant of integration.
Find the missing height
Answer:
5
Step-by-step explanation:
I need help on this problem( picture included)
hmmm first off, let's convert the decimal to a fraction, and then the mixed fraction to an improper fraction and proceed from there.
[tex]\bf 6.\underline{2}\implies \cfrac{62}{1\underline{0}}\implies \cfrac{31}{5}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ 6.2\div (2x+1)=2\frac{1}{3}\div 4\implies \cfrac{31}{5}\div (2x+1) = \cfrac{7}{3}\div 4[/tex]
[tex]\bf \cfrac{31}{5}\div \cfrac{(2x+1)}{1} = \cfrac{7}{3}\div \cfrac{4}{1}\implies \cfrac{31}{5}\cdot \cfrac{1}{(2x+1)} = \cfrac{7}{3}\cdot \cfrac{1}{4}\implies \cfrac{31}{5(2x+1)}=\cfrac{7}{12} \\\\\\ \cfrac{31}{10x+5}=\cfrac{7}{12}\implies \stackrel{\textit{cross multipling}}{372 = 7(10x+5)}\implies 372=70x+35\implies 337=70x \\\\\\ \cfrac{337}{70}=x\implies 4\frac{57}{70}=x\implies 4.81\approx x[/tex]
what is 5 13.5% of ?
Answer:
67.5
Step-by-step explanation:
Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...
A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?
Answer:
67.5
Step-by-step explanation:
Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...
A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?
What value of x is in the solution set of 4x – 12 ≤ 16 + 8x?
Answer:
4x – 12 ≤ 16 + 8x; x>-7
Step-by-step explanation:
i dont remember how i did it
Answer:
x≥-7
Hope this helps
log2 (32) =
Answer this
Answer: 5
Step-by-step explanation:
[tex]log_{2}[/tex] 32
32 can be written in index form as 2x2x2x2x2 , which could be written as [tex]2^{5}[/tex].
[tex]log_{2}[/tex] 32 the becomes
[tex]log_{2}[/tex] [tex]2^{5}[/tex]
Which could be written as
5 [tex]log_{2}[/tex] 2
From law of logarithms; [tex]log_{2}[/tex] 2 = 1
Therefore : 5 [tex]log_{2}[/tex] 2 = 5 x 1 = 5
17•blank=1. As a fraction ASAP pls
the answer for this question is:
1/17
|6 3/8-2|+|-8 5/8+(-1)|
To answer the question, we evaluated two absolute value expressions individually by converting mixed numbers to improper fractions, performing the operations, and taking absolute values. The sum of these evaluations is 14.
The question involves evaluating two absolute value expressions and adding the results. We will work through each expression step by step.
First Expression
|6 3/8 - 2|
To solve this, convert the mixed number to an improper fraction, subtract 2, and then find the absolute value.
Convert 6 3/8 to an improper fraction: (6 × 8) + 3 = 51/8.
Subtract 2 (written as 16/8) from 51/8: 51/8 - 16/8 = 35/8.
The absolute value of 35/8 is 35/8, as it is already positive.
Second Expression
|-8 5/8 + (-1)|
Similar approach: convert to an improper fraction, add -1, and find the absolute value.
Convert -8 5/8 to an improper fraction: (-8 × 8) - 5 = -69/8.
Add -1 (written as -8/8) to -69/8: -69/8 - 8/8 = -77/8.
The absolute value of -77/8 is 77/8, as we discard the negative sign in absolute value operations.
Add the results of both expressions: 35/8 + 77/8 = 112/8 = 14.
i go backwards 8m in 4s what is my velocity
Answer:2m/s
Step-by-step explanation:
Velocity=distance÷time
Velocity=8÷4
Velocity=2m/s
Line b passes through the Point(-3, -4) and has a slope of -1/2. What is the equation of Line b in standard form?
x + 2y = -11
x + 2y = -10
2x + y = -11
2x + y = -10
Answer:
[tex]x+2y=-11[/tex]
Step-by-step explanation:
Slope intercept form of a line is given by:
[tex]y=mx+b[/tex]
Where
m is the slope and b is the y-intercept
Given slope is [tex]-\frac{1}{2}[/tex]
We can write:
[tex]y=-\frac{1}{2}x+b[/tex]
Now to find b, we replace x with -3 and y with -4, given, so we have:
[tex]y=-\frac{1}{2}x+b\\-4=-\frac{1}{2}(-3)+b\\-4=\frac{3}{2}+b\\b=-5.5[/tex]
So, the equation is:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]
Now,
The standard form is given by:
[tex]Ax+By=C[/tex]
So, we take x and y to left side and the constant to right side. Rearranging, we get:
[tex]y=-\frac{1}{2}x-\frac{11}{2}\\2y=-x-11\\x+2y=-11[/tex]
The first answer choice is right.
Final answer:
The equation of line b that passes through the point (-3, -4) and has a slope of -1/2 in standard form is x + 2y = -11.
Explanation:
To find the equation of line b that passes through the point (-3, -4) and has a slope of -1/2, we will start with the slope-intercept form of a line equation y = mx + b, where m is the slope and b is the y-intercept. While we know the slope (-1/2), we do not yet have the y-intercept. We can use the given point to solve for b. Plugging the point into the equation gives -4 = (-1/2)(-3) + b, which simplifies to -4 = 3/2 + b. Solving for b yields b = -11/2.
Now we have the slope-intercept form of the line: y = (-1/2)x - 11/2. To convert this to standard form, which is Ax + By = C, we multiply through by 2 to clear the fractions, which gives us 2y = -x - 11. Rearranging this, we add x to both sides to get x + 2y = -11. Therefore the correct equation in standard form is x + 2y = -11.
find one terminating decimal and one repeating decimal between -1 1/2 and -1 7/9
Answer:
-1.777...
Step-by-step explanation:
Using the LCM of 18 for the denominator, these values are:
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
So, the easy values to identify are: -31/18, -30/18, -29/18, and -28/18
All of these numbers have repeating decimals (because 9 is a factor of the denominator).
Now, you may realize that -1 3/4 is within the range specified.
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
|
-1 3/4
-1.75
This is because -1.75 is between -1.5 and -1.7777.... Note that it is not repeating.
Upvote
•
1
Downvote
Add comment
which of the following are solutions to this equation 3n+4=24-n a) n=1 b) n=3 c) n=5 d) n=7
Answer:
The correct option is c) n=5.
Therefore the solution to
[tex]3n+4=24-n[/tex]
is
[tex]n=5[/tex]
Step-by-step explanation:
Given:
[tex]3n+4=24-n[/tex]
To Find;
n = ?
Solution:
[tex]3n+4=24-n[/tex] ........Given
Add + n to both the side
[tex]3n+4+ n=24-n+n\\4n+4=24[/tex]
Now Subtract 4 on both the side
[tex]4n+4-4=24-4\\4n=20[/tex]
Dividing by 4 on both side
[tex]\dfrac{4n}{4}=\dfrac{20}{4}\\\\n=5[/tex]
Therefore the solution to
[tex]3n+4=24-n[/tex]
is
[tex]n=5[/tex]