Answers
Problem 10, Part A
The larger outer square is x cm by x cm, where x is some placeholder for a positive number. For example, if x = 10, then we have a 10 cm by 10 cm square.
Unfortunately, we don't know what number replaces x.
What we can determine is the connection between the larger square and the smaller one. The frame is 3 cm wide in all directions (aka it's a uniform width). What this allows for is that the smaller square is x-6 by x-6. The 6 is from subtracting two copies of 3, so ultimately we're subtracting off 2*3 = 6 to form the smaller dimensions.
You can think of it like x-3-3 = x-6
So we need to expand out (x-6)(x-6) like so
(x-6)(x-6)
y(x-6)
xy - 6y
x(x-6) - 6(x-6)
x^2-6x - 6x+36
x^2-12x+36
In the second step, I replaced one copy of (x-6) with y, after which I used the distributive rule. After distributing, I plugged in y = x-6 and distributed again. The last step is combining like terms. As an alternative, you can use either the box method or the FOIL rule to find the answer.
The expression x^2-12x+36 is the expanded form of the area of the smaller square, which is the picture itself without the frame involved.
Answer: x^2 - 12x + 36===========================================================
Problem 10, Part B
We follow the same idea as the previous part. This time, we have a rectangle that isn't a square.
Along the horizontal, the (x+30) will drop to (x+30)-5-5 = x+20 when we consider just the picture without the frame. In other words, the smaller inner rectangle has a horizontal dimension of (x+20) cm.
The vertical component of this smaller rectangle is x-5-5 = x-10 cm
So,
area = length*width
area = (horizontal dimension)*(vertical dimension)
area = (x+20)(x-10)
area = y(x-10) ..... let y = x+20
area = xy - 10y ...... distribute
area = x(x+20) - 10(x+20) ... plug in y = x+20
area = x^2+20x - 10x - 200 ..... distribute again
area = x^2 + 10x - 200
Answer: x^2 + 10x - 200Side note: the units for this area, and for part A, are in square cm.
Related Questions
57 plus what equals 86
Answers
Answer:
29
Step-by-step explanation:
57+x=86
x=86-57
x=29
86-57=29Answer:
Step-by-step explanation:
X 5
Find the Quotient.
3)34
I don’t get this
Is not showing just the answer if it’s 3)34 wat is the quotient
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Division of 34 by 3 :
quotient will be equal to 11and remainder = 1
Find the length of the third side. If necessary, write in simplest radical form.
Answers
_________
[tex] \: [/tex]
b² = c² - a²
b² = 10² - (√19)²
b² = 100 - 19
b² = 81
b = √81
b = 9
the ratio of men to women working for a company is 7 to 4. If there are 264 employees total, how many women work for the company?
Answers
[tex]7 ratio2 = \frac{7}{2} \div 264 \\ \\ \ \frac{2}{7} \times \frac{264}{x} \\ \\ cross \: multiply \\ 2 \times x = 264 \times 7 \\ \frac{2x}{2x } = \frac{1848}{2x} \\ x = 924[/tex]
264/11
=24
Women = 24*4
= 96
Men = 24*7
= 168
A customer buys 12oz of honey for $5.40. How much honey can you buy per dollar
Answers
Answer:
0.45oz or honey
Step-by-step explanation:
5.40/12
enter the next 3 terms from the geometric sequence below -2,1,-1/2
Answers
Answer:
1/4, -1/8, 1/16
Step-by-step explanation:
Sean is travelling. He has a flight of 3 hours 40 minutes, a stopover of 40 minutes and then another flight of 5.5 hours. What is his total travel time? Give your answer in hours and minutes.
Answers
Answer:
converting to minutes
Step-by-step explanation:
3*60+20+40+2.75*60=405 min = 6 hours 45 minutes
Please help with this math problem ASAP! Will give brainliest!
Answers
Answer:
x=16
y=23°
z=16
Step-by-step explanation:
we assume it is a kite.
[tex]NM=\sqrt{NQ^2+MQ^2} \\z=\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10[/tex]
∠NQM=90°
4y-2=90
4y=90+2=92
y=92/4=23°·
NP=2Nq
x=2×8=16
y is directly proportional to x. When y = 30, x = 6 a) Work out an equation connecting y and x. b) Work out the value of y when x = 12.
Answers
y=5x (your equation)
y=60 (your answer)
Step by step explanation:
You are given two numbers, 6 and 30. Since 6 goes into 30, 5 times, then y(which is equal to 30) is equal to x(which is equal to 6) multiplied by 5, so you get your equation,
Y=5X
then you have to solve for y, so just substitute
Y=5(12)
And simplify
Y=60
And there’s your answer
11. If 1 is subtracted from the numerator and from
the denominator of a fraction, the value obtained
1
is z. If 1 is added to its numerator and to its
denominator, the resulting value is Ž. Find the
fraction.
Answers
Answer:
3/5
Step-by-step explanation:
Let x be the numerator
Let y be the denominator
1st equation:
(x-1) / (y-1) = 1/2
By simplifying the equation, 2(x-1) = y-1
y = 2(x-1) + 1
2nd equation:
(x+1) / (y+1) = 2/3
By simplifying the equation, 3(x+1) = 2(y+1)
3x + 3 = 2y + 2
2y = 3x + 1
y = (3x + 1) / 2
Substituting the value of y from the 1st equation to the 2nd equation:
1st equation: y = 2(x-1) + 1
2nd equation: y = (3x + 1) / 2
2(x-1) + 1 = (3x+1) / 2
x = 3
After finding the value of x, let's find y using the 2nd equation:
y = (3x + 1) / 2
y = [(3)(3) + 1] / 2
y = 5
Alternatively, we may also find the value of x using the first equation, and the result is still the same:
y = 2(x-1) + 1
y = 2(3-1) + 1
y = 5
CHECKING TIME!!!
Substituting the values of x and y:
Let x be the numerator, x = 3
Let y be the denominator, y = 5
1st equation: (x-1) / (y-1) = 1/2
(3-1) / (5-1) = 1/2
2/4 = 1/2
By simplification, 1/2 = 1/2
2nd equation:
(x+1) / (y+1) = 2/3
(3+1) / (5+1) = 2/3
4/6 = 2/3
By simplification, 2/3 = 2/3
Quis
bentuk dari
[tex]5 {}^{125} \div 5 {}^{124} = [/tex]
Answers
Answer:
[tex]5 {}^{125} \div 5 {}^{124} = \\ 5 {}^{125} - {}^{124} = \\ = 5 {}^{1} [/tex]
Answer:
5¹²⁵ ÷ 5¹²⁴
=5¹²⁵-¹²⁴
=5¹
Maia was baking cupcakes for a party. She mixed 4 drops of red food coloring for every 6 drops of yellow food coloring to dye her icing orange. Circle the ratios of food coloring drops that would create the same orange color and justify your choices
Choice 1: 2 red to 3 yellow
Choice 2: 24 red to 26 yellow
Choice 3: 40 yellow to 100 red
Answers
To make the same orange circle, you would need 2:3 drops of food coloring.
A ratio is defined as:A ratio is a mathematical statement that compares and equals two variables.
Fractions, percentages, and decimals are used to represent ratios.
According to this ratio (2:3), Maia uses 60% of yellow food coloring to create an orange circle for every 40% of red food coloring.
Information and calculations: 4 red food coloring drops
Yellow food coloring drops equal six.
Food coloring ratio = 4:6 or 2:3.
The ratios are as follows in percentages:
Red food coloring drops equal 40% (2/5 x 100)
60 (3/5 x 100) drops of yellow food coloring
As a result, the food coloring is divided into 40% red and 60% yellow.
Ratios are discussed in greater detail at
https://brainly.com/question/13419413
#SPJ1
Please solve this law of indices
Answers
4√36^-1 = 36^-1/4
36^3/4 • 36^-1/4
=36^2/4
or √36 = 6
[tex]\sf Formulas: \displaystyle \\\\\ 1) \ a^{n} \cdot a^{m}=a^{n+m} \\\\ 2) \sf \ \sqrt[n]{\sf a^{m}} = a^{\tfrac{m}{n} } \\\\\\ Solution : \\\\\\\sf \large \boldsymbol {} \displaystyle (36)^{\tfrac{3}{4} } \cdot \sqrt[\sf 4 ]{\sf 36^{-1}} }= 36^{\tfrac{3}{4} } \cdot 36^{\tfrac{-1}{4} } =36^{\tfrac{3}{4}+\big(-\tfrac{1}{4} \big ) }= \\\\\\\ 36^{\tfrac{3}{4} -\tfrac{1}{4} } =36^{\tfrac{2}{4} }=(6^ {\backslash \!\!\!2})^{\tfrac{1}{\backslash\!\!\!2} }= 6^1=\boxed{\sf 6}[/tex]
Mumbai is approximately 845 kilometers (km) away from Bangalore, and Mumbai is approximately
1160 km away from Delhi. The distances, measured in centimeters (cm), between the cities on Allyson's
map are proportional to the real distances.
Which of the following could be the distances on Allyson's map?
Answers
Answer:
42.25 cm & 58 cm,16.9 & 23.2 cm, 25.35 & 34.8 cm could be the distances on Allyson's map.
Step-by-step explanation:
Is 4.5 equal to...
-nine-halves
-thirty-one eighths
-thirteen-fourths
Answers
Answer:
Step-by-step explanation:
4.5 is equal to nine halves because if you divide 9 you get 4.5
Answer:
it's equal to nine halves
Which value is represented by point P?
Answers
Round about these points
Krishnan had $10.he bought box of crayons and a pen. A box of crayons cost twice as much as a pen. He received $4 change.how much did the pen cost?
Answers
The cost of the Crayons will be $4 and the cost of the Pen will be $2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Krishnan had $10. He had to purchase a box of pastels and a pen. A case of pastels costs two times as much as a pen. He got a $4 change.
Let c be the cost of crayons and p be the cost of a pen. Then the equations are given as,
c = 2p ...1
c + p = 10 - 4 ...2
From equations 1 and 2, then we have
2p + p = 10 - 4
3p = 6
p = 2
Then the cost of the crayons will be given as,
c = 2 x 2
c = 4
The cost of the Crayons will be $4 and the cost of the Pen will be $2.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Deandre$252 made for 18 hours of work.At the same rate, how many hours would he have to work to $168 make?
Answers
Answer:
14 hours he have to work to $168 make
Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)
Answers
Answer: [tex]7\sqrt{2[/tex]
Step-by-step explanation:
a²+b²=c²
7²+7²=c²
49+49=c²
[tex]\sqrt{98}=\sqrt{c^2}\\\sqrt {49}\sqrt{2} =c\\ 7\sqrt{2} =c[/tex]
Answer:
7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
To find the missing length of a right triangle use the Pythagorean theorem. This theorem is [tex]a^2+b^2=c^2[/tex]. The variables a and b are the legs (shorter sides) and c is the hypotenuse (longest side). In this case, the hypotenuse is the missing side. So, add and square 7. This looks like [tex]7^2+7^2=x^2[/tex]. So, [tex]98=x^2[/tex]. Finally, square root 98 to get the final answer, [tex]\sqrt{98}[/tex]. This can be simplified to [tex]7\sqrt{2}[/tex].
Additionally, this is a special right triangle because the legs are of equal length. If the legs are equal then the hypotenuse with be equal to x[tex]\sqrt{2}[/tex], where x is the length of the legs. So this problem can also be solved using this method.
An office supply store sells boxes of 7 pencils for $0.63 and boxes of 11 pencils at $1.10. Which is the better buy?
Answers
Answer:
The better buy is the box of 7 pencils each costing .09 versus .10 for the box of 11 pencils.
7/.063=9 cents per pencil
11/1.10=10 cents per pencil
Please allow me to know if I helped by clicking thank you, rating or brainly.
Miss Hawaii
Each costume needs 46 cm of yellow ribbon the blue ribbon is 3 times larger than the 46 cm there are 64 costumes what is the total length of all the ribbon? I NEED HELP!
Answers
Answer:
981.3
Step-by-step explanation:
hello mathematicians help me pls Multiply (x + 1)^2
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Using identity :
[tex] \boxed{(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab}[/tex]the Above term can be written as :
[tex](x + 1) {}^{2} [/tex][tex]( {x})^{2} + (1 ){}^{2} + (2 \times 1 \times x)[/tex][tex] {x}^{2} + 1 + 2x[/tex]This is the second time asking this question
Which symbol correctly compares these fractions?
−35□−23
>
<
=
Answers
Answer:
The answer is -2/3 < -3/5
Please help me, I will be really thankful
Answers
Answer:
h(-4) = -1
h(-1) = -1
h(0) = 2
Step-by-step explanation:
h(-4) = -1 because -4<-1 and from the instructions if x < -1, it is -1
h(-1) = -1 because -1 = -1
h(0) = 2 because if 1<x<2 than we have to solute this -(x-1)^2 + 3
in this we have to replace x with 0
-(0-1)^2 + 3= -(-1)^2 + 3 = -1 +3 = 2
hope it will help you ;)
What's 1+1? I must have a detailed explanation on the answer.
Answers
Answer:
Sally has 1 muffin on the counter and she finds another muffin in the oven and she adds up how many muffins she has and she gets 2
Step-by-step explanation:
Hope this helped you if it did please mark brainliest
Answer:
1 + 1 = 2
Explanation:
Take a quick look at an addition chart, and you'll see that 1 + 1 = 2. Why is this? This is because when you add one and one you get two.
Simplify (-2x^3y)^5 without the parentheses
Answers
(-2x^3y)^5 = (-2)^5 (x^3)^5 (y)^5
= -32 x^15 y^5
1. Apply the 5 to each factor.
2. Simplify each piece. On (x^3)^5, you multiply the 3 and 5.
PLEASE HELP ME WITH THIS!! THIS IXL IS DUE AT 10 AND IT 926!!
Answers
Answer:
The answer is 4/1 or simplified it would be 4.
Step-by-step explanation:
The rise is 4 and the run is 1. 4/1!
there are 500 children in a school for the PT drill they have to stand in such a manner that the number of rows is equal to the number of columns.how many children would be left out in this arangement
Answers
Answer:
16 children would be left out in this arrangement
Step-by-step explanation:
Total number of children in a school = 500
For P.T. Drill number of rows = number of columns =x
The number of children who will be left out = 500−x^2 .
The square root of 500 gives remainder as 16 that means, the square of 22 is less than 500 by 16
To make it a perfect square = 500−16=484 Therefore, number of children left will be 16
= 16 children would be left out in this arrangement
(Hope this helps can I pls have brainlist (crown)☺️)
angles homework please help
Answers
Answer:
4 = 60 5 = 120 6 = 120 7 = 60
Step-by-step explanation:
Question
Write 5x−y=14 in slope-intercept form.
Answers
Move over the 5x, making it look like, -y=-5x+14
Then, just simply divide by the negative one in front of the y.
y=5x-14.